'"HHsfl aii' wa6&:y 3 ^^=4ii^S^ QJr^ lIBRARy OF THE UNIVERSITY OF CUIFORNK 1 Of THE UNIVERSITT OF GilLIFORNIA LIBRARY OF THE UNIVERSITY Of GiLIFORNIA LIBRARY OF THE UNIVERSITY OF CALIFORNIA I OF THE UNIVERSITY OF CALIFORNIA LIDRARY Of THE ONIVER'^ITY Of CALIFORNIA LIBRARY OF THE UNIVERSITY OF CALIFORNIA ^^^^^^gl ^^^.-^. ^m^ .^^^ ^ Y OF THE UNIVERSITY OF CALIFORNIA LIRRARY OF THE UNIVERSITY OF CALIFORNIA Ty_-oj \N = --7 00 — « — I — E — I — 1 — r oc LIBRARY OF THE UNIVERSITY OF CALIFORNIA m IE UNIVERSITY OF CUIFORNU 5^. LIBRARY OF THE UNIVERSITY DF CALIFORNIA {Tb ...- ... ^ LIBRARY OF THE UNIVERSITY OF CALIFORNIA jTb IE UNIVERSITY OF CALIFORNIA LIBRARY OF THE UNIVERSITY OF CALIFORNIA LIBRARY OF THE UNIVERSITY OF CALIFORNIA \l U NIVERSITY DF CALIFORNIA LIBRARY OF. THE UNIVERSITY OF CUIFORNIA LIBRARY OF THE UNIVERSITY OF CALIFORNIA 'i\^.ji^_y,^^. ^ ••«.inn:-^' «f "NIVERSITY OF CALIFORNIA f LIBRARY OF THE UNIVERSITY OF CALIFORNIA -/ft) f\%,: t M '■ a b a;^ -',.•' ^S ^.' -,-V r-T v. LIBRARY OF THE UNIVERSITY OF CALIFORNIA m \ e. 1^ ^-jV^tk ""^ °i £ 11 COURSE OF LECTURES ON NATURAL PHILOSOPHY AND THE MECHANICAL ARTS. BY THOMAS YOUNG, M.D. FOR. SEC. R.S. F. L.S. MEMBER OF EMMANUEL COLLEGE, CAMBRIDGE, AND LATE PROFESSOR OF NATURAL PHILOSOPHY IN THE ROYAL INSTITUTION OF GREAT BRITAIN, IN TWO VOLUMES. VOLUME IL LONDON: PRINTED FOR JOSEPH JOHNSON, ST. PAUL's CHURCH YARU, BY WILLIAM SAVAGE, BEDFORD BURY. 1807. 4^jSfy (X PREFACE. The first part of this volume, consisting of the mathematical elements of natural philosopliy, is in part reprinted from the syllabus of the lectures, but considerable additions have been made to it, both of elementary matter and of original investigations. These elements are perfectly in- dependent of every other work introductory to any branch of the ma- thematics, and they comprehend all the propositions which are required for forming a complete series of demonstrations, leading to every case of importance that occurs in natural philosophy, with the exception of some of the more intricate calculations of astronomy. It was therefore absolutely necessary that they should be expressed in the most concise manner that was possible ; yet except a few propositions which have been cursorily introduced in sonic of the scholia, no essential step of a demon- stration has ever been omitted. The best use, that a student could make of these elements, would be to read over each theorem or problem superficially, then to endeavour to form for himself a more particular demonstration, and to compare this again with that which is here given: for the exertion of a certain degree of invention is by far tlic surest mole of fixing any principle of science in the mind. The catalogue of references has been methodically subdivided, as faras it was possible to do it with convenience and accuracy, and the works and passages belonging to each subdivision have in general been arranged in chrono'ogical order; except that the different productions of the samo author have been placed together. The divisions of the catalogue fol- low very nearly the same order as the text of the lectures, so that there has been no occasion for any references from one to the other. This ar- iv PREFACE. rangement may be the most conveniently understood from the table of contents prefixed to the catalogue; and the method of classing the subdivisions and titles, which become more and more particular, has been as much as possible such, that if sufficient information cannot be found under the head to which the subject immediately belongs, there may always be a chance of obtaining it from some more extensive work,under the last head, of a more general nature, which may be found, in the catalogue, by looking back for a change of type, or in the table of contents, by recurring to a column situated one degree more to the left. On the other hand, in order to faciUtate, in some measure, the la- bour of selection, such works, as appeared to possess superior merit and originality, have been distinguished by asteriscs; and those, on tlic con- trary, that have been thought either erroneous or unimportant, have been marked with an obelise. It must not however be understood, that all the other works mentioned are considered as deservins: neither com- mendation nor censure, since with respect to the greater number of them the evidence must necessarily be imperfect. The extracts occa- sionally inserted, as well as the original remarks which are sometimes in- troduced, are not so much intended for the general reader, as for those who make any single department their particular study; many of them being only brief hints, which may serve to direct their attention to a fur- ther pursuit of the subjects. In the mathematical and astronomical parts, all references to the transactions of foreign societies have in gene- ral been omitted ; partly because they would have been too numerous for insertion, and partly because they may be found at large in the copious works of Murhard and of Reuss. The references to periodical pub- lications have been continued, where it was possible, to the beginning of the year 1805. For the convenience of those who have access to the libraries of the Royal Institution, of the Royal Society, of its most liberal and illustri- ous President, and of the British Museum, such works as are to be PREFACE. V found in these collections are marked respectively, R. I, R. S, B. B, and M. B: and where the same book is contained in more than one of them, it has generally been marked as belonging to that which is most accessible to the pablic,the preference being given to the library of the Royal Institution. The articles printed in Italics are intended to form, if taken separately, a complete catalogue of the books which are quoted, without repetitions. The capital Roman numerals refer to volumes, the smaller ones to divisions or sections, and the figures to pages or years. The miscellaneous papers are reprinted with some corrections and additions, but with no other alterations, of any kind, than might have been made at the time when they were first })ublished: except the in- sertion of the last section of the essay on the cohesion of fluids, which consists of comparative extracts from a later memoir of Laplace, and of remarks on the method of investigation which he has employed. The abstract of the papers read before the Royal Society consists of such potes, as have in general been inserted in their places among the references; but as they constitute a continued account of the pro- ceedings of the society for the whole of one season, it has been thought most eligible to preserve them united in order of time. Welbeck Street, 30th March, 1807. SOLD BY MR. JOHNSON. 1. De corporis humani viribus conservatricibus, dissertatio, auctore Thoma Young, M. D. 8vo. Price 2s. 2. A Reply to the animadversions of the, Edinburgh Reviewers on some papers published in the Philosophical Transactions. By Thomas Young, M.D. 8vo. Price Is. CONTENTS. MATHEMATICAL ELEMENTS OP NATURAL PHILOSOPHY; P. 1. Part I. Pure Mathematics. Section 1. Of quantity and number ; 1. Powers of numbers ; 4. Table of re- ciprocals ; 5. Logarithms of prime numbers ; 6. 2. Of the comparison of variable quantities; 7- 3. Of space; 8. 4. Of tlie properties of curves; 22. Part II. Mechanics. Of the motions of solid bodies. Section 1. Of motion; 27. 2. Of accelerating forces ; 28. 3. Of central forces ; SO. 4. Of projectiles ; 32. 5. Of motion confined to given surfaces ; 33. 6. Of the centre of inertia, and of momentum ; 35. 7. Of pressure and equilibrium; 37. 8. Of the attraction of gravitat- ing bodies ; 45. 9. Of the equilibrium and strength of elastic substances; 46, 83. 10. Of collision, and of energy ; 51. 11. Of rotatory power , 52. 12. Of preponderance, and the maximum of effect ; 54. 13. Of the velocity and friction of wheelwork ; 53, Part III. Ilydrodpiamici. Of the motiont of fluids. Section 1. Of hydrostatic equilibrium; 57. 2. Of floating bodies; 59. 3. Of specific gravities ; 59. 4. Of pneumatic equilibrium; GO. 5. Of hydraulics; GO. 6. Of sound ; Go, 84. 7. Of dioptrics and catoptrics ; 70. 8. Of optical instruments; 76- 9. Of physical optics. To p. 80, Art. 46l. A SYSTEMATIC CATALOGUE OF WORKS RELATIIvrG TO NATURAL PHILOSOPHY AND THE MECHANICAL ARTS; WITH REFERENCES TO PARTICULAR PAS- SAGES, AND OCCASIONAL ABSTRACTS AND REMARKS; 8?. Contents of the catalogue; 89. MISCELLANEOUS PAPERS ; 521. I. Observations on vision ; 523. Subjects of the paper ; l. Of the quantity of air discharged rr< ^,-.„ t .u A.- <■ .u -KT through an aperture; 531. a. Of the direction and velo- Iheories of the accommodation of the eye; 523. New „„,,„,,■ .„, c 1 •• f .• I ■ r city of a stream of air ; 532. 3. Ocular evidence of the explanation; 525. Solution of optical queries; 527. Ex- nature of sound ; 538. 4. Of the velocity of sound ; 5. Of sonorous cavities; 537. fi- Of the divergence of sound; 538. 7. Of the decay of sound. 8. Of the harmonic soundi of pipes, g. Of the vibrations of different elastic fluids f planation of plate l ; 530. II. Outlines of experiments and inquiries respecting sound and light; 531. vm CONTENTS. 10. Of the analogy between light and sound; 541. ii. Of the coalescence of musical sounds; 544. 12. Of the fre- quency of vibrations constituting a given note; 545. 13. Of the vibrations of chords ; 546. 14. Of the vibrations of rods and plates, is. Of the human voice ; 549. 16. Of the temperament of musical intervals; 551. Explanation of plate 2 . . 7 ; 553. III. An essay on cydoidal curves^ with introductory observations; 555. 1, On mathematical symbols; 555. 2. On cycloidal curves; 558. IV. An e.'^say on music ; 563. 1. Of music in general; 563. 2. Of the origin of the scale; 566. 3. Practical application of the scales; 568. 4. Of the terms expressive of time ; 571. V. The Bakerian Lecture for 1800. On the mechanism of the eye ; 573. 1 . Changes of opinions respecting the crystalline lens ; S73. a. Division of the subjects to be investigated. 3. General consideration of the sense of vision ; 574. 4. Description of an optometer; 575. 5. Dimensions and powers of the author's eye ; 57 8. 6. Extent of the changes required for the accommodation of the eye ; 585. 7. Exa- mination of the state of the cornea ; 586. 8. Examination of the length of the axis; 589. O- Examination of the changes of the lens; 592. 10. Anatomical remarks on the eyes of different animals; 597- Explanation of plate 8. . 13; 604. VI. A letter to Mr. Nicholson, respecling sound and hght, and in reply to some obser- vations of Professor Robison ; 607. Heads of the paper on sound and light ; 607. Remarks on Smith's harmonics ; 609. On temperament ; 610. VII. The Bakerian lecture for 1801. On the theory of light and colours; 6l3. Excellence of Newton's experiments ; 613. Hypothesis of an elastic ether; 614. Undulations; ai5. Cofours ; 616. Constitution of material bodies; Transmission of impulses; 618. Spherical divergence; 6I9. New di- vergence; 620. Partial reflection; 622. Refraction ; Total reflection; Dispersion; 623. Combination of undulations ; 624; Striated surfaces; 625. Thin plates; 62S. Thick plates; 628. Inflection; General conclusion respecting the nature of light ; Iceland crystal ; 629. Momentum of light ; Solar phosphori ; 630. Heat ; Experiment pro- posed ; 631. Plate 14; 632. VIII. An account of some cases of the production of colours not hitherto described ; 633. General law of double lights ; Colours of fibres ; 633. Colours of mixed plates ; fijs. Internal reflection ; 638. Dispersion; Dr. WoUaston's experiments ; 637. Blue light of a candle ; Dispersive powers of the eye ; 638. IX. The Bakerian lecture for 1803. Ex- periments and calculations relative to physi- cal optics ; 639- 1. Experimental demonstration of tht general law of the interference of light; 639. 2. Comparison of measure* deduced from various experiments; 640. 3. Application to the supernumerary rainbows ; 643; 4. Argumentative inference respecting the nature of light; 645. 5. Remarks on the colours of natural bodies ; 646. Experiment on the dark rays of Ritler; 647. X. An essay on the cohesion of fluids ; 649. 1. General principles; 649. 2. Form of the surface of a fluid; 649. 3. Analysis of the simplest forms; 650. 4. Appli- cation te the elevation of particular fluids ; 651. i. Of ap- parent attractions and repulsions ; 655. 6. Physical foun- dation of the law of superficial cohesion ; 657. 7. Cohe- sive attraction of solids and fluids; 658. 8. Additional. Extracts from Laplace, with remarks; 6«o. Plate 15; 670. ACCOUNT OF THE PROCEEDINGS OF THE ROYAL SOCIETY, FROM NOVEMBER 1801 TO JULY 1802; 67I. INDEX ; 683. ADDITIONS AND CORRECTIONS. p. 2. Art. 20, last line, for- read a:b. h P. 20. Art. ng, 1. 2, for "planes" read " parallel planes." P. 23. Col. 2. L. 35, for " being opposite to them" read since these lines have the same side A B opposite to them in the triangles ABC, A B I, and their equals BC, BI are opposite to the same angle BAG. P. 35, after article 2fi5, insert, 26a. B. Theorem. Supposing the force retarding a pendulum or balance to be to the force of gravitation or of elasticity at the ex- treme point of each vibration as / to 1, the circumference of a circle to its diameter being as c to 1, the time of each vibration will be increased in tht ratio of 1 to 1 + S^, or ^ + c .fi4^ very nearly. The nnpulse being supposed to _. be momentary, and to be given at CAD A, the pendulum, will move to B as if completing a vibration of which C is the middle point, AC being to AB as/to 1 : in its return the middle point will be D, and the extent of the vibration being BE, the space DA, which is equal to C A, will be described in a time as much longer than would have been required for describing C A, as D E or D B IS shorter than C B, that is, in the ratio of i-o/,o i very nearly. But the whole time of describing C A is less' than .f the velocity were equable, in the ratio of the diameter of a circle to its semicircumference, or of i to f, and is there- fore to that ofasemivibration as/to f, and to that of a complete vibration as/to c; consequently we have for the retardation -^ the time of a vibration being unity. Scholium. If the propelling force of a balance or pen- dulum, and the friction which retards it.'be increased in the same proportion, the extent of the v ibration will remain un- altered, and the motion will be retarded in proportion to the VOL. II. square of the fraction expressing the friction. But if the propelling force be increased in a greater proportion than the friction, the extent of the vibration will be increased in the ratio of this excess, and the value of the fraction /will be diminished in the same proportion. Thus, if the friction were doubled, and the propelling force quadrupled, the extent of vibration would be doubled, and the time would remain unaltered; but if the propelling force were only tripled, the fraction/ would on the whole be increased \, and the retardation i. P. 54, after art. 359, insert, 359. B. Theorem. Every compound body has at least three axes of permanent rota- tion, at right angles to each other. When a body revolves round any axis, it is necessary, in order that the revolution may be permanent, that the cen- trifugal forces on all sides balance each other, so that the axismay not be urged to revolve rouijd the centre of gravity. The centrifugal force of each particle being pioportional to its distance from the axis, its tendency to turn the axis, in a given direction, being represented by the force reduced to that direction, will be proportional to its distance from a plane passing through the axis, perpendicular to the sup- l)osed direction ; and its effect will also be the greater as its distance from the equatorial plane is greater ; since the axis may te considered as a lever, and the centre of gravity as its fulcrum. Now if a plane be made to revolve on a line passing through the centre of gravity, it is obvious that there is a position in which the sums of all the products of the particles into their distances from this planeand from a plane perpendicular to it, passing through the same line, will be equal on both sides of the plane ; and the plane . remainmg in this position, if another plane be sup- posed to turn round any line out of the first plane until it acquire a similar property with it, it may easily be under- stood that the intersection of these planes vr.ll be an axis of permanent rotation, since any other plane passing through it will possess the same property with respect to the parts of the solid on each side of it. If then two planes perpendicu- lar to each other be supposed to revolve round this axis, until they acquire that position in which either of them b ADDITIONS AND CORRECTIOXS. divides the solid into parts possessing equal powers to turn the axis, the other will also divide it in a similar manner, and their intersections with the equatorial plane of the first iixis will also be permanent axes of rotation : for the same sums will express the action of the particles in both cases, the distance from either plane being equally concerned in the effect of each particle,and the effects of those particles which are in contiguous sections of the solid either way counter- acting each other, and cooperating with the effects of the sections diagonally opposite. And in the same manner it may be shown that the equatorial plane divides the solid in such a manner with respect to both these axes as to enable the body to maintain a permanent rotation round them. 35y. C. Theorem. If a bod}', revolving freely round any axis, be caused for a mo- meat to revolve at the same time round an- other, the joint result of both motions will be a revolution round a third axis, in an in- termediate position, which will continue to be the axis of rotation, provided that tlic body be capable of revolving permanently round it. If the angle formed by the axes be divided into two parts, of which the sines are inversely proportional to the velocity of revolution round the contiguous axes, it is obvious that the line thus dividing the angle will remain at rest, in con- sequence of the equ^al velocities of the two motions, the angle divided being supposed to be one of those in which the revolutions are in opposite directions: and the angular velocity of rotation round the new axis will be to the greater of the former velocities as the sine of the whole angle to the sine of the greater portion thus determined, as may be inferred from considering the motion of the poles of either of the primitive revolutions. The position of the new axis, and the motion of any other point of the body, is obviously sufficient to determine the velocities and directions of the motions of every other part, since the form of the body is supposed to be unchangeable ; so that it is unnecessary to demonstrate that the motion re- sulting from the separate motions of each point is such as belongs to its place with respect to the new axis of rotation ; and the body, beginning once to revolve upon this axis, will continue its rotation exactly in the same manner as if it bad arisen from a simpler cause. P. .'i5. Col. 2, after art. 304, insert, ScHpLiu.M. In the same manner it may be shown, that if B E D be any circle, or in general any curve, rolling on the wheel A, and describing the line C D, and if the same curve, rolling within the circle of which B is the centre, and which touches A, describe the line B D, whctlicr straight or curved, the force will still be directed to the point of contact E, and the motitn of the wheels will be uniform. P. 58. Col. 2. L. 2g,for "CD" read CB. P.34.CM.2.L. 1 5, for " 70^°" read 160-;^. P. 64. At the end, Scholium 2. It maybe demonstrated that an impulse communicated to a liquid at any point of the margin of a reservoir, of which the bottom is an inclined plane, termi- nated by that margin, will advance every way in a cycloi- dal direction j by reasoning similar to that which is employ- ed for the demonstration of the property of the cycloid, as the curve of swiftest descent (261). The form of the wave will be that of a curve cutting an infinite number of cy- cloids at right angles ; and any number of points in it may be found, by drawing on any points in a parabola as centres, a number of circles touching the vertical tangent of the parabola, and laying off on each from the point of contact an arc equal to the distance of that point from the vertex of the parabola. The truth of this may easily be shown from the properties of cycloidal pendulums, (25£>). P. 76. Col. 2. L. 5, omit " or." P. 79. Col. 2. L.6, for " differs . . in" read, scarcely differs from this except in. P.80. Before art. 461, insert, Section XX. OF physical OPTICS. P. 122. Col. 1, after 1. 20, insert, Such solids of revolutioa are generally called spindles, where the curve is convex out- wards ; in this case, where it is concave, they might be called trochi. P. 139. Col. 2, after 1. 14, insert. Pressure of Bodies in Motion. Hee on' the pressure of weights in machines. Ph. tr. 1 755.J. P. 144. Col. 1, after 1. 28, insert. From the British Magazine for March, 1801 The pinacographic instrument resembles in its construc- tion a musical pen, but is much broader, so as to dravr parallel lines at one or two strokes over the whole surface of any page. Its use is to manufacture an index. It is to be accompanied by inks of nine different colours, such as are the most easily distinguished from each other at first sight. In order to construct an index, procure two copies of the best edition of your work ; — cover each page with paral- lel lines, expressive of its number, drawing them vertical for units, horizontal for tens, and oblique for hundreds, de- noting each figure by the ink of the bottle on which you find it marked; then, with the assistance of your wife and daughters, cut the pages first into lines, and tlien into words ; distribute all the words into little boxes, marked with the two initial letters, and then paste them on the pages of a blank book in the precise order of the alphabet. The index being thus complettd, — if you print it, a very little habit will 4 ADDITIONS AND CORnECTIONS. Xt ensile the cempositors to read ofF the references as correctly fifom this method of notation as if they were written out at length. If the number of coloars be found too great, the difficulty may be easily removed by using only five, and supplying the deficiency either by providing two instruments •f different constructions, or by drawing the lines in a greater variety of positions. P. 106. Col. 2, at the end, insert. The work ofacoalhea\'er on the river Thames is considered as very laborious, but the effect produced is not comparatively great. Four men are employed in filling baskets in the hold of the lighters.andjfour in " whipping"or elevat- ing them from 1 2 to 20 feet, which is performed by ascending three or four steps, and standing on a stage, which descends while the baskets are raised ; and the labour of filling and raising them is nearly equal. The usual work of a day is to raise 42 chaldrons, weighing about 126 000 pounds, that is, 31 500 pounds for each labour- er, to the height of 16 feet, making 504 000 pounds, raised 1 foot, instead of 3 600 000, or .14 But it is not difficult to do twice or twice and a halfasmuch, andioschaldronareoften raised,or .3J There have even been instances in which IBS chaldron have been raised, or .65 P. 167. Col. 1. L. 4 from the bottom, for " Cazand" read Cazaud. P. igs. Col. 1. L. 2, for " barculus" read barulcus. ' P. 25S.Col. l.L. 12, for "aerostation," read aerostatation. P. 278. Col. 2. L. ]?, for " v", read U. P. 319. Col. 1. L. 11 from the bottom, for " 170 " and " l»0", read, ^Land J5. Col. 2. L, 7, after " case" insert as. L. 22, for " specimen" read spectrum. L. 24, after " in," insert a. P. 330. Col. 1. L. 3. from the bottom, for " 3553", read .3553. P. 354. Col. 1. 1. 20. for " '^' read nearly J. P. 356. Col. 2. After 1. 3 from the bottom, insert, Olseroalions on the Sun's Light, Heliostate. S'Gravesande's Natural Philosophy. P. 382. Col. 2, last Line, for " 56707° . . SneUius," read, ,S6070 to 50802 Klostermann. Si° 18' S. 57037 Lacaille, 1752. ( 56740 or 57070 Fernelius 55021 SneUius. ) P. 364. Col. 1. L. 9 from the bottom, for "or" read the diameters. P. 367. Col. 1. L. 29. for / read 1". P. 367. Col. 2. L. 18, for "73j," read 39, or perhaps 48. P. 337. C0I.2. L. 11. from the bottom, for " areometry" read aerometry. P. 452. Col. 2, after 1. 2, insert. According to Kirwan's theorem, the mean temperature of the year, and that of the month of April, is 84° — 26. 5 T. s. 2 I. The greatest mean heat of the summer months may be found very nearly, according to Kirwan's table, by this formula, 86— isv.s. 2Z — i.7v.s.i2 (/+15°), and the mean heat of the month of January, which is the coldest month by 80^29. 5 v. s. 22 — v. s. ' * I — ^v. s. 18 (1+7°). The error seldom amounts to more than adegree. P. 455. Col. 1, after 1.20, insert, Laplace Exp. du syst. du monde, 267. Asserts that " the attraction of the sun and moon does not produce, ei. ther in the sea, or in the atmospfiere, any constant motion from east to west." P. 455. Col. 2. after 1. 7 from the bottom, insert. Remarks on the Effects of the Sun's Heat on the Atmo- sphere. It is very difficult to demonstrate conclusively that the sun's relative motion from east to west has or has not such a tendency as Halley attributed to it, to cause an easterly wind in the neighbourhood of the equator ; it appears however to be possible to show that no effect of this kind can be pro- duced in any sensible degree. The immediate effect of the expansion of the air at any place must be to cause a partial elevation of the surface of the atmosphere : for the instant that this elevation remains, the lateral pressure will be unequal at every part of the height of the column except the basis, and the inequality must become greater in ascending, being always proportional to the difference cf the weights of the columns contiguous en each side to any given point. The elevation may there- fore be considered as the beginning of a wave, which will be propagated each way with a certain velocity; and this velocity must at first be less than that of a similar wave in a fluid perfectly homogeneous, but will approach to it as it spreads, the inequality of temperature soon disappearing. If the cause of expansion continues, new waves will con- tinually succeed each other, so that the surface will remain horizontal. Hence will arise a pressure ; forcing the lower parts of the air towards the point of expansion, and a cur- rent will be produced, which will cause a continual circula- tion. But it is obvious that no parts of the atmosphere can Xll ADDITIOXS AND CORRECTIONS. be urged towards the pitce of expansion, until the first wave has reached them, and if the velocity of this wave be great- er in one direction than in another, the effect must be more extensive on that side. Now in the case of the successive expansion of the air by the sun, all the points af expansion move westwards with a velocity of about 1500 feet in a second, which is considerably greater than that of a wave moving upon the atmosphere, or that of sound propagated through it, which is more immediately comparable to that of the effect in question ; consequently the Wave cannot precede the point of expansion, so as to produce any .cur- rent in the more westerly parts ; the current from east to west must, therefore, prevail. But, at the opposite part of the globe, the refrigeration must produce an effect precisely contrary to that of theheat ; the air tending to descend and flow from the parts which are coolest ; the depression not being transmitted to the more westerly parts with sufficient velocity, to produce a current from east to west by these means, the easterly parts only will be affected by a current from west to east, which will probably exactly counter- balance the easterly tendency produced at the opposite part of the globe, so that the breezes thus excited must be mere- ly transitory, and in opposite directions. P. 463. Col. 2. L. 4 and 5 from the bottom must be transposed. P. 471. Col. 1. L. a after the table, for " above " read about. P. 481. Col. 2. L. 0. for " charged ", read charred. P. 500. In the columns " Refractive force" and " simple refractive power", the numbers opposite to " White wax" and " Oak" should be opposite to " Olive oil" and " White wax", respectively. P. 560. Col. 1. L. 39, after" purpose", insert, Mr.Giddy has observed that an equiangular spiral may impel another similar curve without friction: it is indeed easy to see that two such spirals must always touch each other in tlie line joining their centres. P 562. Col. l.L.ll,for ";", read, -;. L. 5 from the bottom, for " concentrat- ing", read generating.] MATHEMATICAL ELEMENTS OF NATURAL PHILOSOPHY DEDUCED FROM AXIOMATICAL PRINCIPLES. MATHEMATICAL ELEMENTS OF NATURAL PHILOSOPHY. PART I. PURE MATHEMATICS. SECTION I. OF QUANTITY AND NUMBER. 1. Definition. The letters of the al- phabet are employed at pleasure for de- noting any quantities, as algebraical sym- bols or abbreviations. But, in general, the first letters in order are used to denote known quantities, and the last to denote unknown quantities ; and constant quantities are often distingwished from variable quantities in the same manner. 2. Definition. Quantities are equal when they are of the same magnitude. Scholium. The abbreviation al^i implies that a is equal to hi a'>h that a is greater than h; and a < i that « is less than /•. 3. Definition. Addition is the join- ing of magnitudes into one sum. Scholium. The symbol of addition is an erect cross: « + i implies the sum of a and I; and is called a more b. 4. Definition. Subtraction is the tak- ing as much from one quantity as is equal to another. Scholium. Subtraction is denoted by a single line, as a—b, or a less b, which is the part of a remaining when a part equal to b has been taken from it. VOL. II. 5. Definition. A negative quantity is of an opposite nature to a positive one, with respect to addition or subtraction ; the con- dition of its determination being such, that it must be subtracted where a positive quan- tity would be added, and the reverse. Scholium. A negative quantify is denoted by the sign of subtraction ; thus if a + ''^o— <",'!'——<" and cr: — b, A debt is a negative kind of property, a loss a negative gain, and a gain a negative loss. 6. Definition. A unit is a magnitude con- sidered as a whole complete within itself. Scholium. When any quantities are enclosed in a pa- renthesis, or have a line drawn over them, they are con- sidered as one quantity with respect to other symbols; thusa— (fc+c) or a—b-{-c implies the excess of a above the sum of b and c. 7. Definition. A whole number is a number composed of units by continued ad- dition. Thus one and one compose two, 2+1—3, 34-i::z4, or 2-f-2=4. Such numbers are also calltd multiples of unity. 8. Definition. A simple fraction is a number which by continual addition coni- B OF QUANTI.Xr AND NUMBER. poses a unit, and the number of such frac- tions contained in a unit, is denoted by the denominator, or number below the line. Thusi+i+i=l. 9. Definition. A number composed of such simple fractions by continual addition, may properly be termed a multiple fraction ; the number of simple fractions composing it is denoted by the upper figure or nu- merator. In this sense |, -3, i, are multiple fractions, and j— 1, 5=Hi=l+i,ori.. 10. Definition. Sucli quantities as are expressible by the relations denoted by whole numbers, or fractions, are called commen- surable quantities. Scholium. All quantities may, in practice, be con- sidered as commensurable, since all quantities are expres- sible by numbers, either accurately, or with an error less than any assignable quantity. 11. Definitjon, Multiplication is the adding together so many numbers equal to the multiplicand as there are units in the multiplier, into one sum, called the product. Scholium. Multiplication is expressed by an oblique cross, by a point, or by simple apposition ; a x ''—a. t—a('. 12. Definition. Division is the sub- traction of a number from another as often its it is contained in it; or the finding of that quotient, which, when multiplied by a given divisor, produces a given dividend. Scholium. Division is denoted by placing the divi- dend before the sign -r- or :, and the divisor after it ; as a—b^:a : I. 13. Axiom. When no difl^erence can be shown or imagined between two quantities, they are equal. 14. Axiom. Quantities equal to the same quantity, are equal ^o each other. If azzl and c~?', then azzc. 15. Axiom. If to equal quantities equal quantities be added, the wholes will be equal. If azzb, then a+c'Zll+c; if a—lzzc, then adding b, a—l+c; if a-fi— c=d, then adding c, a+i:=c+<2. 16. Axiom. If from equal quantities equal quantities be subtracted, the re- mainders will be equal. If azzb, a—cizb — c, if a-f-ir:i-f-c, a~c. 17. Axiom. If equal quantities be mul- tiplied by equal numbers, the products will be equal. If aZZ.b, aa^-Zb ; if a:^b : 3, 3a:z.b ; and if aZZb, caZZcb. 18. Axiom. If equal quantities be divided by equal numbers, the quotients will be equal. If 50^10/', azzai ; and if ca~cb, aZZb. Scholium. Articles 16, 17, 18, might have been dedu- ced from art. 15, but they are all easily admitted as axioms. 19. Theorem. A multiple fraction is equal to the quotient of the numerator di- vided by the denominator. a a 1 , , " , 1 Or, — r:a:t,for ■— = -T-.a (9); and (•.— -=:i.— -a b b b b b (17); but ;•.-—=: 1 (8) ; and i.-:-.a:=i.a=a, therefore b.—r=.a (14), s^nAa-.b—— (12). Scholium. Hence — is a common symbol for a : b. b 20. Theorem. A quantity multiplied by a simple fraction, is equal to the same quan- tity divided by its denominator. 1 la a Or a. — "ZZa : b; for a. — =1 — (9), and -—ZZa :b(lii), b b b V therefore a.-r-= — (l*)- b b 21. Theorem. A quantity divided by a simple fraction, is equal to the same quantity multiplied by its denominator. -= ab, for if a : -^=c,a=c.—{l2')=Z——c b Or a ; b ' ~ b^ ■ b 1 (20), and multiplying by b, ab — c — a : —. 22. Theorem. Aquantity multiplied by a multiple fraction is equal to the same quan- tity multiplied by the numerator, and then di- vided by the denominator. Or a.— — ah:c; for a.—-=.aji. —— at. — =:ai;f (aa). c ' c c t OF QUANTITY AND NyMBER. 23. Theorem, A quantity divided by a mnltiple fraction is equal to the same quan- tity multiplied by the denominator, and di- vided by the numerator. b h / 1 \ , 1 Or a: — zzac:l-, for a: — r: a:l b. — ]—a:b: — — c c \ c / c a: l.c[l\), ZZac -.1. Scholium. A beginner may perhaps render these de- monstrations more intelligible by substituting any numbers at pleasure for the characters. For example, the demon- stration of the first theorem may be written thus. Twelve fourths, y, are equal to 12 divided by 4 ; for, by the defi- nition of a multiple fraction, 'Jnia.i, and multiplying these equals by 4, 4.^:^4.12.^ ; but by the definition of a simple fraction 4.i3:i, therefore iAi-^^xt, whence 4.u.= 12, and by the definition of division, 12:4z:l^. But, in fact, the proposition is too evident to admit much demon- strative confirmation. 24. Theorem. A positive number or quantity being multiplied by a positive one, the product is positive. For the repeated addition of a positive quantity must make the result actually greater. What is true of numbers, may practically be affirmed of quantities in general (lo). 25. Theorem. A negative number or quantity being multiplied by a positive one, the product is negative. For since adding a negative quantity is equivalent to sub- tracting a positive one, the more of such quantities that are added, the greater will the whole diminution be, and the sum of the whole, or the product, must be negative. 26. Theorem. A negative number or quantity being multiplied by a negative one, the product is positive. Oi —a.—h=:al: For a — l-=.—aT]{ib): that is, when the positive quantity a is multiplied by the negative h, the product indicates that a must be subtracted as often as there are units inb: but when a is negative, its subtraction is equivalent to the addition of an equal positive number ; therefore in this case an equal positive number must be add- ed as often as there are units in I. 27. Definition. If the quotients of two pairs of numbers are equal, the numbers are proportional, and the first is to the second, it-s the third to the fourth ; and any quantities expressed by such numbers, are also pro- portional. If a : lyZlc : d, a is to b is c to d, or a, : b : : c ■ d. 28. Theorem. Of four proportionals, the product of the extremes is equal to that of the means. Since a:b~c : d, a : b. bd::Zc : d. bd. (l7), or adzzcb. 29. Theorem. If the product of the ex- tremes of four numbers is equal to that of the means, the numbers are proportional. If adZZjcb, ad : bd^Zcb : bd (is), and a : bzZc : d ; also ad i cdZZcb : cd, and a : c~t : d. 30. Theorem. Four proportionals are proportional alternately. If a : b::c:d, adZZbc (as), therefore a:c::b:d (29). 31. Theorem. Four proportionals are proportional by inversion. 1( a : b : : c : d, ad'ZZhc, ad : ac':^bc : ac, and d : c^Zfc : a. 32. Theorem. Four proportionals are proportional by composition. If a: b:: c: d, a+b : b: : c + d : d ; fo; since ad^bc, ad+bd::ibc-{-bd (15), or {a+b). d::z(c+d). b, therefore a+b:b::c-^-d:d (29). 33. Theorem. Four proportionals are proportional by division. If ab::c:d, a — b:b::c — d:d; for since ad^bc, ad—bd:=.bc—bd (16), (a—b). d=:(c— d). i, and a—b:b:: c — d : d (29). 34. -Theorem. If any number of quan- tities are proportional, the sum of the ante- cedents is in the same ratio to the sum of the consequents. 11 a . b : : c : d, a: b : : a+c : i+d ; for since adZZbc, ab+adz:ab-\-bc, a.[b+d):^b.(a+c), and a: b : : a+c:b+d (29). 35. Theorem. If any number of ante- cedents and any number of consequents be added together, the ratio of the sums will be less than the greatest of the single ratios, when those ratios are unequal. a c a4-c a b d b+d b {ori[-=-, e>c. ,«-f e a + c , ^ , a a-\-c and— -->— — (34) ; consequently —> ——-.The same b+a b+d b t'-J-ci demonstration may be extended to any number of ratios. OF QVANTITY AND NUMBER. 36. Definition. A series of numbers formed by the continual addition of the same number to any given number, is called an arithmetical progression. 2, 5, 8, 11, 14, 17, 20, by adding 3. 20, 17, 14, 11,' 8, 5, 2, by adding— 3. o, a+b,a+il;a+3t, a+ (n— l). I, in genetal. Scholium. It may be observed that the sura of each pair of the numbers of these equal progressions is 22=2+20=a+a+ (n— l).t=2a + (m— l).i; the whole sum 22X7= (20 + (n— l). V). n, and the sum of each, na + ^^. b, a being the first term, i the difference, 2 and n the number of terms. 37. Definition. A series of numbers formed by continual multiplication by a given number, is called a geometrical pro- gression. As 2, 0, 18, 54 ; multiplying 2 continually by 3. a, ah, alb, ablb ; multiplying a by b. 38. Definition. If one of the terms of a geometrical progression is unity, the other terms are called powers of the common mul- tiplier. As 1^. ■^. h h v 1' 2' ■•' 8, 16, 32. Each term is de- noted by placing obliquely over the common multiplier a number expressive of its distance from unity, as 8r:2': ne- gative numbers, implying a contrary situation to positive ones, denote that the term precedes instead of follovfing the unit, ■jl% i='2"'. By reversing the series it is obvious that |^(i)', and 2=(i)-'. It appears that the addition of the indices denoting the places of any terms will point out a term which is their product, as 2' X a'xia', or 8 X 4::=32 ; and that the subtrac- tion of the index is equivalent to division by the term. Hence if a'=:i'— i", a'«must be equal to I'i in order that i 2 -f i 2 may make J'rra*. So that simple fractional num- bers serve as indices of the number of times that the quan- tity must be multiplied together, in order that the product may be the common multiplier of the series, or the simple number b. Scholium. Fractional powers are sometimes denoted by the mark \/, meaning root; thus ^ono2,'v'a^a' The second power of a number a, being called its square, and the third its cube, the fractional powers arc called square and cube roots. The sums of geometrical progressions may be thus com- puted, if a-t-at-^-ai' . . . +ai"~':=x, ab-xab^+ab'. . . + ab'^bx, and subtracting the former equation from the lat- ab" — a ter at" — a'^.bx — x, therefore .r:i: -; . Which, when b — 1 i< 1 and nzzos , or infinite, becomes — — . i—b The binomial theorem, for involution, is (a4-i)"=a"-|- a^-^b'-i- . . In simple cases, its truth may be shown by induction. , , n — 1 „., n — 1 n — 2 n.a"~' b+n. . a''~^b-+n. . 2 2 3 POWERS OF NUMBERS. 1st O 2(1 4 3d. ■Hh. 5th. 6th. 7th. 8th. 8 16 32 64 128 256 3 .9 27 81 243 729 2187 6561 ■}• 16 6i 256 1024 4096 16384 65536 5 25 125 625 3125 15625 78125 390625 6 36' 2l6 125)6 7776 46606 279936 1679616 7 49 343 2401 I68O7 117649 823543 57648OI S 64 512 409632768 262144 2097152 16777216 9 81|729 6561 59049 531441 478296r) 43046721 2^1.414213; 3^1.732; 5^, 2.236 ; 6^,2.449; 7=' 2.640 8S2-828;102'3.162. 21=1.26; 31,1.442; 41,1.587; 31, 1.71; 61,1.817; 7^, 1-913; 9^,2.08; 10>> 2.154. 39. Definition. In decimal arithmetic, each figure is supposed to be multiplied by that power of lOi positive or negative, which is expressed by its distance from the figure before the point. Thus 672.53 means 6Xl0H7Xl0'-f-2Xl0'', or2Xl, -1-5X10-', or^or-j''<^-|-3Xlo-«, or ife, together 672,Vo- Scholium. On some occasions other numbers are sub- stituted for 10 in calculations: particularly 12, which has many advantages, and is used in operations respecting car- penter's work ; and sometimes the number 2 facilitates computations; and it may be employed where it is incon- venient to multiply characters; since two different marks, or a mark and a vacant place, are sufficient, when conti- nually repeated, to express all numbers. The powers of 60 arc also used in the subdivisions of time, and of angles. 40. Definition. The reciprocal of a number is the quotient of a given unit tU- vided by that number. OF QUANTITY AXD NUMBER. TABLE OF RECIPROCALS. No. Recipr. No. Recipr. No. Recipr. No. Recipr. No. 213 Recipr. No. Recipr. 1 1000000 54 0185185 107 0093458 160 0062500 0046948 266 0037594 2 5000000 55 OIS1818 108 0092592 161 0062112 ?14 0046729 267 0037453 3 3333333 56 0178571 109 0091743 162 0061728 215 0046512 268 0037313 4 2500000 57 0175439 110 0090909 163 0061350 216 00462.96 269 0037175 5 2000000 58 0172414 111 0090090 164 0060975 217 0046083 270 0037037 6 1666666 59 016.9490 112 00S92S6 165 0060606 218 0045872 271 OO369CO 7 1428571 60 0166666 113 OOS8496 166 0060241 219 0045662 272 0036765 8 1250000 61 0163.934 114 0087719 167 0059s 80 220 0045454 273 0036630 9 llllUl 62 0161290 115 OO86957 168 0059524 221 0045249 274 00364.96 10 1000000 63 0158730 116 OOS6207 169 0059172 222 0045045 275 0036363 11 0909090 64 0156250 117 0085470 170 0058824 223 0044843 276 0036232 12 0833333 65 0153846 118 0084745 171 0058480 224 0044643 277 0036101 13 0769230 66 0151515 119 0084034 172 0058141 225 0044444 27s 0035971 14 0714285 67 0149254 120 0083333 173 0057803 226 0044248 279 0035842 15 0666666 68 0147059 121 0082645 174 0057471 227 0044053 280 0035714 16 0625.000 69 0144.928 122 008 1967 175 0057143 228 0043860 281 0035587 17 0598235 70 0142857 123 008 1 300 176 0056s 1 8 229 0043668 282 0035461 18 0555555 71 0140845 124 0080645 177 0056497 230 0043478 283 0035336 19 0526316 72 0138888 125 0080000 178 0056180 231 0043290 284 0035211 20 0500000 73 0136986 126 0079365 179 0055866 232 0043103 285 0035088 21 0476190 74 0135135 127 0078740 180 0055555 233 00429 18 2S6 0034965 22 0454545 75 0133333 128 0078125 181 0055249 234 0042735 287 0034843 23 0434783 76 0131579 129 0077519 182 0054945 235 0042553 288 0034722 24 0416666 77 0129870 130 0076923 183 0054645 236 0042373 289 0034602 25 0400000 78 0128205 131 0076336 184 0054348 237 00421.94 290 0034483 26 0384615 79 0126582 132 0075757 185 0054054 238 0042017 291 0034364 27 0370370 80 0125000 133 0075 1 88 186 0053763 239 0041841 292 0034246 28 0357143 81 0123457 134 0074627 187 0053476 240 0041666 293 0034130 29 0344828 82 0121950 135 0074074 188 0053191 241 0041494 294 00,34014 30 0333333 83 0120482 136 0073529 189 0052910 242 0041322 295 0033898 31 0322581 84 0119048 137 0072993 190 0052632 243 0041152 296 0033783 32 0312500 85 0117647 138 0072464 i9t 0052356 244 0040984 297 •0033670 33 0303030 86 0116279 139 0071942 192 0052083 j 245 0040816 298 0033557 34 0294118 87 0114943 140 0071429 193 0051813 246 0040650 299 0033445 35 0285714 88 0113636 141 0070922 194 005 1 546 247 0040486 300 0033333 36 0277777 89 0112360 142 0070423 195 0051282 i 248 0040323 301 0033223 37 0270270 90 oiniu 143 00()9930 1.96 005 1 020 i 249 0040161 302 0033113 38 026315s 91 0109890 144 006.9444 197 0050761 I 250 0040000 303 0033005 39 0256410 92 OIO8696 145 OO6H966 198 0050505 ' 251 0039S41 304 0032895 40 0250000 93 0107527 146 0063493 199 0050251 252 0039683 305 0032787 : 41 0243.902 94 01063S3 147 0068027 200 0050000 253 0039526 306 OO3268O 42 0238095 95 0105263 148 OOG7567 201 0049751 254 003.9370 307 0032573 43 0232558 96 0104166 149 UO67114 202 0049504 255 0039216 308 0032468 44 0227272 97 0103093 150 0066666 203 004962 1 256 0039063 309 0032362 45 0222222 98 0102041 lil 0066225 204 0049020 257 0038911 310 0032258 46 0217391 99 0101010 152 0065789 205 0048750 25S 0038760 311 0032154 47 0212766 100 0100000 153 0065359 206 0048544 259 0038610 312 0032051 48 0208333 101 0099009 154 0064.935 207 0048309 260 0038462 313 0031.949 49 0204082 102 OO98O39 155 0064516' 208 0048077 261 0033314 314 0031847 50 0200000 103 0097087 156 0064103 209 0047847 ' 262 0038168 315 0031746 51 0196078 104 0096154 157 00636.94 210 0047619 263 0038023 316 0031646 . 52 0192308 105 0095238 158 0063291 211 0047393 264 0037S7S 317 0031546 53 01886791! 106 0094340 159 0062893 212 0047170 265 0037736 318 0031447 OF QUANTITY AXD NUMBER. 41. Definition. The harmonic mean of two quantities is the quantity of which the reciprocal is the half sum of their recipro- cals.' Thus, the harmonic mean of 3 and 6 is 4 ; for i (l+i)— ^. And the harmonic mean is equal to the pro- duct divided by the half sum. Thus V^— 4. 42. Definition. The common loga- rithm of a number is that power of 10 which expresses it. For instance, 1.1000—3, since lo'mooo. 1.2— .30103, for io™"o"nr2. The principal use of logarithms is de- rived from that property of indices by which their addi- tion and subtraction is equivalent to the multiphcation and division of the respective numbers. TABLE OF LOGARITHMS. Including all Prime Numbers under 1000, nithout the Indices. jNo. Logar. No. Logar. No. Logar. No. Logar. No. 599 Logar. 1 No. Logar. 1 0000000 67 826074s 227 3560259 I401 6031444 7774268 797 ^014583 2 3010300 71 8512583 229 3598355 409 6117233 601 7788745 8O9 9079485 3 4771213 73 8633229 233 3673559 5419 6222140 607 7831887 ail 9090209 4 6020600 79 8976271 239 3783979 421 6242821 613 7874605 821 9143432 5 6989700 83 91 90781 241 3820170 431 6344773 617 7902852 823 9153998 6 7781513 89 9493900 251 3996737 433 6364879 619 7916906 827 9175055 7 8450980 97 9S677U 257 4099331 439 6424645 631 8OOO294 829 9185545 8 9030900 101 0043214 263 4:199557 ; 443 6464037 641 8068580 839 9237620 9 9542425 103 0128372 269 4297523 i 449 6522463 643 8082110 853 9309490 10 0000000 107 0293838 271 4329693 1457 6599162 647 8 109043 857 9329808 11 0413927 109 0374265 277 4424798 U6i 6637009 653 8I49132 859 .9339932 12 0791 81 2 113 0530784 281 4487063 463 6655810 659 8188854 863 9360 108 13 1139434 127 1038037 283 4517864 467 6693169 661 8202015 877 9429996 14 1461280 131 1172713 293 ^668676 479 6803355 673 8280151 881 9ii9759 15 1760913 137 1367206 307 4871384 487 6875290 677 8305887 883 9459607 16 2041200 139 1430148 311 4927604 491 69 108 15 683 8344207 887 9479236 17 2304489 149 173 1863 313 4955443 499 6981005 691 8394780 907 9576073 18 2552725 151 1789769 317 5010593 503 70 15680 701 8457180 911 9595184 19 2787536 '157 1958997 331 5198280 509 7067178 709 8506462 919 9633155 20 3010300 163 2121876 337 5276299 521 7168377 719 8567289 929 9680157 23 3617278 167 2227165 347 5403295 523 7185017 727 8615344 937 9717396 29 4623980 173 2380461 349 5428254 541 7331973 733 8651040 941 9735896 31 4913617 179 2528530 353 5477747 547 737.9873 739 8686444 947 9763500 37 5682017 181 2576786 359 5550944 557 7458552 743 8709888 953 .9790929 41 6127839 191 2810334 367 56i666i 563 7505084 751 S756399 967 9854265 43 6334685 193 2855573 373 571 7088 569 7551123 757 8790959 971 9872192 47 6720979 197 2944662 379 5786392 571 7566361 761 8813847 977 9898946 53 7242759 199 2988531 383 5831988 577 7611758 769 8859263 983 9925535 59 7708520 211 3242825 389 5899496 587 7686381 773 8881795 991 9960737 61 7853298 223 34S3049 397 5987905 593 7730547 787 895.9747 997 9986952 43. Problem. To solve a quadratic squareof half a; then a:i±ar+— =t+— , whencej,± equation. Reduce the equation to the form xx±ax=l!, add the ~— — <\''+-J-)*"'* *-*^^(^+t)~ 'I' OF THE COMPARISON OF VARIABLE QUANTITIES. SECT. II. OF THE COMPARISON OF VAKI ABLE gUANIITIES, 44. Definition. The quantities by which two variable magnitudes are increased or de- creased in the same time, are called tlieir in- crements or decrements, or tlieir increments positive or negative. f' Scholium. They are denoted by an accent placed over the variable quantity ; thus x' and y' are the simultaneous increments of x and y. 45. Definition. The ratio which is the limit of the ratios of the increments of two quantities, as they are taken smaller and smaller, is called the ratio of the velocities of their increase or decrease. Scholium. It vcould be difficult to give any other suf- ficient definition of velocity than this. If both the quan- tities vary in the same proportion, the ratio of x' and y' will be constant (16), and may be determined without consi- dering them as evanescent ; but if they vary according to different laws, that ratio must vary, accordingly as the time of comparison is longer or shorter : and since the degree of variation, at any instant of time, does not depend on the change produced at a finite interval before or after that in- stant, it is necessary, for the comparison of this variation, that the increments should be considered as diminished without limit, and their ultimate ratio determined ; and it is indifferent whether these evanescent increments be taken before, or after the given instant, or whether the mean be- tween both results be employed. 46. Definition. Any finite quantities in the ratio of the velocities of increase or decrease of two or more magnitudes, are tiie fluxions of those magnitudes. Scholium. They are denoted by placing a point over the variable quantity, thus, x, y. And.^ is always ulti- y mately equal to-:-. The variable quantity is called a fluent y with respect to its fluxion, as x is the fluent of ic, or .rr:./i. On the continent the term fluxion is not used, but the evanescent increment is called a difference, and denoted by d or 3, and the variable quantity is conceived to consist of the entire sura or integral of such differences, and marked /, as x:r:/dx, otJUx. This mark has the advantage of dif- fering in form from the short s, which is used as a literal character. 47. Theorem. When the fluxions of two quantities are in a constant ratio, their finite increments are in the same ratio. For if it be denied, let the ratios have a finite difference ; then if the time in which the increments are produced be continually divided, the ratio of the parts may approach nearer to the ratio of the fluxions than any assignable dif- ference, for that ratio is their limit (46), and this is true, by the supposition, in each part ; therefore the sums of all the increments will be to each other in a ratio nearer to that of the fluxfcns than the assigned difference (3 5). 48. Theorem. The fluxion of the pro- duct of two quantities is equal to the sum of the products of the fluxion of each into the other quantity. Or (ry)-^yi+xy. Let the quantities increase from X and y to ar-fa' and y-\-y', then their product will be first xy and afterwards .ri/-|-j/.r'-t-j)/'-(-a;y, of which the difference is yi^' -^xy' -^rx'y' and the ratio of the in- crements of x and xi/ is that of x' to yx'+xy'+x'y' ; or, when the increments vanish, to yx'+xy' since in this case x'y' vanishes in comparison with xy'. But x'-(j/.r'-f-jy');;i' (yi+iy), and the fluxion is rightly determined (46) ; y' V J^v ^v , , , yx' yx , , (orsmce ^ = ^, —, —-^ (18); but:^=4- (is), XXX X X X and yx'-\-xy' yi-^ry (IS). 49. Theorem. The fluxion of any power of a variable quantity is equal to the fluxion of that quantity multiplied by the index of the power, and by the quantity raised to the same power diminished by unity. Or (x")'=:7ix""'i. Let n—i, then (xx)-=:x.i-)-xi (48) ::=2xi=nx"~'i. l(n—3, x"— (xx).x, and its fluxion is x (xx)'-i-(xx)i::r2xxi-fxa:i:^3x'i::;iix""'i'. And the same may be proved of any whole number. If 71 is a fraction, 1 as — , put yzzx", then x^yf, and xzzpy^''y,y::z — — - zz — . j'"'i(38)z:-y. j-^i— 7U[""'i, as before ; and in the same manner the proof may be extended to all postible cases. 8 OF SPACE. 50. Theorem. When the logarithm of a quantity varies equably, the quantity varies proportionally. Or, if 1. x—y, — =: — For xZZ.V f^a), and when v ax becomesy+7/',3:+a.'=i'^ —V.y'—x.b'', andx'zix.i'— aizi. [y — l) ; but y' being constant by the supposition, i>' — 1 is constant, and may be called :—, and .r' ^ — ; a a xu i y therefore inr — , and — n — . a X a Scholium. Numericallogarithms do not, strictly speak- ing, vary by evanescent increments ; but other quantities may flow continually, and be always proportionate to lo- garithms : in either case the proposition is true. In Briggs's logarithms, commonly used, 2i is 10, and a, the modulus, is .43429448)9 ; dividing all the system by a, or multiplying by Q.302585093, we have Napier's original hyperbolical lo- j," garithms, where ^ becomes zz — , and a:z:i. X 61. Theorem. The fluxion of any power of a quantity, of which the exponent], is va- riable, is equiil to the fluxion of the same power considered as constant, together with the fluxion of the exponent multiplied by the power and by the hyperbolical logarithm of the quantity. ^ If .x'-=:z, i:z.yx''-Ki + (h.l.x). x'i/ ; for h. 1. Jzri/. • ^ > (h. 1. .t), (42); now (h. 1. ») — -, (50);and izri. (h.l.^^J' —X. (y. (h. 1. .r)'-s,. (yr_+(h. 1. x).i/), (48, 50)z= X j'x'~'i-f(h. 1. x) xi/. I 52. Theorem. When a variable quan- tity is greatest or least, its fluxion vanishes. For a quantity is greatest when it ceases to increase, and before it begins to decrease ; that is, when it has neither increment nor decrement ; and it is least when it has ceased to have a decrement and has not yet an increment. 53. Problem. To solve a numerical equation by approximation. The most general and useful mode of solving all nume- rical equations is by approximation. Substitute for the unknown quantity a number, found by trial, which nearly answers to the conditions; then the error will be a finite difTerence of the whole equation ; which, when small, will be to the error of the quantity substituted, nearly in the ratio of the evanescent differences, or of the fluxions ; and this ratio may be easily determined. Thus, if I*— 6x'+4x=6699, call 0699, 3/, then Zx'i— y ._._/_ y' I2xjr-J.4x:=y,and irz- and x'— - 3x' — 12X-)-4> Sx''— 12x4-4 nearly; now assume x:=2o, then j/z:5680, and y'— 1019, whence x'zz 1.05, and x corrected is a 1.05; by repeating the operation we may approach still nearer to the true value 21. Ifx"=J(,r=- -' whence the common rule for the extraction of roots is derived. In order to find the nearest integer root, the digits must be divided, beginning with the units, into parcels of as many as there are units in the index, and the nearest root of the last or highest parcel being found, and its power subtracted, the remainder must be divided by its next inferior power multiplied by the given index, in order to find the next figure, adding the next parcel to the remainder before the division. There are also in particular cases other more compendious methods. SECTION III. OF SPACE. 54. Definition. A solid is a portion of space limited in magnitude on all sides. Scholium. Space is a mode of existence incapable of definition, and supposed to be understood by tradition. 55. Definition. A surface is the limit of a solid. 56. Definition. A line is the hmit of a surface. 57. Definition. A point is the limit of a line. Scholium. The paper of which this figure covers a part, is an example of a solid, the shaded portion represents a portion of surface: the boundaries of that surface are lines, and the three ter- minations or intersections of those lines are points. In conformity with this more correct conception, these defi- nitions are illustrated by representations of the respective portions of space of which the limits are considered ; and also by the more usual method of denoting a line by a narrow surface, and a surface by such a line surround- ing it. OF SPACE. 58. Definition. A line joining two points is called their distance. 59. Definition. When the distance of any two or more points remains unchanged, they are said to be at rest; and a space of which all the points are at rest, is a quiescent space. ■Q8BP 60. Definition. A line which must be wholly at rest with respect to any quiescent space when two of its points are at rest in that space, is a straight line. ^ ^ '^ ^ ~^ Cl. Definition. A line which is neither a straight line, nor composed of straight lines, is a curve line. 62. Definition. A plane is a surface, in which if any two points be joined by a straight line, the whole of the straight line will be in the surface. 63. Definition. An angle is the incli- nation of two lines to eadi other. Scholium. An angle is sometimes denoted by this mark z., and is described by three letters placed near the lioes, the middle letter at the angular point. 64. Definition. When a straight line standing on another straight line makes the adjacent angles equal, they are called right angles, 65. Definition. A straight line between two right angles is called a perpendicular to the line on which it stands. 6G. Definition. When a plane surface is contained by a circumference, such that all straight lines drawn to it from a certain point in the plane'are equal, the sur- face is a circle. VOL. II, G7. Definition. The point equally dis- tant from the circumference, is called the centre. G8. Definition, Any straight line drawn from the centre to the circumference, is called a radius. 69. Definition. The term circle also often implies the circumference, and not the circular surface. 70. Definition. A portion of the cir- cumference of a circle is called an arc. 71. Definition. A straight line joining the extremities of an arc, is its chord. 72. Definition, The surface con- tained between an arc and its chord is called a segment of a circle. 73. Definition. A chord passings through the centre is a diameter. ilA^ 74. Defini- tion. A trian- gle is a surface contained between three lines ; and these lines are understood to be straight, unless the contrary is expressed. 75. Definition. ^^g^^^B ~ When two straight ^^^^^ hnes, lying in the same jdane, may be pro- duced both ways indefinitely, without meet- ing, they are parallel. Scholium. The parallelism of lines is sometimes de- noted by this mark II . 7G. Postulate. It is required that the length of a straight line be capable of being identified, whether by the effect of any ob- ject on the senses, or merely in imagination, so that it may remain invariable. Scholium. This is practically performed by making \isible marks on a material surface; although, strictly speaking, no such marks remain at distances absolutely C - 10 OF SPACE. invariable, on account of changes of temperature, and of other circumstances. 77. Postulate. That a straight hne of indefinite length may he diavvu through any two given points. 78. Postulate. That a circle may be described on any given centre with a radius equal to any given straight line. 79. Axiom. A straight line joining two poiiits is the shortest distance between them. Scholium. With respect to all straight lines, this axiom is a demonstrable proposition; but as the demon- stration does not extend to curve lines, it becomes neces- sary to assume it as an axiom. 80. Axiom. Of any two figures meeting in the ends of a straight line, that which is nearer the line has the shorter circumference, provided there be no contrary flexure. 81. Axiom. Two straight lines coinciding in two points, coincide in all points. Scholium. If they did not coincide in all points, the two points of coincidence being at rest, and one of the lines being made the axis of motion, the other must revolve round it, contrarily to the definition of a straight ling. Al- though this is sufficiently obvious, it can scarcely be called a formal demonstration. 82. Axiom. All right angles are equal. 83. Axiom. A straight line, cutting one of two parallel .lines, may be produced till it cut the other. 84. Puoui.em. From the greater of two right lines, AB, to cut oft' a part equal to tlielcss, CD. \ On the centre A describe a circle with A E] B a radius equal to CD (78), and it v>iU C~__~_~D cutoffAE=:CD(;66). 85. Problem. On a given right hne, AB, to describe an equilateral triangle. C ^ ^' On the centres A and B draw two circles, with radii equal to AB, and to their intersec- tion C, draw AC and BC; thenAB:i:AC=:BC (fio), and the triangle ABC is eBCG, therefore much more BGOBCG, to which it was shown to be equal. And the same may be proved in any other position 6f the point G ; therefore the triangle equal to DEF, supposed to be described on AB, coincides with ABC. 90. PROBtEM. To bisect a given angle. A In the right lines forming the angle, take ^ at pleasure ABi^AC; on BC describe an ' equilateral triangle BCD, and AD will bisect the angle BAC. For ABz:AC, BD=CD, and the base AD is common, therefore the triangle ABDrzACD (89), and z.BAD= CAD. Dl. Problem. To bisect a given right line, AB. Describe on it two equilateral triangles, ABC, ABD, and CD, joining their ver- tices, will bisect AB in E. For since ACzzOB, AD=BD, and CD is common to the triangles ACD, BCD, /.ACDz: BCD (sa) ; but CE is common to the triangles ACE and BCE, therefore AE= EB (86). 92. Problem. To erect a [x^rpendicular to a given right Hne at a given point. On each side the point A, take at plea- sure ABziAC, and on BC make an equi- lateral triangle, BCD. Then AD shall be perpendicular to BC. For the sides of BAD and CAD are respectively equal. Bag therefore the angle BADzzCAD (89), and both are right angles (6!), and AD is perpendicular to BC (»5,\ 93. Problem. From a point, A, without a right line^ BC, to let fall a perpendicular on it. On the centre A, through any point D, beyond BC, describe a circle, which E \^must obviously cut BC; join AB and BC. C AC, and bisect the angle BAC by the line AE ; AE will be perpendicular to For ^BAE=CAE, AB:::AC, and AE is common to the triangles BAE, CAR; therefore z.AEBr:AEC (88\ and both are right angles (64). 94. Theorem. The angles which any right line maizes on one bide of another, are> together, equal to two right angles. Let AB be perpendicular to CD, and EB oblique to it, then f:BE + EBDr: CBA4-ABE-|-EBD=CBA+ABD (14). C B 1) 95. Theorem. If tv^o right lines make with a third, at the same point, but on oppo- site sides, angles together equal to two right angles, they are in the same right line. If it be denied, let AB, which together f) with AC, makes with AD, the angles y^ \\ BAD, DAC equal to two right angles, be p ^ \^ not in the right line CAE. Then BAD 4-DAC, being equal to two right angles, is equal to EAD -f-DAC (91), and BAD=:EAD, the k-ss to the greater, which is impossible. 96. Theorem. If two right lines intersect each other, the opposite angles are equal. From the equals,ABC-(- ABD and ABD A-^^ ^^1> -l-DBE (94, 8-2), subtract ABD, and the remainders, ABC, DBE, are equal. In Q the same manner ABD:::CBE. 97. Theorem, If one side of a triangle be produced, the exterior angle will be greater than either of the interior opposite angles. Bisect AB in C, draw DCE ; take CE A E =:CD, and join BE, then the triangle ACD=BCE {c)a, 86), and z.CBE= / /'c^ CAD; but ABF>CBE, therefore AhF> D BF CAD. And in the same manner it may be proved, by producing AB, that ABF is greater than ADB. 98. Theorem. The greater side of any triangle is ojjposite to the greater angle. LetAB>AC, then ^ACB>ABC. For C taking AD=AC,andjoining CD, ^ACD =ADC(87). But aADOCBD (97), A and ACB>ACD, therefore much more Z.ACB>CBD, orABC. D B 12 OF SPACE. 99. Theoeem. Of two triangles on the sartie base, the sides of the interior contain the greater angle. E Produce AB to C, then z.ABD>ACD (07), and /. ACD> AEC, therefore much more ABD>AED. 'B A T) 100. Problem. To make a triangle, hav- ing its sides equal to three given right lines, every one of them being less than the sum of the other two. Take AB equal to one of the lines, and on the centres A and B describe two circles with radii equal to the other two A B lines; draw AC and BC to the intersec- tion C, and ABC will be the triangle required. 101. Problem. At a given point in a right line, to make an angle equal to a given angle. » /" p In the lines forming the given angle ABC, take any two points, A and C, join AC, and taking DEziBC, make S C D E the triangle DEF, having DF=BA and FE=AC (too), then /.FDE=:ABC (sg). 102. Theorem. If two triangles have two angles and a side respectively equal, the whole triangles are equal. p j;^ Let the equal sides be AB and CD, intervening between the equal angles, then if on AB a triangle equal to CDE be supposed to be A Cf 15 C I) constructed, the points A and B, and the angles at A and B being the same in this triangle and in ABF, the sides must coincide both in position and in length ; therefore ABF=:CDE. If the equal sides are AF and CE, opposite to equal angles, then ABz:CD, and the whole triangles are equal. For if AB is not equal to CD, let it be the greater, and let .AGzzCD ; then, by what has been demonstrated, the triangle AFG=:CED, and z.AGF=CDE=rABF, by the supposition-; but AGF>ABF (9"), which is impossible. 103. Theorem. The shortest of all right lines that can be drawn from a given point to a given right line is that which is perpendi- cular to the line, and others arc shorter as they are nearer to it. B. D T) E Let AB be perpendicular to CD, then AB is shorter than AD . Produce AB, take BE=AB, and join DE ; then the triangle ABD=:EBD (86), and AD=: DE. But AB+BE or 2AB is less than AD+DE or 2AD (79), therefore AB < AD (is). In a similar manner 2AD <2AF(80), and ADABC (97). 105. Theorem. A right linCKutling two parallel lines, makes equal angles with them. , Let AB cut the parallels BC, ^ DE; then if /.ABC is not equal Bx^^ C to ADE, let it be equal to ADF, ^y^ jf then BC and DFare parallel (104), andDE, which cuts DF, will also, if produced, cut BC (83), contra- rily to the supposition. 106. Theorem. Right lines, parallel to the same line, are parallel to each other. Let AB and CD be parallel to' EF ; draw GHI cutting them all, -2^ then z.K.GB=KIF (los), and aKHD=:KIF, therefore A KGB =K.HD, and AB|1CD (104). 107. Problem. Through a given point to draw a right line parallel to a given right hne. From A draw, at pleasure, AB, meet- A D ingBCin B, and make /.BAD=ABC (I0l),then ADllCB (104). ,.. C/ li 108. Theorem. The angles of any trian"-le taken together, are equal to two right angles.'X^ Produce AB'to C, and draw BD paral- leltoAE. Then /.EBDrzAEB (IC5), ^ and /.DBC':=EAB; therefore the exter- nal angle EBC is equal to the sum of the internal opposite angles, AEB, EAB, and A n/ r> C a, / D / E 4' F B OF SPACE. 13 Bdding ABE, the sum of all three is equal to ABE+EBC, or to two right angles (94). 109. Theorem. Right lines joining the extremities of equal and parallel right lines, are also equal and parallel. A j^ Let AB and CD be equal, and parallel. / ^-""^ Then AC will be equal and parallel to L^:::__J BD. For, joining BC, aABC=BCD ^' " (105), and the triangles ABC, DCB, are equal (86), and AC=DB; also aACB=:DBC, therefore AC||BD (104). 110. Definition. A figure of which the opposite sides are parallel, is called a paral- lelogram . 111. Definition. A straight line joining the opposite angles of a parallelogram is called its diagonal. 112. Definition. A parallelogram, of which the angles are right angles, is a rect- angle. 113. Definition. An equilateral rect- angle is a square. 1 14. Theorem. The diagonal of a pa- rallelogram divides it into two equal triangles, and its opposite sides are equal. ^ B For ABC is equiangular with DCB \ ^-^ \ (105), and BC is common, therefore they Q- ^ are equal (102), and AB=CD,and AC=: BD. 115. Theorem. Parallelograms on the same base, and between the same parallels, are equal. A B j^ P Since AB=CD, both being equal to EF, AC=BD(i5,or 16), and the triangle AEC is equian- gular (105) and equal (102) to BFD j therefore deducting each of them from the figure AEFD, the remainder ED is equal to the remainder AF. 116. TheoreSi. Parallelograms on equal bases, and between the same parallels, are equal. For each is equal to the paral- lelogram formed by joining the extremities of the base of the one, and of the side opposite to the base of the other (115). 1 17. Theorem. Triangles on equal bases, and between the same pan.llcls, are equal. Take AB and CD equal to the base 4 B C D EF or GH, and join BF and DM. Tiien F.B and GD are parallelograms between the same parallels (lOQ), and on equal bases, therefore they are equal (1 16), and their halves, the triangles AEF, CGVL (114), are also equal (1 8). 118. Theorem. In anv right angled tri- angle, (he square described on the hypote- nuse is equal to the sum of the squares de- scribed on the two other sides. Draw AB parallel to CD the side of the square on the hypotenuse, then the parallelogram CB is double any ' triangle on the same base and be- tween the same parallels (114, 117), as ACD V but ACD=FCG, their angles at C being each equal to ACG increased by a right angle, FC to AC, and GC to DC Again, GAH is a right line (95), parallel to CF, therefore the triangle FCG is half of the square CH on the same base, and CH:z:CB, since they are the doubles of equal triangles. In the same manner it maybe shown that GKr^GB ; therefore the whole CDIG is equal to the sum of CH and GK. 119. Problem. To find a common mea- sure of any two quantities. Subtract the less continually from the greater, the re- mainder from the less, the next remainder from the pre- ceding one, as often as possible, and proceed till there be no further remainder ; then the last remainder will be the. common measure required. For since it measures the pre- ceding remainder, it will measure the preceding quantities in which that remainder was contained, and which, in- creased at each step by the remainders, makes up the origi- nal quantities. For example, if the numbers 54 and 21 be proposed, J4 — 21 — 21 = 12, 21 — 12=9, 12 — 8=3, 9 — 3 — 3 — 3 14 OF SPACE. ~o, therefore 3 is the common ttjeasure, for it measures 9, and 9+3 or 12, and ia+9 or 21, and 2X21 + 12 or it. Scholium. Hence it is obvious, that there can be no greater common measure of the two quantities than the quantity thus found ; for it should measure tl>e difference of the two quantities, and all the successive remainders down to the last, therefore it cannot be greater than this last. It must also be remarked, that in some cases no ac- curate common measure can be f*nnd, but the error, or the last remainder, in this process, itiay always be less than any quantity that can be assigned, since the process may be continued without limit. That there are incommensu- rable quantities, may be thus shown : every number Is either a prime number, that is, a number not capable of being composed by multiplication of other numbers, or \t is composed by the multiplication of factors, which are primes. Let the number a be composed of the prime numbers led, or az^bcd, then aa':^Lcd,tcd'^zlh.cc,dd and each prime factor of aa occurs twice ; so that every square number must be composed of factors in pairs ; and a square number multiplied by a number which is not composed of factors in pairs cannot be a square number : for instance, 2aa or 3aa cannot be a square number, since the factors of 2 are only 1.2, and of 3, 1.3, and not in pairs : there- fore the square rooot of 2 or 3 cannot be expressed by any fractiofi, for the square of its numerator would be twice or th-ice the square of its denominator. But the ratio of the hypotenuse of a triangle to its side may be that of »/ 2 or 4/3 to 1 ; so that quantities numerically incommensurable may be geometrically determined. IGO. Theorem. Triangles and paiallelo- grams of the same height are proportional to their bases. Let AB be a common measure of AC and AD, and let AB=:BE A B E r C 'J) =Efi J°'" GB, 'GE, G¥, then the triangles AGB, BGE, EGF, are equal, and the triangle AGD is the same multiple of AGB that AD is of AB ; and AGC-is the sanre multiple of AGB that AC is of AB, or AGD : AGB=AD : AB, and AGC : AGB rzAC ; AB ; hence, dividing the first equation by the equal terms of the second (is), AGD : AGCnAD : AC, and aAGD : 2AGC=:AD : AC, therefore the parallelograms ■which are double the triangles, are also proportional. ScHOLi u M. The demonstration may easily be extended •to incommensurable quantities. For if it be denied that AC : AD=:AGC : AGD, let AC : AD be the greater, and ■ , ,.^ , I , AC 1 AGC n.AC let the difference be — , then — : :r -— — — n AD n AGD n.AU AD ' n.AW n.AC-AV> . Let m.AD be that multiple of n.AD ' AD which is less than n.AC, but greater than ?i.AC — AD, then a triangle on the base mAD will be equal to m.AGD, which will be less than n.AGC, the tri- angle on n.AC ; now multiplying the former equation by rt 71. AGC 7J.AC— AD , ,„„ ,„ .^„ — , r: , and 7i.AGC.7n..\D=m.AGD. m m.AGD m.AD (ji.AC — ^AD); btjt the first factors have been shown to be respectively greater than the second, therefore their pro- ducts cannot be equal, and the supposition is impossible. l<21. Theorem; The homologous sides oFetjuianguIar triangles are proporliioual. Let the homologous sides AB,BC, p of the equiangular triangles ABD, BCE, be placed contiguous to each other in the same line, then AD 1 1 BE,and BDl ICE; produce AD.CE, ABC till they meet in F, and join AB and BF. Then the tri- angles FAE, EAC, are proportional to their bases FE, EC, and the triangles AFB, BFC, to AB, BC (120). But FAE =:AFB(ll7),andEAC=EBC4-EAB=EBC+EFB=BFC, therefore FAE : EAC=AFB : BFC, and FE : EC=AB : BC; but FEi^DB (114). In the same manner it may be shown that the other homologous sides are proportional. ScHOLrUM. Hence equiangular triangles are also called similar. 122. Theorem. Equal and equiangular parallelograms have their sides reciprocally proportional. If AB=:BC then DB : BE=BF : j^ q. BG. ForDB:BF=.AB:GF(l2o;=: f BC : GF=BE : BG (120) ; or DB : D BErzBF : BG. £/ E C 123. Theorem. Equiangular parallelo- grams, having their sides reciprocally pro- portional, are equal. For they may be placed as in the last proposition, and the demonstration will be exactly similar. ■ Scholium. Hence is derived the common method of finding the contents of rectangles ; let a and b be the sides of a rectangle, then 1 : a: il: al, and the rectangle is equal to that of which the sides are 1 and ab, or to ab square units. Hence the rectangle contained by two lines is equivalent to the product of their numeral representatives. OF SPACE. 15 A IS IZ\ B D 124. Theorem- Equiangular parallelo- "■ranis are tr each other in the ratio com- pounded of the ratios of their side's. p. Or in the ratio of the rectangles or numeral products of their sides. For 'q since AB ; BC=AD : DC (l 20;, and DC : dE=:DB : BE, multiplying the former equation by the ferms of the latter, AB.DB : BC.BE=AD.CE. 125. Theorem, similar triangles, and figures composed of similar triangles, are in the ratio of the squares of their homologous sides. /-< Since similar triangles are the F halves of equiangular parallelograms, which are in the ratio compounded -£ of the ratios of their sides (124), the triangles are in the same ratio, or ABC : DEF=AB.BC : DE.EF ; but AB : DE=BC : EF (121), therefore ABC : DEF=AB.AB: DE.DE, or ABq -. DEq. And the same may be proved of similar polygons, by composition (32J. 12G. Definition. An indefinite right line, meeting a circle and not cutting it, is called a tangent. 127. Theorem. A right line, passing through any point of a circle, and perpen- difcular to the radius at that point, touches the circle. Since the perpendicular AB is shorter than any other line AC that can be drawn from A to BC (los), it is evident that AC is greater than the radius AD, and that C, as well as B C every other point of BC, besides B, is without the circle ; therefore BC does not cut the circle, but touches it. 128. Definition. BC is called the tan- gent of the arc BD, or the angle BAD. 129. Definition. AC is the secant of BD, or BAD. 180. Definition. DE perpendicular to A B, is the sine of BD or BAD. 131. Definition. AE is the cosine of BD or BAD. 132. Definition. of BD or BAD. EB is the versed sine Scholium, The circle is practically supposed to be di- vided into 360 equal parts, called degrees, each of these into 60 minutes, a minute into 60 seconds ; and the divi- sion may be continued without limit ; thus 6o"=:i', 60'=: 1°, 90° make a right angle. Some modern calculators divide the quadrant into 100 equal parts,and subdivide tliese decimally. 133. Theoreji. The angle subtended at the centre of a circle by a given arc, is double the angle subtended at the circumference. Let ABC and ADC be subtended by AC. Draw the diameter DBE, then ^ ABE= ADB-t-BAD(los}=:2ADB (s;). Also Z. CBEzriCDB, therefore ABE— CBE= 2ADB— 2CDB, or ABC=2ADC. In a similar manner it may be proved in other positions. 134. Theorem. The angle contained by the tangent and any chord at the point of contact, is equal to the angle contained in the segment on the opposite side of the chord. Draw the diaimeter AB, and join BC ; then /, BCA is equal to half the angle subtended at the centre by the semicircle AB, or to a right angle, and AHC and BAG make together another right angle . (93), therefore deducting BAC, ABC= CAD. And it ajipears also from the last proposition that the angle contained in the lesser segment CA is equal to the complement of ABC to t«o right angles, or to CAE. 135. Problem. To draw a tangent to a circle from a given point without it. Join AB, bisect it in C, and on C draw a circle, with the radius CB, intersecting the former circle in D, then AD shall touch the circle. For the angle ADB, in a semicircle, is a right angle (134, 12?), and BD is the radius of the given circle. 13f3. Theorem. In equal circles, equal angles stand on equal arcs. 16 or SPACE. / Let AB and BC be the sines ot ...^ j^g angles, ACB, BAC, then AC will be ti,. sine of their sum CBD, qr of ABC. Now- making BE perpendicular to AC, AC" For the chords of equal angles are equal (86), and the segments cut offby them contain equal angles (133) i and if a segment equal to AB be supposed to be described on the chord CD, and on the same side with CED, it must coincide with CED, for since, at each point of each arc, CD subtends the same angle, the points of one arc can never be within those of the other (99) ; the arcs are therefore equal. Scholium. Hence it may easily be shown, that mul- tiple and proportionate angles are subtended by multiple and proportionate arcs. 137. Theorem. If two chords of a given ,^^, , " and EF be always parallel to DG' circle intersect each other, the rectangles the radius of ad, and cm the cen- contained by the segments of each are equal. treF, draw the circle ah; join Join AB and CD. Then ^AEB^: AH, then since Z-EADziiAGD DEC (90}, and /.BAE::=DCE (i33), =:1AFM, the chord AH will coin- 1^ both standing on BD, therefore the cide with the chord AD (133> AE+EC, and rad. : cos. BAC : : AB: AE, and rad. t cos. ACB: :BC:CE (139). 141. Theorem. The ratio of the Eva- nescent tangent, arc, chord, and sine, is that of equality. ' Let AB be the tangent, and CD the sine of the arc AD. Let AE betakenat pleasure in the tangent. triangles AEB, CED, are similar, and AE:CE::EB:ED (li2l), therefore AE.EDrzCE.EB (123). 138. Theorem The rectangle contained by the segments of a right line intercepted by a circle and a given point without it, is equal to the square of the tangent drawn from that point. Join AB, AC; then ^lABCrrCAD (134), and the angle at D is common, therefore the triangles ABD, CAD, are similar, and BD : AD : : AD : CD (121), whence BD.DC=:ADq (123). IS9. Theorem. In every triangle the sides are as the sines of their opposite angles, the radius being given. C Take ABzzCD, and draw BE and 134). And when DA vanishes, DG coinciding with AG, EF will be parallel to AF, and the angle " . EAH will vanish, therefore AH will coincide with AE and with IH parallel to the sine CD ; and by similar triangles the ratio of AB, AD, and CD, is the same as that of AE, AH, and IH, and is ultimately that of equality. But the arc AD is nearer to the chord AD than the figure ABD, and it has no contrary flexure, therefore it is longer than the line AD (79), and shorter than ABD (80>,- until their dif- ference vanishes, and it coincides with both. Scholium. The same is obviously true of any curve coinciding at a given point with any circle ; and all the elements agree as well in position as in length. \\1. Theorem. The fluxion of the arc being constant, the fluxion of the sine varies as the cosine. B B iD CF perpendicular to AD, then they are the sines of the angles A and D, The fluxion of the arc is equal to that of the tangent, since their evanescent incre- ments coincide (141). Let AB be the sine, AC the cosine, BDthe increment of the tan- gent, DE that of the sine: then /.ABC::! EBD (16), and the triangles ABC, EBD, are similar, and BD is to DE as BC to AC ; but the ultimate ratio of the increments is that of the fluxions, therefore the fluxion of the tangent, or of the arc, is to that of the sine as the radius to the cosine. The same may easily be in- E F to tlie radius AB or CD (130), and by similar triangles, AC : CF : : AB ; BE (121), or CD : BE. And the same maybe shown of the other sides and angles. 140. Theorem. The sine of the sum of any two arcs, is equal to the sum of the sines ferred from the theorem for finding the sine of the sum of of .the separate arcs, each being reduced in two arcs (i4o). the ratio of the radius to the cosine of the 143. Theorem. The area of a circle is other arc. equal to half the rectangle contained by OF SPAClf. 17 the radius and a line equal to the circum- ference. Suppose the circle to be described by the revoUition of the radius : the elementary triangle to which the fluxion of the circle is proportional (l4l), is equal to the contempo- raneous increment of the rectangle, of which the base is equal to the circumference, and the height to half the radius : consequently the whole areas are equal (47). 144. Theorem. The circumferences of circles are in the ratio of their diameters. Supposing the circles to be concentric, and to be de- scribed by the revolution of different points of the same right line, the ratio of the fluxions, and consequently that of the whole circumferences,' will be the ratio of the radii, or of the diameters (47). Scholium. The diameter of a circle is to its circum- ference nearly as 7 to 22, and more nearly as 113 : 355, or 1 : 3.14159205359 ; hence the radius is equal to 57.29578° =3437.74S7'=:2oa«04.8"; and, the radius being unity, lO=:.017453293, l'=:.000290888, and l"=.OO0OO4848. 145. Definition. A straight line is perpendicular to a plane, when it is perpen- dicular to every straight line meeting it in that plane. 146. Definition. A plane is perpen- dicular to a plane, when all the straight lines drawn in one of the planes perpendicular to the common section, are perpendicular to the other. 147. Definition. The inclination of a straight line to a plane is the angle contained by that line, and another straight line drawn from its intersection with the plane to the in- tersection of a perpendicular let fall from any point of the line upon the plane. 148. Definition. The inclination of two planes is the inclination of two lines, one in each plane, perpendicular to the common section. 149. Definition. Parallel planes are such as never meet, although indefinitely produced. 150. Definition. A solid angle is made VOL. II. biy the meeting of two or more plane angles, in different planes. 151. Definition. Similar solid figures are such as have all parts of their surfaces si- milar and similarly placed : and which have all their sections, in similar directions, re- spectively similar. 152. Definition. A pyramid is a solid contained by a plane basis and other planes meeting in a point. 153. Definition. A prism is a solid contained by planes of which two that are opposite, are equal, similar, and parallel, and all the rest parallelograms. 154. Definition. A cube is a solid contained by six equal squares. 155. Definition. A solid of revolu- tion is that which is described by the revolu- tion of any figure round a fixed axis. 156. Definition. A sphere is described by the revolution of a semicircle on its dia- meter as an axis. 157. Definition. A cone is a solid described by the revolution of an indefinite right line passing through a vertex and moving round a circular basis. 158. Definition. A cylinder is a solid described by the revolution of a right angled parallelogram about one side. 159. Theorem. Two straight lines cut- ting each other are in one plane. For a plane passing through one of them may be sup- posed to revolve on it as an axis until it meet some point of the other ; and then the second line will be wholly in the plane (62). 160. Theorem. If two planes cut each, other, their section is a straight line. For the straight line joining any two points of the section must be in each plane (92), and must therefore be the common section of the planes. 161. Theorem. A straight hne, making right angles with two other lines at the point D 18 OF SPACE. of their intersection, is at right angles to the plane passing through those lines. Let AB be perpendicular to CD and EF intersecting each other in A : take AC at pleasure and make ACzrAD=AE=AF i draw through A any line GH, and join ' CEi, DF; then the triangles ADH, ACG are equal and equiangular, AH=:AGandDH=CG;butsince he triangles CBE, DBF, are equal, and equiangular, the angles BCG and BDH are equal, and the triangle BCGz: BDH, BG:=BH, and the triangles ABG, ABH, are equal and equiangular : consequently the angle BAG— BAH, and both are right angles : and the same may be proved of any other line passing through A ; therefore AB is perpendicular to the plane passing through CD and EF (145). 162. Theorem. Three straight lines Tvhich meet in one point and are perpendi- cular to one line, are in one plane. Let AB, AC, and AD meet in A, and be perpendicular to AE, then they are all in one plane. For if ei- ther of them AC is out of the plane which passes through the other two, let a plane pass through AE and AC, and let it cut the plane of AB and AD in AF then the angle EAF is a right ang e (I61), and EAr=EAC, the greater to .the less ; which is impossible. 163. Theorem. Two straight lines which are perpendicular to the same plane, are pa- rallel to each other ; and two [)arallel lines are always perpendicular to the same planes. LetAB, CD, be perpendicular to the plane BED : draw DE at right angles to BD, and equal to AB, then the hypotenuses AD, BE, will be equal, and the triangles ABE, EDA, having all their sides equal, will be equiangular, and the angle ADE will be aright angle: consequent y DE is perpendicular to the plane BC (ISi , and to DC (162>, and AB is in the same plane with DC : and ABD and BDC being right angles, ABIICD. Again, if AB ||CD, and AB is perpendicular to the plane BED, the triangles ABE and EDA being equiangular, ADE is a right ang e . tlerefore CDEis a right angle ^l6l) ; but CDB is aii^iiiaJigle (los), therefore CD is perpendicular to BED. 164. Theorem, Straight lines which are parallel to the same straight line, not in the same plane, are parallel to each other. From any point in the third line, draw perpendiculars to the two tirst, and let a plane pass through these per- y pendiculars : then the third line is perpendicular to this plane (161) ; consequently the first and second are perpen- dicular toil, and therefore parallel to each other (1(13). 165. Theorem. If the legs of two angles not in the same plane are parallel, the angles are equal. Let AB 1 1 CD, and BE II DF, then z. B ABE=CDF. TakeAB=:BE=CD=:DF: Ki then AC||=:BD1|=:EF(109), and AE =:CF (log) ; therefore ABE and CDF ^^ are equal and equiangular- 166. Problem. To draw a line perpen- dicular to a plane from a given point above it. From the point A let fall on any line -^i BC in the given plane a perpendicular AD ; draw DE perpendicular to BC in the same plane, and from A draw AE ^^ ^ perpendicular to DE : then AE will be perpendicular to the plane BEC ; for if EF be parallel to BC, it will be per- pendicular to the plane ADE (163), and consequently to AE ; therefore AE, being perpendicular to DE and EF, will be perpendicular to the plane passing through them. 167. Problem. From a given point in a plane, to erect a perpendicular to the plane. From any point above the plane let fall a perpendicular on it, and draw a line parallel to this from the given point : this line will be the perpendicular required. 168. Theorem. If two parallel planes are cut by any third plane, their sections are parallel lines. For if the lines are not parallel, they must meet, and if they meet, the planes in which they are situated must meet, contrarily to the definition of parallel planes. 169. Definition. A parallelepiped is a solid contained by six planes, three of which are parallel to the other three. 170. Theorem. The opposite planes of OF SPACE. 19 every parallelepiped are equal and equian- gular parallelograms. The opposite sides of all the figures are parallel, because they are the sections of one plane with two parallel planes (168): the corresponding sides of two opposite planes be- in", for the same reason, parallel to each other, contain equal angles (165), and they are also equal, as being the opposite sides of parallelograms ; consequently the opposite figures are the doubles of equal triangles, and are therefore equal parallelograms. 171. Theorem. If a prism be divided by a plane parallel to its two opposite sur- faces, its segments will be to each other as the segments of any of the divided surfaces or lines. A. G M O H ■ r ^ =-r 1 Let the prism AB ,Nf\,.Ei\ .Ei,\ -lA be divided by the plane F K L D ' B CDE parallel to AFG and BHI. Find FK a common measure of FD and DB (119), make KL=:FK, and let the planes KMN, LOP be parallel to AFG ; then the prisms AK, ML may b& shown to be contained by similar and equal figures similarly situ- ated, in the same manner as it is shown of parallelepipeds, and there is no imaginable difference between these prisms : they are therefore equal ; and the prism AD is the same multiple of AK that FDisof FK, and AB the same multiple of AK that FB is of FK, or AD : AK=FD : FK, and AB . AK=:FB : FK, whence AD : AB=FD : FB, and the prisms are in the same ratio as the segments of the line FB, or of the parallelogram GB (27), If the segments are incommensurable, they are still in the same ratio, for it may be shown that the ratio of the prisms is neither greater nor less than that of the lines. 172. Theokem. Parallelepipeds on the same base and contained between the same planes, are equal. D The parallelepiped AB is equal to CD standing on the same base BC, and terminated by the plane AED. For each is equal jj to the parallelepiped EF ; since the triangular prism GB is similar and equal IQ the triangular prism HC, and deducting these from the solid HCI, the remainders AB and EF are equal. And in the same manner it may be shown that CD=:EF ; therefore AB=CD. 173. Theorem. Parallelepipeds on equal bases and of the same height are equal. Each parallelepiped is equal to the erect parallelepiped on the same base. Let one of j these be so placed that the plane of one of the sides AB may coincide with the plane BC of the other parallelepiped CD, and that EBC may be a straight line. Then producing FB, and making CG parallel to it, the parallelepiped BH will be equal to CD (172). Now completing the parallel- epiped IK, as the parallelogram CF is to EF, so is KI to AF (171) ; and as CF to BG, so is KI to BH, but EF is equal to the base of AF, and BG to the base of CD, they are therefore equal, and the parallelepipeds AF and BH are equal, and AFz;CD. 174. Theorem. Parallelepipeds of the same height are to each other as their bases. For one of them is equal to a parallelepiped of the same height on an equal base which forms a single parallelogram with the base of the other ; and this is to the other in the ratio of the bases (171) ; consequently the first two are in the same ratio. 175. Theorem. Parallelepipeds are to each other in the joint ratio of their bases and their heights. For one of them is to a third parallelepiped of the same height with itself, but on the basis of the second, in the ratio of the bases, and the third is to the second in the ratio of the heights, consequently the first is to the second in the joint ratio of the bases and the heights. Thus, a and b being the bases, c andd the heights, e,J, and g the three parallel- epipeds, a -.b-.-.e: g, and c.d:: g -.f; ac : Id^Ze-.f. Scholium. Hence is derived tlie common mode of finding the content of a solid, by multiplying the nume- rical representatives of its length, breadth and height, and thus comparing it with the cubic unit of the measure, - 176. Theorem. Similar parallelepi|3eds are in the triplicate ratio of, their homologous sides. For the joint ratio of the bases and heights is the same as the triplicate ratio of the sides. 177. Theorem. A plane pjissing through the diagonals of two opposite sides of a pa- rallelepiped, divides it into two equal prisms. 20 OF SPACE. The diagonals are paraJlel, because the lines in which they terminate are parallel and equal, and every line and C angle of the one prism is equal to the corresponding line and angle of the other prism ; consequently the prisms are ^^ equal. Thus AB=CD, AE=CF, DE= BF, the angle EAB=DCK, EAH=:GCF, and BAH=DCG. 178. Theorem. Prisms are to each oilier in the joint ratio of their bases and their heights. Triangular prisms are in the same ratio as the paral- lelepipeds on bases twice as great, of which they are the halves; and all prisms may be divided into triangular prisms, by planes passing through lines similarly drawn on their ends, and they will be equal together to the half of a parallelepiped on a basis twice as great ; conse- quently two such prisms are in the same ratio as the pa- rallelepipeds. 179. Theorem. All solids of which the opposite surfaces are planes, and the sides such that a straight line may be drawn in them from any point of the circumference of the ends parallel to a given line, are to each other in the joint ratio of their bases and their heights. For if they are terminated by rectilinear figures, the solids are prisms ; and if they are terminated by curvilinear figures, they will always be greater than prismatic figures, of which the bases are inscribed polygons, and less than figures of which the bases are circumscribed polygons; and if the proposition be denied, it will always be possible to inscribe a prism in one of the solids which shall be greater than any solid bearing to the other solid a ratio assignably less than the ratio determined by the proposition, and to circumscribe a prism less than any solid bearing a ratio assignably greater. Such solids may not improperly be called cylindroids. 180. Theorem. The fluxion of any solid described by the revolution of an indefinite line passing through a vertex, and moving round any figure in a plane, is equal to the prismatic or cylindroidal solid, of which the base is the section parallel to the given plane, and the height the fluxion of the height. In any incremen t of the solid, which is cut off by planes determin- ing the increment of the height, sup- pose a prismatic or cylindroidal solid to be inscribed, of which the base is equal to the upper surface of the segment, and the sides such that a line may always be drawn in them parallel to a given line passing through the vertex and the basis of the solid : and let anothtr solid be similarly described on the lower surface of the segment as a basis: then it is obvious that the increment is always greater than the inscribed solid, and less than the circumscribed ; and that when the increment is diminished without limit, its two sur- faces are ultimately in the ratio of equality, and the in- crement coincides with the cylindroid described on its basis. Such solids may be termed in general pyramidoidal. 181. Theorem. All pyramidoidal solids are equal to one third of the circumscribing prismatic or cylindroidal solids of the same height. The area of each section of such a figure parallel to the basis, is proportional to the square of its distance from the plane of the vertex. For each section is either a polygon similar to the basis, or it may have'polygons inscribed and circumscribed, which are similar to polygons inscribed and circumscribed in and round the basis, and which may differ less from each other in magnitude than any assignable quan- tity,consequentlyeach section is as the square of any homo- logous line belonging to it, or, by the properties of similar triangles, as the square of the distance from the vertex, or from the plane of the vertex. If then the area of the base be a, the whole height b, and the distance of any sec- tion from the plane of the vertex x, the area of the section will be — .a, and the fluxion of the solid ttx'x, of which bo bb a the fluent is i — x', and when xzzb, the content is lax, bb which is one third of the content of the whole prismatic or cylindroidal solid. Hence a pyramid is one third of the cir- cumscribing prism, and a cone one third of the circum- scribing cylinder. 182. Theorem. The fluxion of any solid is equal to the parallelepiped of which the base is equal to the section of the solid, and the height to the fluxion of its height. For every part of a solid may be considered as touching some pyramidoidal solid, and having the same fluxion : OF SPACE. tiid the fluxion expressed by a cylindroid is equal to a pa- rallelepiped on the same base and of the same height. 183. Theorem. The curve surface of a sphere is equal to the rectangle contained by its versed sine and the sphere's circumference. The fluxion of the surface is obviously equal to the rect- angle contained by the fluxion of the circumference and the circumference of the circle of which the radius is the sine ; it varies therefore as the sine ; but the fluxion of the cosine or of the versed sine varies as the sine, conse- quently the surface varies as the versed sine. Now where the tangent becomes parallel to the axis, the fluxion of the surface becomes equal to the rectangle contained by the sphere's circumference, and the fluxion of the versed sine : hence the whole surface of any segment is equal to the whole rectangle contained by its versed sine and the sphere's circumference ; and the surface of the whole sphere is four times the area of a great circle. 184. Theorem. The content of a sphere is two thirds of that of the circumscribing cy- linder. The fluxion of the sphere is to that of the cylinder as the square of the sine to the square of the radius ; or if the fluxion of the cylinder be aabi, that of the sphere will be (aor — xx]bi, or labxx — hxxi, of which the fluent is ali* — it'j' ; which, when x-zia, becomes \aH; while the con- tent of the cylinder is a?b.- - 185. Theorem. When a picture is pro- jected on a plane, by right lines supposed to be drawn from each point to the eye, the whole image of every right line, produced without limit, is a right line drawn from its intersection with the plane of projection, to its vanishing point, or the point where a line drawn from the eye, parallel to the given line, meets the plane of projection ; and this image is divided by the image of any given point in the ratio of the portion of the line intercepted by that point and the picture, to the line drawn from the eye to the vanishing point ; so that if any two parallel lines be drawn from the ends of the whole image, and the distances of the eye and of the given point be laid oft' on them respectively, the line joining the points thus found, will deter- \\ mine the place of thg requued image of the point. For A being the eye, and B the vanishing point of r^ B I A. the line CD; AB and CD ~ being parallel, are in the same plane, and AD is also in that plane (62) ; and BC is the intersection of this plane with that of the picture ; therefore E, the image of the point D, is always in the line BC ; and AB : CD :: BE : EC ; and taking the parallel lines BF, CG, in the same ratio, FG will also cut BC in E. When AB is perpendicular to the plane, B is called the point of sight, and is the vanishing point of all lines perpendicular to the plane of the picture ; and the vanishing point of any other line may be found by setting off from B a line equal to the tangent of its inclina- tion to the perpendicular line, the radius being AB. Scholium. When a line becomes parallel to the plane of the picture, the distance of its vanishing point becomes infinite, and the image is therefore parallel to the original. In this case, the magnitude of the image may be deter- mined by means of lines drawn in any other direction through the extremities of the original line. In the ortho- graphical projection, the images of all parallel lines what- ever become parallel, the distance of the eye, and conse- quently that of the vanishing point, becoming infinite. 186. Definition. The subcontrary sec- tion of a scalene cone is that which is per- pendicular to the triangular section of the cone passing through the axis, and perpen- dicular to the base, and which cuts off" IVom it a triangle similar to the whole, but in a contrary position. 187. Theorem. The subcontrary section of a scalene cone is a circle. Through any point A of the section, let a plane be drawn parallel to the base ; then its section will be a circle, as is easily shown by the properties of similar triangles j and the common section of the planes will be perpendicular to the triangular section of the cone to which they are both per- pendicular ; consequently, ABqirCB.BD ; but since the triangles CBE, FBD are equiangular and similar, CB : BE ::BF:BD, and CB.BD=BE.BF=ABq ; therefore EAF is also a circle. 22 OF THE PROPERTIES OF CURVES. 188. Theorem. The stereograpliic pro- jection of any circle of a sphere, seen from a point in its surface, on a plane perpendicular to the diameter passing through that point, is a circle. Let ABC be a great circle of the sphere passing through the point A and the centre of the circle to be projected, then the angle ACB=BAD=BEF, and ABC=CAGzzCHI, and the triangle AHE is similar to CV ~K D ABC, and the plane ABC is perpendicular to the plane BC and the plane HE, there- fore HE is a subcontrary section of the cone ABC, and is consequently a circle. SECTION IV. OF THE PROPERTIES OF CURVES. 189. Definition. Any parallel right lines intercepted between a curve and a given right line, are called ordinates, and each part of that line intercepted between an ordinate and the curve, is the absciss corres- ponding to that ordinate. 190. Theorem. The fluxion of the area of any figure is equal to the parallelogram contained by the ordinate and the fluxion of the absciss. Let AB be the absciss, and BC the ordinate, through C draw DCE [ | AB, and take DC::DE=:half the incre- ment of AB, then the simultaneous increment of the figure ABC will ul- timately coincide with the figure FCGEB, since the curve ultimately coincides with its tangent (l4l), but the triangles CDF, CEG, are equal, therefore the parallelogram DBE is ulti- mately equal to the increment of ABC. And if any other line than DE represent the fluxion of AB, as DE is to this line, so is the parallelogram DBE to the parallelogram con- tained by BC and this line ; therefore that parallelogram is the fluxion of ABC (46). Scholium, Those who prefer the geometrical mode of representation, may deduce from this proposition a demon- stration of the theorem for determining the fluxion of the product of two quantities (48) ; for every rectangle may be diagonally divided into two such figures as are here consi- dered, and the sum of their fluxions, according to this pro- position, will be the same with the fluxion of the rectangle" determined by that theorem. 191. Definition. A flexible line being supposed to be applied to any curve, and to be gradually unbent, the curve described by its extremity is called the involute of the first curve, and that curve the evolute of the se- cond. 192. Definition. The radius of cur- vature of the involute is that portion of the flexible line which is unbent, when any part of it is described. 193. 1 heorem. The radius of curvature always touches the evolute, and is perpendi- cular to the involute. If the radius of curvature did not touch the evolute, it would make an angle with it, and would therefore not be unbent ; and if the evolute were a polygon composed of right lines, each part of the involute would be a portion of a circle, and its tangent therefore perpendicular to the ra- dius : but the number of sides is of no consequence, and if it became infinite, the curvature would be continued, and the curve would still at each point be perpendicular to the radius of curvature. 194. Theorem. The chord cut off" in the ordinate by the circle of curvature, is directly as the square of the fluxion of the curve, and inversely as the second fluxion of the ordi- nate, that is, as the fluxion of its fluxion. The constant fluxion of the absciss being equal to AB, the fluxion of the or- dinate at A , is BC, at D, DE, consequent- ly its increment is CD-I-BE, or CD+AF, twice the sagitta of the arc AD : and the chord is equal to the square of AC divided by CD, and it is therefore always in the direct ratio of the square of the fluxion of the curve, and the inverse ratio of the second fluxion of the ordinate. 195. Theorem. When the curve ap- proaches infinitely near to the absciss, the cur- OF THE PROPERTIES OF CUUVES. 23 vature is simply as the second fluxion of tlie ordinate. For the fluxion of the curve becomes equal to that of the absciss, and the perpendicular chord to the diameter. 196. Definition. If the sum of two right lines drawn from each point of a curve to two given points, is constant, the curve is an ellipsis, and the two points are its foci. 197. Definition. The right line pass- ing through the foci, and terminated by the curve, is the greater axis, and the line bisect- ing it at right angles, the lesser axis. 198. Theorem. A right lino passing through any point of an ellipsis, and making equal angles with the right lines drawn to the foci, is a tangent to the ellipsis. 1''===^ — — — '' Let AB make equal angles with BC and BD, then it will touch the ellipsis in B. Let E be any other point in AB. Produce DB, take BF=;BC,and join CF, then AB bisects the angle CBF, and CAB is a right angle. Join EC, ED, EF, GD, then EC=EF, and EC+ ED=EF+ED, and is greater than DF (79), or BC+BD, or GC+GD, therefore E is not in the ellipsis, and AB touches it. 199. Theorem. The right lines drawn from any point of the ellipsis to the foci, are to each other as the square of half the lesser axis to the square of the perpendicular from either focus, on the tangent at that point. Let A and B be the foci, C the point of contact, and AD the perpendicular to the tangent CD, draw BE and BF parallel to AD and CD, produce AD each way, and let it meet BF and BC in F and G. Then sincez.ACD=BCE =DCG, CG=AC;andBG=:AC+BC. And BFq^TBGq — FGqZ:BAq_FAq (lis), therefore BGq — BAq=:FGq — FAq; but (FG+FA).(FG-FA)=FGq-rAq; and FG4.FA=aFD=2BE, and FG-FA=AG=:2AD; also BG=2BH, and BA=2BI, whence BGq— BAq=:4HIq, therefore BE.AD=HIq, and BE=:— 3, but BE : BC : : AD : AC, and BE^AD.l'^^lUS, or ^=1^ AC AD' AC ADq 200. Theorem. The chord of the circle of equal curvature with an ellipsis at any point, passing through the focus, is equal to twice the harmonic mean of the distances of the foci from the given point, or to the pro- duct of the distances divided by one fourth of the greater axis. Let AB be an eva- nescent arc of the el- lipsis coinciding with the tangent, then the radius of curvature bi- secting always the an- gle CAD or CBD, the point E where the radii AEand BE meet will ul- timately be the centre of the circle Of equal curvature. Let BF, BG, be parallel to AC, AD, then BH, bisecting FBG, will be parallel to AE: but EBH=CBF+FBH— CBEr: CBF-(-^FBG— iCBD = CBF — iCBF -f-iDBG= | (CBF-)- DBG)=:L(ACB-f-ADB). Now in the triangles ABC, ABD, as AC is to the sine of ABC, so is AB to the sine of ACB, and as AD is to the sine of ABD, so is AB to the sine of BDA - but the sines of ABC and ABD are ultimately equal ; con- sequently ACB and ADB are inversely as AC and AD, or as their reciprocals, and EBH or AEB, which is the half sum of ACB and ADB, is as the mean of those reciprocals : let BI be the reciprocal of that mean, or the harmonic mean of AC and AD, then the angle AIBziAEB ; for the evanescent angles ACB, AIB, or their sines, are recipro- cally as AC, AI, beini; opposite to the same angle BAE and having AB opposite to them ; for the same reason taking BK=2BI,AKB is half of AEB; consequently K is in" the circle of curvature, and BK is its chord. 201. Theorem. The square of the per- pendicular falling on the tangent of an ellipsis from its focus, is to the square of the distance of the point of contact from the focus, as a third proportional to the axes is to the focal chord of curvature. Q* OF THE PROPERTIES OF CURVES. gAE.EF CH It has been shown thatABq:CDq-:AE: EF (199), therefore III ABq : AEq : : CDq : AE.EF;butthe chord of curvature EG is , and AE.EF=iEG.CH, therefore ABq : AEq : : CDq : 1 EG.CH : : 2^ : EG. - Scholium. It may easily be demonstrated that a per- pendicular to the normal of the curve, or to the line perpen- dicular to its tangent, passing through the point where it meets the axis, bisects the focal chord of curvature, and that a perpendicular falling from the same point on the chord, cuts off a constant portion from it, equal to_the third proportional to the semiaxes. 202. Theorem. The square of any or- dinate of an ellipsis parallel to the lesser axis, is to die rectangle contained by the segments of the greater axis, as the square of the lesser axis to the square of the greater. On the centre A de- scribe the circle BODE passing through the jtHj focus B ; then EF : BF: : OF: DF ()38). CallHT,a,HB,i.,AB,T, GH,«, then EFr=2a, BF=2J', CF=2BH — 2BG=2GH= 21, DFz;EF— ED=2a— 2x, and 2a : 2i : : 2z : 2a— 2i', a:l::z: a—x, a : a+l : : z : z + a—x : : a+z : 2tt— x +i+x (32) ; also a : a— I : : z : z—{a—x) ■■ : a—z : la _x— (fc-fit), and by multiplying the terras, aa : aa— lb : : (a+»).(a-») : (2a— x)*— (i+^^jS or Hlq.HKq : : IG. GL •. AFq— GFq, or AGq. 203. Theorem. The area of an elhpsis is to that of its circumscribing circle, as the lesser axis to the greater. For since the square of the ordinate is to the rectangle contained by the segments of the axis, or to the square of the correspondingordinateof the circle (13"), as the square of the lesser axis to that of the greater, the ordinate itself is to that of the circle in the constant ratio of the lesser axis to the greater. For if four quantities are proportional, their squares are proportional, and the reverse. But the fluxions of the areas are equal to the rectangles contained by these ordinates and the same fluxion of the absciss (190), they are therefore in the constant ratio of the ordi- nates, and the correspondfng areas are also in the same ratio (47).~ 204. Definition. If the square of the absciss is equal to the rectangle contained by the ordinate and a given quantity, the curve is a parabola, and the given quantity its parameter. Scholium. Thus ABq=:P.BC. If the axes of an ellipsis are supposed infinite it be- comes a parabola, for A JB B B , if a becomes infinite, xx vanishes in smce •—'iz — — comparison of flo", and , , — r~v', and — is the pa- ^ a' ax a a rameter of the parabola ; and the distance from the focus is in a constant ratio to the square of the perpendicular falling on the tangent. 205. Definition. When the ordinate is as any other power of the absciss than the second, the curve is still a parabola of a dif- ferent order. Thus when the ordinate is as the third power of the ab- sciss the curve is a cubic parabola. 206. Theorem. If any figure be sup- posed to roll on another, and any point in its plane to describe a curve, that curve will always be jjerpendicular to the right line joining the describing point and the point of contact. Suppose the figures rectilinear polygons ; then the point of contact will always be the centre of motion, and the figure described will consist of portions of circles meeting each other in finite angles, so that each portion will be always perpendicular to the radius, though no two radii meet in the point of contact. And if the number of sides be increased without limit, the polygons will approach in- finitely near to curves, and each portion of the curve de- scribed will still be perpendicular to the line passing through the point of contact. 207. Definition. A circle being sup- posed to roll on a straight line, the curve described by a point in the circumference is called a cycloid. 208. Theorem. The evolute of a cycloid OF THE PROPERTIES OF CURVES. 25 is an eqiial cycloid, and the length of its arc is double that of the portion of the tangent cut off by the vertical tangent. Let two equal cir- cles AB, BC, rolling on the parallel bases DA and EB, at the distance of a diame- ter of the circles, de- scribe with the points F and G the equal cy- cloids EF and EG. Draw the diameter FH ; then H will be the point that coincided with D, and HA=DA=EB= arc BG, and the remainders AF and GC^re equal, therefore ./.ABF:^CBG (133), and FBG is a right line («a). But FG is perpendi- cular to AF (134), therefore it touches EF (206), and it is always perpendicular to EG (2oa) ; therefore EG will coin- cide with the involute of EF, for they set out together from E, and are always perpendicular to the same line FG (193), which they could not be if they ever separated. Conse- •quently the curve EF is always equal to FG (192), or 2FB, twice the portion of the tangent cut off by EB. 209. Theorem. The fluxion of the cy- cloidal arc is to that of the basis, as tlie evolved radius to the dianieler of the g«ne- rating circle. p For the increment GI=sBK, and BK : BL : : BG : BC, and 2BK. : BL : : FG : BC, which is therefore the ratio of the flux- ions. ScHOiiuM. If the fluxion of the base be constant, that of the curve will v^ry as the distance of the describing point from the point of contact. 210. Definition. If the absciss be «qual to the arc of a given circle, and the perpendicular ordinate to the corresponding sine, the curve will be a figure of sines. 211. Definition. If a second figure of sines be added, by taking ordinates equal to the cosines, the pair may be called conju- gate figures of sines. 212. Theorem. The radius of curvature of the figure of sines at the vertex is equal to the ordinate. VOL. 11. < For the fluxion of the base becoming ultimately equal to that of the absciss in the corresponding circle, while the ordinates are also equal, the curve ultimately coincides with a portion of that circle. 213. Theorem. The area of each half of the figure of sines is equal to the square of the vertical ordinate. For the fluxion of the absciss being constant, tliat of the sine .varies as the cosine (142), there- fore the fluxion of the ordinate of the figure of sines may always be represented by the corresponding ordinate of the conjugate figure. Let AB, CD, be the con- jugate figures, then EF will represent the fluxion of EG, and, since the arcand sine are ultimately equal, the fluxion of EG at C will be equal to that of the absciss, therefore BC will always represent the constant fluxion of the abscisi. But the fluxion of the area AEF, is the rectangle under the fluxion of the absciss AE and the ordinate EF ; that is, the rectangle under BC and the fluxion of EG, and the fluent BC.(AD— EG) is therefore equal to the area, which at C becomes BCq. 214. Definition. Each ordinate of the figure of sines being diminished in a given ratio, the curve becomes the harmonic curve. Scholium. The ordinates being diminished in a con- stant proportion, their increments and fluxions are dimi- nished in the same proportion, the fluxion of the base re- maining constam. 215. Theorem. The radius of curvature at the vertex of the harmonic curve is to that of the figure of sines, on the same base, as the greatest ordinate of the figure of sines to tliat of the harmonic curve. For taking any equal evanescent portions of the vertical tangents the radii will be inversely as the sagittae, which are similar portions of the corresponding ordinates, and ate •therefore to each other in the ratio of those ordinates. 216. Theorem. The figure, of which the ordinates are the sums of the correspond- ing ordinates of any two harmonic curves, oa equal bases, but crossing the absciss at dilfer- ent points, is also a harmonic curve. The absciss of the one curve being x, that of the other will be a-\-x, and the ordinates will be 2i.(sin. x) and c. (sin . 26 OF THE PROPEBTIES OF CURVES. a+x); now sin. o+J;— (cos. Jt).(sin. a) + (cos. o,).(sln. ar) and the joint ordinate will be (i+c.(cos. o)).(sin. x) +c. (sin. a). (cos. x) ; if therefore d be the angle of which the .(sin. a) tangent is ; ■ its sine and cosine will be in the ratio i+c.(cos.n) of c.(sin.o.) to i+c(cos. a), and (cos. (i).(sin. x) + (sin. d). (cos. x), will be to the ordinate in the constant ratio of sin. d to c.(sin. a) ; but (cos. d).(sin. x) + (sin. d).(cos. x) is the sine of rf+x ; consequently the newly formed figure is a harmonic curve. The same maybe shown ^ geometrically, by placing two circles, having their diameters equal to the greatest ordinates of the separate curves, so as to in- tersect each other in an angle equal to twice the angular distance of the origin of the curves : then a right line revolving round their intersec- tion with an equable velocity will have segments cut off by each circle equal to the corresponding ordinate, and the sum or difference of the segments will be the joint ordinate: and if a circle be described through the point of intersec- tion, touching the common chord of the two circles, and having its radius equal to the distance of their centres, this circle will always cut off in the revolving line a portion equal to the ordinate. For if AB be made parallel to CD, and EB toFG,^ABEziCGF=CHK : but EIB is a right angle, as well as HCF, and EI : IB : -. FC : CH : : AE : CH, since AF is equal to twice the distance of the centres, which bisect AH and FH, and therefore to CE, and FC=AE, or EI : AE : : ir : CH ; but EI : AE : : ID : AC, therefore IB : CH : : ID : AC, and the triangles ACH, DIB, are similar, and ii.DBI— CHA=:DKA,and AD is a parallelogram, con- sequently KDzr ABmCG. If the circle CG be supposed to revolve round C, the in- tersection H will always show the angular distance of the point in which the curve crosses the axis ; and the distance of the centres will be equal to the greatest ordinate. If therefore the circles are equal, the greatest ordinate wUlalso vary as the chord of an arc increasing equably, or as the ordinatt of the harmonic curve. MATHEMATICAL ELEMENTS OF NATURAL PHILOSOPHY. PART IL MECHANICS. OF THE MOTIONS OF SOLID BODIES. SECTION I. OF MOTION. 217. Axiom. Like causes produce like effects, or, in similar circumstances, similar consequences ensue. 218. Definition. Motion Is the change of rectilinear distance between two points. 319. Definition. A space or surface, of which all the points remain spontaneously at equal distances from each other, is said to be quiescent, or at rest within itself. Scholium, The term " spontaneously" is introduced, in order to exclude from the definition of a quiescent space any surface, of which the points are only retained at rest by means of a centripetal force, while they revolve round a common centre; for with respect to such a revolving space or surface, the motions of any body will deviate from the laws which govern them in other cases. 220. Definition. When a point is in motion with respect to a quiescent space, the right line joining any two of its proxi- mate places is called its direction ; such a point is often simply denominated a moving point. 221. Theorem. A moving point never quits the line of its direction without a new disturbing cause. A right line being the same with respect tO all sides, no reason can be imagined why the point should incline to one side more than another. Let AB be the direction of -A. the motion of A in the plane ABC, ahd let CB and DB be equal, and perpendicular to AB, then the triangles ABC and ABD are equal (8C), and A is similarly related to C and D. Then if A depart from AB, and be found in any point out of it, as E, ED will be greater than EC (l03), and A will be no longer similarly related to C and D, contrarily to the general law of induc- tion (217). 222. Definition. The times in which a point, moving without disturbance, de- scribes equal parts of the line of its direction, are called equal times. 223. Theorem. The equality of time* being estimated by any one motion, all other points, moving without disturbance, will de- scribe equal portions of their lines of direc- tions in equal times. S8 OF ACCELERATING FORCES. ACE -RDV G Let A and B be " ' ' ' — ■— ' • . moving in the same line, and while A describes AC, let B describe BD; then while A describes CE=:AC, B will describe DI'"^ BD. For suppose AC=2BD, and let AG=2AB, then AB and BG have been equally decrca<;ed in one instance, and tlic relations remaining the same, they will still be equally decreased (217) ; for the relative motion of A and B is ax (a±:x)' . ^ . M'i rd'r tit) W and smce vvzzfi, vzz i;, — ; — -, and — = •' XX («±.ry 2 X ccP /2M' , 9rd'\ , ., /2f\ . — — -,wt;=::+:( K — — ) ; and if c=:o, v—^/ — )<«• a±x \ x a±.xl \^ I Scholium. In the case of a body projected from the moon towards the earth, dr:20,900,ooo feet, arieod, b'zz 32.2 feet, the velocity produced in i" at the earth's surface; _ 1 . . ■. , • 2ig czz—b, nearly; then taking xzz — a, at the moon s sur- face, and — a, at the point where the force becomes neu- 94 tral,we have ( — X220 and { — I ) a V219 70/ a ^84 roo/ X94, of which the I difference is , or .09646M, a and its square root about 8070 feet. Hence, if the velocity of a projectile from the moon exceed 8070 feet, it may pass the neutral point, and descend to the earth ; where its velo- city will become more than 36000 feet in a second. SECTION III. OF CENTRAL FORCES. 238. Definition. An accelerating force tending to a point out of the line of direction of a moving body, deflects it from that line, and is then usually called a central force. 239. Theorem. The force, by which a body is deflected into any curve, is directly as the square of the velocity, and inversely as that chord of the circle of equal curvature, which is in the direction of tl>e force; and the velocity in the curve is equal to that which would be generated by the same force, during the description of one fourth of the chord by its uniform action. For the force is as the space described by its action, beginning from a state of rest, or as the evanescent sagitta through which the body is drawn from the tangent of the _curve in a given instant of time : but the portion AB of the tangent described in a given instant is as the velocity, and BC=: —=, or ultimately ABq CD , which is as the square of the velocity directly, and inversely as the chord of the circle of curvature of the arc AC. Now the velocity generated during the description of BC is expressed by twice BC, since the force maybe considered for an instant as constant : consequently it is to the orbital velocity as twice BC to AB, or as twice AB to ED, or as AB to half CD ; and if the time of the action of the force were continued during the time that half CD would be described with the orbital velocity, it would generate a velocity equal to that velocity ; but in this time one fourth of CD only would be described by its action. 240. Theorem. When a body describes a circle by means of a force directed to its centre, its velocity is every where equal to that which it would acquire in falling by the same uniform force through half tlie radius; and the force is as the square of the velocity directly, and as the radius inversely. For in this case the chord, passing through the centre, becomes a diameter. 241. Theorem. In equal circles the forces are as the squares of the times inversely. For the velocities are inversely as the times, and the de- flective chords are equal. 242. Theorem. If the times are equal, the velocities are as the radii, and the forces are also as the radii, and, in general, ihe forces are as the distances directly, and the squares of the times inversely ; and the squares of the times are directly as the dis- stances, and inversely as the forces. For the velocities are as the distances directly, and as the times inversely ; and the squares of the velocities are as the squares of the distances directly, and as the squares of the times inversely ; consequently the forces are as the radii di- rectly, andthesquarcs of the times inversely; and the squares of the times are as the radii directly, and as the forces in- versely. 243. Theorem. If the forces are in- versely as the squares of the distances, the squares of the times are as the cubes of the disl^ances. OF CENTRAL FORCES. 31 For the squares of the tiines are as the distances directly, and as the forces inversely (24a) ; that is, in this case, as the distances and as the squares of the distances, or as the cubes of the distances. 244. Theorem. The right line joining a revolving body and its centre of attraction, always describes equal areas in equal times, and the velocity of the body is inversely as the perpendicular drawn from the centre to the tangent. Let AB be a tangent to any curve in which a body is retained by an attractive force directed to C, and let AB repre- sent its velocity at A, or the space which would be described in an instant of time without disturbance, and AD the action of C in the same time ; then completing the parallelogram, AE will be the joint result (226) ; again, take EF=AE, and EF will now represent its spontaneous motion in another equal instant of time, and by the action of C it will again describe the diagonal of a parallelogram EG ; but the triangles ABC, AEC ; AEG, ECF ; EOF, EGG, being between the same parallels, are equal (117); and if they be infinitely diminished, and the action of C become continual, they will be the evanescent increments of the area described by the revolving radius, while the body moves in the curvilinear orbit ; and the whole areas described in equal times will therefore be equal. And since the constant area ABC^ AB.iCH (117, 114), AB=2ABC.— , therefore AB, re- presenting the velocity, is always inversely as CH, or 1 u 245. Theorem. Two bodies being at- tracted towards a given centre, with equal forces, at equal distances, if their velocities be once equal at equal distances, they will remain always equal at equal distances, what- ever be their directions. Let one of the bodies descend in the right line AB, towards C, and let the other describe the curve AD, and let the velocities at B and D be equal ; let DE in the tan- gent of AD be the space which would be described in an evanescent portion of time by the ve- locity at D, FG the arc of a circle on the centre C, and GE its tangent; and while BF would be described by the velocity at B, let FH be added to it by the attractive force ; draw the arc HI and its tangent IK, and EL HDC, and KL perpendicular to DK, then DG : DE : : GI : EK : : EK : EL, by si- milar triangles ; therefore, GI is to EL in the duplicate ratio of DG to DE, or as the square of DG to the square of DE (124) : therefore EL will be the space described by the attractive force, while DB would be described by the velocity at D ; for the force may be considered as uniform during the description of the evanescent increments ; and the spaces described by means of such a force are as the squares of the times : hence the joint result will be DL, which is ultimately equal to DK, and the whole velocity will be increased in the ratio of DK to DE, or DI to DG, or BH to BF ; consequently, since H, I, and K, are ultimately equidistant from C, the velocities in AB and AD, being always equally increased at equal distances, will therefore always remain equal at equal distances. 246. Theorem. If a body revolves in an elliptic orbit, by a force directed to one of the foci, the force is inversely as the square of the distance. The force is directly as the square of the velocity, and inversely as the deflective chord ; but the velocity is in- versely as the perpendicular falling on the tangent ; there- fore the force is inversely in the joint ratio of the square of the perpendicular and of the deflective chord ; now in the ellipsis, the focal chord varies directly as the square of the distance, and inversely as the square rrf the perpcndiculai {201), consequently this joint ratio is that of the square of' the distance, and the force is always inversely as the square of the distance. 247. Theorem. Tlie velocity of a body revolving in an ellipsis is equal, at its uaean distance, to the velocity of a body revolving at the same distance in a circle; and the whole times of revolution are equal. For the focal chord of curvature at the meaa distance 32 OF PROJECTIL'ES. becomes equal to twice that distance, or to the diameter of thccircle(200); therefore thevelodties-sreequal (239). But since the perpendicular height of the triangular element of the area, of which tlie base is the element of the orbit at the mean distance, is equal to the lesser axis, this element is to the contemporaneous element in the circle as the lesser to the greater axis, or as the whole ellipsis to the whole circle (203), consequently both areas being uni- formly described, the times of revolution are equal. 248. Theorbm. If a body describes an equiangular spirdl round a given point, the force must be inversely as tlie cube of the distance, and the velocity equal to that with which a circle might be described at the same distance. For the orbit of a body projected in any direction with a velocity equal to that with which a circle may be described at the same distance, will initially coincide with an elliptic orbit as its mean distance ; and the inclination of the orbit to the revolving radius is constant at the mean distance ; for if it were eitherincreasing or diminishing, the two halves of the ellipsis co\M not be equal and similar, since the angles contained between the tangent and the lines drawn to the foci (igs) would be different at equal distances on each side of the lesser axis. It foUows therefore that the velocity must always be equal to the velocity in a circle, in order that the equiangular spiral may be described ; but in this curve, the perpendicular on the tangent is by its fundamental property always proportional to the radius : the velocity must therefore be always inversely as the radius; and the velocities of bodies revolving in circles must be inversely as the radii, and the forces inversely as the squares of the radii and the radii conjointly (24o), or in- versely as the cubes of the radii. 249. Theorem. When a body revolves round a centre by means of a force varying more or less rapidl}' than in the inverse ratio of the squares of the distances, the apsides of the orbit, or the points of greatest and least elongation, will advance or recede respec- tively. In an elliptic orbit, when the body descends from the mean distance, the velocity continually prevails over the central force, so as to deflect the orbit more and more .from the revolving radius, until, at a certain point, it be- comes perpendicularto it : but, if the central force increase in agreater proportion than in the ellipsis, the point where the velocity prevails over it will be more remote than in the ellipsis, and the apsis will move forwards. This be- comes more evident by considering the extreme cases : supposing the central force to vanish, the lower apsis would recede to the point where a perpendicular falls from the centre on the tangent ; but, supposing the force to increase as the cube of the distance decreases, the curve would be an equiangular spiral, and the lower apsis would be infi- nitely distant. Scholium. The action of a second force, varying in the inverse ratio oT the squares of the distances, and directed to a second centre, tends in some parts of the orbit to de- duct a portion of the first force which increases with the distance of the body, and in other parts to increase the first force in a similar manner: but the former effect is consi- derably greater than the latter, so that on the whole, the joint force decreases more rapidly than the square of Ihe distance increases, and the apsides advance. Thus the apsides of the planetary orbits have direct motions, in coa- seguence of their mutual perturbations. SECTION IV. OF PROJECTIIES. 250. Definition. The force of gravi- tation, as far as it concerns the motions of projectiles, is considered as a uniformly acce- lerating force, acting in parallel lines, per- pendicular to the horizon. 251. Theorem. The velocity of a pro« jectile may be resolved into two parts, its horizontal and vertical velocity: the hori- zontal motion will not be affected by the action of gravitation perpendicular to it, and will therefore continue uniform ; and the ver- tical motion will be the same as if it had no horizontal motion. For a uniformly accelerating force is supposed to act equally on a body in motion and at rest, so that the vertical motion will not be affected by the horizontal motion ; and the diagonal motion resulting from the combination will OF MOTIOV CONFINKD TO GIVEN SURFACES. terminate in the same vertical line as the simple horizontal motion; therefore the horizontal motion will remain un- altered. 252. Theorem. The greatest height to which a projectile will rise may be deter- mined by finding the height from which a body must fall in order to gain a velocity equal to its vertical velocity ; and the hori- zontal range may be found by calculating the distance described by its horizontal velo- city in twice the time of rising to its greatest height. This is evident from the equality of the velocity of ascending and descending bodies at equal heights, and from the independence of the vertical and horizontal motions of the projectile. 253- Theorem. With a given velocity, the horizontal range is proportional to the sine of twice the angle of elevation. The time of ascent being as the vertical velocity, or the sine of the angle of elevation, the range is as the product of the vertical and horizontal velocities, or as the product of the sine and cosine ; that is, as the sine of twice the angle (140). 254. Theorem. The path of a projectile moving without resistance, is a parabola. Since the horizontal velocity is uniform, the times of describing AB, AC, or X, are as their lengths, and the spaces BD, CE;, describ- ed by the accelerating force of gravitation, as the squares of these times, or as x-, whence ^"^ay, and ADE is a parabo- la, of which a is the parameter (204). Scholium. In practical cases the resistance of the atmosphere renders this theory of little use, except when the velocity is very small. SECT. V. OF MOTION CONFINED TO GIVEN SURFACES. "255. Theorem. When a body descends along an inclined plane, without friction, the VOL. II. B D force in the direction of the plane is to the whole force of gravity as the height of the plane is to its length. For if AB represent the motion which a would be produced by gravity in a given time, this may be resolved into AC and CB (226) ; by means of AC the body ar- rives at the line CB in the same time as if it were at liberty ; but the motion CB is destroyed by the resistance of the plane ; and as AB to AC so is AD to AB (l2l). But forces are measured by the spaces described in the same time (23o). 256. Theorem. When bodies descend on any inclined planes of equal height, their times of descent are as the lengths of the planes, and the final velocities are equal. (2Jr\ 1 — I (233), and here azz—, «=^/(2Ix)=: a / X v'2.r; and the times vary as the spaces, but the times being greater in the same proportions as the forces are less, the velocities acquired are equal (23o). 257. Theorem. The times of falling through all chords dr.awn to the lowest point of a circle are equal. The accelerating force in any chord AB is to that of gravity as AC to AB, or ]> as AB to AD (l2l), therefore the fortes being as the distances, the times are equal ; for their squares are as the spaces directly and the forces inversely (233). 258. Theorem. When abody is retain- ed in any curve by its attachment to a thread, or descends along any perfectly smooth sur- face of continued curvature, its velocity is the same, at the same height, as if it fell freely. Since the velocity is the same at A, f. whether the body has descended an equal vertical distance from B or C, it will proceed in AD with the same velo- ^ city in both cases, provided that no motion be lost in the change of its direction, and therefore its velocity will be the same after passing any number of surfaces as if it had fallen perpendicularly from the same height. But where F 34 OF MOTION CONFINED TO GIVEN SURFACES. the curvature is continued, no velocity is lost in the change of direction ; for let AB be the thread or its evolved portion, the body B, if no longer actuated by gravity, C would proceed in the circular arc with uni- form motion (240), consequently no velocity is destroyed by the resistance of the thread, nor by that of the surface BC, which can only act in the same direction, perpendicular to the direction of the moving body. 259. Theorem. If a body be suspended by a thread between two cycloidal cheeks, it will describe an equal cycloid by the evolu- tion of the thread (208) ; and the time of descent will be equal, in whatever part of the curve the motion may begin, and will be to the time of falUng through one half of the length of the thread, as half the circum- ference of a circle is to its diameter. And the space described in the cycloid will be al- ways equal to the versed sine of an arc which increases uniformly. For since the accelerating force, in [he direction of the curve, is always (O the force of gravity as AB to BC, -5- or as BC to the constant quantity BD, it varies as BC, or as its double, CE, *hc arc to be described (208). If therefore any two arcs be supposed to be equally divided into an equal num- ber of evanescent spaces, the force will be every where as the space to be described ; and it may be considered for each space, as equable, and the increments of the times, and consequently the whole times, will be equal. Suppo- sing the generating circle to move uniformly, the velocity of the describing point C will always be as CD (209), or, since AD : CD : : CD : BD, and CD=v' (AD.BD), as ^AD ; but the velocity of a body falling in DA, or de- scending in FC, varies in the same ratio (232, 230, 258) ; therefore if the velocity at E be equal to that which a body acquires by falling through GE, the describing point C will always coincide with the place of a heavy body descending in FCE ; and the velocity of the point of contact D is half that of Cat E (209), it would therefore describe a space equal to GE in the time of the fall through GE (232), and ■will describe FG in a time which is to that time as FG to GE, or as half the circumference of a circle to its diameter. and this will be the time of descent in the cyclwdal arc. And since FCziaDB — 2BC, FC is equal to the versed sine of the angle CBD, to the radius 2DB ; but /.CAD increas- ing uniformly, its half, CBD, increases uniformly. And if the motion begin at any other point, the velocity will be in a constant ratio to the velocity in similar points of the whole cycloid. It is also obvious that the arc of ascent will be equal to the arc of descent, and described in an equal time, supposing the motion without friction. 260. Theorem. The times of vibration of different c^'cloidal pendulums are as the square roots of their lengths. For the times of falling through half their lengths are in the ratio of the square roots of these halves, or of the wholes. 261. Theorem. The cycloid is the curve of swiftest descent between any two points not in the same vertical line. GAE r VD Let AB and CD be two parallel ver- tical ordinates at a constant eva- nescent distance, in any part of the curve of swiftest descent, and let a third, EF, be interposed, which is always in length an arithmetical mean between them, and which, as it approaches more or less to AB, will vary the curvature of the element BFD. Call AB, a ; EF, b ; b — a, c; AE, u; and EC,«; then BFrZv' ("«+«), and since CD— EF=EF-AB, FD=v^(dii+cc). But the velocities at B and F are as i/a and i/b, and the elements BF, FD, being supposed to be described with these velocities, the / Mu+cc \ /iT-J-rcA time of describing BD is v' 1 / "*" ^ ( — 7, — J ' which must be a minimum ; therefore its fluxion vanishes, 2i(u . aKi , . . • or ; : — -A rr, : — TT— " i °"t ^mce AC 2v'(a(i'«+"j) 2^/(0 (««+«)) or u+v is constant, M-f-i~o, or «:^ — b ; therefore, -— :z — rr. Let the variable abscis* ^{a{tm+cc)) ^{b{vv+cc)) GA be now called x ; the ordinate AB, y ; and the arc GB z ; then u and v are increments of x, and BF and FD of z, when V becomes zza and b respectively ; and -.is the same in both cases, and is^ therefore constant, or = — , and .-^y Now in the cycloid v'^ 's always xixn OP THE CENTRE OF IKF.aTIA, AND OF MOMENTUM. 35 chord of the generating circle, the di- ameter being I ; and the arc being perpendicular to that chord, its flux- ion, by similar triangles, is to that of the absciss as the diameter to •/}/ : therefore the cycloid answers the con- ditions in every part, and consequently in the whole curve. Scholium. The demonstration implies that the origin ■of the curve must coincide with the uppermost given point : row only one cycloid can fulfil this condition and pass through the other point, and it will often happen that the curve must descend below the second point and rise again. 26'2. Theorem. The time of vibration of a simple circular pendulum in a small arc is ultimately the same as that of a cycloi- dal pendulum of the same length ; but in larger arcs the times are greater. For in small cycloidal arcs the radius of curvature is nearly constant, but, at greater distances from the lowest point, the circular arc falls without the cycloidal, and is less inclined to the horizon. 263. Theorem. If a body suspended by a thread revolve freely round the vertical line, the times of revolution will be the same when the height of the point of suspension above the plane of revolution is the same, whatever be the length of the thread. For by the resolution offerees, the force urging the body towards the vertical line is to that- of gravity as the distance from that line to the vertical height ; the other part of the force being counteracted by the effect of the thread ; and when the forces are as the distances, the times are equal (242). 264. Theorem. The time of a revolu- tion of a body suspended by a thread is equal to the time occupied by a cycloidal pendulum of which the length is equal to the height of the point of suspension above the plane of re- sent the action of the thread, and AC the pressure exerted by A on any obstacle at C (284) ; arid in the same manner BC will represent the pressure of B in the direction BC, supposing the weights A and B equal ; but since they are unequal, the ratio of their masses must be compounded with that of the forces, and A.AC will repre- sent the actual force of A, and B.BC that of B ; but " A : B=:BC : AC, and A.AC=B.BC; ; therefore the pres- sures are equal, and the bodies will remain in equilibrium. But if the centre of inertia ascended towards either weight, as A, the segment AC, which determines the action of A, would be increased, and BC lessened; therefore the weight of A would prevail, and the centre would return to the vertical line. But supposing C above D, the rod and threads must change places, and the same demonstration will hold good; and since in this case the weights pull against each other, the prevalence of A when the centre of inertia descends towards its place will draw it still further from the vertical line, and the equilibrium will be lost. Now the distance of C J) ^ above or below D is ot " q no consequence to the A 2 - equilibrium ; therefore ^ when that distance vanishes, and the thread and rod are united into one inflexible right line or lever, those points will coincide, and there will still be an equilibrium ; which may properly be termed neutral, since no change of the position of the bodies will create a tendency either to return to their places, or to proceed further from them. But the case of an inflexible right line is pe.fectly out of the reach of expe- riment, since the strength necessary for the inflexibility of a mathematical line becomes infinite, and that in an infi- nitely small quantity of matter. If any other mode of con- nexion by inextensibleand incompressible lines be imagin- ed, there will still be an equilibrium ; for instance, if AC, BC, DC, be rods ; and AD,DB, threads; and C the centre of suspension ; or if AE, BE, DE, be rods; and AD, BD, threads. OF PRESSURE AVD EQUIMBRIUM. 39 This case is somewhat intricate, and may be thus demon- strated. Draw BF parallel to CD, and GHI to AE produ- ced to F, thenHE:KE::BE:FE (121), andDE:DL:: KE : HL :: FE : IL, therefore HE : HL :: BE : IL (l?), and BI is parallel to ED. Now A : B .: BC : AC r: FK : AK : : IH : GH, and A.GH=B.HI. But by what has been already demonstrated, the pressure of A and B in the directions AE, BE, are A.GH and B.HB, DH representing the force of gravity, since the lines are parallel to the forces exerted ; and A.GHi^B.HI : therefore the forces of A and B at E being B.HI and B.BH, their result will be parallel to BI, or in the direction ED, and will therefore be wholly counteracted by the rod DE, without any tendency to turn it round D. There is another simple and elegant mode of demon- strating the property of the lever, which deserves to be no- ticed. Supposing the arms to be a little bent, and the forces to act perpendicularly to them, so that their directions may meet in a distant point ; then if their actions be imagined to be concentrated in that point, it will be easy to show that in order that the resulting force may pass through the point of suspension, and that an equilibrium may be thus produced, the forces must be inversely as the perpendicu- lars falling from that point on their directions ; that is, as the arms of the lever inversely; and this will be true whe- ther the lever be more or less bent, and consequently even if it be not bent at all. It is not however strictly shown in this demonstration, that the effect of the forces must be the same as if (hey were applied in the point where their directions meet, and a link appears to be still wanting in the chain. 286. Theorem. A system of any num- ber of gravitating bodies, or a mass composed of such bodies, will remain in equilibrium when its centre of inertia is in tiie vertical line, passing through the point of suspension. Let us first suppose the number of bodies to be three ; let A and ■g ^ ^^ 5° connected as to remain in equilibrium on their centre of ^ inertia C ; and let this centre and the third body E be in any way connected with the point of suspension D : then since C supports the weight of A and B, it will retain E in equili- brium whenever the common centre of inertia F is in the vertical line. And the same may be demonstrated if the bodies be connected in any other manner : for instance, if alt the bodies be suspended from D, and retained in their places by the lines AB, AE, BE. Then A will counter- poise a body at E of which the weight is to its own as AG to GE (78), or HF to FE, and B a weight in the propor- A HPJ-R IF" tion of IF to FE, and both, a weight:::—^ ^ — — FE A.(CF— HC) + B.(CF-|-CI)_(A+B).CF B.CI — A.HC _ FE ~ FE + FE" ' but A : B :: CB : CA :: CI : MC, and B.C1=A.HC; there- fore the last term vanishes, and A and B support a weight at CF E equal to (A-f-B).— ,, or equal to E : and the effect is the same as if they were united in C. Therefore either of the bodies may be divided into two, and the equilibrium will remain, provided their centre of gravity be in the place of the single body : and thus the number of the bodies may be increased without limit. The proposition may also be more generally and com- pendiously demonstrated from other properties of the centre of inertia. Imagine the fulcrum itself to be suspended by a veilical thread, and let the centre of inertia of the system of bodies be so placed, as to be in the same right line with this thread; there will then be a perfect equilibrium: for the motion of each of the bodies in consequence of the action of gravitation, and of course the motion of their common centre of inertia, would, if they were wholly at liberty, be in vertical lines; and since the mutual con- nexion of the bodies suspended, causes only a reciprocat action between them, it can have no effect on the motioiv of their common centre of inertia: consequently the thread) acting in a vertical line directed to that centre, will render its descent impossible, and completely counteract the whole force of gravitation, so that no force will remain to produce any other motion. Now since the fulcrum suspended by a thread would remain at rest, it is obvious that it may be fixed in any other manner, and the equilibrium of the system will remain undisturbed, as long as the centre of inertia is in the same vertical line. Scholium. Hence the place of the centre of inertia of any body may be practically found by determining the intersection of any two positions of the vertical line. 287. Definition. Tlie centre of inertia is also called, on account of these properties, the centre of gravity. 288. Theorem. If a sphere or cylinder be placed on another, the equihbriuni will be either stable or tottering, accordingly as the height of the centre of gravity above the 40 OF PRESSURE AND EQUILIBRIUM. point of contact is less or greater than a fourth proportional to tlie sum of the radii, and the radii taken separately. Let the sphere or cylinder roll from the vertical position into a position infinitely near to it on either side: then the point A of the upper cylinder, which was origi- nally in contact with the lower, may still be considered as in the vertical line BA : and if CD be the vertical line passing through the actual point of contact, BE : AE ; : BC : AD, and if the centre of gravity be at D in the Uhc AE, the point of support being immediately under it, the equilibrium will remain : but if the centre of gravity be below D, the sphere Will return towards AB ; if above, it will retire further from it. For example, if CE be infinite, and the lower surface of the moveable body be a plane, the equilibrium will remain stable, while the height of the centre of gravity above the point of contact is less than the radius of the sphere. If the fixed body have its upper surface horizontal, the equilibrium of any body will be determined by its radius of curvature, as the equilibrium of an egg placed on one end is tottering, but stable when placed on one side. 289. Theorem. If any other equivalent forces be substituted for weights, acting at the same distance from the fulcrum, and with the same inclination to the rods or levers, the phenomena of equilibrium will be pre- cisely the same. Also if either of the forces be transferred to an equal distance on the other side of the point of suspension or ful- crum, and act there in a contrary direction, the equilibrium will still remain. For the arguments derived from the composition of pres- sures are equally applicable to all these cases. 290. Theorem. If a force be applied obliquely to a lever, its effect in turning the lever will be diminished, in the ratio of the sine of the inclination to the radius. For instance, if two levers be connected by a rope, two forces applied perpendicularly to the levers, at the ends of the rope, will be in equilibrium when the forces are as the perpendiculars let fall on the respective levers from the op- posite tads of the rope. For the action of each force in the direction of the rope, and its absolute strength, are as the sides of the triangle formed by the lines of direction, or as the length of the rope and the perpendicular falling from its end on the lever : therefore, each perpendicular representing the absolute force, the length of the rope will in both cases express the relative action. The forces are represented in the figure by arrow heads, and the fulcrums by little circles. 291. Theorem. If two threads, or per- fectly flexible and inextensible lines, be wound in contrary directions round two cy- linders, moveable on the same axis, there will be an equilibrium when the weights at- tached to them are inversely as the radii of the cylinders. For every section of the cylinder perpendicular to the axis, is a circle, and the threads being tangents to the circles, will be at thedistancesof the radii from the vertical plane ; therefore, by similar triangles, (he right line joining the weights will be divided in the ratio of the radii, and the centre of gravity will be in the vertical plane ; and the point of the axis immediately over it is a centre of sus- pension ; therefore there will be an equilibrium (285). 292. Theorem. When the direction of a thread is altered by passing over any per- fecth' smooth curve surface, it communicates the whole force acting on it. For the resistance of the curve is alvrays in a direction perpendicular to that of the thread, and therefore does not impair its action, as is obvious from the composition of forces. 293. Definition. A pulley is a cylinder moving on an axis, in order to change the direction of a thread without friction. Scholium. The comparison of a pulley to a lever is both unnecessary and imperfect. 294. Theorem. By me^ns of a single moveable pulley, each portion of the thread being vertical, a weight may be supported by two forces, each equivalent to half the weight; or by two threads, each passing over a fixed pulley, and connected with ano- OF PRES,SURK AND EQUILIBRIUM. 41 'fT ther weight equal to half die first ; or one of them connected with such a weighty and the other to a fixed point. For it is obvious that each thread supports an equal part of the weight (2 1 7, ag'l,) and the substi- tution of equivalent weights, or of a fixed point, will not impair the equilibrium. 295. Theorem. IF several moveahle pullies be connected with a weight, and pa- lailel portions of the same thread act upon tliem all, there will be an equilibrimn when the weight attached to the thread is to the ■weight attached to the pullies, as one to the number of threads at the lower block. For the force being equably communicated throughout the length of the thread, each portion will co-operate equally in sup- porting the w^eight, and will sup- port that portion of it which is to the whole as 1 to the number of threads ; consequently a weight equal to that portion will retain any part of the thread in equili- brium, and with it the whole thread, and the ■ whote weight- And if the radii of the pullies be taken in arithmetical progression, their angular velocity may be made equal, and they may be fixed to thi same axis. Cy6. Theorem. If one end of a thread, supporting a moveable pulley, be fixed, and the other attached to another moveable pul- iey, and the threads of tliis pulley be simi- larly arranged, the weigi)t will be counterpoised by a power which is found by halving it as many times tis-there are moveable pul- lies. The proposition Is ob\ious from aconsiderationofthefigure.atidthe law ofthe single moveable pull^. -VOL. II. k )k 6 * 297- Theorem. If two threads be at- tached to a weiglit and passed over fixed puUie?, there will be an equilibrium when the distance of the weiglit from the hori- zontal line is to its distance from either pul- ley, as the weight to tlve sum of the equal forces acting on the threads. By producing the oblique lines, and crossing them with a vertical one, a triangle will be formed of which the sides will represent the forces (284) ; whence the truth of the proposition will appear. And if the weights ate unequal, their ^tuation may be determitied by the same general law. In th£ same manner the force may be found, which is requisite for sustaining a weight, by in- flecting a thread -connected in any manner with it, -ftt by means of a lever or a bar. , ,i 1,. .f.j 298. Theorem. If -two threads are wound in contrary directions round a cylin- der, the first perpendicularly, the second ob- liquely, tl>ere will be an equilibrium whew the forces are as the perpendicular distance of any point of the oblique thread from the axis, to its distanqe from the i>oiul of coi)i< tact. Since AB, which is equal to the distance of C from the axis, is the portion of the force BC, which is efficient in turning the cylinder, it will be counteracted by an equal force acting on tl-.e direct thread. The force AC is lost in the direction of tlie cylinder; bur this is the force which tends to shorten a twisted rope. ' 299. Tn F.OREM. When a thread is coiled round a cylinder, the pressure on any part of the circumfcretice is to tlietension as its lenetb to the radius; when the direction of the line is oblique, the pressure on the whole circuni- ferenc« is to the tension as the-circumferenc'e to the radius ; and the tension of the oblique line is to a force straining it in the direction 6 42 OF PRESSURE AXD EQUILIBRXUHr, of the c)'linilerj as the length of a coil to the length of the axis. Let AB anil BC be tangents of the small arc AC ; then if BC, and BA re- present the force of tension, at A and C, the diagonal of the parallelogram BD will be the joint result ; but BD=2BE, and by the properties of similar triangles BE : BC : : EC : CF, BD : BC : : AC ; CF. If the position of the thread be oblique, we shall find by the composition of forces, supposing it uncoiled, and its extremities retained in a line parallel to the axis, that its tension is to a force acting in the direction of the axis, as the oblique length of any portion to its height. Now this tension produces on any small oblique portion of the cir- cumference, a pressure equal to that which would be pro- duced on the corresponding transverse portion by an equal force acting transversely ; for the versed sine of the arc is the same in both cases ; consequently the pressure on the whole circumference is equal to that which would be pro- duced by the same tension acting transversely. 300. Theorem. The perpendicular pres- sure of a weight resting on an inclined plane, and retained in its situation by u resistance in the direction of the plane, is to the weight, as the horizontal length of the plane to its oblique length, and to the resistance, as the horizontal length to the height. The truth of the proposition is evident from the propor- tioiu of the sides of the triangle conesponding to the direc- tions of the forces. Scholium. Hence the proportion of the friction to the weight may be determined by measuring the tangent of the angle at which the weight begins to slide down the plane. 301. Definition. A wedge is a solid Included by two equal triangles joined by thi'ee rectangles ; and we shall suppose the surfaces to be perfectly smooth. 302. Theorem. Three forces acting di- rectly on the sides and base of a wedge will be in equilibrium when each force ispropor- y tional to the side on which it acts ; provided l!hat they be all applied at such parts, that thek directions may meet in one point. For the triangle formed by three lines perpendicular to the sides of another triangle, is equiangular with it, and if the forces act completely on any point, it will remain in equilibrium (2S4). •• 303. Theorem. Supposing a moveable inclined plane, orarectangular wedge to slide without friction on a horizontal plane, it will remain in equilibrium with a weight acting vertically, when the horizontal force is to the weight as the height to the horizontal length. -% c The triangle ABC is similar to ADB, and to BDC; and if AD represent the weight, its perpen- dicular pressure on the plane will be AB (284), which will be held in equilibrium by a force on the base, which is to it, as BD to AB (302) ; and this force will be to the weight, as BD to AD, or as CD to BD. 304. Definition. By rolling a thin and flexible wedge round a cylinder, we form a screw. 305. Theorem. A force acting in the direction of the circumference of a screw, supposed to move freely round its axis, will counterbalance a weight pressing vertically on the screw, which is to it as the circum- ference is to the height of one spire. For when the horizontal length of the wedge becomes equal to the circumference of the circle, its height is the height of the first spire of the screw, or the distance be- tween any tvro spires or threads. Scholium. The cylinder may be either convex or con- cave, making a cylindrical or a tubular screw, together sometimes called a screw and a nut. The nut acts on th« screw as a single point would do, only dividing the pres- sure. In general the screw is applied in combination with a lever. 306. Theorem. If it be required to find. the position of four equal beams capable of supporting each other in equihbrium, two of them fixed at the extremities of the base of OP PRESSURE AND EQUILIBRIUM. ^S ft given isosceles triangle, and the other two meeting in its vertex, a circle being circum- scribed round the triangle, and perpendicu- lars erected from the quadrisections of the base, the lower t)eam on each side must be directed to the nearest intersection of the perpendiculars with the circle, and the upper one must be in a chord of equal length. C The two upper beams act against each other in a ho- rizontal direction B K C; H only, consequently the horizontal thrust of the lower beams must be equal to that of the upper beams, produced by their own weight only, while the thrust of the lower beams is derived not only from their own weight, but also from that -of the upper beams, acting at their extremities ; but the horizontal effect of the weight of the upper beam is to its weight as balf AB to BC, since the centre of gravity may be supposed to act on a lever of half the length of AB, and the hori- Eontal force on a lever of the length BC (290) ; but the ho- riiontal thrust of AD is equal to that of AC, and is to the force acting vertically at A as DE to AE ; and the force acting vertically at A is the whole weight of AC and half the weight of AD, which is three times as much as the DE weight acting vertically at C ; consequently — ; must be Aci equal to — — ; now the triangle ADE is similar to FDG, and ABC to HFG, since the angle DFH=DCH, and GFH =DFH— DFGzzDFH— (DIG-1DF)=:DCH— (BCH— ACD)=DCB4.ACD=ACB, therefore £f=^,and-^ ACj rG . 3BC _GH 3DG DG — -T7;— — -— -iz:-—^, as IS required for the equilibrium. 307. Theorem. When an arch is com- posed of blocks acting on each other without friction, the weight of the arch must increase at each step as the portion of the vertical tangent cut off by lines drawn from a given point in a direction parallel to that of the joints. The thrust in the direction AB, by which the block A is supported, must be to its weight as AB to BC, or as DE to EF, and to the horizontal thrust, as AB to AC, or DE to DF : and for the same reason the weight of any other part FG must be to the horizontal thrust as HI to IG, or as FK to FD : but the horizontal thrust is equal throughout the arch, being propagated froir* the abutments, since the weight of the blocks, acting in a vertical direction, can neither increase nor diminish it ; and it may therefore always be represented by the line DF, while FE, EK, represent the weight of the arch and of its parts ; and it will be equal to the weight of a portion of the length of the radius DF and of the depth of the block AC, as is obvious from considering the cfTect of the upper block acting as a wedge. 308. Theorem. A spherical dome of equable thickness, having its joints in the di- rection of theradii, may remain in equilibrium if its height do not exceed 392 thousandths of the radius. The action of the weight of the dome resembles that of a wedge, pressing on each horizontal course with a force which is to its weight as the radius to the sine of the angular distance from the vertex x, and its pressure is sup- ported by the weight of the course, acting also as a wedge ; this weight is first reduced by the inclination of the joint in the ratio of the cosine of the angular distance from the vertex y, to the radius, and its effect is increased in the ratio of the lengthof the wedge to its base, or of the radius to the breadth of the course : the effect will therefore be equal to the weight of a portion equal in breadth to the radius, reduced by the obliquity of the joint in the ratio of 1 to the cosine j. While therefore the weight of a circum- ference of the breadth y is greater than that of the dome increased in the ratio of 1 to x, the course will retain the incumbent dome in equilibrium ; but when it it in a smaller proportion, the course will be forced outwards, unless it be restrained by external pressure ; and the limit will be when the weight of the dome is equal to that of a cylindrical sur^ face of the breadth xy, and of the radius x. Now the spherical surface is equal to a cylindrical surface of the breadth 1— j and of the radius 1, therefore xxy~l — y, (1— i/y) j=i— !/. (i+y)y=Uy+yy+i=hy=->/i—i =.61803. — 2 SO9. Theorem. In order that a spherical dome of the span 2x, may stand without ex- ternal pressure, the thickness must Ikj in- 44 OF ^PRESSURE AND EQUILIBRIUM.' crensed, where x is greater than 78G thou- sandths of the radiusj so as to he every where inversely as x— x'. ■The equilibrium requiring that xxy should be at least equal t& l — . j/, where the thickness is equable, if the thick- ness at any part be to the mean thickness of the supeiin- cumbeiU pardon as 7 to r, the equilibrium may be pre- . _ r(l~y) served while qxxy is equal to r.(i — y), or 9— . Now the whole weight being p, the mean thickness r is — ^ — . c being the circumference of the circle of which the radius is 1, hence q~ — ^— ani the increment ;/• is CXXTf expressed by the increment of the circular circumference r', multiplied by cxq ; therefore pzzcqxs; but :=-, andf— ^3±=IL, and i =-i-=(h.l.iy. since. (i)=^ y ^yy p ^yy \ y ' . }y' v ■ ■ . . ,. '.MM ■Til .T X V V ' — •TV/ , _^, which divided by - is -=■-■„,; '■ i but xjr+i/y 1/a y X y xyy =:i,thereforexiz:—jy)andtheexpres§ion becomes —^^^^^j — — _ — ; consequently h.l.p— h.l.- ±0, and p—- , or — ; xyy ' ^ ■'• y y y then V^~ — ^^~- Therefore the thickness must be cxxy cxyy inversely as xyy, or as x—x' ; but if we estimate the b thickness in a vertical cUrection, it becomes cxy If we wish to give a certain degree of stability to the domej we must make q dr(i — y) — p ^y dCh.l.-)±aandp=:4 (-) , therefore if d=:i+e, 9= _*£_.( 5 V. And the constant quantities may be so deter- cxyi/\y/ mined as to correspond to the weight at any particular part, whether the centre of the dome be closed nr open, b being I - J p, and the slability will be secure if all the lower parts bFmadeof the thickness 9 •, forthelower parts can never force up the higher, however they may be loaded, since their pressure will always be resisted by the collateral parts of the course. Py making 9 a miniraum, we find that the thick- ness is least where i^iv'f—--), or, if rfi=i,wheni= .J78, if d=:i.5, when 1=. 408, if d=2, when 1=0, so that in this case the dome must become gradually thipkef, from the vertex. In practice, considering the friction of the materials, it will be amply s\4fficientto make dzizi.i, or even J, and in this case 9 is least when r:::. 5, consequently the thickness of the lower parts must begin to be augmented- at the distance of 30° from the vertex, at 60° it must be- come 3.28 times as great, and if the dome be continued much lower, it will be proper to employ a chain to confine it, since at 80° from the vertex a thickness 50 times as great as at 30° would be required for the equiiibritjm. 310. Theorem. When a weight is sup- ported by a bar resting on two fulcrums, the- pressure ou each is inversely as its distance from the weight. >or, by the property of the lever, it is to the wholeweight,. as the distaiice of the weight from the other fulcrum to the whole length of the lever. ."Jll. Theorem. The strain on a uiven point of a bar, supported at the ends, from a weight phiced on it, is proportional to the rectangle of the segments into whicb the point divides the bar. ~ For, considering A as the fulcrum of the lever, the weight B produces \^ Bq at C a pressure^::- AB AC" C and the strain at B is as the length of the lever by whieh it is ap- AB BC plied, or as — 7^:; — j it is therefore equal to the strain pro- duced by the weight applied at the end of.a, levei of whicb AB.BC the length is — 77;— • At/ 312. Theorem. The strain produced by the weight of an equable bar at any pointof its length is equal to the strain produced by half the weight of one segment acting at the end of a lever equal to the other segment. _ o C The strain produced-at any point A. j^ by a weight B on either side is equal ^ to the strain of the same weight act- BC.AD li ing at the distance - DC ; therefore the strain produced by the portion AC of the bar, of which the weight may be imagined to be collected into its centre of gravity, is as AC. — . — ; and for the same reason the weight of AD 2 DC AD AC produces a strain AD. =5^ ;. therefore, both togethwr OF THE ATTUACTIOIC OF GRAVITATING BODIES-. 45 produce a strain of '———, which is equal to the efiect of half the weight of AC, actiaig at the distance AD. 313. Theorem. In all cases of equili- brium one general law prevails ; if motion were imparted to the weights, their momenta in the direction of gravity would be equal and contrary. Taking the lever for an exampfe, it fs obvious that the velochy of the bodies must be as their distances from the fulcrum; and their weights being inversely in the same ratio, their momenta must be equal, and always in direc- tions perpendicular tt> the same line ; so that if the one ascend vertically, the other must descend vertically. This has been considered by some a* a sufficient foundation for the demonstration of all cases of equilibrium, since it ap- pears to be an absurdity to suppose, that any cause should so act as to produce two equal effects, of which the one must be contrary to the other, and to the operation of the com.- mon cause. But it is more satisfactory to haye direct de- monstrations in every case, and to deduce the general law from all. Scholium. This.principle was extendetf still'further by Jbhn Bernoulli, under the name of the law of virtual vela- cities. Where the forces acting on the different bodies are different, there is always an equilibrium when the sum of all the products of the masses into the forces by which they are actuated, and then into the initial velocities with which they would be obliged to move, referred to the di- rection of these forces, becomes equal to nothing. SECTION VIII. OF THE ATTHACTION OF GRAVITATING BODIES. 314. Definition. Graviuiting bodies arc those of which the particles attract each other with forces varying inversely as tlic squares of the distances.. 315. Theorem. All parallel sections of a given cone or pyramid, supposed to be gravit.iting surfaces, of a given evanescent tliickness, attract a particle of gravitating mutter placed at the vertex with equal force. The sections being considered as composed of evanescent rectilinear figures terminated by the same right Unes, meeting in the vertex, their areas are in the duplicate ratio of their homologous sides, or of their distances from the vertex (125, lai) ; and the whole areas, and the number of material particles are in the same ratio ; therefore the in- crease of the number exactly compensates for the increase of the distance, and the forces acting in each line are the same ; therefore the attractions of the whole section's are the same. 316. Theorem. A gravitating point placed within a gravitatiiig spherical surface, remains at rest. Conceive one half of the surface to be divided into eva- nescent areolas, and cones or pyramids to stand on thcni all, and to be continued through the given point as a ver- tex, till they reach the surface on the opposite side : then the inclination of each of two opposite cones to its base is the same, and the magnitude of the section is the same as if the sections were parallel, consequently the two opposite and equal attractions destroy each other, and the same is true of each particle of the surface, and of the whole sur- face. 317. Theorem. A gravitating point, placed without a giavitating spherical sur- face, or sphere, is attracted towards its cen- tre with the same force as if the whole matter of the surface or sphere were collected there. Call the radius unity, and the distance of the ordinate of the sphere from the centre, x, then the fluxion of the curve, £, will be - , ,, ; (i4a), and if the ratio of the circum- ^/^l— J^-fj ference of a circle to its diameter be that of p to 1, the cir- cumference corresponding to a^ will be 'ip.y {\—xx), the fluxion of the surface 2pi, and the superficial area itself 2//T, and, when xz^l, lp. The distance of the given point from the centre being a, the absolute attraction of the 2px' circular element of the superficies will be _ V'^' {a+xy + i — xj; -, and the effect in the direction of the axis oa-(-'2a.r4-l being diminished in the ratio of a+x to v^(aa-f 2ar-f-i), the fluxion of the attraction in that direction will be 2p.(a-fr)..T /lp ax + 1 a-t-2aa'-t-l)| \aa v ( -)■. and while x in- (aa-t-2aa'-t-l)| \aa ^ {aa-^-lax+l ~— 2P creases from — 1 to ) , the fluent increases from — — to • 46 OF THE EQUILIBRIUM AND STRENGTH OF ELASTIC SUBSTANCES. 30 4p — , therefore the whole effect is — , which repreients the aa aa attraction of the whole surface at the distance a. SECTION IX, OF THE EQUILIBRIUM' AND STRENGTH OF ELASTIC SUBSTANCES. 318. Definition. A substance perfectly elastic is initially extended and compressed in equal degrees by equal forces, and pro- portionally by proportional forces. 319. Definition. The modulus of the elasticity of any substance is a column of tiie same substance, capable of producing a pressure on its base which is to the weight causing a certain degree of compression, as the length of the substance is to the dimi- nution of its length. 320. Theorem. When a force is applied to an elastic column, of a rectangular pris- matic form, in a direction parallel to the axis, the parts nearest to the line of direction of the force exert a resistance in an opposite direction; those particles, which are at a distance beyond the axis, equal to a third proportional to the depth and twelve times the distance of the line of direction of the force, remain in their natural state ; and the parts beyond them act in the direction of the force. The forces of repulsion and cohesion are initially propor- tional to the compression or extension of the strata, and these to their ilistance from the point of indifference : the fojces may therefore be represented by the weight of two triangles, formed by the intersection of two lines in the point of indifference ; and their actions may be considered OS concentrated in the centres of gravity of the trianf,les, which are at the distance of two thirds of tlie length of each from the vertex, and at the distanceof two thirds of the depth from each other. This distance constitutes one arm of a lever, which is of constant length, while the distance of the line of direction of the force from the centre of gravity of the nearest triangle constitutes the other arm ; and calling the distance ei the line of direction of the lo.ce from the axis, a, and the depth, b, the length of this arm, on the supposition that the point of indifference is at the assigned distance, will be lb f hb \ lb a-\ IIt^H l.ora-1 \l, that of the con- slant arm being \b. The cohesive and repulsive force* lb hb must therefore be as o+- 3(ia -i'to°+-^+T^ since that vthich serves as the fulcrum of the lever must bear a force equal to the sum of the two forces applied at the ends, which are proportional to the opposite arms of the lever ; or as Z6aa — laai+td toSBaa+iaoi+M, that is, as {6a — i)« to (6n+i>)' : but these forces arc actually as the squares of the sides of the similar triangles which represent them, that is, as ^ \b- ~) to(^ '-1 +-^^ , or as (6a— i)' to (Ba+t)', which is the ratio required : there will there- fore be an equilibrium under the circumstauces of the pro- position. 321. Theorem. The weight of the mo- dulus of the elasticity of a column being »», a weight bending it in any mannery, the dis- tance of the line of its application from any point of the axis, a, and the depth of the column, b, the radius of curvature will be bbm Supposing first the force to act longitudinally, and azi. ^, the point of indifference will be in the remoter surface of the column, and the compression or extension of the nearer surface will be twice as great as if the force had been applied equally to all the strata; and will therefore be to the length of any portion as ifro m ; but as this distance is to the length, so is the depth to the radius of curvature, or bm ftf : m : : b : — , which is the radius of curvature when azz^l. But when a varies, the curvature will vary i the same ratio ; for the curvature is proportional to the angle of the triangles representing the forces, and the angle of either triangle to its area divided by the square of its length; but the force exerted by the remoter part of the column is II to/ as 0-1 ii to ib, or as ( greater than the sine of the arc corresponding to its distance from the origin of the curve, or as the secant of the nrc corresponding to its distance from the middle of the curve is greater than the radius, and the excess of this secant above the radius will express the deflection produced by the action of the force ; f / ^ \ but this arc is to the quadrant — as f to 1;c^ I — -, 1 , and 2 \V\I I /Sf\ ' is therefore equal to ^/ f — V — Scholium. Hence it appears that when the other quantities are constant, the deflection varies in the simple ratio of «. The radius of curvature at the vertex is I'hm liaf. (sec. arc ^/ — /"T" )> ^™'" which the degree of ex- tension and compression of the substance may be deter- mined. 39,5. Theorem. The form of an elastic bar> fixed at one end, and bearing a weight at the extremity, becomes ultimately a cubic parabola, and tlie depression is ^ of the versed si nfi of an equal arc, in the smallest circle of curvature. The ordinate of the cubic parabola being ax' its fluxion, is 2ax'.r, and its second fluxion 4axxi, which varies as x the absciss. If the curvature had been constant, the second fluxion would have been bii, the first fluxion bxi, and the ordinate ^bxx ; but as ii is bix — xii, the first fluxion is bxi — ^'x, and the fluent ^i'— ir', which, when b—x becomes it', instead of t. 3i26. Theorem. The weight of the modu- lus of the elasticity of a bar is to a weight acting at its extremity only, as four times the cube of the length to the product of the square of the depth and the depression. If the depression be d, the versed sine of an equal arc in the smallest circle of curvature will be jd, and the radius of cc curvature — , e being the length ; but the radius of curva- 3d bbm ture is also expressed by , a bemg here equal to e, \1af therefore ——-^.lle^f—Zbbdm, andm=-— -./. If/ 3d I'lcf bbd be the weight of a portion of the beam of which the 4e' length is g, the height of the modulus will be —^.g. SciioLii'M. In an experiment on a bar of iron, men- tioned by Mr. Banks, e was 18 inches, b and d each 1, / 490 pounds, and g about 150 feet : hence the height of the modulus could not have been less than 3,500,000 feet. But d was probably much less than this, as the depression was only measured at the point of breaking, and m must have been larger in the same proportion. 327. Theorem. If an equable bar be fixed horizontally at one end, and bent by its own weight, the depression at the extrc- r ON THE EQUILIBRIUM AND STRENGTH OF ELASTIC SUBSTANCES. 49 mity will be half the versed sine of an equal arc ia the circle of curvature at the fixed point. The strain on each part is here equal to the weight of the portion beyond it, acting at the end of a lever of half ^s length : the curvature will therefore be as the square of the distance from the extremity. And if the second fluxion at the vertex be aa.fi, it will be every where (a— .r)*i.r: aaii 2arJi+x'ix ; the first fluxions of these quantities are aaxi and aaxi — ax'i+^i, and the fluents ^aV, and ioV — ^ length. Since TOZi—./ (326), and m varies as Ih, h being the breadth, I'dh varies as e'/, and/as , that is, when d , is given, as h, as P, and inversely as e'. 334. Theorem, The direct cohesive or repulsive strength of a body is in the joint ' ratio of its primitive elasticity, of its tough- ness, and the magnitude of its section. Since the force required to produce a given extension is as the extension, where the elasticity is equal, the force at the instant of breaking is as the extension which the body ^11 bear without breaking, or as its toughness. And the force of each panicle being equal, the whole force must be as the number of the particles, or as the section. ScHOitUM. Though most natural substances appear 50 ON THE EQUILIBRIUM AND STRENGTH OF ELASTIC SUBSTANCES. in their intimate constitution to be perfectly elastic, yet it often happens that their toughness with respect to exten- sion and compression differs very materially. In general, bodies are said to have less toughness in resisting extension _?han compression. 335. Theore.m. The transverse strengtli of a beam is directly as the breadth and as the square of the depth, and inversely as the length. The strength U limited by the extension or compression wliich the substance will bear without failing ; the curva- ture at the instant of fracture must therefore be inversely as the depth, and the radius of curvature as the depth, or Hm hm ■ — -, as b, consequently bm must be as a/*, and/ as — , or, bhh since m is as Ih, as — . a SciioMUM. If one of the siufaces of a beam wrerc in- compressible, and the cohesive force of all its strata collect- ed in the other, its strength would be six times as great as in the natural state ; for the radius of curvature would be —— , which could not be less than twice as great as in the oj natural state, because the strata would be twice as much extended, with the same curvature, as when the neutrd point is in the axis ; and/ would then be six times as great. 3.36. Definition. The resilience of a beam jnay be considered as proportional to the lieight from which a given body must fall to break it 337. Theorem. The resilience of pris- matic beams is simply as their bulk. The space through which the force or stiffness of a beam acts, in generating or destroying motion, is determined by the curvature that it will bear without breaking ; and this cur- vature is inversely as the depth-, ■consequently, the depres- sion will be as the square of the length directly, and as the depth inversely : but the force in similar parts of the spaces to be described is every where as the strength, ex as the square of the depth directly, and as the length inversely t . therefore the joint ratio of the spaces and the forces is the ratio of the products of the length by the depth ; but this ratio is that of the squares of the velocities generated or des- troyed, or of the heights from which a body must fall to acquire these velocities. And if the breadth vary, the force Will obviously vary in the same ratio ; therefore the resili- ence will be in the joint ratio of the length, breadth, and ilcpth, ^ 338. Theorem, The stiffest beam that can be cut out of a given cylinder is that of which the depth is to the breadth as the square root of 3 to 1, and the strongest as the square root of 2 to ] ; but the most resilient will be that which has its depth and breadth equal. Let the diameter or diagonal be o, and the breadth x ; then the depth being ^/■ {aa — xx),the stiffness is {aa — xxfx, and the strength aax — i*, which must be maximvims ; and [aa — xxYxx must be a maximum ; so that 3(oa — xt)'. ( — 2ir).xx-t-(aa — Tr)'(2.ri)— 0, aa — rir:3xx; and the squares of the breadth and depth are as 1 to 3 ; also aaizz 3x'i,x^^ia, and the depth v' jo, for the strongest form. It is evident that the bulk, and consequently the resilience; will be greatest when the depth and breadth are equal. 33Q. Theorem. Supposing a tube of evanescent thickness to be expanded into a similar tube of greater diameter, but of equal length, the quantity of matter remain- ing the same, the strength will be increased in the ratio of the diameter, and the stiffness in the ratio of the square of the diameter, but the resilience will remain unaltered. For the quantity of matter remaining the same, its actioa is in both cases simply as its distance from the fulcrum, or from the axis of motion, and this distance is simply as tho diameter, since the section remains similar in all its parts : the tension at a given angular flexure being also increased with the distance, the stiffness will be as the square of the dis- tance, and the force in similar parts of the space described being always inversely as the space, the square gf the velo- city produced or destroyed will remain unaltered. Scholium. When a beam of finite thickness is made hollow, retaining the same quantity of matter, the strength is increased in a ratio somewhat greater than that of the diameter, because the tension of the internal fibres at the instant of breaking is increased. 340. Theorem. If a column, subjected to a longitudinal force, be cut out of a plank or slab of equable depth, in order that the extension and compression of the surfaces may be initially every where equal, its out- line must be a circular arc. Neglecting the distance of the neutral point from the sxis. OF COLLISION, AND OF ENERGY. 51 the cutvalure must be constant, in order that the tension of the superficial fibrer. may be equal ; and the breadth must be as the distance of the line of application of the force ; that is, as the ordinate of a circular arc, or, when the curva- ture is smkll, it must be equal to the ordinate of another circular arc, of which the chord is equal to the axis. 341. Theoeem. If a column be cut out of a planT< of equable breadth, and the out- line limiting its depth be composed of two triangles, joined at their bases, the tension of the surfaces produced by a longitudinal force, will be every where equal, when the radius of curvature at the middle becomes equal to half the length of the column ; and in this case the curve will be a cycloid. For in the cycloid, the radius of curvature varies as the distance, in the curve, from its origin, or as the square root of the ordinate a, and if the depth i be as this distance, a will vary as lb, and the curvature, which is proportional to — , will be always as -, and the tensioa wUl be equable throughout. In every cycloirf the radius of curvature at the middle point is half of the length. Scholium. When the curvature at the mTddle differs from that of the cycloid, the figure of the column becomes of more difficult investigation. It may however be delineated mechanically, making both the depth of the column and its radius of curvature proportional always to ^a. If the breadth of the column vary in the same proportion as the depth, they must both be every where as the cube rootof a. SECT. X. OF COLLISION, AND OF ENERGY. 342. Theorem. When, two elastic bodies approach each other with a uniform motion, until at a certain point a repulsive force com^ mences, their relative velocities, in their re- turn back from that point, will again be uni- form, and equal to what they were, but in a contrary direction, Fcr according to the definition of elastic bodies, their, forces are always the same at the same distances from the centres, since they depend on the degree of compression. And if two bodies act reciprocally, so as to change the di- Tcci ion of each other's motions, by any forces which are Jtlways the same at the same distance,'tbeii relative velocities in approaching and receding will be equal at equal distances. For since the velocity generated in describing each ele- ment of the distance in returning, is equal to that which was destroyed while the same element of space was describ- ed in approaching, the whole velocities at any equal dis- tances must also be equal. Scholium. Bodies which communicate motion without a permanent repulsive force, or in circumstances which more or less prevent its action, are called more or less in- elastic. 343. Theorem. When two elastic bodies meet each other directly, their velocities after collision are equal to twice the velocity of the common centre of inertia, diminished by their respective velocities. For the motion of the centre of inertia remains unaltered, and the motions of the bodies with respect to each other and with respect to the centre of inertia being, after colli- sion, equal and in contrary directions, the velocity of each, must be changed by twice the difference of its velocity and that of the centre of inertia, and will therefore become equal to twice the velocity of the centre of inertia diminish- ed by its own velbcity. 344. Theorem. When two equal elastic bodies meet each other directlyj their motions will be e.xchangedi For twice the velocity of the centre ofinertia is here the. sum of the velocities ; therefore either deducted from this will leave a remainder equal to the other, for the motion of. the body to which it belongs. - 345. Theorem. An elastic body striking a larger one at rest, is partially reflected, and a body striking a smaller one, continues- to move forwards. For the velocity in the first case is greater than twice that of the centre of inertia, in the second smaller. 346. Theorem. When the impulse of an elastic body is communicated to another through a series of bodies differing infinitely httle from each other in bulk, the momen- tum of the last is to that of the first' in the siibduplicate ratio of their bulks. Let the first be 1 — T, the second 1 -f-a-, and the velocity of ; the first 1 ; then the velocity of the centre of gravity will 1— a: be — - — ,. and the velocity of the. second after the. inif. 52 OF ROTATORT POWER. pul?e will be 1 — x; and Us momentum (i — t).()-(-i), therefore the momentum is increased in the ratio of 1 to l+x, or in the subduplicate ratio of 1 to i+2r +XX, which as x is diminished, approaches infinitely near to the subduplicate ratio of 1 — x, to 1+x, or i to l+2«+5!.r^ + 2.T^... since all the succeeding terms vanish in comparison with the preceding : and in the same man- ner it may be shown that at every succeeding step the mo- mentum will be increased in the subduplicate ratio of the bulk ; therefore the joint ratio of all the changes of momen- . turn will be the subduplicate ratio of the corresponding change of bulk. Scholium. The first body will also have a retrograde motion after the collision, with the velocity x, and the subse- quent bodies will recoil with velocities gradually smaller, in the same proportion as their progressive velocities have been smaller. If a second impulse be communicated to the first body, it will impel the second with a velocity infinitely near to that which the first impulse produces, and will itself re- coil with a double velocity.* 347- DF.riNiTioN. The product of the mass of a body into the square of its velo- city may properly be termed its energy. Scholium. This product has been called the living or ascending force, since the height of vertical ascent is in pro- portion to it ; and some have considered it as the true mea- sure of the quantity of motion ; but .although this opinion has been very universally rejected, yet the force thus esti- mated well deserves a distinct denomination. 348. Theorem. In two bodies perfectly elastic, the joint energy, with respect to any quiescent space, is unaltered by collision. Let the bodies A and B have a relative motion ; then their velocities towards the centre of inertia will be reciprocally as their masses ; and the momenta in opposite directions will be A.B and B.A. Now if the centre of inertia have also a motion C with respect to a quiescent space, in the direction of A, the velocities will be C;-f B and C — A respectively, and the joint energies will be A.(C-f-B)'-t- B.(C— A)'. But after collision, the velocities B and A relative to the centre of inertia are in a contrary direction^ the motion of that centre remaining the same (28g), there- fore the velocities are C— B and C+A respectively, and the energies A.(C- B)'+B.(C+A)*; but A.(C4-B)'— A.(C— B)"=:2ABC=:B.(C+A)*— B.(C— A)S and the two sums •re equal. Scholium. The energy must be estimated in the re- spective directions of the velocities before and after coUi- sioa, while the sum of the momenta, which also remaint unaltered, requires to be rcductd to the same direction. The reason of this difference is, that the square of a nega- tive quantity is the same as that of the same quantity taken positively. SECTION XI. OF RQTATORT POWER. 349. Theorem. When a system of bo- dies has a rotatory motion round any centre, the effect of each body in turning the system round a given point must be estimated by the product of its momentum into the dis- tance of tlie body from that point ; and the power of each body, with respect to the ori- ginal centre of rotation, will be expressed by the product of the mass into the square of the distance. Suppose the bodies A and B, fixed to the ends of two equal levers, to meet each other, and simply to communi- cate their motion, and let B be twice A, and moving with half its velocity, then the motion of A will exactly destroy the motion of B, and this effect is therefore the measure of the motion of A : but if the bodies A and B be connected with the arms of an inflexible line, and move vvith equal velocities in the same direction, they will be totally stopped by the application of a fulcrum at the centre of gravity ; for the propositions respecting equilibrium are as well deduci- ble from the computation of motion as from that of force, and the motion of A is here equivalent to the motion of B, moving with equal velocity at half the distance : but it was before shown to be equal to the motion of B with half the velocity at its own distance : therefore these two motions of Bare equivalent with respect to effect in producirj; rotatory motion ; and the same may be shown in other cases. And the distance from the centre of rotation being as the velo- city, the power is as the square of the velocity. 350. Definition. The centre of gyra- tion is a point into which if all the particles of a revolving body were condensed, it would retain the same degree of rotatory power. 351. Theorem. The centre of gyration of two equal points is at the distance of the square root of half the sum of the squares of the separate distances from the axis. OF ROTATOny POWER. 5.1 The distance of the points from the axis being a and b, the whole rotatory power will be «*+//, which is equal to the sum of the particles multiplied by the square of 352. Theorem. The distance of the cen- tre of gyration of a right line from an axis at its extremity, is to its length, as 1 to v^3. The fluxion of the rotatory power is x''i, consequently the whole rotatory power is ^r', which is equivalent to the effect of .T at the distance of i/lx'. But if the centre of mo- tion does not coincide with the end of the line, the rotatory power will be the sum or difference of the two values of .r at the end of the line, as \{a^±b'], and the distance of the centre of gyration becomes •/ (^(o'd:''')), divided by a±l. 353. Theorem. The distsince of the centre of gyration of a circle or any circular sector from its centre of rotation and of cur- vature is to the radius as 1 to v'Q. The area of any increment of the circle, of which the radius is x, will be as x*',and its rotatory power x*!', the flux- Ion x'x and the fluent ^r' ; but the whole area will be as fr', and the rotatory power the same as if the whole were at the distance v' (i^*)- 354. Definition. The centre of percus- sion is a point in which an obstacle must be placed in order to receive the whole effect of the motion of a revolving body, without pro- ducing any pressure on the axis. 335. Definition. The centre of oscil- lation of a body is a point of which the dis- tance from the axis of motion is equal to the length of a pendulum vibrating in tlie same time with the body, 356. Theorem. The centres of percus- sion and of oscillation coincide always in the same point. The effect of the velocity of every part of the body, re- duced to the direction in which the obstacle opposes it, is expressed by the product of each particle, into its distance from the line drawn through the axis, parallel to that direc- tion : now the joint effect of all these reduced momenta is equal to the resistance of the obstacle, since the axis is sup posed to be free from any pressure in consequence of the percussion ; and the resistance of the obstacle acting at the given diitancc is also equivalent to the rotatory power of the whole body. But the sura of the reduced momenta is als* expressed by the product of the whole mass into the distance of the centre of gravity from the line drawn through the axis (27fl) which is equal, acting at the distance of the centre of percussion, to the whole rotatory power, or the sum of the products of all the particles by the squares of their distances, and the distance of the centre of percussion from the centre of suspension is found by dividing the rotatory power by the mass and the distance of the centre of gravity. In the same mannerj when a body is suspended as a pen- dulum, the tendency of the weight of each particle, to turn it round the axis, is proportional to the distance frorh the vertical line passing through the point of suspension ; and the sum of the forces of all the particles is expressed by the product of the whole weight into tlie distance of the centre ofgravity from the same line; and the rotatory mass to be moved is to be estimated by the joint products of the'parti- cles into the squares of their distances: and in order that the angular velocity of the equivalent pendulum may be equal, its distance from the vertical line must be to the square of its distance from the centre, in the same ratio, as the product of the distance of the centre of gravity into the whole weight,to the rotatory mass ; but the distance of these points from the vertical line is as the distance from the cen- tre, therefore the distance of the centre of oscillation is ex- pressed by the rotatory mass divided by the weight and the distance of the centre of gravity from the point of suspen- sion ; consequently it is equal to the distance of the centre of percussion from the same point. Scholium. It may also be shown that the distance of the centre of oscillation from the centre of gravity varies in- versely as the distance of the centre of suspension from the same point. 357. Theorem. The centre of oscilla- tion of two equal points in a right line pass- ing through the'axis is found by dividing the sum of the squares of iheir distances by the sum or diflerence of their distances. For the rotatory power is a'+i'', and the weight mul» tiplied by the distance of the centre of gravity is a±/'. S58. Theorem. The centre of oscilla- tion of a right line suspended at its extre- mity is at the distance of two thirds of its length, 7 he fluxion of the rotatoiy power is x'i, the fluent ^', the distance of the centre of gravity ^, the product ix', and the quotient j*. 54 OF PREPONDERANCE, AND THE MAXIMUM OF EFFECT. 559. Theorem. The centre of oscilla- tion of a triiinj^le, suspended at its vertej^, and vibrating in a direction perpendicular to its plane, is at the distance of ^^ of its height from the vertex. Calling, for the sake of simplicity, the base of the triangle unity, the fluxion of the rotatory power is x'i, the fluent Jx', the distance of the centre of gravity |r, the product ^«', and the quotient Jr. SECTION Xn. OF PREPONDERANCE, AND THE MAXIMUM OF EFFECT. 560. Theorem. In order that a smaller weight may raise a greater to a given height on an inclined plane in the shortest time possible, the length of the plane must be to its height as twice the greater weight to the smaller. Let the descending weight be i , the ascending a, and the length of the plane to its height as x lo l, the weights being simply connected by a thread and pulley ; then the portion of the power employed m maintaining the equilibrium is —(255), and the remaining portion 1 ; and the weight lo be moved being constantly 0+1, the velocity produced a a by the acting power 1 will »ary as 1 , and the square of the time of describing i, as x : f 1 l (233), or XX — — , thefluxion of which vanishes when it is a minimum; Suppose the two weights fixed nt opposite ends of a lerer, and let it be required to determine their respective distances from the fulcrum, so that the velocity of the ascending weight may be the greatest possible ; let this weight be called a, and its distance from the fulcrum unity, the de- scending weight being I, and its distance x. Then, if the weights were in equilibrium, a wouldbe zzx; and the dif- ference o(x and a, or x—a, is the force tending to raise a j but the mass to be raised is equivalent to a+arx, for tjie mass of the weight 1 acts in the duplicate ratio of its dis- tance from the fulcrum (349), and the velocity of a wiH fx — a)ixi =0, hence no; and multiplyrngby ■ [x—a)' " ^ " ' XX therefore — X a(x — o) — x=:o, X — 2«:=0, and xzz^a, 361. Theorem. If a given weight, or any equivalent force, be employed to raise another given weight by means of levers, wheels, pullies, or any similar powers, the greatest effect will be produced, if the acting weight be able to sustain in equilibrium a weight about twice as great as the weight to be raised, when thi* weight is very large ; or about twice and a half as great, when the weights are nearly equal. X — a ... . ' be — , and its fluxion — — a+xx o+xx (a+xx)' a+xx— 2xx+2axz:o, orrxx — 2ax, and adding aa, xx— 2nr+(7n=a+oa, {x—ay'=Za+aa, x—azZy/{a+aa),x::: a+ — r; (x— a).- 3XXT-{-2aaxi 0, x'-i^a'x — (*• — a).{3x::z-ia')zzo, *''4-a'a- — 3x' — 2a"i-l-3a.r + 2a'=0, •2T' + (a''- — 3a).x— 20% x=:v'ia' + -i\{a' — 3a)') — J(a^ — 3a)=..(v'(aa+l0a+Q) — a+s). Mence, ifar: 4 I, yr: ., and when a is diminished without limit, r— -o ; when it is increased without limit, j-::r:2a ; for in 2 this case ^(aa+ioa+v) approaches infinitely near to a+S- This proposition has not always been sufficiently distinguished from the preceding one. Scholium. If the force accumulated during the opera- tion of the machine, as that of a stream ol water collected continually in a reservoir, there would be no limit to the »dv»ntage of a slow motion. 363. Theorem. If a weight be drawn along a horizontal surface by a given force, with a resistance in the direction of the sur- face which is always a certain portion of the pressure, the force will act with the greatest advantage when the tangent of its inclina- tion is to the radius as the resistance to the pressure. Let AB represent the force, and let BC be to CD as the pressure to the friction, then K. CD AD will represent the sura of the horizontal forces, AC being the efficient portion of the forc» AB, and CD the diminution of the friction. But the »ngle D is given, since the proportion of BC to CD is given, and BCD is a right angle ; and AB being given, AD will vary as the sine of the angle ABD, which is greatest when ABD is a right angle; and ACB is then similar to BCD; but BC is the tangent of the angle BAC, AC being the ra- dius. The angle BAC is also the same at which the weight would begin to slide along the given surface if it were in- clined to the horizon (soo). SECTION Xlll. OF THE VELOCITY AND FRICTION OF WHEEL WORK. 364. Theorem. The angular motion of two wheels may be made uniform at the eame time by means of a right line sliding on an epicycloida! surface, or by two surfaces which are involutes of circles, acting on each otlier. Let A and B be the centres of the wheels, and CD a portion of an epicycloid, described by the point D of the circle BDE, equal in diameter to the radius of the wheel B, in rolling on the wheel A : then if the tooth of the wheel B be terminated by the right line BD, and touch CD in D, the line DE perpendicular to BD, will pass through the point of contact of the circles, E (206) ; and the force will be communicated in the direction DE, so that the angular motion of each wheel will be the same, as if it acted immediately at the end of the perpendicular AF, and the angular motion of A will be to that of B, in the constant ratio of BD to AF, or BE to AE. It is obvi- ous, that BD cannot act in the same manner on CD be- yond the line BA, unless its extremity be made epicycloidal, and tl'.e corresponding part of the tooth of A a' right line. Let each tooth now terminate in the curve described by the evolution of a thread from its res- pective circle : then the curve will be always perpendicular to the thread (l93), which is the tangent of the circle, and the force will al- ways act in the direction of the circumference of the circles at E and G, and the motion will be uniform as before. 365. Theorem, The relative velocity of the teeth of two wheels, or the velocity with which the surfaces slide on each other, varies ultimately as the sum of the angular distances of the point of contact from the line joining the centres. Let A and B be the two centres, C the point of contact, and CD the com- mon ungent there ; and suppose the teeth to move to the positions E, F, and G to be the new point of contact ; and let BD and BH be perpendicular to CD and to AC produced ; then CE and CF, the elements of the paths of the points which were at C, will ba perpendicular to AC and BC ; and the difference of EG and FG, which re- presejiu the friction, ultimately equa) .56 OF THE VEIOCITV AND FUICTIO-!f OF WHEEL WORK. 40 EF, EFG becoming a right line parallel to CD, and the angle CFG:iDCF=DBC ; but the angle ECFrrBCH, and in the triangle ECF, sin. CFE : sin. ECF : : CE : EF (139) : : sin. CBD : sin. BCH : : CD : BH. For the sub- stance of this demonstration I am indebted to Mr. Ca- vendish. In the epicycloidal tooth, CD coincides with CB, and CBD is a right angle, so that the friction is to the mo- tion CE of the tooth of A, as the sine of BCH, or of ACB, to the radius. In the involute, CD is constant, and the fric- tion varies as BH, supposing the motion in CE constant. If the pinion acted within the concave surface of a cylin- drical wheel, the friction would be as the sine of the differ- ence, instead of the sura, of the angular distances from the line of junction. Scholium. The immediate quantity of the force of friction does not appear to be materially altered by the re- lative velocity of the surfaces : but its mechSnical effect in resisting the motion of a machine is so much the greater as the relative velocity is greater. 360. Theokem. If a given number of "iceih are to be disposed on an unlimited number of wheels and pinions, so as to in- crease or diminish the velocity of the last wheels of the series as much as possible, the proportion of each pinion to its wheel must be nearly that of 1 to 3,59. In order to increase the angular velocity in the ratio of 1 to a, with the least possible number y of wheels, each having to its pinion the ratio of a to i, we must make x the number of which the hyperbolical logarithm exceeds the reciprocal by unity. For x'lza I :c=n'; and y.{x+i), the number of teeth, must be st minimum: but y.(j;+l)=a'j/-f-y, and orjr — y{h.l. a)a> Z.+i/=.0, a'+ 1 =a'_!li2, or x+ l=Zx(h.\.x] since h.l.a= yv y yii>.\^); therefore 1-f— =h.l.i, and x is found =3.iB» This is therefore the most advantageous proportion for pro- ducing the greatest velocity with a given number of tcicth. jSIATHEMATICAL ELEMENTS OF NATURAL PHILOSOPHY. PART III. HYDRODYNAMICS. OF THE MOTIONS OF FLUIDS. SECTION J. OF HYDROSTATIC E^WiLlBR^TJM. 367. Definition. A fluid is a collection of particles considered as infinitely small spheres, moving freely on each other without friction. Scholium. Some have defined a fluid, as a substance which communicates pressure equally in all directions ; but this appears clearly to be a property derivable from a simpler assumption, although, from the deficiency of our analysis, all attempts to investigate mathematically the af- fections of fluids, have hitherto been so unsuccessful, that even this fundamental law can scarcely be strictly demon- strated. 368. Theorem. The surface of a gra- vitating fluid at rest, is horizontal. Suppose two minute straight tubes differently inclined to the horizon, and joined at the bottom by a curved portion, and let them be filled with evanescent spherules : then the relative force of gravity is inversely as the length, when the height is the same ("255), and the number of particles is di- rectly as the length : consequently the absolute pressures will be equal, and there will be an equilibiium ; and if the fluid in cither arm be higher, it will preponderate. The pressure on the tube at any part is only the effect of the pat- VOL. II. tide immediately in contact with it, and is communicated in the direction perpendicular to the tube, therefore if ano- ther similar row of particles in equilibrium were placed on the first, this pressure, acting in the same direction, wouJd not disturb the equilibrium of the particles among them- selves, however they might be situated with respect to the first. And conceiving any fluid to be divided into an infi- nite number of tubes, bent or straight, in which the par- ticles form a continuous series, there can be no force to preserve the equilibrium in each of them, unless the height of each portion be equal. Yet some may perhaps hesitate to admit the conclusiveness of this reasoning, without an appeal to our experience of the phenomenon as observed in nature : it may however be admitted by such as an illustra- tion of that phenomenon. Scholium. In the equilibrium of fluids, there is some analogy to the general law of mechanical equilibrium (313) ; thus, supposing the whole body of the fluid to begin to move either way, the initial momenta of the par- ticles in the surfaces of the unequal portions of a bent tu&e will be equal. For instance, if one surface be ten times as large as the other, its subsidence will raise the other ten times as much as it sinks. 369. Theorem. The surface of a gravi- tating fluid, revolving round an axis, is para- bolic. The centrifugal force is simply as' the distance from the axis, and may be represented by tlie ordinate, while the I 53 OF HYDROSTATIC EQUILIBRIUM. constant force of gravity is represented by the subnormal, or the portion of the axis intercepted between the ordinate and the perpendicular to the curve, the perpendicular or normal being the result of the two forces. But the curvp , in which the subnormal is constant is a parabola ; for the triangle composed by the increments of the curve, the ordi- "nate and the absciss, is similar to that which is formed by the normal, the subnormal, and the ordinate, consequently "yii y':3f::i:y, i) : i :: s : y, yil=si, and s—~ ; but m . . 2?/y the parabola, since «x=yi/ (204}, ai—-2yy, ^—~' ^"° a J— — , which IS constant. 370. Theorem. The pressure of a fluid on every particle of the vessel containing it, or of any other surface, real or imaginjiry, in contact with it, is equal to the weight of a co- . lunin of the fluid of which the base is equal to that particle, and the height to its depth below the surface of the fluid. Imagine an equable tube to be so bent that one of its arms may be ver- tical, and the other perpendicular to the given surface : then drawing a horizontal line AB, the fluid in the portion of the tube AB will remain in cquinbrium, and will only transmit the pressure of BC to the surface at A, and this will be true whatever be the position of the imaginary tube ; and since some particles of the fluid may be so arranged as to be no more disturbed in their initial tendency to motion than the fluid in such a tube would be, the equilibrium can never be permanent unless the pressures be such as are here assigned. Scholium. If therefore any portion of the superior part of a fluid be replaced by a part of the vessel, the pres- sure against this from below will be the same which before supported the weight of the fluid removed, and, every part remaining in equilibrium, the pressure on the bottom will be the sarhe as if the horizontal section of the vessel were every where of equal dimensions. In this manner the smallest given quantity of a fluid may be made to produce a pressure capable of sustaining a weight of any magnitude, either by diifiinishing the diameter of the column and in- creasing its height, or by increasing the surface which sup- ports the weight. 371. Theorem, The pressure on any vertical or oblique, plane surface is equal to the weight of a column of a fluid of which the base is equal to the surface, and the height to the distance of its centre of gravity below the level surface 'bf the fluid. Suppose the surface to be divided into a number of equal evanescent portions, then the number of particles in each column standing^ on the same base being as its length, the weight will be is Ihe: length and the base conjointly, or as the numerical product of the base and length : but from the property of the centre of gravity or of inertia, the sum of tlie products of each particle of the surface into its depth, is equal to the product of the whole into the distance of the centre of gravity (276), which represents a column of the same height, and on the same base. 372. Theorem. A hemisphere or semi- cylinder of uniform densitj', having its axis fi.xed in the surface of a fluid, and remaining in equilibrium in any one position, will re- main in equilibrium when its position is changed by the iiijcrease or diminution of the quantity of the fluid. The pressure of the fluid on the convex surffi.ce.of the solid will have no effect .in turning it round its axis, consequently we have only to consider the pressure exerted on its plane surface. Thecentre of gravity of this^urface AB or CD being at A or C, the pressure of the fluid will be always as the depth AB, CD : but the eflfect of the weight of the solid will be always as EB, FB, the distance of the centre of gravity E, G from the vertical line AB : but the triangle BDC is always similar to the triangle GFB, con- setjuently CD varies always as FB, and if the forces are once equal, they will remain always equal in any position of the solid. Scholium. If the surface of the fluid be below the axis, and there be an equilibrium, for instance when the surface is at A, there will be an equilibrium, for a similar reason, when the fluid rises to C in the oblique position of he solid. 373. Theorem. If fluids are of different specific gravities, that is, if equal bulks of them have different weights, they will coun- terbalance each other in a bent tube, whea OF FT.OATING BODIES. — OF SPECIFIC, CRAVITIES. 60 their heights above the common surface are inversely as their specific gravities. For if the tube be equable, and its arms similar, the actual weights above the common surface will be equal ; and if otherwise, the efficient weights will be equal, since, in either fluid, the pressures on the common surEa(^ are simply as the heights. SECTION II. or FLOATING BODIES. 374. Theorem. If an}' body floats on a fluid, it displaces a quantity of the fluid equal to itself in weight. - For since the body is supposed to remain at rest, and to retain the pressure of the fluid below it in equilibrium, it must exert by its weight a pressure downwards, equal to that of the quantity of fluid which would retain the same pressure in equilibrium, or to the quantity displaced. 375. Theorem. When the centre of gravity of the floating body is in the same vertical hne with the centre of gravity of the fluid displaced, the body remains in equili- brium. .:• - • If a uniform fluid, of the same specific gravity as the fluid, occupied the place of the portion removed, it would remain at rest, in consequence of the contrary actions of the fluid and of gravity. Now the efTect of any forces on the motion of the centre of gravity of a compound body, is the same as if they were applied to the same mass placed in the centre ^f gravity ; therefore since the direction of gravitation is .•vertical, the. result of the combined pressures of the fluid which counteract it, would, if united at the centre of gra- vity, be also vertical: and if the actual centre of gravity of the body of equal wdight be placed in this line, there will be an equilibrium; but if otherwise, the centre of gravity will descend towards this line, and a part of the immersed portion will in the mean time be somewhat raised by the • pressure of the fluid. 376. Theorem. If a floating body have its section, made by the surface of the fluid, a |iarallelogram, its equilibrium will be stable or tottering, accordingly as the height of its centre of gravity, above that of the portion of the fluid displaced, is smaller or greater than one twelfth of the cube of the breadth, divid- ed by the area of the transverse vertical sec- tion of the immersed part. Let the body be inclin- ed in a small degree from the position of equilibrium ABC, into the position DEF; then the triangles GHI and KHL will be equal, since the area of the section immersed must remain constant, and GK and IL will ultimately bi- sect each other in H. Now the centre of gravity of thu section ILF, is the common centre of gravity of its parts IHMF and LHM, making K,M=GI ; but N the centre of gravity of IHMF is in the line HF bisecting it, and the com- mon centre of gravity may be found by making NO parallel to HKortoHL,in the same ratio to the distance of the centre of gravity of LHM from H that LHM bears to IFL. Now the distance of the centre of gravity of any triangle from the vertex is two thirds of the line which bisects the base (277) ; that is in this case |HK, and the area of the triangle LHM is *1fK.KP, therefore NO : SHK :: HK.KP : LFI, NO=: ^HKo KP •2 — ; but drawing Oa vertically through O, NO : NO :: KP :. HK and ^^^^2^^mS^=^.'}f^. KP IFL '' 11-L If therefore the centre of gravity be in Q, the body will remain in its position in any small inclination; since the result of the pressure of the fluid acts in the direction OQ, if the centre of gravity be below Q, it will descend towards the line €lO, and the body will recover its situation; if above Q, the body will overset. . Hence the point Q is sometimes called the centre of pressure, or the mctaccntrc. The theorem may be easily accommodated to bodies of other forms. SECTION III. OF SIT.CIFIC GRAVITIE'S. 377. Theorem. If a body is immersed in a fluid, it loses as much qf its weight as is equivalent to an equal bulk of the fluid. For if the body were of the same specific gravity with the fluid, it would remain at rest, without any tendency to ascend or to descend,' the pressure of the fluid counteracting its whole weight: butthat pressure will belhesamewhatever GO OF PKKUMATIC EQUILIBRIUM. — OF HYDRAULICS. may be the weight of the body, and will support an equal weight in both cases. Scholium. Hence the specific gravity of any fluid may be determined by finding how much weight it deducts from a body of known dimensions immersed in it. And the di- mensions of a solid may be found by weighing it in a fluid of known specific gravity, and thence its specific gravity may also be ascertained. SECTION IV. OF PNEUMATIC EQUILIBRIUM. 378. Definition. Elastic fluids are such as have a tendency to expand when at liberty, with a force which is proportional to their density. Atmospheric air, gases, and vapours, are examples of such fluids. 379. Theorem. Supposing the force of gravitation constant, the logarithm of the rarity of the atmosphere must be in a con- stant ratio to the height. Let the length of a column of air increase equably in de- scending, then the densities at each point being as the pres- sures which counteract the expansive force (378), and the increments of the pressures being as these densities, the pressures vary proportionally while the heights vary equa- bly ; therefore the heights are in a constant ratio to the lo- garithms of the numbers representing the pressures (50) : and in ascending, the same logarithms, taken negatively, are the logarithms of the reciprocals of the densities (38), or of the rarities. So that if a, I; h, r; be corresponding heights and rarities, a : l.t :: A : l.r. Suppose a 7 miles, and /-zlt.thcn 7 -.lA-.-.h: l.r, and l.rlz-^Ar: , and ' 7 1.1026 h h *=!. 16-26 (l.r), also since l.r=:(1.4). — , r=(4)7. Practi- cally 7i:i;ioooo (l.r), in fathoms. 380. Theorem. The height of a column of air, of equal density with the atmosphere at any part, capable of producing a pressure equal to the atmospheric pressure at that part, is the same at all distances above the earth's surface. The height of such a homogeoeous atmosphere must b« directly as the pressure to be produced, and inversely as the density, and since the density varies as the pressure, the result will be constant. This height is found to be some- what more than 5 miles : in very great elevations it proba- bly varies. 381. Theorem. Ifa fluid be contained in a tube closed at the top, it will be support- ed by the pressure of the atmosphere at such a height, that its weight will be equal to that of a column of air on the same base, and of the height of the atmosphere. For if an upright tube be partly immersed in a fliiid, a heavier fluid will be sustained in it at a proportionate height, provided that the access of the fluid to its upper part be prevented ; and in this case, the pressure of the atmosphere is as effectually removed from the upper surface of the fluid in the tube, as if the tube were continued throughout thi height of the atmosphere. SECTION V. OF HYDRAULICS* 382. Theorem. The velocity of a small jet of water issuing in any direction from a reservoir, is nearly equal, in favourable cir- cumstances, to the velocity acquired by a body in falling through the height of the surface of the reservoir above the orifice. Supposing a very small plate of water immediately with- in the orifice, to be put in motion at each instant by means of the whole pressure of the fluid; which is equal to the weight of a column on the same bascj of the height of the reservoir, and supposing the whole pressure to be employed in generating the velocity of the thin stratum, neglecting the motion of the surrounding fluid, this stratum would be urged by a force as much greater than its own weight as the column is higher than its thickness, through a space which is shorter than the heighl of the column in the same ratio. But the spaces being inversely as the forces, the final velo- cities are equal ; and the velocity thus generated would be -equal to that of a body falling through the height of the column. And although a part of the pressure of the co- lumn is expended in producing motion in its own particlesi this part is not wholly lost, because tlie velocity of these OF HYDRAULICS. 61 pirticles renders »hem more easily actuated by the pressure of the succeeding column. Still, however, some deduction must be made for the lateral motions of the neighbouring particles, which tend rather to diminish the quantity of the discharge, than to lessen the actual velocity of the jet: the particles approaching and even passing through the orifice obliquely, contract the diameter of the stream nearly in the ratio of 4 to 5, when the aperture is in a thin plate ; but the velocity in the contracted part is only one fortieth or one fiftieth less thart»that which is due to the height. Scholium. The velocity of the discharge through dif- ferent kinds of apertures may be found by multiplying the square root of the height in feet by 'a certain coefficient; this, for the undiminished velocity, is 8.0229 ; for an orifice imitating the form of the contracted stream 7.8 ; for bridges with pointed piers 7.7 ; for bridges with square piers O.y ; for short pipes, from two to four times as long as their dia- meter, 6.6 ; for orifices in a thin plate, and for weres, about i. When the orifice is made between two reservoirs, the discharge is nearly in the same relation to the ditference of their heights. 383. Theorem. A jet of water issuing from aa orifice of a proper form, and directed upwards, rises nearly to the lieight of the head of water in the reservoir. For it has been shown, that the velocity is nearly equal to that which is produced by the fall of a body through the height, and each of the particles may be considered nearly its a separate projectile. 384. Theorem. If a jet issue horizon- tally from any part of the side of a vessel standing on a horizontal plane, and a circle be described having the whole height of the fluid for its diameter, the fluid will reach the plane at a distance from the vessel, eqnal to that chord of the circle in which the jet ini- tially moves. The horizontal velocity ot the jet, being equal to that which is acquired by a body falling through the distance AB below the sur- face, would describe in the time of falling through AB, a distance equal to 2AB (233), and in the time of falling through BC, in which the jet will reach the horizontal plane (25l), a distance greater in the ratio of those times, or of the square roots of the spaces (235)- Call AC, 1, then (121) 1 : AD ;: A 5a.D K AD ! AB, ADq=:AB, and AD=v^ AB ; in the same man- ner CD" v'BC, therefore the times are as AD and CD: but AD : CD : : AB : BD, and 2BD, or DE will be equal to the space CF described by the horizontal velocity (251} in the time of falling through BC. 385. Theorem. When a cylindrical or prismatic vessel empties itself by a small ori- fice, the velocity at the surface is uniformly retarded; and in the lime which it occupies in eiilptying itself, twice the quantity would be discharged if it were kept full by a new supply. For the velocity of the surface is in a constant ratio to that at the orifice; and since the velocity varies as the square root of the height, or of the space to be described, the law of the motion will be the same as in the ascent of a projectile (230, 233, 236), and the space described by every such motion is half the space that would be described by the initial velocity. 386. Theorem, The quantity of a fluid • discharged through an aperture of equal breadth, continued from the bottom of a re- servoir to the surface, is two thirds of that which would be discharged with the velocity at the bottom. ^ For the velocity at the distance x below the surface is Os/r, and the fluxion of the discharge a^/xi or ax'i, of which the fluent is § oa'x, which is |of what would be dis- charged with the velocity ov'.r. 387. Theorem. The friction of 'fluids varies nearly as the square of the velocity. The friction appear? to depend principally on the centri- fugal force of the particles of the fluid moving in certain curves in order to surmount minute obstacles; hence it may be compared with the force of a revolving body, which always varies as the square of the velocity. The identity of the curves in all cases could however scarcely be inferred from theory only, if it were not suppor«d by experience. The viscidity of the fluid seldom adds much to the resist- ance. 388. Definition. The hydraulic mean depth of a river is the quotient of the area of its section, divided by the length of the out- line of the section in contact with the bot- tom. ^2 OF HYDRAULICS. consequently 111. u'+i-r: A; k being the actual heighf, 389. Theorem. When a river flows with a uniform niotiorij its velocity varies as the square roots of the hydraulic mean depth ^""^ {aib'+d).v'=b^dk, and «'=_!____ and of the sine of the inclination conjointly. c^„„, , _, _ . , . . , . J J ScHoiioM. The coefficient t IS in this case 8.8, and For since the relative weight produces no acceleration, it "''* '^ "early .0211, where the velocity is moderate : but it must be exactly balanced by the friction : but the friction is is more accurate to make t)=:50^ (— £L_) ; all the mea- as the square of the velocity, therefore the relative weight \ '+50d/ must be as tlie square of the velocity, and the velocity as ^"^" ''^'"S ejcpressed in English feet. When the pipe is the square root of the relative weight, or of the sine of the ''^"'' ^'^ ""^y '^"'' ^'^^ •'«'Sht employed in*ovcrcoming the inclination. And since the friction produced by the bed ailditional resistance, by multiplying the square of the ve- of the river is for any given portion of water, as the extent ^°'^''>' ^y ^'^^ ^'"= of «he angle of inflection, and by .0038. of the bed directly and inversely as the quantity of water, ^* "^V "'^o ''^^"cs '''^ velocity of a river from the same that is inversely as the hydraulic mean depth, the square of f'"''""'*' supposing the pipe to be in train, or so constituted, the velocity must vary in the direct ratio of the depth in '^'" ''" velocity is independent of its length ; for mating order to produce a given friction, and the velocity must be A=zc+A/, we have ^""^"^^^'^ constant, whatever may be as the square root of the mean depth, +5oa the magnitude of 2,andif /:::aO ,V=.bo ■/ {kd) ; but(/t)is the Scholium. It is found by experience that the mean ve- sine of the inclination, and e being the mean depth, d:=.ie locity of a river in a second is nearly nine tenths of a mean and riz y (i ooooAr?) ; or, if we employ .02 1 1 as the value of proportional between the hydraulic mean depth, and the at-Si;=^/(828oie); whilethcrule deducedfrom observation fall in two English miles. And if this velocity be ex- is equivalent to «:r:v/[BS53*e.) pressed in inches and increased by its square root, it will _, ^^ i , i. . , ... ,. , 1 1 ■ u J I ■. SQL Iheorem. The hydraulic pressure give tne velocity of the surface, if diminished by its square j r ^ root, the velocity at the bottom. It appears however that O^ ^ j^t acting directly on a plane surface, the velocity increases a little more rapidly than the square SO as to lose its whole progressive motion, is root of the fall. The discharge of a were may be found by equal to twice the weight of a column OU determining the velocity due to the sum of its height, and ^i , j i- .u i • i .. i " . , , the same base, and or the heieht correspond- the height corresponding to the velocity with which the ■■ water arrives at it. ing tO the Velocity. 390. Theorem. The square of the velo- ^°' '" '^^ '""" '"'•"''"'^ ^°' ^ ^°'^5' '° f"" *™"5h this ,„.,,., , , , . height, each particle of the jet would lose its velocity by city or a fluid discharged throus^h a pipe va- ^ . ,. , .... u . • .u- .- •' ° o r r ti)£ immediate action of gravitation ; but in this time the ries d irectly as the height multiplied by the ^^^^ number of particles lose their velocity by the reaction diameter, and inversely as the diameter in- of the surface as are contained in a column on the same creased by a certain constant fraction of the base, and of twice the height = therefore the effects being Ipno-tVi ■ equal, the causes must also be equal. 392. Theorem. The resistance of a fluid The height of the reservoir above the orifice of the pipe , . , 1 • . 1 ■., , ,. ij . . .u 1 J to a body moving through It, is as the square may beconsidered as divided into twopartSjtheoneemployed tv^ " "- j a o ' 1 in overcoming the friction, the other in producing the ve- Oi the velocity. locity. Now the whole friction varies directly as the length For the relative motions are nearly the same as in the of the pipe, inversely as its hydraulic mean depth, which is impulse of a jet ; and the height of the column varies ac one fourth of its diameter, and directly as the square of the the square of the velocity. velocity ; or calling the height employed on the friction,/, ScHOiruM. When the impulse is oblique, the resistance /=1. v\ a being a constant quantity. But the height tnay be calculated from the laws of the decomposition of force ; but the results are not accurate enough to be of any employed in producing the velocity v, is 2L,ibeingthepro- use witliout a comparison with experiments. per coefficient fw determining the velocity from the height; 393. THEOREM. When the whole of a OF HYDRAULICS. .(«N "JRNiA-.y 63 given quantity of a fluid acts upon a body, its effect is simply as the relative velocity. For the length of the stream being given, the time of its operation will be inversely as the relative velocity, and the eflect being as the pressure and the time, or as the square of the velocity directly, and inversely as the velocity, wriU be simply as the velocity. If the fluid acts in such a manner that the time does not vary, the proposition may be proved from considering simply the quantity of motion that the fluid loses, which must be the measure of the force with which it acts on the solid. 394. Theorem. The rotatory power of a limited stream is greatest when it impels an obstacle moving with half its own ve- locity. For the rotatory power is as the force and the velocity conjointly j now the length of the stream being limited, its force is simply as the relative velocity, or as a—v, a being the velocity of the stream, and v that of the obstacle ; but av — «v is a maximum when oi'~2!)(', or 2ii~o. 395. Theorem. When the surface of an incompressible fluid, contained in a narrow prismatic canal, is elevated or depressed a little at any part above the general level, if we suppose a point to move in the surface each way with a velocity equal to that of a heavy body falling tbrough half the depth of the fluid, the surface of the fluid at the part first affected will always be in a right line between the two moveable points. The particles constituting any column of the fluid are actuated by two forces, derived from the hydrostatic pres- sures of the columns on each side, and these pressures are • supposed to extend to the bottom of the canal, with an in- ■ tensity regulated only by the height of the columns them- selves; and this supposition would be either perfectly or very nearly true if the particles of the fluid were infinitely elastic, or absolutely incomjlressible. The difference of these forces constituting a partial pressure, is the immediate cause of the horizontal motion, and the vertical motion is the effect : and this difference is every where to the weight of the column, or of any of its portions, as the difference of the heights to the thickness of the column, or as the fluxion of the height to that of the horizontal length of the canal. Such therefore is the force acting horizontally on any ele- DMntary column ; but the elongation or abbreviation of the column depends on the difference of tbe velocities with which its surfaces are made to advance, and this elevation or depression is therefore to the whole height, as the varia- tion of the fluxion of the length, produced by the operation of the force, is to the whole fluxion of the length. While therefore one of the supposed moveable points describes 3 given elementary arc, and the column is elevated or de- pressed through its versed sine, which expresses half the second fluxion of the height, its limits will approach each other horizontally through a space as much less, as the fluxion of the length is less than the whole height, and the whole horizontal velocity being as much greater than this relative velocity, as the force is greater than its fluxion, or as the first fluxion of the height is greater than its second fluxion, it follows that the whole horizontal velocity will describe a space equal to half the first fluxion of tlic height, diminished in the ratio of the fluxion of the length to the height ; but if the force were altered so as to become equal to that of gravity, or in the ratio of the fluxion of the height to that of the length, the space described would become equal to half the fluxion of the length, diminished in the ratio of the fluxion of the length to the height ; and if the time were increased in the ratio of the elementary arc, or the fluxion of the length, to the height the space described would be increased in the duplicate ratio, and would be- come equal to half the height : since therefore the move- able point describes a space equal to the depth, in the time that half that space would be described by the action of gravity, its velocity is equal to that which is acquired by a heavy body in falling through half the depth, and the sur- face of the fluid will initially describe a space equal to the versed sine of an arc thus described by the moveable point. In this manner the initial change of situation of every part of the given surface may be determined, and the figure which it^wiU have acquired at the end of any instant may be considered as determining the acceleration of the motion for a successive instant, which will always be such as to add to the space described with the velocity acquired at the beginning of the instant, a space equal to the mean of the versed sines of the equal elementary arcs of the new curve on each side of the point. But the sura of these versed.sincs is always half the sum of the second fluxions of the height of the original surface at equal distancesoneach side, correspond- ing to the placeof the moveable points,.for the extremities of the new elementary arcs being determined by the bisections of two equal ch.ords, removed to the distance of the arc on each side, the sagitta at each end is half of the excess of the increment on one side above the increment adjoining to the corresponding one on the other side, and the sum of the sa- gittas is therefore halfof thesuraof tbe differences of the in- 64 6t HrDRAULICS. crements from the contiguous increments on the same side, and the mean of the sagittas is half of the mean of the se- cond fluxions: but the second fluxion of the space may always be expressed by twice its second increment ; the se- cond fluxion of the space is therefore equal to the mean of the second fluxions of thesagittas corresponding to the places of the moveable points, and the space to the mean of tlie sagittas themselves, since the same mode of reasoning may be extended step by step throughout the length of the surface. The actions of any two or more forces being always ex- pressed by the addition or subtraction of the results pro- duced by their single operations, it may easily be under- stood that any two or more impressions may be propagated in a similar manner through the canal, without impeding each other, the inclination of the surface, which is the ori- ginal cause of the acting force, being the joint effect of the inclinations produced by the separate impressions, and pro- ducing singly the same force as would have resulted from the combination of the two separate inclinations ; and the elevation or depression becoming always the sum or differ- ence of those which belong to the separate impressions. If then we suppose two similar impulses, waves, or scries of waves, to meet each other in directions precisely oppo- site, they will still pursue their course, but the point, in which their similar parts meet must be free from all horizon- tal motion, since tlie motions peculiar to each, destroy each other : consequently a solid obstacle fixed in a vertical di- rection would produce precisely the same effect on either series, as is produced by the opposition of a similar scries, •and would refleci it in a form similar to that of the opposite series. Scholium. The limited elasticity of liquids actually existing produces some variations in the phenomena of waves, which have not yet been investigated; but its effect may be in some degree estimated by approximation. For a finite time is actually required in order for the propagation of any effect to the parts of the fluid situated at any given depth below the surface, and for the return of the impulse or pressure to the superficial pans : so that the summit of every wave must have^ravelled through a certain portion of its track before the neighbouring parts of the fluid can have partaken in the whole effects which its pressure would pro- duce by means of th« displacement of the lower part of the fluid. This cause probably cooperates with the cohesion of the liquid in rounding off any sharp angles which may ori- ginally have existed ; it limits the effect that an increase of depth can produce in the velocity of the transmission of •waves of a finite magnitude, and diminishes the velocity of all waves the more u the depth approaches more to Jhfa limit. If the surface was originally in the form of the harmo- nic curve, it may be shown that the force acting at any time on a given point in consequence of the sum of (he results of the forces derived from the effect of a given portion of a wave which has already passed by, will still follow the law of the same curve : but the force will be diminished in the ratio of the arc corresponding to half the space described by the wave while the impulse returns from the bottom, to its sine, the whole distance of the wave being considered as the cir- cumference; and the velocity will be diminished in the sub- duplicate ratio ; but the arc which, when diminished in the subduplicate ratio that it bears to the sine, is the greatest, is that of which the length is equal to the tangent of its ex- cess above a right angle, or an arc of about 70°^, its sine Is .94 and its lengtli a. 8, the subduplicate ratio that of 1 to .57, andthe velocity will be so much less than that which is due to the height : but v^-ith this velocity the wave will de- scribe a portion equal to |^ of its breadth, while the effect descends and reasccnds to the depth concerned ; and sup- posing the velocity with which the impulse is transmitted through the fluid to be equal to that which is acquired by a body falling through a space equal to \m, and calling the depth h, and the breadth of the wave o, while JiJo is- de- scribed by V, 2/1 is described by that which is due to im, or hy bv' ( — j i andv being .57l'^/{~J, as .57iv(-) '° sis'^> «o '5 *v^ ( —V° ^Aj and 1 .14A ' :i:2^fl ^ m, whence hz:.5{a:'m)'. For water, according to Mr. Canton's ex- riments, m is not more than 7 50,000 feet, but we may ven- ture to call it a million ; then if a, the breadth of the wave, were 1 foot, h would be 50, and the velocity nearly 23 feet in a second. If a were 1000 feet, h would be 5000 ; and the addition of a greater depth could not increase the velo- city. Where the depth is given, the correction may be made in a similar manner. For h being in this case given, we must find the arc which is to its sine in the duplicate ratio of the velocity due to the height to the diminished ve- locity, represented by that arc, while that of the impulse propagated in the medium is expressed by twice the depth- Thus if h were 8 feet, and o a foot, the velocity being u, the arc must be to its sine as 256 to rv, and v to 5660 a^ twice the arc to twice the depth and the arc ^3, or in degrees .blv ; but this arc is somewhat more than 6°, and exceeds its sine so little that the velocity is scarcely dimi- nished one thousandth by the compressibility of the water. The ftiction and tenacity of the water must also tend ia some degree to lessen the velocity of the waves. OF SOUND. 6S SECTION VI. OF SOUND. 396. Theorem. When a uniform and perfectly flexible chord, extended by a given weight, is inflected into any form, difiering little from a straight line, and then suflPered to vibrate, it returns to its primitive state in tlie time which would be occupied by a heavy body in falling through a height which is to the length of the chord as twice the weight of the chord to the tension ; and the intermediate positions of each point may be found by delineating the initial figure, and repeating it in an inverted position below the absciss, then taking, in the absciss, each way, a distance proportionate to the time, and the half sum of the corresponding ordi- nates will indicate the place of the point at the expiration of that time. We may first suppose the initial figure of the chord to be a harmonic curve ; then the force impelling each particle will be proportional to its distance from the quiescent po- sition, or the base of the curve. For the force acting on any element i' ia to the whole force of tension p, as the ele- ments' tothe radius of curvature r (299), therefore the force is inversely as the radius of curvature, or directly as the cur- vature, that is, in this case, as the second fluxion of the ordinate (195) ; but the second fluxion of the ordinate of the harmonic curve is proportional tothe ordinate itself; for the fluxion of the sine is as the cosine, and its fluxion again as the sine ; the force being therefore always as tlie distance from a certain point, as in the cycloidal pendulum, the vibrations will be isochronous, and the ordinates will be proportionally diminished, .so that (he figure will be always a harmonic curve. Now calling the length of the chord «, and the greatest ordinate y, tlie ordinate of the figure of sines being to the length as the diameter of a circle to its a c>rcuniference,.or ::: — , the radius of curvature of the har- c iBonic curve will be — , and the force'acting on the ele- ccy ment z' will be ; but the weight of the chord being aa q, ihat of z' is il ,and the force is to the weight as ccyp to q, or as ff^ to 1: therefore the time of vibration will be to that of a pendulum of the length y as 1 to v' ^^1^1\ and to that of a pendulum of the length atn a ratio as much less as yfy is less than v'a, or as 1 toc.^/". But the time of the vibration of a pendulum of the length a is to the time in which a body would fall through half a, as c to 1, consequently a single vibration of the chord will be per- formed in the time of falling through ? 3, and a double vi- bration in the time of falling through 2a.?. Now the ele- P ment z', moving according to the law of the cycloidal pen- dulum, describes spaces which are the versed sines of arcs, inc'reasing equably (259), and the difference of the sine at any point from the half sum of the sines of two equidiffer- ent arcs, is in a constant ratio to the versed sine of the dif- ference, therefore, by taking the half sum of two equidistant ordinates, we find the space remaining to be described, after a time proportionate to the absciss. If tlie base be divided into two equal parts, and a harmonic curve be described on different sides of each part, the same demonstration is ap- plicable to both parts, as if they were two separate chords : since the middle point will always be retained at rest by equal and opposite forces ; and nothing prevents us from combining this compound vibration with the original one, since, by adding together the ordinates, we increase or di- minish the fluxions and increments, in proportion to the spaces that are to be described, and the same construction of two equidistant ordinates, will determine the motion of each part. Such a compound figure may be made to pass through any two points at pleasure, and it may easily be conceived, that by subdividing the chord still further, and multiplying the subordinate curves, we may accommodate it to any greater numhcr of points, so as to approximate in- finitely near to any given figure ; by which means the pro- position is extended to all possible forms. Scholium. If the initial figure consist of several equal portions crossing the axis, the chord will continue to vibrate like the same number of separate chords ; and it is some- times necessary to consider such subordinate vibrations as compounded with a general one. It usually happens also that the vibration deviates from its plane, and becomes a rotation, which is often exceedingly complicated, and may be considered as composed of various vibrations in different planes. 397. Theorem. The chord and its ten- VOL. II. K 66 OF SOUND. sion remaining the same, the time of vibra- tion is as the length ; and if the tension be changed, the frequency will be as its square root : the time also varies as the square root of the weight of the chord. It has been shown, that the time varies in the subdupli- cate ratio of the force, that is, of the tension directly, and of the weight inversely ; and since the weight varies as the length, the equivalent space will vary as the squate of the length, and the time of describing it simply as the length. Scholium. The properties of vibrating chords have been demonstrated in a more direct and general manner by means of a branch of the fiuxionary calculus which has been called the method of variations, and which is employed in comparing the changes of the properties of a curve existing at once in its different parts, with the variations which it undergoes in successive portions of time from an alteration of its form. An example'of this mode of calculation has already been given in the investigation of the motions of waves (395), and it may be applied with equal simplicity to the vibrations of chords, and to the propagation of sound, notwithstanding tlie intricacy and prolixity with which it has been always hitherto treated. It may be shown that every small change of form is propagated along an extended chord with a velocity equal to that of a heavy body falling through a height equal to half the length of a portion of the chord, of which the weight is equivalent to a force produc- ing the tension, and which may be called the modulus of the tension ; ' and that the change is continually reflected when it arrives at the extremities of the chord ; and from this proposition all the properties of vibrating chords may be immediately deduced. For the force, acting on any small portion of the chord, being to the tension as its length to the radius of curvature, and its weight being to the tension as its length is to the modulus of tension, the force is to the weight as the length of the modulus to the radius. By this force the whole por- tion is initially impelled, since the change of curvature in its immediate neighbourhood is inconsiderable with respect to the whole : and it will describe a space equal to its versed sine, which is to the arc as the arc to the diameter, in the time in which a body falling by the force of gravity would describe a space as much less, as the modulus of tension is greater than the radius, that is, a space which is to the arc as the arc to twice the modulus ; and if the time be in- creased in the ratio of the arc to the modulus, the space described by the falling body will be increased in the du- plicate ratio, and will become equal to half the modulus : If tlierefore a point move in the original curve with such a velocity as to describe the arc, while its versed sine is d^ scribed by the motion of the chord, it would describe the length of the modulus while a heavy body would descend through half that length, and its velocity will therefore be equal to that which is acquired by a body falling through half the length : and supposing a point to move each way with such a velocity, the successive places of the given point of the chord will be initially in a straight line be- tween these moving points. The place of the given point will also remain in a straight line between the two moving points as long as the motion continues. For the figure of the curve being initially changed in a small degree accord- ing to this law, each of the points of the chord will be found in a situation which is determined by it, and its mo- tion will be continued in consequence of the inertia of the chord, and will receive an additional velocity from the ef- fect of the new curvature. The space described in the first instant being equal to the mean of the versed sines of the arcs included by the two moveable points, the velocity, as well as the second fluxion of the versed sine, may be repre- sented by twice that mean : the increment of this velocity in the next succeeding position of the curve will be repie- sented by the new mean of the versed sines, which is al- ways half of the mean of the second fluxions of the ordi- nates on each side ; for the extremities of the new ele- mentary arcs being determined by the bisections of two equal chords removed to the distance of the arc on each side, the versed sine of each is half of the excess of the in- crement on one side above the increment adjoining to the corresponding one on the other side, and the sum of the versed sines is therefore half the sum of the differences of the increments from the contiguous increments on the same side, consequently the fluxion, or rather the variation of the velocity, which is represented by twice the mean versed sine, is equal to the half sum of the second fluxions of the original curve at the parts in which the moveable points are found, and the second fluxion or variation of the space, which is as the variation of the velocity, is equal to the mean of the second fluxions of the ordinates ; there- fore the space described is always equal to the diminu- tion of the mean of the ordinates. And the same mode of reasoning may be extended through the whole curve. If the initial figure be such that two of its contiguous portions, lying on opposite sides of the absciss, are similar to each other, and placed in an inverted position, it is obvious that the point in which they cross the axis must remain at rest, consequently its place may be supplied by a fixed point, and either portion of the cun-e will continue its motion. OF SOUND. when vibrating separately-) in the same manner as if the chord were prolonged without end by a repetition of si- milar portions, of which the alternate ones arc in an in- verted position. 398. Theokem. The times, occupied by the similar vibrations of elastic rods, are di- rectly as the squares of tlieir lengths, and in- versely as their depths. If the length vary, the force at a given depression will vary inversely as its cube, and the weight will vary as the length, consequently the relative force will be inversely as the fourth power of the length ; and where the spaces are given, the times are as the square roots of the forces. The weight is also directly as the depth, and the force as its cube ; the accelerating force is therefore as the square of the depth, and the time inversely as the depth. SCHOHUM. It may be shown that the accelerating force, which acts on any point of an elastic rod, is as the difference of the curvature at the given point from the sum of the curvatures at equal small distances on each side, that is, as the second fluxion of the curvature, or ultimately, as the fourth fluxion of the ordinate. In the harmonic curve, the second fluxion of the curvature, aswell as the second fluxion of the ordinate, is proportional to the ordinate itself; hence it follows that a rod infinitely long being bent into a series of harmonic curves, each of its points would reach the basis at the same instant ; that a finite rod, loosely fixed at both ends, might vibrate in a similar manner ; and that a ring is also capable of similar vibrations, if it be divided into any even number of vibrating portions. The time of such a vibration may be thus determined. The extremities of the rod, when loosely fixed, may be considered as simply sub- jected to a transverse force, since the curvature ultimately disappears : the sum of these transverse forces being equal to the whole of the forces which urge the rod towards the basis, and each of them being expressed by the area of one half of the curve. Now the curvature of a bar fixed at one end, and depressed a little by a weight at the other, increas- es uniformly in advancing towards the fixid point, until the radius of curvature there becomes f32i) : and this 120/ ^ curvature may be represented by the ordinate of the har- monic curve produced until it meets the tangent at the ori- gin ; so that the radius of curvature at the vertex of the har- ... , , ll>m monic curve will be greater than m the same ratio Via/ as the produced ordinate is longer than the original ordinate, that is, as the quadrant of a circle is greater than the tadius, and will therefore be equal to ; but the radius of •248/ curvature is also — (398), I being the length, and y ^ ,■ i*afn . , 19ft' the ordinate, therefore y=,-r-; — , or, smce 2=:2a, r—'- bbc'm blc^m The weight of the element of the rod j;' is to m as x' to the height of thi modulus h, and is therefore n-r-m.andtht h force urging it is to/i as the area corresponding to i', is to yl half the area of the curve, that is, as yx* to — , or as x' to c I . . , cfx' , , /■J'c'mv , cfx" . — , and is equal to —-; but/=— — -= , and -i-— is to the . , iic'my m , Ibc'hy weight as ,' j to -r-x , or as ^ to l ; the time I'll* h 121' of vibration is therefore at much less than that of a pendu- bc^ ny\ lum of which the length isy, as — v'l-.-j is greater than unity, and as much less than that of a pendulum of which the length is 12 A, as — — is greater than unity, and the time of a complete vibration is to the time of falling through 64 as 2l^ to Ich, 399. Definition. A sound, of which, the number of vibrations in a second is any integer power of 2, is denoted in music by the letter c. Scholium. Hence we may form a table of the number of vibrations of each note in a second. i 221 _____ ^^ 8 C 1 1^ ' ' 3i 04 138 c = 4 c c iia 1024 3048 32768 68 OF dov^jy. c c«: (1 eb 0 f tSR g ab ti bb b c i -^^©.fe^o-sXfis: ,(ytot|d^t^o^ ScalesofC. 256 288 307 320341 Equal tem- perament. Progressive X temperaments./*^® 270 28? 3o3 321 341 360 383 405 427 455 481 512, 384 409 427 451 480 512. [•256 271287 304 323 342 36S 384 406 431 456 483 512. 400. Theorem. All minute impulses are conveyed through a homogeneous eUislic medium with a uniform velocity, equal to that which a heavy body would acquire by falling through half the height of the me- dium causing the pressm-e. If a moveable point be urged through a small space by the difference of two forces, varying inversely as its distance from two equidistant fixed points, in the same right line, the times of describing that space will be ultimately equal, whatever be its magnitude. For, calling the distance of each point a, and the space to be described x, the forces TrviU be and , and their difTerence _ a—x a+x aa — xx ,which IS to _ as nx to a ; but smce x is evanescent, this a a ratio becomes that of 2x to a, and the force varies as the space to be described, consequently the times are equal. If therefore all the particles of an elastic medium contiguous to any plane, be agitated at the same time by a motion varying according to any law, they will communicate a motion to the particles on each side, and this motion will be propagated in each direction with a uniform velocity, and so that each particle shall observe the same law in its motion. For, as in the collisions of elastic balls (344), each ball communicates its whole motion to the next, and then remains at rest, so each particle of the medium will communicate its motion to the next in order; the common centre of inertia of two neighbouring particles supplying the place of a fixed point ; and the retrograde motions will also be similarly communicated by the expansive force and pressure of the medium ; and since the magnitude of the motion, while it is considered as evanescent, -does not affect the time of its communication from one particle to the next, the velocity will not be affected by this magnitude, and the whole successive motions will be transferred to the neigh- bouring panicles in their original order and proportion. For computing the velocity, it is convenient to assume Sf certain law for the motion of each particle, and it is simplest to suppose it moving according 10 the law of the cycloidal pendulum. Let AB be the minute space described by the particle A, in one semi- vibration, while the undulation is transmitted through AC- DA, and let DE be a figiue of sines, of which DA is the half basis ; then if EF flow uniformly with the-time, that is, if it increase with the velocity of the undulation, the versed sine FG will be in a constant ratio to (he motion of A (259) ; the velocity of A will be as the fluxion of the space, or of FG, that i?, as the conjugate ordinate HI (142); the fo'ce will be as the fluxion of the velocity, or as FG ; and the force being as the change of density, or as its fluxion, the density, or rather the excess above the na.- tural density, will be again as HI, and the fluent of'tfae pro- duct of HI into the fluxion of the base, will giva the whole excess of density in DA, which will therefore be represented by the figure DAK (190). But when A arrives at B, ihe be- ginning of, the undulation reaches C, and the whole fluid which oci;upied A is condensed into BC, so that its meaa density is increased in the ratio of AC to BC, and AB re- presents the excess above the natural density; therefore let the rectangle DLMA be to DAK, or DKq (203), as BC to AB, or ultimately as AC or DA to AH ; that is, let DA.DL : DKq : : DA : AB, or DL: -DKq AB then DL will represent the natural density, while the ordinates HI every where represent its increase. Let NA be the evanescent length of the particle A, then the force actuating it will be as the difference of the densities at its extremities, or as NO, which is equal to NA (l4l) ; therefore the force impelling A, is to the whole elasticity, as NA to DL. Now if h be the height of a column of the fluid, equal in vreight ta OF SOUND. 69 the whole elasticity, this weight will be to the weight of A as /i to NA ; and the force impelling A being A.NA ; DL, this force will be to the weight of A as h to DL, or as ;, ^^ to 1. Let there be two pendulums, of which the 'DKq lengths are h and AB, then with the same force, they will vibrate in times which are as ^ h and ^/^ AB, and if the force in AB become h. ^^. , the time being inversely in the sub- DKq duplicate ratio of the force, the vibrations will be as v^ A to ^ AB. v/ f^^ ^ or as A to DK ; and in the time of [h.ABj this semivibration in AB, tlie undulation will be transmitted through DA, therefore in a semivibration of h, it will be transmitted through a space greater in the ratio of h to DK, which will be to h as DA to DK, or as half the circum- ference of a circle to its diameter ; and while a heavy body falls through half /i, the undulation will describe /i (25g), its velocity will therefore be equal to the final velocity of the body falling through half A (23l). Accordfng to this theorem the mean velocity of sound should be gifi feet in a second, h being 2788O feet, but it is found to be nearly 1 130, which is one fifth greater than the computed velo- city. The most probable reason that has been assigned for this difference is the partial increase of elasticity occasioned by the heat and rold produced by condensation and ex- pansion. 401. Theorem. The Tieight of the ba- rometer will not affect the velocity of sound; but, if the density vary, the pressure remain- ing the same, the velocity will vary in its subduplicate ratio. For the velocity varies in the subduplicate ratio of the height of a homogeneous atmosphere, and that height re- mains the same while the density is only varied by means of pressure. Scholium. The velocity of the transmission of an im- pulse through an clastic medium of any kind may be more generally determined without the consideration cf any par- ticular law for the variation of the density; and it may be directly demonstrated, that the velocity, with which any impulse is transmitted by an elastic substance, is equal to that which is acquired by a heavy body in falling through half the height of the modulus of its elasticity. The density of the different parts of the medium, throughout the finite space, which is affected by the impulse at anyone time, may be represented by the ordinatcs of a curve ; that which cor- responds to the natural density being equal to the height of the modulus of the elasticity. Tlie force acting on any small portion will be expressed by the difference of the ordinates at its extremities, that is, by the weight of a pojr- tion of the modulus equal in height to that difference ; this force is to the weight, which is to be moved, as the fluxion of the ordinate to that of the absciss; and the velocity with which the density increases will be as the difference of the forces at the extremities of the portions, or as the second fluxion of the ordinate of the curve ; and the increment of the ordinate expressing (he density will be to the whole, as half of its second fluxion to its first fluxion ; while therefore the density varies so as to be represented by the mean of two ordinates at a small distance on each side of the first ordi- nate, tlie increment of the ordinate being represented by the mean versed sine of the arcs, or half the second fluxion, of the mean ordinate, the decrement of the space occupied by the particles will be as much less as the fluxion of the ab- sciss is less than the ordinate, and the whole velocity being as much greater than the difference of the velocities, as the force is greater than its fluxion, or as the first fluxion of the ordinate is greater than its second fluxion, it follows that, in the same time, the particles will actually describe a space equal to half of the first' fluxion of the ordinate, diminished in the ratio of the fluxion of the absciss to the ordinate; but if the forcewere altered in theratioof the fluxion of the ordinate ' to that of the absciss, so as to become equal to that of gra- \ity, the space described would become equal to half the fluxion of the absciss, diminished in the ratio of the fluxion' of the absciss to the ordinate ; and if the time were increas- ed in the ratio of the fluxion of the absciss to the ordinate, the space described would be increased in the duplicate ra- tio, and would become equal to half tlie ordinate ; and if a point move each way through the curve so as to describe an arc while the variation of density causes the ordinate to- be diminished by a space equal to the mean versed sine, it wouJd describe a space equal to the ordinate or the height of the modulus, while half that space wouldbe described by the action of gravity ^ consequently the velocity of the- points would be initially equal to that of a heavy body fall- ing through half the height of the modulus. And that it would always remain equal to this velocity, so that the density of the medium might always be expressed by the mean ordinate, may be shown exactly in the same manner as has already been done with respect to the motions of waves and of vibrating chords. The variation of the velo- city, and the change of place of the particles may be easily deduced from the successive fonms of the curve representing the density ; and the whole eft'ect may also be considered as arising from the progressive motion of the. same curves which express the cotemporary affections of the different parts of the medium, and which will also show the succcs- shestates of any one portion of it- at different times,. 70 OF DIOPTRICS AND CATOPTRICS. SECTION YII. I OF mOPTKICS AND CATOP- TRICS. 402. Definition. Light is an influence capable of entering the eye, and of aflFecting it with a sense of vision. A ray of hght is considered as an evanescent element of a stream of light ; and a pencil as a collection of such rays accompanying each other. 403. Definition. Light is distinguished by its effect on the sense of vision, into white and coloured light; and coloured light into a great number of various hues : but they may all be referred to the three primitive colours, red, green, and violet. 404. Definition. Those substances, through which light passes uninterrupted in straight lines, are called homogeneous trans- parent mediums. 405. Phenomenon. When rays of light arrive at a surface, which is the boundary of two mediums not homogeneous, they con- tinue in the same planes ; but a part of them, and sometimes nearly the whole, is reflected, making with the perpendicular an angle of reflection equal to the angle of in- cidence; and another part is transmitted, making such an angle of refraction, that at the same surface, and for rays of the same kind, the ratio of the sines of incidence and refraction is constant, whatever may be their magnitude. 406. Phenomenon. If the same re- fracted ray return to the surface in an oppo- site direction, it will be transmitted back in the direction of the incident ra3^ 406. Definition. ITie medium, in which the ray is nearer to the perpendicular, is said to have the greater refractive density ; and a ray of light being supposed to pass from an empty space into a transpaient medium, the index of the refractive density of the medium is that number which is to unity as the sine of incidence to the sine of refraction. 408. Phenomenon. When, between two transparent mediums, a third is in- terposed, terminated by parallel surfaces, the whole angular refraction remains un- changed. Scholium. The proportions of the sines of the angles of incidence and refraction may be deduced from the me- chanical laws of motion, whether we consider refraction as produced by a constant attractive force, acting in a given small space on the. particles of light as projected corpuscles, or by the change in the velocity with which an undulation is transmitted through mediums of different densities. For when a moving body approaches a surface obliquely, its ve- locity may be resolved into two parts, one In a direction parallel, and the other perpendicular to the surface ; and the attractive force, being supposed to be perpendicular to the surface, will not affect its lateral motion. Now, since the fluxion of the square of the velocity varies as the flux- ion of the space, and as the force, conjointly (23S), the space and the force remaining the same, the finite increments of the squares of any two perpendicular velocities will also be equal. Calling the whole velocity in the hypotenuse a, and the perpendicular velocity x, the lateral velocity will be ■/(aa — xx) ; and after refraction, we have ,i/{xx+ll) for the perpendicular velocity, and v" (aa+ib) for the whole velocity, which is therefore in a constant ratio to the former velocity a. But the lateral velocity remaining, in any one refraction, constant, may be made radius, and the virhole velocities will be the cosecaiUs of the angles, which, bysi- milar triangles, are inversely as the sines of the same angles, and the ratio of the sines is therefore constant. In the un- dulatory system, the distance between any two points of the surface being made radius, the perpendicular distance which the same undulation passes over, while it travels from the first to the second, is the sine of the respective angle in each medium, and # thesedistances,beingdescribed in the same time, must be in the constant ratio of the Telo- cities appropriate to the mediums. 409. Theorem. The index of refraction # ^^" .^ ^ X ^ ^!>i^^ '' OP DIOPTRICS AXD CATOPTRICS. 71 at the common surface of two mediums is the of the focus of incident rays, the sum, divided quotient of their respective indices. ^ b}' the index of refraction, is equal to the For the indices being r and qr, if the sine of incidence sum of the reciprocals of the rudius, and of from a v.cuum be ;, the sine of refraction in the first me- jj^g distance of the focUS of refracted rayS : dium will be 2., and this interposed medium being ter- tlie distances being considered as negative minated by parallel surfaces, the sine of refraction in the when the respective focl are On the COncave . second medium will be the same as in the absence of the side of the surface. first, or -L, which is toi. as 1 to?. Let AB be the axis, and AC a f-^q ?'' *" ray infinitely near it ; let D be 410. Theorem. The angle of deviation the centre, and e the focus con- a being given, the angles of incidence and re- jugate to A. Call BD, a, ab, fl-action will be equal to the angles at the '^'^^' '' '^' '"''"" °^ refraction, r. and the angle CAB, or base of any triangle, of which the sides are as 1 to the index of refraction, including an angle equal to the angle of deviation. For the sines of the angles of a triangle are proportional to the sides opposite to them. 411. Definition. The point of inter- section of the directions of any two or more rays of light is called their focus y and the focus is either actual or virtual, accordingly as they meet in it, or only tend to or from it. 412. Definition. When the divergence or convergence of rays is altered by refrac- tion or reflection at any surface, the foci of the incident and refracted or reflected rays 415. Theorem. The distances of the are called conjugate to each other ; and the conjugate foci from a plane refracting sur new focus is called the image of the former its sine, s. Then CD : CA : : Z.CAB : /_CVB, the arcs coincidingultimatelywiththeirsines,and z.CDBzr s, and a the angle of incidence ACF=— s+s, whence DCE=:;— a r ACF—{d+a).. But sin. DCE : sin. CDE : : DE : CE, or (d+a). s d , : .—5 : ra a , rdcczrde e—a -de- ■■e, ae. d+a r d:: rda i — a : 1 ■ dc+ae r _ 1 1 rd —d- -a c a ra -<- ,and^-f — ::: — — . But since E is on the con- rd ra rd a e cave side, we must substitute — e for « to make the theorgm general,and 1 — l— ra rd a e 1 _ 1 1 1 c ra ^'' rd focus. 413. Theore-M. In reflections at a plane surface, the conjugate foci are at equal dis- tances from the surface, and in the same perpendiculai'. For in the triangles ABCj DBC, z.ABC=DBC, since EBC=:ABF=:DBF ; and z. ACBrrDCB, and CB is com- mon to both triangles ; there- fore BD=AB, and the triangle BDF=BAF, and DF=AF. 414. Theorem. For rays falling on a spherical surface nearly in the direction of the axis, the reciprocal of the radius being itncreased by the reciprocal of the distance face are in the ratio of the sines ; and both are on the same side. For here azz 33 , and — _ , or rd'ZZe, and both dis- e rd tances are positive, pr both negative. 416. Definition. When the focus of incident rays becomes infinitely distant, the rays are parallel, and the conjugate focus of such rays is called the principal focus of a. surface or substance. 417. Theorem. The principal focus of a spherical reflecting surface is at the dis- tance of half the radius. By making r= — 1 , we accommodate the general theorem for refraction to reflecting surfaces, and — — - + a a a 72 OF DIOPTRICS AND CATOPTRICS. I 141 JL,_ 1 " — , or — — ; and when dzzco, _— ::.. e e a d e a and (!= — \a. 418. Theorem. When diverging rays fall on a concave mirror, the reciprocal of the distance of the focus of reflected rays is the difference of the reciprocals of the prin- cipal focal length and the distance of the focus of incident rays ; and the same is true whea converging rays fall on a convex mirror ; and in either case, when the focus of incident rays is within the principal focal distance, the focus of reflected rays is on the convex side of the surface. J 1 Q The distance iJ being negative,—— — — —, and when e d a — > — ,— being positive, the focus is on the convex a fi e side. 419- Theorem. When converging rays fall on a concave mirror, or diverging rays on a convex mirror, the reciprocal of the focal distance of reflected rays is the sum of the reciprocals of the principal focal length, and of the focal distance of incident rays ; and the focus of reflected rays is in either case within the sphere. Here d remains positive, and — (JL.4.1.\, e \ a d / 420. Definition. A lens i« a detached portion of a transparent substance, of which the opposite sides are regular polished sur- faces, of such forms as may be described by a line revolving round an axis. In general, one of the sides is a portion of a spherical surface, and the other, either a portion of a spherical surftice, or a plane ; whence we have double convex, double concave, plano- convex, planoconcave, and meniscus lenses. It is simplest to suppose the lens of evanes- cent thickness, and denser than the surround- ing medium. 421. Theorem. The reciprocal of the principal focal length of any lens, is equal to the sum or difference of the reciprocals of the radii, multiplied by the index lessened by unity : and when diverging rays fall on a convex lens, or converging rays on a con- cave one, the reciprocal of the principal focal length is equal to the sum of the reci- procals of the distances of the conjugate foci ; but to their difference, when converg- ing rays fall on a convex lens, or diverging rays on a concave one. For the focus after the first refraction wc have — — _L j. e ra — , and changing the signs, on account of the chanre ru a ° of direction of the convexity, — — - ra rd to be sub- stituted for — in the second refraction, where the radius is .a I', and the index — j hence — : T e ._r_ , j; t I 1 _ l> a a d b (r — i)-f-7-H — j — j> and when d= oo,-t- vanishes, and 1 /i i\ 1 — •— ('■ — l)'l "T"H )--~f' '" "'^ concave lens, d be- 1 _ 1 '7 ing negative, ~—-7+—- In the meniscus, the signs not being changed, —c=l.-I-+^+2- — L—(r—i\. \l a J^ d Scholium. Iftheindex be J, as in some kinds of glass, the focal length of a double convex or a double concave lens, will be equal to the common radius ; and of a plano- convex or planoconcave, equal to the diameter : if the in- dex be |, as in water, the focal length will be to that of an equal lens of glass, as 3 to 2. 422. Theorem. The joint focus of two lenses is found by adding or subtracting the reciprocals of their separate focal lengths, accordingly as they agree or differ with re- spect to convexity and concavity ; or by di- viding their product by their sum or differ- ence. For it may be sboivn in the same manner as for two sur- OF DIOPTRICS AXD CATaPTRICS. 73 faces, that — r:-T+-,or — zz— ■ — - (421} ; and e— c J a e J a f±d 423. Definition. The centre of a lens is a point, between which and the centres of the surfaces, segments of the axis are inter- cepted, proportional to the respective radii, and lying on the concave or convex sides of bolh surfaces. 424. Theorem. All rays, which in their passage through the lens, tend to the cen- tre, are transmitted in a direction parallel to their original direction. LetABpass *. A \ // through the g ANy(^^ jj cVi-LJL centre C, and join AD and BE;thensince CD : E : ; AD : BE, AD is psrallel to BE ; and the sur- faces at A and B being also parallel, the ray is equally re- fracted in contrary directions at A and B. Scholium. In some cases, the optical centre may be without the lens, but no practical inconvenience results from considering it as always within the lens, especially when the thickness is evanescent ; and then the two pa- rallel directions of the rays passing through it must coincide in the same line. Now when the focus of incident rays is removed a httle from the axis, the inclination of each ray to the surface being increased or diminished nearly alike, their mutual inclination after refraction or reflection remains but little changed, and the conjugate focus is nearly at the same distance as before. Hence we may find the place of the conjugate focus of a point without the axis ; for since the ray, which passes through the centre of the surface or lens, preserves its rectifmear direction, the focus must necessarily be in this line, and at the distance already determined for rays in the direction of the axis : and thus we have the magnitude, as well as the place, of the image of any object, sufficiently near the truth for common purposes. 425. Theorem. When a ray of light is refracted at the surface of a sphere, the inter- sections of the incident ray with a concen- tric sphere of which the diameter is greater in the ratio of the index of refraction to unity, VOL. II. and of the refracted ray with another con- centric sphere which is smaller in the same proportion, are in the same radius. LetAB:AC::AC:AD:: 1 :r; then the triangles ABC, ACD are equiangular, and ^ACD~ABC. But sin. ABC : sin. .\CB :: AC : AB :: T : 1, and ACB is the angle of refraction correspond- ing to the angle of incidence ACD. This theorem affords an easy method of constructing problems relative to sphe- rical refraction. Scholium. It may easily be shown, that if the ray CD were reflected at D, it would meet the ray CE at E ; and supposing the velocity greater in the rarer medium, in the ratio of the densities, it would arrive there in the same time ; and if DE were again reflected at E, it would coincide with CE again refracted. 426. Definition. When a pencil of rays falls obliquely on the surface of a sphere, the point towards which those rays, which are situated in any plane passing through the axis, are made to converge, may be called the peripheric focus. Scholium. These points form a line of concourse, which is a part of the circumference of a circle; and this is the focus at which the image of a circular circumference becomes most distinct. It has hitherto been in general ex- clusively considered, under the name of the geometrical focus of oblique rays. 427. Definition. The focus of colla- teral rays, situated in a conical surface hav- ing the same axis with the sphere, may be called the radial focus. Scholium. It is obvious that the rays of the collateral planes, which are always perpendicular to the surfoce of the sphere, can only meet in the axis: therefore the points in which the collateral rays of a pencil meet, constitute a portion of the axis. The image of any radiating lines, cross- ing the axis, must evidently be most distinct at the radial focus. 428. Theorem. When rays fall ob- liquely on a spherical surface, the index of refraction being r, the actual cosine of in- cidence t, the cosine of refraction u, and the 74 OF DIOPTRICS AND CATOPTRICS. focal distance of the incident rays d, the distance of the peripheric focus of refracted •n u '■'^"" rays will be -^ •, n=^^- •' rail— at— tt Let AB be d, BC, t, BD, », then CE and DE being the sines of incidence and refraction, are to each other as r to 1, or making EFi^r.EB, as EF to EB, and since CEF be- becomes equal to the angle of refraction, or BED, z.BEF= CBDirCED, and BEF, DEC are equiangular, and DEG is also similar to BEC, and FB : BC : : CD : DG, and if GH||BC, •.: BC:GH=^; also FB : FC :: CD :CG:: FB BD : BH=-^:ir-, and AI : BH (=IG} : : AB : BK, or AB Let AB and AC be two incident rays infinitely near to each other, refracted into the positions BD, CD ; then EF, GH, will be the increments of the sines EI, GI, which are in the constant ratio of r to l. Now the angle at A being to the radius unity as EF GH J . EF to AE, is =— -,, andtheangleatD=— -,and/.A: AE GU ^D; AE — ::r.GD GD : AE. But /.A: /.BKCr: BK ! AB, and z.BKC(=;BLC) : Z.D :: BD : BL, therefore /_K: /_n: : BK.BD : AB.BL :: BE.BD : AB.BG :: r.GD : AE, or te : du ■■: r{e—u) : d+t, det+eitzzdurf—duru, rdue—dle—ltezzrdiiu, and err— — -. If for t and rdu — dl— U u we substitute it and au, taking t and u the cosines to the rdavu , . , , radius unity, we have e=— -, which,wben a— go , ' rdu — dt — all becomes rdim rami -I and if (i=: oo, e — - —tl ' r 429. Definition. The relative centre is the point of intersection of the right lines joining any two pairs of conjugate peripheric foci of pencils of oblique rays, falling on the same point of a curved surface in the same direction. Scholium. For the radial foci, the relative centre is always the centre of the sphere. 430. Theoeem. The relative centre is situated in the bisection of that chord of the circle of curvature which bisects the two chqfds cut off from the incident and refract- ed rays, A I F E. BCq " FB FB BD.FC .: AB: BK=:- AB.BD.FC But since FB AB.FB— BCq FEr:r.BE, FC=r.BD=ru, and FB=ru— «, whence BK: ditru -zne. And it is obvious that AI and HK are the rdu — dt — tt distances of the conjugate foci from the foci of parallel rays coming in a contrary direction, and that their product is always equal to IB.BH. 431. Theorem. For parallel rays fall- ing obliquely on a double convex or double concave lens of inconsiderable thickness, of which the radii are a and b, thedistanpe of the peripheric locus is er: — — r-. -; r ^ '^ a + o ru—t'~. and u being the cosines corresjjonding to the radius unity. This expression is obtained by substitution and reduc- tion, from ez:- for u, t; for d, raduu -, taking for r, — ; for a, — t; and for t, u. rdu — dt — at t rauu ru — t 432. Theobem. The radius of a sphere being a, the actual cosine of incidence t, that of refraction, m, the distance of the fo- cus of incident rays from the given point d, from the centre of the sphere c, the distance of the radial focus from the point of inci- rdaa . . . dence is -r: rr > ^"^d from the centre d.{ju—t) — aa caa Let AB be =:r.AC, thet» J" /. BAC will be the angle of deviation, and BCmru — (; and if DE 1 1 CF, the triangles OF DIOPTRICS AND CATOPTRICS. 75 ABC and DEC are similar, and AC : BC : : DC : CE=: -, and AE-—^, AC ; but AE : AD : : AC : AF AC AD.ACq AC caa d+it b+'i Tab "DC.BC — ACq d.{ru—t)—aa ; also 1 : r :: CA : BA :: — |. If we substitute for EE its ultimate value •a / FA ■=. ~ .ABwiU become . ( ru — t — qa. — — 1. qb—a {qi—ay- \ i + 20/ d.(ru — t) — aa (xtY Now, when x' is small, x'zz ' , since (xx)-—2xx, there- DE.ACq 21- DC.BC — ACq fore since 'El=^(2ay — yy), or ^/(■2a7/), DE or dz:^ —f. yVheaa—CO,f=rd; whenrf=co, ((Z' + 2/)' + 2a i/)z=i'+ —i/; and since the small angle ACEG ._ is equal to EDC+ECD, its'sine may be considered as the CD : DE=rd; and AE : DE :: AC : CF=: rdna fc: . If t and u denote the tabular cosines, /~ ru — t rda , , , /._»■« , and when o::i CO , /~ . d.{ru—t]—a' ■' ru—t 433. Theorem. For parallel rays, fall- / a \ cc 1 of their sines, and srz^(2aj/}.l ' +7 ), sszz^ay .—, cc ss ^{a when i=: 00 , becomes 434. Theorem. The longitudinal aber- X7- "When c la, the aberration vanishes, the point D ration of rays refracted at a spherical surface being in the circumference of the outer circle employed for qc}(T(l +c) . determining the refraction (425). is ultimately— i; ; — .?/, o beina; r—\, a .„ r^. r^, , . ,. , ^ rbiqb-ay-^'^ =" ' 435. Theorem. The longitudinal aber- the radius, b the focal distance of incident ration of parallel rays refracted by a double raySjC-f 6 = c, and 3^ the versed sine of the sire convex or double concave lens of incoiisi- of the surface; and, for parallel rays, -^. qr The focus of the rays ^ ^— i& next the axis being A, the longitudinal aber-e? ration will be AB. Now AC is b.{qa) — aa , and BC=:- ..„ caa.(d.(ru — 4) — aab) , ^„ rdaa andABn- — ; — !— 1 '- — ' but EBz:- (qub — aa).{d.{ru — (] — aaj and AB=EB.iif^-Z?h:!^z::EB.- d.{ru — t) — aa ■(ru—i derable thickness, and of equal radii, the re- fractive density being 1.5, is to the thickness of the lens as 130 to 81. The effect of the aberration at the first surface is modified by the refraction of the second, and instead of — , or — , qr 3 becomes — y ; for the first focal length is — which may 81 q be called — d, and — =: — | — ■ , whence — =: , e ra rd a ee rrdd 1 , , "^ ,1 , , , rraa nearly, and e'zz-—d'; but rftf— z:oaa and ezza. Tad qq rd[qab — aa) r{qab — aaj h \ I) f/_l_o/ o g — qa— ) ; but FD : ED : : GD : HD, and — =-— , whence e'=— d' =~y. Then substituting in the formula " / o i'+2a 27 81 AB : AK, which is ultimately =;EI. ri^qab — ao) / r«— t— rb{qb — a)' — Il6a'(aa + 4a) 16.14 28 f, 4a, we have — ■■ — ■ .t/ — .1/^ — y, 2a(,2aj'' ■' 72^0-^ 76 OF OPTICAI. IXSTRUMENTS. ^- , , , , " . 260 130 ^ , ^. , Which uddeil to — '/, makes , or of the thickness. «i 81 81 SciiOLiUM. In a similar manner it maybe shown, that If the radii are a and ?•, and the versed sines y and z, the aberration will be .y-^ .( ~ -H'-\ qr*[a-\-lij' i^a-^0)' \ rra r l-\ ].;. llcncc, by proper substitutions, the aberration may be expressed in terms of the focal length and one of the radii, and by making its fluxion vanish, the form of the lens of least aberration may be determined. The aberration of a system of lenses may be found in a similar manner, and their proportions may be so determined that the whole aber- ration may be destroyed. 43G. Theorem. The radial image of an object infinitely distant, formed by a double convex lens of equal radii, is a por- tion of a spherical surface of whic-li the radius is to the focal length of the lens as r to r + 1 ; and the peripheric image coincides at the axis with a surface of which the radius is to the focal length as r to Sr + 1 . The focal length for oblique rays is AB=:- -;but if CD ■l(Ui—t) :z.r.AC, C being the centre of cur- vature, AD is (rit — t)a (43i), and drawing the circle DE, AE^ AF.AG (rn + q^na a — —— = — — ^-^=rq+tj = 2(n7-f9).AB. The AJJ (ru — Ija 'ru — t i. ' t /; point B will therefore always be situated in a figure similar to DE, that is, in a circle, and the radius of this circle will CD ra ; but the focal length of the be •irq + iq 'iiq+1q tens being — , the radius will be to the focal length as 2j to 1, or asr to r-J-l. Now the distance of the peri- att pheric focus is -zrAB . It, and the curvature of '2{ru—t) the image may be found by adding the sagitta of any small arc jf in the circle BH to the difference of AB and AB./f. The sagitta belonging to' BH is —^ and ultimately AB.(1— ((;=:AH.(2— 2()=: — , and thesum is — i — ^^—, the radius of curiaturc, which is to the focal length e as r to 3r-f 1. Scholium. Hence the mean radius of curvature of the image at the axis may be called- 'ir+i •, which istoc, when rzz^, or as 3 to 8. It has hitherto been usual to neglect the effect of the obliquity, and to consider the focal length as the radius of curvature of the image ; but it is obvious that this estimation is extremely erroneous. By similar calcu- lations it may be found that the radius of curvature of the image of a right line, formed by a single spherical surface, with a diaphragm placed at its centre, so as to exclude all oblique rays, is equal to the principal focal length of the surface, whatever roay be the distaace of the line. SECTION VIII. OF OPTICAL INSTRUMENTS. 437. Theorem. When an angle is mea- sured by means of Hadley's quadrant, and the ray proceeding from one of the objects is made to coincide, after two reflections, with the ray coming immediately from the other, the inclination of the reflecting sur- faces is half the angular distance of the ob- jects. ^ *,^ A The angle ABC=2CBD, and ~P"~>4b BCE=:2BCF; therefore BAC=: X 2BCF— 2CBD=2CBD (108). and XX divided by this becomes 3r-|-i •, therefore 3r+i 438. Theorem. When an imaoe of an actual object is formed by anj- lens or spe- culum, it is inverted if the rays become con- vergent to an actual focus, but erect if they diverge from a virtual focus; and the object and image subtend equal angles at the cen- tre of the lens ; so that a convex lens and a concave mirror form an image smaller than the object, when the object is at a greater dis- tance than twice the principal focal length; but larger, when the object is within this dis- OF OPTICAL INSTRUMENTS. 77 tance ; and when it is within the principal focus, the magnified image is virtual, and erect : but a concave lens and a convex mirror, always form a virtual image, which is erect, and smaller than the object. For in a lens, if the rays con- verge after refraction, it must be to a point beyond the centre, and the rectilinear rays will de- cussate in the centre ; and if hey diverge, it must be from a point on the same side of the centre with the object, and the rectilinear rays have not cross- ed. In the concave mirror the foci are always on opposite sides of the centre of the sphere, since the sum of the reciprocals of their distance is equal to twice the reciprocal of the ra- dius (418), except when the object is within the principal focus, and then there is an erect virtual image beyond the Surface. In the convex mirror the image is always virtual and erect, being between the surface and the principal focus (419) ; and m the plane mirror the image is obviously erect andeijual to the object. 439. Theorem. The image of any ob- ject formed by a spherical reflecting surface subtends the same angle as the object both from the surface and from its centre. It is obvious that the rays which^ass through the centre must remain in the same right line ; and since in this case aa — ad the distances from the centre are a— d and e—a, and (/and e are the distances from the surface ; consequently the image and object are in both cases the bases of similar tri- angles. 440. Axiom. The intensity of light is inversely as the surface on which any given portion of it is spread. Scholium. Hence the illumination is said to decrease as the square of the distance increases. 441. Theorem. The illumination of the image, formed by any lens or mirror, is equal to that which would be produced by the im- mediate effect of the surface of the lens or mirror, if equally illuminated with the object. Supposing the whole quantity of light that falls on the lens or mirror to be collected into the image, the condensation is in the ratio of the surface of the lens to that of the image. Now the illumination produced by a surface equal to the image at the distance of the lens or mirror, is equal to the illumination produced by the object at its actual distance, supposing the brightness equal, since the linear magnitudes of the object and image are proportional to their distances from the lens or mirror, and the surfaces are as the squares of the distances ; the intensity _of the light falling on the lens is therefore such as the supposed surface would pro- duce; and when this is increased in the ratio of the surface of the lens to that of the image, it becomes equal to the il- lumination produced by the surface of the lens, supposing it similar to that of the luminous objiect. 442. Theorem. The intensity of illu- mination of the image of a luminous point, formed by a spherical surface, is inversely as the fourth power of the cube root of the dis- tance from the centre. The quantity of light which falls on any portion of the surface is as the square of its sine xx, or as the versed sine y i and the lateral aberration varies as the longitudinal aberration and as the aperture conjointly, that is as xy o» as x' ; now the intensity of light is as the fluxion of the quantity of light, divided by the fluxion of the surface, or as 2xi 1 J^> or as—, or inversely as the fourth power of the aper- ture, or of the cube root of the radius of the circle of aber- ration. Scholium. This is not the least circle of aberration but it is probably the circle in which the aberration has the least effect in producing indistinctness, and therefore it must be considered as determining the degree of distinctness bi the image. 443. Theorem. If the whole of the light falling uniformly on an infinitely small sphere were regularly reflected, it would be scattered equally in all directions. The quantity of parallel rays falling on a ring, of which the breadth is z', the evanescent increment of the circle, and represented by a hollow^ cylinder, must be as xx', x being 78 OF OPTICAL INSTRUMENTS. the SIM, or as xy%', y being the cosine : but the angular dissipation after reflection is as the product of twice %' and the sine of twice the arc z, since the light forms twice as great an angle with the axis after reflection as before. But the sine of twice the arc z is lyx, and the product Axyz' is ilways proportional to the former product xyz', expressing the space in which the light was uniformly spread before re- flection ; it will therefore be uniformly spread after reflection. Scholium. If the quantity of light reflected varied ac- cording to any given function of the obliquity, the density of the reflected light would vary according to the same law, considering the obliquity as determined by half the angular distance of the reflected light from the axis. The density of the light reflected by a cylinder varies as the cosine y, supposing none to be lost. 444. Definition. Iu telescopes and compound microscopes, the image formed by one lens or mirror stands in the place of a new object for another. 445. Definition. In the astronomical telescope, the object glas.s first forms an ac- tual inverted image nearly in the principal focus of the eyeglass, and the eyeglass a se- cond virtual and inverted image of the first. 446. Theorem. Tite inagnifying power of the astronomical telescope is expressed by the quotient of the focal lengths of the glasses. For the object and image subtend equal angles at the centre of theobject glass ; and the an- gles subtended by the image at the centre of the eyeglass and object glass are ultimately in the inverse ratio of the distances (199, I4l). 447. Definition. The double mlcro- scrope resembles in its construction the astro- nomical telescope, excepting that the dis- tance of the lenses much exceeds their joint focal length. 448. Theorem. Tlie angular magnitude of an object viewed through a double micro- scope is greater than wiien viewed through the eyeglass alone, in the ratio of the dis- tances of the object and first image, from the object glass. For the first image may be con- sidered as a new object in the focus of the eyeglass (424). 449. Definition. In the Galilean te- lescope, or opera glass, a concave eyeglass is placed so near the object glass, that the first image would be formed beyond it, and near its principal focus. 450. Theorem. In the Galilean tele- scope, the second virtual image, formed by the eyeglass, is inverted with respect to this image, and erect with respect to the object; and the magnifying power is the quotient of the focal lengths. Since, for a con- cave lens —zz— e d — (421), when d is little greater than/, e becomes very 'large ; and the two images are on different sides of the eye- glass. The magnifying power is ultimately the quotient of the distances of the glasses from the first image. 451. Definition. In day telescopes, one or more eyeglasses are added, in order to restore the image to its natural position. Scholium. In the common day telescopes of Rheita, two eyeglasses are employed, of nearly equal focus, and so placed, as scarcely to affect the magnifying power ; but in either case, they may be so disposed as to Vary it at plea- sure ; for such an eye piece is a species of compound rai- croscope. OF OPTICAL INSTRUMENTS. 79 452. Definition. Dr. Herschel's re- principal rays are received and reflected fleeting telescopes resemble, in their effects, somewhat obliquely, in order to allow the the simple astronomical telescope: but the light free access to the speculum. [ 453. Definition. The Newtonian re- for the convenience of fixing the eyeglass in flector has a plane speculum placed in its the jde of the tube. axis, at the inclination of half a right angle. Scholium. Dr. Herschel's construction differs from this only in the omission of the plane speculum. r 454. Definition. In the Gregorian te- smaller concave speculum, which also re- lescope, the object speculum is perforated, verts it : it is afterwards submitted to one and the image formed by it, is transmitted or more eyeglasses, through the aperture, after reflection from a ~ " 4.55. Definition. The telescope of Cas- the first image falls near its principal focus, segrain has a convex speculum instead of and the second is thrown back into the focus Gregory's smaller concave, placed within the of the eyeglass. focal distance of the large speculum, so that Scholium. The image is here inverted. 456. Definition. Dr. Smith's reflect- and prevented by a screen from falling im- ing microscope resembles Cassegrain's tele- mediately on the eye. The radii of the sur- scope, but the rays of light are first admitted faces ar6 equal, through a perforation in the small speculum. 80 OF OPTICAL INSTRUMENTS. 457. Theorem. In all refracting te le- ficopes and microscopes^ the diameter of the object glass is to that of its image formed beyond the eyeglass, as the angle subtended by the magnified image of the object at the place of this image, is to the angle subtended by the object at the object glass. Suppo«ng all the rays to be <:ollected in their foci, those which proceed from the centre of the object glass will meet in each of its images ; and those rays coincide iu direction with the rays from different parts of the distant object which cross in that centre, therefore these will also meet in the same point, and with the same inclination, deter- mining the angular magnitude of the ultimate image at an infinite distance. But the inverse ratio of these angles is the same as that of the magnitude of the object glass to its image, and the successive images to each other : for the images and objects are always as the distance from the cen- tre, and the angles are inversely as the distances. 458. Theorem. The field of view, or the angular magnitude of the part of the object of which the telescope forms an ultimate image, is nearly equal, in the astronomical telescope, to the angle subtended by the eye- glass at the object glass ; the whole image comprehending somewhat more, and its brightest part somewhat less. ^ B The extreme ray being AB, the angle CDB limits the whole image : but no rays coming to the eye- glass from E fall above F, thetefore CDF limits the part fully illuminated. Scholium. If a lens be added at the place of the first image, it will ha\e no effect on the distance of any subse- quent image, nor on the magnifying power, but it will en- large the field of view, by throwing more rays on the ori- ginal eyeglass. But, if the image fell exactly on such a lens, a particle of dust attached to the lens, or any acci- dental opacity, would intercept a portion of the image, since all the rays belonging to each point of the object are col- lected in the respective points of the image : the field glass is therefore generally placed somewhat nearer to the ob- ject glass, both in telescopes, and in the common com- pound microscopes. The best places for the vari6us lenses in an eyepiece are partly determined from similar consi- derations. 459. Definition. Mr. Dollond's achro- matic object glasses are composed of two or more lenses, of different kinds of glass, which produce equal dispersions of tlie rays of dif- ferent colours, with different angular deviar tions; the joint deviation being employed to produce an image, while the equal disper- sions are opposed to each other in such a manner as to prevent a separation of colours. 460. Theorem. The focallengths of the two lenses of an achromatic object glass must be in the ratio of the dispersive powers of the respective substances, at an equal de- viation. If the ratios of the sines be for one glass 1 +m : 1, and l+m+n: 1, and for the other l+p : I, and l+p+1 : 1 ; 71 Q then the dispersive powers will be as — and — . Let the '^ m p focal lengths of the lenses for the first kind of rays be there- fore — and —, then for the second they will be ; — m p m^n. and —2— respectively (421) ; and the reciprocal of the P+1 m p ... 1 "<+" joint focus in the first case — , and m the second — — . n half as much, and EI one fourth. Scholium. If 9^ — 1, or rt~a, this expression fails, the numerator and divisor vanishing : in such cases the value of a fraction is evidently equal to the quotient of the ray within the nucleus, and CD a diameter parallel to evanescent incremenu, or of the fluxions. Now' -■ AB ; call EF, s, then EG perpendicular to CH will be rs, rs to -7- ; and b and the sine of EHG to that of EAF as lince the angles are evanescent, they will be in the same ratio as their sines, and the deviation ECH is — — f — — j-f 1 rob but ECH : EH : EHC : EC al- ?+l } ' s.{rb — a) , and if EI 1 1 CH, it is obvious that the focal q rb — a diitancc EI is half CG or C£ ; and that if AB be diminished rab rait 9+1 rb — a 2 9 rb — a of which the latter factor only fails j and its value may be found by substituting for r, and mak- ing the exponent q variable 5 thus rb:^( yb and the fluxion of ( — y is (h. 1. — J rq, which is to q ai ( h. 1. — Jr. to' 1; and the focal distance become* ,,.(h.l.(l) 2(h.l.r)" ADDITIONS. jifter article 331. 331. B. Theorem. The force acting on any point of a uniform elastic rod, bent a little from the axis^ varies as the second flux- ion of the curvature, or as the fourth fluxion, of the ordinate. For if we consider the rod as composed of an infinite number of small inflexible pieces, united by elastic joints, the strain, produced by the elasticity of each joint, must be considered at the cause of two effects, a force tending to press the joint towards its concave side, and a force half as great as this, urging the remoter extremities of the pieces in a contrary direction ; for it is only by external pressures, applied so as to counteract these three forces, that the pieces can be held in equilibrium. Now when the force, acting against the convex side of each joint, is equal to the sum of the forces derived from the flexure of the two neighbouring joints, the whole will remain in equilibrium : and this will be the case vrhither the curvature be equal thioughou, or vary uni- formly, since in either case the curvature at any point is equal to the half sum of the neighbouring curvatures ; and it is only the difference of the curvature from this half s m, which is as the econd fluxion Of the curvature, that deter- mines the acceleiating force. Jfter article 33S). 339. B. Theorem. The stiffness of a cy- linder is to that of its circumscribing prism as three times tlie bulk of the cylinder to four times that of the prism. The force of each stratum of the cylinder may be consi- dered as acting on a lever of which the length is equal to its distance x from the axis : for although there is no fixed ful- crum at the axis, yet the whole force is exactly the same as if such a fulcrum were placed there, since the opposite ac- tions of the opposite parts would remove all pressure from the fulcrum. The tension of each stratum being also as the distance x, and the breadth being called 2y, the fluxion of the force on either side of the axis will be ix'yi, while that of the force of the prism is 2,r^x, and its fluent 3x'. But' the fluent of iJfyi, or 2v/(l — xx)x^x, calling tlie radius unity, is ^(j — y'x), » being the area of the portion of the section included between the stratum and the axis, of which the fluxion isyi; fur tlie fluxion of i—-i/'x is i/.i — i/'i — 2y xi/z^yx^i — 3y •<=r> :jx*.i:+3i/:i'.i^:4!/x'x; and whenx=i, and y::zo, the fluent becomes ii, while the force of the prism is expressed by |. 84 ADDITIONS. Scholium. It is obvious that the strength and resilience are in this case in the same ratio as the stiffness. The strength of a tube may be found by deducting from the strength of the whole cylinder that of the part removed, re- duced in the ratio of the diameters. JJier article 371. ScHOMtM. The Strain produced by the pressure of a fluid on an elastic substance which confines it, may be de- termined from the principles which have been already laid down respecting the flexure of such substances. Thus if a plank placed in a vertical situation, be suiiported at its two extremities only, and exposed to the pressure of a cistern of water of which the surface coincides with its upper end, the curvature will be every where as ax—x", x being the distance from the surface, and will be greatest where the depth is to the length of the plank as 1 to v' 3. If we wish to find the strength of a circular plate, simply supported at its circumference, we must consider the effect of the curva- tures in two directions at right angles to each other ; and we shall find that the second fluxion of the curvature in a direction perpendicular to a radius of the circle at any point, is simply as the curvature in the direction of the radius. The curvature may therefore be represented by the difference between a constant quantity and the ordinate of an elastic curve, the ordinate itself representing the force immediately arising from the curvature ; and since this curve is supposed to deviate but little from a right line, its ordinates become equal to the mean of the ordinates of two logarithmic curves, and the position of its tangent may be determined accord- ingly. Hence it may be shown, that in order to break such a plate, the height of the fluid must be to the height which would break a square plate of the same length, supported at the ends only, as v'S.h.l. (2 + ^/3) or 2.2811 to i. The height required to break a square plate is twice as great, as if the weight of the fluid were collected in the middle of the length of the square (312). For article 398. 398. Theorem. When a prismatic elas- tic rod is fixed at one end, its vibrations are performed in the same time with those of a .9707/* «»/♦ feet, h will be 1.1907 -^; and if a prismatic rod be loosely supported at two points only, the length of the synchronous pendulum will and in this case, for a cylindrical rod of which d'ls the diameter, h=- did'- the time ddh of vibration being to that of the circumscrib- ing prismatic rod as 2 to the square root of 3. We must suppose the form of the curve, in which the rod vibrates, to be such, that all its points may perform their vi- brations in a similar manner, and arrive at the line of rest at the same time ; on this supposition we may determine the time in which the rod is capable of vibrating ; and if the time of vibration is the same in all cases, the determi- nation will hold good in all ; if not, the problem is not ca- pable of a general resolution ; but there appears to be little or no difference in the simple sounds excited in various man- ners, this variety arising principally from a combination of secondary sounds. The form of the curve must therefore be such, that the fourth fluxion of the ordinate may be pro- portional to the ordinate itself ; its equation may be found either by means of logarithmic and angular measures, or more simply by an infinite series. The conditions of the vibration must determine the va- lue of the coefficients : supposing the loose extremity to be the origin of the curve, the curvature and its fluxion must begin from nothing : for the curvature at the end cannot be finite, nor can its fluxion be finite, since in these cases an infinite force, or a finite force applied to an infinitely small portion of the rod, would be required, and the force could not be proportional to the ordinate ; the initial ordinate must also be independent of the absciss ; in the case of a rod fixed at the end, the ordinate and its fluxion must both vanish at the fixed point ; and in the case of a tod not fixed, the second and third fluxions of the ordinate must also va- nish at the remoter end, and the centre of gravity of the curve must remain in the quiescent line, the whole area, con- sidered as belonging to either side of the basis, becoming equal to nothing ; a condition which will be found identical pendulum of which the length is I being the length, d the depth, and h the with that of the third fluxion vanishing at the remoter end. , . , . , , , I- 1 ^- •, I -c The series for a c^l^ve, in which the fourth fluxion of the heieht of the modulus or elasticity : also \t n , . , , v r ,. ^ ' o •' ordinate is to be as the ordinate, can only be of this form, denote the number of complete vibrations in j^^, ,,i„^. „^ i.^x^ a second, the measures being expressed in ^""''■^s.3.4.i' 3.3.4.5.6.-. si' ••■■*'T'"*' 2.3.4.5^* h'eaa^ dax* , Idax' + ir+; ADDITIONS beax' 85 2 . . gJ'^ " ■ ■ I' ■ 3 . . ei" ■ ■ ■ P ' i . .yP + . , . , for the fourth fluxion of this expression, divided by b, is of the same form with the expression itself ; and the number of terms allows it to fulfil all the conditions that may be required. In both the cases here proposed, the co- efficients d and e vanish, because the second and third flux- ions are initially evanescent, and the equation becomes y=a+ l-a.T* b'ax'^ b'ax" i '""'"^i '"'"^ b^cax^ 'a . .' gP In the first case, when b x—l,OT-'^l, y—0, and i'^0, whence 1-) — b* P Q . . 8 2 . . 12 + ...+C + b be 2 . . 5 b-c 2 . . 9 . 4 b'c ■*-... =0, and 1 1 — + <•+ 13 be t'c iV 1+- 2 . . 8 b . 12 b' 11 2 . .4 + . . . =0 ; therefore — cz:: — + • • . , and z: 2 . . 12 i + - 2 . . 5 b . V -+■- 2 . . 9 2 . . 7 2 2 . :+.■ 13 1 + b b' 2 . 4 a . r+a, i^ Hence, by mul- 12 tiplying the numerator of each fraction by the denominator of the other, and arranging the products according to the 1 4 Powersoft, we obtain the equation i b+ i'— 3 .4 3 . .8 — — i'+ . . .=0, which has an infinite number of roots; 3. . 12 * the first two being ir:i2.3623, and ^=489.4. In a simi- lar manner we obtain, for the second case, making the se- cond fluxion of y, and either its third fluxion, or the area, 16 here call d : but the weight of the particle x' is -- x', and A ddh "y . . „, the force is to that of gravity as — r-;-"^ '* '° unity. Now y _ ba.x" , . . . , ; for, when x is evanescent, the subsequent terms XX ll are inconsiderable in comparison with this, and the force is , the space to be described being a ; and if the spate 12i' 12^4 became , and the force equal to that of gravity, the bddk vibration would be performed in the same time : this is therefore the length of the synchronous pendulum ; that is, •9707 1* for the fundamental sound, in the first case j., , and in be thesecond.023976-^Tr' A pendulum, of which the length is ^^j, feet. makes and ddh / h 39.13\ .^ . . I . I vibrations m a second, \.9707 1.2 / ' — ^( .— ^ )=:n double vibrations, such as 2/'^ \.9707 12 / /nll\i A=l.igo7( — ) • And in the same manner, for a rod vanish when x:=2, the equation b -f. 3.4 3 . .8 ^3..ia 106 CATALOGUE.- —COLLECTIONS « Vol.4. n, 45 . . 56. 1669. Vol.44.ii. n.482 . . 484. 1747. 5. 57 . , . 68. 1670. 45. 485 . . 490. 1748. 6. 69 . . . 80. 1671. ' 46. 491 . . 497. 1749—50. 7. 81 , , . 91. 1672. 47. 1751—2. 8. 92. . 100. 1673. 48. i. 1753. 9. 101. . 111. 1674. , ii. 1754. "10. 112. . 122. 1675. 49. i. 1755. )]. 123 . . 132. 1676. ii. 1756. 12. 133. . 142. 1677—8. 50. i. 1757. 13. 143 . . 154. 1683. ii. 1758. 14. 155 . . 166. 1684. 51. i. 1759. 1.5. 167. . 178. 1685. ii. 1760. 16. 179. . 191. 1686—7. 52. i. 1761. 17. 192 . .206. 1691—3. ii. 1762. 18. 207. .214. 1694. 53. 1763. 19. 215. .235. 1695—7. 54. 1764. 20. ^ 236. .247. 1698. 55. 1765. 21. ,248. .259. 1699. 56. 1766. 22. 260. .276. 1700—1. 57. 1767. 23. 2?7. . 288. 1702—3. 58. 1768. 24. 289. . 304. 1704—5. 59. 1769. ^5. 305 . . 312. 1606—7. 60. 1770. 26. 313 . .324. 1708—9. 61. 1771. 27. 325 . .336. 1710—2. 62. 1772. 28. 337 . 1715. 63. 1773. 29. 338 . . 350. 1714—6. 64. 1774. J SO. 351 . .363. 1717—9. 65. 1775. R.I. 31. 364. .369. 1720—1. Philosophical transactions of the Royal So- 32. 370 . .380. 1722—3. ciety of Lond( an. 33. 381 . . 391. 1724—5. Vol. 66. . . 81, 1776. . 1791- 34. 392 . . 398. 1726—7. For the year 1792 . . . 4. London. 35. 399. . 406. 1727- 8. R.I. 36. 407 . .416. 1729—30. Maty's general index to the philosophical 37. 417 . .426. 1731—2. transactions, to the end of the 70th volume. 38. 427 . .435. 1733—4. 4. Lond. 1787 . R. I. 59. 436 . . 444. 1735—6. *Philosophical transactions to 1 750, abridged 40. 445 . . 451. 1737-8. by Lowthorp, Jones, Eames, and Martin. 41. 452 . .461. 1739 — 41. 1 1 V. 4. Lond. (Vol. i. to vii. R.I) 42. 462 . .471. 1742—3. Abrege des transactions philosophiques, re- 43. 472 . .477. 1744—5. dige par M. Gibehn" 13 v. . 8. Par. 1787 44. i. 478 . .481. 1746. —91. R.I. CATALOGUE. COLLECTIOKS. 107 Sprafs history of the Royal Society. 4. Lond. 1687. *Birch's history of the Royal Society, as a supplement to the philosophical transac- tions; to 1687. 4. V. 4. Lond. 1756—7. R. I. *Hookt's philosophical collections, n. 1..7, 16/9—82. 4. Lond. R. L Derham's miscellanea curiosa, being the most valuable discourses read and delivered to the Royal Society 3 v. 8. Lond. 1723. R. L Philosophical transactions abridged b}' Hut- ton, Shaw, and Pearson. 4. Lond. 1803. B.B. Imperial Academy der Naturforscher, 1654. Miscellanea curiosa. Decur. L . IIL 4. Nu- remb. 1670. .1706. B. B. Ephemerides academiae Caesareae. Cent. L X. 1712. .1722. B. B. Acta physicomedica academiae Caesareae, 10 V. 1727 ..1754. B.B. Nova acta academiae Caesareae. Nuremb. 1757 ... B.B. Abhandlungen der Kaiserlichen academic. 4. Nuremb. 1755... Kellneri index rerum memorabilium in E. N. C. 4. Nuremb. 1739- B. B. Bilchneri historia academiae naturae curio- sorum. 4. Hal. 1756. B. B. Archiducal Academy del Cimento, 1657. *S(tggi di naturali esperienze fatte nel' aca- demia del Cimento. f. Flor. 1667. 1691. R. L With additions, in Tozzetti Aggrandlmenti delle scienze fisiche. 4. 1780. H. B. B. Tentamina academiae del Cimento, a Mus- schenbroek. 4. L. B. 1731. M. B. Experiments of the academy del Cimento, translated by Waller. 4. Lond. Extr. Ph. tr. 1684. XIV. 757. Journal des savans. 12. Paris. 1665 . . . R. L Royal Academy of Sciences at Paris, iflCfl. *(A. P.) Histoire et memoires de TAcademie royale des sciences depuis I666, jusq'a 1699. llv. 4. Par. 17S3. Annee 1699 . . . Par. 1702 ... R. L Reprinted 12. Amst. l692...(To 1754.R.I.) Recueil des pieces qui ont remporte le prix. Par. 1721 . . . 1771. M.B. *(S. E.) Memoires de mathematique et de physique presentes a I'Academie. 1 1 v. 4. Par. 1750 R. L *(Mach. A.) Machines et inventions approu- vees par I'Academie. 7 v. 4. 1735 .. 1777. Vol.L 1666... n. 1702. ..HI. 1713.. .IV. 1720 ... V. 1727 ... VI 1732. VII. 1734.. 54. R.I. RozierTahle des articles, depuis l666jusqu'en 1770. 4 V. 4. 1775—6. 11. I. Duhamel H'istoiia academiae regiae scientia- rum. 4. Par. I698. B. B. j^c^a eruditorumLipsiensia. 4. Leipz. 1682... 1731. B. B. Nova actaeruditorum. 4. Leipz. 1732 . . 1776. B.B. Academy of Sciences at Siena, 1891. *Atli deir academia di Siena. 176O. 4. Siena. 1761 . . . B. B. Harris Lexicon technicum. f. Lond. 1699. 1704. M. B. Extr. Ph. tr. 1704. XXIV, Royal Society of Sciences at Berlin, 1700. Academy, 1743. * Miscellanea Berolinensia. 7 v. 4. Bcrl. 17 10 ..1743. B. B. *Histoire et memoires de I'academie royale des sciences et belles lettres de Berlin. 25 v. 4. Bed. 1746.. 1771. B. B. *Nouveaux memoires de I'academie royale. 16 v. 4. BerL 1770 . . 1787. B. B. * Memoires de I'academie royale. 1792 . . . B.B. Histoire de I'academie royale depuis son ori- gine jusqu' a present. 4. Berl. 1752. B. B; 108 CATALOGUE. — COLLECTIONS. Institute of Bologna, 1712. *(C. Bon.) Commentarii de Bononiensi sci- entiarum et artium instituto atque acade- mia. 4. Bologn. 1731 . . . B. B. Imperial Academy of Sciences at Petersburgh, 1725. *(C. Petr.) Commentarii academiae Petropo- litanae. 14 v. 4. Petersb. 1726 . . 1752. B.B. *(N. C. Petr.) Novi commentarii academiae Petropolitanae. 20 v. 4. Vol. 1. 1747 — 8 ... Petersb. 1750 .. . 1770. B. B. *(A. Petr.) jicta academiae Petropolitanae. 1777 ... 1782. B.B. *(N. A. Petr.) Nova acta academiae Petro- politanae. Praecedit historia academiae, ad annum 1783. 4. Vol. I. .. Petersb. 1787 ... Royal Academy of Sciences at Upsal, 1725. Acta literaria Sueciae. 4 v. 4. Ups. 1720 . . 1739. B. B. Acta societatis rcgiae Upsaliensis. 5 v. Ups. 1744.. 1751. B.B. Nora acta societatis Upsaliensis. 4. Ups. 1773 . . . B. B. Commercinm litterarium Norimbergense. 15 \. Nuremb. 1731 .. 1745. B. B. Royal Academy of Sciences at Stockliolni, 1739- J'fonw/. Svenskavetenskaps acadcmiens band- lingar, 1739 ... 8. Stockh. 1740 . . 1779- B.B. Nya handlingar. Vol. I. . . 1780 . . . B. B. *(Scb\v. Abb.) AbhandhiJigen der kciniglicben Schwedischen akademie, von K'astnerund andern. 40 v. 8. Hamb. 1749 . • . Neue Abhandlungen, 1780 ... 8. Leipz. 1784 . . (To 1790. 11. I.) Physical Society at Danzig. f'ersucht und Abhandlungen der naturfor- schenden Gcsellschaft in Danzig. 3 th. Danz. 1747 . . 175G. B. B. Neue sammlung. 8. Danz. 1778. Royal Society of Denmark. Skrifter, som udi det Kiobenbavnske Sel- sbab ere fremlagde. 12 v. 4. Copenb. 1745 . . 1779. B. B. In Latin, Scripta societatis Hafniensis. 3 v. 1745. . 1747. Acta literaria universitatis Hafniensis. 177*. 4. Copenh. 'Nt/e Samling af det kongelige Danske viden- skabers selskabs skrifter. Cop, 1781 . . . B.B. Abhundhmgen die von der D. G. den preis erbalten. Copenh. 1781. Ilamhirsisches Masrazin. 26 v. 8. Hamb. 1747 . . 1763. Neues Hamburgiscbes magazin. 8. Hamb. 17O7 . . 1781. B. B. Royal Society of Sciences at Gottingen, 1750. *(C. Gott.) Commentarii societatis regiae scientiarum Gottingensis. 4 vol. 4. Gott. 1752, 1755. B. B. *(N. C. Gott.) Novi commentarii societatis Gottingensis. 8 v. 4. I769 . . 1778. B. B. *(Conimentat. Gott.) Commeutatloms socie- tatis Gottingensis. 4. 1778 . . . B. B. Deutsche schriften von der koniglichen so- cietal zu Gottingen. 8.' Getting. 1771. B.B. Assemhlee publique de I'academie de ^lont- pelier. 1751. Pki/sikalische Belnstigungcn. SO st. 8. Berl. 1751 . . 1756. B. B. Society of Basle. Acta Helvetica physicomathematicobotani- comedica. 4. Basil. 1751 . . 1777. B. B. Nova acta Helvetica. Vol. I. Bas. 1787. B.B. Society of Edinburgh. *Essaijs and observations, physical and lite- rary, of a society in Edinburgh. 3 v. 8. Ed. 1754. . 1771. R.I. CATALOGUE. — COLLECTIONS, loy ♦"(Ed. tr.) Transactions of the Royal Society of Edinburgh. 4. v. 1788 . . . R. I. Dutch Society of Sciences at Haarlem, 173-2. Verhandelingen uitgegeeven door de Hol- landse maatschappy der weetenschappen te Haarlem. 8. Haarl. 1775 . . . In German, by K'astner. Altenb. 8. 1785. AUgemeines Magazin. 2 v. 8. Leipz. 1753 . > 1767. Electoral Academy of useful Sciences at Erfurt, 1 7 5-1. j^ctoacademiaeeiectoralisMoguntinaescien- tiarum utilium quae Erfordiae est. 8. Vol. I.. Erf. 1751. . . B. B. Dresdniscltes Magazin. 2 v. 8. Dresd. 1759 . . . B.B. Physical Society at Zurich. Abhandhingen der naturforschenden gesell- schaft zu ZUrich. 3 v. 8. Zurich, I76I . . 176G. . .B.B. Electoral Bavarian Academy of Sciences, 1759. Ahhandlmigen der Baierischen academic. 4. Munich. 1763 . . . B. B. Royal Society of Sciences at Turin, 1 760. *(M.Taur.) Miscellanea })liilosophicomathe- matica societatis privatae Taurinensis. 4. Tur. 1759. B.B. *(M. Tur.) Melanges de la societe royale de Turin. 4. Vol. 2 . . 5. Tur. 1761 . . 1776. (To vol. 3. B. B.) *Memoires de I'academie de Turin. 5 v. (Vol. 3 . . 5. B. B.) Brcmisches mixgazin. 7 v. 8. Bremen, 176O. . 1764. Neues Bremisches magazin. 8. Brem. I676 . . . Royal Society of Norway. Trondliiemske selskabs skrifter. Copenh, 1761 . . 1774. B.B. In German, Copenh. 1765. .176?. 3 v. 8. Det Kongelige Morske videnskabers selskabs skrifter. v. 4, 5. 8. Copenh. 1768 . . 74. B.B. Nye Samling af dct kongelige Norske vi- denskabers selskabs skrifter. 8. Copenh. 1784. B;B, Electoral Palatine Academy of Sciences, 1763. Historiaet commentationes academiae scien- tiarumetelegantiorumliterarumTheodoro- palatinae. 4. Manh. 1776 ... B. B. Zealand Society at Vliessingen, 17C5. Ferliandelingcn u'ltgegeeyendoor lietZeeuvvsch genootschap der vvetenschappen te Vlis- singen. 8. Middelb. 1769. B.B. Berlinisches magazin. 8. Berl. 1765 — 7- B.B. .Bfr/««/sc/(e sauimkingcn. 8. Berl. 1768 — 79- B.B. Stralsundischesmagaz'm.'^. Berlin. 1767 . . . B. B. Mannichfaltigkeiten. 8. Berl, 1769 . . . Batavian Society of Experimental Philosophy at Rotter- dam, 1769. Vtrhandelitigen van het Bataafsch genoot- schap der proefondervindelyke wisbe- ' geertc. 4. Rotterd. 1774 ... B. B. Hessian Academy of Sciences at Giessen, Ada philosophicomedica academiae scicn- tiarum principalis Hassiacae. 4. Giessae, 1771. B.B. • American Philosophical Society at Philadelphia, J 769. (Am. tr.) Transactions of the American phi- losophical society for promoting useful knowledge. 4. Philad. 1771 ... R.I. Neue physikalische Belustigungen. 8. Prag. 1770 ... Imperial and Royal Academy of Sciences at Brussels. Memoires de I'academie des sciences et belles lettres de Bru.xelies. 5 v. 4. 1777 — 88. B.B, Journal de physique. *Ilozierf Introduction aux observations sur no CATALOGUE. — COLLECTIONS. la physique, sur I'histoire naturelle, et sur les arts. 2 v. 4. Paris, 1777. B. B. * ObseiTotmiS' sur la physique, par Rozier, Mohgez, et Lametlierie. Paris, 1773 — 92. B. B. Lametherie, Journal de physique, de chimie, et d'histoire naturelle. 4. Par. an 2 . . . R.I. Physical Society of Friends at Berlin, 1773. Beschaftigungm der Berlinischen Gesell- schaft naturforschender Freunde. 4 v. 8. Berl. 1775—9. B. B. Sckriften, 11 v. 1787-93. B. B. Vol. 7. is also entitled Beobachtungen, vol. 1. Nc«e Schrrften. 4. Berl. 1795. B.B. Iliitton's diarian miscellany, from 1704 to 1773. 5 V. 12. Hutton's mathematical and philosophical dictionarj'. 2 v. 4. R. I. The Preceptor. 2 v. 8. London. Erxfebens physikalische bibliotliek. 4 v. 8. 1 . .Gottingen, 1774—79. B. B. A review. Mathematical Society of Bohemia. . Mhandlungen einer privatgesellschafft in Bohmen. fi v. 8. Prag. 1775 — 84. B. B. Abhandlungen der Bbhmischen gesellschafti der wissenschaften. 4. Prag. 1785 . . . B. B. Ebivhard's philosophisches magazin. Bcrnisches Magazin. 8. Bern, 1775. Scelta di opuscoli interessanti, 3Q\\ 12. Mil. 1775—7. B. B. Opuscoli scelti suUe scienze e suUe arti. 4. 18 V. Mil. 1778—95. B. B. BrugnatelU biblioteca fisica d'Europa. 8. Pavia. Crf/Zs chemisches journal. 8. Lemgo, 1778 —81. B. B. Crelh neueste entdeckungen in der cheniie. 8. Leipz. 1781 — 4. Crelh chemische annalen. 8. Ilelmstadt, 17S4. ..B.B. R. I. Genevan Society for Arts and Agriculture. Mtmoires de la societe ^tabiie a Geneve. Gen. 1778. R. I. Sammtuiigen zur physik und natingeschichte, 4 V. 8. Leipz. 1778—92. B. B. \Gottiugischts magazin der wissenchaft und 1 1 litteratur, von G. C. Lichtenberg und G.I Forster. 8. Gott. 1780 — 5. B.B. Leipziger magazin zur naturkunde, mathc- matik, und okonomie, von Funk, Leske, und Hindenburg. Leipz. 1781 — 4, B.B. Leipziger magazin zur naturkunde und oko- nomie, von Leske und andern. Leipz. 1786—8. B. B. Leipziger magazin der reinen und angevvand- ten mathematik, von Bernoulli und Hin- denburg. 1786. . . 'Gothaisches magazin fur das neueste aus der J physik und naturgeschichte, . von L. C. I Lichtenberg und J. H. Voigt. 8. Gotha, 1781 . . . B. B. * Memoire di mathemutica e fisica della so- cieta Italiana. Veron. 4. 1782 ... B. B. Nouveaux memoires de I'academie de Dijon, pour la paitie des sciences et arts. 1782... Dijon, 1783 ... B. B. * (E. M.) Enci/clopidie methodique. 4. Pa- ris, 1782. . . R.L (E. M. A.) Arts et metiers. 8 v. (E. M. M.) Manufactures el arts. 4 t. (E. M. PI.) Plates of the Encyclopedic. These have sometimes been quoted merely to save the labour of referring to the text. *(S. A.) Transactions of the society for the en- couragement of arts, manufactures, and commerce. 8. London, 1783 ... R.L Began to distribute premiums, 17 Ji. CATALOGUE. — SINGLE AUTHORS. Ill Physikaliscke aibeiten der eintrachtigen freunde in Wien, aufgesammelt von Born, 4. Vienn, 1783- 87. B. B. Memoires de la societe des sciences physifiues de Lausanne. 4. Vol. 1. Laus. 1784. B. B. *Memoirs of tlie literary and philosophical society of Manchester. 8. Vol. 1 . . War- rington, 1785. . . llepr. Lond. R. I. (Am. Ac.) Memoirs of the American acade- my of arts and sciences. 4. Boston, 1785. B.B. *(Ir. Tr.) Transactions' pi the Royal Irish aca- demy. 3 V. 4. Dubl. 1787—9. R. I. Vol. 4. Dubl. (As. Res.) Asiatic tesearches of the society of Bengal. 4. Calcutta. 1788 . . . B. B. Atmales de chimie, par Morveau, Lavoisier, Monge, Berthollet, Fourcroy, Dietrich, Hasseufratz, et Adet. 20 v. 8. Par. 1789. • . R. L Annates de chimie, par Guyton, Monge, Berthollet, Fourcroy, Adet, Seguin, Vau- quelin, Pelletier, Prieur, Chaptal, et Van Mons. Vol. 21 . . . Par. 1797 ... R. L ♦Grfws journal der physik. 8. Halle, 1790... *Gilherts journal der physik. 8. Halle, 1799 . . . R. [. *Memoires de I'lnstitut national. 4. Paris, 1798 ... R. 1. * Bulletin de la societe philomatique. 4. Paris. R. L Monthly magazine, London. (From Vol. 9. R. L) ' *Repertory of arts. London, 1794 . • • R. L Magazin encyclopedique, par Millin, Noel, et Warens. 8. Par. an 3 . . . B. B. Hindenburgs archiv der mathematik. 2 v. 8. Leipz. 1795 ... R. I. Pictet, Bibliotheque Britannique, Geneva, 1796... R.I. Beckinamis history of inventions and disco- veries, by Johnson. 3 v, Lond, 1797. R. t. Auswahl der neuesten abhandlungen. 2 v. in 1. Quedlinburg, 1797. R.I. *(Enc. Br.) Encyclopaedia Britannica. 18 v. 4. Supplement. 2 v. Edinburgh, 1797 . • 1800. R.I, *(Nich,) Mc/«o/son's journal of natural philo- sophy, chemistry, and the arts. 5 v, 4.' London, 1797—1801. R.I. (Nich. 8.) New series. 8. London, 1802 , . . R. L *(Ph. M.) Tillock's philosophical magazine, Lond. 1798 ,. . R.L y/««a/s of philosophy. 8. London, 1800,.. R.L Annales des arts et manufactures. 8, Paris. R.I. Jourtuil polytechnique, 4. Paris. R. 1. Gehters physikalisches wcirterbuch. 5 v. 8. Leipz. 1798. R.L ^«r/€rso«'s recreations. 6v. 8. Loud. 1799. •• R. I. Commercial and agricultural magazine. 8. Lond. 1799 ... R.L Memoires sur I'Egypte. 8. Par. an 8 ... R. I. MemoiresAu musee de Paris. Sciences. Vol. 1 1. 8. Par. an 8. R. I. Decfl^e literaire et politique. 8. Par. an 8 ... R.L Willich/s domestic encyclopaedia. 4 v. 8. Lond. 1802... R,L COLLECTIONS OF THE WORKS OF SINGLE AUTHORS. * Aristotelis o^itxB, ommSi. f. Lyons, 1590. *B«co?t's works. 5 v. 4. London, 1765. R.L B.B. JBrtcon's works, by Shaw. 3 v. 4. Lond. 1733. * Archimedes, f. 0.\f, 1792. R.L R.I, 11« CATALOGUE. SINGLE AUTHORS, *Galilaei Galilael opera. 4. Bologna. R. I. Barrow's works. 3 v. f. Lontl. 1683. M. B. *Cartesii opera omnia. 4 v. 4. Amst. 1692. Mostly M.B. Dechaics Cursus niathematicus. 3 v, f. Lyons, 1674. M. B. Extr. Phil. Trans. 1674. IX. *Bo!//c's works. 3 v. f. Lond. 1665, 1744. M.B. TorriceUii opera matheniatica. M . B. *Hugemi opera varia, a Gravesande. 2 v, 4. Leyden, 1724. R.I. *ff?/gf»»i opera rcliqua. 2 v. 4. Amst. 1728, R.I. *Hooke's posthumous works, by Waller, f, Lond. 1705. R.I. •JYooAe's Cutlerian lectures. 4. R.I. *Mnriotte Oeuvres. 2 v. 4. Leyden, 1717. Vol. 1. M, B. *JVallisii opera, 3 v. f. Oxf. 1713. R.I. **Newtoni opera, edente Horsley. 5 v. 4. Loud. 1779. R.I. Leibnitii opera, a Dutens. 6 v, 4. Genev. 1768. R. I. Pascal Oeuvres. R. I. Fossil opera. R.I. Leeuwenkoek's select works. 4 v. 4. Lond. 1798. R.I. _ JoaH«js Bernoullii opera. 4v, 4. Laus. 1742. R.I. Jacobi Bernoullii opera. 2 v. 4. Genev. 1744. R. I. Leonardi Euleri opuscula varii argnmenti. 3 V. 4. Berlin, 174,6 — ol. MaiipertuisOcuvres. 4 v. 8. Lj'ons, 1756. R. I. Rohim's mathematical tracts, 2 v, 8. Land. 1761. R.I. lioUmamii commentationumsylloge. 4. Gott, 1764. R.S. Sylloge altera. 1784. i-Vaw/n/iVs works. 2 v. 8. London. R.I. Ftrgmons tables and tracts on arts and sciences. 8. R.S, Emerson's cyclomathesis. Emerson's nii3celianie.s. Mayeri opera inedita, a Lichtenberg. 4. Gott. 1774. R.S. Priftgle's six discourses. 8. itaesfwendissertationes mathematicae etphy- sicac. 4. Altenb. 1776. Achards chymisch physische schriften, 8. Berl. 1780. Fontana Opuscoli scientific!. Flor. 1783. Setiibier Essais de physique et de chimie. Bergmann Opuscula physica et chemica. 6 v. 8. B.B. Garnett's tracts. 2 v. 8. R. I. Jngenhousz Vermischte schriften physischen und medicinischen inhalts, von Molitor. 2v.~8. Vienn. 1785. Ilutton's tracts, mathematical and philoso- phical. 4. London, 1786. R. S. Basse, Kleine beitrage zur mathematik und physik, Leipz. 1786. Links beytr.nge zur physik und chemie. Vol. I. 8. Bostoch, 1797. Rumford's essays, political, economical, and philosophical. 3 v. 8. Lond. 1800. R. I. Rumford's philosophical papers. Vol. I. 8. London, 1802. R. I. CATALOGUE. — MATHEMATICS, GEXERAI.. 113 MATHEMATICS IN GENErxi\L. The numerous jpapers purely mathematical, contained fn the memoirs of foreign academies, are in general omitted in this catalogue. Mathematici velere^. f. 1(593. R-T. Pai)j)i coUectaneii matliematica. Pellii idea Matheseos, about l638. Hooke Ph. coll. V. 127. Mersennus in Pellii ideam. 1639- Hooke Ph. coll. V. 135. Cartesius de Pellii idea. Ilooke Ph. coll. v. 144. Pellii responsio. Hooke Ph. coll. V. 137. Barrow Lectiones opticae et geometricae. 4. Lond. 1669. Extr. Ph. tr. 1671. IV. 2258, 2264. Papers an mathematics. Ph.tr. abr.I.i.J.ii. 120. IV. i. l.VI. i. 1. VHI. i. l.X.4. 1. Dechales Cursus mathematicus. WaJIis's mathematical works. 2 v. f. Extr. Ph. tr. 1695. XIX. 73. JoiiesSynopeis palmariorum matheseos. Lond^ 1706. ^ Extr.Ph.tr. 1713. *Simpso}i's mathematical dissertations and tables. 4. 1743. R. I. Simpson's exercises for young proficients, a. 1752. R.I. Simsorii opera reliqua. 4. R.I. Simpson's essays. 4. Stewart's mathematical tracts. 8. Stewart's creneral theorems. Dodson's mathematical repository. 3 v. 12. Emerson's cyclomathesisj or Introduction to the mathematics. lOv. 8. Lond. 1770. R.I. Emerson's miscellanies. 8. Lond. 1771. IJendon's six mathematical tracts. 8. R. S. Lockie's military mathematics. 2 v. 8. R. S. VOL. 11. Ghcrli elementi teoricoprattici dellc itiathe- matiche pure. 7 v. 4. R. S. Karsteus Anfangsgrlinde dcr matliematik. 2v. 8. Greifsw. 1780. Unterbergers anfangsgrlinde der mathematiL 1781. Vegas vorlesungen iiber die matheniatik. 3 v. 8. Vienna, 1782. R. I. Siurms kurzer begriff" der gesammten ma- thesis. Encyclopedic methodique. Mathematiques. 3 V. By D'Alembert, Bossut, and others. Amusemens de mathematique. 1 v. A7«gf/.s encyclopadie. 1784. Waring Excerpta mathematlca, 4. Tabies to be used with the nautical almanac. 8. B. B. /Z«f/oM's mathematical tables. 8. Lond. 1785. R.S, Hiitton's miscellanea matheniatica. 12. Hutton's translation of Montucla's recrea- tions. 4v. 8. Lond. 1803. R.I. Lsnden's mathematical memoirs. 2. v. 4. London. R. I. /fc//?«s's mathematical essays. 4. Lond. 1788. R.S. OF QUANTITY AND NUMBER, OR ALGEBRA. Wallis's algebra. *Nevvton's universal arithmetic. Extr. Ph. tr. 1685. XV. 1095. *Demoivre Miscellanea analytica. 4. 1730. n. L Saunderson's aigehra. 2 v. 4. 1740. R.I. *Maclaurin's algebra. 8. 1788. R. I. e 114 CATALOGUE. MATHEMATICS, ALGEBRA. Emerson's cyclomathesis. IV. Condorcef, Essai d'analyse. 4. R. S. Davison's algebra. 8. Davis Miscellanea analytica. 4. Waring Meditationes algebraicae. 4. Waring Miscellanea analytica. 4. R. S. *Waring meditaliones analylicae. 4. Cambr. 1785. R. S. Nicolai analyseos elementa. 4. Pad. 1786. R.S. Eukr's elements of algebra. 2 v. 8. Lond. 1797. R. I. Lacroix Elemens d'algebre. R. I. Lacroix Complement des elemens d'algebre. Paris, an 7. R. I. Pront/'s mechanical algebra. Journ. Polyt. II. 92. *Donna JgnesVs analytical institutions^ by Colson. 2 V. 4. Lond. 1801. R. S. Woodhouse on the independence of algebra and geometry. Ph. tr. 1802. 85. *Woodhomes principles of analytical calcu- lation. 4. Cambr. 1803. R. S. PROPORTION. Glenie on tlie Jaws of proportion. Ph. tr. 1777.450. Glenie on universal comparison. 4. Lond. 1789. R. S. GUnie on the antecedental calculus. Ed. tr. IV. 65. Separate. Lond. 179^. R. S. Slusii mesolabum. 4, Liege, 1688. *■ Ace. Ph. tr. 1699. IV. 903. FRACTIONS, ' Demoivrede fractionibus algebraicisreducen- dis. Phil. tr. 1722. XXXII. 102. Landen on the resolution of fractions by the circle. Ph. tn 1754. oQQ. GENERAL THEOREMS. Castillioneus de formula polynomia Newtoui. Ph.tr. 1742. XLII. 91. On the binomial theorem. Demoivre's multinomial theorem. Ph. tr. 1697. XIX. 610. Ji/Wfwfturof liber den polynomial lehrsatz. 8. Leipz. 1795. Roberts on the binomial theorem. Ph. tr. 1795. 292. Sewell on the binomial theorem. Ph. tr. 1796. 882. Brougham's general theorems. Ph. tr. 1798. 378. IMPOSSIBLE QUANTITIES. Playfair on the arithmetic of impossible quantities. Ph.tr. 1778.318. Woodhouse on the truth of conclusions from imaginary quantities. Ph. tr. 1801. 89. EQUATIONS. Collins on some defects in algebra. Ph. tr. 1684. XIV. 575. Halley on finding the roots of equations. Ph. tr, 1674. XVIII. 210. Demoivre Aequationum superiorum resolutio. Ph. tr. 1707. XXV. 2368. Maclaurin on the roots of equations. Ph. tr. 1729. XXXVI. 59. Mallet Analysis aequationum. 4. R. S. Hatfks Analysis aequationum. 4. Waring's problems on equations. Ph. tr. 1763. 294. Waring on the general resolution of equa. tions. Ph. tr. 1779. 86. Waring on the method of corresponding va- lues. Ph. tr. 1789. 166. Lord Stanhope on the roots of equations Ph. tr. 1781. 195. CATALOGUE. —MATHEMATICS, ALGEBRA. 115 Wales on the use of angular tables in solv- ing equations. Ph. tr. 1781. 459. Hellins on the equal roots of equations. Ph. tr. 1782. 417. Wood on the roots of equations. Ph. tr. 1798. 369. Wilson on algebraic equations. Ph. tr. 1799- 265. Equations with Radical Quantities. Demoivre de reductione radicajium. Ph. tr. 1738. XL. 403. Simpson on equations involving radical quantities. Ph. tr. 175 1. 20. Mooney on clearing equations from radicals. Ir. tr. VI. 221. Removes 3 or 6 quadratic surds. Impossible Roots of Equations. Maclaurin on equations with impossible roots. Ph.tr. 1726. XXXIV. 104. Campbell on the impossible roots of equa- tions. Ph. tr. 1728. XXXV. 315. Cubic and Biquadratic Equations. Colson Aequationum cubicarum et biqua- draticarum resolutio. Ph. tr. 1707. XXV. 2333, Maseres on the irreducible case of a cubic equation. Ph. tr. 1778. 902. Maseres on the extension of Cardan's rule. Ph. tr. 1780. 85. Button on cubic equations. Ph.tr. 1780.387. Meredith on cubic equations. Ir. tr. VII. G9. Ivory on cubic equations. Ed. tr. V. 99. Limits of Equations. Milner on the limiis of algebraic equations. Ph. tr. 1778. 380. Machine f 07' Equations. Rowning on a machine for solving equa tions. Ph. tr. 1770. 240. AUITHMETIC. *Archimedis Psammites Wallisii. O.xf. I676- Acc. Ph. tr. 1676. XI. 067. Archimcdeii Arenarius, by Anderson. 8. * Dioi)hantus'Qi\.c\\ei\ et Fermatii. f. Toulouse, 1670. Ace. Ph. tr. 1671. VI. 2185. Collins on the resolution of numerical equa- tions. Ph.tr. 1G69. IV.929. Tabula numerorum quadratorum. Lond. 1672. Ace. Ph. tr. 1672. VII. 4050. fWood on infinite fractions. HookePh. coll. n. iii. p. 45. Wallis on the extraction of roots. Ph.tr. 1695. XIX. 2. Taylor on approximation in numerical equa- tions. Ph. tr. 1717. XXX. 610. Leupold Thealrum arithmeticum. f. Leipz. R.I. Reckoning by the fingers. Tab. 1. Colson's negativo-aflirmative arithmetic. Ph. tr. 1726. XXXIV. 161. Emerson's cyclomathesis. I. II. Robertson on circulating decimals. Ph. tr. 1768.207. Horsley's sieve of Eratosthenes. Ph. tr. 1772. , 327. Ilittton's table of powers and products, f. R. S. Clarke's rationale of circulating numbers. 8. R. S. ;M . Young on the extraction of roots. Jr. tr. 1787. 59. 116 CATALOGUE. — MATHEMATICS, ALGKBRA. ti^ Waring on the sums of divisors. Ph.tr. 1788. 388. Goodwyn on the.reciprocals of primes. Nich. IV. 402. * Lagrange dc hi resolution des equations numeriques. Par. 1798. K. I. IVernehurgs reine zahlen system. 8. 1800. Duodecimal arithmetic. Calls I2taun. Gough on primes and factors. Nich. 8. I. 1. TJie African nations employ a quinary arithmetic, calling six five and one. Winterbottom's Sierra Leone. Numerical equations may often be easily resolved by finding the result of two conjectural values of the quaoitity sought ; then the difference or sura of the errors will be to the diflference of the supposed values nearly in the same proportion as cither of the errors to the error of the cor- responding supposed value. SEKIES. Demoivrc on the roots of an infinite equa- tion. Ph. tr. 1G93. XX. 190. Monmort et Taylor de scricbus infinitis. Ph. " tr. 1717. XXX. 633. Simson on Gerard's remark upon series and fractions. Ph. tr. 1753.368. Simpson on the partial sum of a series. Ph. tr. 1758. 757. Landen on the sums of series. Ph. tr. 1760.553. Landen on converging series. 4. R. S. Landeh's observations on coaverging series. 8. R. S. Lorgiia specimen de seriebus convergenti- bus. 4. 11. S. *Clarke's translation of Lorgna on series. 4. R;S. Hutton on quickly converging series. Ph. tr. 1776^476. Hutton pn infinite series. Ph. tr. 1780. 387. Maseres on a slowly converging series. Ph. tr. 1777. 187. 1778. 895. Vince on infinite series. Ph. tr. 1782. 389. 1785. 32. 1780. 1791. 295. Waring on infinite series. Ph. tr, 1784. 385, 1786.81. 1787. 71. Rotheram on geomctiical series. Manch. IVL III. 330. L'Huilicr on scries. Ph. tr. 1796. 142. Brinkley on the transformation and reversioa of series. Ir. tr. VII. 321. Hellhis on a coaverging, scries. Ph.tr.~17-98^ 183. INTERPOLATIONS, AND REDUCTION Of OUSF.aVATIONS, Emerson's miscellanies. 199. *Lagrange on taking the mean of observa- tions. M. Taur. V. ii. I67. Waring on interpolations. Ph. tr. 1779; 59. Euler on Lagrange's mode of taking a mean,. N. A. Petr.IlI. 1785.289. LeGARIXHMS. Mercatoris Logarithmotechnia. Extr. Ph. tr. 1668. III. 753, Hallcy on logarithms. Ph.tr. 1695.XIX.58. Craig Logarithmotechnia generalis. Ph. tr. i7iO.XX.VII. 19L. Long's new method for making logarithms. Ph.tr. 1714. XXIX. 51. Taylor's method of computing logarithms. Ph.tr. 1717. XXX. 610. Dodson on a series for computing logarithms. Ph. tr. 1753. 273. Bayeson a logarithmic series. Ph. tr. 1 7.63.260. Emerson's miscellanies. 189. Jones onlogarithms. Ph. tr. 1771.455. Ferroni theoria magnitudinum exponentiali- um. 4. R. S. Ilellins's theorems for computing logarithms. Ph. tr. 1780. 307. 1796. 135. ilfrtseresscriptoreslogarithmici.^3v. 4. 1791.. 6. R. I. CATALOGUE. MATHEMATICS, GEOMETRY. 117 Allman on logarithms. Ir. tr. VI. 391. Murray on Halley's series for logarithms. Ir. tp. IX. 3. Tables of Logarithms. Sfitncin's tables of logarithms. 8. DoJsoM'santilogarithmic canon, f. 174G. R.I. Bernoulli's sexcentenary tables for propor- tions below 10'. 4. R. Sv Fegfl's tafelnund formuln. 8. R. S. Fega Logarithmische tafelu . f.Leipz. 1 794.R.I. *Tai/lor's tables of logarithms. 4. *Calkt, tables de logaiithraes, edition ste- reotype. 8. Par. 1795. ♦Errors of Callet's tables. Zach Mon. corr. VI. 398. Borda et Delambre tables trigonometriques decimales. 4. Par. 1801. II. S. Account of the new decimal tables of loga- rithms. M. Inst. V. 49. COMBINATIONS AND CHANCES. On the credibility of human testimony. Ph. tr. 1699. XXI. 359. Robertson on the chances of lotteries. Ph.tr. 1693. XVII. 677. Thornycroft on combination. Ph. tr. 170*5. XXV. 1961. *Demoivre de mensura sortis. Ph. tr. 1711. XXVII. 213.. Deinoivr£ probleniatis solutioscombinatoria. Ph. tr. 1714. XXIX. 145.. Dftnoivre's doctjine of chances. 4.. U . BeriKJulii de pvoblemate Moivraei. Plu tr. 1714. XXIX. 133. Simpson's laws of chance. 4. Combinations. Emerson's cyclomathesis. X. Laws of chance. Emerson's miscellanies. I. 13ayes on a problem on chancesj with Price's letter.. Ph. tr. 1763.370. Price's continuation of Bayes's paper. Ph. tr. 1764. 29s. S. C'/rtrft's laws of chance. 8. *Sevcral papers of Laplace and Condorcet. A. P. 1781, and elsewhere. Lambert on lotteries at cards. Hindenb. Arch. III. Hindenburg on the combinatorial analysis. Hindenb. i^r.ch. rNTEREST AND ANNUITIES. Martindale on compound interest. Ilooke- Ph. coll. n. 1. 34. Halley on the value of annuities. Ph. tr. 1693. XVII. 596. 653. Walkinson interest. Ph. tr. 17 14.XXIX. 111. Demoivre on the calculation of annuities. Ph. tr. 1744. XLIir. n. 473. p. 65.- Emerson's miscellanies. 49. 121. 226. Price on the expectations of lives.. Ph. tr. 1769. 89. Price on survivorships. Ph.tr. 1770. 268. Pnce on life annuities. Ph.tr. 1776. 109. Pr/ce on reversionary payments. 8. 2 copies. R.Si. * Price on annuities, by Moi-gan. 8; London. *Robertson on compound interest.. Ph. tr. 1770. 508. Morgan on the value of a contingent rever- sion.. Ph. tr. 1789. 40. GEOMETRY. OF SPACE IN GE- NERAL. *Euclides Gregarii. f. Oxford, 1703. R. I.- Extr. Ph. tr. 1704. * Bar rote's Euclid. 8. London. Cunn's Euclid. 8. London, 1762. R. I. . *67wsa?j's Euclid. 8. 1801. London, R.I. Cow(ei/'s appendix to Euclid. 4. ^4[po//o?«?nnclinationumlibrialIorsley.4.R.S. Jpollonii loci plani, a Simson. 4. 118 CATALOG UK. — MATHEMATICS, GEOMETRV, JpoUoiilm on tangencies.by Lawson. 4. R. S. Apoltonim de sectione rationis et spatii. 8. Burrow's restitution of ApoUonius on incli- nations. 4. R. S. Archimedes a Barrow. 4. London, l675. Extr. Ph. tr. 1675. X. *Archimedes. f. Oxford. R. I. Gregorii geometriae pars universalis. Pavia, 16G8. Extr.Ph.tr. lf)68. 111,685. P and Wren's of the cycloid in 1658. Ph.tr. 1673. VIII. 6146. 6149, Wallis on~the history of the cycloid. Ph. tr. 1697. XIX. 561. Wallis affirms that he extracted the square root of a num- ber of 53 figures, to 27 places, by memory, in bed. Gregory on the tFue authors of some inveu- tidrre. Ph. tr. 1694. XVIII. 233. Vindiciae matheseos Gregorianae. Ph. tr. 1706. XXV. 2336. Commercium epistolicum Collinsii et alio- runi. R. I. Extr. Ph. tr. 1715. XXIX. 173. On the invention of flu.\ions. Coiiti and Leibnitz on the method of flux- ions. Ph.tr. 1718. XXX. 923. Taylor Apologia contra J. Bernoullinm. Ph. tr. 1719. XXX. 955. History of the quadrature of the circle, by Montucla, 1754, Extr. in Mutton's recreations. I. Maseres on the discovery of Cardan's rules. Ph. tr. 1780. 221. *Montucla, Histoire des malhematiques, par Lalande. 4 v. 4. Par. I799. Kastner Geschichte der mathcmatik. 8. Gotting. 1796-^7. It is said that figures were employed by the Arabs in 8 13, in Europe in 9m, in England 1253 ; that decimal arithme- tic was introduced in 1402, Napier's logarithms in 1614. NATURAL PHILOSOPHY AND MECHANICAL ARTS IN GENERAL. Some works belonging to thii class are arranged under the article Mathematics. *Aristotelis naturalis auscultationis libri. I/Mcrf^j«s de rerum natura. 4. Lond. 1722. Litcretius de rerum natura, a Creech. 8, Oxf, 1695. Basil, 1770. MaiJiematici veteres., Senecae quaestiones naturalcs. Ven. 1522. R. I. R. Bacon 0})us majus, by Jebb. 173,'J. R.I. Ramelli Artificiose machine, f. Par. 1588. R.I. Baconis scripta in philosophia. 12. Anist. 1653. *Bacon's philosophical works, methodized by Shaw. 3 v. 4. Lond. 1733. R.I. On induction. Bacon's novum organum. Sennerti philosophia naturalis. 4. Wittemb. 1618. Epitome Sennerti. 12, Amst. 1651. Mersenni cogitata phj'sicomathematica. Par. . 1644, M. B. B. Porta Magia naturalis. 8. 1650. M. B. Descartes Principia philosophiae. Opp. II. Schotti magia universalis. 4 v. 4. Wurtzb. 1657. M. B. Schotti technica curiosa. 4. Nur. 1664. M. B. M. of JVorcester's scantlings of inventions. 24. Loud. 1663. B.B. Repr. Ph. m. XIII. 43. Jungii doxoscopiae physicae miuores. 4. Hamb. 1663. Power's experimental philosophy. 4. 1664. M. B. Clauhergii physica. 4. Amst. 1664. *Hooke's micrographia, f. Lond. 1665. R. I. Hooke's experiments and observations, by Dcrham. 8. Lond. 1726. R.I. Dni/icss of Newcastle on experimental phi- losophy, f. 1666. M. B, CATALOGUE. PHILOSOPHY AND ARTS. 125 Boyle on the usefulness of experimental phi- losophy. 4. Oxf. 1^71. Extr.Ph.tr. I671. VI. Rohault Tr-Mte de physique. Par. I671. Extr. Ph.tr. 1671. VI. 2138. *RohaulH physica Clarkii. 2 v. 8. Lond. 1711.1729. Rohault's natural philosophy. 2 v. 8. 1728. R.I. Petty on the use of the duplicate proportion in natural philosophy. Birch. III. 156. Dechales mundus mathematicus. Duhamel philosophia vetus et nova. 4. Par. 168I. M.B. Senguerdi Philosophia naturalis. 4. Leyd. 1685. M. B. **Newtoni philosophiae naturalis principia mathematica. 4. Lond. 1687- Extr. Ph. tr. 1687. XVI. 297- " It may be justly said, that so many valuable philoso- phical truths as are herein discovered and put past dispute, were never yet owing to the capacity and industry of any one man." *Newtoni principia, a Jaquier et liC Seur. 3 V. 4. Genev. 1739. K. I. Newiotti principia, a Tfssanek. 4. P. 1. Prague, 1780. Newton's mathematical principles. 2 v. 8. Lond. 1729. R. I. Newton's mathematical principles, by Davis. 8. Lond. 1803. R. S. Enurson's commentary on Newton's princi- pia. 8. Lond. 1770. R. I. Sturmii physicae conamina. 12. Nuremb. 1687. M. B. Slurmii physica electiva. 4. Nuremb. l697. 1722. M. B. Sturmii collegium experimentale. 2 v. 4. 1676. 1685. M. B. Amontons Remarques et experiences de phy- sique. Par. 1695. M. B. Hofmanni lexicon universale. 4 v. f. Leyd. ifiya. R. I. Keillii introductio ad veram physicam. 8. Oxf. 1700. Lond. 1719. Keil's natural philosophy. 8. 1726. R. I. J/aaAsiee's mechanical experiments. 4. Lond. 1709. 8. 1719. R. I. Muys Elementa phy sices. 4. Amst. 1 7 1 1 • M .B. Sc/ieuchzers naturwissenschaft. 2 v. 8. Zur. 1711. Derham'i physicoth^ology. 8. Lond. 1754. R.I. Nieuwenti/t regt gebruyk der wereltbeschou- wingen. 4. Amst. 17 16. B. B. Nieuzventi/t's religious philosopher. 3 v. 8. 1719. R. I. WhistOH on Newton's philosophy. 8. 17 16. M.B. Servihe, Recueil d'ouvrages curieux. Lyons, 1719. R. I. S'Gravesande Physices elementa mathema- tica. 2 V. 4. Leyd. 1742. M.B. S'Gravcsaiide's natural philosophy, by De- saguliers. 2 v. 4. Lond. 1747- R. I. S'Gravesande's explanation of Newton, 8. Verdries Conspectus philosopliiae naturalis. 8. Giess. 1720. M. B. Wolff's niitzUche versuche. 3 v, 8. Halle, 1721—43. Wo/J's vernunftige gedanken. 3 v. 8. Halle, 1723—5. *Leupolds theatrum machinarum. 9 v. f. Leipz. 1724 . . . R. I. * Pembcrton'sNev/toinan philosophy. 4. 1728, R.I. Musschenbroek dissertationes physicae. 4. Leyd. 1729. M. B. Musclienbroek Elementa physices. 8. Leyd. 1734. Musschenbroeh's natural philosophy, by Col- son. 2 v. 8. 1744. R. I. 126 CATALOGUE. — PHILOSOPHY AND ARTS, *Musschejtb)0€klnlTo6iucUo ad philosopbiam naturalem. 2 v. 4. Leyd. 1762. II. I. Moliires Recueil de legons de physique. M.B. Abstr. A. P. 1734,1736—8. H. Teichmeyeri elementa philosophiae naturalis. 4. Jena, 1733. M. B. Vanderzyl Theatrum inachinarum. f. Amst. 1734. J^a/Kicrgfn elementa physices. 8. Jen. 1735. M.B. Voltaire Pliilosophie de Newton. 8. Amst. 1738. M. B. Ilehham's lectures on natural philosophy. 8. 1739. R. I. Martints medical and philosophical essays. 8. 1740. R. I. Institutions de physique. 8. Amst. 1741. Cw//rngen' elementa physices. 8. Leipz. 1742. * Maclauriii's account of Newton's discove- ries. 4. Lond. 1743. 8. 1750. R. I. Nolkt Le9()ns de physique experimentale. 6 V. 12. Par. 1743. . . M. B. AbsU. A.P. 174.S, 1745, 1748, 1755, 1764, H. ?»^o//e< Andes experiences. 3 v. 12. Par. 1770. Segners einleitung in die naturlehre. 8. 1746. 1770. Rutherforth's natural philosophy. 2 v. 4. 1748. R. I. Crusius iiber naturliche begebenheilen. 8. Leipz. 1750. Kraftii praelectiones in physicam theorett- cam. 3 V. 8. Tubing. 1750. Krugers naturlehre. 8. Halle, 1750. Gordon Physicae elementa. 2 v. Erfurt. 1751, Khell physica. 2 v. 4. Vicnn. 1751. Eberlmrds erste grlinde der naturlehre. 8. Halle, 1752—67. Eberhards sammlung der ausgemachten wahrheiten. 8. Halle, 1755. Eberhards beitrage zur maihesi applicatae. o Saverien Dictionnaire de niathematiqueetde physique 2 v. 4. Par. 1753. Winklers anfangsgrlinde der physik. 8. Leipz. 1753. 1754. Winkler's natural philosophy. 2 v. 8. 1757. R. L Desaguliers's course of experimental philo- sophy. 2 V. 4. Lond. 1763. R. L Martin's philosophia Britannica. 3 v. 8. 1759. R. 1. Martin's young gentleman and lady's philo- sophy. 3 V. 8. 1781. R. L Boscovich Philosophiae naturalis theoria re- dacta ad unicam legem. 4. Vienn. 1759. R. S. Suckow Entwurf einer naturlehre. 1761. Jones's first principles of natural philosophy. 4. 17!52. R. 1. Jones's physiological disquisitions. 4. Lond, 1781. Guyton de Morveau Essais de physique. 12. Dijon, 1762. R. L Euler Briefe an eine Deutsche prinzessinn. 3 V. 8. Leipz. 17:)9— 74. Euler Lettres a une princesse d'Allemagne, 3 V. 8. Mituu, 1770 — 4. Avec les additions de Condorcet et de La- croix. 2 V, Par. 1787—8. Euler's letters to a German princess, by Hun- ter. 2 V. 8. Lond. 1795. 1802. R. L Hanovii philosophia naturalis. 4. Hal. 1763. Lovett's elements of natural j)hilosophy. 8. Handmaid to the arts. 8. London, 1764. R.I. Emerson's remarks on the rules of philoso- phizing. Em. misc. 405. Kdstners einleitung in die mathematik. 4 v. 8. Golt. 1764—86. Kaestneri dissertationesnjathematicaeet phy- sicae. 4. Altenb. 1776. From the transactions of the E. S. Gott. CATALOGUE. PHILOSOPHY AND AHTS. 127 Karstem Lehrbegriff der gesammten mathe- matik. Greifsw. 1764. Karstens Anfangsgiiinde der naturlehre. 8. Halle, 1790. R. I. Karstens Anleitung zur kenntniss der natur. 8. Malic, 1783. R. I. Krislens Kiirzer entwurf der naturwissen- schaft. 8. Halle, 1785. Rowiiings natural philosophy. 2 v. 8. 1765. R.I. Jkffl/f7« pliysik. 8. Cailsruhe, I767. Sigaud de la Fond Lemons de physique 61e- mentairc. 2 v. 8. Paris, 1767- R. f. Sigaud de la Fond Elemens de physique. 4 v. 8. Par. 1771. Sigaud de la Fond Description d'un cabinet de physique. 2 v. 8. Par. 1785. R. 1. Silberschlags ausgesuchte versuche. 8. Berl. 1768. Slattleri physica. 8 v. 8. Augsb. 1772. Die tiatur der dinge erki'art. 8. Hannov. 1 773. Bet/tr'dge zur allgemeinen naturlehre. 4. Erf. 1773. Hambergers aligemeine experimental natur- lehre. 8. Jen. 1774. Titii physicae dogmaticae elementa. 8. Wit- tcmb. 1774. Tilii physicae experimentalis elementa. 8. Leipz. 1782. Bockmanns naturlehre. 8. Carlsr. 1775. Maler improved. Senebier Art d'observer. 2 v. 8. Genev. 1775. JEierriCS. Central Forces. trooke on central forces. Birch. II. 90. *Huygens de vi cenlrifuga. Op. Posth. V'arignon on central forces. A. P. 1700. 83. H. 78. 1701. 20. H. 80. 1703. 140. ai'2. H. 65. 73. 1706. 178. H. 56. 1710.533. 11. 102. Bomie on central forces. A. P. 1707.477. H. 97. Keill on central forces. Ph. tr. 1708. XXVI. 174. *Keill de inverse problemate virium centri- petaruni. Ph. tr. 1714. XXIX. 91. Hermann and Bernoulli on' the converse pi o- Riccati. C. Bon. V. ii. 421. Jones's demonstration of Machin's law of equal solids. Ph. tr. 1769. 74. Lexell. A. Petr. 1782. VI. i. 157. Waring on the resolution of attractive force. Ph. tr. 1789. 185. Projectiles. Halley on gunnery. Ph. tr. I686. XVI. 3. 1695. XIX. 68. Taylor de projectilium motu. Ph.tr. 1726. XXXIV. 151. Maupertuis's arithmetical balistics. A. P. 1731.297. H. 72. blem of central forces. A. P. 1710.519. Simpson on projectiles, independently of conic sections. Ph. tr. 1748. 137. Casali's machine for measuring the motions of projectiles. C. Bon. V. i. C. 121. ii. 71. Bernoulli on a balistic machine. A. Bed. 1781. 847. Tennis. E. M. A. Art. Paumier. ♦Robison. Eiic. Br. Art. Projectiles. H. 102. *Demoivre de viribiis centripetis. Ph. tr. 1717. XXX. 622. *Maclaurin Geomelria organica. Montigny on the motion of bodies round a ' centre. A. P. 1741. 280. H. 143. Emerson's fluxions. Riccati on curvilinear motions. C. Bon. IV. O. 139. Zanotti. C. Bon. V. i. C. 184. David. Roz. XIX. 229. Waring. Ph. tr. 1788. 67. Cesaris. Soc. Ital. II. 325. *On the inverse method of central forces. Manch. M. IV. 369. V. 101. Trenibley on trajectories. A. Berl. 1797. 36. BrinCley. Ir. tr. VIII. 215. Compound Central Forces. Euler. A. Berl. 176O. 228. N. C. Petr. X. 207. XI. 152. Euler on central forces in curves not lying- in a plane. N. A. Petr. 1785. III. 111. Lagrange. M.Taur, II. ii. 196. ]V. iv. 188. Coiifined Motion. Hugenii h'orologium osciliatonum. f. Par. 1653. On the isochronism of vibrations in a cycloid. Ph. tr. 1673. VIH. 6032. On descent in a cycloid. Ph.tr. I697. XIX. 424. Sault on the curve of swiftest descent. Ph. tr. 1698. XX. 425. . Varignon orl the motion of bodies on united planes. A. P. X. 301. Varignon on certain curves of descent. A. P. 1699- 1. H. 68. 1703. 140. H. 65. Varignon on Sebastian's machine. A. P. 1699. H. 116. Craig on the curve of swiftest descent. Ph. tr. 1701. XXII. 746. CATALOGUE. — PHILOSOPHV AND ARTS, MECHANICS. 13S Carre on pendulums. A. P. 1707. 49. V. 58. Parent on the descent of a body producing a constant pressure. A. P. 1708. 224. H. 84. Sanrin on the shortest descent to a given line. A. P. 1709. 257. H. 68. 1710. 203. Machin de curva celerrimi descensus vi data. Ph.tr. 1718. XXX. 86. Bernoulli on isochronous and brachistochro- nous curves. A. P. 1718. 136. H. 55. Louville on a difficulty respecting the eva- nescent arc and chord. A. P. 1722. 128. H.82. Euler on brachistochronous curves. C. Petr. II. 126. IV. 49. V. 143. VI. 28. VII. 135. N, C.Petr. XVII. 488. A. Petr. I.ii. 70. Euler on vibrations in finite arcs. A. Petr. I. ii. 159. Euler on a rotatory pendulum. A. Petr. 1780. IV. ii. 133. 164. Euler Theoria motus solidorum. Euler on the pressure upon the pivot of a pendulum. N. A. Petr. VI. 145. Krafit on the conical paradox. C. Petr. VI. 389. Krafft on descent upon an inclined plane. C.Petr. XII. 261. XIII. 100. Krafft on circular pendulums. N. A. Petr. 1791. IX. 225. Fontaine on tautochronous' curves. A. P. 1734. 371. 1768.460. Courtivron on a circular pendulum. A. P. 1744. 384. H. 30. Niicker on a tautochronous curve. S. E. IV. 99. Lagrange on isochronous curves. A. Berl. 1765. 361. 1770. 97. Dalenibert on isochronous curves. A. Berl, 1765. 381. Borda on the maxima of curves. A. P. 1767. 551. H. 90. Landen's properties of the circular pendu- lum. Ph.tr. 1771.308. 1775.287. Ktistner on the cylinder rolling up a plane. D.Schr. S.Gott. 113. Maseres's series for a circular pendulum. Ph. tr. 1777. 215. Fontana on the descent of bodies in convex lines. Soc. Ital, I. 174.. Legendre on the cycloid. A. P. 1786. 30. Lcgendrc's example of a circular pendulum. A. P. 1786.637. Riccati on the tension of the thread of & pendulum. Soc. Ital. IV. 81. Malfatti on circular descent. Soc. Ital. VH., 462. Monlucla Hist, math, IV. i. 5. Biot on tautochronous curves. B. Soc. Phil. n. 73. Brunings on the motion of a double cone. Hind. Arch. II. 321. Bunce's governor for steam engines. Nich^ II. 46. A conical pendulum. Variable Pendulums and Elastic Surfaces. Bossut on a pendulum of variable length. A. P, 1778. 199. Euler on pendulums hanging by an elastic thread. A. Petr. III. ii. 95. Bernoulli on a rotatory pendulum with an extensible thread. N. A. Petr. 1783. 1.213. 1784. II. 131. 1785. III. 162. 1786. IV. H. 102. Fuss on the descent of a. body on an inclin- ed plane, with one or more elastic sup- ports. N. A, Petr. 1791. IX. 252. 1792. X. 91. 134 CATALOGUE. PHILOSOPHY AND ARTS, MECHANICS. Confined Motion with Resistance. Krafi"t on the inclined plane. C. Petr. XII. 2G1. XIII. 100. Euler on descent upon an inclined plane with resistance. C. Petr. XIII. 197. Euler on a rotatory pendulum with resist- ance. A. Petr. 1780. IV. ir. lG4. JSacker. S. E. IV. 95. Kastner on the inclined plane. Leipz. Mag. II. 1. See Hydraulic Resistance. MOTIONS OF SIMPLE MASSES. Centre of Inertia. See Centre of Gravity. Lahire on the motion of the centre of iner- tia. A. P. IX. 175. Laura Bassi on the motion of the centre of inertia. C. Bon. IV. O. 74. Robison Enc. Br. Suppl. Art. Position. Momentum. Bulfinger on momentum. C. Petr. I. 43. EOUILTBRIUM OF SYSTEMS OR OF COM- POUND BODIES. Pressure and Composition of Force. See Composition of Motion. Sttviii Oeuvres matbematiques. 4. lG34. M. B. Varignon's machine not admitting equilibri- um. A. P. II. 76. Unstable equilibrium. Varignon on a combination of forces. A. P. 1714. G80. H. 87. Loupold. Th. St. t. 1.2. KrafTt on the apparent ascent of a double cone. N. C. Petr. VI. 389. Kotehiikow. N. C. Petr. VIII. 28G. Maupertuis on the laws of rest. A. P. 1740. 170. Riccati on equilibrium, and on the composi- tion of forces. C. Bon. 11. ii. 305. iii. Q15. V. ii. 186. Bernoulli. C. Petr. I. 126. Kaestner de vecte et compositione virium. 4. Leipz. 1753. Kastner on a cylinder appearing to roll up- wards. D. Schr. Soc. Gott. 113. Foncenex M. Taur. II. ii. 299. Journal des sav. 1764. Dalenibert, Dynamique. Dalembert A. P. 1769. Euler on the effect of friction in equilibrium. A.Berl. 1762. 265. Euler on the distribution of pressure on a plane. N. C. Petr. XVIII, 289. Hind. Arch. I. 74. Euler on some cases of equilibrium. A. Petr. HI. ii. 106. Bclidor Ingenieur Francois. Matteucci. C. Bonon. VI. O. 286. Gr. Fontana on the resolution of force. Soc. Ital. III. 519. Frisii cosmographia. Fuss on the equilibrium of weights on curved surfaces. N. A. Petr. 1788. VI. 197. Biiija Grundlehren der statik. 1789. Delangez on a case of pressure. Soc. Ital. V. 107. Salimbcni's elements of statics. Soc. Ital. V. 426. Paoli on the distribution of pressure. Soc. Ital. VI. 534. Lorgna on the pressure of a body on its sup- ports. Soc. Ital. VH. 178. La])lace Mecanique celeste. I. *Robison Enc. Br. Suppl. Art, Dynamics. CATALOOUE. PHILOSOPHY AND ARTS, MECHANICS. 13J Mechanical Powers. Archimedes. Hamilton. Ph. tr. 1 703. 103. His demonstration of the property of the lever is deduced from that u{ Archimedes. Landen's essfiy on the mechanical powers. Edgeworth's pauorganon. Nich. IV. 443. Lever. • - Lahire on the leveV. A. VAX! 6. 'I'ot Koberval's paradox. Leup. Th. St. 4. t. 17. Desagidiers on a paradoxical biilance. Ph. tr. 1731. 1^5. Aepinus on a new property of the lever. N.C. Petr.Vm.271. " ' A peculiar maximum. Kaestner vectis theoria. Vince on the lever. Ph.tr. 1794. 331 Ke- perti Xi 49. Schwab and Burja on the lever. A. Berl. 1797. 137. Uobison Enc. Br. Art. Statics. Steelyard. Cylinders. Hotchkiss's patent mechanical power. Re- pert. XIV. 24. A double capstan. Wedge. 7J«r>n«wH de cuneo. 4. Witteinb. 1751. Ludlam's essays. Screw. Leupold Th. Macliinarium. t. 6. 7. C. Bon. III. 131. 304. Hunter on a new way of applying the screw. Ph. tr. 1781. 58. Kastner on the screw. Commentar. Gott. XIII. 1795. M. 1,47. XIV. 1797. M.3. Kaestner de theoria cochleae. Diss. vi. 38. Nich. 1. 1. -58. Props. Desaguliers's new statical experiments, on props. Ph. tr. 1737. 62. Compound Machines, Marcorelle on the statics of the human body. S. E. 1. 191. Centre of Graviti/. Sea Centre of Inertia. Walhs de certtro gravitatis hyperbolae. Ph. tr. 1672. VII. 3074. lii,j|.)>i Roberval on the centres of gravity of solids. A. P. VI. 270. 282. Varignon on the centre of gravity of spheres. A. P. X. 508. Clairauton finding the centre of gravity. A. P. 1731. 159. Bossut on the centres of gravity of cycloidal surfaces and solids. S. E. III. 603. Illustrations of the centre of gravity. E. ^l. PI. VIII. Amiiscmens de mecaniquc. Gr. Fontana on the axis of equihbriuni and the centre of gravit}'. Ac. Sienn. VI. 177. L'Huilier's theorem respecting the centre of gravity. N. A. Petr. 1786. IV. H. 39. Kramp on the centre of gravity o(] spherical triangles. Hind. x\rch. II. 2y6. Equilibrium of heavy Si/sfems. See Architecture. D. Gregorii catenaria. Ph. tr. 1697. XIX. 637. 1699. XXI. 419- Clairaut on catenariae. M. Berl. 1743. VII. 270. Krafft on catenariae. N. C. Petr. V. 145. Canterzani on the catenaria. C. Bon. VI. p. 265. Legendre on the catenaria. A. P. 1786. 20. Kastner on chains of unequal thickness. Hind. Arch. I. 69. 13^ CATALOGUE. — PHILOSOPUY ANB AllTS, MCHANICS. Fuss on the equilibrium of flexible threads, loiwled with weights. N. A. Petr. 1794. XII. 145. EquiUhnum of Elastic Bodies. Jo. Bernoulli on the elastic curve. Acta Lips. lGy4. 1695. Bernoulli On the cohesion and resistance of beams fixed atone end. A. Bed. 1706. 78. Euler ohthe elastic curve. C. Petr. II I. 70. Euler on the equilibrium of elastic bodies. N. CPetr. XV. 381. XX. 28(i. A. Petr. III. ii. 188. jEuler on the rectangular elastic curve. A. Petr. 1782. VI. ii. 34. Lexelli A. Petr. 1781. V. ii. 207. MOTIONS OF SYSTEMS, OU OF COMPOUND BODIES. Collision. Of impulsion. Galileo. Op. I. 957- II- 479- .BortZ/us de vi percussionis. Abstr. Ph. tr. 16G7. II. C2(i. Wallis, Wren, and Huygens. Ph. tr. I668, III. 1G69. IV. Huygens, Journal des savans. Mars. I669. A. P. X. 341. Op. II. 73. Huygens Opusc. posth. Huygens was the earliest in discovering the laws of col- lision, but not in publishing them. Mariotte Traite de la percussion. Op. I. 1. Lahire on percussion. A. P. IX. lO'S. Leibnitz Hypothesis physica. Leibnitz Theoria motus abstracti. Hermanni phorononiia. .Saulmon on the collision of elastic bodies. A. P. 1721. 126. H. 8G. 1723. H. 101. Mairan on the reflection of bodies. A. P. 1722. 6. H. 109. 1723. 343. H. 107. 1738. I. II. 82. 1740. 1. H. 89. Moliercs on tin? collision of clastic bodies. A. P. 1726. 7. H. 53. Barnes on the forces of moving bodies. Ph. tr. 172fi. 183. N. Bernoulli on percussion. C. Petr. I. 121. Jean Bernoulli sur les loix de la communi- cation de la motion. Par. 1727. Op. III. *iVIaclaurin's demonstratipn, of tjie ^wsr of collision. A. P. Pr. I. Hi. . " ,-., *Maclaurin's fluxions. *Maclaurin's Newtonian philosophy. Mazieres on the collision of bodies more ,or less elastic. A. P. Pr. f. F. , .5 j / ,. -. Bernoulli on the communication of motion. A. P. Pr. I. vii. ,' Euler on collision. C. Petr. V. 159, Euler-on oblique collision. C. Petr. IX. 50. Euler on percussion. A. Berl. 1745. 21. Euler on the impulse of a bullet on a plane. N. C. Petr.XV. 414. Euler on the oblique collision of revolving pendulums. N, C. Petr. XVII. 315. Euler Theoria motus corporum solidorum. Louville's comparison of gravity and percus- sion. A. P. 1732. H. 100. Hamberger. El. phys. Gravesande on triple collision. Nat. PliiL Sect. 1257. v.uvV'.i! Rizzetti. C. Bon. I. 497- Zanotti. C. Bon. I. 557. IV. O. 219. Zanotti on elastic springs. C. Bon. HI. iii. 413. Manfredi on the impulse of springs. C. Bon. II. iii. 383- Eberhard. Roz. Introd. I. 159. Milner on the communication of motion by impact. Ph. tr. 1778.344. Lamberts scdanken liber das gleichsjewicht. Beytrage. II. 3()3. tJATALOGUE. — PHILOSOPHY AND ARTS, MECHANICS. 137 Billiards. E. M. PI. IV. Art. Paulmerie, pi. 4. 5. E. M. Amusemens de mecanique. Kastner Hohere mechanik. Ja. Beraoulir on the stroke of a ball on a ■ ' board. N. A. Petr. IV. 1786. US. Gr.Fontana. See. Ital. III. 509. 513, Biisch Mathematik. Bruchhauscn Anweisung, I. 31. BernstorlTs problem relating to billiards. Journ. Phys. XLV. (II.) 45. *Robison. Enc, Br, Suppl. Art. Impulsion. Percussion. Rotatory Power, and Centres of Gy~ ration. Percussion, and Oscillation. Lahire on the effect of weights striking a ••''lever, A. P. IX. 175. Huygens on the centres of oscillation and agitation. A. P. X. 446. 462. Parent on the centres of conversion and fric- tion. A. P. 1700. H. 149. Bernoulli on the centres of agitation and percussion. A. P. 1703. 78. 272. H. 114. 1704. 136. H. 89. Taylor de centro oscillationis. Ph.tr. 1713. XXVIII. 11. D. Bernoulli on mechanical centres. C. Petr. II. 208. D. Bernoulli on eccentric percussion, C.Petr. IX. 189, D. Bernoulli on oscillation, C.Petr. XVIII. 245. Clairaut on the oscillations of a suspended body. A. P. 1735. 281. H. 92. Camus on a problem respecting weights on a wheel. A, P. 1740. 201. H. 103.. Montigny on the motion of a system of bo- dies round an immoveable centre. A. P. 1741. 280. H. 143. VOL. II. Euler on a new principle of mechanics, A> Berl. 1750. 185. Euler on rotation upon a variable axis. A, Berl. 1758. \tA. 1760. 176. Euler on the collision of revolving bodies, N. C. Petr, XVII. 272. Euler on the mechanical centres -of triangles. A. Petr. III. ii. 126. Euler on the momentum of rotation with re- spect to any axis. N. A. Petr. 1789. VIL 191. 205. Short on Serson's horizontal top. Ph. tr. 1751. 35. It spun in vacuo 2 h. is'. Bouguer on the forms fittest for rotation, A. P. 1751. 1. Segner de motu turbinum. Halle, 1755. First pointed out the three natural axes of rotation oC all bodies : their existence was demonstrated by Albrecht Euler in 1760. Mechanical centres. Emerson's fluxions. Emerson's mechanics, vi. D'Alembert Opuscules. Lagrange on the free rotation of a body of any figure. A. Berl.. 1773. 85. Frisi de rotatione corporum. 4. R. S. Frision rotation. C Bon. VI. O. 45. Frisii Cosmographia. Smeaton on mechanic power. Ph. tr. 1776. 450. Landen's new theory of rotatory motion. Ph. tr, 1777. 266. Landen's mathematicio>/s art of painting, by Dryden. 12. 2 On painting. Ph. tr. abr. 1. ix. 593. VI. ix. 469. Lahire on the practice of painting and draw- ing. A. P. IX. 425, 431, 464. Despiles's principles of painting. 8. Mazeas and Parsons on encaustic painting. Ph. tr. 1756. 652 — 5. HaTidmaid to the arts. 8. Lond. 1758. On the materials for drawing and painting. Colebrooke on encaustic painting. From Vitruvius. Ph. tr. 1759- 40, 53. Draughtsman's assistant. 4. Caylus on encaustic painting. 8. Lond. Magellan on the use of caoutchouc. A. P. 1772. i. H. 10. *Reynolds's discourses. 8. Russd on painting in crayons. 4. Drawing aiid painiing. E. M. Beaux Arts. 2 V. Painting. E. M. A. VI. Art. Peintnre. Brushes and pencils. E. M. M. I. Art. Crin. Crayons. E. M. A. VI. Art. Pastel. Mosaic work. E. M. A. V. Art. Mosai'que. Prangens schule der mahlung. 8. Halle, 1782. . . *Cooper on the painting of the ancients. Manch. xM. III. 510. Bayley's proportional scale for drawing. S.A. IX. 156. Repert. I. 144. Lorgna on painting with compound oil. Soc. Ital. VI. 560. Conte's crayons. Ann. Ch» XX. 370. Lomet on crayons. Ann. Ch. XXX. 284. Nich. III.416. Neveu on design. Journ. Polyt. i. 78. ii. 107. . iv. 698. V. 119. vi.419. Salmon's method of transferring pictures. Repert. VIIL 257. Fc^bbroni on encaustic painting. Ph. M. I. 23, 141. Gilb, V. 357. Fabbronion cleaning prints. Repert. XL 14]. CATALOGUE.— PHILOSOPHY AND ARTS, PRACTICAL MrCHA>riCS. 143 Tatliam on encaustic paintings, with hard resins. Ph. M. I. 406. Blackman's oil colour cakes. S. A. XII. Ph. M. XVIII. 268. Sheldrake on the Venetian painting. Ph. M. II. 302. Repert. X. 56. Dayes on colouring. Ph. M. VIII. 1. Inlaying marble. Repert. X. 326. On mosaic work. Ph. M. IX. 289- *Mechanics of drawing. Imison's elements. II. 240. Copying drawings. 327- Davy on Wedgwood's mode of copying by a metallic solution. Journ. R. I. I. 173. Nich. 8. III. 167. Gill on Indian ink. Ph. M. XVII. 210. Malton's portfolios. Nich. IX. 128. Gilb. XIII. 113. :/ 7/:.U i Writino;, Characters, Signals. Caneparius de atramentis. On the Chinese characters. Ph. Ir. 1686. XVni.63. '* Chaumette's knife for making a pen at a stroke, with an inkstand for a handle. A. P. 1715. H.66. Mach. A.III.57. 61. On speaking with the hands. Leup. Th. Ar. t.2. Ckric de stylis vcterum et chartanim generi- bus. Ace. by Gale. Ph. tr. 1731. XXXVII. 157. Jcake and Byron on slwrthand. Ph. tr. 1748. XLV. 345, 388. .Byro/j'i shorthand. 8. Lalaiide Art de faire le papier, f. Par. 176I. Lalandc Art du parcheminier. 1762. Cotteneuve's polygraph. A. P. 1763- H. 147. Vaussenville on ruhng paper. A. P. 1766. H. 162. Lambert 6n ink and paper. A. Berl. 1770. 58. *BUttner on the alphabets of all nations. N. C. Gott. 1776. VI r. 106. Holdsworth and Aldridge's short hand. 8. Essji/ on signals. 8. ♦Characters. E. M.'A. I. Art. Caracteres. With 25 plates by Deshauteiayes. Writing. E. M. A. II. Art. Ecriture. Multiplying copies. E. M. A. VI. Art. Poly- graphe. Signals. E. M. A. VII. Art. Signaux. Tablets for writing with silver. E. M. A. VIII. Art. Tabletier. Short hand. E. M. A. VIII. Art. Tachy- graphe. *Astlt's origin and progress of writing. 4. R.L Blanchard's short hand. 4. Gwrffey's shorthand. 12. Wakefield on the origin of alphabetical cha- racters. jVlanch. M. II. 278. Grenville's reckoning board for the blind. S. A. IV. 129, 144. Blagden on ancient inks. Pb.tff. 1787i 451. Repert. II. 389- I The letters, may be made visible by moistening them first with a prussiatcd alkali, and then with a diluted acid. Report on Coulou's tachygraphy. A.P, 1787. H,9. Harvey on alphabetical characters.. Manch. M. IV. '135. nticknesse. on dccyphering^. Thornton on the elements of written lan- guage. Am. tr. III. 262. On intelligible signals. Am.tr. IV. 162. Cooke on signals. Ir. tr. VI. 77- Edgworlh on the telegraph. Ir. tr. VI. 95. 319. Nich. II. 319. On writing. Nich. I. 18. On pasigrapliy. Nich. II. 342.' Chap}>e, Breguet, and Betancourt on the tele- graph. B. Soc. Phil. n. 16, Coqucbert's mode ef copying. B. Soc. Phil. n.50. 144 CATALOGUE. PHILOSOPHY AND ARTS, MECHANICS. *Frys pantographia. 8. Lond. 1799- R. S. On a telegraph. M. Inst. III. H. 22. Telegrapli. Ph. M. I. 312. A telegraph with lamps. Repert, L 382. Northmore on the pangraph, or universal character. Repert. II. 307. HI. 91. Ribaucourt on ink. Repert. IX. 125. Galls, log^vood, gum, sulfate of iron and of copper, and sugarcandy. Nocturnal telegraph. Rejpert. X. 28. Brunei's patent double pen. Repert. XIII. 153. : .)(/ . • Boaz's patent telegraph. Repert. XVI. 223. ■ Ph. M. XII. 84. Enc. Br. Aft. Signals. Telegraph. Anderson on a univeisal char.icter. Manch. M. V. 89. Anderson's Recreations. VI. 1. Brown on a written character. Manch. M. V. 275. Berard's palpable mathematics. Melanges. 182. Nich. 8. III. 189. Close's writing ink. Nich. 8. II. 145. Sheldrake's indelible ink., Nich. 8. II. 237. Edelcrantz on telegraphs. Journ. Phjs. LVI. 468. JSich. 8. V. 193. Gough's scotiography. Nich. VII. 53. For the blind. A simple telegraph. Nich. VIII. l64. Geometrical Instruments in ge- nerai. Diggfs's pantometria. Lond. 1571. Schotti organum mathemalicum. 2 v. Wiirtzb. I668. Varignon on the utility of mechanics in geometry. A. P. 1714. 77- H. 45. Leopold. Th.Ar.Th. Suppl. Mayer on geometrical instruments. C. Gott. II. 325. Bion on mathematical instruments, f. 1758. R. I. Fletcher's universal measurer. Robertson on the use of mathematical instru- ments. 8. London. E. M. A. in. Art. Instrumens de matbiSma* tique. li Fontana's account of the grand duke's ca- binet. Roz. IX. 41. . . Barrow on mathematical instruments. Adams's geometrical and graphical essay*, by Jones. 2 v. 8. London. !, * P(ns and Rules. Steel pens. Leup. Th. Ar. t. 24. Parallel rules. Leup. Th. Ar. t. 21. a. Among otfclecs tite scales made of late by Marquois. Compasses. Duval's new compasses. A. P. 1717. H. 83. Compasses. Leup. Th. Ar. t. 20. a. b. Triangular compasses. Leup. Th. Ar. t. 28. Gallonde's wheel and pinion compasses. A. P. 1745. H. 83. Tiliere's spiral compasses. A. P. 1742. H. 150. Mach.A. VII. 163. Elliptic compasses. Vince Ph. tr. 1780. Lorgna on the organic description of the conic sections. C. Bon. VII. O. 32. Beam compasses. Shuckburgh, Ph. tr. 1798. Proportional Compasses. Vinci's M.SS. Leup. Th. Ar. p. 121. Toussaint de St. Marcel's proportional com- passes. A. P. 1768. H. 131. Pantograpfts. Pantometer. Leup. Th. Ar. t. 26. Langlois's pantograph. Mach. A. VII. 207. Compound pantograph. Leup. Th. Suppl. t. 14. 15. Enc. Br. Art. Pantograph. Sike's pantograph. A. P. 1778. CATALOGUE. PHILOSOPHT AND ART3, PRACTICAL MECHANICS. 145 Triangles. Triangle. Leup. Th. Ar. t. 18. Cramer's trigonometrical instrument. Leup. Th. A. t. 31. Bouffer's trigonometrical instrument. A. P. 1758. H. 101. Measurement of Angles in general, and con- struction of Instruments. Hooice's dividing engine with a screw. Ani- niadv. on Heveiius. Mayer on gonionietrical instruments. C. Gott. II. 3-25. Passement's mode of dividing the quadrant. Mach. A. VJI. 341. Due de Chaulnes on the dividing machine. A. P. 1765. H. 140. Due de Chaulnes Art pour diviser les instru- mens de mathematique. A. P. Arts. f. Ace. A. P. 1768. H. 127. Pattier's dividing tools. A. P. 1771, *Ramsden's description of a dividing engine. Lond. R. S. Roz. I. 147. Romain on the division of an angle. Roz. VIII. 55. Rochon. A. P. 1777- H. 64. Castilion on modes of division employed by Bird and by the D. de Chaulnes. A. Berl. 1780. 310. Perez Trihchanon goniarithmetron. 4. Flor. 1781. R. S. Perez sopra il suo stromento goniomctro tri- plindice. 4. Bologna, 1786. R. S. Carangeot's goniometer. Roz. XXII. 193. XXXI. 204. Hutton's proposal for a new division of the quadrant. Ph. tr. 1784. 21. Into parts of the radius. Smeaton on the graduation of instruments. Ph. tr. 1786. 1. Hindley's method was to drill equidistant holes in a brass plate, and then to make a hoop of it. Smeaton recom- mends to take from a scale the chord of 16^, and then to bisect it continually. He thinks divisions can only be as- certained to j^ of an inch, even by microscopes; and proposes several indices to be employed at once. Ludlam on Bird's method of dividing. 4. Lond. 1786. U.S. Hill's machine for measuring angles. S. A. VL 183. A simple instrument for measuring height. Repert. III. 234. Komarzewski on a subterraneous graphomc- ter. Par. 1803. R. S. Nich. 8. V. 283. Micrometer. Hooke's lectures. Anim. on Heveiius. Lambert liber die Branderschen micrometer. 12. Augsb. 1769. Hunter's screw. Ph. tr. 1781. 58. Enc. Br. Art. Micrometer. Austin's mode of cutting fine screws. Ir. tr. IV. 145. Repert. 11. 399. On the use of the screw. Nich. I. 158. Hoi'nblower on the micrometer screw. Nich. VI. 247. Huddart's station pointer. Nich. VII. 1. See dso optical instruments. Theodolites, Quadrants, and Sextants. See Practical Astronomy. Protractors, and Compasses for measuring Angles. Calibers. Leup. Th. Suppl. t. 24. Enc. Br. Robertson Math, instr. Mechanical trisection of an angle, by Ceva. 1694. Leup. Th. Ar. p. I67. t. 27. Duval. Mach. A. III. 113. Carangeau's graphometer for crystals. Nich, 8. I. 132. VOL. II. ]46" CATALOGUE. PHILOSOPHY AXD ARTS, PRACTICAL MECHANICS. Angular surveying. See Figure of the Earth. I'othinot on determining the position of a place concealed from view. A. ^. X. 150. Beighton's new plotting table. Ph. tr. 1741. XLI. 747. On the height of the ascent of rockets. Ro- bins. Ph. tr. 1749. XLVI. 131. Ellicott. Ph.tr. 1750. XLVI. 578. Gensanne's machine for measaring small distances from a single station. Mach. A. VII. 111. Langlois's machine for fixing instruments. A. P. 1751. H. 174. Michel! on the use of Hadley's quadrant in surveying. Ph. tr. 1765. 70. Enc. Br. Ar. Circumferentor. Meister on Meyer's scale for reducing angles to the horizon. Commentat. Gott. 1785. VIII. 75. The white lights were found the best object by night. Ph. tr. 1790. Levels. See Astronomical Instruments. Mathematical Machines. Hooke in Birch III. 85. Leibnitz's arithmetical machine. M.Berl. I. 317. Napier's reckoning rods. Leup. Th. Ar. t. 4.5. Biler's logarithmic circle. 1696. Leup. Th. Ar. t. 13. Reckoning machines. Leup. Th. Ar. t. 6.-9. Perrault's rhabdological abacus. Mach. A. I. 55. Lepini's arithmetical machine. A. P. 1725. H. 103. Mach. A. IV. 131. Pascal's machine. Macl). A. IV. 137. E. M. Pi. VII. Algebre 2. Clairaut's tiigonoraetrical instrument. Mach. A. V. 3. Clairaut's circular instrument. A. P. 1727. H. 142. Nich. V. 40. Hillerin de Boissandeay's arithmetical ma- chine. A. P. 1730. H. 116. Mach. A. V. 103. Mean's arithmetical tarif. Mach. A. V. 165. Gersten's arithmetical machine. Ph. tr. 1735. XXXIX. 79. Fig. Smethurst's shwanpan, or account table. Ph. tr. 1749. XLVI. 22. Robertson on Gunter's scale. Ph. tr. 1753. 96. Description, of Robertson's improved Gun- ter's scale. R. S. Rowning's machine for finding the roots of equations. R. S. Described Ph. tr. 1770. 240. Nicholson's logistic circle and scales. Ph. tr. 1787. 246. Nich V. Lorgna Fabrica delle squadre. 4. R. S. Pearson on Gunter's scale. Nich. I. 45. Measures. Modes of obtaining a Standard. Condamine on an invariable measure. A. P. 1747.439. H. 83. Blaket/ on a universal measure. 8. R. S. Rosier XV. 59. Hatton's machine for finding a standard. S. A. I. 238. If hitehurst's attempt to obtain measures of length from the measurement of time, 4. London, 1787. Fordyce bought his apparatus : when well fixed it kept time very accurately. Ph. tr. 1794. 2. Wkitehurst on pendulums. 1792. R. 1. Boscovich on finding the length of the pen- dulum. Op. ined. V. 179. Report on the choice of a unit of measures. CATALOGUE. PHILOSOPHY AND ARTS, PRACTICAL MKCHANICS. 147 'By Bovda, Lagrange, Laplace, Monge, and Condorcet. A. P. ]7S8. H. 7- 17. The preference is given to the measurement of the meri- dian. Brisson on uniformity of measures, and on standards. A. P. 1788. 722. Recommends the pendulum as a standard, and measures of wood. Bonne Principes sur les mesures. 8. Paris, 1790. R. S. Cotte on standards and universal measures. Roz. XXXVIIL 171. XXXIX. 89. Boulard's invariable toise. Roz. XL. 198. f Cooke on a standard. Am. tr. IIL 328. Deduced from the discharge of wat^ *Reports to the National Institute on the measurement of the meridian. Roz. XLIII. 169. Journ. phys. XLIV. ([.) 81. B. Soc. Phil. n.28. Nich.III. 316. Account of the measurement of a base in France, and of the standards of platina. Ph. M. 1. 269. Prony on the reduction of observations of the pendulum. B. Soc. Phil. n. 44. Leslie on a standard pendulum. Repert. I. 170. *Remarks on experiments with pendulums. Nich. III. 29. Comparison of Measures. Jiernardus de ponderibus et mensuris. Oxf. 1685. Ace. Ph. tr. 1685. XV. 1242. With a comparative engraving. Cumberland on the Jewish weights and mea- sures. 8. Lond. 1686. M. B. Ace. Ph.tr. 1686. XVI. 33. Cassini on some Italian measures. A. P. VII. i. ii. 37. Picard de mensura liquidorum et aridorum. A. P. VIL i. 321. Cassini on ancient itinerary measures. A. P. 1702. 13. H. 80. Delisle on the ancient geographical mea- ^ sures. A. P. 1714. 175. H. 80. ({ ^ Lahire on the old Roman foot. A. P. 1714. 394. Arhuthnot on antient coins. 4. Lond. 1727. *Folkes on the standards in the capitol at Rome. Ph. tr. 1736. XXXIX. 262. D'Ons en Bra}' on measures. A. P. 1739. XLI.51. Barlow on the analogy between English weights and measures of capacity. Ph. tr. 1740. XLI.457. ♦Comparison of English and Frenali mea- sures. Ph. tr. 1742. XLII. 185. *Comparison of English standards. Ph. tr. 1743. XLII. 541. Hellot and Camus on the standard ell. A. P. 1746. 607. H. 109. *Gray on the measures of Scotland. Ed. ess. I. 200. Berk on the Swedish measures. Swedish transactions. Raper on the Roman foot. Ph.tr. 176O, 774. From monuments and buildings. *Christiani delle misure. 4. Ven. 176O. Tillet on measures of corn and liquids. A. P. 1765.452. H. 128. Emerson's cyclomathesis. X. La Condamine on the toise of the Chatelet. A. P. 1772. ii. 482. H. 8. Norris's inquiry into the ancient English weights and measures. Ph. tr. 1775. 48. *Paucton Metrologie. 1780. E. M. A. VJI. Superficies. E. M. Commerce. 3 V. Howard on lazarettos. 5. Rome de I'lsle Metrologie des anciens. Roz. XXXIV. 471. 148 CATALOGUE. PHILOSOPHY AND ARTS, PRACTICAL MECHANICS. Rennel on the travelling of camels. Ph. tr. 1791. 129. Carney sur les poids et les mesures. 8. Montp. 1792.11.8. Cotte on measures. Jouru. phys. XLIV. (I.) 291. Dawes's pantometry. 12. Lend. 1797. R. S. Coquebert on the old and new measures. B. Soc. Ph. n. 5. Nich. I. 193. *Shuckbiu"gh on a standard of weights and measures. Ph. tr. 1798. 133. Nich. III. 97. Fait's tables. R. S. Fiiftdzcein on tiie Pnissian weights and mea- sures. Goodwyn's tables of English and French measures and weights. 11. S. Nich. IV. 163. Colebrooke on Indian weights and measures. As. Res. V. 91. Tables of measures. Nich. I. Z39,. Ph. M. I. 245. On the metre. Journ. Phys. XLVIII. 4(50. Buija on the length of the pendulum at Ber- lin. A. Berl. 1799.3. On the cubit of the Nile. Nich. III. 330. Vega and von Zuch on measures and weights. • Zach. Mon. corr. I. 6 10. 1 • • Beigel on the weights and measures of Ba- varia. Zach. Mon. corr. I. GlO. Metrologie constitutionelle. 2 v. 4. Pm-. 1801. B. B. Xesj9«rorMetrologie. 2 v. 4. Par. 1801, R. S. BnV/af Metrologie FrangaisCi 1802. 11. I. Reports to the National Institute. M. Inst. Egyptian measures. Nouet. Ph. M. XII. 208. Pictet on the English and French mea- sures. Bibl. Brit. n. 148. Journ. R. I., I. Ph. M. XII. 229. Nich. 8. II. 244. Re- pert, ii. III. 444. . Cavallo Exp. Ph. IV. Mutton's recreations. I. 434. On the Parisian pint. M. Inst. V. 29. Gerard on the Egyptian measure. To bt printed. S. E. Tables of Measures. Standards. The English yard is said to have been taken from the arm of King Henry I. in liol. Graham found the length of the pendulum vibrating se- conds accurately equal to 39-13 inches. Desaguliers. Bird's parliamentary standard is considered as of the highest authority: it agrees sufficiently with Sir Georgs Shuckburgh's and Professor Pictet's scales made by Trough- ton. The Royal Society's standard by Graham is perhaps about a thousandth of an inch longer than Bird's ; but it is not quite uniform throughout its length.' Maskelyne. Ph. tr. The standard in the exchequer is about .007 5 inch shorter than the yard of the Royal Society. Ph. tr. 1743. 541. General Roy employed a scale of Sisson, divided by Bird. He says, that it agreed exactly with the Tower standard on the scale of the Royal Society. Ph. tr. 1785. 385. Taking Troughton's scales for the standard. Sir G. Shuck- burgh finds the original Tower standard 36.004, the yard E. on the Royal society's scale by Graham 36.0013 inches, the yard Exch. of the same scale 35.9933, Roy's scale 36.00030, the Royal Society's scale by Bird 35.99955, Bird's parliamentary standard of 1758, 36.00023. The English standards are adjusted and employed at the temperature of 62° of Fahrenheit's thermometer: the French at the freezing point of water. The French metre, the ten millionth part of the quadrant of the meridian, is 39-37100 English inehes. Pictet, and Journ. R. I., I. 129. Y. The metre has been found to contain 36.9413 French inches, or 3 feet 11.296 lines. Hence the French toise of 72 inches is equal to 70.736 English inches. One of Lalandc's standards measured by Dr. Maskelyne, was 76.73a, the other "6.736. Ph.tr. 17C5. 327- In latitude 4 5°, a pendulum of the length of a metre would perform in a vacuum 86116.5 vibrations in a day. Borda. The length of the second pendulum is .993827 at Paris. M. Inst. H. CATALOGUE. PHILOSOPHY AND ARTS, PRACTICAL JIECHAXICS. 14^ Prony's Report to the National Institute of Sciences and Arts. 6 Nivose, year lo, (27th December, I801). Journ. R. I., I. 123. A member read, in the name of a committee, the fol- lowing report on the comparison of the standard metre of the Institute, with the English foot. Mr. Pictet, Professor of Natural Philosophy at Geneva, submitted to the inspection of the class in the month of Vendc'miaire, an interesting collection of objects relative to the sciences and arts, which he collected in his journey to Englahd. Among them was a standard of the English linear mea- sure, engraved on a scale of brass, of 4y inches in length, divided by very fine and clear lines into tenths of an inch. It was made for Mr. Pictet by Troughton, an artist in London, who has deservedly the reputation of dividing in- struments with singular accuracy , it was compared with another standard made by the same person for Sir George Shuckburgh, and it was found that the difference between the two was not greater than the difference between the di- visions of each ; that is, it was a quantity absolutely insen- sible. This standard may therefore be considered as iden- tical with the standard described by Sir George Shuckburgh in the Philosophical Transactions for 1798. M. Pictet also exhibited to the Institute a comparer, or an instrument for ascertaining minute differences between measures, constructed also by Mr. Troughton. It consists of two microscopes with cross wires, placed in a vertical si- tuation, the surface of the scale being horizontal, and fixed at proper distances upon a metallic rod. One of them ic- mains stationary at one end of the scale, the other is occa- sionally fixed near to the other end ; and its cross wires are moveable by means of a scrnw, desciibing in its revolution yig of an inch, and furnished with a circular index, dividing each mrn into 100 parts ; so that having two lengths which differ only one tenth of an inch from each other, we may determine their difference in ten thousandths of an inch. The wires are placed obliquely with respect to the scale, so that the line of division must bisect the acute angle that they form, in order to coincide with their intersection. Ge- neral Roy has described, in the 7ath volume of the Philo- sophical Transactions, a similar instrument made by Rams- den, for measuring the expansion of metals. M. Pictet offered to the class the use of the standard, with the micrometer described, for the determination of the comparative length of ths metre, and the English foot : the offer was accepted with gratitude, and MM. Legendre, Mcchain, and Prony, were appointed to cooperate with M. Pictet in the comparison of the standard metre of platina and the English foot, The first meeting was on the 28th Vendemiaire (21st of October), at the house of Mr. Lenoir. At first a difficulty occurred from the different manner in which the measures were defined : the English scale was graduated by lines ; the French standards were simply cut off to the length of a metre : hence the length of the metre could not easily be taken by the microscopes ; nor could the English scale be measured by the method employed for making new standard metres, which consists in fixing one end against a firm support, and bringing the otlier into con- tact with the face of a cock or slider, adjusted so as barely to admit the original standard between it and the fixed surface. Mr. Lenoir attempted to overcome this difficulty by re- ducing to a thin edge the terminations of a piece of brass of the length of a metre ; so that it was compared with the standard metre in the usual manner ; and its extremities, when placed on the English scale, constituted two lines parallel to those which were really engraved on the scale, and capable of being viewed by the microscopes. The standard metre of platina, and another standard of iron, belonging also to the Institute, were thus compared with the English foot ; each of these two measures being equal, at the temperature of melting ice, to the ten millionth part of the quadrant of the meridian. At the temperature of 15.3° of the decimal thermometer, or 59.5'^ of Fahren- heit, the metre of platina was equal to 39.3775 English inches ; and that of iron to 39.3788, measured on Mr. Pic- tct's scale. These first experiments showed, however, that the me. thod employed was liable to some uncertainty, arising from the difficulty of placing the cross wires precisely at the ex- tremity of the thin edge of the plate of brass employed in the comiratison ; a reflection or irradiation of fight, which took place at that extremity, prevented its being distinctly observed if the optical axis of the microscope was precisely a tangent to the surface exactly at the termination. In order to remove this inconvenience, another arranger ment was proposed by one of the committee. (It was Mr. Prony that suggested this ingenious method, and M. Paul of Geneva, who happened to be present, that executed it. B. B.) A line was traced on a small metallic ruler, per- pendicular to its length ; the end of the ruler was fixed against a solid obstacle, and the cross wires made to coin- cide with the line : the standaid metre was then interposed between the same obstacle and the end of the piece, and the line traced on it, which had now obviously advanced the length of the metre, was subjected to the other micro- scope. The microscopes, thus fixed, were transferred to the graduated scale ; one of them was placed exactly over one of the divisions, and the micrometer screw was turned liO CATALOGUE. — ^PHILOSOPHY AND ARTS, PRACTICAL MECHANICS. ih order to measure the fraction, expressing the distance of the other microscope from another division. The comparison was repeated in the same manner the 4th Brumaira (aOth October) last, at the house of one of the committee, and after several experiments, agreeing very satisfactorily with each other, it was found that at the tem- perature 12.75°', or 55° of Fahrenheit, the standard of platina was 39.378I, and that of iron 39.3795 English inches. The two metres being intended to be equal at the tem- perature of melting ice, these operations may be verified by reducing their results to that temperature. For this deter- mination we are provided with the accurate exiitriments made by Borda, and the committee of weights and mea- sures, on the dilatation of platina, brass, and iron ; from which it appears, that for every degree of the decimal tlicr- mometer, platina expands .00000856; iron .00001156; and brass .00001783 ; for Fahrenheit's scale these quanti- ties become 476,642, and 990 parts in a hundred millions. From these data we find, that, at the freezing point, the standard metre of platina was equal to 39.38280, and that of iron to 39-38265 English inchesof M. Pictet's scale. The difference is less than the 500thof a line, 'or the 200000th of the whole metre, and is therefore wholly inconsiderable. The result of the whole comparison is therefore this. Supposing all the measures at the temperature of melting ice, each of the standard metres is equal to the loooooooth part of the quadrant of the meridian, and to 39-38272 Eng- lish inchesof M. Pictet's scale. Paris, 16. Jan. IB02. On examining the reduction of the standards of platina and iron to the freezing point, it appears that they differ somewhat less than is stated in the report, and that they coincide within a unit in the last place of the decimals expressing their magnitudes, or one ten thousandth of an inch. The standard of platina at ^e freezing point be- comes equal to 39.373SO, and that of iron to 39.37370 English inches on the scale of brass at 55°, and the mean of these to 39.37100 English inches at 62°, which is the temperature that has been universally employed in the comparison of British standards, and in the late trigoi ome- trical operations in paiticular. This result agrees surprisingly with Mr. Bird's determination of the lengths of the toiscs sent by Mr. Lalandc to Dr. Maskelyne, of which the mean ■was 76.734 inches : hence the metre, having been found to contain 36.9413 French inches, appears to be equal to 39.3702 English inches: or rather to be either 39.3694 or 39.3710, accordingly as the one or the other of the two toises happens to have been the more correct ; we may therefore give the preference to that which measured 76.738 Inches. Allowing the accuracy of the French measurements of the arc of the meridian, the whole circumference of the globe will be 24S55.43 English miles, and its mean diame- ter 7911.73. Joum, R. I., I. 129. In tlie Bibliotheque Britannique, Vol. 19, No. 4. we find a description of the comparer of Lenoir, by Mr. Prony. Its peculiarity consists in the application of a bent lever, of which the shorter arm is pressed against the end of the substance to be measured, while the longer serves as an index, carrying a vernier, and pointing out on a graduated arch the divisions of a scale, which by this contrivance is considerably extended in magnitude. It does not, however, at first sight, appear to be certain that the difficulty of fix- ing the a.tis of the lever with perfect accuracy, and of form- ing a curve for the surface of the shorter arm, or of reducing the graduation of the arc to equal parts of the right line in the direction of the substance to be measured, might not in practice more than counterbalance the advantage of this ^ mechanical amplification of the scale, over the simpler optical method employed in the English instruments. Journ. R. I., I. 180. Eug lish Measures. A foot is 12 inches. A Viird 3() A pole or 1 •od 198 A furlong 7920 A mile 63360 A link 7.92 A chain 792 A nail of cloth 2.^ A quarter 9 A yard 36 An ell 45 A hand 4 An acre 4840 square yards, By an act of Oueen Anne, the wine gallon is fixed at 231 cubic inches. Hence, A pint is 28.87-5 cubic inches. A quart 57-73 A barrel 7276.5 A hogshead 14553. A pint, beer measure, ale measure, and country measure, is 35-25 cubic inches. CATALOGUE. PHILOSOPHY AND ARTS, PRACTICAL MECHANICS'. 151 A quart 70.5 cubic inches. A gallon 282. A barrel, beer measure, is 10152 A barrel, ale measure, is 9024 A barrel, country measure, is 9588 A hogshead, beer measure, is 15228 A hogshead, ale measure, is 13336 A hogshead, country measure, is 14382 A pint, dry measure, is 33.6 cubic inches. A quart G7.2 A pottle 134.4 A gallon 268.8 A peck, 537.6 A Winchester bushel 2150.42 A heaped bushel is one third more. A quarter 17203.36 Five quarters make a way or load ; two loads, a last of wheat. A bushel of wheat, at a mean, weighs 60 pounds, of bar- ley 50, of oats 38. A chaldron of coals is 3fi heaped bushels, weighing about 2988 pounds. ' Ten yards of inch pipe contain exactly an ale gallon, weighing 10| pounds. Emerson. The old Standard wine gallon of Guildhall contains 224 cubic inches. It is conjectured, that some centuries before ^he conquest, a cubic foot of water weighing looo ounces, 32 cubic feet weighed iooo pounds or a ton ; that the same quantity was a tun of liquids, and a boghead 8 cubic feet, or 1382* cubic incles, one sixtythird of which was 219.4 inches, or a gallon. A quarter of wheat was a quarter of a ton, weighing about 500 pounds, a bushel one eighth of this, equivalent to a cubic foot of water. A chaldron of coals was a ton, and weighed 2000 pounds. Barlow. At present, 12 wine gallons of distilled water weigh exactly 100 pounds avoirdupois. Scotch Measures. An ell is 37.2 E. inches. A fall 223.2 A furlong 8928. A mile 71424. A link 8.928 * A chain, or short rood 892.8 E- inches. A long rood 1339-2 An acre is 55.353.6 square feet, English, or 1.27 English acre. A gill is A mutchkin A choppin A pint A quart A crallon 6.462 cubic inches E. 25.85 51.7 103.4 206.8 827.23 A hogshead 13235.7, or I6 gallons. By the act of union, 12 Scotch gallons are reckoned equal to an English barrel, or 9588 cubic inches, instead of 9927. A lippie or feed is 200.345 cubic inches English. Old French Measures. A point is .0 148025 E. inch, or nearly -j^. A line .088815, or nearly -^. An inch 1.06578, or -^-j^y' °'" t?* Thus, if a tall man were six feet four, French measure, 81 he would be precisely six feet nine, English, And — i^ 76 9X9 4X19 A foot 12.78933. An ell 46.8947, or 44 French inches; or, according to Vega, 43.9. A sonde 63.9967, or 5 French feet, about I E. fathom. Bonne, E. M. A toise 76.7360, or 6 French feet. A former comparison made it 76.7 1. Ph. tr. 1742. 185. The Bothnian toise was found too short by ^y or ->^ line; but this was supposed to be froin its having been acciden- tall injured. Laeondamine. Aperche 230.2080, or 18 French feet. A perche, mesure royale, 22 French feet. A league, 2282 toises, or ^'-5- of a degree. A square inch, 1.13582 square inches, E. An arpent was 100 square perches, about 152 CATALOGUE. — PHILOSOPHY AND AETS, PRACTICAL MECHAVICS. -\ E. acio, in the measure commonly used about Paris. An arpent, mesure royule, was about l^ E. acre. A cubic inch is 1.21063 cubic inches, E. A litron 65.34 A boisseau 1045.44, or l61itrons. A minot 2090.875, or 3 boisseaux, or nearly. an E. bushel. , A mine 4181.75, or 2 minots. A septier 8363.5, or 2 mines, or 6912 inches, Fr. For oats the septier was double. A muid 100362. or 12 septiers. A ton of shipping contains 42 cubic feet. New French Measures. Journals R. I., 1. 130. The barbarous terms of the new nomenclature are here reduced to a form more consistent with their etymology. English Inches. Millimetre .03937 Centimetre .3937 1 Decimetre 3.937 10 Metre 3.281 feet 39-37100 Decametre 393.71000 Hecatometre 3937.10000 Chiliometre 39371.00000 Myriometre 393710.00000 A metre is 1.093(54 yards, or neaily 1 yard, 1^ nail, or 443.2959 lines Fr. or .513074 toise. A decametre is 10 yards 2 feet 9-7 inches. A hecatometre 1 09 y. if. i in. A chiliometre 4 furl. 213 y. 1 f. 10.2 in. A micrometre 6 miles 1 f. 158 y. O f. 6 in. 8 chiliometres are nearly five miles. An inch is .0254 m. 2441 inches 62 metres, looo feet nearly 305 metres. An are, a square decametre, is 3.95 perches, E. A hecatare, 2 acres 1 rood, 35.4 p. Cubic Inches, E. Millilitre .06103 Centilitre .61028 Decilitre 6.10280 Litre, a cubic decimetre 6l .02800 Decahtre 610.28000 2 Cubic inches, E. Hecatolitre 6102.80000 Chiliolitrc 61028.00000 Myriolitre 610280.00000 A litre is nearly 2J wine pints; 14 decilitres are nearly 3 wine pinu; achiliolitre is 1 tun, 12.75 wine gallons. A decistere for fire wood is 3.5317 cubic feet, E. A stere, a cubic metre, 35.3171 Various Measures, ancient and modern. From Folkes, Raper, Shuckburgh, Vega, Hutton, Cavallo, and others. Ancient Measures. Arabian, foot 1.095 Engl. H. „ , , . , C 1.144 H. liabylonian, toot < ■' i 1.135 H. Drusian, foot ] .090 H. Eg3'ptian, foot 1.421 H. Egyptian, stadium 730.8 Greek, foot 1.009 H. 1.006 "^FoTkes, 1^ 1.007 3 Roman f. 1.007 C. Greek, phyleterian foot 1.167 H. Hebrew, foot 1.212 H. Hebrew, cubit 1.817 H. Hebrew, sacred cubit 2.002 H. Hebrew, great cubit=6 common cubits. H. Macedonian, foot 1.160 H. Natural foot .814 H. Ptolemaic = Greek foot. H. Roman, foot .970 Bernard. .967 .966 ^ Picard and I. G reaves. .966 ■> .967 3 Folkes. .970 before Titus. Raper. .965 after Titus. Raper. CATALOGUE. — PHILOSOtHY AND ARTS, PRACTICAL MECHANICS. 153 Roman, foot .9672 from rules. Sli. .9681 from build- ings. Sii. .9696 from a stone, Sh. .967 H. Roman mileof Pliny 4840.5 C. Roman mileof Strabo 4903. Sicilian foot of Ar- chimedes .730 H. Modern Altdorf, foot Amsterdam, foot Amsterdam, ell Ancona, foot Antwerp, fobt Aquileia, foot Aries, foot Augsburg, foot Avignon =: Aries. Barcelona, foot Basle, foot Bavarian, foot Bergamo, foot Berlin, foot Bern, foot Besan5on, foot Bologna, foot Bourg en Bresse, foot Brabant, ell, in Germany Bremen, foot Brescia, foot Brescian, braccio Breslau, foot Bruges, foot VOL. II. Measures. .775 .927 .930 .931 2.233 1.282 .940 1.128 .888 .972 Engl. H. H. C. Howard. C. H. H. H. . H. H. .992 .944 .968 1.431 .992 .962 1.015 1.244 1.250 1.030 2.268 .955 1.060 2.092 1.125 .749 H. H. Beigel. See Munich. H. H. Howard. H. H. C. H. V. H. H. C. H. H. Brussels, foot Brussels, greater ell Brussels, lesser ell Castilian, vara Chambery, foot China,mathematical China, imperial foot Chinese, li Cologne, foot Constantinople, foot Copenhagen, foot Cracau, foot Cracau, greater ell Cracau, smaller ell Dantzic, foot Dauphine, foot Delft, foot Denmark, foot Dijon, foot Dordrecht, foot Dresden, foot Dresden, ell =2 feet Ferrara, foot Florence, foot Florence, braccio .902 H. 954 V. 2.278 V. 2.245 V. 2.746 C. 1.107 H. foot 1.127 H. 1.051 H. 1.050 C. CjOG. C. .903 H. 2.195 "^H. l.l6o>H. 1.049 H. 1.169 H.V. 2.024 V. 1.855 V. .923 H. 1.119 H. .547 H. 1 .047 H. 1.030 H. .771 H. .929 Wolfe, Ph.tr. 1769. V. 1.857 V. 1.317 H. .995 H. Franche comte, foot Frankfort =: Hamburg Genoa, palm Genoa, canna Geneva, foot Gr6noble= Dauphine Haarlem, foot Halle, foot Hamburg, foot C. 1.900"? 1.9103 1.172 H. H. .812 H. .8173 7.300 C. 1.919 H. H. .937 H. .977 H. .933 H, 154 CATALOGUE, — PHILOSOPHY AlfD ARTS, PRACTICAL MECHANICS. Heidelberg, foot Inspruck, loot Leghorn, foot Leipzig, foot Leipzig, ell Leyden, foot Liege, foot fcisbon, foot Lucca, braccio Lyons=Dauphine. Madrid, foot .903 H. 1.101 H. .992 H. 1.034 H. 1.833 H.Journ.R.L 1.023 H. .944 H. '^ .952 H. 1.958 e. .915 H. .918 Howard. Madrid, vara , 3.263 C. Maestricht, foot .916 H. Malta, palm .915 H. Mantua, brasso 1.521 H. Mantuan, braccio =:Bresci an. C. Marseilles, foot .814 H. Mechlin, foot .753 H. Mentz, foot .988 H. Milan, decimal foot .855 H. Milan, aliprand foot 1.426 H. Milanese, braccio 1.725 C. Modena, foot 2.081 H. Monaco, foot .771 H Montpclier, pan .777 H. Moravian, foot .971 V. Moravian, ell 2.594 V. Moscow, foot .928 H. - Munich, foot .947 H. Naples, palm .861 H. .859 C. Naples, canna 6.908 C, Nuremberg, town foot .996 H. .997 V. Nuremberg, country foot .907 H. Nuremberg, artillery foot .96I V. Nuremberg, ell 2.166 V. Padua, foot 1.406 H. Palermo, foot .747 H. Paris, foot I.O66 H. Paris, metre Parma, foot Parmesan, braccio Pavia, foot Placentia=Parnaa Prague, foot 3.281 Y. 1.869 H. 2.242 C. 1.540 H. 0. .987 H. .972 V. 1.948 V. Prague, ell Provence= Marseilles Khinland, foot (f 1.023 H.) 1.030 V. Eytelwein. Riga=Hamburg Rome, palm .733 H. Rome, foot .966 Folkes. Rome, deto, tV f- '0604 F. Rome, oncia, -^ f. .0805 F. Rome, palmo .2515 F. Rome, palmo di architet- tura .7325 F. Rome, canna di architet- tura 7.325 F. Rome, staiolo 4.212 F. Rome, canna deimercanti6.5S65 F. 8 palms Rome, braccio dei mer- canti 2.7876 F. 4 palms. 2.856 C. Rome, braccio di tessitor di tela 2.0868 F. Rome, braccio di archi- tettura 2.561 C. Rouen = Paris. H. Russian, archine 2.3625 C. Russian, arschin 2.3333 Pli.M.XIX. Russian, verschock, -^ ar- schin .1458 Savoy = Chambery H. Seville =: Barcelona H. Seville, vara 2.760 C. Sienna, foot , 1.239 H. Stettin, foot 1.224 H. Stockholm, foot 1.073 H. CATALOGUE. — PHfiOSOPHV AND ARTS, PRACtlCAL MKCHAKICS. 15.* Stockholm, foot (.974 CelsiusPh.lr.) Strasburg, town foot .956 H. Strasbuig, country foot .969 H. ToletIo= Madrid H. Trent, foot 1.201 H. Trieste, ell for woollens 2.220 H. Trieste, ell for silk 2.107 H. Turin, foot I.C76 H. 1.681 C. Turin, ras 1-958 C. Turin, trabuco 10.085 C. Tyrol, foot I.O96 V. Tyrol, ell 2.639 V. Valladolid, foot .9O8 H. Venice, foot 1.137 H. 1.140 Bernard, Howard, V. I.1G7 C. Venice, braccio of silk 2.108 C. Venice, ell 2.089 V, Venice, braccio of cloth 2.250 C. Verona, foot 1.117 H. Vicenza, foot 1.136 H. Vienna, foot 1 .036 H. 1.037 Howard,C.V. Vienna, ell 2.557 V. Vienna, post mile 24688. V. Vienne in Dauphinc, foot 1.058 H. Ulm, foot .826 H. Urbino, foot I.162 H. Utrecht, foot .741 H. Warsaw, foot I.I69 H. Weseln Dordrecht H. Zurich, foot .979 H. .984. Ph. M. VIII. 289. Modern Measures of surface and capacity. In Austria, a yoke of land contain! isoo square fathoms; 1 laetz or bushel 1.9471 cubic feet, 1 eimerz:*o kannen:: 1.79a cubic feet, of Vienna; 1 fassmo eimer. Vega. In Sweden, a kanne contains io( cubic inches Swedish. C. Measuring Instruments. For their expansion see Heat. Ph. tr. 1790. 121. Rods. Lemonnier on the increase of length of two rods. A. P. 1761. H. 26. Boulard's invariable toise. Roz. XL. 198. Roy found that deal rods, not varnished, were lengthened about half an inch in 300 feet by exposure for one night to moisture. Glass tubes were substituted for them, with caps of bell metal at the ends, connected with them by springs, which were brought in each operation to a certain mark on the rods ; in order that unequal compression of the rods might be avoided. The French have employed rods of metal not brought perfectly into contact, measuring the short distance by a micrometer. Chains. Ramsden's steel chain. Ph. tr. 1785. .394. The chain was found in the course of the trigonometrical survey began by General Roy not only the most convenient but also the most accurate measure. It was extended, when used, by a considerable weight, which was always equal . See Figure of the earth . A chain of 40 links each 2^ feet long. Ph. tr. 1795. 423. Scales. Hooke on diagonal divisions. Animadv. on Hevelius. Wallis on diagonal divisions. Ph. Ir. 1674. IX. 243. Calibers, Leup. Th. Suppl. t. 24. Robertson on instruments. Ramsden's description of a machine for di- viding straight lines. 4, R. S. Beam compasses. See compasses. Enc. Br. Art. Calibers. Micrometers. See Measurement of Angles-. 156 CATALOGUK. — PHLOSOPHY AND ARTS, PRACTICAL MECHANICS. Hodometers, Machines for Measuring Distances. Vitruvius describes a hodometer which told the miles by the fall of a pebble into a bason. A. P. 1.45. Lcup.Th. Suppl. t. 3 . .6. Meynier. A. P. 1724. H. 96. Mach. A. IV. ga. 101. 105. For carriages. Outhier. A. P. 1742. II. 143. Mach. A. VII. 17.5. For carriages. Boistissandeau. A. P. 1744. H. 61. Edgeworth's perambuhitor. Bailey's mach. I. 59. A long screw serves as an axis to several spokes or radii with which it revolves, and carries an index hanging always vertically. Enc. Br. Art. Perambulator. Tugweli's pedometer. Repert. VI. 249. Edge- worth's improved. Gout's patent watch pedometers. Repert. XIII. 73. Instruments for observing Distances. See Practical Astronomy. Gensanne's machine. Mach. A. VII. 111. Vantometrum Pauccianum. 4. For a single station. R. S. Wenz on measuring distances from a single station. Act. Helv. 176O. IV. 55. An instrument for measuring distances. Soc. Lausanne. Roz. XXXII. 95. Peacock's reflecting instrument for measur- ing distances. Repert. 1. 163. Pitt's dendrometer. Repert. II. 238. With and without reflection. Fallon's reflecting engymeter. Zach. mon. corr. VI. 46. Surveying. Ph. tr. abr. I. ii. 120. VI, iv. 271. VIII. jv. 228. E. M. PI. VII. Art. Arpentage. Emerson's cyclomathesis. X. Wild on subterraneous surveying, and on sur- veying mountainous countries. M. Laus, 1789. 11.328. 333. Meagher. Ir. tr. V. 325. Drallet on surveying hilly ground. Journ. Phys. XLVIII. 321. Pfleiderer on determining 8 points from 4 sta- tions, after Lambert. Hind. Arch. III. 190. Dam's surveying. 8. Lond. 1802. Burckhardt on a problem in surveying. Zach. mon. corr. IV. 359. 653. Lomet on the use of balloons in surveying. Nich. VI. 194. b. Maritime Surveying. Murdoch Mackenzie on maritime surveying. 4. R. S. Sounding line. E. M. A. VII. Art. Sonde. Cooke on measuring a ship'sway. Nich. V. 48. Gauging, and Measurement of Solids. On the tonnage of ships. A. P. I. 243. Varignon on the tonnage of ships. A. P. 1721.44. H.43. Mairan on the tonnage of ships. A. P. 1721. 76. H. 43. 1724. 227. Gamacheson gauging casks. A. P. 1726. H. 74. Mach. A. IV. 223. Pezenas on gauging casks. A.P. 1741.H. 100. Camus's instrument for gauging. A.P. 1741.- 385. H. 105. Chatelain on gauging casks. A. P. 1759. H. 237. Tillet's two machines for determining mea- sures of capacity. A. P. 1765. 452. H. 128. Emerson's cyclomathesis. X. Hutton's mensuration. Deson the theory of gauging. S. E. 1773. xvi. E. M. A. VIII. Art. Veltage. E. M. PI. VII. Matheinatique PI. 8. CATALOOUE. PHILOSOPHY AND ARTS, PRACTICAL BIECHAMICS. 157 Say's instrument for measuring volumes. Ann. Ch. XXIII. 1. Faiey on measuring timber. Pii. M. XIX. 2 13. Modelling. Aurum musivum for bronzing. Birch. I. 103. Moulage. E. M. A. V. Porcelaine. E. M. A. VI. Artificial gems. E. M. A. VI. 739- Papier mache. E. M. A, VI. Art. P&tes moulees. Beads. E. M. A. VI. Art. Paternotrier. E. M. Beaux Arts. Impressions in wax. Duhamel Art du cirier. f. Par. p. 93. On multiplying copies in relief. Wilson. Nich.II. 60. Gray. Nich. IV. 286. Wedgwood's patent for ornamented porce- lain. Repert. VII. 309- Yates's patent for multiplying engravings. Report. XII. 309. Thin plates filled up with lead. Casting. Modelling for foundery. Valvasor on cast- ing statues. Ph. tr. l686. XVI. 259. E. M. A. III. Art. Fondeur. E. M. PI. II. Art. Per. iii. PI. 3 . . Q. MauHin's patept for casting screws. Repeit. XIII. 6. Imison's elements. II. 555. Lenormand on moulding carvings. Ph.^ M. XVI. 247. Sculpture. Ph. tr. Abr. I. ix. 598. E. M. A. VIT. Art Sculpture. E. M. Beaux Arts. On the use of steatite for gems. Ph. M. XVIII. 83. To be hardened by heat. Perspective. Aleaume Perspective speculative et pratique. 4. Paris, 1643. R. S. La perspective practique. 3 v. 4. Par. 1647. • M. B. * Jesuit's perspective. 4. Lond. Perspective. Ph. tr. abr. I. ix. 598. Huret Optique de portraiture, f. Par. 1670. Ace. Ph. tr. 1672. VII. 5048. * Brook Taylors linear perspective. 8. Lond. R. I. Ace. Ph.tr. 1719- XXX. 300. Zanotti's general theorem for perspective. C. Bon. III. 169. Emerson's cyclomathesis. VI. Malton's perspective. 4. R. I. i^far^m's graphical perspective. 8. 1771. Priestley's perspective. 8. Kirhy's perspective. Kirby's perspective of architecture. Clark's practical perspective. 8. R. S. Perspective. E. M. PI. VII. E. M. PI. VIII. Art. Amusemens d'optique. Torelli Elementa perspectivae. 4. Veron, 1788. R. S. Lambert on perspective. Hind. Arch. III. 1. Valenciennes Elemens de perspective pra- tique. 4. Par. an 7. R. 1. *Monge Geometric descriptive. 4. R. I. JSc?aYirrfs on perspective. 4. Lond. 1803. R.S. Perspective Instruments. Wren's insuument for drawing in perspec- tive. Ph. tr. 1669. IV. 898. Saint tlare Parallelogrammum prosopogra- phicum. Ph. tr. 1673. VIII. 6079- L'ouvrier's instrument for drawing fiom na- ture. A. P. 1753. H. 301. Edgeworth's instrument for drawing. Nich. 8.1.281. 158 CATALOGUE. — PHILOSOPHT AND ARTS, PRACTICAL MECHANICS. Ilettlinger's machine for drawing. Roz. XXIV. 389. With glass. Peacock's instmments for drawing in per- spective. Repert. I. 313. +Storer's patent delineator. Repert. IV. 239. A camera obscura. A frame for drawing in perspective. Hut- ton's recreations. II. 208. Edgeworth's instrument for drawing. Nich. 8.1.281. Berard's steganographic scale. Nich. 8. IV. 246. Projections of the Sphere. See Geography. Engraving and Etching. Evcli/ris art of engraving. 8. Lond. l6G2. M. B. Mortimer on an antique metal stamp. Ph. tr. 1738. XL. 388. Gravure. E. M. A. III. E. M. Beaux Arts. Jackson oa engraving in chiaroscuro. 8. R. I. Cutting letters in copper. E. M. A. VI. Art. Plaques de cuivre. Etching. E. M. A. VI. Art. Pinceau. Rochon's mode of engraving by a machine. Rochon Recueil de mecanique. Journ. Phys. XLVII.(IV) 365. Nich. III. 6l. Enc. Br. Art. Type. Nicholson's instrument for drawing parallel lines. Nich. II. 429. Lowry's ruling machine. Nich. II. 523. Accum upon etching on glass. Nich. IV. 1. Puymarin on engraving upon glass. Repert. V. 210. Longhi's moveable table for engiavers. Re- pert. V. 354. The aquatinter. 4. London. Imison's elements. II. 345. The ground for etching is made of white wax and asphat- tum, each 40 parts, black pitch and Burgundy pitch, each one part : the wax and pitch are melted together, and the asphaltum is added ; the whole is then kept simmering, till it becomes of a proper consistence. The plate is to be heated over a chafing dish, so as to melt the ground. The margin is surrounded with a mixtuie of one part of bees wax with two of pitch. Turpentine varaish, mixed with lamp- black, is occasionally used during the progress of the work. Imison. Printing, For PresseSj see Compression. Fournier Manuel typographique. 2 v. 8. Par. 1764. R. I. Printing cards. Duhamel du Monceau Art de faire les cartes a jouer. f. Paris. *Luckombe on printing 8. 1771. R. I. Anisson on printing, and on a new press, with figures. S. E. 1785. X. 6l3. E. M. A. III. Art. Imprimerie. Imprimerie en taille douce. Imprimerie en couleurs. Printers grammar. 8. 1787. R. I. Nicholson on printing with rollers. Nich. I. IS. On stereotype printing. M. Inst. Nich. III. 43. Rochon on typography. See Engraving. Niebuhr on the Babylonian bricks. Zach, mon. corr. VII. 435. Tilloch on stereotype printing. Ph. M. X. 267. Magrath's Printers' Assistant. 8. 1805. Types. Moricherel's new matri.ves for types. A. P. 1751. H. 171. Types. E. M. A. I. Art. Caracteres d'impri- merie. Luce's vignettes for printing. A. P. 1772. i. ■^Barclay's patent types. Repert. II. 4. Sage on type metal. Repert. VIII. 418. Ashby on printing types. Repert. XI. 18, CATALOGUE, — PHILOSOPIiy AND AUTS, PRACTICAL MECHANICS. 159 Enc. Br. Art. Printing press. Rusher's patent types, lleperl. ii. I. 91. Musical Types. Fournier's musical types. A. P. 1762. H. 192. Gando on printing music. A. P. 1763. H. 134. Copijlng. Watt's patent for copying writings. Repert. I. 13. Coquebert's simple method of copying. B. Soc. Phil. n. 50. Nich. 8. T 147- By putting sugar in the ink, and passing a hot iron over unsized paper laid on the writing. Toplis's method of multiplying copies. Re- pert. IV. 111. Printing ink is applied to the block, and the correspond- ing parts of the impression remain white. Paper. See Union of^ Fibres. Bookbinding. Dudin Art du relieur doreur de livres. f. Par. E.M. M. III. Art. Relieur. Williams's patent for bookbinding. Repert. XLI. 89. Palmer's patent for binding books, with hinges of metal. Repert. XIV. 305. Unrolling old books. E. M. A. VI. 732. Statics. Effect of the Air. Fuss on the application of statics to geome- try. N. A. Petr. 1793. XI. 220. Homberg on the difference of weight in the air and in a vacuum. A. P. X. 257. See Hydrostatics. Balances. Lahire on balances. A. P. IX. 42. Roberval's new balances. A. P. X. 343. Illustrations of balances. Leup. Th. Slat. 3, 6 . . 9. Euler on balances. C. Petr. X. 3. Emerson's mechanics. Fig. 188. 205. 206. Brander Beschreibung einerhydrostatischen • wage. 8. Augsburg, 1771. Magellan's balances. Roz.II.253. XVII. 44. 432. Scanegatty's hydrostatic balance. Roz. XVII. 82. E. M. A. I. Art. Balancier. E. M. Physique. Art. Balance. Ramsden's balance. Roz. XXXIII. 144. Turns with •fjriisooi of 'he weight, and weighs ten poands. Ramsuen's hydrometrical balance. Roz. XL. 432. Shuckbilrgh on a balance. Ph. tr. 1798. Liidicke's balance. Gilb. I. 123. Troughton's balance. Nich. III. 233. ' Andrews's patent balance. Repert. XI. 16. Prony's universal support for balances. Ann. Ch. XXXVI. 3. JNich. V. 313. Repert. XV. 51. Guyton's report on a balance. Ann. Ch. XLII. 23. Atwoodon balances. Gilb. IV. 148. Dillon's balance approved. M. Inst. IV. Wilson's patent weights. Repert. ii. II. 100. Studer remarks, that beams of steel become sometimes erroneous by acquiring magnetic polarity. Gilb. XIII, 124. For weighing air or gases, the apparatus may be plunged in water, to lessen the pressure on the beam. Robison. Money is sometimes weiglied by a simple lever with « fixed weight : by flattening it, it might be made to prepon- derate. Weighing Machines. Weighing machines. Leup. Th. Stat. t. 45. 10 . . 19. Th. M. G. t. 33. 34. l60 CATALOGUE. — PHLOSOPIIT AND ARTS, PRACTICAL MECHANICS. Desaguliers. p. 23. Emerson's mechanics, f. 312. A weighing machine with chains. Salmon's patent weighing machine. Repert. VI. 73 A weight acting on a spiral. Whitmore's patent weighing machine. Re- pert. IX. 103. Secured from rust. Weighing machine. R^es Cyclop. II. PI. Engine. Steelyards. Hooke's steelyard. Birch. IV. 242. Roemer's Danish balance. Mach. A. I. 79. Lahire on the steelyard. A. P. IX. 46. fEmerson's mechanics. F. 190. Compound steelyard. F. 288. Lambert. Act. Helv. III. 13. Steelyard for iron. E. M. PI. II. Art. Fer. ii. Pi. X. Cassini's steelyard shows the price of goods weighed. Pictet on Paul's steelyard. Ph. M. III. 408. A coarse steelyard with a moveable fulcrum is sometimes made of wood. Bent Levers. Lahire on the bent lever balance. A. P. II- 9- Lambert. Act. Helv. III. IS. Desaguliers on the balance with an oblique thrust. Ph. tr. 1729- XXXVI. 128. Ludlam's bent lever balance for yarn. Ph. tr. 1765. 205. A balance with a curved surface a* ■ fulcrum it a bad substitute for a bent lever balance. Spring Steelyards. A spring steelyard. Musch. Introd. I. PI. 4. Formed like a pair of shears. Hanin's spring steelyard. A. P. 1765. H. 135. S. A. IX. 151. Roz. XXXIX. Enc. Br. Regnier's spring steelyard, approved. M. Inst. Standard Weights. See Standard Measures. Rkemniiis Fannius Palaemon de ponderibus at mensuris. Commonly published with Priscian. Norris's inquiry into the ancient English weights and measures. Ph.tr. 1775.48. Desaguliers on the French and English weights. Ph. tr. 1720. XXXI. 112. *Barlow on the analogy between English weights and measures of capacity. Ph. tr. 1740. XLI. 457. Comparison oT English and French weights. Ph. tr. 1742. XLII. 185. 1743. XLII. 541. ♦Reynardson on English weights and mea- sures of capacity. Ph. ir. 1749- XLVI.54. Considers the avoirdupois as the true standard, and the ounce as equal to the old Roman ounce. Chrtsttani delle misure d'ogni genere. 4. Ven. 1760. Tillet on French and foreign weights. A. P. 1767.300. H. 175. Raper on the Greek and Roman money. Ph. tr. 1771.462. Brookes on East Indian weights. Colebrooke on Indian weights. As. res. V. 91. E. M. Commerce. 3 v. Coquebert on the Chinese weights. B. Soc. Phil. n. 1. Coquebert on the Dutch weights. B. Soc. Phil. n. 74. Fair's tables. R. S. Shuckburgh's experiments on standards. Ph. tr. 1798. Studer on the weight of water. Gilb. XIII. 122. Eytelwein. See Journ. R. I., I. 150. Cavallo's Philosophy. IV. CATALOGUE. PHILOSOPHY AN'D ARTS, PUACTICAL MECHANICS. l6l Hutton's recreations. II. 152. Fletcher onShuckburgh's experiments. Nich. 8. IV. 55. A gramme, the standard of the new French weights, is the weight of a cubic centimetre of pure water, at its maxi- mum of density,n.08l0280 cubic inches, English. The cubic dfcimetre vias found to weigh in a vacuum 1 S8-37.I5 grains of the marc of Charlemagne, which differed a little from Tillet's. The chiliogramme of platina wa^ adapted for a vacuum, that of brass for the air. The cubic foot of water weighed 70 pounds 223 grains, at its maximum ; 70 pounds 130 grains at the freezing point. M. Inst. H. "01. Hence a pound is 489.5058 grammes, a gramme I8.82;i5 grains French. According to Coquebert Montbret, a pound is only 48y.l47 grammes. B. Soc. Phil. n. 74. It may be inferred from Sir George Shuckburgh'j experi- ments, that the diameter of a sphere being 6.0074 5 inches, it loses 28715.85 grains of Troughton in water, reduced to Jy°, or the maximum of density of water, the air at 39°, the barometer at 30., the standard brass scale employed at 62^. Hence, under these circumstances, tire weight of a cubic inch of water, weighed against brass in air, is 252.8033 parliamentary grains: in vacuo 253.094; of a cubic foot in air 43684.41 grains::z998.5 oz. av.i::62.4063 pounds av. ; in vacuo 43735.6 grains— 999. C? ounces:z62.48 pounds. If we reduce these measures to more usual temperatures, the barometer being still at 30, the weight of a cubic inch at 52° will be found 252.08 grains ; of a cubic foot 998 ounces ; at 60°, the temperature employed by Gilpin, 252.56 grains, and 997.0 ounces; at 62°, the standard temperature of English measures, 252.52 grains, and 997.4 ounces. At this temperature, four cubic inches make 1010 grains, and 12 gallons exactly 100 pounds avoirdupois. Mr. Fletcher finds some other experiments of Sir G. Shuckburgh more accurate than the author supposed them, and therefore takes a mean of the whole. After all cor- rections, the barometer standing at 29.5, the temperature 60°, th« cubic inch of water appears to weigh in air 252.519 grains from the experiments on the cube, 252.432 from the cylinder, and 252.568 from the sphere ; the mean being 252.500 ; in a vacuum 252.806. _If the barometer be at 30, the weight from the sphere will be 252.563, nearly, as already stated, and the mean 252.501 ; we may there- fore call it accurately 252.50; in a vacuum 252.77; for we must not add .3, which is the whole weight of a cubic inch of air, but only the difference between the weight of air and of brass. The French experiments, reduced to the same circumsunces, give 252.56, and 352.83, agreeing VOL. II. with the sphere ; taking the gramme— 1 5.44 403 gr. If we prefer Mr. Fletcher's mean, we must make the gramme— 15.440 grains. Professor Robison found a cubic foot at 55° weigh 998.74 ounces. Enc. Br. Art. Specific gravity. Hence, a cubic inch is equal to 252j at 50° ; but his weights were not so well authenticated as Sir G. Shuckburgh's. Atkins on Specifie Gravity. Jacquin found a cylinder, 1 inch in diameter, 2 inches long, lose,'in distilled water, 393.6 grains apothecaries weight of V'ienna, the thermometer being at 43°, the baroraetcf 2Si inches of Vienna ; it was weighed in air. English Weights. The avoirdupois ounce is supposed by Barlow to be the thousandth part of a cubic foot of water. The avoirdupois pound has been found to weigh 7001.5 or 7000.5 grains troy. Ph.tr. 1743. A pennj'wcight, troy is G4 gr. An ouncCj or 20 pennyweights, 480 A pound, or 12 ounces, 5700 A drachm, avoirdupois, is 27.35 gr. troy. An ounce, or \6 drachms, 437.5 A pound, or iG oz. about 7000. A stone is 14 pounds; a quarter 28 pounds; a hundred weight 112 pounds; a ton 20 hundred weight, or 2240 pounds. A scruple, 9j, apoth. weight, is 20 gr. troy. A drachm, 5j, or 9iij, 60 An ounce, ^, or S^'U' '^SO A pound, ftj, or ^xij. 5760 Ten ounces troy are nearly Cijual to 1 1 avoirdu] 17 pounds troy to 14 avoirdupois. Scotch Weights. An ounce is 476 grains troy. A pound trone is 20 ounces ; a stone 16 pounds. Old French Weights. A grain is .8203 gr. Eng. A denier, 24 gr. French, 19.69 A gros, 3 deniers, 59.06 An ouuce^ 8 gros, 478.5, ^i oz. troy. A marc, 8 ounces, ^780. Y I6''i CATALOGUE. — PHILOSOPHY AND ARTS, PRACTICAL MECHANICS. A pound, 2 marcs, 7560. ii ll>- troy. 1.08 1b. av. Milligramme Centigramme Decigramme Gramme Decagramme Hecatogramme Chiliogramme New French Weights. .0154 grains Eng. .1544 1.5444 15.4440 = ^?-°-f^, or 18.827 gr.Fr. 154.4402, or 5.65 dr.av. 1544.4023, or 3 oz. 8.5 dr. av. 15444.0234, or 2 lb, 3oz. 5 dr. av. Myriogramme 154440.2344, or 22 lb. 1.15 oz. av. A hundred myriogramraes are nearly a ton. The sous and the franc weigh each 5 grammes. The franc contains one tenth of copper. ^indent and Modern Weights. Ancient Weights, from Hutton. Greek Weights, in English grains. 8.2 Christian!. 9.1 Arbuthnot. 51.9 Christiani. 54.6 Arbuthnot. 3892. =75drachms.Chr. Attic greater mina 5189. =100 dr. Chr. 5464. Arbuthnot. Attic medicalmina 6994. Arbuthnot. Attic and other talents=:60 minae. Old Greek drachm 146.5 Arbuthnot. An othei: Gr. drachm 62.5 = Ronian denari- us. Arbuthnot. Old Greek mina 6425. Arbuthnot. Egyptian mina 8326. Ptolemaic mina of Cleopatra 8985. Alexandrian mina of Dioscorides 9992. Attic obolus Attic drachma Attic lesser mina Roman Weights. Denarius 51. 9 Christiani, | oz. 62.5 Arbuthnot, yoz. Ounce 415.1 Christiani. 437.2 Arbuthnot. Pound of 10 ounces 4151. Christiani. Pound of 12 ounces 4981. Christiani. 5246. Arbuthnot. Various Modern Weights, from Hutton, Ca- vallo and Vega. Pounds. E. grai: ns. Aleppo, rotolo 30985. H. Alexandria 6159. H. Alicant 6909. H. Amsterdam 7461. H. Amsterdam, com - mercial pound 7636. = 10280 ases = 1.1 494.048 grammes. Coquebert. = 493.93 grammes. Vega. Amsterdam, troy pound 7602. Adjusted at Brussels 1553,= 10240ases = 491.96 gram. Coquebert, = 492.0044 gram. Vega. A stone is l6pounds,apound 16 ounces, an ounce 16 drops. Amsterdam, apothecaries pound, 369 gram. Vega. Antwerp 7048. H. Avignon 6217. H. Basle 7713. H. Bayonne 7461. H. c 4664. H. ^^■■S^"^ I1166O. H. Bergen 7833. H. CATALOGUE. — PHILOSOPHY AND ARTS, PRACTICAL MECHANICS. 16S China, kin Fbunds. E. grains. Berlin 7232. Eytelwein. A cubic foot Fr. of water, weighing 63.9308 pounds. Bern 6722. BiIboa=Bayonne. H. Bois le Due 7105. H. Bourdeaux = Bayonne ' .Bourg 7074. H, Brabant pound of Amsterdam 7249.=469.12 grammes. Coquebert. Brescia 4497. H. Brussels, heavy pound =Troys. V. Brussels, light pound 7201 .=466.3 grammes. V. Cadiz 7038. H. r9223. H. l5802. = 37.5.708 grammes- =:12 oz. 2 gros24 gr. Fr.= 10 leangs =: 100 tsiens. Coquebert. f 7220. H. O2I8. Eytelwein. A cubic foot Fr. of water, making OO.ofisfl pounds. 7223. =467.74 grammes. Vega. A cubic inch Fr. of water, at 59°, weighs 330.04 grains ef Cologne. Studer, in Gilb. XL 11. 122. Constantinople 7578. H. Copenhagen 6941 H. Cracau, commer- cial pound 6252. H. =404.85 gram. Vega. Cracau mint mark 3071. = 198.82 grammes.' Vega. Damascus 25613. H. Dresden 7210. = 468.83grammes.V. Dantzic 6574. H. Dublin 7774. H. Florence 5287. H. Geneva 8407- H. , Cologne Pounds. E. grains. r. ("4426. H. uenoa < ,(.6638. H. Germany, apoth. pound 5523. = S57.66 grammes. Vega. Hamburg 7315. H. Konigsberg 5968. H. Leghorn 3146. H. Leyden 7038. H. Liege 7089. H. Lille 6544. H. Lisbon 7005. H. London, avoirdu- pois 7000. = 453.61 grammes. Vega. London,troy 5760. H.=373.14gram.V. Lucca 5273. H. Lyons, silk 6946. H. Lyons,to\vn weight 6432. H. Madrid 6544. H. Marseilles 6041. H. Melun 4441. H. Messina 4844. H. Montpelier 6218. H. Namur 7174. H. Nancy 7038. H. Naples 4932. H. Nuremberg 7871. = 509.78 grammes. Vega. Paris 7561. H, =489.5 gram.V. Prague, commer- cial pound 7947. = 514.35 grammes. Vega. Revel 6574. H. Riga 6149. H. Rome 5^57. H. Rouen 7772. 11. Saragossa 4707- IL Seville=Cadiz. Smyrna 6544. IL 164 CATALOGUE. — PHILOSOPHY AXD AUTS, PRACTICAL MECHANICS. Pounds. Stettin Stockholm Strasburg Toulouse E. grains. 6782. H. 9211. H. 7277. H. 6323. H. Venice Troys. See Amsterdam. Turin 4940. H. Tunis 7140. H. Tyrol 8693. = 562.92grammes.V. t"4215. H. 16827. H. Venice, libra sottile oi' 12 ounces=302.03 grammes. Vega. Venice, pound of 12 ouuces=:358.1 grammes. Vega. Venice, pound of 12 ounces, peso grosser: 468.17 grammes. Vega. Venice, libra grossa=477.49 grammes. Vega. Verona 5374. V. C4676. H. (.6879. H. Vienna, commer- cial pound 8648. =560.01 grammes. Vega. Vienna, apoth. pound=:420.01 grammes. Vega. Vienna, mint mark =280.64 grammes. V. The jeweller's carat at Vienna is .206085 grammes. Vega. Apothecaries Grains of different countries, from Vega. Vicenza Portugal Rome Spain Sweden Venice Austria Bern France Genoa Germany Hanover Holland Naples Piemont 1.125 = 1 .956 .981 .850. .958 .959=-H- Gilbert. .978 .989 .860 .824 { .864 .909 .925 .955 .809 Sources of IMotion. For the application, see Machinery. Deschamps on the force of machines. A. P. 1723. H. 120. *Leup. Th. M. G. t. 33. 34. On the measure and expense of first movers. Nich. H. 459. jinimal Mechanics. *BorelU de motu animalium. R. I. Perrault on animal uieclianics. A. P. I. 181. Parent on animal mechanics. -A. P. 1702. H. 95. J). Bernoulli on the muscles and the nerves. C. Petr. I. 297. Mairan on the position of the legs in walk- ing. A. P. 1721. H. 24. Bourgelat on the motions of a horse. S. E. HI. 531. Motions of animals, flying, and swimming. Emerson's mechanics, f. 222 . . 226, p. 206. Horses. E. M. A. IV. Art. Marechal ier- rant. Pinel on animal mechanics. Roz. XXXI. 350. XXXIII. 12. XXXV. 457. Barthez Elemens de la science de I'homme. Extr. Journ. Phys. XLVII. (IV.) 271. Imison's elements. I. 73. Animal Force. A. P. On the strength of men and horses. . 1.47. Lahire on the strength of men and horse*. A. P. 1699. 153. H. 96. CATALOGUE.— PHILOSOPHY ANB ARTS, PUACTICAL MECHANICS. \65 Aiiiontonson moving powers. A. P. 1703. H. * Camus Traite des forces mouvantes. 8. Par. 1722. ]\I. B. Instances of Inimaa strength. Desag. Lect. I. '289. Deparcieux on the draught of horses. A. P. 1760. 263. H. 151. Emerson's mechanics. Ferguson's mechanics. Lambert on human strength and its appiica- catiou. A. Berl. 1776. 19. Cazaucl on sugar mills. Ph. tr. 1780. SIS. Horses. E. M. A. I. Art. Chevaux. Schulze on the strength of men and horses. A. Berl. 1783. 3S3. Rennel on the rate of travelling of camels. Ph. tr. 1791- 1'29. About ll miles an hour. Kegnier's dynamometer. Journ. Polyt. II. v. 160. Gilb. li. 91. Ph. M. I. 399. Coulomb on the daily labour of men. B. Soc. ■ Phil. n. 16. M.Inst. II. 380. Nich. III. 416. Buchanan on human hibour. Repert. XV. 319. The comparative force exerted in the action of pumping was ]74i, by a winch 2856, in ringing 3 s 83, in rowing 4095. On the powers of horses and steam engines. Nich. IX. 214. According to Schulze's experiments, the force which a man or a horse can exert with the velocity v, is n: / ( 1 Y ,/ being the force in equilibrium, and a the ve- locity without resistance. This is a formula of Euler : ano- ther of his expressions// 1 \ does not agree so well with Schulze's experiments. But Euler's theory is founded on assumptions wholly arbitrary. According to the first formula, the greatest mechanical effect would be wlien jizi ^a ; according to the second, when D=:v' I". In order to compare the different estimates of the force of moving powers, it will be convenient to take a unit which may be considered as the mean effect of the labour of an active man, working to the greatest possible advantage, and without impediment ; this will be found, upon a moderate estimation, sufficient to raise 10 pounds 10 feet in a second, for 1 0 hours in a day : or to raise 1 oo pounds, which is the weight of 12 wine gallons of water, 1 foot in a second, or scooofcetinaday; or afiooooo pounds, or 432 000 gallons, 1 foot in a day. This we may call a force of 1. continued 36000". Immediate Force of men, without deductioii for friction. Force. Continu- Days ation. work. A man weighing 133 pounds Fr. ascended 62 feet Fr. by steps, in 34", but was completely exhausted. Amontons. 2.8 3-t" A sawyer made 200 strokes of 18 inches Fr. each in 14 5", with a force of 25 pounds Kr. He could not have gone on above 3 minutes. Amontons. .6 145" A man can raise 00 pounds Fr. 1 foot Fr. in 1", for 8 hours a day. Bernoulli. .69 sh. .a-i A man of ordinary strength can turn a winch, with a force of 30 pounds, and with a velocity of 3^ feet in l", for lO hours a day. Desaguliers. i.Oj loh. 1.05 Two men working at a windlass, with handles at right angles, can raise 70 pounds more easily than one can raise 30. Desaguliers. 1.22 1.22 .A man can exert a force of 40 pounds for a whole day, with the assistance of a fly, " when the motion is pretty quick, as about 4 or 5 feet in a second." Desaguliers, Lect. 4. But from the annotation it appears to be doub'.ful whether the force is 40 pounds or 20. 2. 2. For a siiort time, a man may exert a force of 80 pounds, with a fly, " when the motion is pretty quick." Desaguliers. 3. 1' A man going up stairs ascends 14 metres in 1'. Coulomb. 1.182 l' A man going up stairs for a day raises 205 chiliogramme* to the 1(56 CATAI.OGUK.— rillLOSOPHY AN4 yarns, a circumference of 28 lines, and a weight of 12^ gros for 6 inches, the untarrcd rope showed a rigidity of 2 2 172 CATALOGUE. PHILOSOPHY AND ARTS, PEACTICAL MECHANICS. pounds, and ■ ■ of the weight, and the tarred rope, of 3.3 pounds and — - of the weight. 10.34 These results were confirmed by experiments on a roller allowed to move on a horizontal plane, while a rope was coiled completely round it. Here it becomes necessary to make an allowance for the friction of the roller on the plane, which varies as its weight, and inversely as its diameter. For a roller of guaiacum or lignum vitae, 1 8.8 inches in diameter, moving' on oak, it was of the Weight ; for a roller of elm |- more. Mr. Coulomb proceeds to relate experiments made imme- diately on a simple pulley, where the fiiction of the axis and the rigidity of the rope produce a joint resistance. When guaiacum moved on iron, the friction was — or— of 5.4 6.4 the weight in all velocities, besides the rigidity of the rope ; the mean was — , or, with a small weight, a little greater. For axes of iron on copper — or , where the velocity was 11 11.5 small : the friction being always a litde less than for plane 1 surfaces. With grease, the friction was about — . 7.5 With an axis of green oak, or ilex, and a pulley of guaia- cum, the friction with tallow was — '; without it-L ; with ae 17 a pulley of elm, these quantities became 1- 3, i. An 33 20 axis of box, with a pulley of guaiacum, 'gave i. and — . 23 14 ' •with a pulley of elm, — and J.. An axis of iron, and a 29 20 pulley of guaiacum gave, with tallow, _L. 20 The velocity had little effect on the rigidity of ropes, ex- cept to increase the resistance slightly, when the pressure was small. Mr. Coulomb suggests that the lower surface of a dray ought to be a little convex, in order to facilitate a slight agi- tation, and to diminish the friction. For launching ships, he recommends oak sliding on elm, previously well rubbed with tallow, by means of heavy weights ; and ob- serves that the velocity ought not to be so great as to melt the tallow. In the pulley, the friction on the axis is somewhat modi- fied by the simation of the surface of contact, which is not perfectly horizontal, but the difference may be neglected in practice. This excellent memoir is concluded by a cal- culation of the force requisite to raise 8O00 pounds by a capstan, and a rope of 120 strands, with a purchase of 12 to 1 ; and it appears, by inferences from the experiments al- ready stated, that about one ninth of the force employed would in this case be lost. Architecture in General. Vitruvius. Vitruve par Perrault. f. Par. ] 673. Newton's Vitruvius. 2 v. f. R. S. Palladio. i. 1721. R.I. Pli. tr. Abr. I. viii. 588. VI. viii. 4Go. Blondel's resolution of the four principal problems of architecture. A. P. V. ii. 1. Aldriclis elements of civil architecture. 8. Oxf. 1789. Krafft's theory of the orders of architecture. C. Petr.XI. 288. Nollet's observations on architecture in Italy. A. P. 1749. 473. H. 15. Emerson's mechanics. Emerson's miscellanies, 322. Vitruvius Britannicus. 3 v. f. Continued. 2 v. f. London. Kent's Inigo Jones, f. 1770. R. I. Pini dialoghi dell' architettura. 4. Milan, 1770. R. S. Huths biirgerliche baukiinst. *Coulomb's application of the rules of max- ima and minima to problems of architec- ture. S. E. 1773. 343. E. M. Architecturo, 1^ vol. to Es. R. I. Chambers on civil architecture, f. 1791. R. I. Rudiments of antient architecture. London. Essai/s on Gothic architecture. 8. London. R.I. S Davis's portable cart crane. S. A. XV. 278. Ph. M. V. 392. Repert. X. 273. A perpetual screw for cranes. Repert. II. 312. Collins's elevator. Am. tr. IV. 5 19. Repert XV. 26. A lever with pullies. CATALOGUE. — PHILOJSOPIIY AND ARTS, VTIACTICAL MECHANICS. JQg Millington's double capstan crane. Repert. XIII. £99. Inclined plane with cranes. Fulton on ca- nals. Gent's crane. S. A. XIX. 293- Repert. ii. I. 418. With a quadrant for raising or lowering the gih. Keir's crane at Ramsgate. Nich. 8. ill. 124. Marriott's engine. Nioh. 8. IV. 41. Brainah'sjib for a crane. Nich. VIII. 99. With a rope in the axis, which is perforated. Modes of raising Weights of par- ticular Descriptions. See seamanship. Blondel on raising marshes. A. P. I. 234. Labalme's machine for clearing harbours. A. P. 1718. H. 74. Gonffe's machine for clearingharbours.Mach. A. II. 63. Ressin's mode of raising materials in build- ing. Mach. A. III. 27. Ressin's mode ofloading and unloading ships. Mach. A. III. 29. A machine for ^clearing harbours. Mach. A. Ill, 167. Perpoint'sjack for pump rods. Mach, A. IV. 33. Machine for pulling up trees. Leup. Th. Hydrot. t. 11. Mode of raising scaffolding or shears. Leup. Th. Machinarium. t. 33. Pump rods raised by screws or by oblique circles. Leup. Th. Hydrot. ii. t. 36. Mairan'sjack for telescopes. Mach. A. V. 31. Dubois's machine for clearing harbours. A. P. 1726. H. 70. Guyot's machine for clearing harbours. A. P. 17.53. H. 98. Mach. A. VI. l63. Briandferes machine for raising stones. A. P. 1737. H. 106. Macary's machine for clearing harbours. A. P. 1744. H. 62. Mach. A. VII. 259. Lav'ier's machine for clearing harbours. A. P. 1745. H. 81. Lonce's machine with revolving buckets for raising ballast. Mach. A. VII. 449. Clearing harbours. Belidor. Arch. Hydr. II. ■ ii. 131. 156. Machine employed for clearing the port of Toulon. Belidor. Arch. Hydr. II. ii. PI. 20. Walking wheel for raising a sluice board. Belidor. Arch. Hydr. If. ii. PI. 54 . . 56. Robertson's account of the raising of the Royal William. Ph. tr. 1757.288. Jurine's machine for pulling up trees. A. P. 1765. H. 136. Redelykheid Machine a creuser les pores, f. Hague, 1774. Chatel's machine for clearing harbours, A. P. 1777. H. Frazer's tongs for fishing up goods. Bailey's mach. II. 72. Mode of climbing up a steeple. E. M. PI. L Couvreur. 2. Suspended scaffolding. E. M. PI. IV. Pein- tre en batimens. Cranes used in glass houses. E. M. PI. II. Glaces. PI. 16. Machine for clearing harbours. E. M. PI. I. 27. E. M. PI. V. Marine. PI. 76. Machine for pulling up trees. E. M. Art. Aratoire. Bertrand's machine for clearing harbours.. Journ. Phys. XLVIII. 373. EUicott's corn mill with buckets for raising flour. Repert. IV. 319. Sparrow's patent machine for raising earth. Repert. V. 77. Davis's cart crane. See cranes.. A machine for pulling up trees, Enc. Br. Art. Bern machine. 200 CATALOGUE. — PHILOSOPHY AND ARTS, PRACTICAL MECHANICS. Arkwrighi's machine for raising ore. S. A. XIX. 278. Nich. 8. I. 303. Repert. ii. I. 261. Buckets connected by frames. Raising and lowering boats. Fulton on ca- nals. Whidbey on the recovery of the Ambuscade. Ph.tr. 1803.321. Machine for raising floating wood out of the water. Person Recueil. PI. 11. Ponti's stone gatherer. Repert. IV. 137. Willich Dom. Enc. Art. Stones. Saint Victor's machine for rooting up trees. Nich. 8. IV. 243. Antis's register for the draughts from a mine. S. A. XXI. 380. Nich. IX. 114. Lowering Weights. Most machines for raising weights are also employed for lowering them ; some are appropriated to this purpose only. See regulation of descent. Removing Weights. Friction. Diminishing Lahire on lessening friction. A. P. IX. 119. Hermand's mode of diminishing friction. Mach. A. III. 7. Mondran's machine for diminishing friction. A. P. 1725. H. 102. Mach. A. IV. 1 19- Fitzgerald on friction wheels. Ph. tr. 1763. 139. By means of friction quadrants a Steam engine was ena- bled to do the work of 6 hours in 5, the friction of its beams being reduced from 95 pounds to ;J of a pound, and from 425 pounds to 2-^i)ounds. Removing AVeiglits without Wheel Can"iages. Duncombe's patent sedan chairs. 1634. Blondel's mode of raising marshes. A. P. I. Perrault's machine for drawing weights. Mach. A. I. 31. Machine for drawing weights. Mach. A. I. 129. Willin's sedan chair. Mach. A. II. 137. Hermand's dray on connected rollers. 1713. H. 76. Mach. A. III. 7. Such a carriage was lately made in London. Alix's machine for drawing weights. Mach. A.m. 193. Sebastien's machine for moving trees. Mach. A. IV. 107.' Coetnisan's machine for moving trees. Mach. A. IV. 109. Rollers. Leup. Th. Machinarium. t. 8. 9- Buckets hung on a rope for moving earth. Leup. Th. Hydrot. t. 20. Fenel on the alternate tensions of cords drawing a load. A. P. 1741. H. 155. PuUies. Emers. mech. f. 239. CarburiTnxvaux pour transporter un rocher. 8. Paris, 1777. R. I. Riding. E. M. Equitation. 1 vol. Monge on the best mode of moving a given quantity of matter into a given situation, deblais et remblais, Fr. A. P. 1781. 666. H. 34. Screws for removing flour. EUicott's corn mill. Repert. IV. 319. Coulomb on carrying weights. See sources of motion. Coulomb observes, that the surface of drays ought to be made convex, in order that they may be more shaken, and that the friction maybe diminished. See Friction. Removing goods in fires. Person's parafeu. Recueil. PI. 12 . . 15. Heavy blocks may be removed on rollers mounted upon wheels, so as to avoid the friction on the axles. But this is not great. In Holland, when wooden drays are employed, it is usual to carry water for moistening them, in order to prevent their taking fire. CAtALOGUE. — PHILOSOPHY AND ARTS, PRACTICAL MECHANICS. 201 Tlieory of Wheel Carnages. On the benefit of high wheels. Ph. tr. lG85. XV. 856. Lahire on the magnitude of wlieels. A. P. IX. 116. Parent on the friction upon axles. A. P. 1712.96. Reaumur on the axles of wheels. A. P. 1724. 300. Couplet on the draught of carriages. A. P. 1733. 49. H. 82: Dupin de Chenoncenu on fourwheeled car- riages. A. P. 1753. H. 301. Emerson's mech. 194. The axis is conical, that it may not wear loose ; and it must be a little inclined in order to avoid its working against the linch pin. Beparcleux. A. P. I76O. 263. H. 151. Boulard and jSlargueron on broad wheels. Eoz. XIX, 424. Jacob on the draught of wheel carriages. 4. Anstice on wheel carriages. 8. Rizzetti Riforma d^' carri di quattro ruote, 8. Trevigi, 1785. 'R. S. Edgeworth's experiments on wheel carriages. Ir. tr 1788. II. 73. Repert. I. 101. Lamber on four wheeled carriages. Hind. Arch. II. 51. The axes of the wheels should be as their diameters, the rcntre of gravity should divide the distance in the ratio of the cubes of the diameters. A good proportion for the wheels is 4 to i, the centre of gravity being twice as near the hind as the fore wheels. This is nbl ¥ery remote from the usual practice. Grobert sur les voitures a deux roues. 1797. Enc. Br. Art. Mechanics. A. Young, annals of agr. XVIII. Strongly in favour of carts. Fuss Versufch einer theorie des widerstandes zwey-und-vier-r'adiger fuhrWerke. Copenb . 1798.- Extr. Ph.M. Xm. 115. On muddy roads, four wheels have the advantage, if they VOL. II. run in the same ruts. On harder roads, whether smooth or rough, if not very steep, two wheels have the advantage, and sometimes on soft roads, where there is much lateral friction on the flat surfaces of the wheels. Anderson's institutes of physics. Mech. xvii. quoted by Cavallo. N. Phil. A horse can draw 25 cwt. on a level road in a cart weigh- ing 10 cwt. with wheels 8 feet high. In a common cart 1 horses easily draw 30 cwt. In a common waggon 6 horses draw 80 cwt. : in 3 carts they might draw QO, in 6, 150 cwt. : and 3 carts cost less than a waggon. Gumming on the effect of conical wheel*. Board Agr. II. 351. Repert. XIII. 256. Would have the axis straight and the wheels cyUndricat« but somewhat dished. Montucia and Lalande. III. 732. Imison's elements. I. 129. Ferguson's lectures by Brewster. 3 v. 1 805, With many useful additions, yet not without mistakes. The great advantage of broad wheels is in deep road*, where the resistance is derived from the depth of immer* sion. Particular kinds of Carriages. Sailing carriages. Wilkins's mathematical magic. Gusset's cart for moving great weights, hi nurd Fr. ]Mach. A. I. 99- Thomas's cart with a windlass. Mach. A. II. 39. Beza'« ehrnr on castors. Mach. A. II. 173. Girard's machine for moving a chair. Mach. A. II. 187. Descainns's coach suspended in the middle. A. P. 1713. H. 76. Descamus's improvements in coaches; A. P^ 1717. H. 83. Mach. A. III. 65. 109. Godefroy'sinversable chair. Mach. A. III. 97. Lelarge's jointed car. A. P. 1719- H. 81. Mach. A. III. 197. Tanney de Gourney's inversable coach. A. P. 1719- H. 82. Mach. A. III. 207. Reaumur's carriage^ for narrow streets. A.P. 1721. 224. Dd 202 CATALOGUE. — PHILOSOPHY AND ARTS, PRACTICAL MECHANICS. Mondran's carriage with little friction. Mach. A. IV. 123. Coetnisan's machine for moving trees. A. P. 1724.H. Qfi. Maillard's chairs driven by winches. A. P. 1731. H. 92. Mach. A. V. 171. 173. Maillard's chair with an artificial horse. Mach. A. VI. 141. Lievre'slandaulet. A.P. 1732. H. 118. Mach. A. VI. 3. Duquel's inversable coach. Mach. A. VI. 7. Brodier's chair for driving one's self. S. E. IV. 351. E. M. PI. VII. Mecanique. PI. 3. Chenonceaux's carriage. Mach. A. VII. 439. The lowest wheels 4 feet high. Loriot's machine for moving statues. A. P. 1755. H. 144. Loriot's jointed cart for barrels. A. P. 1761. H. 16I. Garsault's new berline. A. P. 1756. H. 127. Cart. Emerson's mech. f. 201. Waggon, driven within. Emerson's mech.*f. 202. Brethon's carriage remaining horizontal. A. P^ 1763. H. 147. Brethon's chaise for bad roads. A. P. 1766. H. 159. Roubo Art du menuisier carossier. f. Paris. Ace. A.P. 1770. Ferry's arm chair on wheels. A. P. 1770. H. 117. La Gabrielle, a cart for sculpture. Roz. XI. 522. Carriages. Bailey's mach. I. 185. Bailey's waggon for short turnings. Bailey's mach. II. 59. The axles connected diagonally. Waggons and carts. E. M. A, I. Art. Char- ron. .Carriages. E. M. A. IV. Art. Menuiserie. Parts. Carriages for casks. E. M. PI. IV. Tonnelier. PI. 8. With a windlass. Scavenger's carts. E. M. A. VIII. Art. Vui- dangeur. Carriages used in glass houses. E. M. PI. II. Glaces. PL I6. Wheelbarrows. E. M. Art. Aratoire. Boulard's cart. Roz. XXVII. 426. Hatchett's plates of the coach of safety. R.S. Besant's high wheeled timber carriage. S. A. VI. 203. Anderson's conveyance for boats. Repert. II. 21. Weldon's patent machine for conveying ves- sels. Repert. II. 235. Middleton's machine for dragging haj'. S. A. XIV. 197. Repert. VI. 27. Beatson's mode of avoiding deep ruts. Re- pert. vin. 26. Jeffrey's patent for conveying coals. Repert. XI. 145. Overend's patent carriage on castors. Repert. XI. 159. Bakewell's improved car. Repert. XIV. 1 10. Reddel's patent land and water carriages. Repert. XIV. 369. •f-A coach. Walker's philosophy. Lect. iii. Lord Somerville's dray cart. Board Agr. II. 415. Repert. XVI. 49. Capable of elevation, so as to bear more or less on the horses; with Mr. Cumming's drag, applied laterally to the wheels. Improved Irish car. Board Agr. 11.417. Low and easily laden, the wheels cylindrical and under it. Lord R. Seymour's cart. Willich's Dom. Enc, Art. Cart. Wheelbarrows. Person Recueil. PI. 6, 7. Bauer's patent carriages. Repert. ii. I, 250. With small axles. Mason's patent waggon making two carts. Repert. ii. III. 249. CATALOGUE. PHILOSOPHY AND ARTS, PRACTICAL MECHANICS, 203 For deep roads, a dray may be combined with a cart, so as to support tlie weight when the wheels sink too much. Parts of Carriages. Thomas's suspension of carriages. Mach. A. II. 43. Godefroi's mode of hanging post chaises. A. P. 1716. H.78. Zacharie's suspension for coaches. A. P. 1761. H. 156. Reynal on carriage springs. A. P. 1765. H. 134. Maillard's suspension for chairs with wheels. Mach. A. VI. 95. Jacob's spiral carriage springs. Bailey's mach. I. 167. Jacob's patent box for axles. Repert. ii. III. 170. Wheelwright's work. E. M. A. IV. Art. Ma- rechal grossier. VI [. Art. Roue. Coach springs. E. M. PI. IV. Serrurerie. PI. 29. Dodson's patent naves of wheels. Repert. XII. 235. With rollers. " Appendages to Carriages. Drags, Harnesses, Sadlery. Horses. See Statics. Dalesme's simple mode of stopping horses. A. P. 1708. H. 141. Mach. A. II. 153. By blindfolding them. Lahire's machine for unlocking horses. A.P^ 1712.242. Ressin's mode of facilitating descents to car- riages. Mach. A. III. 31. Harness and sadlery. Garsault Artdu Bour- relier et du Sellier. f. Par. E. M. M. IH. Art. Sellier. Accoutrements and harness. E. M. A. II. Art. Eperonnier. Black's Roman yoke. S. A. II. 87. Colley's locking pole for a carriage. S. A. XI. 198. Jones's patent woman's saddle. Repert. IV^. 9. Kneebone's wheel drag. S. A. XIII. 262. Re- pert. IV. 25. Hesse's elastic stirrups. Repert. XIII. 371. Inglis's patent saddle. Repert. XV. 217. Snart's alexippus, or sliding 1 ever for a cart S. A. XVIII. 230. Repert. XV. 110. Davis's mode of unlocking horses and stop- ping the wheels. S. A. XVIII. 256. Re- pert. XV. 166. Dickinson's patent saddles. Repert. XVI. 294. Dickinson's patent saddle straps. Repert. ii. I. 247. Cumming's drag. See Lord Somerville's cart. Williams's patent for disengaging horses. Re- pert. ii. I. 86. Pottinger's patent for disengaging horses. Repert. ii. III. 96. Bowler's gripe for carriages. S. A. XXI. 358. Nich. IX. 177. Meyer has a patent for a method of stopping horses by winding up the reins on an axis turned by a wheel of the carriage. Roads. See Inclined Planes. Agricultural Instruments. Lelarge's mode of paving roads. Mach. A. III. 129. Considerations on roads. 8. Lond 1734. R. S. Lambert on the best ascent of roads. A. BerL 1776. 19. Meister on the shortest roads to different places. N. C. Gott. 1777. VIII. 124, Pinchbeck's road plough. Bailey's mach. II. 21. Harriott's road harrow. S. A. VII. 205. With sweeps. 204 CATALOGUE. — PHILOSOPHY AND ARTS, PRACTICAL MECHANICS. Beatson's roller for preventing deep ruts. Simple press with a windlass. E. M. PI. IV. Repert. VIII. £6. Edgeworth oa rail roads. Nich. 8. 1. 221. Roads. Board Agr. I. 119. Harrows and rollers for roads. Board Agr. I. 150. Wilkes, Board Agr. I. 199- Concave roads are much approved in Leicestershire, Wilkes on iron railways. Board Agr. II. 474. Repert. XIII. 167. ^ Iron roads. Board Agr. I. 203. A horse drew 3 tons up a railway rising 7 inches in 144. The draught was 327 pounds besides friction. Woodhouse's patent rail roads. Repert. ii. III. 15. Woodhouse on concave iron roads. Repert. ii.III.i7. Wyatt on a railway. Repert. ii. III. 283. Hollister's patent machinery for making . roads. Repert. ii. III. 401. Winterbottom's machine for clearing roads from mud. S. A. XXI. 334. Nich. VIII. 29. Compression. Presses, strictly so called. See Printing. Leupold. Th. Moulins's machine for folding stuffs. A. P. 1737. H. 107. Cheese press. Emers. mech. f. 189- Lloyd's cyder press. Bailey's mach. II. 5. Without a screw. » Hunter's screw. Ph. tr. 1781. 58. Nich. VII. 50. Press with a water wheel. E. M. PL I. Char- pentier. t. 18. Cheese press. E. M. A. HI. Art. Fromage. Printing press. E. M. A. III. Art. Impri- Wooden vices. E. M. PI. H. Ebeniste. PI. merie. VI. . Parfumeur. PI. 2. Tobacco and snuff presses. E. M. A. VIII. Art. Tabac. An oil press with screws. E. M. PI. VIII. Moulin £l huile. Wine press. E. M. Art Aratoire. Anisson Description d'une presse d'imprime- rie. 4. R. S. S. E. X. 613. Many figures ; somewhat complicated. Haas Description d'une presse d'imprimerie. 4. Basle. 1791. R.S. Ridley's printing press with a lever. S. A. XIII. 243. Repert. V. 26. Peck's packing press. S. A. XV. 267. Rep. VIII. 46. Sabatier's patent mode of packing. Repert. VIII. 73. Prosser's patent printing press. Repert. VIII, 368. With springs.. Whieldon's patent press. Repert. IX. 217. With wheelwork. ' ' Enc. Br. Art. Cyder Press. Press. Printing Press. Buschendorfs packing press. Repert. ii. Ill, 362. Bowler's press with a spiral spring. S. A. XXI. 363. To continue an active pressure. Vices, Pincers, and Pliers. HuUot's new vice. A. P. 1756. H. 127. E. M. PI. III. Horlogerie. E. M. PI. IV. Taillanderie. Clamp vice. E. M. PI. II. Doreur. PI. 2. f. 20. CATALOGUE. PHILOSOPHY AND ARTS, PRACTICAL MECHANICS. 205 Caleoder Mills and Mangles, with Rollers. Bunting's calender mill, worked by a crank supported on rollers. S. A. XV. 269. Re- pert. YUl. 176. Jee's mangle worked by a crank. S. A. XVI. 303. Repert. XIV. 109. Ph. M. II. 419- Calendering is usually performed by a polishing stone or glass pressed down by a spring, and moved backwards and forwards by a mill. Compression between Rollers. Rolling press. Emers. mech. f. 273. Cazaud connaissances pour juger des moulins acannes. Pli.lr. 1780.318. The work of 36 mules produces 80 or lOO gallons of li- quor in an hour : making 120 to 150 hogsheads in a season; the immediate resistance being about 19,000 pounds ; a good water mill should do twice as much. Sugar mill. E. M. PI. IV. Sucrerie. Watt's patent for copying writings. Repert. I. 13. Kirkwood's patent copperplate printing press. Repert. ii. III. 245. Compression by Percussion. Dubois's rams or stampers for beating the earth. A. P. 1726. H. 70. Mach. A. IV. 163,169, 171. Extension. Simple Extension. Glass blowing and drawing threads of glass. £. M. A. VIII. Art. Verre. Reaumur thinks that glass as fine as spider's webs might be woven. Extension by Pressure. A. P. 1714. H. Dalesme proposed to draw leaden pipes with a core, ift the way that the patent pipes are now made. Fayolle's machine for laminating lead. A. P. 1728. H. 108. Mach. A. V. 43. Blackey on drawing steel wire. A. P. 1744. H. Gl.Mach.A. VII. 2.'>5. Chopitel's machine for laminating iron. A. P. 1752. H. 148. Vaucanson's machine for laminating silver and gold thread. A. P. 1757. 155. H. I6I. Plating mill. Emers. mech. f. 251. Glazier's vice. Emers. mech. f. 305. Duhamel Art de reduire le fer en fil d'archal. f. Par. Ace. A. P. 1768. H. 128. 1770. H. 110. E. M. A. IV. Art. Laminage. Wire drawing. E. M. A. VIII. Art. Tireur- fileur. Trefilerie. Drawing rods for bolts. E. M. PI. IV. Serru- rerie. PI. 24. Glazier's vice. E. M. PI. V. Vitrier. PI. 3. Wilkinson's patent pipes, drawn on a core. Repert. XVI. 92. Extension by Percussion. Compagnot's forge hammer. A. P. 1730. H. 115. Mach. A. V. 101. Forge hammer. Emers. mech. f. 236.237. Courtivron et Bouchet Art des forges a fer. f. Paris. Ace. A. P. 1761. H. 153. 1762. H. 187. Duhamel Art de forger les enclumes. f. Par. Ace. A. P. 1762. H. 188. Forges. Roz. Introd. II. 76. Forges. E. M. A. II. Art. Fer. Hand forge. E. M. PI. IV. Serrurerie. PI. 32. Gold and silver leaf. E. M. A. I. Art. Bat- teur. Forges at Carron. Smeaton's reports. On hammering metals into plates. Nich. I. 131. Hand forge. PesronRecueil. PI. 9, 17. Walby's forge hammer worked by a man. S. A. XXII. 335. A hammer of 70 pounds making 300 strokes in a minute. 206 CATALOGUE. — PHILOSOPHY AKD ARTS, PRACTICAL MECHANICS. Arts depending principally on Ex- tension. See Appendages to Clothes. Plumbery. F;i3olle's machine for casting lead pipes. Mach. A. V. 53. Coining. Dubuisson's machine for prevent- ing accidents in coining. A. P. 1731. H. 91. Mach. A. V. 155. Gold and silver plate. .Dufay on applying reliefs of gold to gold or silver plate. A. P. 1745. H. 45. Horn plate vvoik. D'Incarville on the Chi- nese lanterns. S. E. II. 350. Plumbery. Art du plonibier. f. Paris, Pipemaking. Duhamd Art de fabriquer les pipes, f. Paris. Porcelain. Milli Art de la porcelaine. f. Par. Pottery. Duhamd du Monceau Art du potier deterre. f. Paris. Anchors. Duhamd Art de la fabrique des ancres. Ace. A. P. 1761. H. 152. Baking pottery. Roz. Intr. II. 266. Pottery. Bosc d'Antic on pottery. S. E. VI. 372. Defensive arms. E. M. A. I. Art. Armurier. Coppersmith's work. E. M. A. I. Art. Chau- dronnier. Brass work. E. M. A. II. Art. Cuivrejaune. Pewter ware. E. M. A. II. Art. Etain. Pottery. E. M. A. II. Art. Fayencerie. VI. Art. Poterie, Tin plate work. E. M. A. II. Art. Ferblan- tier. Blacksmith's work. E. M. A. IV. Art. Mare- chal-grossier. Coining. E. M. A. V. Art. Monnoyage. With an account of the coins of difTerent nations. Goldsmith's work and jewellery. E. M. A. V. Art. Orfevre. Rcsingue is an elastic anvil, which rebounds, and acts as a hammer in the inside of a vessel. Vocab. Art. Rc- singue. Pipemaking. E. M. A. VI. Art. Pipes a fu- mer. Plumber's work. E. M. A. Art. Plomb. Pewter. Salmon Art du potier d'etain. f. Par. 1788. R. S. Coining. Montu's coining press, with a swing lever. B. Soc. Phil. n. 14. Pottery. Lasteyrie on the alcarraza, for cool- ing water. Ph. m. I. Smith's work. Moorcroft's patent horse shoes. Repert. VI. 157. Made by machinery. Porcelain. Dechemant's patent paste for teeth. Repert. VI. 379- Porcelain. Turner's patent. Repert. XII. 294. Nails. Spencer's patent horse nails. Repert. XV. 316. Coining. Hatchett and Cavendish on the wear of gold. Ph.tr. 1803.43. Nich. 8. V.286. Journ. R. I. II. Tenetration and Division. Theory of Penetration. Camus on a board pierced by a bullet, and scarcely moved. A. P. 1738. 147. H. 98. Euler on the strokes of bullets on a board. N. C. Petr. XV.414. Ja. Bernoulli on the stroke of a bullet upon a board. N. A. Petr. 1786. IV. 148. Gough on the motion of a cylinder urged by a falling block. Manch. M. IV. 273. Merely speculative. Observes, that in driving piles, the resistance is neither uniform nor proportional to the depth. The velocity of a carpenter's baminet is about 2i feet in a second, Robison, CATALOGUE. — PHILOSOPHY AND ARTS, PRACTICAL MECHANICS. 207 Instruments of Penetration in ge- neral, and Substances of which they are composed. Military engines. Mathematici veteres Vege- tius, and Ammianus Marcellinus. Reaumur Art de convertir le fer en acier. 4. Paris. Silbersciilag on the warlike machines of the ancients. A. Berl. 176O. 378. Ferret Art du coutelier. f. Paris. Ace. A. P. 1769. H. 131. Fougeroux Art du coutelier en ouvrages communs. f. Paris. Duhamel Art du serrurier. f. Paris. Cutlery. E. M. A. II. Art. Coutelier. Sword cutlery. E. M. A. III. Art. Fourbis- seur. Coarse tool?, files, and ironmongery. E. M. A. VIII. Art. Taillanderie. Agricultural instruments. E. M. Agriculture, 3^ volumes io Ey. Instruments of agriculture and horticulture. E. M. Art Aratoire. I vol. Little on making steel. Am. Ac. I. 525. ■ Vandermonde on steel and cutlery. Amii Ch. XIX. 13. Franklarid on welding cast steel. Ph. tr. 1795. 296. Repert. V. 327. Pearson on woolz. Ph. tr. 1795. 322. Pearson on some ancient arms. Ph. tr. 1796. 395. 422. Consisting of copper with some tin, from g to 14 per cent. The ancients sometimes also employed cast steel, of which some specimens were examined. A mixture of cop- per and iron was less hard than an alloy with tin. On steel. Nich. I. 468. II. 64. Ann. Ch. XXVU. 186. Stodarron steel. Nich. IV. 127. Wild's patent for uniting steel and hon. Re- pert. 11. 368. Cort's patent for preparing iron. Repert. III. 289, 361. Dize on the copper cutting instruments of the ancients. Repert. IV. 62. Hartley's patent for tempering instruments. Repert. IV. 310. By a thermometer. Clouet on cast steel. B. Soc. Phil. n. 14. Varley on steel and its preparation. Ph. M. II. 92. 178. Mushet on iron and steel. Ph. M. II. 155. 340. Collier on iron and steel. Manch. m. V. IO9. Repert. X. 97- Saws are quenched in oil 5 penknives are tempered till they become light yellow ; scissors light brown ; table knives, swords, and watch springs, blue. Edgill's patent steel. Repert. XI. 157. Gazeran on steel. Ann. Ch. XXXVI. 6l. On gilding cutlery. Cecum's chemistry. 11.172. Nich. VI. 142. Conte sa.ys, that oil varnish with half its weight of spirit of turpentine, is a good preservative from rust. Stodart on Damascus sword blades. Nich. VII. 120. Penetration by Pointed Instru- , inents. Taking whales. Buch. I; 325. Pile engine. Mach. A. I. 125. Lahire's pile engine. A. P. 1707. 188. Camus's pile engine. A. P. 1713. H. 76. Mach. A. III. 3. Vergier's machine 'for driving piles. Mach. A. III. 189. Driving piles. Leup. Th. Hydrot. t. 24, 25, 29. Raucourt's invention for shooting with cross bows. Mach. A. VI. 157. Murtin's pile engine. A. P. 1742. H. 156.. Bond on killing whales by means of a ba- lista. Ph. tr. 1751.429. 208 CATALOGUE. — PHILOSOPHY AND ARTS, PIIACTICAL MECHANICS. L'Herbctte's pile engine. A. P. 17.59- H. Q36, Q5G. Arrows. Emers. mech. f. 220. Revolving in order to move more steadily. Old pile engine. Emers. mech. f. 245. Loriol's pife engine. A. P. 17.C3. H. 14«. Vauloue's pile engine. Belidor. Arch. hydr. I. ii. 107. Fish hooks. Duhamel Art de peche. f. Par. p. 12. Piles. Bugge Theoria sublicarum. Ph. tr. 1779- 120. Staghold's gun harpoon. Bailey's mach. II. 61. Needles. E. M. A. Art. Aiguillier. Pile engines. E. M. PI. I. Charpente. PI. 11. Balistas,Bows. E. M. PI. VII. Art. Militaire. , PI. 2, 4. A gun harpoon. S. A. II. IQl- Moore's harpoon gun. S. A. IX. l64. Bell's harpoon gun, S. A. XI. IQl. £nc. Br. Art. Balista. Bow. Kirby's fish-hooks are of an improved form, the point being turned more inwards, so as to be in the direction of the line. Cutting Instruments, or Edge Tools. Du verger's machine for cutting files. Mach. A. I. 155. Chaumette's flexible knives. Mach. A. II. 117. Cutting machine. Leup. Th. M. G. t. 15. Fardouel's machine for cutting files. A. P. 1725. H. 103. Mach. A. IV. 125. Focq's plane for iron. A. P. 1751. H. Mach. A. Vfl. 407. Brachet's machine for cutting files. A. P. 1756. H. 128. Messier's chaff cutter. A. P. 1758. H. 100. Mury's machine for pruning large trees. A- P. 1760. H. 159- Razors. Garsault Art du peiruquier. f. Par. Perrtt Pogonotomie. A machine for cutting files. Am. ir. I. 365. Ringrose's tliistle cutter. Bailey's mach. I. 36. Edgill's chaffcutter, with a spiral knife. Bai- ley's mach. I. 43. Edgill's machine for slicing turnips. Bailey's mach. I. 65. Scythes from Brabant and Hainault. Bailey's mach. I. 65. Smith's machine for cutting straw, with a double, knife. Barley's mach. II. 24. Cork cutting. • E. M. A. I. Art. Bouchon- nier. Engraving plate. E. M. A. I. Art. Ciseleur. Shtting mill, E. M. PI. II. Fer. v. pi. 1..8. Razors. E. M. A. VI. Art. Perruquier. From Perret. W^orking stones. E. M. A. VI. Art. Pierres. Sword blades. E. M. VII. Art. Sabres. Stone cutting. E,,M._A- VIII. Art. Tailleur de Pierres. ' .„ ' /, Shears. E. M. M. I. Art. Forces. Potatoe cutter, scythes, chaff cutter, root cutter, and compound chaff cutter with knives placed side by side. E. M. Art. Aratoiie, Pike's chaff cutter, with a revolving knife. S. A. V. 63. Betancourt Molina's machine for cutting weeds. S. A. XIV. 317. Repert. VI. 175. Salmon's chaff cutter, with two knives, cut- ting to 20 different lengths. S. A. XV. 281. Repert. Vll. 40LPh. M. III.292. Choumert's machine for splitting hides. Repert. IV. 104. Scythe of Milan. Repert. V. 62. Sandilands's sward cutter. Repert. X. 329- CATALOGUE. PHILOSOPHY AND ARTS, PRACTICAL MECHANICS. 205 Enc. Br. Art. Chaff cutter. On a ipachine for cutting files. Nich. II. 309. Repert. V. 179- Bentham's patent modes of working. Repert. X. 250. 293. Willich's Dom. Enc. Art. Scytlies. Riesch's straw cutter. Willicii's Dom. Enc. Art. Straw. Sward cutter. Willich's Dom. Enc. Reaping wheelbarrow. Person Rccueil, PI. 8. Nicholson on razors. Nich. 8. I. 47, 210. Gilb. XVII. 453. Nicholsoo's patent for cutting files. Repert. ii. II. 258. Sawdon's patent straw cuttei-. Repert. ii. I. 409. Bramah's patent machinery for planing. Repert. ii. II. l65. Brown's patent machine for slicing turnips and tallow. Repert. ii. III. 405. Lathes. Flumier Art de tourner. Fr. Lat. f. 1710. M. B. Lahire's machine for turning polygons. A. P. 1719.320. Leup. Th. Suppl. t. 26. Grandjean de Fouchy's lathe for screws. ' Mach. A. V. 83, 89,91. La Condamine on the lathe. A. P. 1734. 216, 295. Balzac on turning silver plate. A. P. 1756. H. 129. JRoubo Art du menuisier ebeniste. f. Paris. p. 902. Arquier's wheel lathe. A. P. 1769. H. 128. Hullot Art du tourneur mecaniclen. 1776. Ludlam on the oval lathe. Ph. tr. 1780. 378. Lathe, for ornamental plate. E. M. PI. IV. Orf^vre grossier. PI, 11. VOL. II. Turning ivory and snufF boxes. E. M. A. VIII. Art. Tabletier. E. M. A. VIII. Art. Tourneur. Common spring lathe. E. M. PI. IV. Tour- neur. PI. 2. Tournant's lathe for mouldings. Roz. XLII. 215. Ridley's foot lathe. S. A. XV. 273. Repert. Vin.395. Bentham's patent. Repert. X. 250. Cook's mode of turning spheres. Repert. XIV. 260. ' Healy on turning screws. Ph. M. XIX. 172. Division, or Separation without sharp Instruments. Lahire on separating millstones from tlieir blocks. A. P. IX. 327. Parent on the force of the wedge in separa- tion. A. P. 1704. 186. H. 96. On the wedge. Leup. Th. M. G. t. l6. Ph. tr. 1729. XXXVI. Stones are sometimes divided by drawing lines on them with fat or oil, and then exposing them to heat. It may be doubted whether the oil, by preventing the eva- poration of moisture, allows the stone to be more heated at the part oiled, and by the irregularity of the expansion produces a separation ; or on the contrary, the oil, having insinuated itself, is converted into vapour at a high temperature, and forces the stone asunder. fSiitting mill for iron. Eniers. mech. f. 251. Working slate. Fougeroux de Bondaroy Art de I'ardoisier. f. Paris. Ace. A. P. 1762. H. 186. -, Stonequarries and limekilns. E. M. A. I. Art. Carrier. Slitting whalebone. E, M. A. II. Art Fa- nons de Baleine. Slitting mill for iron. E. M. PI. II. Fer. v. PI. 1 . . 8. Ee 210 CATALOGUE.— PHILOSOPHY AND ARTS, PRACTICAL MECHANICS. Working stones. E. M. A. VI. Art. Pierres. E. M. A. VIII. Art. Tailleur de Pierres. Unrolling old books. E. M. A. VI. 732. P. Nicholson on the wedge. Ph. M. I. 3I6. Sawing. Lahire's machine for moving saws. A. P. IX. 159. Sawing machine. JNlach. A. I. 115. Duguet'ssaw for curved work. Mach. A. I. 169. Fonsjean's machine for sawing marble. Mach. A. I. 199. Guyot's sawing machine. A. P. 1720. H. 114. Mach. A. IV. 3, 7. Chambon's mode of making saws act. A. P. 1740. H. 111. Pommyer's machine for sawing off piles un- der water by the force of the stream. A. P. 1753. H. 302. Mach. A. VII. 453. Euler on saws. A. Berl. 1756. 267. Sawing machine. Emers. mech. f. 263. Sawing mill. Belidor Arch; Hydr. 1.1.321. Machine for sawing piles. Belidor Arch. Hydr. II. ii. PI. CO. Model of a sawing mill. A. Petr. I. i. H. 60. Standfield's saw mill. Bailey's mach. I. 136. Saw under water. E. M. Pi. I. Charpente. PI. 9. Sawing mill. E. M. PI. I. Charpente, PI. 21. Mill for sawing stones. E. M. PI. III. After Ma^onnerie. Saws and sawing. E. M. A. VII. Art. Scie. Benlham'iJ patent rotatory saw. Repert. X. 250. Fould's semicircular and circular saws for piles. S. A. XIII. 241. Repert. XI. 171. An improvement on the old method of working a saw backwards and forwards by a lever, with ropes and puUies. Bundy's patent for cutting combs. Repert. XI. 227. Wilde's patent saws. Repert. XVI. 389. Wheelcutting, Filing, and Cutting Screws. VVheelcutter. See Machinery, Structure of Wheels. Files. See Cutting Instruments. Zeiher's two machines for cutting screws. N. C. Petr. VIII. 279. On files. Repert. XVI. 60. Grinding and Polishing. Jenkins's machine for grinding spherical lenses. Ph. tr. 1741. XLI. 553. Jeffries on diamonds and pearls. 8. 175]. R.I. Polishing iron and steel. Perret Art du cou- telier. Duhamel Art du serrurier. Songy's polishing machines. A. P. 1763. H. 143. Cone's composition for whetstones and razor- straps. A. P. 1766. IT. 160. Polishing gems. E. M. A. II. Art. Diaman- taire. Polishing looking glasses. E. M. A. III. Art. Glacerie. Working stone. E. M. A. VI. Art. Pierres. VIII. Art. Tailleur de Pierres. Polishing. E. M. A. VI. Art. Poliment. Polishing gunpowder. E. M. PI. IV. Poudre a canon, Lissoir. Grindstones. E. M. PI. IV. Tourneur, PI. 10. Tripoli. E. M. A. VIII. Art. Tripoli. Cutting glass. E. M. A. VIII. Art. Verre tourne. Pajot's machine for polishing glass and cop- per. Roz. XXXIII. 430. Lambert on the velocity of vessels in which balls are rounded. Hind. Arch. II. 287. Grinding glass. Enc. Br. Art. Burrough's machine. Glass, Lens. CATALOGUE. — PHILOSOPHY AND ARTS, PRACTICAL MECHANICS. 211 On grinding. Nich. I. 131. Person's grindstone. Pers. Recueil. PI. 18. F. Cuvier on an oxid of iron. B. Soc- Phil. n. 67. Guyton on an oxid of iron for polishing. Ph. M. XIV. 276. Made from old hats. Looking glasses are polished by a block, moved by a crank; sometimes one glass is made to slide on another. See optical instruments. Boring. Leu p. Th. Hydrot. t. 12, 25. Boring mills. Belidor Arch. Hydr. I. i. 321. Boring for coals. Morand Art d'e.\ploiter les mines de charbon. II. ii. 388. Boring small cannon. Roz. Introd. I. 137. Bailey's auger with wheelwork. Bailey's mach. I. 159. Cook's spiral auger. Bailey's mach. I. 163. Boring for coals. E. M. PI. I. Charbon de terre. PI. 1. Boring gun barrels. E. M. PI. I. PI. 17. Boring cannon. E. M. PI. I. 58. Old method. Drill with a bob or weight. E. M. PI. II. PI. 7. f. 34. Boring. E. M. A. VII. Art. Sonde. Boring mill. Smeaton's reports. Enc. Br. Art. Pipe borer. Bailiet's borer and sounding instrument. B. Soc. Phil. n. 39. Nich. IV. 227. Howell's patent for boring wooden pipes, Repert. IX. 45. By a hollow cylindrical borer. Eccleston's peat borer. S. A. XIX. 168. Repert. XVI. 317. Nich. 8. V. 28. Poterat's boring mill approved. IM. Inst. IV. Billingsley's patent boring machine. Repert. ii. II. 321. Digging. See Clearing Harboun Leup. Th. Hydrot. t. 7 • . . VCf/ ' '^'^^Ty Laplatriere, Art du tourbier. 4. R. S?^^^;^^NW Digging trenches. E. iM. A. VII. Art. Sa- peur. Cutting turf. E. M. A. Vtll. Art. Tourbe. Cook's hoe. E. M. Art. Aratoire. Stone quarries and lime kilns. E. M. A. I. Art. Carrier. Macdougall's turnip hoe. S. A. XI. Frontisp. Eckhardt on a machine for deepening canals. f. R. S. Ducket's hand hoe. Board Agr. II. 424. Repert. XIV. 112. Horse hoes. See ploughing. IMining, and Subterraneous Work in general. Moray on the mines at Liege, and on blast- ing rocks. Ph. ir. 166'5 ..6.1. 79, 83. Leup. Th. Hydrot. Belidor on military mining. A. P. 1756. 1. 184. H. 11. Jjcach on navigation and mines. 8. Coal mines. Dithamel Art du charbon nier. f. Paris. Ace. A. P. 1761. H. 152. Morand Art d'exploiter les mines de charbon de terre. f. Paris. Ace. A. P. 1768. H. 129. Calvor vom Oberharze. Brunsw. 17(53. Ddim Anleitung zur bergbaukunst. Vienna, 1773. Coal mines. E, M. A. I. Art. Charbon mi- neral. Bituminous coal. E. M. A. III. Art. Houijle. E. M. A. VIII. Art. Travaux des mines. White on the quarries under Paris. Manch. M.II. 3G1. 212 CATALOGUE. PHILOSOPHY A>fD ARTS, PRACTICAL MECHANICS. Kirwan on coal mines. Ir. tr. 1788. II. 157. Proposal for a tunnel under the Thames. Ph. M. I. 223. Lefebure on the French coal mines. Ph. M. XVI. 15. ■ Taylor on mining in Devonshire and Corn- wall. Fh. M.V. 357. Marescot on military mines. M. Inst. III. 370. Props used in mining. Rees's Cyclop. II. pi- Art. Mineralogy. PloughingjSowing, and Harrowing. Evelyn on the Spanish sembrador, for plough- ing, sowing, and harrowing. Ph. tr. I(;i70. V. 1055. Lassisi's windmill for ploughing. A. P. 1726. H. 69. Mach. A. IV. 157- Jaravaglia's plough without cattle. Mach. A. V. 35. Tuirs horse hoeing husbandry. 8. Clark and Lord Kaimes on shallow plough- ing. Ed. ess. III. 06, 6'8. Knowles's open drain plough. Bailey's mach. I. S. With three coulters, and with wheels. Makin's drain plough. Bailey's mach. I. 4. Without wheels. Gee's six furrow plough. Bailey's mach. I. 8. Ducket's three furrow plough. Bailey's mach. I. 13. Ducket's trenching plough. Bailey's mach. I. 16. Willey's drill plough. Bailey's mach. I. 19. Hewit's horse hoe and harrow. Bailey's mach. 1.22. Riugrose's plough for turning up heath. Bailey's mach. I. 26. Arbuthnot's double furrow plough. Bailey's mach. I. 29. Clarke's plough, with adjustments for the di- rection of the draught. Bailey's mach. 1.32. Lloyd's horse hoe and harrow. Bailey's macb. I.S9. Various ploughs described. Bailey's mach. I. 68. Clark's drain plough. Bailey's mach. I. 68. Chateau Veaiix's cultivators. Bailey's mach. L71. Baker's scarificator. Bailej''s mach. II. 9. Peters's plough. Bailey's mach. II. 11. With a circular coulter, for ploughing up furze. Brand's iron plough. Bailey's mach. II. 13. Hope and Clare's drill plough. Bailey's mach. XL 17. Pinchbeck's road plough. Bailey's mach. II. 21. Blanchard'sdrill plough. Bailey's mach. II. 30. Meister on the best direction for ploughing. Commentat. Gott. 1*81. IV. 26. Drills. E. M. A. VII. Art. Semoir. Ploughs, drills, and hairows. E. M. Art. Aratoire. Harrows and rollers for roads. Board Agr. I. 150. Snow plough. Board Agr. I. 198. Halcott on the oriental drill plough. Board Agr. I. 352. A figure of the plough long used in the east. Close's frame for setting wheat. S. A. IV. 8. Harriott's road harrow. S. A. VII. 205. With sweeps. A mould board. Am. tr. IV. 313. Coquebert on the arrangement of ploughs, with an account of a plough with two shares. B. Soc. Phil. n. 6. Journ. Phys. XLV. (II).311. Knight's harrow with wheels. S. A. XIV. 201. Repert. VI, 311. Knight's drill machine. S. A. XIX. 128. Repert. XVI. 319- Ph. M. XII. 271. For turnips. Kirkpatrick's instrument for transplanting turnips. Repert. VII. 196. CATALOGUE. PHILOSOPHY AND ARTS, PRACTICAL MECHANICS. 213 Duke of Bridgewater's drain plough. S. A. XIX. 128. Repert. ii. I. 340. Ph. M. XII. 269. Scott's mole plough. S. A. XVI. 234. Rep. VIII. 316. Watt's patent implement for draining. Rep. VIII. 225. A mole plough. Sandilands's harrows. Repert. X. 329- Euc. Br. Art. Agriculture, Brakes, Drill- plough, Harrow, Plough. Wynne's harrows and drag. Repert. XIII. 102. Francois de Neufchateau sur ies charrues. 8. Par. 1801. U. S. Manning's drill machine. S. A. XIX. l68. Repert. XVI. 306. Lester's cultivator. S. A. XIX. l68. Repert. XVI. 314. Ph. M. XIII. 20. With seven shares, for pulverising fallovirs. Wright's patent machine for sowing wheat. Repert. XV. 369. Jackson's patent turnip drill. Repert. XVI. 220. Harrows and rollers for roads. Board Agr. I. 150. Lord Somerville's two furrow plough. Board Agr. II. 418. With and without wheels. Willich. Dom. Enc. Art. Drill, Plough. Green's hand drill. S. A. XXI. 230. Nich. VIII. 19. Charles's machine for levelling lands. S. A. XXI. 272. Nich. VIII. 181. A kind of plough. Ploughs and other instruments. Dickson's practical agriculture. Curtwright's three lurrow plough. Nich. VIII. 24. Trituration, Pulverisation, Leviga- tion, Mills. Langelot's philosophical mill. Ph. tr. 1672. VII. 5056, 5058. Beale's remarks on mills. Ph. tr. 1677. XII. 846. Garouste's four corn mills united. Mach. A. II. 143. Moralec's powder mills. A. P. 1722. H. 122. Mach. A. IV. 41. Windmills. Leup. Th. M. G. t. 39 . . 47. Auger's bark mill. A. P. 1726. H. 71. La Cache's little mill. Mach. A. IV. 37. Dubuissou's machine for beating plaster. Mach. A.VL 129. Limperch Architectura mechanica of Moele- boek. f. Amst. 1727. R. I. SnufF mills. Mach. A.VL 161. Soumille's snuff mill. A. P. 1735. 103. Mach. A. VII. 37. Mansard's portable mill. A. P. 1741. H. 167. D'Ons en Bray's snuff mill. A. P. 1745. 31. Gensanne's paper mill. Mach. A. VIL 201. Mill for grinding madder. Duhamel sur la Garance. Ace. A. P. 1767. H. 50. Jodin's washing mill for goldsmiths. A. P. 1759. H. 233. Mills in general. Emerson's mech. Wind- mill, f. 203. Common grist mill. f. 260. Horse mill. f. 294. Powder mill. f. 297. Corn mills. Belidor Arch. Hydr. I. i. 27(). Windmills, handmills, and horsemilJs. Beli- dor Arch. Hydr. 1. i. Pi. n. 26. Powder mills. Behdor Arch. Hydr. Li. 343. Belidor Arch. Hydr. I. i. 359. Mill for grinding mortar. Loriot's machine for grinding ore. A P J76l H. 159. 214 CATALOGUE. PHILOSOPHY AND AETS, PRACTICAL MECHANICS. A machine for washing and stamping. A. P. 1761. H. 161. Flour mills. Malouin Ait du meunier. f. Par. Ace. A. P. 1767. H. 182. Chamoy's watermill forsnufF. A. P. 1767- H. 184. Leather mill. Lalandc Art du chamoiseur. p. 7. Kastner on the lifters of stamping mills. N. C. Gott. 1770. II. 117. On oil mills. Roz. VIII. 417. XII. 399. Dutch oil mills. Roz. X. 417. Mortar mill. Roz. XIII. 199. Quatremere Dijonval on a handmill for grinding indigo. S. E. IX. 78. PI. 7- A machine for grinding colours. Roz. XIX. 314. Evers's windmill for threshing and grinding corn. Bailey's mach. 1. 54. Various mills. Bailey's mach. I. 175. Lloyd's cider and maltmill. Bailey's mach. II. 1. Lloyd's handmill. Bailey's mach. II. 44. Verrier's windmill. Bailey's mach. II. 47- Malt mills. E M.Pl. I. Brasserie. PI. 45. ' Cider mill. E. M. PI. I. Cidre. Coffee mills. E. M. PI. II. I)istillateur.P1.4. Mills for pOtteiy. E. M. PI. II. Fayencerie. PI. 9. Washing and stamping mills for ore. E. M. Pi. fl. Fer. i. PI. 7 • . 10. vi. Pi. 1, 2. Some mills. E. M. PI. III. Art. Instrumens de mathematique. Stamping mills. E. M. A. IV. Art. Lavage. Corn mills. E. M. A. V. Art. Meunier. Hesiod's pestle worked by the foot. E. M. A. VI. Art. Piler. E. M. A. VI. Art. Pulverisation. Stamping and rolling mills for gunpowder. E.- M. PI. IV. Poudre ti canon. Tobacco and snuff mills. E. M. A. VIII. Art. Tabac. Stamping mill for bark. E. M. PI. V. Tan- neur. PI. 7. Handmill, and mill driven by an ox in a walking wheel. E. M. Art. Aratoire. Baunie on polatoe mills. A. P. 1786. 689. Repert. III. 62. Boulard's mode of preserving the health of colourgrinders. Roz. XXXVII. 353. Re- port. V. 138. Mills and millstones. Langsdorfs Hydrauhk. PI. 44 . . 46, 48 . . 50. Stamping mills. Langsdorfs Hydr. PI. 52. Banks on mills. 8. London, 1795. Nancarrovv on mills. Am. tr. IV. 348. A paper mill. Kunze. I. f. 1 10. Howard's engine for beating tanning mate- rials. Lasterie's machine for powdering bones. B. Soc.Phil. n. 14. A corn mill at Kilrie. Board Agr. I. 52. Ellicott's corn mill. Repert. IV. 319. Grenet's machine for granulating potatoes Repert. IV. 353. Ward's prevention of injury from grinding white lead. S. A. XIII. 229. Repert. V. 249. Dearman's patent malt mill. Repert. V. • 247. Weldon's patent bark mill. Repert. X. 77. XV. 90. Rustall's family mill and bolter. S.A.XVIIL 222. Repert. XIV, 197. Terry's mill for hard substances. S. A. XIX. 282. Nich. 8. II. 206. Repert. ii. II. 182. With a spring regulator. Bagnall's machine for chopping and pound- ing bark. Repert. XV. J 45. CATALOGUE. PHILOSOPHY AND ARTS, PRACTICAL MECHANICS. 215 Barralt's patent machine for grinding corn. Repnt.XVI. 79- A windmill. Enr. Br. Art. Levigation, Oil mill. Paper mill. Rasping mill. Berard Melanges. 147. Pounding mill. Berard Melanges. l6l. Powder mill. Person Recueil. PI. 5. Moved by a luver. Hand mill. Person Recueil. PI. 16. With a fly. Stamping mill. Person Recueil. PI. 17. By hand. The Indian hand mill. Nich.8. III. 18(3. On the Scotch querns or hand mills. Nicli. 8. IV. 220. Hawkins's patent floating mill. Repert. ii. I. 162. Table for the construction of mills. Imison's elements. I. 90. Corn mill. Imison's elements. I. PI. 3. Mills of all kinds. Gj^ys experienced mill- wright. London. With plates. Jppnuh/ges to Mills. Preparation of Corn and Flour. Threshing machine with flails. M. Berl. I. 325. Descamus's machine for working several sieves. A. P. 171 1. H. 101. Knopperf's fan for corn. A. P. I716. H. 78. Mach. A. III. 101, 103. Duquet's threshing machine. A. P. 1722. H. 121. Mach. A. IV. 27, 31. Meiffien's threshing machine. A. P. 1737. H. 108. Malassagny's threshing machine. A.P. 1762. H. 193. Loriot's threshing machine. A.P. ]763."H, 141. Poix's cylindrical sieve for corn. A.P. 1763. H. 14.5. Gambler's sieve for corn. A. P. 1768. H. 131. Munier's winnowing machine. Roz. Intr. II. 79. A>M«?7z Drcschkunst. 8. Bcrl. 177G. Rawlinson's colour mills. S. A. XXII. 260. Tlireshing, threshing mills, wooden fan. E. ♦Ferguson's lectures by Brewster. M. Art. Aratoire. Enters much into the form of the teeth of wheels. Evers's winnowing machine. Bailey's mach. Paper mills. See union of fibres. I. 51. Pearl barley is prepared by first pounding the barley, to ^vers's mill for threshing by Stampers. Bai- separate the husks, then grinding the corns between mill ^^y S mach. 1.54. stones set wide, and separating them by sieves of different Stedman's bolting, mill. Bailey's mach. If. sizes. . ;;- •J i . Bolting mills. Langsdorfs hydraulik. PI. 47. Desmazi's machine for dressing corn. Joura. Parts of Milk. Phys. XL[V.(I.)314. Cranks connected by rods. Millstones. E. M. A. V. Art. Meulier. Threshing mills. Board Agr. I. 51, 52. Pratt's patent composition for millstones. Re- Wardrop's threshing machine with elastic pert. VII. 1. flails. Repert. IV. 243. Bowes on a quarry of millstones. Repert. Steedman's patent threshing machine with XIV. 189. flails. Repert. VII. 305. 216 CATALOGUE. — PHILOSOPHY AND ARTS, HISTORY OF MECHANICS. Meikle's patent machine for separating corn from straw. Repert. X. 217. Tunstall's hand engine for threshing. Repert. XIII. 361. Machine to thresh, sift, and winnow at once. Person Recueil. PI. 1, 2. Threshing machines. WiUich's Dom. Enc. Art. Thrashing. Polfreeman's winnowing machine. WiUich's Doiii. Enc. Art. Winnow. Winnowing. See Pneumatic Machines. Bolting. See Mills, Machines f 07' Agitation, nearly allied to Mills. Solignac's machine for kneading dough. A. P. 1760. H. 156. Churns. E. M. PI. II. Fromage. Bowles's pendulum churn. S. A. XIII. 252. Repert. IV. 107. Ph. M. XIX. 56. Machine for kneading dough with horses. Journ. Phys. LI. 64. Nich. IV. 281. Rep. III. 283. Ph. M. VII. 261. Raby's patent churn. Repert. VII. 289. Jones's machine for mixing malt. Repert. IX. 242. Fischer's washing machine. WiUich's Dom. Enc. Art. Washing. Jumilhacon churning. Nich. 8. IV. 241. Machines for bleaching and washing. Rees Cyclop. III. PI. Art. Bleaching. Demolition. Military engines. Malhematici veteres, Ve- getius, and Ammianus Marcellinus. Beaumont on blasting rocks. Ph. tr. 1685. XV. 854. Dubois's spoon for the removal of earth beaten down by a ram. A. P. 1726. H.70. Mach. A. IV. 165. Lavier's machine for breaking ice. A. P. 1743. H. 167. Belidor on military mining. A. P. 1756. 1, 184. H. 11. See mining. Machine for drawing piles. Belidor Arch. Hydr. I. ii. PI. 12. Silberschlag on the military engines of the antients. A. Berl. 1760.378. Loriot's machine for breaking ice. A.P..1763. H. 141. Saverland's machine for levelling land. Bai- ley's mach. 1.61. Rollers for breaking clods of earth. E. M. Art. Aratoire. Rich's nail drawer. S. A.IX. 156. Repert. I. 246. Hill's nail drawer. S. A. X. 224. Bolton's bolt drawer. S. A. XVI. 315. Re- pert. Xr. 39. Ph. M. III. 189. Enc. Br. Art. Catapulta, Shipbolt drawer. Knight's apparatus for blasting wood. S. A. XX. 258. Repert. ii. II. 342. Nich. 8. V. 31. Gilb. XIV. 342. Baillet on blasting rocks under water. Ph. M. XIII. 268. Sonnini's machine for blasting. Gilb. XIV. 345. Common crow. Cavall. N. Ph. I. PI. v. f. ig. Charles's machine for levelling land. S. A. XXI. 272. A kind of plough. See Pneumatic machines. HISTORY OF MECHANICS. Diogenes Laertius Meibomii. 2 v. 4. Amst. 1692. R. I. P. Vergilius de inventoribus rerum. Basle, 1521. R. I. Hooke on Hevelius. Claims the invention of the circular pendulum in 1665. CATALOGUE. PHILOSOPHY AND ARTS, HISTORY OF MECHANICS. 217 Hooke Lect. Cutl. on Helioscopes. Claims the invention of the balance spring. Huygens on tlie invention of watches. A. P. X. 381. Bagford on the invention of printing. Ph. tr. 1707. XXV. 2397. Pancirollus's history of memorable things. 3 V. 12. 1715. R. I. Lahire on the invention of clocks. A. P. 1717.78. Derham's artificial clockmaker. Leup.Th. Arithm. Says, that proportional compasses were invented by Justus Byrgius in 1600. Perhaps reinvented after Vinci. Regnault Origine ancienne de la physique nouvelle. 3 v. Amst. 1735. Mairan on Des Piles's balance of painters. A. P. 17.55. l.H. 79. Maitaire, Marchand, Borcyer, Ames, and Le- moine's works on the history of printing. R.I. Borvyer and Nichols's origin of printing. 8. R. S. Rolliti's history of the arts and sciences of the ancients. 3 v. 8. 1768. R. I. Luckombe's history of printing. 8. 1771. R.I. Luckombe s tablet of memoiy. 12. London. Waring's prefaces to his mathematical works. De Loys Abrege chronologique. Degoguet's origin of laws, arts, and sciences. 3 V. 8. 1775. R.I. '*Pti€stky's chart of biography. R. I. Dictionnaire des origines des inventions utiles. 6 V. 12. Par. 1777. R. I. *Astle's origin and progress of writing. Brugraans on the mechanics of the antients. Commentat. Gott. 1784. VII. M. 75. Lord Charlemont on the antiquity of the woollen manufacture in Ireland. Ir. tr. 1787. 1. Ant. 17. Burja on the mathematical knowledge of Aristotle. A. Berl. 1790. 257. VOL. II. *Cooper on the art of painting among the ancients. Manch. M. III. 510. Shows that it was highly improved. Mongezon ancient coining. Roz. XL. 426. Dutefis on the origin of discoveries. 4. R. I. Beckmmins history of inventions. 3 v. 8. Lond. 1797. R. I. Camus Histoire du polytypage et de la stereo- typic. 1801. Foppe Geschichte der uhrmacherkunst. 8. 1801. *Montucla et Lalande Histoire "des mathe- matiques. 4 v. 4. Par. R. I. Fischer sur les monumens typographiques de Gutenberg. 4. Mentz, 1802. R. S. Account of Newton. Tumor's collections for the history of Grantham. 4. Lond. 1806. B. B. Contains the original papers sent by Mr. Conduit to Fon- tenelle, and some other documents. Particular Dates, chiefly from Luckombe's Tablet of Memory. Scipio Nasica's clepsydra. B. C. 159 Scissors invented in Africa. Diophantus employed some algebraic symbols. Montucla. Pens made from quills. A. D. 635 Glass introduced into England 674 Silk worked in Greece about 700 Paper of linen introduced about 1100 Glass commonly used in England 1 180 Some Greek weavers settled at Venice 1207 Linen first made in England 1253 A clock at Westminster Hall about 1288 • A clock at Canterbury 1292 Faenza's earthern ware invented 1299 Two weavers from Brabant settled at York 1331 Wire invented at Nuremberg 1351 Engraving on metal and rolling press printing invented 1423 Ff 218 CATALOGUE. — PHILOSOPHY AND ARTS, HISTORY OF MECHANICS. Pins brought from France Needles made in England Printing invented by Faust 1441 Delft ware invented at Florence 1450 Printing thade public by Gutenberg 1458 Wood cuts invented 1460 Casts in plaster, by Verocchio 14*0 Watches made at Nuremberg 1477 Diamonds polished at Bruges 1489 Hats made at Paris 1504 Etching on copper invented 1512 Proportional compasses invented by L. da Vinci, before 1519 Spinning wheel invented by Jiirgen of Brunswick 1530 1543 1545 Stockings first knit in Spain about 1550 Many Flemish weavers were driven to England by the Duke of Alva's persecution 156? Three clockmakers came to England from Delft 1568 Log line used 1570 Coaches used in England 1580 Stocking weaving invented by Lee of Cambridge 1589 A slitting mill erected at Dartford 1590 The dimensions of bricks regulated 1625 Vernier's index made known 1031 Clocks and watches generally used about 1631 Bows and arrows still used in Eng- land, and artillery with stone bullets l640 Newton born 1642 Fromantil is said to have applied pendulums to clocks in 1655 Hooke's watch with a balance spring 1658 Threshing machines with flails in- vented 1700 China made at Dresden 1702 China made at Chelsea 1753 Wedgwood's improvements in pot- tery 1 763 Muslins made in England 1781 In 1787 about 23 million pounds of cotton were manu- factured in Britain ; about 6 were imported from the British colonies, 6 from the Levant, and lo from the settlements of other European nations. Half the quantity was employed in white goods, one fourth in fustians, one fourth in ho- siery, mixtures, and candle wicks ; giving employment to 60 000 spinners, and 360 000 other manufacturers. In 1791, the quantity was increased from 23 millions to 32. The value of the wool annually manufactured in England is about 3 millions sterling ; it employs above a million per- sons, who receive for their work about 9 millions. Thread has been,spun so fine as to be sold for L.4 an ounce ; lace for L.40. The premiums annually proposed by the society for the encouragement of arts, enable us to form some opi- nion of the present state of our machinery and manufac- tures. Some of their objects are, a substitute for white lead paint, a red pigment, a machine for cardin.; silk, cloth made from hop stalks, paper made from raw vegetables, transparent paper, the prevention of accidents from horses falling, cleaning turnpike roads, machines for raising coals, and for making bricks, instruments for harpooning whales ; machines for reaping or mowing corn, for dibbling wheat, for threshing ; a family mill, a gunpowder mill, a quarry of millstones 3 and a mode of boring and blasting rocks 1803. CATALOGUE. HYDRODVXAMICS, HYDROSTATICS. 919 HYDRODYNAMICS IN GENERAL. Schotti raechanica hydraulico-pneumatica.4. 1657. M.B. Ph. tr. Ahr.I. vi.515.IV. v.423. VI. vi.526. VIII. vi. 321. X. V. 247. *Newtoni principia. Z)/«ow on fluids. 8. Lond. 1719- M.B. *D. Bernoulli Hydrodynamica. 4. 1738. R.I. Cotes's hydroslatical and pneuniatical lec- tures. 8. 1747. R. I. S'Gravesande. Nat. Phil. Musschenbroek Introd. Belidor Architecture hydraulique. 4 p. 4. Par. 1782. R. I. D'Alembtrt de i'equilibre et du mouvcment des fluides. Ace. A. P. 1744. H. 55. LeccAf Idrostatica e Idraulica. Mil, 1765. K'astner Anfangsgriinde der hydrodynamik. 8. Gott. 1769. *Bos.'>ut Traite d'hydrodynaniique. 2 v. 8. Paris, 177 1. R.I. Ace. A. P. 1771. H. 61. German by Langsdorf. Frankf. 1792. *Buat Traite d'hydraulique. 2 v. 8. E.M.Pl.VII.Matheinatique. Hydrostatique. Emerson's hydrostatics. ' Cousin on the mathematical theory of fluids. A. P. 1783. 665. Lambert on fluids. A. Berl. 1784. 299. Karstens Lehrbegriff". V. VI. Langsdorfs theorie der hydrodynamischen. grundlehren. Frankf. 1787. Langsdorfs hydraulik. 4. Altenb. 1794. Klugei's remarks on Langsdorf. Hind. Arch. 11.221. , Parkinson's hydrostatics. 4. 1789. R. T. *Lagrange Mecanique analitique. Pfw/tj/Architecture hydraulique. 4.PariS; 1790. Burja Grundlehren der hydrostatik. 1790.. Busch Mathemjitik. II. Enc. Br. Art. Hydrostatic Amusements. Venturi Recherches experimentales. 8. Par. 1797. liinmann and Nordwall's essay on the me- chanics of mining. 4. Stockholm. Abstr. Ph. M. XIII. 76. Eytelweins mechanik und h3'draulik. 8. Ber- lin, 1801. Trembley on the uncertainty of hydrody- namics. A. Berl. 1801. Ph. 33. HYDROSTATICS. Stevini hydrostatica. Boyle's hydrostatica] paradoxes. Ace. Ph. tr. \m5—Q. I. Boyle on the weiglit of water in water. Ph. tr. 1669. IV. 1001. Sinclari ars gravitatis et levitatis. Rotterdam, 1669. Ace. Ph. tr. 1669. IV. 1017. Luni}/ Mecanique. 12. Par. 1674. M. B. Mariotte on hydrostatics. A. P. I. 69. On the equilibrium of liquids. A P. II. 78. Lahire. A. P. IX. 144. Describes an arrangement of levers by which a single weight is made to produce a pressure on each side of a box equal to the hydrostatic pressure. Varignon on conical vessels. A. P. X. 10. Saulmon on the principles of the actions of fluids. A. P. 1717. H. 73. Leup. Th. M. G. t. 55, 5Q. Th. Hydraul. I. t. 1, 41. Switzer's hydrostatics. R. I. Belidor. Arch. hydr. I. i. 126. Nollet's experiments on the affections of 220 CATALOGUE. PNEUMATOSTATICS; fluids in a revolving globe. A. P. 1741. 184. H. 1. Nollet's new hydrostatical phenoniena. A.P. 1766. 431. H. 150. Gulielmini on hydrostatics. C. Bon. I. 545. fSegner on the surfaces of fluids. C. Gott. 1751.1.301. Euler's principles of hydrostatics. A. Berl. 1755. 217. Euler on the equilibrium of fluids. N. C. Petr. XIII. XIV. XV. Lambert on the fluidity of sand and earth. A. Beri. 1772. ."JS. Meister on oil swimming upon water. Com- mentat. Gott. 1778. I. 35. Matteucci on a principle of statics and hy- drostatics. C. Bon. VI. O. 286. Gr. Fontana on the pressure of fluids. Soc. Ital. 11.142. J. Bernoulli's hydrostatical considerations. N. Act. Heiv.1.229. ♦Delangez on the statics and mechanics of semifluids. Soc. Ital. IV. 329- Kastner on the pressure of a fluid covering a sphere. Hind. Arch. 1. 424. EquUibrium of Floating Bodies. Regulating counterpoise. See Hydraulic In- struments. **Archimedes de insidentibus humido. Parent on floating bodies. A. P. 1700. H. 154. D. Bernoulli on the equilibrium of floating bodies. C. Petr. X.147. XI. 100. Bouguer on the oscillations of floating bo- dies. A.P. 1755.481. H. 135. E. M. PI. V. Marine. PI. 152. 153. English on floating bodies, from Chapman. N. Svensk. Hand!. 1787. Ph. M. I. 371, 393. PNEUMATOSTATICS, OR PNl^UMATIC EQUILIBRIUM. See Properties of Matter. Boyle on the spring and weiglit of the air. 4. Oxf. 1663. Ace. Ph. tr. 1668. III. 845. Boyle's statical baroscope. Ph. tr. 1665. 1. 231. Boyle on air. 4. Lond. 1670. Ace. Ph. tr. 1670. V. 2052. See airpumps. Boyle on the effects of atmospherical pres- sure. Ph. tr. 1672. VII. 5155. Guericke Experimenta nova Magdeburgica. f. Amst. 1670. Ace. Ph. tr. 1672. VII. 5103. Table of the compression of air.- Ph. tr. I671. VI. 2191, 2239. Hooke on the elasticity of the air. Birch. Ill, 384, 387. Mariotte sur la nature del'air. 1676. Mariotte and Horn berg on the weight of air. A. P. II. 41. Homberg on the spring of air in vacuo. A.P, IF. 105. VVallis on the air's gravity. Ph. tr. 1685.XV 1002. Lahire on the condensation and dilatation of the air. A. P. 1705. 1 10. H. 10. Wo^'ielementaaerometriae. 12. Leipz. 1706. Amontons on the rarefaction of air. A. P. 1705. 119. H. 10. +Hauksbee on condensing the air perma- nently. Ph. tr. 1708.217. Carry's experiment on the spring of air. A.P. 1710. l.H. 1. Varignon on the densities of elastic fluids from pressure, according to given laws of compression. A. P. 17 16. 107. H. 40. Pressure of the atmosphere. Leup. Th. Aero- staticum. CATALOGUE. — THEORY OP HYDRAULICS. 221 Btdaut's atmospherical machines. Mach. A. VI. 27- Elasticity of the air. C. Bon. I. 208. Kichmann on the compression of the air by ice. N. C. Petr. II. 1G2. The air was compressed tncclianically to ^ig, without much deviation from Hooke's law ; by freezing it was re- duced to ^of its bulk. • Lowilz Versuche Uber die luft. 4. Nurem- berg, 1754. Belidor. Arch. Hydr.II. i. 1. Achard on the properties of gases. A. Berl. 1778.27. Beds of air or bladders. E. M. A. VI. 731. E. M. Physique. Art. Air. Cavallo on air and elastic fluids. 4. R. I. Fontana on the eUisticity of gases.. Soc. Itul. 1.83. Gerstners luftwage. Gren. IV. 172; Hutton's recreations. IV. 135. Dalton's theory of mixed gases. See Meteo- rology. Barometers and manometers. See Meteo- jology. According to Lavoisier l cubic inch Fr. of air weighs 48 grains. A. P. V77*. 364. According to Fouchy a, cubic foot weighs 10 gros. A. P. 17 80. 3. A hundred English wine gallons weigh a pound avoirdupois. Roy thinks that there are some exceptions to the law of Boyle and Mariotte. Ph.tr. 1777. Others attribute these irregularities to the presence of water. THEORY OF HYDRAULICS.- Baliani de motu gravium. 4. Genev. I646. M.B. Davis and Papin on the siphon. Ph. tr. 1685. XV. 846. Papin on the air rushing into a vacuum. Ph. tr. 1686. XVI. 193. Assumes the specific gravity of air equal to -^ of that of water, and deduces thence a velocity of ISOS feet in a se- cond. *Mariotte Traite du mouvemeni des eaux. 8. Par. 1686. Acc.Ph.tr. 1686. XVI. 119. Contains a good account of ajutages. Nevvtoni principia. L. ii, Varignon on the principle of the motion of water. A. P. II. 162. Varignon on the motion of fluids. A. P. 1703. 238. H. 125. Picard de aquis effluentibus. A. P. VII. 323. Lahire on the motion of fluids. A. P. X. l62. Lahire on the motion of waves. A. P. X. 264. Hauksbee's experiment ilhistiative of the ef- fects of wind. Ph. tr. 1704. XXIV. 1629. A blast produced by a condensation to 3 or 4 times the natural density caused a column of mercury connected with a vessel through which the blast passed to fall two inches or more, f Carre on the discharge of long pipes. A. P. 1705. 275. H. 135. ^ Saulmon's experiments on bodies in a vortex. A. P. 1712. 279. H. 77. 1714. 381. H. 102. 1715. 61. H. 61. 1716. 244. H. 68. Bodies floating on the surface of water in an eddy are impelled either towards the centre or towards the circum- ference, according to circumstances ; they are not made to approachthe centre on accountof their levity, since they only displace as much water as is equal to their own weight, but probably because the resistance of the air causes them to move more slowly, and to have less centrifugal force than the water. When they move towards the circumference, it is probably because of the greater retardation of the water from the friction of the vessel. Y. Hermanni phoronomia. Poleni de motu aquae mixto. 4. Pad. 1717. Extr. Ph. tr. 1717. XXX. 723. Polenus de castellis. •j-Jurin de motu aquarum fluentium. Ph. tr, 1718. XXX. 748. 1739. XL. l, 5. Follows Newton, with some inconclusive and erroneous inferences. Juiin de motu cordis. Ph. tr. 1718. XXX. 863,929. 1719- XXX. 1039. / 222 CATALOGUE. — THEORY OF HVDRAULIC3. Juiin defensio contra Miclielottium, Ph. tr. 1722. XXXir. 179- Keill de viiibus cordis contra Jurinum. Ph. tr. 1719. XXX. 995. Huccolta di autori chi trattano del moto dell' acque. 3 v. 4. Flor. 1723. Contains Archimedes, Albici, Galileo, Castelli, Michcl- inl, Borelli, Montanari, Viviani, Cassini, Guglielmi, Grand!, Manfredi, Picard, and Nanducci. Eanies on the estimation of force in hv- draulicexperiments. Ph.tr. 1727. XXXIV. 343. D. Bernoulli on the motion, action, and lateral pressm-e of fluids. C. Petr. II. Ill, 304. IV. 194. Pitot on the motion of fluids. A. P. 1730. 336. H. 110. Couplet on the motion of fluids. A. P. 1732. 113.11.107. Dufay on two streams crossing each other. A. P. 1736 191. H. 118. Mairan on the analogy of sound and waves. A. P. 1737. 4j. H.97. S'Gravesande. Nat. Phil. Clare on the motion of fluids. 8. 1737. R.I. Jo. Bernoulli on the motion of water in pipes. C. Petr. IX. 3, 19. X. Op. IV. Krafit on hydraulics. C. Petr. X. 207. Wolf Cursus mathemal. On cataracts or weres. C. Bon. II. i. 413. Mackenzie. Ph.tr. 1749. 149. Says, that eddies with a cavity of 2 or 3 feet, which sometimes swallow up small boats, may be broken and filled up by throwing in an oar. Petit Vandin on hydraulics. S. E. I. 261. Euler on the motion of water in pipes. A. Berl. 1752. 111. Euler's principles of hydraulics. A. Berl. 1755. 274,316. N. C. Petr. VI. 271. Euler on the reaction of water in pipes. N. C. Petr. VI. 312. Euler on the equilibrium of fluids, and the efl'ects of heat. N. C. Petr. XIII. 305. XIV. i. 270. X. 1. 210,219. Emerson's fluxions, iii. Robertson on weres. Ph. tr. 1758. 492. See Hydr. Architect. Belidor. Arch. Hydr. I. i. 165. Laura Bassi on a hydraulic problem. C. Bon. IV. O. 61. Batarra and Pistoi on the descent of water in bent pipes. A. Sienn. III. 85. *Borda on the discharge of fluids. A. P. 1766. 579. H. 143. Nuovo raccolta. 7 v. 4. Parm. 1766. . . K'astner on hydraulics, after Bernoulli. N. C. Gott. 1769. 1.45. Mkhelotti Sperienze idrauliche. 2 v. 4. Turin, 1771. R.S. Stattleri physica. *D'Alembert Opuscules. VI. Ace. A. P. 1773. H. 87. Lagrange on the motion of fluids. A. Berl. 1781. 151. *Lagrange Mecanique analitique. *Bossut. Buat Principes d'hydraulique. Ed. 2. Paris, 1786. R. L Ximenes Nuove sperienze idrauliche. Riccati on the cavity of a fluid in a funnel. Soc. Ital. III. 238. Lametherie on the motion of fluids. Roz. XXVril. 283. M. Young on spouting fluids. Ir. tr. 1788. II. 81. VII. 53. Repert. XV. 95. Shows by experiments on a long pipe through which mercury runs in a vacuum, that the pressure of the atmo- sphere increases the discharge in some cases in the ratio of 28 to 19. Jo. Bernoulli on the reaction of water in pipes. N. A. Petr. 1788. VI. 185. Lateral friction. Saint Martin's ventilator. Roz. XXXIII. 161. Btrnhard Hydraulique. Germ, by Langsdorf, Leipz. 1790. CATALOGUE. — THEORY OF HYDRAULICS, OSCILLATIONS. 223 Prony Archit. hydraulique. Lorgna on spouting fluids. Soc. Ital. IV. 369. Loigna on the discharge of weres. Soc. Ital. V. 313. Lorgna on the principles of Castelli. Soc. Ital. VI. 218. Lempe BegrifF der maschinenlehre. Leipz. Vince on the motions of fluids. Ph. tr. 1798. Gilb. II. 399. IV. 34. *Gerstner on the discharge of water at differ- ent temperatures. BiJhm. (ieseliech. 1798. Gilb. V. IfiO. Bonati on the discharge of a vessel with diaphragms, and of a lengthened pipe. Soc. ital. V. 501. With experiments on the lateral communication of mo- tion. 1700. Stratico on the pressure of fluids, Soc. Ital. V. 525. On the lateral friction. Girard on the pressure of running water. Roz. XLir.429. Shows that it is not perceptibly dimijiished by atty com- mon velocity. Venturi sur la communication laterale du mouvement dans les fluides. Par. 1798. R. S. Journ. Phys. XLV. (11.) 3G2. B. Soc. Phil. n. 8. Gilb. 11.418. III. 35. Nich. II. 172. Venturi found the discharge of a pipe greatest when the ajutage diverged in an angle of 3° : when the angle be- came 11°, the augmentation ceased. The diameter of tht external orifice of a conical pipe may be to that of the vena contracta as is to 10. Busse's remarks on Venturi. Gilb. IV. Il6. Eytehvein's experiments with Venturi's ap- paratus. Gilb. VII. 295. Afterwards published in his Handbuch, Hobison. Enc. Br. Art. River. Banks on the velocity of air. Manch. M. V. 398. Nich. 8. II. 2G9. Report, ii. 1.342. The area of an aperture being .0046, 425.1 cubic inches of air were expelled in 33" by a pressure of so inches of water; by a pressure of 6 feet in 21.3". This gi-ves .634 to 1 for the contractionof the stream: the velocities being 233.3 and 3C1.0. Hence a pressure of a foot gives 14?^, of an inch 42, or 20 miles an hour. "Young's summary of hydraulics from Eytel- wein. Journ. R. I., I. Nich. 8. III. 25. Young on the discharge of a vertical pipe. Journ. R. I., I. Rep.ii. II. 45. Nidi. VI. 56. Leslie found that hydrogen gas admitted through an aper- ture filled a given space in an inverted jar in 45" ; common air in 130"; hence he infers that the defisities were as 1:81. Lesl. on heat. The same mode might be applied to steam. Miehelotti found a stream of water a little more contracted as the velocity was greater. Kobison. Air is subject to friction in pipes in the same manner as water. Oscillations of Fluids, and of Floating Bodies. Mairan on the analogy of sound and waves. A. P. 1737. 45. H, 97. D. Bernoulli on the oscillation of floating bodies. C. Petr. 100. Franklin's works. Franklin observed, that when oil swimming on water was contained in a vibrating vessel, the water was agitated while the oil remained still. Meister on the eifect of oil svvimminsr on water. Commentat. Gott. 1778. 1. 35. On the oscillations observed by Franklin. Achard on calming the agitation of a fluid. A. Bed. 1778. 19. fPercivalon attraction and repulsion. Manch. M. II. 429. Bennet on Prankliu's e.xpciiment. Manch. M. III. 116. Shows, that if the lower part of a vessel of water be tinged with any colour, it may be made to exhibit the same appearance with water on which oil is swimming. The fact is easily explained by considering the distance of the different parts of the fluid from the axis of vibration. Stratico on the agitation of fluids in oscillat- ing vessels. Ac. Pad. I. 242. 224 CATALOGUE. — THEORY OF HYDRAULICS, RIVERS. Flaugergues on waves. Journ. Sav. Oct. 1789. Montucla and Lai. III. 717. Found the velocity of waves independent of their mag- nitude. Paterson on Franklin's experiments upon the oscillations of a fluid. Am. tr. HI. 13. Dr. WoUaston observed, that a bore or large wave, 80o feet Wide, moved a mile in a minute, where the depth of the vrater was said to be 50 fathoms. Lagrange's theorem gives about 40 fathoms for the depth with this velocity. I have also ob- served the waves or oscillations of water in a cistern, moving with a velocity smaller than that of a body falling through half the height, and nearly in the same proportion. Pheno)nenll of Rivers. From Mann. " Fronlinus Poleni. 1722. M. B. Aleotti. *Castdli de mensura aquarum currentium. M. B. Baratteri dell architettura d'acque lib. vi. Piacenz. 1656. M. B. Bdtinzoli. Cabaeus in Aristotelis meteora. M. B. Galileo. *Baliani de motu liquidorum. Riccioli geographia et hydrographia refor- mata. M. B. *Deschales de fontibus et fluminibus. Vartnnius by Jurin and Shaw. 1765. I. 295—358. M. B. Jurin. Ph. tr. n. 355. p. 748. Mariotte Trait6 du mouvement des eaux. Varignon. A. P. l699. 1703. Newton Princip. ii. 7. ed. 1726. *D. Bernoulli hydrodynamica. 4. Strasb. 1738. *Guglielmini della natura dei fiumi. 4. Bo- logn. 1697. *Polei)us de castellis et demotu aquae mixto. Patav. 1697. 1718. 1723. *Raccolta d'autori. 3 vol. 4. Fiorenz. 1723. Hermanni plioronomia. X. 226. Wolf cursus matliem. Hydraul. c. vi. -4. Genev. 1740. Buffon Hist. Nat. II. 38. ed. in 12. Pitot and others. A. P. 1730. 1732. S'Gravesande Elementa physices. I. ii. c. 10. *Lecchi hydrostatica. Milan, 1765. With some pieces of Boscovich. Statlleri physica. 111.^232. 8 vol. 8. Augsb. 1772. Frisius de fluviis. Lalande's history of canals, fol. Forfait on clearing^canals. Mantua." fMann on rivers and canals. Ph. tr. 1779- 555. ■ Marks the best with asterisks. Danubius illustratus. Grandi de castellis. Guglielmini de fluviis et castellis. Guglielmini on running water. M. Berl. I. 188. Pitot on the confluence of rivers. A. P. 1738. 299. H. 101. Belidor Arch. Hydr. II. ii. 273. Condaniine's voyage on the river Amazons. A. P. 1745. 391. H. 63. Euler on the motion of rivers. A. Berl. 176O. 101. Carena on the course of the Po. M. Taur. II. Ximenes on the velocity of rivers. A. Sien. III. 16. VI. 31. Ximenes on the effect of obstacles in a river. ASienn. VII. 1. Ximenes Nuove sperienze idrauliche. Bacialli on the mouths of rivers. C. Bon. V. ii. 99. Michelotli Sperienze idrauliche CATALOGUE. THEOUY OF HYDRAULICS, RiVEUS. Zendrini de motu aquarum. Bossut. Genette Tableau des rivieres. Buat. Measurement of the depth of a river. Roz. III. 64. Lespiiiasse and Frisi on the velocity of rivers. Roz. IX. 145, 398. XI. 58. Lorgna Memorie intorno all' acque correnti. Veron. 1777. Lorgna Ricerche intorno alia distributione delle velocita nella sectione de fiumi. 4. R. S. Rennel on the Gansres. Ph. tr. o Brilnings iiber die geschwindigkeit des flies- senden wassers, von Kronke. Frankf. Woltmann's beitr'age zurhydr. arch. III. Aubry on the force of torrents. Roz. XIV. 101. Bernhard Hydraulique. Stratico on rivers. Ac. Pad. III. 3S3. IV. 114. Trembley on the course of rivers. A. Berl. 1794. 3. 1798.62. 1799- 8. Hennert on the velocity of water in rivers. Hind. Arch. I. 1. Smeaton's reports. Fabre sur Ics torrens et les rivieres. Par. 1797. R.I. Robison Enc. Br. Art. River. Silbenchlag Theorie des fleuves. Ace. Montucl. and Lalande. III. 712. Venturi on the motions of fluids. On friction in watercourses. Nich. III. 252. Edelbrooke on the Ganges. As. Res. VII. 1. Cavallo Nat. Phil. 11. 173. . .Chiefly from Venturi. The friction of rivers is not quite proportional to the square of the velocity, the velocity increasing somewhat more rapidly than the square root of the fall. The excess VOL. II. of the siiperficial velocity v above the vc-locity at the bottom, is 2v/k — li V being expressed in French inches. The mean \'elocity is z) — ^v-\-l. Buat. Gerstner finds Buat's formula not perfectly accurate at any temperature, for small pipes. But in fact the formula can by no means have been intended to be applied to such 47Si pipes. Buat's theorems are i=- l being the length ~478A — v'' of the pipe wrhich employs the pressure of an inch of the head of water in overcoming its friction, I the length of the pipe, h the whole height of the head, and v the velocity, all in French inches; but for the number 478 Langsdorf substitutes 4S2; then un^ •1) — .l),e being the hydraulic mean depth, or one fourth of the diameter d ; and for the determination of v, I- may be taken _H-45£ ~ k /+45rf In English measures, we may use the same valutj •fori,andt)~Cv'e — .l).i . ,V ^ Vv^i— h.l.v/(/'+i.e) / Instead of h.l.^/ (1+1.6), we may substitute .851"' which is nearly the same, for moderate velocities. The ex- pression f^aorCv'e — iJ.(J_+i:L_.ooi)wiIlalso be found to agree extremely well with Buat's formula, and will perhaps be in many respects more useful ; and we may employ, with very little inaccuracy, i-*" instead of i-", 1.6 ^ . i.ei' ^. , the term -r—— becoming — ; — , which may be determin- l'-° 0 ed without logarithms, and the whole formula may be thus e^tpressed: vz:i53(y/d — .'i).[-/l )+1.6 \ \l-\-4id I (-— — -j" — .001.1. These formulas may also be ". ORhHA '•*7r; S52 CATALOGUE. —PXEUM ATI C MACHINES. and could not continue the exertion long: this raised 6 gallons in a minute. Much water was raised with 50 turns, but very little with only 30 turns in a minute. The rope soon decays, especially if it is not made of hair. Sharpies on raising water by the fall of waste Water. JSich. VII. 298. A hydraulic machine from Servifere's cabinet. Nich. VIII. 35. Two pinions fitted tight and revolving within abox. Draining. Dickson's practical agriculture. Harriott's patent pump capstan is preferred to Dodgson's patent double headed ship pump. The lever works hori- zontally by means of wheelwork, and this motion is said to be less fatiguing to the men, so that they can work for an hour or more : and a rope may be applied so that any num- ber may work together. The friction is said to be dimi- nished to Jj by applying a guide to the pistons. A pump should have a valve near the moveable piston, and another below the level of the water. Robison. A bag like a powder puff with valves makes a good sim- ple pump. Robison. Quantity of water raised by pumps. See animal force. PNEUMATIC MACHINES. *Heronis spiritalia. Leupold.Th. M. G. E. M. PI. VIII. Amusemens de physique. Machines simply Pneumatic. Bellows, Fans, and other Mecha- nical Ventilators. Papin on the Hessian or rotatory bellows. Ph. tr. 1705. XXIV. 1990. Knopperf's fan for corn. A. P. 1716. H. 78. Mach.A. II. 101, 103. Barrieres's leathern ventilator. A. P. 1723- H. 120. Mach. A. IV. 53. Desagulievs's pump ventilator. Ph. tr. 1727- ■ XXXV. 353. Desaguliers on the centrifugal ventilator. Ph. tr. 1735. XXXIX. 40. Rayncs's bellows. A. P. 1728. H. 108. Terral's bellows for foimderies and forges. A. P. 1729. H. 92. Mach. A. V. 41,93. VI. 121. Farel's mode of working bellows. A. P. 173.'!. H.99. Hales on ventilators. 8. 1743. R. I. 2 v. 8. ' Lond. 1758. Hales on ventilation. Ph. tr. 1748. XLV. 410. Halcs's ventilator. Bailey's mach. I. 170. Ellison the effect of ventilation. Ph.tr. 1751. 211. A ventilator erected in the Hotel des Inva- lides. Much. A. VII. 379. ^ Pommier's ventilator improved after Hales. Mach. A. VII. 413. Bellows moved by water. Emers. mech. f. 240, 241. Smith's bellows. Emers. mech. f. 244. Blowing wheel. Emers. mech. f. 284. The Hessian or centrifugal bellows of Papin. Gensanne's bellows for ventilating mines. S. E. IV. 158. Jars on the circulation of air in mines. A. P. 1768. 218. H. 18. Bellows. Gauger Mecanique du feu. Munier's winnowing machine. Roz. Introd, ' n-79. De Bory on purifying the air of vessels. A. P. 1780. lll.H, 13. Leroi's simple ventilation by windsails. A. P. 1780. 598. H. 13. Evers's winnowing machine. Bailey's mach. 1.51. Fitzgerald's ventilator. Bailey's mach. I. 172. Hill's ventilator for mercurial vapours. Bai- ley's mach. II. 70. Wilson's patent for applying vapours. Rep. XII. 1. Elastic tubes. Fans. E. M. A. II. Art. Eventaillisle. Wooden bellows. E. M. PI. II. PI. 5. CATALOG UK. — PNEUMATIC MACHINES. 2*3 Ventilation. E. M. A. VIII. Art. Tuyaiix aeriques, Ventilateur. Bellows. E. M. M. III. Art. Soufflet. Ventilators for ships. E. M. PI. V. Marine. PI. 156. n. 2. Wooden fan for corn. E. M. Art. Aratoire.' Hassenfratz's bellows for a blowpipe. Roz. XXVIII. 345. Rozier's apparatus for breathing in cellars. Roz. XXVin.418. Leblond on the blow pipe. Roz. XXX. 92. Saint Martin's ventilator. Roz. XXXIH- l6l. Acting by lateral friction. On antimephilic pumps. Ann. Ch. VI. 86. Whitehur&t on ventilation. 4. Lond. 1794. Robins on ventilation. Am. tr. III. 324. Repert. I. 119. Lambert on the theory of bellows. Hind. Arch. III. 1. Blast machine at Carron. SmCalon's reports. Bobtrt von luftwechsel maschinen. 4. Petersb. 1797. R.S. Salmon's ventilator. Repert. IX. 252. Boswell's blast ventilator. Nich. IV. 4. Gilb. V. 304. Roebuck on blast furnaces. See economy of heat. South's ventilator for corn on shipboard. Repert. XI. 397. Ph. M. V. 393. Mushet on an airvault. Ph. M. VI. 362. Sir G. O. Paul's stoves and windows for ven- tilating hospitals. S. A. XIX. 330. Rep. ii. II. 268. Polfreeman's winnowing machine. Willich's dom. enc. Art. Winnow. Bellows. Banks on machines. 9. Gardner's patent ventilator. Repert. ii. II. 241. Dobson's patent zephyr. Repert. ii. II, 404. Haas's blowpipe. Nich. 8. III. 119. The pistons of large bellows are sometimes fitted witli .^ wool and black lead, but Laurie's hydraulic bellows are much preferable. Robison. We can draw mercury 2 or 3 inches by the lungs, 25 by the mouth ; we can force it 5 or 6 inches, but not without pain. Robison. Air Pumps, Condensers, and Air Guns. Casp. Schotti mechanicahydraulicopneuma- tica. 4. 1637. Boyle's new experiments touching the spring of the air. 8. Oxf. I66O. Works. I. 1. Boyle's continuation of experiments. Oxf. 1669. Works. III. 1. Boyle on the rarefaction of air. 4. London, 1671. Works. 111.202. Boyle's second continuation. 8. Lond. 168I. Works. IV. 96. Boyle's general history of the air. 4. Lond, 1692. Works. V. 105. Guericke experimenta nova Magdeburgica. f. Amsl. 1672. Ace. Ph. tr. 1672. VII. 5103. Papin uouvclles experiences du vuide. 4. Par. 1674. Papin on shooting by rarefaction. Ph. tr. 16«6. XVI. 21. Gallois on an air gun remaining charged 16 years. A. P. II. 146. Varignon on the exhaustion of air pumps. A. P. X. 285. Mariotte de la nature de I'air. 12. Par. I699. Oeuvr. I. 148. SengMfrd de aeris natura. 4. Lond. 1699- Leupolds Beschreibung der luftpumpe. 4. Leipz. 1707. 1712. Leupold. Th. Aerostat. _ ) Ilauksbee's physicoraechanical experiments. S'Gravesande's natural philosophy. Desaguliers's natural philosophy. 254 CATALOGUE. — PNEUMATIC MACHINES. Nollet on pneumatic experiments. A. P. 1740. 385, 067. 174). 3,'38. H. 145. Smeaton's air pump. Ph.tr. 1751.415. Lozi'iVz liber die eigenschaften derluft. 1754. Emers. mechanics. Air pump. f. 277- Leisteiis Beschreibung einer lultpumpe. 4. Wolfenb. 1772. Nairne's experiments on the pear gage, with Smeaton's pump, explained by Cavendish. Ph. tr. 1777. 614. There still remained some anomalous experiments, in ■which the pear gage indicated a less complete exhaustion than the barometrical gage. On Nairne's pneumatic experiments. R02. XI. 159. Coulomb on condensing with an air pump of any kind. Roz. XVII. 301. Oreppin and Billiaux on a condenser. Roz. XIX. 438. Cavallo on Haas and Hurter's pump with a stopcock. Ph. tr. 1783. 435. The pump when in good order rarefied to -j^. Cavallo on Nairne's improved air pump. Roz. XXV. 261. With a figure. Cuthbertson's description of an air pump. 1783. Is said to rarefy to jjjj. Ingenhousz Vermischte schriften. I97. Ingen'housz has proposed to make a vacuum by the ab- sorption of air into ignited charcoal while acting. Mode of boiling mercury in a gage. Ph. tr. 1785. 276. Hiiidenburg de antlia Baaderiana. 4. Leipz. 1787. A mercurial pump. Hindatburg de antlia nova. 4. Leipz. 1789. Goth. Mag. V. ii. 81. Cazalet's air pump. K02. XXXIV. 334. A Torricellian vacuum made by means of water. Hervieu's air pump. Roz. XXXV. 60. Michel's mercurial air pump. Roz. XXXV. 209. Schrader's air pump. Gren. III. 357. On the imperfections of gages. Brook on electricity. Lichtenherg's account of Smeaton's air pump. Licht in. Erxieb. p. xxxvi. *Robison. Enc. Br. Art. Pneumatics. Jones's note on airp^mps. Adams's lectures. I. 153. Prince's air pump. Am. Acad. 1.497. Prince and Cuthbertson's air pump. Nich. I. 119. Gilb. I. 352. Prince's improved air pump. Nich. VI. 235. Sadler's air pump. Nich. I. 441. Gilb. I. .352. Van Marum's simple air pump. Gilb. I. 379. With a stopcock turned by external force. Gilbert thinks it preferable to Cuthbertson's, which is said to be liable to become clogged by the thickening of the oil. Little's air pump. Ir. tr. VI. 319. Nich. II. 501. Gilb.V. L Mackenzie's air pump. Nich. II. 28. On the air pump with metallic valves. Nich. If. 370. Clare's two air pumps. Nich. IV. 261. One of them mercurial. Smith's air pump vapour bath. Ph. M. XIV. 293. Cuthbertson's air pump. Air gun. Rees's cy- clop. II. Plates. Art. Pneum;%tics. Edelcrantz's mercurial air pump. Nich. VII. 188. Swedenberg made a mercurial air pump. Pneumatic Machines and Apparatus, connected with Hydraulics. Bellows and Gasholders Shower bellows. Belidor. Arch. Hydr. II. i. PI. n. 24. Bellows and gasholders. Triewald's water bellows, worked by troughs as a beam. Ph. tr. 1738. XL. 231. CAT A LOG UK. -PNEUMATIC MACHINES. 255 Bartlifes on shower bellows. A. P. 1742. H. 132. S. E. III. 378. Stilling on shower bellows. Ph. tr. 1745. XLUl. 315. Guignon's machine for breathing vapour. Mach. A. VII. 467. Cavendish. Ph.tr. 1766- 141. Pneumatic apparatus. Meusnier on the gazometer. A. P. 1782. 466. Shower bellows. E. M. PI. 11. Fer. ii. PI. 34. Trompes. VenUiri's inquiry. Prop. 8. Boulard's gasholder lor making hydrogen. Roz. XXIX. 172. Sahice on pneumatic apparatus. Mem. Tur. 1788. IV. 83. Bonati on shower bellows. Soc. Ital. V. 501. Tries's gazometer. Roz. XL. 11 6. Van Marum sur un gazometre. 4. Harl. 1796. Van Marum's gazometer. Ann. Ch. XII. 113. XIV.313. Ph. M. 11.85. Liidicke on Baader's hydraulic bellows. Gilb. I. 1. Cavallo's poeumatip apparatus. Ph. M. I. 305. Robison. Enc. Br. Art. Pneumatics. Seguin's gazometer. B. Soc. Phil. n. 10. On gazometers. Gilb. II. 185. Pepys's mercurial gazometer. Ph. WkV. 154. Pepys's apparatus for gases. Ph. M. XI. 253. Pepys's new gasholder. Ph. M. XIII. 153. Willson's patent for applying vapours. Rep. XII. 1. Hindmarsh's stream bellows. Repert. XII. 217. Clayfield's mercurial air holder. Ph. M. VII, 148. Warwick's gasholder. Ph.M. XIII. 256. Hornblower's hydraulic bellows. Nich. 8. I. 219. Read's cheap pneumatic apparatus. Nich. 8. III. 55. On pneumatic apparatus. Nich. 8. IV. 4. Edelcrantz's mode of extracting air from boilers supplied by siphons. Nich. VII. 81. Michelotti's gazometer. Journ. Phys. LIII. 284. Submarine Apparatus. Hooke on measuring the depth of the sea. Ph. tr. 1665 . . 6. I. n. 9- n. 14. n. 24. Boyle and Ray on the bladders of fish. Ph. tr. 1675. X. 114,310, 349. On the pressure of water upon sunk bottles. Ph. tr. 1693. XVII. 504. Halley's art of living under water. Ph. tr. 1716. XXIX. 492. 1721. XXXI. 177. Halley was one of five that were 9 or lo fathom under water for an hour and a half. Describes a cap for subm»- rine excursions. Diving bells. Leup. Th. Pontific. t. 26. D'Achery on a corked bottle let down 130 fathom. A. P. 1725. H. 6. Says, that the water forced into it was much less salt than common sea water. H ales and Desaguliers's machine for measuring the depth of the sea. Ph. tr. 1728. XXXV. 559. Letting go a weight at the bottom. Triewald on the diving bell. Ph. tr. 1736. XXXIX. 377. Wkh a pipe for breathing the cooler part of the air. Cossigny on an experiment of sinking a cork- ed bottle. A. P. 1737. H.8. Krafft on a bottle sunk 60 fathom without effect. A. P. 1745. H. 19. E. M. PI. V. Marine. PI. 159- Enc. Br. Art. Diving Bell, Sea Gage. 256 CATALOGUE. — PNEUMATIC MACHINES, AEROSTATION. Spalding's diving bell. S. A. I. 236. , Bushnell on submarine vessels. Am. tr. IV. 303. Repert. XV. 385. Nich. IV. 229- Like two tortoise shells combined. Diving bell. Walker's philosophy. Lect. vi. Fulton's diving boat. Montuclaand Lalande. III. 782. Healy on diving bells. Ph. M. XV. 9. Succeeded in supplying the air by a condenser. Aerostation, either hy heated Air, or by Gases. Lichtenberg suggests the term aerostation. Lohmekr de artificio navigandi per aerem. 1676. Repr. 4. R. S. Lohmeier was of Rinteln. Rosnier's mode of flying. Hooke. Ph. Coll. n. 1. p. 15. Rosnier is said to have descended obliquely over some houses. Francesco Lana on exhausted globes ; after Albertus de Saxonia and Wilkins. Hooke. Ph. Coll. n. 1. p. 18. Mdngez on imitating the flight of birds. Roz. II. 140. Euler on the ascent of balloons. A. P. 1781. H.40. This paper was found on his slate after his death. E. M. A. VIII. Theoriedes a6rostats. E. M. Physique. Art. Ballon. Report of a committee on Montgolfier's ma- chine. A. P. 1783. H. 5. Roz. XXIV. 81. Saint Fond sur les experiences de Montgol- fier. 8. R. S. UArt de faire les ballons. 8. Amst. 1783. Reneaux sur les machines aerottatiques. 4. R.S. Galvez sur un moyen de donner la direction aux machines a^rostatiques. Ph. tr. 1784, 469. An experiment tried with a boat. Three pairs of wrings each worked by a man, impelled a boat as feet long, at the rate of 393 feet in about 2 minutes, about 2-1 miles an hour. Martin's hints on aerostatic globes. 8. Lond. 1784. Roherl freres sur les experiences aerostatiques. Par. 1784. L'jirt dc voyager dans les airs. 8. Par. 1734. Bertholon sur les globes aerostatiques. Mont- pel. 1784. I^rachute. Bertholon's esssiys. Kramp Geschichte der aerostatik. 2 Parts. 8. Strasb. 1784. Anhang, 1786. Hallens Magic. 11. Millyon aerostatic experiments. Roz. XXIV. 64, 156. Cavallo's history and practice of aerostation. 8. Lond. 1785. Cavallo's N. Ph. IV. 3l6. Southern on aerostatic machines. 8. Birm. 1785. R. S. Meusnieron aerostatic machines. Roz. XXV. 39. Baldwin's aeropaidie. «. Chester, 1786. Burja hydroslatik. ix. Henzion sopra le machine aerostatiche. 4. Flor. 1788. R, S. , Prieur on parachutes. Ann. Ch. XXXI. 269. Le Normand on parachutes. Ann. Ch. XXXVI. 94. O'l the i^^achate. Nich. I. 523. Wriiiht on aerostation. Ph. M. XIV. SS7. On Garnerin's voyages. Nich. 8. III. 57. Gilbert on the ascent of Garnerin, Robert- son, and others. Gilb. XVI. 1. 164, 257- Hydrogen gas is seldom procured more than 5 or 6 times as rare as common air. On the parachute. Gilb. XVI. 156. Balloons. Rees's cyclop. III. Plates. Art. Pneumatics. Aerial excursions. Ph. M. XVII. 188. CATALOGUE. PNEUMATIC JfACHINES, 257 Ventilation by Heat. Chimnies and furnaces. See Physics, Eco- nomy of Heat. Sutton on extracting foul air from ships. 3. M. B, Sutton's ventilator. Ph.tr. 1742. XLII. 42. Watson on Sutton's ventilator for ships. Ph. tr. 1742. X LI I. 62. jj^ Thinks it preferable to windsails or funnels. Lomonosow on the currents of air in mines. N. C. Petr. I. 267. Euler on the equilibrium of fluids, with the effects of heat. N. C. Petr. XI. XIII XIV. XV. Steam Engine. Force of steam. See Physics, Heat. Marquis of Worcester's century of inventions. Papin Recueil de pieces. 8. Cassel, 1695. Acc.Ph.tr. 1697. XIX. 481. Proposes a mode of employing the force of steam by re- moving the fire continually from one part of the machine to another. Savery's steam engine. Ph. tr. I699. XXI. 228. The model was exhibited 10 June 1599. Amontons's mode of employing the force of fire. A. P. 1699. 112. H. 101. Leup. Th. M. G. t. 53. Newcomen's patent. Dated 1705. Robison. He introduced the piston. Mey and Meyer's steam engine for raising water. Mach. A. IV. 185. Bosfrand's steam engine. Mach. A. IV. igi, 199. Leup'.ld's fire wheel. Th. M. G. t. 50. Steam engine. Leup. Th. M. G. Th. Hy- draul. 2. Belidor. Arch. Hydr. II. i. 308. Desagiiliers. N. Ph. II. Dupuys's steam engine, with Moura's im- provements. A. P. 1740. 111. TOL. II. Payne's new invention of expanding fluids. Ph. tr. 1741.821. Thinks that much may be saved by making the boilerg red hot. Makes steam in specific gravity -Jjj. Gensanne's steam engine. A. P. 1744. U. 60. Mach. i4. VII. 227. Blake on steam engine cylinders. Ph. tr. 1751. 197. Smeaton on Ue Moura's improvement of Savery's steam engine. Ph. tr. 1751. .436. fFitzgerald on increasing steam by ventila- tion. Ph. tr. 1757. 53, 370. Fitzgerald's ventilators worked by steam en- gines. Ph. tr. 1758. 727. Emers. mech. f. 274. Beighton's steam engine. Bossut Hydrody- namique. Morand Art d'exploiter les mines de char- bon. f. Paris, p. 408. Cancrins Bergmaschinenkunst. Falck on the steam engine. Lavoisier on the expense of steam en A. P. 1771. 17. H. 63. A. P, 1771.20. Blackey sur les pompes a feu. 4. Amst. 1774, Maillard sur la th^orie des machines mues par la force de la vapeur. E. M. Math^matique. Art. Hydraulique, pompe a feu. Francois's steam engine without a piston. M. Laus. I. 51. Repert. IV. 203. Working the cocks by a tumbler. Langsdorfs Hydr. und pyr. grundl. c. II. LangsdorPs proposal for a steam engine. L. Hydr. PI. 19, 20. A tumbler. PI. 40. Kempel's rotatory eolipile. Langsdorfs Hydr. PI. 22. f. 129. Beighton's and Watt's steam engines. Langsd. Hydr. PI. 23, 24. £58 CATALOGUE. — PNEUMATIC MACHINES. Cooke's rotatory steam engine. Ir. tr. 1789. 113. Repert. Ili.401. Driving a wheel with falling flaps. Gehler's phys. wbrterb. Prony. Arch. hydr. Burja Grundlehren der hydrostatik. II. §. 28. * Walt's patent for saving fuel in steam en- gines. Repert. I. 217. Robison. Enc. Br. Art. Steam. Steam en- gine. Nancarrow on the dimensions of a steam en- gine. Am. tr. IV. 348. Repert. XIV. 329. Nich. IV. 545. Ph. M. IX.- 300. Giib. XVI. 152. On Savery's construction, with a condenser. Thomson's furnace for steam engines. Rep. IV. 316. For burning smoke. Droz's steam engine without a beam, ap- proved by the Institute. B. Soc. Phil. n. 3. Gilb.XVI.356. Curr's coal viewer and engine builder. 4. Sheffield, 1797. R. S. Nicholson on the steam engine without a piston. Nich. I. 44. Gilb. XVI. 129. With a piston. Nich. II. 228. Gilb. XVI. 336. On Ciirtwright's patent steam engme. Ph. M. I. 1. Repert. X. 1. After Watt. Retains the water of injection for the boiler, without exposing it to the air ; proposes to apply the vapour of spirits during distillation to the purposes of a steam engine ; and desoribes a rotatory engine. Cartwright's patent improvements on steam engines. Repert. XIV. 36l. For making them more compact. The cylinder is placed within the boiler, as in some other engines. Remarks on Cartwright's piston. Nich. II. 364, 476. Reply. Ph. M. 11. 221. Hornblower's patent steam engine. Repert. IV. .361. Hornblower's patent rotatory steam engine. Repert. IX. 289. Producing a rotatory motion by diaphragmt. Hornblower's beams for engines. Nich. 8. 11.68. On the boiler. Nich. III. 86. Boulton's steam engine. W^alker's philoso- phy. Lect. vi. Walker's improved steam engine. Walker'i philosophy. Lect. vi. Sadler's patent rotatory steam engine. Rep. VII. 170. Murray's patent steam engine. Repert. XL 309. A horizontal cylinder and a piston with racks. Murray's patent steam engine. Repert. XVI. 298. Murray's patent rotatory steam engines. Repert. ii. IL 175. Repeated. III. 235. Keir's improved boiler. Nich. V. 147. Nieuwe Verhandelingen van bet Batafsch Genootschap. I. Rotterd. 1800. On steam engines. Murdock's patent for manufacturing steam engines. Hase's patent improvement in steam engines. Repert. XV. 220. For saving the heated water. Roberton's patent steam engines. Repert. XVI. 366. Savery's Newcomen's, and Watt's engines. Imis. elem. I. PI. 10, 11. Good figures. Woolf's apparatus for employing waste steam. Nich. 8. II. 203. Woolf on equalising the motion of steam en- gines. Nich. VI. 218. Woolf's steam regulator. Nich. VI. 249. A bent lever. Woolf's boiler consisting of several cylinders. Ph. M. XVII. 40. Woolf's steam valve. Ph. M. XVII. 164. WoolPs improvements in steam engines. Nich. VIIL 262. Ph. M. XIX. 133. CATALOGUE.—- PyiUMATIC MACHINES. S59 Account of the explosion of Trevithick's steam engine. Repert. ii. III. 394. Ph. M, XVI. 372. Saint's patent steam engines. Repert. ii. III. 408. The flue carried through the boiler. On the force of steam engines. Nich. IX. 214. Perier on the employment of the steam en- gine in coal mines. M. Inst. V. 360. Edelcranz's safety valve for emitting steam or admitting air. S. A. XXII. 329. Tn the original form of the steam engine, the pressure of steam, and not that of the atmosphere, forced down the pis- ton. Kobison. Enc. Br. Mr. Watt finds it most advantageous to work his engine at a high temperature. Robison. Enc. Br. The whole force obtained from steam stopped when it has filled one fourth of the cylinder, appears from calcula- tion to be twice as great as when it is continually admitted. Robison. Enc. Br. But perhaps a greater quantity of heat would be required. The boiler should contain about ten times as much steam as the cylinder. M.Young. An account of Mr, Symington's new Steam Boat. From the Journals of the Royal Institution. I. 195. Several attempts have been made to apply the force of steam to the purpose of propelling boats in canals, and there seems to be no reason to think the undertaking by any means liable to insuperable difficulties. Mr. Syming- ton appears already to have had considerable success, and the method that he has employed for making a connexion between the piston and the water wheel is attended with many advantages. By placing the cylinder nearly in a horizontal position, he avoids the introduction of a beam, which has always been a troublesome and expensive part of the common steam engines : the piston is supported in its position by friction wheels, and communicates, by means of a joint, with a crank, connected with a wheel, which gives the water wheel, by means of its teeth, a motion somewhat slower than its own ; the water wheel serving also as a fly. The steam engine differs butlittle with respect to the condensation of the steam, from those of Boulton and Watt now in ge- neral use ; there is an apparatus for opening and shiitting the cocks at pleasure, in order to revert the motion of the boat whenevei it may be necessary. The watet wheel is si- tuated in a cavity near the stern, and in the middle of the breadth of the boat, so that it becomes necessary to have two rudders, one on each side, connected together by rods, which are moved by a winch near the head of the boat, so that the person who attends the engine may also steer. It has been found most advantageous to have a very small number of float boards in the water wheel. Another material part of the invention consists in the arrangement of stampers, at the head of the boat, for the purpose of breaking the ice on canals, an operation which is often attended with great labour and expense. These stampers are raised in succession by means of levers, of which the ends are depressed by the pins of wheels, turned by an axis communicating with the water wheel. Mr. Symington calculates, that a boat capable of doing the work of twelve horses may be built for eight or nine hundred pounds. An engine of the kind has been actually constructed at the expense of the proprietors of the Forth and Clyde navigation, and under the patronage tf the go- vernor. Lord Dundas : it was tried in December last, and it drew three vessels, of from flo to 70 tons burden, at the usual rate of two miles and a half an hour. Mr. Syming- ton is at present employed in attempting still further im- provements, and when he has completed his invention, it may, perhaps, ultimately become productive of very exten- sive utility. Steam Air Pump. Carradori on Berretray's steam air pump. R02. XXXVIII. 150. Inflammable Vapours. Street's patent inflammable vapour force. Repert. I. 154. •fBarber's patent for procuring motion by in- flammable air. Repert. VIII. 371. A stream of ignited air impelling a fly wheel. Gunnery. Theory of Gunnery, and Operation of Powder. See Projectiles. Resistance of Fluids. Hooke's powder proof. Birch. I. S02. Fig. Greaves on the force of guns. Ph. tr. 1685.. XV. lOQO. , . 260 CATALOGUE.— PNEUMATIC MACHINES. Blondel on throwing bombs. A. P. I. 150, 165. Mariotte on the recoil of fire arms. A. P. I. 233. Perrauh's machine for increasing the effect of fire arms. A. P. I. 272. Mach. A. I. 11- Lahire on projectiles. A. P. IX. 187, 198. 1700. 205. H. 147- Lahire on the theory of the air in powder. A. P. 1702. H. 9. Cassini on the recoil. A. P. 1703. H. 98. Cassini on the effect of different charges. A. P. 1707. H. 3. Guisnee's Galilean theory,. A. P. 1707. 140. H. 120. Chevalier on the effect of powder. ' A. P. 1707. 526. H. 152. Eessons on throwing bombs. A. P. 1716. 79. Ressons on the force of powder. A. P. 1719. H. 20. 1720. H. 112. Maupertuis on throwing bombs. A. P. 1731. 297. H. 72. B61idor on gunpowder. M. Berl. 1734. IV. 116. Bigot de Morogue on the effects of powder, according to the laws of accelerating forces. A. P. 1735. H. 98. Leutmann on gunnery. C. Petr. IV. 265. Dulacq's theory of the mechanism of artil- lery. A. P. 1740. H. 108. Deidier on throwing bombs. A. P. 1741. H. 133. Report of a committee on gunnery. Ph. tr. 1742. 172. Found that the whole of the powder is not fired, that the ball is moved before all that is fired takes effect ; and that " the longest chamber is the most efficacious. Mobins's new principles of gunnery, R. I. Extr.Ph.tr. 1743. 437. In support of the opinions controverted by the committee, as allowable approximations. Attributes the whole effect to fluids permanently elastic. Missiessy on the escape of powder at the touch hole. A. P. 1748. H. 28. Dnhamel on the escape of powder at the touch hole. A. P. 1750. 1. H. 30. D'Arcy on the theory of artillery. A. P. 1751. 45. H. 1. D'Arcy Essai sur la theorie de I'artilleri^. Ace. A. P. 1760. H. 142. Montalembert on the rotation of balls. A. P. 1755. 463. H. 34. Montalembert on proving cannon. A. P. 1759. 358. H. 227- Vandelli on the force of steam in gunpowder. C.Bon. III. 92 IV. 106. Saluce on the elastic fluids produced from gunpowder. M. Taur. I. il. Casali on the force of powder. C. Bon. V. ii. 345, 357. Simpson's exercises. Euler's gunnery, by Brown. 4. R. S. jiiiderson's gunnery. Fortification and gunnery. Emers. misc. 242, 277. Treatise on gunpowder and fire arms. 8. Glenie's history of gunnery. 8. R. S. St. Auban sur les nouveaux sysiemes d'artil- lerie. 8. R S. *Boida on projectiles. A. P. 1769. 247. H. 116. Devalliere on the superiority of long and heavy pieces of cannon. A. P. 1772. ii. 77- H. 44. Examen de la poudre. 8. 1773. R. I. Hutton on the force of fired gunpowder. Ph. tr. 1778. 50. The powder appears to fire almost instantaneously, for the force is nearly in the direct proportion of the powder, the velocity in its subduplicate ratio, and in the subdupli- cate ratio of the ball inversely. The height and the range a^e therefore at the weight of powder. CATALOGUE. — PNEUMATIC MACHINES. £61 Two ounces of powder impelled a ball of 28| oz. with a Telocity of 013 feet in a second : this would carry it to a height of 5930 feet, producing an effect equal to the labour of a man continued 105 seconds, and 10 hours of such la- bour would produce an effect equal to that of 43 pounds of powder. This force is therefore not comparatively cheap, lupposing the whole effort of the powder to be consumed : but it would be almost impossible to find mechanical means •o convenient for producing velocity. Air, compressed in ah air gun, would never move even into a vacuum with a velocity greater than about 1400 feet in a second : much less could it carry before it the weight of a cannon ball with a velocity of 2000 feet : and a bow or a spring of any kind would have a still greater disadvantage. The great rarity of the heated elastic fluids disengaged from powder, combined with their great elasticity, gives them the faculty of imparting so prodigious a velocity. Hydrogen gas, suffi- ciently condensed, would escape with a velocity 3 times as great as common air. Hutton thinks the force equal to 1500 or 1600 atmospheres. Y. Ingenliousz. Ph. tr. 1779. Robins found the force of gunpowder equal to 1000 at- mospheres, and observed, that a red heat made air expand to 4 times its bulk; hence he inferred that powder produced 450 times its bulk of air. Hauksbee, Amontons, Belidor, and Saluces agree that it yields 322 times its bulk. Thompson's e.^periments on gunpowder. Ph. tr. 1781. '4J29. Count Rumford observes, that the piece is heated sooner when fired without than with balls, perhaps because the great velocity of the air excites more heat by friction. When the piece is become warm, a smaller quantity of powder serves. The operation of ramming increases the force of powder in the ratio of 6 to 5, or more : the velocity is nearly in the subduplicate ratio of the weight of the powder, at least for musket bullets. The situation of the vent has very little effect ; the cavity of the piece should have a hemi- ■pherical terminarion. The Telocity is more accurately de- termined by measuring the recoil of the piece when sus- pended than by the motion of a pendulum struck by the ball, deducting always that which would be produced without any ball. The velocity was sometimes greater than 2000 feet in a second. Robins makes the force of gunpowder equal to looo atmospheres ; but, upon his own principles, it is equal at least to 1308. The velocity is very nearly in the subtriplicate ratio of the weight of the -ball, increased by half that of the powder, inversely. The force of aurum fulminans appears ts be but one fourth •f that of gunpowder. The experiments were made with a bore of about f inch. It is surprising that there should be so much difference between these experiments and others, that a quadraple weigh; in the one case should have pro- duced the same effect with an octuple weight in the other. It may be questionel whether the difference of the squares of the velocities ought not rather to be taken in making the correction for the recoil. Y. Rumford on the force of fired gunpowder. Ph.tr. 1797. 222. Nich. I. 439. Gilb. IV. 257, 377. Bernoulli makes the expansive force of gunpowder equal to 1 0 000 atmospheres ; Rumford, from the bursting of a barrel of iron, so 000, from some more direct experiment!, from 20 000 to 40 000. The utmost that can be justly in- ferred from the bunting of the barrel is in reality about 30 000, since the tension could by no means be equal through every part of its substance. The force was, in at- 1 + .4X mospheres 1.841 (looox) x being the quantity of powder, the whole capacity of the cavity being unity. In some other experiments the multiplier, instead of 1.841, ap- pears to be 6.37; giving 101021 atmospheres instead of 29 178, when X becomes 1. A cubic inch of gunpowder contains nearly 11 grains of water of crystallization, and j, of moisture, which Count Rumford thinks, would be suffi- cient for furnishing the steam. This is however a great mistake : a heat of 1200 would scarcely more than double, or at most quadruple, the expansive force of a given portion of steam, consequently the density of steam at this temper- amre, exerting a pressure of 50 000 atmospheres, ought to be more than 1 0 000 times as great as under the usual pressure, that is, probably, almost 4 times as great as the density of water. Count Rumford finds that much of the powder it discharged unfired. E. M. A. VI. Art. Poudre a canon. Massey on saltpetre. Mauch. M. I. 184. Rep. I. 248. S. E. XI. A collection of memoirs on saltpetre. At first there were 38 unsuccessful attempts ; in the second instance Thouve- nel gained the first prize of 8000 livres, among 28 competi- tors. A few of the best memoirs only are printed at large. Napier on gunpowder. Ir. tr. 1788. II. 97. Rep. II. 276. Robison. Enc. Br. Art. Projectiles, Resist- ance. Bullion on saltpetre and gunpowder. Repert. VI. 49. 262 CATALOGUE. — PNEUMATIC MACHINES. Howard on a fulminating mercury. Ph. tr. 1800. 204. On increasing the effects of powder. Journ. Phys. Repert. VII. 135. By leaving a vacant space behind the wadding. Thus a bomb if but partly filled breaks into a larger number of pieces ; but they are not scattered so far as when it is quite filled. Regnier's powder proof. Nich. III. 198. Ph. M. IV. 394. Gilb. IV. 400. With a spring. fVandelli on the force of gunpowder. Rep. X. 286. Griffith on mixing lime with gunpowder. Repert. XII. 341. Coleman on gunpowder. Ph. M. IX. 355. Jessop on blasting rocks. Nich. IX. 230. Farey on blasting rocks. Ph. M. XX. 208. The best charge of powder is about i or i of the weight of the ball, for battering |. A 24 pounder with 16 pounds of gunpowder at an elevation of 45° ranges 20 S50 feet, about I of the range that would take place in a vacuum. The resistance is at first 400 pounds or more, and reduces the velocity in a second from 2000 to laoo feet in the first ISOO feet. Cavallo, from Robins. It has been found, that the velocity of a ball is not mate- rially affccted by increasing the weight or firmness of a piece of ordnance, beyond'very moderate limits. Particular Constructions of Cum and their Parts. Chaumette's horse pistols. Mach. A. I. 201. Jointed carbine. A. P. 1715. H. 66. Mach. A. II. 27. Guns loaded at the breech. A. P. 1715. H. 66. Mach. A. II. 79, 99, 101. III. 53. Jointed powder horn. Mach. A. III. 49. Powder horn with balls. Mach, A. III. 51. Appendages to locks. Mach. A.m. 59. Bedaut's machine for red hot balls. Mach. A. II. 61. fDestau's roUing battery of muskets. Mach. A. II. 75. Villon's machines for making gunbarrels and cannons. A. P. 17 16. H. 77. Mach. A. III. 71,73,77,79. Machine for boring cannons. Mach. A. III. 81. Deschamps's improvements of guns. A. P. 1718. H. 74. Mach. A. III. 171, 177, 181, 183. Rifle muskets and cannons. Leutmann on rifle barrels. C. Petr. HI. 156. D'Arcy's light cannons. A. P. 1733. H. 70. Raucourt's inventions for throwing bombs. Mach. A. VI. 157. Lacq on the mechanism of artillery. A. P. 1740. H. 108. Ladoyreau on cannons of wrought iron. A. P. 1742. H. 141. Reinier's double barrelled gun. A. P. 174S. 155. Fusil tournant a deux coups. Pasde Loup's machine for charging artillery.. A. P. 1742. H. 157. Maty's gunpowder air gun. Condamine. A. P. 1757. 405. Ingenhousz. Ph. tr. 1779. Shot a bullet So paces with the air of 2 ounces, Which served 1 8 times. Montalembert on priming cannons. A. P. 1759.358. H. 227. Challier's gun lock. A. P. 1762. H. 192. Descourtieux's gun barrels. A. P. 1765. H. 133. Boullet's gun acting by the circular motion of the barrel, A. P. 1767.H. 186. Delaunay's gun easily primed. A. P. 1771. H. 68. E. M. A. I. Art. Arquebusier. Canons. Watts's patent for making small shot. Rep. HI. 313. On shot. Nich. I. 260, 380. Aitken's patent for loading fire arms. Rep. VI. 239. CATALOGUE. — HISTORY OF HTDRAULICS AND PNEUMATICS. 263 Many charges introduced at once. Wilson's patent fire arms. Repert. VI. 304. Preserved from rust. Marescot on shooting grenades. M. Inst. II. 242. Dodd's safe gun lock. S. A. XXII. 296. Haycraft's patent gun carriage. Repert. XII. , 16. Dolomieu on the art of cutting gun flints. M. Inst. in. 348. Nich. 8. 1. 88. Prosser'a patent guns and pistols. Repert. XV. 224. On casting shot. Gilb. VIII. 2,50. A wheelbarrow for throwing grenades. Per- son, Recueil. PI. 7. De Poggi's patent ordnance. Repert. ii. I. 169. Webb's safe gun lock. S. A. XX. 247. Nich. 8. V. 29. A magazine pistol. Nich. 8. IV. 250. From Lord Camelford, who had " used it in various parts of the worlJ." Two muskets for quick firing. Nich. 8. V. 116. On a gun for throwing double shot. Nich. VII. 146. Rockets, and oth^r Fireworks. Pasdeloup's machine for loading fireworks. Mach. A. I. 125. Buffon on rockets. A. P. 1740. H. 105. Robins on the height of the ascent of rockets. Ph. tr. 1749. 131. A rocket of a pound ascended 45« or 500 yards, in 7" ; a roclcet of 4 pounds remained 14". Ellicott on the height of the ascent of rockets. Ph. tr. 1750. 578. Rockets two inches and a half in diameter a proper size. A rocket fired at Hackney was seen at Barkway. Some of three inches in diameter rose laoo yards. HISTORY OF HYDRAULICS AND PNEU- MATICS. Balloons. See Aerostatics. Lowther examined inflammable air in 1733. Ph. tr. 1733. Belidor's history of antient and modern ca- nals. Arch. Hydr. II. ii. 343, 357. Leroy sur les navires des anciens. 8. R. S. Luckombe's tablet of memory. Glenie's history pf gunnery. R. S. jKtfp/er Bergm. Journal. 1791. Matthesius is said to have mentioned a steam engine in his Sarepta before 1SS8. Phillips's history of inland navigation. 4. R. I. On the Chinese canal. Staunton's voyage. R. I. Charnock's history of marine architecture. 3 V. 4. Lond. 1800. Montucla and Lalande. Hist. Mathem. History of shipbuilding. IV. 381. Prieur and Lenonnand on parachutes. Ann. Ch. XXXI. 269. XXXVI. 94. Gilb. XVI. 156. Beckmann on the invention of fire engines. Ph. M. XI. 238. Gilb. XVI. 385. Erraan observes, that Aristotle weighed the carbonic acid gas exhaled from the lungs, when he found that a blown bladder was heavier than an empty one. W^iegleb on the antiquity of gunpowder. ■ Nich. VI. 71. Hints towards a steam engine in 1637. Nich. VII. 311.Brunau. Particular Dates. A. D. The Chinese canal 806 miles long, fi- nished by 30 000 men in 43 years 980 The first canal in England, from the Trent to the Witham ] 134 Windmills invented 1299 Canhons invented 1330 Gunpowder used according to Lan- glais 1338 864 CATALOGUE. — ACUSTICS, PROPAGATION OF SOUND. Battle of Cressy 1346 Gunpowder used at Lyons in Brabant. Wiegleb 1356 Muskets used at the siege of Arras 1414 Shipping improved, and port holes in- vented by Decliarges 1500 Air guns made at Nuremberg 1560 Bombs invented at Venloo 1588 New River brought to London I6l4 Guericke invented the air pump 1654 Hooke finished his air pump 1658 Savery had erected steam engines I696 Chain shot invented by Dewit I666 Balloons invented by Monigolfier 1783 Lunardi ascended in Moorfields 1784 The Society for the encouragement of arts still offer pre- miums to the inventors of new hydraulic machines for irri- gation and other purposes, as well as for the improvement of ventilators. ACUSTICS. «OBND IN GENERAL. •Aristotle. Bacon Sylva sylvarum. Contains many experiments. *Mersenne Haimonie universelle. f. Paris, 1636. M.B. Mersenni cogitala physicomathematica. 4. Par. 1644. M. B. •Galilei Discorsi mathematichi. 16.98. Acustics. Ph. tr. Abr. I. v. 457. IV. iv. 346. X. iv. 160. Bartolide] sono. I68O. M. B. Bishop of Ferns on sound. Ph. tr. 1684. XIV". 471. Perraulton sound. A. P. I. 145. Carre on the production of sound. A. P. 1704. H. 88. Lahire's experiments on sound. A. P. 1716. 26e, 264. H. 66. On numbering the vibrations of sound. C. Bon. L 180. From the sound of a wheel with teeth, striking the air only. Haller Elementa physiologiae. V. *Lagrange on sound. M. Taur. I. II, i^nVz vomschalle. 4. Berl. 1764. Euler. A. Berl. 1765. Burdach de vi aeris in sono. 4. Leipz. 1767. Halts Doctrina sonorum. 4. Lond. 1778. Funicim de sono et tono. 4. Leipz. 1779. Germ, in Leipz. Mag. 178 1. Jones's physiological disquisitions. 4. Lond. 1781. M Young on sounds and musical strings. 8. Dubl. 1784. Busse kleine beytr'age zur math, und phys, 131. *Chladni Entdeckungen Uberdie theorie de« plauges. 4. Leipz. 1787. R. I. Chladni. Berl. naturf fr. Chladni promises a general work on acustics. Hind. Arch. IH. 234. fPerrolle on the vibrations of sounding bo- dies. Roz. XXXV. 423. *Forktl Allgemeine literatur der musik. 8. Leipz. 1792. Suremain Missery theorie acousticomusicale. 8. Par. 1793. Extr. by Lalande. Roz. XLII. I6I. *Robison. Enc. Br. Art. Sound. Trumpet. Suppl. Art. Temperament Trumpet. T. Young on sound and light. Ph. tr. 1800. 106. Nich. V. 72. I6I. Terzi del suno. 8. R. S. Propagation of Sound. See Longitudinal Vibrations. Papin's whistle fitted to the mouth of the tube of an air pump. Birch. IV. 379. To show the effect of the air on the force of sound. Walker on the velocity of sound. Ph. tr. I698. XX. 433. CATALOGUE. ACUSTICS, PROPAGATION OF SOUKD. 265 Observed the time occupied in the return of an echo. Found the velocity from 1 1 50 to 1526 feet in a second. Hawksbee on sound in condensed and rare- fied air. Ph. tr. 1705. XXIV. I902. 1709. XXVI. 367. A bell was heard at the distance of 30 yards when the air was in its common state, at 60 with the force of two at- mospheres, at 90 with the force of three : beyond tliis the intensity did not much increase. A vacuum was made be- tween two receivers, the bell being within the innermost, and the sound was not transmitted. Hawksbee on the propagation of sound through water, Ph.tr. 1709- XXVI. S71. *Derhain de soni motu. Ph. tr. 1708. XXVI. 2. Velocities observed by different persons. Roberts. Ph.tr. n. 209 I'JOO Boyle. Essay on motion 1200 , Walker. Ph.tr. 1338 Mersennus, Balistica 1474 Flamsteed and Hallcy 1142 Florentine academicians 1148 Cassini and others, Duhamel. H. A. 1 172 Derham 1142 Derham found the effect of the wind, but not of any changes of weather. Mairan. A. P. 1737. II. 1. Cassini on the propagation of sound. A. P. 1738. 128. H. 1. Makes the velocity 1 107 feet. Cassini. A. P. 1739. .Biancoiii delLa diversa velocita del suono. Venice. Bianconi on the velocity of sound. C. Bon. II. i. 3G5. In summer, the thermometer being at 20°, 76 vibrations of the pendulum elapsed while a sound passed over )3 miles; in winter 79 seconds, the thermometer being at — 1.2°. In a cloud or mist 155" elapsed while the sound passed and repassed. Hence the air should expand ^ for 21.2°, or ^^ for \° of the thermometer employed, probably Reaumur's, which is j^ for l°of Fahrenheit. The mean difference of the temperature of the air was probably somewhat less than is sup)X)sed, perhaps 17° or 1S°. VOL. n. Zanotti on the intensity of sound in air of different densities. C. Bon. II. Coll. Ac. X. fEulcr on the propagation of pulses. N. C. Petr. I. 67. jE)(/( ri conjectura physica circa propagatio- neni soni et luminis. 4. Berl. 175O. Opusc. Euler on the propagation of sound. A. Berl. 17.0 9. Euler on the propagation of agitations. M. Taur. II. ii. 1. Euler on the generation and propagation of sound. A. Berl. 1765. 33.5. n7«A/erTentamina circa soni celeritatem. 4. Leipz. 17(33. Lagrange. M. Taur. I. II. fLamberton the velocity of sound. A. Berl. 1768. 70. 1772. 103. Hoz. XVIII. 126. Thinks that the air contains about i of foreign matter. Blagden. Ph. tr. 1784. 201. Observes, that many witnesses agreed that they heard the whizzing of a very distant meteor at the instant of its ap- pearance ; but that this was probably a fallacy. PerrolJcon the propagation of sound in gases. M. Tur. 1786. Ul. Coir. 1. 1790. V. Corr. 195. Roz, XXIII. 378. Journ. Phys. XLIX. 382. Nich. I. 411. Gilb. III. 167. IV. 112. Founl it very weak in hydrogen gas. W^unsch on tiie velocity of sound in wood. A. Berl. Dciitsch. abii. 17S8. 87. Sound was conveyed instantaneously through 3fi con- nected laths of 24 feet each, or8S4 feet, if not through 7?. which was the whole number employed. Robison. Enc. Br. XVllI. Art, Trumpet arti- culate. Alleges many facts in favour of the nondivergence of sound and waves. He observes, that "all the general co- rollaries respecting the. lateral divergence of waves are little more than sagacious guesses." fLamarck on the medium of sound. Journ. Phys. XLIX. 397. Thinks it a medium more subtile 'ban air. M m t66 CATALOGUE. — ACU8TICS, SOURCES OF SOUND. ♦Chladni on the propagation of sound. Gilb. III. 159, 177, 182, 184. Its velocity in different mediums. Chladni infers from the longitudinal vibrations of different substances, a velocity of 7800 feet in a second in tin, OSOO in silver, 12500 in copper, 17500 in glass and iron, 1 lOOO to 18000 in wood, and loooo to 12000 in tobacco pipes. His observations are fully confirmed by calculations from different grounds. According to the elasticity of fir, as inferred from an experiment of Mr. Leslie, the velocity of an impulse should be 17300. The velocity may be easily calculated from the sound of a loose rod ; if the number of vibrations of the gravest sound in a second be n, the velocity will be .973 — , I being the length, and d the depth in feet. d From an experiment of this kind, I find the velocity 1 7700 in crown glass, and 11 800 in brass. Von Arnim on the propagation of sound. Gilb. III. 1G7. IV. 112. Gough. Manch. M. V. fias. Observes, that sound does not diverge equally. Englefield and Young on the effect of sound on the barometer. Journ. R. f ., I. Repert. ii. I. HI. Nich. 8. II. 181. Gilb. XIV. 214. Biot on the effect of heat in thepropagalion of sound. B.Soc.Phil. n. 63. Journ. Phys. LV. 173. It will appear under the article Capacity for Heat, that some of Dalton's experiments agree more nearly with Biot's calculations than his own conclusions from others warrant- ed us to suppose. See Journ. R. I., L At first sight, it might be imagined, that a loud sound ought to be more accelerated by heat than a weak one ; but, on a more accurate examination, we shall find that the law of isochronism of small vibrations will remain un- impaired. Parseval on the propagation of sound in all directions. To be printed, S. E. Ca»sini makes the velocity of sound 110? feet, Meyer JIGS, Miiller 1109, Pictet about 1130. See Vibrations of Fluids. Sound conveyed by pipes. See Hearing. Decay of Sound. The human voice has been heard more than ten miles at Gibraltar. Derham. Echos. On an echo in Gloucester cathedral. Birch. I. 120. Quesnet on an echo. A. P. II. 87- X. 127. Grandi de sono. Ph. tr. 1709- XXVI. 270. Echo from two towers. A. P. 1710. H. 18. Southwell on echos. Ph. tr. 1746. XLIV. 219. A building vrith projecting wings produced 60 repeti- tions. Euler on echos. A. Berl. 1765. 335. Guynet on an echo repeating 14 syllables. A. P. 1770. H. 23. Actis on an echo at Girgenti. M. Tur. 1788. IV. App. 43. From the parabolic form of a church. An echo in Woodstock park repeats 17 syllables by day, and 20 by night. An echo on the north side of Shipley church in Sussex repeats 21 syllables. Cavallo, &om Plot and Harris. Sources of Sound. Vibrations of Fluids. Mariotte on the sounds of the trumpet. A. P. I. 209. Bernoulli on organ pipes. A. P. I762. 431. H. 170. E.xtr. Hauy Traite de Phys. I. 3l6. Euler on the motion of air in pipes. N. C. Petr. XVI. 281. Equal and unequal, hyperbolical and conical. All shut pipes are unmusical, except cylindrical ones. On the sounds of gases. Nich. III. 43. Chladni on the tones of an organ pipe in different gases. Ph. M. IV. 275. CATAtOGiJE.— ACUSTies, SOURCES OF SOUND. 267 The sound of carbonic acid gas, nitrous gas, and oxygen gas, agreed with the theory ; but azote, of which the spe- cific gra»ity was .Q85, common air being unity, gave a note half a tone lower than common air. Hydrogen gas pro- duced a note an octave or a minor tenth higher. Delarive on the sounds from hydrogen o-as. Journ. Phys. LV. l65. Nich. 8. IV. 23. Ph. M. XIV. 24. Higgins on the sound from hydroj^en gas. Nich. 8. I. 129. A harmonica. Gilb. XVIJ. 482. A glass tube sounding while hot. The air in a flute is like a slow river with waves moving npidly along it. Account o/M. Delarive's Memoir on the Sounds produced by Imrning Hydrogen Gas. Journ. R. I., I. sag. It is well known, that when a stream of hydrogen gas passes through a small tube, and is inflamed at its orifice, if a large tube be held over the flame so as partially to in- close it, an agreeable sound is frequently produced. The frequent failure of the experiment, and the impossibility of producing the same effect with other kinds of flame, left considerable obscurity with respect to the immediate cause of the sound. M. Delarive appears to have been very successful in his attempts to remove these difficulties. He supposes the continual production and condensation of aqueous vapour to cause a brisk vibratory motion, which must be able, in order to produce a sound, to harmonize with the dimensions of the tube, and is then regulated and equalised by the regular reflections from the tube, so as to constitute together a clear musical sound : he observes that for this purpose there must be a great difference of tempe- rature in the air and the tube near the flame ; hence the failure of the vapour of ether, which produces too slight a degree of heat, and the difficulty of succeeding in a warm room, for want of a sufficient supply of cool air. This ex- planation is confirmed by a curious experiment on tubes with bulbs resembling that of a thermometer, in which a small particle of water or mercury is exposed to a conside- rable heat, so as to be wholly converted into vapour, while the upper part of the tube remains cool ; in this case a sound is produced somewhat similar to that of hydrogen gas, but much fainter. Brugnatdli has obtained a sound from Idiosphorus burnt in a tube ; and M. Delarive supposes that the phosphorous acid, in the form of a vapour, pos- sesses a high degree of elasticity, and that it is condensed with sufficient rapidity for the production of the sonorous effects. Y. Vibrations of Solids. Chords. Lahire on the trumpet Marigni, A. P, IX. 530. Taylor de motu nervi tensi. Ph. tr. 1713 XXVIII. 26. Sauveur on the sounds of chords. A P. 1713. 324. H. 68. Jo. Bernoulli on vibratins: chords. C Petr III. 13. D. Bernoulli on the curvature of an extended chord. C. Petr. III. 62. D. Bernoulli on vibrating chords. A. Bierl. 1753. 147, 173. Bernoulli on the vibrations of unequal chords. A. Berl. 1765. 28 J. Some may be harmonious though unequal ; others in- harmonious. Bernoulli on the vibrations of compound chords. N. C. Petr. XVI. 257. Euler on the vibrations of flexible and rigid bodies. C. Petr. VII. pg. Euler on the oscillations of flexible bodies. C. Petr. XIII. 124. XIV. 182. On the motion of flexible bodies. A. Berl 1745.11.54. Euler on the vibration of chords. A. Berl 1748.69. Euler's remarks on Bernoulli. A. Berl 1753 196. Euler on the vibrations of a loaded thread N. C. Petr. IX. 215. Euler on the vibrations of unequal chords N. C. Petr. IX. 246. Euler on the propagation of agitations. M. Taur. II. ii. 1 . Euler on the agitations of chords. A. Berl. 1765.307,^335. Euler on equal and unequal chords. M. Taur. III. ii. 1, 27. 268 CATALOGUE. — ACUS TICS, SOURCES OF SOUND. Eulcr on the equilibrium and motion of flex- ible and elastic bodies. N. C. Petr. XV. 381.XX.28G. Euier on unequal vibrating chords. N. C. Petr. XVII. 381. A. Petr. 1780. IV. ii. 99. EuIer finds, that a chSrd composed of two parts, of which the length is reciprocally as the thickness, will sound like a single one. A chord composed of two parts equal in length, one four times as heavy as the other will produce sounds related as .30)08 .69501, 1.30408, 1.60501,2.30408, and will therefore be very discordant. Euler on the vibrations and revolutions of extended musical chords. N. C. Petr. XIX. 340. XX. 304. A.Petr. Ill.ii. 116. 1782. VI. ii. 148. Observes, that the revolutions may be reduced to com- pound vibrations. Euler on the perturbation of the motion of a chord from its weight. A. Petr. 1781.V. i. 178. When the chord is horizontal the perturbation vanishes. Dalembert on the curve of a vibrating chord. A. Berl. 1747.214, 220. 1750.355. Dalembert's remarks on vibrating chords. A. Berl. 1763. 235. M. Taur. III. ii. 389. Kiccati on elastic force. C. Bon. I. 523. M.Young on sounds and musical strings. J. Bernoulli on the problem of vibrating chords. Hind. Arch. III. 266. Montucla and Lalande. III. 659. Voigt on the nodes of chords. Ph. M. IV. 347. Surfaces. Euler on the vibrations of drums. N. C. Petr. X. 243. Riccati on the vibrations of drums. Ac. Pad. 1.419. Biot on the vibrations of surfaces. M. Inst. IV. 21. Extr. B. Soc. Phil. n. 43. Says, that the time of vibration depends on the initial fi- gure. This doe« not however appear to agree with expe- riment. Vibrations from Elasticity. Lateral Vibrations. Birch. II. 475. Hooke explained the vibrations of a glass bell by putting fiouron it, which moved differently, according to the differ- ence of the sounds. Blondel on the sound of a glass full of wa- ter. A. P. I. 209. Carre on the sounds of cj'linders. A. P. 1709. 47. H. 93. -j-Lahire on the extinction of sounds at the ends of a cylinder. A. P. 1709. H. 96 Bernoulli on the curvature of an elastic rod. C. Petr. III. 62. Bernoulli on the vibrations of plates. C.Petr. XIII. 105, 167. The sounds are related as 1, 6.32. 17.63, 34.54, 57. 1, 86.3. The length of a pendulum vibrating with equal fre- quency is to the linear deflection by a given weight at the end of a rod fixed at the extremity, as 12 times the weight of the rod to 49 times the deflecting weight ; thus a knitting needle weighing 15.5 grains was deflected by a weight of 1000 grains -^^L. of the length of the second pendulum : hence the length of the synchronous pendulum is .1025, and it makes 175 or 178 vibrations in a second, the note being G, as it was found. The length was -j^'i ; half the length gave the double octave, the time of vibration be- ing always as the square of the length. At the standard concert pitch the note would be nearly F. Bernoulli. N. C. Petr. XV. 361. Euler on the vibrations of rigid bodies. C. Petr. VH. 99. Euler on bells. N. C. Petr. X. 26. Makes the sounds as l , ^/o, v'20, \/50; considering the bell as composed of rjpgs. Euler on the vibrations of plates. N. C. Petr. XVII. 449. ' The progression of sounds as 1.192, 6.9977» I9.638a. Euler on the vibrations of plates. A. Petr. III. i. 103. The sounds of rings are as the squares of the natural numbers. CATALOGUE. ACUSTICS, EFFECTS OF SOUXD. &69 Riccati on elastic force. C. Bon. I. 523. •Kiccati on ihe sounds of cylinders. Soc. Ital. I. 444. With many experiments, and tables for forming the scale. Corrects some material errors of Euler. Lexell on the vibrations of rings. A. Petr. 1781. V.ii. 18.3. Lambert on the sounds of elastic bodies. N. Act. Helv. I. 42. With experiments. Makes the series 1, 0.267,17.54?, 34.38. An approximation only. *Chladni Entdeckungen liber die theorie des klangcs. Finds the vibrations generally agreeing with theory ; that is, nearly as the squares of the odd numbers in most cases ; in one, as the squares of the natural numbers. The sounds of rings do not agree with either of Euler's supposi- tions, but are nearly as the squares of the odd numbers. Acccount of Cliiadni's figures. Journ. Pliys. XLVII. (IV.) 390. Ph. M. II. ,'315, 3yi. Jo. Bernoulli on the vibrations of rectangular plates. N. A. Petr. 1787. V. 19.7. Compared with Chladni's experiments. PerroUe. M. Tiir. 1790. 1. App. 209. Voigt on Chladni's figures. Ph. M. HI. 389. Parseval on the complete integration of the formulae for the vibrations of plates. To be printed in the Mem., des sav.etr. of the Institute. See page 84. Longitudinal Vibrations. ChlaSni liber die longitudinal schwebungen der stabe. 4. From the transactions of the society at Erfurt. On Chladni's longitudinal sound. Ph. M. IV. Spiral Vibrations. Chladni on spiral vibrations. Gilb. II. 87. Ph. M. XII. 259. From the memoirs of the Naturf. Fr. These vibrations »re found to be a fifth lower than the longitudinal vibrations. Effects of Sound. Remarks on the Effect of Sound upon the Ba> omeler. By Sir Henby C. Englefield, Bart. F. R.S. Journ. R. I., I. 157. During the time I spent at Brussels in the years 1773 and 1774, it occurred to me, that the effect of sound on the barometer had not, to my knowledge, been attended to ; and that it was by no means certain, whether that in- strument was capable of being sensibly affected by those elastic vibrations caused in the atmosphere, by the percus- sion of a sonorous body. I thought the idea worthy of be- ing pursued, and the means of making satisfactory experi- ments were most opportunely in my power. The sound of a very large bell appeared to me the most powerful, and, at the same time, to be approached with the greatest security and ease to the observer. The explosion of artillery, besides the very disagreeable smoke and danger ofthe recoil, might be objected to, on account of the sud- den production of elastic and heated vapour, which might,, independent of the sound, instantaneously alter the state of the atmosphere, and thereby lead the observer into very great and unavoidable errors. Every one who has been in the Low Countries must know, that very large bells, and immense numbers of them, are the pride of theh: churches, and that they are rung quite out, not tolled, on every great festival. The great bell of the collegiate church of St. Gudula, at Bru.ssels, weighs, as I was told, sixteen thousand pounds, and on this I deter- mined to found my experiment. Two objections only could be made to the result of this trial, the one, that the motion of the bell might cause a vi- bration in the \\'alls of the building, v.hich would hinder the placing the barometer in a state of repose ; the other, that the swinging so large a mass with a considerable de- gree of velocity, might of itself agitate the air so as to cause vibrations in the mercury, totally independent of sound. The strength of the walls of the steeple, and manner of hanging the bell, which was contained in a frame of timber, founded on a strong vault, and totally independent of the walls of the steeple, might alone have answered the first of. these objections, but happily a most complete and satisfac- tory answer to both of them was furnished by the manner in which the bell was rung. As the bell was to ting out full in an instant, at a signal given from below ; it is necessary to have it in motion some time beforehand ; and during that time, the clapper is fixed to one side by a strong stick crossmg the mouth of the bell, which, at the signal, is pulled out by the hand of a person placed for that purpose. If, then, our barometer showed: ^70 C'ATAEOGUE. — ACUSTICS, EFFECTS' OP SOtTNlX no variation during tvU this time-; wo were* absolutely cer- tain, that whatever motion wa» perceived afterwards, was wholly owing to the sound. Mr. Pigott, who was then at Brussels, was kind enough to lend me one of his barometers, made by Ramsden, and his son made the following observations jointly with myself. At two o'clock in the afternoon of the first of November, 1773, we went into the northwest tower of St. Gudula's church, and having fixed the barometer firmly in the open- ing of a window, not above seven feet from the bottom of the bell, we waited quiedy for its ringing. The height of the mercury before the bell began to swing, as observed by Mr. Pigott, was 29.478 inches. The bell being iri^fuU swing no alteration whatever was perceptible. The instant that the clapper was loosed, the mercury leaped up, and continued that sort of springing motion at every stroke of the clapper, during the whole time of the ringing of the bell. These were our observations. During the ringing of the bell, Mr. P. 29.409 During the ringing, by myself Highest 29.480 Lowest 29.474 Highest 29.482 Lowest 29.472 These observations were made with the greatest atten- tion ; and considering their delicacy and the difBculty of observing, agree very nearly. They appear to give from 6 to 10 thousandths of an inch for the effect of this sound on the barometer. It is to be observed, that Mr. Pigott in general, estimated the height of the mercury about five thousandths lower than myself, which brings our observa- tions to a very near agreement. The following observations prove this. On the top of the tower, Mr. P. 29.424 Ditto, by me 29.430 At the foot of the tower, Mr. P. 29.639 Ditto, by me 29.642 In the court of the English Nuns, by Mr. Pigott 29.676 Ditto, by me 29.682 And I should think, that the difference of eyes may fre- quently cause Euch a variation among different observers; at least, in delicate observations, it will be always prudent to make the experiment. Note ly Dr. Young. These observations appear to agree too well with each other, to allow us to doubt of their accuracy. It therefore becomes necessary to inquire after the cause of the differ- ent heights of the barometer. It is indeed barely possible, that a sudden stroke of the clapper of the bell might pro- duce a greater agitation of the buiMiof^ than the preceding alternate motion of the bell itself: but this explanation cannot be called satisfactory. It is certain, that there was neither more nor less air in the tower while the bell waj sounding, than while it was silent ; the mean density of the air could therefore not have been changed ; and if the al- ternate motions of the particles of air which constitute sound, had ttken place by equal degrees and with equal velocities in each opposite direction, there is no reason to suppose that the increase of pressure on the surface of the mercury, at one instant, could have tended to raise it, more than the decrease of pressure, in the opposite state of the undulation, would have depressed it. But the same conse- quence does not follow, if we conceive the motion of the air in advancing to be more rapid, but of shorter continu- ance, than its retrograde motion. For if the wind blew for one hour with a velocity of four, and the same air returned in the course of two hours with a velocity of two, an ob- stacle upon which it had acted in both directions, would not be found in its original place ; for the action of the wind upon anobstacle, is as the square of the velocity, and the time would not compensate for the difference of force. It is therefore easy to suppose, that the law of the bell's vi- bration was in this experiment such, that the air advanced towards the barometer wiih a greater velocity than it re- ceded, although for a shorter time, and that hence the whole effect was the same as if the mean pressure of the air had been increased. Such a law might easily result from a combination of a more regular principal vibration with one or more subordinate ones, in different relations ; and simi- lar cases may sometimes be observed in the vibration* of chords. * Sympathetic Sounds. Morhofii stentor hyaloclastes, de scypho vitreo fracto. Kiel, 1662. 1683. Wallis on the paitial sympathetic tremors of chords. Ph. tr. 1677. XII. 839. Shown by bits of paper laid on the chords. Lahire ou a buttress at Rheims that vi- brates when one of the bells is rung. A. P. II. 87. Probably from being capable of vibrations equally fre- quent with the swinging of the bell. *Ellicotton the mutual influenceof twoclocks. Ph. tr. 1739- 126. A curious instance of sympathetic vibration ; the motion of one of the clocks put the pendulum of the other in mo- CATALOGUE. ACUSTICS, EFFECTS OF SOUND. 271 «ion, even yrhen they stood on a stone pavement near each other : the effects were accelerated when the communication was more direct. See Timekeepers. *Hiulcllestone's observations on sound. Nich. 8. 1. 329. Showing the sympathy of chords and even of organ pipes, materially influencing the frequency of each others vibra- tions. Ear and Hearing. Instruments for Hearing. Perrault on the organ of hearing. A. P. I. 158. Duverney on hearing. A. P. I. 256. Duvtrnejf de I'ouie. 12. M. B. Valsalva de aure. 4. Bologn. 1704. M. B. Acc.byDouglas.Ph.tr. 1705. XXIV. 1978. Duquet's hearing trumpet. Much. A. II. 119. Duquet's chair for the deaf. Mach. A. II. 129. £lair on the organ of hearing in elephants. Ph. tr. 1718. XXX. 885. Mai ran on the ett'ect of sound on the ear. A. P. 1737.49. H.97. Leprotti on the perforation of the membrana tympani. Coil. Acad. X. 518. On a perforated membrana tympani. C. Bon. I. 350. The hearittg unimpaired. Rivinus called it his foramen. Martiani's model of the ear. A. P. 1743. H. 85. NoUet on the hearing of fishes. A. P. 1743. 199. Brocklesby's extract from Klein on the hear- ing of fishes. Ph. tr. 1748. 233. Arderon on the hearing of fish. Ph.tr. 1748. 149. Thinks that river fish have no hearing : observes, that sound is transmitted but faintly through water. A hand grenade bursting under Water produced prodigious tremors. Geoffroy on the hearing of reptile*. S. E. II. 164. Haller. Physiol. V. Camper on the hearing of fishes. S. E. VI. 177. Elliot on vision and hearing. 8. Vicq D'Azyr on the ear of birds. A. P. 1778. 381. H.5. Hunter on the organ of hearing in fish. Ph. tr. 1782.379. Shows that they hear. Galvani on the ear of birds. C. Bon. VI. O^ 420. *Scarpa de auditu et olfactu. f. Pav. 1789- Comparetti de aure interna. 4. Pad. 1789- R. S. Extr. Roz. XLII. 344. Brunelli on the hearing of reptiles. C. Boo. VII. O. 301. Lentin on deafness. Commentat. Gott. 17^1. XI. Ph. 39. Caldani suUa m«mbrana del timpano. 8. Pad». 1794. R. S. Home on the membrana tympani. Ph. 4r. 1800. 1. Nich. V, 93. Cooper on the destruction of the membrana tympani. Ph. tr. 1800. 151. Nich. 8. I. 102. Cooper on an operation for deafness. Ph. tr. 1801. 435. On hearing by the teeth. B. Soc. Phil. n.41. Nich. IV. 383. Beaumont's hearing instrument approved^. M. Inst. IV. Gilb. X. 567. The deaf sometimes hear acute sounds. Gough on the method of judging of the po- sition of sonorous bodies. Manch. M. V.. Thinks the bones of the head assist us in forming the judg- ment. A sound just audible at 240 feet was distinguished, as being nearer at 40 feet than at 42. A horizontal angu^ lar difference of 8° was perceptible, an elevation of 10°. On the invisible girl. Nich. 8. IIL 56.. 272 CATALOGUE. ACUSTICS, THEORY OF MUSIC. Sound conveyed by pipes, which open in a crevice of the moulding of a frame. li. Walker's apparatus for conducting sound. Nieh. 8. IV. 69. Gilb. XIV. 220. Vieth's acustic observation. Gilb. XVII. II7. Asserts, that there is a point precisely in the axis of hear- ing w^here the sound is not audible. Darwin's zoonomia. II. 487. " The late blind Justice Fielding walked for the first time into my room, when he once visited me, and after speaking a few words said, this room is about 22 feet long, 18 wide, and 12 high ; all which he guessed by the ear with great accuracy." Darwin. Theory of Music. Musicae antiquae scriptores, Meiboinii. 4. Amst. i632. R. f. •CI. Ptolemaei harmonica a Wallis. 4. Oxf. 1682. Op. III. Zarlmo Istitutioni harmoniche. f. Ven. 1558. 1573. M. B. Salinas de musica. f. Salamanc. 1577. M.B. *Merstnm harmonica, f. Par. 1635. *Merserine Harmonie universelle. f. Paris, 1636. *Kircheri musurgia. 2 v. f. Rom. 1660. M. B. * XtVcAen phonurgia. f. I673. M.B. Cartesn musicae compendium. Utr. 1650. M. B. Dechales mundus mathemAticus. Ph. tr. abr. I. x. 606. IV. vii. 469. Memoli Musica speculativa. 4. Bologna, 1670. Ace. Ph. tr. 1673. VIII. 6194. ' -.Sa//720« on music. 8. London, 1672. M.B. Ace. Ph. tr. 1671. VI. 3095. Wallis on the'division of the monoehord. Pii. tr. 1698. XX. 80. Wallis on the imperfections of the organ. Ph. tr. 1698. XX. 249. Wallis's Works, vol. D. f. Oxford, IG99. Ace. Pb. tr. 1699. XXI. 259. Sauveur's general system of intervals. A. P. 1701. 299. H. 121. Sauvcur on the organ. A. P. 1702. ■j-Salmon's music reduced to proportions. Ph. tr. 1705. XXIV. 2069. Henfling's musical system. M. Berl. I. 265. Jlfa/co/m on music. 8. Edinb. 1721. R. I. RameauTxMX.^ de I'harmonie. 4. Par. 1722. M. B. i?a»jf«?« systeme de musique. 4. Par. 1726. liameau du principe d'harmonic. Ace. A. P. 1750. H. 160. Rameau on the principles of music. Mem. Trev. Aug. I762. Rameau's other musical works. See Forkel. fEukr tcntamen novae theoriae musicae 4. Petersb. 1729. M. B. Euler on some discords, and on the charac- ter of modern music. A. Berl. 1764. l65, 175. Euler on the true principles of harmony. N. C. Petr. XVIII. 330. Euler's speculum musicum. F COD A E B r» C* G« D« Bb. Montvallon on musical intervals. A. P. 1742. H. 117. On numbering vibnitions. C. Bon. I. 180. By the teeth of a wheel striking the air only. Smit/is hannouies. 8. Cambr. 1749. 1759. R.I. Esthie gurrharmonie. Ace. A. P. 1750. H. l65. Est^ve on tlie best system of music, and on temperament. S. E. II. 113. Romieu on grave harmonics. Ac. Montpel. 1751. Romieu on tempered sj'stoms ofmusic. A. P. i 1758.483. Agrees nearly with the progressive temperament CATALOGUE. — ACU5TICS, THIOKY OF MUSIC. 273 Avison on musical expression. 12. 1752. Dolimbert Elemens tie musique. 8. Paris, 1752. fTartiiii delta vera scienza dell' armonia. 4. Pad. 1754. M.B. RoHsseau Dictionnaire de musique, Rousseau's musical dictionary. Marpurg Anfangsgrlinde der •theoretischen musik. 4. Leipz. 1757. On ratios and temperaments. Marpurgs versuch iiber die temperatur. 8. Bresi. 1776. Jamard sur la theorie de la musique. 8. Par. 1768. Emerson's miscellanies. 353. *Hulden on a rational system of music. 4. Lond. 1770. M. B. *Kirnberger Kunst des reinen satzes. 4. Berl. 1771 ... Sulzers tlieorie der schonen kiinste. 4 v. 8. Leipz. 1772. Laniheit on musical temperament. A. Berl. 1774. 55. Harrison on clockwork and on music. 8. 1775. n.s. Geduitken iiber Kirnbergers temperatur. 8. Berl. 1775. Vandermonde Systeme d'harmonie. 8. R. S. Ace. A. P. 1778. H. 51. Bemetzrieder Essai sur I'harmonie. 8. R. S. Bemetzrieder Methode de musique. 8. R, S. Bemetzrieder Trait6 de musique. 8. R. S. 5^ee/e's prosodia rationalis. 4. Lond. 1779. Good theory, but inaccurate declamation. Essay on tune. 8. Edinb. 1782. M. B. Jones's treatise on music, f. E. M. Musique, i vol to Cyt. by Framery and Ginguene. Barca on anew theory of music. A. Pad. L 365. IL329. IV. 71. Cavalloon temperament. Ph. tr. 1788. 238. VOL. II. ' Recommends the equal temperament. , Sacchi's theory of music. C. Bon. VIL O, 139. *Forkel Allgemeine litteratur der musik. 8. Leipz. 1792, Jones on the musical modes of the Hindoos. As. Res. in. 55. Suremain Missery Theorie acousticomusi- cale. Patterson's notation of music. Am. tr. III. 139. Young. Ph. tr. 1800. Additional remarks. Nich. V. 141. Young on compound sounds, in answer to Gough. Kich. 8. II. 264, HI. 145. IV. 72. Young's harmonic sliders. Journ. R. I. Nich. 8. IV. 101. Robison. Enc. Br. Suppl. Art. Temperament> Trumpet. Enc. Br. Suppl. II. 650. "The perception of harmonious^ound is the sensation pro- duced by another definite form of the agitation. This is the composition of two other agitations ; lul it is the com- pount agitation only that affects the ear, and it is its form or kind which determines the sensation, making it pleasant or unpleasant." Robison. Chladnion finding the velocity of vibrations. Gilb. V. 1. Proposes to number the vibrations of a long rod, and to observe the sound of a portion of it. Suggests Sauveur's last pitch as a new idea. Gough on the theory of compound sounds. Manch. M. V. 653. Nich. 8. IV. 152, Defends Smith against Dr. Young, but misunderstands both. Gough on compound sounds and grave har- monics, in reply. Nich. 8. III. 39. IV. 1, 139. Mrs. M. Young's patent for teaching music. Repert. XVI. 9. N n ■27* CATALOGUE. ^-ACUSTICS, MUSICAL INSTR.UME N Musical Instrumtnts. Mersenne Harnionie univeiselle. Kircheri musurgia ct pbonurgia. Schotti niechanica hydraulicopneumatica. 4. Wurzb. 16.57. Carre on musical instruments. A. P. 1702. H. 136. Miller's harmonic gate. Ac. Sienna. II. 132. E. M. A. IV. Art. Instrumens demusique. Cavallo. N. Pli. JI. 384, The note A was found by experiment to consist of 10? vibrations in a second. The A of the progressive temperament, derived from Sau- veur's pitch, consists of 106^, which agrees within the pos- sible limits of error. Stringed Instruments. Roberts on the trumpet marine. Ph. tr. 1693. XVII. 559. Lahire on the trumpet marine. A. P. IX. 330. Molyneuxou the. ancient Ijre. Ph. tr. 1703. XXIII. 1267. Marius's harpsichords. Mach. A. I. 193. A. P. 1716. H. 77. Mach.A. III. 89. Marius's pianoforte. Mach. A. III. 83, 85, 87. Cuisinier's harpsicliord. Mach. A. II. 155. Cuisinier's harpsichord or vielle. A. P. 1734. H. 105. -f-Maupfertuis on the form of musical instru- ments. A. P. 17'^4. 215. H. 90. Thevenart's sinj^le stringed harpsichord. A. P. 1727. H. 142. A. Mach. A. V. 11. Bellot's harpsichord. A. P. 1732. H. 118. Levoir's harpsichord. A. P. 1742. H. 146. Mach. A. Vn. 183. Domenjoud's head for viohns. A. P. 1756. II. 130. Wehmann's harpsichord. A. P. 1759. H. 241 ." Laborde Clavecin electrique. 12. Par. 1761. A play thing. Legay's keyed instrument with harp strings. A. P. 1762. H. 191. Berger's organized harpsichord. A. P. 1765. H. 138. Vireboy's harpsichord. A. P. 1766. H. I61. Joubert's organized vielle. A. P. 1768. H. 130. Gosset's division of the finger board. A. P. 1769. H. 131. . . ■ ■ Lepine's pianoforte. A. P.'l77'2.'i. H. A pianoforte. E. M. A. VII. Supplement. M. Young on the harp 6f Eolus. Y. on sound. Nich.IlI.310. Bagatella regole per la costruzione de' viohni. Pad. 1786. A prize essay. Hopkinson on quilling a harpsichord. Am. tr. II. 185. Perolle on the resonance of musical instru- ments. M.Tur. 1790. V. Corr. 195. Nich. I. 411. Against Maupertuis. Fowke on the Indian lyre. As. Res. I. 295. Drums. E. M. M. III. Art. Tambour. Riceati. Ac. Pad. I. Elastic Instruments. Franklin's harmonica. A. P. 1773. H. 8i. On the harmonica. Roz. VII. 462. Golovin on the theory of the harmonica. A. Petr. 1781. V.ii. 176. Bells. E. M. A. I. Art. Cloches. Dcudon's harmonica. Roz. XXXIK. 183. Laiande on the weight of bells. Journ. Phys. XLIV.(I.)85. CATALOGUE, — ACUSTICS, SPEECH. 275 Burja on musical instruments of glass. A. Berl. 1796 i-. 3. Cliladiii's euphon. Ph. M, 11. 315, 391. Made of glass cylinders. Cliludni's clavicylinder. Gilb. IV. 494. AVind Instruments.. Roberts on the trumpet. Ph.tr. 1693. XVII. 559. *Sauveur on the composition of organ pipes. A. P. 1702. 308. H.90. Miirius's organ, willi bellows to each pipe. Mach. A. III. 91. Organ. Emerson's mech. f. 313. *Bidos Art du facteur d'orgues. f. Par; 176G . . 1778. Ace. A. P. 1767. H. 180. Meister on the antient hydraulum. iN. C. Gott. 1770. II. 152. With good figures. Steele on nmsical instruments from the South Seas. Ph. tr. 1775. 67. EiisramcUe Tonotechnie. 8. Par. 1775. On hand organs. Lambert on flutes. A. Berl. 1775. 13. Halle Kunst des orgelbaues. 4. Brandenb. 1779. Trumpets. E. M. PI. I. Chaudronnier. PI. 4. Organs. ^E. M. PI. III. Luthi^r. E. M. PI. III. Bagpipes have drones with reed mouth pieces. Pini pantaulo. 8. Milan, 1783. R. S, Fitzgerald's patent signal trumpet. Repert. XI. 100. For conveying the sound of d, pistol. Close on the properties of wincT'instruments. Nich. V. 213. Longman's patent barrel organs. Repert. XIV. 367. For a more steady connexion of the parts. Godfry's patent banel organs with a tabor and pipe. Kepert. XV. 36l. fBeyer on the glass chord. Journ. Phys. XLVIII. 408. On silk strings. Nich. I. 328; Ludicke's micrometer for wires. Gilb. I. 137. Becker's patent harps. Repert. XVI. 146. Making the half notes by a change of tension. Bemetzrieder's patent pianoforte. Repert. ii. in. 324. . Langguth's Eolian harp. Gilb. XV. 305. Robison. Enc. Br. Siippl. Art. Pianoforte, Trum})et. Euler's clavichord produced the twelfth of each string Aat was struck, dividing it into three parts ; and had a very sweet tone. Robison. Voice and SpeecK; Organs of the Human Voice. *Dodart on the human voice. A. P. 1700. 244. H. 17. 1706. 136, 388. 1707. 66. H. 18. *.Perrein on the human voice. A. P. 1741. 409. H. 51. Vieq d' Azyr on the organs of voice. A. P. 1779. 178. H. 5. Speech, //oMd?''* elements of speech. 8. Lond. I669. Ace. Ph. tr. 1669. IV. 958. FbssjMS de poematum cantu. 8. Oxf. 1673. Ace. Ph. tr. 1673. VIII. 6024. Amman de loquela. Lodvvick's universal alphabet. Ph. tr. 1686. XVI. 126. Byrom on Lodwick's universal alphabet. Ph. tr. 1748. XLV. 401. Debrosses Formation mecanique des langiies. Steele on the melody and measure of speech* 4. 1779- K., S. Good theory, but bad declamation. 2176 CATALOGUE. — ACUSTICS, SPEECH. *Kratzenstein Tentaraen coronatum de voce. Kratzenstein on the imitation of the human voice. A. Petr. 1780. IV. ii. H. l6. Made pipes imitating the vowels. *Kratzenstein on the vowels, Roz. XXI. 358. Figures of the different pipes. Gough on the variety of voices. Manch. M. V.58. Deduces the variety of tones from different combinations of imperfect unisons. Goiigh on ventriloquism. Manch. M.V. 650. Mich. 8.TI. 122. V. 247- Attributes the effect to the reflection of sound. Nicholson on ventriloquism. Nich. 8. IV. 202. V. 247. Shows that the effect is in general only a fallacy. Gibbon's life, quoted by Cavallo. N. Ph. I. « A rapid orator pronounces about two English words .in a second." h A Description of Articulate Sounds, with Ap- propriate Characters. Classes of Letters. Class 1. Pure vowels consist of a vocal sound formed in the larynx, not interrupted by the tongue and lips, nor passing in any degree through the nose. Class 2. Nasal vowels consist of a vocal sound, passing without interruption through both the mouth and the nose. Class S. Pure semivowels consist of a vo- cal sound, much impeded in its passage, yet capable of being prolonged, not passing through the nose. Class 4. Nasal semivowels consist of a vo- cal sound, stopped in the mouth, and passing only through the nose. Class S. Mixed semivowels consist of a vocal sound, much impeded in its passage through the mouth, and passing partly through xbe nose. Class 6. Explosive letters consist of a vocal sound, stopped in its passage. Class 7. Susurrant or whispering letters have no vocal sound, but are capable of being continued. Class 8. Mute letters have no vocal sound, and are incapable of being sounded alone or continued. Class 1. Pure vowels." E. The tongue and lips in their most na- tural position, without exertion. A. The tongue drawn backwards, and a little upwards, so as to contract the passage immediately above the larynx. 0. The contraction of the mouth greatest innnediately under the uvula. The lips must be also somewhat contracted. U.^The contraction continued below the whole of the soft palate. 1. The contraction formed by bringing the tongue nearly into contact with the bony pa- late. From these principal vowels all others may be deduced by considering them as partaking more or less of the nature of each, accordingly as they are situated nearer to them in this scheme. O a V Class 2. Nasal vowels. The nasal vowels are derived from the pure vowels by lowering the soft palate so as to CATALOGUE. ACUSTICS, SPEECH. %n suffer the sound to pass in part through the nose : they may be marked by the same characters as denote the pure vowels, with the addition of the grave accent. Class 3. Pure semivowels. L. Tlie point of the tongue is pressed against the palate, the sound escapes laterally. A. The point of the tongue is brought very near to the palate, but the contact is closer a little behind the point, the sound still escaping further back. n. The point and middle of the tongue press against the palate, the sound escaping at the base, but not without difficulty. R. The middle and point of the tongue strike the palate with a vibrating motion, the point being drawn back. r. The point of the tongue is drawn back- ward, and is brought very near to the palate, but without a distinct vibration. V. The lower lip presses on the upper teeth. A. The tongue presses against the upper teeth. r. The middle of the tongue is brought nearly into contact with the palate, the point being a little depressed. Z. The point of the tongue is brought nearly into contact with the upper teeth, the air being forced against the edges of the teeth with violence. J. The air is forced with violence against the teeth, being first confined between the tongue and palate immediately behind the upper teeth. Class 4. Nasal semivowels. M. The passage of the mouth is closed by the lips. N. The passage of the mouth is closed by the point of the tongue. n. The passage of the mouth is closed by the middle of the tongue. Class 5. Mixed semivowels. V. The passage of the mouth is very nearly closed by the approach of the base of the tongue to the soft palate. Class f). Explosive letters. B, D, G. The tongue is placed as in M, N, n, respectively. Class 7. Susurrant letters. H. The breath is forced through the mouth, which is every where a little contracted. F, 0, X, S, 2. Differ from V, A, r, Z, J, respectively, only in the absence of the vocal sound. Class 8. Mutes. P, T, K, are distinguished from B, D, G, by the absence of the sound formed in the larynx. Examples, with the mode of writing the words in these characters. I.E.Theman, eye, a window. E.aE MAN, EI. E UiNDE. Le, repos. Fr. LE, REPO. 2. A. Father. E. FAAEr. 3. a. Ame, femme. Fr. M, FaM. Dank. G. D«nK. 4. n. All, not, joy, owl. E. ilL, NiiT> DJii/, aUL. 5. a. Homme de robe. Fr.aMDERaB 6. O. Old. E. OLD. Eaux. Fr.O. 7. s. Jeu, oeil, Fr. Je, sIa. 8. to. Jeux, noeuds. Fr. Jcu. Nw. 9. u. But, shut. E. BuT,2uT. 10.U.Toofull.E.TUFUL. Vous, Fr. VU. 11. y. Lugen. G. LurEN. 12. T. Une laitue. Fr. tN LETt! In Norfolk and in Devonshire the English U is sometimes pronounced T. 13. I. Ye see. E. d SI. Ici. Fr. ISI. 14. 1. Lip. E. L?P. Mit. G. Mj'T. When ' lip' is lengthened in singing, it does not be- come ' leap.' 2/8 CATALOGUE. ACUSTICS, SPEECH. 15. e^ Hate. E, HeT. Nez, eclat. Fr. Ne, eKLa. ]G. c.^Met, pen. E. McT, PcN. Gl^be. peine, pere. Fr. GLcB, PcN, PcR. 17. 5). Bleme, seize, mes, mets, mais. Fr. BL^IM, SvjZ, M:,, M,,, M,. 18. a. An, camp, tems. Fr. a, Ka, Ta. 19. 6. Mon nom. Fr. Mo N6. 20. \ Unparf'um, iijeun. Fr. s PaRFE,aj£\ 21. u. The Erse term for a calf is ITuE, as pronounced in llossshire. 22. ^. Main, cheniin. M^\ 2EM^\ 23. L. Love. E. LuV. Loi. Fr. LU^ _24. A. Fille. Fr. FlA. Ciglio It. TslAlO. 25. n. Llangollen. W. HANGiineN. 26. R. Rouge. Fr. RUJ. The Scotch and Irish give this sound to the Knglish r. 27. r. Round, under. E. rriUND. uNDEr. 28. V. Vow. E. VnU. Vous. Fr. VU. 29. A. Though. E. aO. The S of the modern Greeks. 30. r. Sagen. G. ZarEN. Gemir. Sp. reMIR. 31. Z. Zeal. E. ZLL. Oser. Fr. Oze. 32. J. Measure, judge. E. McJEr, DJuDJ. Juge. Fr.jTJ. 33. M. Man. E. MAN. Mort. Fr. MaR. 34. N. Nine. E. NEeN. Nonne, Fr. NaN or NaNNE.. 35. n. Thank. E. 0AnK. Denken. G. DcnKEN or DcnKN. 36. V. Regner. Fr. Rcye. 37. B. Bow. E. BO. Beau. Fr. BO. 38. D. Dark. E. DArK.Dame. Fr. DaM. 39. G. Good. E. GUD. Gueux. Fr. Gw. 40. H. Home. E. HOM. Hameau. Fr. H«MO. 41. F. Fall. E. FiiL.Foi. Fr.FUi,. 42. 0. Think. E. OinK. Luz. Sp. LU©. . 43. X. Nach. G. NaX. Ax, ojo. Sp. ax, 0x0. The Scotch give this sound to gh Ire ' night.' 44. S. Sing. E. Sin. Sage. Fr. SAJ. 45. 2. Shun. E. ^uN. Chou. Fr. 2U.- Mucho. .Sp. MUT2O. 46. P. Pump. E. PuMP. Peur. Fr. PgR. 47. T. Tongue. E. Tun. Tout. Fr. TU. 48. K. Call. E. KfiL. Courir. Fr. KURIR. SPECIMEN. HlJcN LaV Lt iJ^MEN STlJPS TE Fau, END FEjNDZ TU LTT AET McN _B2Tre?, iHUilT TSArM KEN SUA Her McLENKnLt ? iHliirT_ArT KEN UEP HEr GiLT Eue? ? Some would read' in the first line TU, and not TE. Teaching the Deqf^ Wallis on teaching the deaf to speak. Ph. tr» 1698. XX. 353. Amman Surdus loquens. Ernaud on the deaf and dumb. S. E. V. 233. Pereire on conversing with the dumb. A. P. 1749. H..183..S. E. V. 500. Pereire's machine for making the deaf speak.. A. P. 1750. H. 169. E. M. A. V. Art. Muets et Sourds. *Fox oculis subjecta, with an account of Braidwood's academy. 8. R. S. Thornton on teaching the dumb to speak. Am. tr. HI. 2G2. Sicard Graramaire pour les sourds muets. Paris. Pectdiarities of Speech. Jussieu on speech without a tongue. A. P. 1718.6. CATALOGUE. — ACUSTICS, HISTORY OF ACUSTICS. 279 . Account of a woman who spoke fluently without a vestige of a tongue. Ph. tr. 174'2. 143. Parsons's account of IM. Cutting, who had lost her tongue. Pir. tr. 1747. 621. Ph. M. IV. 214. Maunoir and Paul observed, that hydrogen gas inspired made their voices shrill. From Prevost's Journal. Per- haps ratlier harsh ftian shrill. Y. Speaking Trumpet, . Kirclier. Moreland on the speaking trumpet. London, 1671. Ace. Ph. tr. 1671. VI. 3056. Conyers's improved speaking trumpet. Ph. tr. 1677. XII. 1027. With an internal tube. J/a<2S2Ms de tubis stentoreis. 4. Leipz. 1719. *Lambert on some acustic instruments. A. Berl. 1763. 87. E. M. PI. V. Marine. PI. XIII. Hassenfratz on speaking trumpets, Ann. Ch. Nich. IX. 233. Considers the effect as similar to that of a trumpet, or of a reed organ pipe, and thinks that reflection is not con- cerned. Voices of different Animals. Duverney on the voice of the fowls. A. P. II. 4. On the organ of voice of the horse, ass, and mule. Coll. Acad. VIII. App. 24. Herissant on the organs of voice in quadrupeds and birds. A. P. 1753. 279. H. 107. Parsons on the windpipes of birds. Ph. tr. 1766. 204. Bariington on singing birds. Ph. tr. 1773. 249. Camper on the organs of speech of the oran outang. Ph. tr. 1779- 139- Observes, after Galen, that it is impossible for these ani mals to speak. But had they intellect sufficient, they might certainly whisper. Vicq d'Azyr on the organs of voice. A. P. 1779. 178. H. 5. Daubenton on the tracheae of birds. A. P. 1781.369. II. 12. Ballanti on the organ of voice in animals. C. Bon. VI. C. 50. Cuvicr on the voice of' birds. B. Soc. Pliil. n. 15. Journ. Phys. I. 426. Latham Trans. Linn. Soc. Instruments subservient to Music. Loulie's sonometer. Mach. A. I. 187, I89. A monochord. Sauveur's echometer. A. P. 1701. 317. H. 121. A tabular instrument. Demotz's mode of writing music. A. P. 1726. H. 73. 0ns en Bray's metrometer. A. P. 1732. 182. For beating time. Creed's proposal for a method of writing vo- luntaries. Ph.tr. 17't7.445. Sulzer's instrument for writing voluntaries. A. Berl. 1771.538. Fig. L'z/gfrs entwurf einer maschine. 4. Brunsw. 1774. For writing voluntaries. Burja Beschreibung eines zeitmessers. 8. Berl. 1790. For measuring time. Weisskens tactmesser, Leipz. 1790. Montu's sonometer. Ph. M. XII. 187. His fori/ of Acustics. Dodart on antient and modern music. A."]*. 1706.388. Pepusch on the genera and species of music among the ancients. Ph.tr. 1 746. 266. Styles on the modes of the antients. Ph. tr. 1760. 695, Burney on an infiint musician. Ph.tr. 1779. 183. , 280 CATALOGUE. — OPTICS IN GENERAL. Crotch, who played " God »ave the King" at the age o^ 2 years and 3 weeks. jBurncy's history of. music. 4 v. 4. R.I. Hawkins's history of mwsic. 5 v. 4. M.B. Dalberg on the music of the Hindoos. Ph. M. II. 105. Forkels Geschichte der musiii. 4. J. Bernoulli on the problem of vibrating chords. Hind. Arch. III. 266. Montucla and Lalande. IV. 644. Guide lived 1025; the present notes were introduced ta34 ; chimes were applied to bells at Alost 1487 ; Frank- lin invented the harmonica 1760. Luckombe. OPTICS IN GENERAL. Heliodorus de opticis. 4. Par. l657. M. B. , Risneri opticae thesaurus, f. Bas. 1585. M.B. Faulhaberi descriptio instrumentorum geo- metriae et opticorum. 4. Frankf. I6IO. De Dominis de radiis visus et lucis. 4. Vea. 1611. M.B. Rliodi OpUqae.S. I6l2. Eskinard's century of optical problems. I6l5. Kircheri ars magna lucis et umbrae, f. Rom. 1646. M. B. Zucchii optica philosophia. 1652. M. B. J. Gregom optica promota. Lond. 1663.M.B. *Grimaldi physicomathesis de lumine. 4. Bo- logna, 1665. M.B. Ace. Ph. tr. I67I. VI. 3068. Ph. tr. abr. I. iii. 128. IV. ii. 173. Vl.ii. 110. VIII. ii. 111. X. ii. 29. *Newton's optics. 4. Lond. 1701. Bouguer Trait6 d'optique. Par. 1729. En- larged. 17^0. M. B. Newtonianismo per le donne. 4. Napl. 1737. By Algarotti. iSffji^A's optics. 4. Cambr. 1738. R. I. Germ. by Kastner. 4. Altenb. 1755. Courtivron Trait^ d'optique. Ace. A. P. 1752. H. 131. Im Caille lecliones opticae. 4. Vienn. 1757. Lthrgebaude der gaxizen optik. Alt. 1757. Emers. cyclomathesis. VI. Misc. 453. * Lambert Pholomeirla. 8. Augsb. I76O. R.I. *Priestley's history and present state of disco- veries relating to vision, light, and colours. 4. London, 1772. R. I. Germ, by Kliigel. 4. Leipz. 1776. Harris's optics. 4. Lond. 1775. R. I. Boscovich opera pertinentia ad opticam et astronomiam. 5 v. 4. Bassano, 1785. R.I. Gothe Beytrage zur optik. 8 Weimar, 1792. Traite d'optique par les el^ves de I'^cole po- lytechnique. 8. Par. Haliy. Phys. II. 144. Theorij of Dioptrics and Catoptrics. Euclidis optica. Gr. L. 4. Par. 1557. Alhazen et Vitellio. f. Bale, 1572. M. B. Kepleri paralipomena ad Viteilionem. 4. Frankf. l604. M. B. Xfp/eri dioptrica. 4. Augsb. I6II. M. B. Descartes dioptrica. Opusc. II. Barrow lectiones opticae. 4. Lond. I669. Hugens and Slusius on the problem of Al- hazen. Ph. tr. 1673. VIII. 6119. 6140. *Hugenii dioptrica. Op. rel. II. Halley on the foci of optical glasses. Ph. tr^ I6y3. XVII. 960. Hartsoeker Essai de dioptrique. 4. Par. I694. * M. B. Gregorii catoptrices et dioptrices elementa. 8. Oxf. 1695. M. B. Ace. Ph. tr. 1696. XIX. 214. Gregory's elementsof catoptrics and dioptrics. 8. 1735. Picard's fragmentsof dioptrics. A.P. VII. 335. Liihire on the caustic of a circle. A. P. IX. 294, 303. L'Hopital on caustics by refraction. A. P. X. 260. Carre's rectification of caustics by reflection. A. P. 1703. 183. H. 69. CATALOG UE. OPTICAL INSTRUMENTS. 281 Carre's abridgement of catoptrics. A. P. 1710. 46. H. 112. Guisnee on the focus of lenses. A. P. 1704. 24. H. 76. RoUe on foci. A. P. 1706.284. Ditton theorema catoptricum universale. Ph. tr. 1705. XXIV. 1810. Krafft on a catoptrical problem. C. Petr. V. 82. Krafft on the caustic of the cycloid. C. Petr. VII. 3. Krafft on the image of a point. C. Petr. XII. 243. Krafft on foci. N. C. Petr. II. 39. Mairan on anaclastics. A. P. 1740. 2. Kaestner on the aberrations of lenses. C. Gott. I. 185. II. 183. Kaestner on Alhazen's problem. N. C. Gott. 1776. VII. 92. Employ! tables of sines and tangents. Klingeiistierna on refraction. Schw. Abh. 1754. 300. Klingenstierna on aberration. Schw. Abh. 1760. 79. *Klingenstierna de aberrationibus luminis in superficiebus sphaericis. Ph. tr. 1760. 944. Klingenstierna de aberrationibus luminis. 4. y*etersb. 1762. Redern on dioptrics. A. Berl. 1759, 1760 1761. Maskelyne's theorem for spherical aberra- tion. Ph.tr. 1761. 17. Euler on the confusion of dioptric glasses. A. Berl. 1761. 1762. Euler on vision through spherical segments. N. C. Petr. XI. 185. Euleri^dioptrice. Petersb. 1771. Ace. A. P. 1765. 555. H. 124. Euler. N. C. Petr. XVIII. Supersedes his dioptrics. Klugel. VOL. II. Lagrange's dioptrical formulae. M. Taur. III. ii. 152. A. Berl. 1778. l62. Boscovich on the improvement of dioptrics. C. Bon. V. i. O. 169. .Boscow'cA Dissertationcs dioptricae. 4. R.S. Meister on the effect of oil swimming on wa- ter. Commentat. Gott. 1781. I. 35. KlUgeh analytischedioptrik. 4. Leipz. 1778. Wales's example of a tentative calculation in Alhazen's problem. Ph. tr. 1781.472. Gr. Fontana on refraction. Soc. Ital. III. 498. Fuss on the caustic of a parabola. N. A. Petr. 1790. VIII. 182. M. Young on Newton's theorem for aberra- tion. Ir. tr. IV. 171. Mallet on the construction of problems con- cerning refraction. Schw. Abh. XII. 238. Biirja on lenses not spherical. A. Berl. 1797. ii. 3. BUrja on the track of hght in a prism. A. Berl. 1798. 3. Halistrbm on refraction. Gilb. III. 235. VI. 431. On the place of the image of a mirror. Nich. VII. 71. Klingenstierna gives for the lens of least aberration a _(r+4— 2rrOd-H2rr+r)e T — 7 — 7~. — :; — ^ — 7~, : — TT> "■ ^nd 0 being the first and h (r + 4 — 2rr)e+(2rr+r)d ° second radii, r the index of refraction, i the focal distance of incident, and t of refracted rays ; this expression, when r=:jand d=<», becomes { when r=:i680, — ,oraplano- convex. See Telescopes. Optical Instruments in general. Lehrgebaiide der ganzen optik. Altona, 1 757, D. de Chaulnes's dioptrical experiments. A. P. 1767. 423. H. 162. Fontana's account of the Grand Duke's ca- binet. Roz. IX. 41. . . E. M. PI. VIII. Amusemens d'optique. o o 282 CATALOGUE. — OPTICAL INSTRUMENTS. Photometers. Bouguer Traite d'optique. B'ougueron the measurement of light. A. P. 1757. 1 H. 145. Celsius on the measure of light. A. P. 1735. H.5. Confirms Bouguet's estimate of the moon's light as 15^ of 'hat of the sun. *Lanibert Photometria. 8. R.I. Nux's mode of determining the magnitude of the stars. A. P. 1762. H. 135. By viewing them through semitransparent substances of diflPerent thicknesses. Priestley's o[)tics, vi. §. 7. Fontaiia on the measurement of light. Soc. Ital. I. in. Count Humford's photometer. Ph. tr. 1794. 67. Rcpert. IV. 255. Leslie's i hotometer. Nich. Ill, 46l, 518. Glib. V. 286. . A thermometer. Measurement of Refractive Powers, Clairaut on the measurement of refrangibility, A. P. 1756.408. Martin's optics. Euler on the examination of refraction by prisms. A. Berl. 1766. 202. Due de Ch;iulnes. A. P. 1767. 423. H. 162. Priestley's optics, v. §. 8. c. 2. Venturi on measuring dispersion. Soc. Ital. III. 268. Rochon Recueil de m6moires sur la meca- nique et la physique. Mem. sur la mesure de la dispersion et de la refraction. His diasporometer is a compound prism. *Wollaslon's mode of examining refractive and dispersive powers. Ph. tr. 1802. 365. Nich, 8. IV, 89. Measurement of Transparency. Murhard on Saussure's diaphanometer, for measuring the transparency of the air. Ph. M. III. 377. Catoptric Instruments, Account of Vilette's concave, 30 inches in diameter, 3 feet focus. Ph. tr. 1665 — 6. I. 95. Vilette's second concave of metal, 34 inches in diameter. Ph. tr. 1669.IV. 986. A speculum 3 Leipzig ells in diameter, of thin copper plate. Ph. tr. I686. XVI. 352. Not very good. •j-Gray on specula nearly parabolic, Ph, tr, 1697. XIX. 787. In the form of the catenaiia. Lagarouste on a burning mirror. A. P. I. 276. Lahire on the multiplication of images by plane glasses. A. P. 1699- 75. H. 86. Leupold Anamorphosis nova. 4. Leipz. 1713. Harris and Desaguliers on Vilette's concave, 47 incliesindiameter, 38 inches focus. Ph. tr. 1719. XXX. 976. They say, that it burnt less powerfully when it grew hot. Perhaps for the same reason as Herschel's glasses transmitted more heat when they were hot, and reflected less, Dufay's catoptrical experiments. A, P. 1726. 165. H. 47. Obsenes how much culinary heat is intercepted by glass. Leutinann's anamorphosis. C. Petr. IV. 202. Cal. Smith's glass speculums. Ph. tr. 1739- XLI. Newton's paper on a reflecting instrument like Hadley's. Ph. tr. 1742. 155. Speculums. Smith's optics, iii. c. 2. Chateau Blanc's reflecting lamps. A. P. 1744. H, 62. Mach.A.VII. 273. Cassiui on burning mirrors. A. P. 1747. 25. H. 113. Courtivron's comparison of plane and spheri- cal mirrors. A. P. 1747. 449. H. 117. Needham on Buffon's mirror, burning at the distance of 66 feet Fr. Ph. tr. 1747, 493. CATALOGUE. — OPTICAL INSTRUMENTS. a 83 Kicolini on Buffon's mirror. Ph. tr. 1747. Composed of 108 plane mirrors each 6 inches square ; burning wood at the distance of 1 50 feet ; melting a silver plate at 10 feet. BufFon's account of his burning speculum. Ph. tr. 1748. 504. It was 6 feet broad and of the same height ; burnt wood at the distance of aoo feet, melted tin and lead at 120, silver at so'. Parsons on the burning instrument of Archi- medes. Ph. tr. 1754. 621. Lievreville's reflecting lamps. A. P. 1759- H. 234. Zeiheron burning mirrors. N.C. Petr. VII. 237. On mirrors. Abat Amusemens philosophiques. 1763. Montucia and Lalande. HI. 554. Reflecting lamps. Art du Vitrier. f. Paris, ii. 224. Wolfe de speculis Dni. Hoesen. Ph. tr. 1769. 4. They are made of brass plates, fined on wood of a para- bolic form ; one 9 Dresden feet 7 inches in diameter, 4 feet in focus ; the diameter of the focus being not more than half an inch. Melted in Hoffman's experiments a large nail in 3', a pistole in 2'. Hoffman used the two opposite each other, as Dufay had done before and Pictet has done since. They reflected very powerfully the heat of a strongly heated stove. 2 Sept. 1768. Lambert on portelumieres. A. Berl. 1770. 51. Cones of tin for directing light. On speculum metal. Roz. Introd. I. 433. Alut on looking glasses. Roz. III. 328. Kaestner on the multiplication of images in looking glasses. Dissert, ii. 8. Kaestner on the magnitude of images in a spherical mirror. N. C. Gott, 1777. VIII. 06. Mudge on the composition and formation of speculums. Ph. tr. 1777- 296. CastiUon on conductors of light. A. Berl. 1777. 42. E. M. A. V. Art. Metal blanc. Miroitier. Miroirs de metal. VI. 742. Reflecting lamps. E. M. Physique. Art. Ardent. Edwards on metal for speculums. Nautical almanac. 1787. Nich. HI. 490. Gilb. Xll. 167. Sickingen on platina. Recommends 6 parts platina, 3 iron, and 1 gold. Lich- tcnb. in Erxleb. Rochon on platina. Gilb. IV. 282. Klaproth on an ancient mirror. A. Berl. 1797. 14. Copper 62, tin 32, lead 6. On Descharmes's art of soldering glass. Journ. Phys. XLIX. 305. Gilb. V. 232. Bernard on the manufactory of looking glasses. Journ. Polyt. II. 71. Repert. X. 351. Beiard's photophorus. Melanges. 1. Benzetiberg on speculums. Gilb. XII. 496. Herschel on the action of mirrors. Ph. tr. 1803. 214. Nich. 8. V. 304. See Radiant Heat. Lenses. Son's parabolic glasses. Ph. tr. 1665 — 6. I. 119. Smethwick's lenses not spherical. Ph. tr. 1668. 111.631. On grinding glasses on a plane. Ph. tr. 1668. . HI. 837. Wren's mode of grinding hyperbolic glasses. Ph. tr. 1669. IV. 1059. Two cylinders revolving in contact across each otherj be- come hyperbolic cylindroids, and form the glass revolving below them into a hyperbolic conoid. Cheruhin Dioptrique oculaire. f. Paris, 1 67 1 . Ace. Ph. tr. 1671. VI. 3045. Butterfield on making glass globules. Ph. tr. 1677. XII. 1026. Of pounded glass held on a pin, in the flame of a spirit lamp with a wick of wire. Borelli on finding the focns of an object glass. A. P. X. 457. 284 CATALOGUE. — OPTICAL INSTRUMENTS. Compares the focal image formed by oblique rayj to the profile of Saturn with his ring. Lahire on centering lenses. A. P. 1699. 139. H. 86. Borrichius on burning glasses three or four feet in diameter. A. P. 1699- II. 90. Tschirnhaus's large lens, of 32 feet focus. A. P. 1700. H. 131. Parent on a tool for hyperbolic glasses. A. P. 1702. H.92. Cassini on centering glasses. A. P. 1710. 223. Homberg on the ancient burning glasses. A. P. 1711. H. 16. Bianchini and Reaumur's stipport for large lenses. A. P. 1713.299^ Hertel on grinding lenses. M. Berl. III. 146, Noilet's machine for grinding lenses. Mach. A. VI. 127. Deparcieux's machine for grinding glasses. A. P. 1736. H. 120. Mach. A. Vil. 50. Jenkins's machine for grinding spherical lenses. Ph.tr. 1741. XLI. 555. A cup and ball both revolving. Short's method of working object glasses truly spherical. Ph. tr. 176y. 507. Delivered sealed 1753. Zeiher on burning lenses. N. C. Petr. VII. 237. Euler on polishing lenses. N. C. Petr. VIII. 254. For preserving the form. Euler on optical glasses. A. Berl. 1761. 107, 147.1762. 117, 195. Antheaulme on polishing object glasses. S. E. VI. 465. Libaudeon making flint glass. S. E. 1773. Cadet and Brisson onTrudaine's lens. A. P. 1774. 62. H. 1. Made of plate glass bent, with 1 40 pints of spirit of wine. On a spherometer for measuring lenses. Roz. VII. 484. Fig. VIII. 398. Bunows's machine for grinding glass. Bai- ley's mach. I. 142. E. M. A. IV. Art. Lunettier. Water lens. E. M. A. VI. 733. Canterzani on grinding lenses. C. Bon. VI. O. 382. Achard on optical glass. A. Berl. 1788. 14. 1790. 40. Enc. Br. Art. Burroughs's machine. Glass po- lishing, Lens. Diek Anvveisung vergrosserungsgl'aser zu schleifen. Hamb. 1793. Macquer on flint glass. Repert. VII. 211. Globules for microscopes. Nich. I. 131. On optical glass. Nich. I. 180. On achromatic lenses. Nich. II. 233. Benzenbergon the improvement of flint glass. Gilb. XI. 255. Dr. Benzenberg warmly recommends, that the glass be suflFered to cool in the pots without stirring, and that the mass be then divided in a horizontal direction, so that the variation of density may be regular, and then, by a proper form of the glasses, the errors of refraction may be correct- ed. The idea is not new, but it does not appear to have been carried into practice. Dr. Benzenberg considers achromatic telescopes as promising much more than reflect- ors, and thinks that they intercept much less light. The dishes in which lenses are sometimes ground are of bell metal ; the emery is prepared by elutriation. The large clumps now used for lamps are first formed in hemispheri- cal ladles This mode was proposed by Gessner in 1726. Optical Scenery. Hook on forming pictures on a wall. Ph. tr. 1668. III. 741. Noilet's camera obscura. Mach. A. VI. 125. Euler's improved magic lantern and solar microscope. N. C. Petr. III. 363, fStorer's patent delineator, Repert. IV. 239. A camera obscura. CATALOGUE. — OPTICAL INSTRUMENTS. 285 On the phiintasmagoria. Montucla and La- lande. III. 551. Nicholson on the phantasmagoria. Nich. 5. I. 147. PhiHpsthal's patent phantasmagoria. Rep. XVI. 303. R. B.'s perspective instrument. Nich. IX. 122. Panorama. See Vision, Aerial perspective. Microscopes, Simple and Com- pound. *//ooA:e's Mi crograp hi a. f. Lend. l6G5. R.I. Ace. Ph. tr. 1665. I. 27. On a microscope of Fabri. Ph. tr. 16G8. [II. 842. Leeuwenhoek's microscopes. Ph. tr. 1673. VIH. 6037. •f-Gray on microscopes of water. Ph. tr. 1696. XIX. 280, 353, 539. Some of the images thus seen are shadows. Y. Huygeus on a microscope. A. P. X. 427. Wilson's description of his pocket micro- scopes. Ph.tr. 1702. XXin. 1241. Adams on microscopes. Ph. tr. 1710. XXVII. 24. Globules. Folkes on Leeuwenhoek's microscopes. Ph.tr. 1723. XXXII. n. 380. Baker's catoptric microscope. Ph. tr. 1736. XXXIX. 442. Like the Gregorian telescope. Baker on Leeuwenhoek's microscopes. Ph. 1r. 1740. XLI. 503. The deepest Jj of an inch focal length. A Wilson's micro- scope made by Cuff for Folkes, had a lens of i^. Account of Lieberkuhn's opaque and solar microscope, p. 518. Lieberkuhn's anatomical microscope. A. Berl. 1745. 14. Euler's solar microscope. N. C. Petr. III. 363. Euler on microscopes. A. Berl. 1757. 283, 323. 1761. 191, 201. 1764. 10.5, ll7. N. C. Petr. XII. 195, 224. Wideburg de raicroscopio solari. Erlang. 1755. Widtburg Beschreibung eines sonnenmikro- scops. Nuremb. 1758. Aepinus's solar microscope. N. C. Petr. IX. 316. For opaque objects. Aepinus on an achromatic microscope. N. A. Petr. II. 1784. H. 41. Aepinus Description des nouveaux micro- scopes. 8. Petr. Zeiher's doul)ie solar microscope for opaque objects. N. C. Petr. X. 299- Stiles on some microscopes made at Naples. Ph. tr. 1765. 246. These globules were made by F&ther Latorre, one of them was ^ of an inch in diameter, magnifying 2500 times. Describe!, among many other objects, the globules of the. blood, as articulated rings. Baker's report of Latorre's globules. Ph. tr. 1766. 67. Found them uselesi. Baker on microscopes, 2 v. 8. 1785. R. I. D. de Chaulnes's dioptrical experiments. A. P. 1767.423. H. 162. Selva's catoptric microscope. A. P. 1769. H.. 129- Dallebarre's microscope. A. P. 1771. H. Datlebarre Memoire sur le microscope. R.S. Gltichen vom sonnenmikroscop. 4. Nuremb. 1781. Beguelin's remark on Aepinus's microtele- scope. A. Berl. 1784. H. 46. Ph. tr. 1785. See Telescopes. Ramsden applied to his pyrometer a microscope calcu- lated for an equable enlargement of the image. The mi- croscopes that he at first applied to Roy'$ theodolite were afterwards much improved. QS6 CATALOGUE. OPTICAL INSTRUMENTS. Enc. Br. Art. Microscope. distance's machine for preparing sections of plants for microscopical inspection. Ph. M. HI. 302. Adams on the microscope, by Kanmacher. 4. Lond. 1798. Microscopes of varnish. Ferguson's lectures, by Brewster. The eyepiece of a telescope makes a good solar micro- scope. Robison, Telescopes. Hooke, Auzout, and Campani on telescopes. Ph. tr. 1665—6. I. 2, 55, 56, 63, 68, 74, 131, 123, 203. A. P. VII. part. 2. i. ♦Newton's new telescope. Ph. tr. 1672. VII. 4004, n032. Birch. III. 2, 5. Newton's remavks on Cassegrain's telescope. Ph. tr. 1672. VII. 4051. Thinks Cassegrain's telescope no improvement on Gre- gory's. Hugens's aerial telescope. Ph. tr. 1684, XIV. 668. Hugens on Newton's telescope. A. P. X. 351. Huygens's telescopic level. A. P. X. 439. Molineux on the telescope with four glasses. Ph. tr. 1686. XVI. 169. Gray on telescopes. Ph. tr. l697. XIX. 5S9. Lahire on colours seen in telescopes. A. P. IX. 390. Lahire's telescopes without tubes. A. P. 1715. 4. Borelli on large telescopes. A. P. X. 393. Cassini on telescopic glasses. A. P. X. 492. Perrault's mirror for a telescope. Mach. A. 1.35. Sebastian's machine for a telescope of 100 feet. Mach. A. I. 93. Derham on Gascoigne's telescopic sights. Ph. ir. 1717. XXX. 603. Hadley's account of a catadioptric telescope. Ph. tr. 1723. XXXI1.303. A Newtonian telescope 5^ feet long, equal to one of Hu- gens of 123 feet. Pound on Hadley's telescope. Ph. tr. 1723. XXXII. 382. Mairan's jacks for telescopes. Mach. A. V. 31 . Smith's optics. Caleb Smith on catadioptrical telescopes with glass speculums. Ph. tr. 1740. XLI. 326. From theory only. Le Maire's reflecting telescope. Mach. A. VI. 61. Like Dr. Herschel's. ConstructioJi d'un telescope par reflexion. 8. Amst. 1741. Euler on/telescopes and object glasses. A. Berl. 1747.274. 1757.283,323. 1761. 107, 147, 181,201,212. 1762. 117, 143, 185, 195, 226, 249. 1764. 200. 1766. 119, 171. M. Taur. III. ii. 60, 90. A. Berl. 1767. 131. N. C. Petr. XII. 195, 224. XVIII. 377 .. . Kratzenstein on the management of long tubes. N. C. Pelr. I. 291. Kratzenstein and Euler on the iconantidip- tic telescope. A. Petr. III. i. 192, 201. Hertel Anweisung telescopia zu verfertigen. 8. Halle, 1747. Kaestner on the aberration of lenses. C.Gott. See Theory of Dioptrics. J. Dollond on an improvement of refracting telescopes. Ph.tr. 1753. 103. Adding a sixth lens. Dollond and Euler on chromatic corrections. Ph. tr. 1753. 287. *Dollond on the different refrangibility of light. Ph. U. 1758. 733. CATALOGUE. — OPTICAL INSTRUMENTS. 287 KliDgenstierna on refraction. Schw. Abh. 1754. 300. ♦Clairaut on the improvement of telescopes. A. P. 17o6. 380. H. 112. 1757. 524. H. 153. 1762. 578. H. 160. Finds the index of refraction of plate glass from 1.54 to 1.S6 : of flint 1.5S5 to l.flis ; the dispersion of water equal to that of plate glass : thinks the colours dilTerently diatributed by different mediutns. Legentil on the aberration of light passing through two lenses. A. P. 1757. 545. Legentil on binocular telescopes. A. P. 1787. 401. Roz. XXXI. 3. Recommending them. "Redern on object glasses. A. Berl. 1759. 89. 1760. 3. 1761. 3. J. A. Euler on object glasses with water. A. Berl. 1761.231. Beguelin on achromatic prisms. A. Berl. 1762. 66. Beguelin on the improvement of telescopes. A. Berl. 1762.343. ♦Beguelin on telescopes. A. Berl. 1769- 1. Beguelin on Aepinus's achromatic micro- telescope. A. Berl. 1784. 11. 40. Murdoch on achromatic refraction. Ph. tr. 1763. 173. Defends Newton. Fougeroux on Campani's object glasses. A. P. 1764.251. H. 169. P. Dollond on achromatic telescopes with triple object glasses. Ph. tr. 1765. 54. D'Alembert on achromatic telescopes. A. P. 1764. 75. H. 175. 1765. 53. H. II9. 1767. 43. H. 153. D'Alembert Opuscules, vol. I. A. Berl. 1769. 254. Acknowledges some mistakes of his own and of Clairaut. Lagrange's dioptrical formulae. M. Taur. in. ii. 152. Lagrange on the theory of telescopes. A. Berl. 1778. l62. Cotes's theorem. Boscovich on achromatic glasses. C. Bon. V. ii. 265. Germ. 8. Vienn. 1765. Due de Chaulnes on achromatic lenses. A. P. 1767.423. H. 162. Scherfer on dioptrical telescopes, by Hardy. 8. 1768. Darquier on the focus of telescopes. S. E. V. 367. Zeiher de novis dioptricae augmentis. 4. VVittenb. I768. Jeaurat on the refraction and dispersion of crown glass and flint glass, with tables for object glasses. A. P. 1770. 461. H. 103. Lambert on achromatic telescopes of one kind of glass. A. Berl. 1771. 338. Rochon's achromatic telescope. A. P. 1773. 299. Gilb. IV. 300. Rochon on reflecting telescopes. Ph. M. II. 19. 170. Navarre's telescope. A. P. 1778. H. 56. Ftiss sur les telescopes. Germ, by Klugel. 4. Leipz. 1778. Telescopic appearances of the stars. Her- schel. Ph. tr. 1782. 82. Herschel on the magnifying powers of his telescopes. Ph. tr. 1782. 173. Herschel on the front view of the reflecting telescope. Ph. tr, 1786. 499. Herschel on the magnitude of the optic pen- cil. Ph. tr. 1786. 500. A pencil of j^ of an inch was sufficient for distinct vision with a high magnifying power. Suspects that the aperture ought to be in a certain ratio to the focal length, even in a large telescope. *Herschel on his forty feet telescope. Ph. tr. 1795. 347. Herschel on darkening telescopes. Ph. tr Mich. 8. 1. 224. Herschel on the action of mirrors. Ph. tr. 1803. 214. Nich, 8. V. 304. 288 CATALOGUE. — OPTICAL INSTRUMENTS. Ilanisden on the eyeglasses of telescopes applied to mathematical instruments. Ph. tr. 1783. 94. Corrects the chromatic abeiration nearly in the manner of Ealer and Boscovich, and proposes to remedy the cur- vature of the first image, by placing a planoconvex lens a little beyond it, with the flat side towards it. By complet- ing the investigation; it will be found, that in order to pro- duce the greatest effect, the distance of the first image from the lens should be between a half and the whole of its ra- dius ; and in this case the centre of curvature of the mean image formed by the lens will be about the length of the ladius beyond Che lens, supposing it to have been at first a plane. Thus, for an object glass of 2 feet focal lengch, the radius of curvature of the mean image being about 9 inches, if the image be about 2 inches distant from a planoconvex lens of 4 inches radius, the effect of the curvature of a circle of 1.000276 B.29.6, Th.50°.3 ^ Ice, by observation. W. 7 , - ., T , ^ 1 , • r 1 , V J- 1-310 Ice, by calculation tromhalos. i.} Water. W. H. > Vitreous humour. \\.y Lime water. C. - (1.334) Well water. C. - - 1.336 Spirit of hartshorn. C. - 1.337 Solution of caustic ammonia. C. 1.349' Solution of soda. C. - 1 .352 Ether. VV. - - 1.358 French brandy. C. - ^ ' , •^ (.(1.368) Albumen. W. - - I.36 Hawksbee - (1.351) Alcohol. W. - - 1.37 C. - - 1.371 Distilled vinegar. Hawksbee. 1.372 Euler - (1.344) Saturated solution of salt. C. 1.375 Sahl, water 27. C. - - (1.348) Solution of sal ammoniac 1.382 CATALOGUE. — PHTSICAL OPTICS. 257 Index of refraction. Solution of [)otash. C. - 1.390 Nitric acid, sp.gr. 1.48. W. 1.410 Nitric acid. C. - 1.412 Fluor spar. W. - 1.433 Sulfuric acid. W. - 1.435 C. - - (1.426) Spermaceti, melted. W. - 1.446 Crystalline lens of an ox. W. 1.447 (to 1.380) C. (1.463) Oil of wax. C. - 1.452 Alum. VV. - - 1.457 C. - - 1.458 Tallow, melted. W. - 1.460 Borax. C. - - 1.467 Oil of lavender. W. - - 1.467 C. (1.469) Oil of peppermint. W. 1.468 Oil of olives. W. - - 1.469 C. - (1.465) Oil of almonds. W. Oil of turpentine, rectified. W. 1.470 Oil of turpentine, common. W. 1.476 C. (1.482) Essence of lemon. W. - 1.476 Butter, coW. W. - - 1.480 Linseed oil. W. - 1.485 Camphor. W. - - 1.487 C. - (1.500) Iceland spar, weakest. W. 1.488 strongest. W. (1.657) Taflow, cold. W. - 1.49 Sulfate of potash. W. - 1.495 Oil of nutmeg. W. - 1.497 French plate glass. W. 1.500 English plate glass. W. 1 .504 Oil of amber. VV. - 1.505 C. - (1.501) Balsam of capivi. W. - 1.507 Gum Arabic. W. - 1.514 VOL. II. Index of refraction. Gum arable. C. - (1.477) -Human cuticle. VV. Dutch plate glass. W. 1.517 Gum lac. W. Caoutchouc. W. ' 1.524 Nitre. C. - 1.524 Selenite. W. - - 1.525 Crown glass, common. W. 1 525 Canada balsam. VV. - 1.528 Centre of the crystalline of fish, and dry crystalline of an ox. W. 1.530 Pitch. W. Crown glass, sp. gr. 2.52. C. 1.532 Yellow plate or Venetian glass, sp. gr. 2.52. C. 1.532 Brazil pebble, sp. gr. 2.62. C. 1.532 RadcUffe crown glass. W. 1 533 Anime. W. - 1.535 Copal. VV, - - 1.535 Oil of cloves. W. - 1.535 White wax, cold. W. Elemi. W. Mastic. W. Arseniate of potash. W. Sugar, after fusion. VV. Sugar, 1, water 27. C. - (1.346) Spermaceti, cold. W. Red sealing wax. VV. Oil of sassafras. W^. - 1.536 C - (1.544) Bees wax. W. - - 1.542 Boxwood. VV. Colophony. W. - 1.543 Glassof St. Gobin. C. - 1.543 Old plate glass. \V. - 1.345 Rock crystal (double). VV. , 1.547 C. C (1.568) C (1.575) Amber. W. 1.547 C. (1.556) 298 CATALOGUE. ?HYSICAt OPTICS. Index of refraction. Opium. W. Mica. W. Plate glass, or coach glass, sp. gr. 2.76. C. - - 1.573 Phosphorus. W. - - 1.579 Horn. W. Flint gliiss. W. C 1 .583 C 1.586 Benzoin. W Guaiacum. W. - - 1.596 Balsam of Tolu. W. - I.60 White flint glass, sp. gr. 3.29- C. 1 .600 A yellow pseudotopaz. C. 1.643 Sulfate of barytes (double). W. 1.646 Iceland spar, strongest. W. 1.657 ^ Glass, of lead 1, flint 4. C. 1.664 Gum dragon. W. Glass, tinged red by gold. C. 1.715 -Glass, of lead 1, flint 2. C. 1.724 Glass, of lead 3, flint 4. C. 1.732 White sapphire. W. - I.768 Glass, of lead 1, flint 1. C. 1.787 Muriate of antimony, variable. W. Arsenic. W. (A good test). 1.811 Spinelle ruby. W. - 1.812 Glass, of lead 2, flint 1. C. 1.830 Jargon. W. - - 1.95 Glass of antimony. W. - 1.98 C. - (1.89) Glass, of lead 6, sand 1. W. Doubt- ful. - - 1.987 Glass, of lead 3, flint 1. C. 2.028 Native sulfur (double). W. 2.04 Scaly oxid of iron. Y. About 2.1 Oxid of lead, by induction. Y. 2.15 Plumbago. W. Diamond. Newton. - 2.44 Rochon. - fi.755 - From Dr. WoUaston's mode of obserration, it may be in- ferred that his numbers belong correctly to the extreme red rays. Table of the order of Dispersive Powers, from Wollaston, the Numbers from llochon and from Cavallo's table. Sulfur. W. Glass, of lead 6, sand 1. W Glass, of lead 3, flint 1. r.2.028. 7.09 Glass, of lead 2, flint 1. r. 1.830. 5.24 Glass,oflead 1, flint 1. r.1.787. 4.82 Glass, of lead 3, flint 4. r. 1 .732. 3.25 Glas», tinged by gold, r.l .7 15. 2.90 Glass, of lead 1, flint 2. r. 1 .724. 2.65 Glass, of lead I, flint 4. r.1.664. 2.00 Balsam of Tolu. W. Oil of sassafras. W, Muriate of antimony. W. Guaiacum. W. Oil of cloves. W. Flint glass, r.l. 6. - - 1.80 Flint glass. W. Colophony. W. Canada balsam. \y. Oil of amber. W. Jargon. W. Oil of turpentine. W. Copal. W. Balsam of capivi. W. Anime. W. Iceland spar. W. Iceland spar r. 1.562 Cl.69 1.625 12.33 Amber. W. Diamond. W. Diamond, r.2.755. - fl.86 Alum., W. Plate glass, r. 1.573 - 1.65 , Brazil pebble, r. 1.532. - 1.59 Nitric acid, r.1.412. - I.54 Plate glass. Dutch. W. CATALOGUE. PlirsiCAL OPTICS. 259 Plate glass, English. W. Glass of St. Gobln. r.1.543. 1.49 Crown glass. W. Crown glass, r. 1.532. 1-48 Solution of sul ammoniac, r.1.382. 1.34 Ilwby, spinelle. W, Saturated solution of salt. r. 1.375. 1.22 Water. VV. - - 1.00 Sulfuric acid. W. Alcohol. W. Sulfate of barytes. W. Selenite. W. Rock crystal. W. Rock crystal. r.l.5fiO. (^1.21 1.5'75. ^ 1.24 Sulfate of potash. W. White sapphire. W. Fluor spar. W. It is obvious, that many of the results of these obsenra- tions cannot be reconciled; and it is probable, that the num- bers are frequently inaccurate. Wollaston's Table of the Refractive Powers of solutions equal in Dispersive Powers to Plate Glass. In water. In alcohol. Nitroniuriate of gold. 1.364 1.390 Nitromuriate of platina. Nitrate of iron. Sulfuret of potash. Red muriate of iron. Nitrate of magnesia. Nitric acid. Nitrate of jargon. Balsam of Tolu Acetite of litharge. Nitrate of silver. Nitrate of cop'per. Oil of sassafras Muriate of antimony Nitrate of lime Nitrate of zinc 1.370 1.375 1.375 1.385 1.395 1.400 1.410 1.400 1.405 1.410 1.422 In water, |nalcohol. Green muriate of iron 1.415 Muriate of magnesia 1.416 Essence of lemojx - 1 .430 Muriate of lime 1 .425 1 .440 Muriate of zinc 1.425 Balsam of capivi - 1.440 Hence it seems to follow, that the dispersion of the nitric acid is a fourth more than that of plate glass : a dispropor- tion much greater than appears in the numbers of CaTaUo'a table. With crown glass the nitric acid was diluted to l.3?5, and the muriatic from 1.39 to i.sga. Ordinary Atmospheric Refraction, Cekstia or Terrestrial. See Meteorology, to which this subject partlj belongs. Refractio solis inoccidui. See Irregular Refraction. Cassini on refraction. Bologn. 1672. Ace. Ph. tr. 1672. VII. 500. Cassini on refractions. A. P. I. 103. 1700. 39. H. 112. 1714. 33. H. 61. 1742. 203. H. 72. 1743. 249. H. 140. Cassini on tlie dip. A. P. VIII. 71. 1707. 195. H. 89. Lahireon the atmospheric refraction at Tou- lon. A. P. VII. i. 174. fLahire on the path of light in the atmo- sphere. A. P. 1702. 32. 182. H. 54. Laval on refractions. A. P. 1708. H. 105.. 1710. H. 109. Delisle on the refraction of the air. A. P. 1719. 330. H. 71. Halley on atmospherical refraction, -with Newton's table. Ph. tr. 1721. XXXI. 169. Taylor Methodus incrementorum. Bouguer on refraction in the torrid zone. A. P. 1739. 407. H. 45. 1749. 75. H. 152. Mairan on the refraction of the air. A. P. 1740. 32. H. 89. 300 GATALOGUK. PHYSICAL OPTICS* Euler on atmospheric refractions at different teaiperatures. A. Berl. 17.'54. 131. Euler on terrestrial refraction. A. Petr. I. ii. 129. La Cailie on refractions. A. P. 1755.547. H. 111. Thinks that it is nearly the same throughout the tempe- rate zones. Lumbert Route de la lumiere par les airs. 8. ■ Hague, 1758. Lambej-t on the density of the air. A. Berl. 1772. lOS. Roz. XVIII. 126. Heinsius on northern refraction. N. C. Petr. VII. 411. At Olenek, lat. 73° 4', certainly not greater than in Cas- »ini'i tables, which give 6' 23" at 8° 3o' altitude. *Simpson Math, dissert. Lemonnier's proposal for observations on refraction. A. P. 1766. 6O8. H. 104. Lemonnier on horizontal refraction at sunset. A. P. 1773.77. H. 53. lemonnier. A. P. 1781. Found a horizontal refraction of 50' in verycold weather. Lagrange on astronomical refractions. A. Berl. 1772. 259. A formula like Simpson's. Kastner on refraction. N. C. Gott. 1772. III. 122. Cassini on refractions. A. P. 1773. 323. H. 54. Thinks that they are somewhat greater at equal altitude! «n the south side of the zenith than on the nortti. Legentil on atmospherical refraction in the torrid zone. A. P. 1774. 330. H. 47. Legentil. A. P. 1789. 224. Fmds the horizontal refraction a'.S less in India than in France. Table of refraction for the coast of Coro- mandel. A. P. 1774. 399- Dionis du Sejour on the effects of refraction in eclipses. A. P. 1775. 265. Attributes a refraction of about 5" to the lunar atmo- sphere. Dignis du Sejour on the curve described by light in the atmosphere ; upon the optical hypothesis of its density. A. P. 1776. 273. Maskelyne. Ph. tr. 1777- 7'22. The terrestrial refraction is equal to the angle subtended by about l of the distance of two objects ; in order to cor- rect for the joint effect of curvature anJ refraction, we may divide the square of the distance by i of the diameter of the earth. Bradley's rule for refraction. Maskelyne. Ph. tr. 1787. 156. At 45° 3' 57", correcting for the temperature in the ratio of 400 to 350+f^, and for the barometerin the ratio of its height to 2g.O inches. But even from some observations here insetted, this correction for temperature appears to be too great. At 45°, Maskelyne makes the refraction 56". 5, from another comparison of observations 55". 8; Lord Mac- clesfield 54". 6, which agrees exactly with Hawkskee's ex- periment ; La Cailie 06". 0, which is much too great. Maskelyne recommends that a table of refractions be made for each instrument by immediate observation. Ilerschel. Ph.tr. 1785. 88. Found that t, 20, Sagittarii appeared to form a spectrum measuring 18" g'" vertically, s" 35'' horizontally, the dif- ference 7" 34'", near the meridian, 4th May 1783. The altitude mUst have been about 4°, and the refractioi* 2l', the declination being 34° 27'|. A. P. 1787. 355. The terrestrial refraction was found equal to ^ of the angular distance. Roy on terrestrial refraction. Ph. tr. 1790. 233 Gilb. III.281. Found it vary from i to ^ of the angular distance. Bou- guer made it ,, Maskelyne -^, Lambert Jj. A correction for temperature is given in a note by Dr. Maskelyne, but there is some mistake in it. Oriani Ephem. Milan. Cagnoli on refraction. Soc. Ital. V. 259. At Verona J^ less than in Bradley's tables, and agreeing with those of Oriani. Zanotti. C. Bon. VII. O. 1. Finds the barometrical and thermometrical corrections of little use. Deluc on refractions. Roz. XLIII. 422. Principally on the correction for temperature. Dalby. Ph.tr. 1795.581. Gilb. III. 281. The terrestrial refraction varied from \ to ^, but was ge- nerally ^ of the arc. CATALOGUE. — PHYSICAL OPTICS. 301 M aycr. Op. ined. *Henneit on refraction, and on its correc- tions. Hind. Arch II. 1, 12[). Gives .ooo7ao» for the logarithmic difference to be em- ployed in tlie calculation. Piazzi's tabic. Bode Jahrb. 1798. Makes the retraction 57.2" at 4 5°. Kramp on refractions. Hind. Arch. II. S80, 499- Calculates them according to the true constitutloa of the atmosphere, and finds that they agree with Newton's table, and With Bradley's as far as 90" zenith distance, below this they differ sometimes 30", but agree at the horizon. As- sumes for the effect of temperature a correction far too great, •o as to agree with the Reffactia solis inoccidui. Kramp Analyse des refractions. 4. 179B. Kratup. Hind. Arch. HI. 228. Mayer's rule agrees in principle with Bradley's. He em- ploys Shuckburgh's expansions instead of Bradley's. Ph. ir. 1797. The terrestrial refraction was in general ^ of the angle, in one case \-. Madge. Ph. tr. 1800. 7l6, 724. Found the terrestrial refraction from J to -j^ of the arc, but generally from -j^ to ^. ♦Laplace Mecanique celeste. IV. Brandes on terrestrial refraction. Gilb. XVII. 129. Takes ^3£ a. mean. Irregular Atmospheric Refraction. Near the horizon, or some heated surface. Horizontal Refraction. Hevelius. See Beams of Light. Cassini on two mock suns. A. P. II. 103. and X. 159. January 1093, 34' above and below the sun's centre. Cassini on a double sun. A. P. VII. 2. P. ii- 18. Supposes reflection and refiaction. Cassini on the irregularities of the dip. A. P. 1707. 195. 11. 89. Malezieux on three suns seen at Sceaux. A. P. 1722. H. IS. In October, touching each other vertically. Conti on the elevation of the sea on certain coasts. A. P. 1743. H. 40. Minasi sopra la Fata Morgana. 8. Rome, 1773. R. S. Gilb. XII. 20. R.S. Legentil on atmospherical refraction. A. P. 1774. 330. H. 47. The horizontal refraction at Pondicherry was" usually 2' greater in summer than in winter. Boscovich. Gilb. III. 302. Biisch trartatus duo optici argumentl. Hamb. 1788. R.S. Gilb. III. 290. EHicotton terrestrial re''raction. Am. tr. III. 62. Nich. I. 152. Gilb. III. 302. Ph.tr. 1795.581. D&lby found a difference of 9' 28" in two measures of the elevation of St. Ann's hill. Another case of irregular refraction was observed where the sun was warm, and there was much dew. Fata Morgana at Reggio. Nich. I. 298. Huddart on horizontal refractions. Ph. tr. 1797. 29. Nich. I. 145. Attributes them to vapours less dense than the air. The curvature of the rays is justly delineated, for the simplest cases. Latham on atmospheric refraction. Ph. tr. 1798. 357. Ph. M. 11. 232. Nich. II. 417. Gilb. IV. 147. The clifft of France fifty miles ofiT were seen distinctly at , Hastings, much magnified, and even Dieppe was said to be visible from 5 to 6 in the afternoon ; in July, the weather hot and no wind. Monge on the mirage in Egypt, Ann. Ch. XXIX. 207. Ph. M. II. 427. Gilb. III. 302. Vince on horizontal refraction. Ph. tr. 1799. 13. Ph. M. VII. 54. Nich. IH. 141. Gilb. IV. 129. Additional appearances of inverted images. *W(,llaston on double images, Ph.tr. 1800. 239- Nich. IV. 298. «Jilb. XI. 1. Caused by afmospherical refraction. With satisfactory experiments. Ihe refraction being greatest where the change of density is the most rapid, and less on each side of 502 CATALOGUE.— PHrSICAL OPTICS. this point, the whole effect must be similar to that of a con- vex lens. Wollaston on horizontal refraction and on the dip. Ph. tr. 1803. 1. Repert. ii. III. 419- Nich. VI.46. Mudge. Ph. tr. 1800. 720. Looking over Sedgraoor, after a warm day, Glastonbury tor was depressed 29' 50". DeUic on the apparent elevation of horizontal objects. Ph. M. XII. 148. Horizontal refraction at Youghal. Beauford. Ph. M. XIII. 336. Gruber on refraction near a warm surface. Gilb. III. 377, 439. Woltmann on terrestrhal refraction. Gilb. III. 397- Heim on an unusual refraction. Gilb. V. 370. Dangos on a horizontal refraction at Malta. Ph. M. XIV. 176. Gorsse on mirage. Ann. Ch. XXXIX. 211. Wrede on an atmospherical refraction by the walls of Berhn. Gilb. XI. 421. Giovene on the fata morgana. Gilb. XII. 1; Gilb. XVII. 129. Brandes found the terrestrial refraction diminished when- ever the air cooled suddenly. Castberg on the fata morgana at Reggio. Gilb. XVII. 183. Thinks it a shadow. It may frequendy happen in a medium gradually vary- ing, that a number of difTercnt rays of light may be inflect- ed into angles equal to the angles of incidence, and in this respect the effect resembles reflection rather more than re- fraction. Y. Abstract of the Bakerian Lecture, by Dr. Wollastok, con- sisting of observations on the quantity of horizontal re- fraction, and the method of measuring (he dip at sea. Journ. R. I. Dr. Wollaston notice* Mr. Monge's memoir on the " mirage" observed in Egypt, as containing facts, which fully agree with his own theory formerly published. From his observations on the degree of refraction produced by the air near the surface of the Thames, it appears that the va- riations derived from changes of temperature and moistnre in the atmosphere, are by no means easily calculable ; but that a practical correction may be dbtained, which, for nautical uses, may supersede the necessity of such a calcu- lation. Dr. Wollaston first observed an image of an oar at a distance of about a mile, which was evidently caused by refraction, and when he placed his eye near the water, the lower part of distant objects was hidden, as if by a cur- vature of the surface. This was at a time when a continu- ation of hot weather had been succeeded by a colder day, and the water was sensibly warmer than the atmosphere above it. He afterwards procured a telescope, with a plans speculum placed obliquely before its object glass, and pro- vided with a micrometer, for measuring the angular depres- sion of the image of a distant oar, or other oblique object ; this was sometimes greatest when the object glass was within an inch or two of the ^vater, and sometimes when at the height of a foot or two. The greatest angle observed was somewhat more than nine minutes, when the air was at 50°, and the water at 63" ; in general the dryness of the air lessened the effect, probably by producing evaporation, but sometimes the refraction was considerable, notwith- standing the air was dry. Dr. Wollaston has observed but one instance which appeared to encourage the idea, that the solution of water in the atmosphere may diminish it> refractive power. In order to correct the error, to which nautical observa- tions may be liable, firom the depression of the apparent horizon, in consequence of such a refraction, or from its elevation in contrary circumstances, and at the same time to make a proper correction for the dip. Dr. Wollaston re- commends, that the whole vertical angle between two op- posite points of the horizon, be measured by the back ob- servation, either before or after taking an altitude ; and that half its excess above 180° be taken for the dip : or if there be any doubt respecting the adjustment of the instru- ment, that it be reversed, so as to measure the angle below the horizon, and that one fourth of the diffisrence of the two angles, thus determined, be taken as extremely near to the true dip. It is indeed possible, that the refraction may be somewhat different at different parts of the surface, but Dr. Wollaston is of opinion that this can rarely happen, except in the neighbourhood of land. Y. Irregular Refraction at various Altitudes. Kffractio solis inoccidui. 4. Stockh. 1695. Engl. 8. London. Ace. Ph. tr. 1697. XIX. Lahire's remarks. A. P. 1700.37. H. 112. CATAIOOUE. — PHVSICAi:, OPTICS. 303 In lat. 96' 45' the sun was three diameters above the ho- rizon, 14 June at midnisht. The Dutch are said to have seen it 4° too high in Nova Zembla. At Stockhelm the horizontal refraction is sometimes 47'. Mairan on llie sun apj)eaiing oval at 10° al- titude. A. P. 1733. 329. H. 23. Elliptic appearance of the sun at a consider- ablehcight. A. P. 1741. H. 134. Dicquemare on a distorted iris. Roz. X. ISG. Probably by irregular refraction. Beams of Light from Atmospherical Refrac- tion or Reflection. Hevelius on a mock sun and a vertical train of light seen in Russia. Ph. tr. IG74. IX. 26. A red mock sun below the real sun, and a vertical train from the sun upwards. At first the mock sun was at the distance of a few degrees, at last the sun descended and united with it. A severe frost followed. Derham on a pyramidal light. Ph. tr. 1707. 2411. April 7, 1707, after sunset, perpendicular to the horizon, succeeded by a halo. I have also observed such a beam in June. Y. Messier on two vertical cones of light at- tached to the moon. A. P. 1771. 434. The moon being covered with thin clouds. Gilbert on a singular meteor. Giib. III. 360. A perpendicular beam of light above the sun after sunset, in August. Remarks on the zodiacal light. Zach. Mon. corr, VII. Observations of Parhelia^ or Paraselenes, and Halos of about 22° or 44°, in general. Zahn Mundi oeconomia. 2 v. f. M. B. Li/coithenis chronicon prodigiorum. f. Bas. 1557. M. B. Fritsck on meteors. Particular Accounts. In order of time, with the angles, where they have been measured. Roman parhelia. Descartes meteorol. C. X. Journal dessavans. 1666. Ph. tr. l665 — 6.1. "" 219. Brown on parhelia in Hungary. Ph. tr. 1669. IV. 953. Observation of the French academy. Ph. tr. 1670. V. 1065. A halo 22" 0'. Petto on parhelia at Sudbury. Ph. tr. I699. XXI. 107. Stephen Gray on parhelia at Canterbury. Ph. ,r. .699. XXI. 126. X^^fUm^. H. 23» O'. /7 ^ " "" ^ Lahire. A. P. II. 208. ' ■ — VKKS'TV , Lahire. A.P. X. 47. H. n. 1. 21" 30'. n. a. 23" 20'. n. s. aa" 45'. n. 4. 21° 0'. Cassini and Grillon. X. 152, I68, 275, 454. A circle 22" above and 23° below the sun, 168. A. P. X. 411. Chazellesand Feuillee. A. P. I699. H.82. St. Gray on a parhelion and halo. Ph. tr. 1700. XXII. 535. ♦Halley. Ph. tr. 1702. XXIfl. 1127. The arches touching the halo appeared to be portions of circles having their centres near the opposite side ofth« halo : the upper one was continued across the horizontal circle, and at the intersections were parhelia 31 °i. distant from the sun. The sun's altitude was from 40° to 4S°. The clouds were seen to drive under the circles : they were therefore formed high in the atmosphere. A circle at Clermont. A. P. 1708. H. 109. Cassini. A. P. 1713. H. 67. Halley. Ph. tr. 1721. XXXI. 204. The air apparently replete with snowy particles. Ok- serves, that an explanation " seems wanting." Whistoa. Ph. tr. 1721. XXXI. 212. An inverted arch not much bent touched the halo. The external tangent arch was without a halo, it seemed 00° long: its centre near the aenith ; sun's altitude 23°i, distance of the extctnal arch from the zenith 2o°. The halo became 'J&i CATALOGUE. — PHYSICAL OPTICS, ovil ; in horizontal diameter the shorter ; the parhelia a dejree or two beyond it. Maraldi on two meteors. A. P. 1721. 231. H.4. The internal tangent arc appeared like two portions hav- ing their centres in the lateral parhelia. Observes, that there are always delicate and almost invisible clouds when they appear : the wind N. E. or E. and a little frost, suc- ceeded by a milder air. Some slender melting snow fell two dayt after. v Dobbs on a parhelion seen in Ireland. Pli. fr. 1722. XXXll. 89. Three parhelia without halos. Two inverted arches above. .Whiston. Ph. tr. 1727. XXXV. 257. The halo was touched by two curves above and by one below : the lateral parhelia were without the halo, but not in the intersection of either of the tangent arches produced with the horizontal circle : there was a small portion of a secondary halo about one third larger than the primary: perhaps belonging to the tangent arch. There were two anthelia, further apart than the parhelia. IVIarch i, Rafter 10. Kensington. The two tangent curves appeared to be in- dependent of each other, one only appearing at first. Academy of Bezieres. /. P. 1729- H. 2. June, from 10 to 12. H.'JO° 3l'. Musschenbroek. Ph. tr. 1732. XXXVIf. 357. A white horizontal circle above the sun, 58° is' in dia- meter, crossed by the coloured halo. At 50° 30' from this crossing was a parhelion in the horizontal circle. Apr. as, from 1 p. 10 to I p. 11. H. 45° 3o', externally. Scliultz. Coll. Acad. VI. 270. Mentzelius. 301. Others. 445. Trisch on a halo. M. Berl. 1734. IV. 64. Some anomalous arcs passing through the sun. Diifay. A. P. 1735. 87- Chiefly from 27 observations of Musschenbroek in 1734. The thin clouds forming them are always higher than the common clouds. N. l.H. 23° li' internally, lunar. N. 2. H- 23^. A second arc was seen near the zenith, its dia- meter varying from 24° to 30°, 28°i, and 27°|, being greatest ai. 1 1 o'clock, in January. The halo changed also from 23° disunce to 19° 50', 19°, and 18° 30". N. 3. More than half the circumference of an inverted arc touch- ing the first halo, and of the same curvature with it : the circle about the zenith appeared of a constant diameter while the sun's altitude varied i this altitude was Aout 1 4°i. N. 4. A train of light ascended from the sun. N. 7. Lastcd^l! day, June 17, exactly 23°i radius. N. 8. Ex- actly 23°i, from the red edge to the centre of the sun, about 1' I bioad. N. 9. H. 22°. Grandjean de Fouchy on a paraselene. A. P. 1735.585. The moon in a cross, 20° altitude. Neve. Ph.tr. 1737. XL. 50. At Petersburg. Weidler. Ph. Ir. 1737- XL. 54. Sun's altitude 15°1. Ext. H. 45°f Lateral parhelion at 20° exactly. Foikes on three mock suns. Ph. tr. 1737. XL. 51). Weidler de parhelils anni 1736. 4. \Vittemb. 1738. M. B. Ace. by Stack. Ph. tr. 1740. XLI. 459. Bad theory. Weidler de anthelio. Ph. tr. 1739. XLI. 209. This was an appearance in the north, at J p. g. I8 Jan. 1738, of two arcs crossing at an angle of 00°, with a halo 2°i horizontally, and i°i vertically in diameter, red within. Snow fell soon after. A similar appearance it related by llevelius de Mercurio in sole viso. Mills on parhelia seen in Kent. Ph.tr. 1742. XLII. 47. Gostling. Ph. tr. 1742. 60. December. From sunrise till noon. Halos and parhelia seen once or twice a week in Hudson's bay. Middleton. Ph.tr. 1742. XLIL 1.57. Lacroix. A. P. 1743. H. 33. Says the horizontal band was coloured ; the tangent are nearly straight. Two suns at VVilna. A. P. 1745. H. 19. Grischow on lunar circles and paraselenae. Ph. tr. 1748. XLV. 524. The two inverted arches concentric with the zenith. Arderon. Pli.tr, 1749 XLV1.203. A halo surrounding the zenith, 1 1 July, s P. M. Appears from the figure to be about j° or 8° in diameter ; the sun's rays were seen shining through the cloud. CATALOGUE. — PHYSICAL OPTICS, 305 Macfait. Ed. ess. I. 29". October. Musschenbroek. A. P. 1753.11. 7.5. A parhelion about 30° from the sun, with arcs crossing in it. Boscovich on a halo. A. P. 1754. H. 32. No clouds were visibk, but the sun was obicure. NoUet. A. P. 1755. H. 37. Braun's observations in Siberia. N. C. Pctr. VI. 425. X. 375. One March J760, 21° above the sun 25° below it; another in August, the thermometer 65.6° F. in the shade: thin clouds floating from e o'clock to two. Pingre. A. P. 1758. H. 23. Moeren. Coll. Acad. VI. 299. Barker on a halo. Ph. tr. 1761. 3. . H. 22°i. Vertical diameter of the external halo 45°, with an elliptical curve 4° narrower or wider horizontally, coinciding with it at the summit, without parhelia. May 30, 1737, {before 11, Aepinus; N. C, Petr. VIII. 392. An ellipsis, including the interior halo, touching it above and below ; another with the horizontal diameter of the ellipsis about 51°, the Yeitical 45°. Swinton on an anthelion. Ph, tr, I76I, 94, July 24, -very cold. Dunn on a parhelion. Ph. tr. 1763. 351. Many days in September and October. •Wales, Ph, tr. 1770. 129- There are constant parhelia in Hudson's Bay, the sun's rising being preceded by two streams of light about 20" dis- tant from him ; these accompany the sun the whole day in the winter, with three parhelia. Saint Amans. Roz. XI. 377, Atkins. Ph.tr. 1784.59- Terminating in a field of snow. Rozi^res on a paraselene. A, P. 1786. 44. With a tail. In a halo 7° or 8° in diameter, but not es- sentially connected with it. Hamilton. Ir. tr. 1787. I. 23. An obscure light at 00°. Parh. 2e". •Baxter on hales seen in North America, Ph, tr. 1787. 44. Fig. Ji. 33° i*'- An anthelion in the boiizontal circle, like a VOL. U. St. Andrew's cross : A second and third anthelion about halfway between the first and the halo. Reynier. Roz. XXXVII. 308. 23 Jul. 7 evening. Ussheron two parhelia, Ir, tr, 1789, III, 143. Parhelia at Caumont. Ph. M. I. Hall. Ed. tr. IV, 174. Nich. II. 485, Gilb. III. 257. A large circle not horizontal. Scheiner's was also oblique. Wrede on a paraselene. Ph. M. XII. 346. Elliptic, the horizontal diameter being about 60°. *Lowitz. N. A. Petr. 1790. VIII. 384. At Petersburg, isJune 1700; the most complicated halos and parhelia that have been observed. Sargeant on parheha in Cumberland. Nich. IV. 178. A third concentric halo. Ph. M. XII. 373. Not very circumstantially described. Englefield. Journ. R. I. II. 1. Nich. VI. 54. H. 24°, 48°. Brandes. Gilb. XI. 414. H. 21° to 22°. See Weigelsgrundriss der cheniie. May 14, IS 04, J before 12 at night, I observed a lunar halo, the internal limit passed nearly through gamma leonis, but more accurately half way between gamma and Regulus. Hence the distance from the middle of the illuminated part of the raoon was accurately 21° 20' or 22', without a proba- bility of an error of more than a few minutes. June 16, 1804. I saw a portion of a halo in the evening, the clouds were light and high. Out of 58 of these observations 2 only were in July, 3 in August, 4 in January, 4 in September, s in March, 5 in June, 6 in February, 6 in October, 6 in December, 1 in April, and 9 in May. Theory of Halos and Par/ielia. - tHugens. Ph. tr. 167O. V. 1065. Hugenius de coronis et parhehis. Op. rel. II. ♦Mariotte Trait6 des couleurs. Paris, 1 686. Oeuvr. I. 272. Wood's theory of halos. Manch. M. ill, 336. B t 306 CATALOGUE. — ^PHYSICAL OPTICS. Supposes them produced by vesicles of which the thick- ness is yJ, of the diameter. Brandes on parhelia. Gilb. XI. 414. Supposes vesicles filled with a medium of a certain den- sity, producing the halos as the drops ofvrater produce the rainbow. MuHotte Phenomenon \i. The great Coronae. " Sometimes when the air is pretty serene, a circle of about 4i° diameter is seen round the sun or moon : the colours are not in general very lively, the blue is without and the red within, their breadth is nearly as in the common external rainbow. Explanation. I take for the cause of this ap- pearance small filaments of snow, moderately transparent, having the form of an equilateral triangular prism. I con- jecture that tl^ smair flat flakes of snow, which fall during a hard frost, and which have the figure of stars, are com- posed of little filaments like equilateral prisms, particularly those which are like fern leaves, as is easily seen by the microscope. I have often looked at the filaments which compose the hoar frost, that appears like little trees or plants in the cold mornings of spring and autumn ': and I have found them cutinto three equal facets ; and when viewed in the sunshine they exhibited rainbow colours. Now it is very probable, that before these little figures of trees or stars are formed, there are floating among the thin vapours in the air, some Of these separate prisms, which when they unite form the compound figures. These little stars arc very thin, and very light, and the little filaments, which compose them, are still more so, and may often be sup- ported a long time ih the air by the winds : hence when the air is rtvoderately filled with them, so as not to be much darkened, many of them, whether separate or united, will turn in ever.-' direction as the air impels them, and will be disposed to transmit to the eye for some time, a coloured light nearly like to that which would be produced by equi- lateral prisms of glass." The angles are then calculated, and 16' being deducted for the semidiameter of the sun, and 3o' for the deviation of the red rays, there remnins 22° 5o' for the ultimate an- gular distance of the halo, ■P. 2?6. Phenomenon 13. Parhelia or moek suns. " The most usual are at the same altitude as the sun. Among the prisms of snow there are often many heavier at one end than at the other, and consequently situated in a vertical direction : these cause a bright parhelion, with a tail, which cannot be above 70° long. I havejcad an ac- count of a halo seen in May, soon after sunrise, with par- helia in its circumference, which after two or three hours were more than a degree distant from it. This appearance arises from the coincidence of the sun's rays with the trans- verse section of the prism when they are nearly horizontal, and from their obliquity when the sun is elevated, causing a greater deviation, and throwing the parhelia outwards, as may be shown by an experiment on t^vo prisms. There are also accounts of parhelia above and below the sun, of an- thelia, and of a white horizontal circle. I do not undertake to explain these appearances, because I have never seen any of them, and I have not certain information of the circum- stances attending them." Rem Meiy on the principal organ of vision. A. P. 1704.261. H. 12. Petit on the vision of infants. A. P. 1727. 246. H. 10. *Porterfield on the external and internal mo- tions of the eye. Ediiib. med. essays. III. IV. Porterfieldon\heeye. 2 v. 8. Weiibrecht on the motions of the pupil. C. Petr. XIII. 349. Leroy on the accommodation of the eye to different distances. A. P. 1 755. 594. Mayer on the powers of sight. C. Gott. 1754. IV. 120. Roz. Intr. 1.241. The minimum .*' for detached objects, ]' for contiguou* objects in common day light : and in a different degree of illumination the angle varies as the 6th root of the light. Dalembert. A. P. 1765. - Maintains that the eye is not achromatic. Darcy on the duration of the sensation of sight. A. P. 1765. 439. Fontana dei moti dell' iride. 4. R. S. Roz. X. 25. On the changes of the eye. Nich. I. 305. Olbcrs de oculi mutationibus internis. 4. Gott. 1780. R.S. Herschel on the magnitude of the optic pen- cil. Ph. tr. 1786.500. A pencil of j,iyj of an inch was sufBcient, with a high magnifier. Herschel on the powers of the prismatic co- lours to heat and illuminate. Ph. tr. 800. 255. Ph. M, VII. 311. The greenish yellow rays the most effective. Venturi's optical considerations. Soc. Ital. III. 268. Finds the dispersion of the eye nearly equal to that of glass. Maskelyne on the effect of the different refran- gibility of light in vision. Ph. tr. 1789. 256. Thinks the effect too small to be perceived. Young on vision. Ph. tr. 1793- I69. CATALOGUE, — PHYSICAL OPTICS. 313 Young on the mechanism of the eye. Ph. tr. 1801. 23. Home's tacts relative to Hunter's intended Croonian lecture. Ph.tr. 1794. 21. On the muscularity of the crystalline lens of the sepia. Home's Croonian lecture. Ph. tr. 1795. 1. ■• Attributes the change of the eye to the cornea. Home's Croonian lecture. Ph. tr. 179G. 1. Abandons a part of the effect of the cornea. Home's experiments on persons deprived of the crystalline Jens. Ph. tr. 1802. 1. Ph. Ir. 1796. Brougham shows, after Musschenbroek, the effect of the refraction of light by the moisture of the eyelids. MoUweide on the dispersion of the e^-e. Gilb. XVn. 328. Perception of external Objects. On the apparent form of the heavens. Des- cartes, Desaguliers, Rowning, Smith, Priestley, Ferguson. Hooke on the horizontal moon. Birch. III. 503, 507. The true explanation. Molineux and Wallis on the apparent mag- nitude of the sun and moon. Ph. tr. IG8G. XVI. 314,323. Chesselden's account of a person who was couched. Ph. tr. 1728. XXXV. 447. Desaguliers on the horizontal moon. Ph. tr. 1736. XXXIX. 390. . As Molineux. Mairan on the apparent curvature of the heavens. A. P. 1740. 47. Gmelin de visione fallaci per microscopia. Ph.tr. 1745. XLIII. 387. The effect was probably owing to the inversion of the image by the microscope, causing the lights to fall on the contrary side with respect to external objects, so that the image appeared convex instead of concave. Y. *Berkelcy on vision. A good theory of erect vision, p. 312. Dutour on single vision. S. E. III. 514. VI. 241. H. 88. VOL. II. Euler on vision through spherical segments, N. C. Petr. XI. 185. fDunn on the horizontal sun and moon. Ph. tr. 17G2. 462. Jetze's remarks on the estimation of distance. Leipz. Mag. 1783. Gr. Fontana on the apparent brightness of objects. Ac. Sienn. V. 103. After BufTonr Robinson on single vision. Roz. XII. 329. Rittcnhouse on an optical deception. Am. tr, II. 37. A true explanation of Gmelin's experiment. Walter on erect vision. A. Berl. Deutsche abh, 1788. 3. Wells on single vision with two eyes. 8. Lond. 1792. R. S. Atkins on the horizontal moon. 8. Lond. 1793. Lambert on the place of images. Hind. Arch. III. 61. Explains some difficulties suggested by Barrow and others. Ware on a recovery of sight. Ph. tr. 1801. 382. Nich. 8. I. 57. Nicholson on the horizontal moon. Nich. VII. 236. fWalker on the horizontal moon, with re- marks by C. L. Nich. IX. l64, 235. The apparent distance of the horizontal moon is increased by Its fainmess. Shadows. Picard on shadows. E. P. VII. i. 185. Lahire on the strength of a penumbra. A. P. 1711. 157. H. 74. Maraldi on shadows. A. P. 1 723. 1 1 1 . H. -90. On shadows and penumbras. Lambert Pho- tometria. §. 1218. Monge on shadows and penumbras. S. E. IX. 1780. 400. Mathematical. Fourcroy on the shadow of a lattice. A. P. 1784. .555. s s 314 CATALOGUE, — PHYSICAL OPTICS. The lights appeared to answer to the shades ot a perfect shadow, except when part of the sun's disc was covered by clouds. Hence the effect must have been owing to the penumbra. Y. Jordan on the spectre of the Brocken. Ph. M. I. 232. A shadow falling on clouds. Gilb. XVII. 183 Castberg thinks the fata morgana at Reggio a shadow thrown on a mist. Colours, as aff'ecting the Ei/e. Waller's catalogue of simple and mixed co- lours. Ph, tr. 1686. XVI. 24. With specimens annexed, many of which now only serve as tests of the want of permanence of the colours employed. Ph. tr. 1716. XXIX. 449,451. A different colour being viewed with each eye at the same time, the result is not a mixed colour, but a contem- poraneous sensation of both. Sometimes the colours appear to succeed each other alternately. Y. Lambert's farbenpyramide. 4. Berl. 1772. Dicquemare on the vision of colours. Roz. VIII. 64. Prangens farben lexicon. 4. Halle, 1782. Opoix on colours. Roz. XXIIl. 402, Opitz sur les couleurs. MS. R. S. Mayer de affinitatecolorum. Op. ined. I. 31. Saussure on the light required for viewing dif- ferent colours. Mem. Tur. 1788. IV. 441. Says, that an electric spark in a Torricellian \acuum with a few drops of ether appears green to an eye near it, and red at the distance of a few yards. Probably some imperfection of the focus was concerned. Analytical determination of tints in painting. Journ. polyt. I. i I67. Barker's patent panorama. Repert. IV. 165, Montucla and Lalande. III. 565. Ocular Spectra and coloured shadows. Jurin in Smith's optics. Buifon on accidental colours. A. P. 1743. 147. H. 1. Aepinus's optical observations. N. C. Petv. X. 282. Roz. XXVI. Darcy. A. P. 1765. Beguelin on coloured shadows. A. Berl. 1767. 27. Beguelin on a deception of sight with respect to colour. A. Berl. 1771.8. Franklin's experiments and observations. Lond. 1769. 470. Roz. II. 383. Mongez on ocular spectra. Roz. VI. 481. Mongez on blue shadows. Roz, XII, 127. Godard on ocular spectra, Roz. VII. 509. VIII. 1, 269, 341. XXV. 219. Dicquemare on illusions of sight. Roz. XI. 403. Legentil on objects viewed through coloured Observations sur les ombres color^es.' 8. Par. glasses. Ann. Ch.X. 225. Herschel on the illumination of different colours. Ph. tr. 1800. 255. The greenish yellow rays the brightest. Aerial Perspective, and management of colours. Lambert on photometry, as subservient to painting. A. Berl. 1768. 80. Lambert on aerial perspective. A. Berl. 1774. 74. Pfannenschmid uber das mischen der farben. S.Hann. 1781. Prangens schule der mahlung. 8. Halle, 1782. Morgan.Ph.tr, 1785. 1782, Scherffer and Aepinus on accidental colours. Roz. XXVI. 175,273,291. *R. W. Darwin on ocular spectra. Ph. tr. 1786. 313. Explains some phenomena very satisfactorily fiora the contrast of sensations ; but others might be better understood from the analogy of coloured shadows, especially Ihe direct spectra. Darwin thinks, that the stimulus of light accord- ingly as its intensity becomes greater, produces, first simple spasmodic action ; 2, intermittrng spasmodic action ; 3, opposite spasmodic action ; 4, various successive actions; 5, fixed spasmodic action ; 6, paralysis. Mentions the effect of light coming, through the eyelifls, and a mode of observing the circulation of the blood in the eye. CATALOGUE. — PHYSICAL OPTICS, 315 On accidental colours. Roz. XXX. 407. Marat sur la lumi^re. Monge on coloured shadows. Ann. Ch. III. 131. Rumford on coloured shadows. Ph. tr. 1794. 107. Nich. I. 101. Shows that they are mere fallacies. Hassenfratz on coloured shadows. Journ. polyt. IV. xi. 272. Nich. VI. 282. VII. 23.. Impirfectiom of sight. Defects of focal distance. i-Myopibus juvamen. R. H. Hooke. Ph. coll. n. 3. p.5!j. Lahire on the use of spectacles. A. P. IX. 366.417. Desaguliers on telescopes for myopic per- sons. Ph. tr. 1719. XXX. 1017. On the effect of glasses upon the flexibility of sight. A. P. 1770. H.50. Spectacles. E. M. A. IV. Art. Lunettier. Henry on a person becoming short sighted in advanced age. Manch. M. III. 182. At 50, probably from reading a small print frequently without much light. » Richardson's patent spectacles. Repert. X. 145. With additional glasses, which raay be turned back at pleasure. Woliaston's improved periscopic spectacles. Nich. VII. 143, 241. Ph. M. XVII. 327. XVIII. 165. Meniscus lenses. Jones on Woliaston's spectacles. Nich. VII. 192. VIII. 38. Ph. M. XVIII. 6.5, 273. i-E. Walker on spectacles. Nich. VII. 291. Imperfection of focus. Lahire on the obliquity of the crystalline lens. A. P. IX. 399. Aepinus on the apparent diameter of a small hole. N. C. Petr. VII. 303. Telescopic appearances of stars. Herschel. Ph. tr. 1782. Stack on improving defective sight. Ir. trans. 1788. II. 27. Supposes myopia to depend on aberration. Irradiation. See diffraction, as affecting astronomical observations. Squinting. Buffon. A. P. 1743. 231. H. 68. Dutour. S. E. VI. 470. Darwin. Ph. tr. 1778. 86. Arnim on a case of double vision. Gilb. III. 249. Confusion of colours. Ph.tr. 1738. All objects appeared red to some persons who had eaten henbane roots. Huddart on persons who could not distin- guish colours. Ph. tr. 1777. 260. Harris, a shoemaker, could only tell black from white ; had two brothers equally defective : one of them mistook orange for green. Scott's imperfection of sight. Ph. tr. 1778. 613. Full reds and full greens appeared alike ; but yellows and dark blues were very nicely distinguished. Roz. XIII, 86. Monge. Ann. Chim. III. 13I. Dalton on some facts relating to the vision of colours. Manch. M. V. 28. His own case, agreeing with those of several other persons. He cannot distinguish blue from pink by daylight, but by candlelight the pink appears red ; in the solar spectrum the red is scarcely visible, the rest appears to consist of two colours, yellow and blue, or of yellow, blue, and purple. He thinks it probable that the vitreous humour is of a deep blue tinge : but this has never been observed by anatomists, and it is much more simple to suppose the absence or para- lysis of those fibres of the retina, which are calculated to perceive red ; this supposition explains all the phenomena. 316 CATALOGUE. — PHYSICAL OPTICS. except that greens appe»» to become bluish when viewed by candlelight ; but in this circumstance there is perhaps no great singularity. Debility of sight. Taper tubes assisting weak sight. Ph. tr. 1G68. ill. 727, 765. Biiggs's case of indistinct vision at night. Ph. tr. 1684. IV. 539. Dale on a blindness at night. Ph. tr. 1694. XVIII. 158. Cataract. Young on the extraction of the cataract. Ed. ess. II. 324. Employment for the Blind. Cheese's musical machine for the blind. S. A .V. 125. Bew on employment in blindness. Manch. M. I. 159. Berard's palpable mathematics for the blind. B. Melanges, 1 83. Some books have been printed in Paris in palpable cha- racters. Production of Colo'urs in Double Lights. See diffraction. Hooke on the colours of a bubble. Bircli. III. 29. Newton on the colours of thin plates. Birch. III. 247, 278. Lahire on the iris round candles. A. P. IX. 364. Langwith and Pemberton on supernume- rary rainbows. Ph. tr. 1723. XXXII. 241, 245. Mairan on diffraction. A. P. 1738. 53. H. 82. Daval on an extraordinary rainbow. Ph. tr, 1749. XLVI. 193. Confirming Langwith's account. " Within the purple of the common rainbow there were arches of the following colours. 1. Yellowish green, darker green, purple, a. Green, purple. 3. Green, purple." These colours were not visible near the horizon, although the bow was very bright there. Boscovich on a halo near the sun. A. P. 1754. H. S.2. Mazeas on the colours produced by friction. A. Berl. 1752. 248. S. E. II. 26. Euler on the colours of thin plates. A. Berl. 1752. 262. Due de Chaulnes on some experiments of Newton. Book 2, part 4. A. P. 1755. 136. H. 130. Gives an explanation, which is confuted by his ovm sug- gestion, that the same eflect ought to be expected from a lens as from a mirror. N. C. Petr. VI. 420. Biilfinger saw in 1741 three supernumerary rainbows within the primary one, the first red, the second blue, green, and red, the third dark and red. There are also three other similar observations. Dutour on coloured rings and on diffraction. S.E. IV. 285. V. 635. VI. 19. Dutour on the phenomena of thin plates, flaws, and thick plates. Roz. I. 368. II. 1 1, 349. V. 120, 230. VII. 330, 341. Dutour on fringes of colours. Roz. VI. 135, 412. Delaval on the colours produced by metak. Ph.tr. 1765. 10. Benvenuti de lumine. 4. Vienn. 1766. Boscovich's theory. Diequemaie. lloz. VIL 300. Observed a third iris beyond the second, as much weaker than the second as the second was than the first, and at the distance of its breadth, or at 1 of the distance of the first from the second : the red was internal, as in the secon- dary rainbow- Cockin on an extraordinary appearance in amist.Ph.tr. 1780. 157. CATALOGUE. PHYSICAl- OPTICS. 317 An oblong shadow, surrounded by two luminous and coloured arches : the centre being dark, yellow next, then dark, then a rainbow. Quotes Priestley and others for three parallel cases. Barker. Ph. tr. 1783. 245. 1787. 370. Some coronae. Stratico on the diffraction of light. Ac. Pad. II. 185. Hopkinson and Rittenhouse on inflection through cloth. Am. tr. II. 201. Nich. 1. 13. Comparetti de luce inflexa et coloritus. 4. Pad. 1787. R.S. Contains some curious experiments, but generally in very complicated circumstances. Brougham on inflection and colours. Ph. tr. 1796. 227. 1797. 352. Nich. 11. 147. Jordan's observations on light and colours, 8. Lond. 1799. 1800. R. I. Ace. Nich. IV. 78. Colours produced by distant glasses. Nich. II. 312. Probably from a slight difference in the thickness of the glasses, the rays twice reflected within the first glass only, in- terfering with the rays twice reflected in the second only. The analogy with the colours of thin plates is wholly foreign to the subject. Colours of steel. Nich. IV. 127. Young on some cases of the production of colours. Ph. tr. 1802. 387- Nich. 8. TV. 180. Young on the colours of thin plates shown by the solar microscope. Journ. R. I., 1.241. Nich. 8. III. 283. Young on physical optics. Ph. tr. 1804. 1. Nich. IX. 63. Messier on a lunar corona. M. Inst. V. 130. Anthelia. See Glories, Parhelia. Description of Dr. Young's Apparatus for exhiliting the Colours of thin Plates, by means of the Solar Micro- . scope. Journ, R, 7. I. 241. The colours of thin plates were observed by Boyle and Hooke, and more aecurately analysed by Newton : but lit- tle or nothing was added to the account that Newton gave of them, until some attempts were lately made to explain them, and to build at the same time on the explanation, the principal arguments in favour of a new system of light and colours. The phenomena themselves were very little known, except from Newton's description ; it had hap- pened but to few to observe them : and they had never been made conspicuous to a public audience in a form equally beautiful and interesting. * It appeared, however, that there would be little difficulty in applying the apparatus for representing opaque objects in the solar microscope, to the exhibition of these colours on a large scale : but several precautions were necessary, in order to obtain the most advantageous representation ; and, these precautions having been completely successful, it may beof some utility to give a detached account of them. The colours of thin substances must often have been seen in bubbles of water or of other fluids, and in the filin produced by a drop of oil spreading on water ; they were more particularly observed in the plates of talc, or of selenite, into which those substances readily divide. Sir Isaac Newton made his experiments principally on the colours of soap bubbles, and on those which are produced by the con- tact of two lenses. For inspecting the colours of soapy water, the most convenient method is that of Mr. Jordan. He dips a wine glass into a weak solution of soap, and thea holds it in a horizontal position against an upright substance, for example, a window shutter ; the filrn covering the glars being in a vertical position, the gravity of the fluid tends to make it thicker at the lower part, and it becomes every where gradually thinner and thinner, till at lengtii it bursts at the uppermost point. The colours assume, in this case, the form of hcrizontal stripes, similar to the rings which are to be more particularly described. It has been observed by Newton, that the colours thus reflected from a plate of a denser medium, are more vivid than when a plate of a rarer medium is interposed between two denser meiiiums. But the cause of this apparent dif- ference is, probably, the quantity of foreign light that is ge- nerally present in the experiment, reflected as well from the upper surface of the superior medium as frcm-the 1 Jwcr surface of the inferior, both these surfaces being often nearly parallel to the surface;; in contact. It becomes therefore desirable to remove this foreign light : this may be done efTectually, by employing one glass in the form of a prism, and coiituig the lower surface of the other with black sealing wax : the light reflected by the oblique surfacc ofthe first is thus thrown into another direction; and the. reflection of the inferior surface of the second is either destroyed or rendered imperceptible. And, with these.pre- cautions, the rings of colours, produced in the reflectediight. 318 CATALOGUE. — PHySICAl OPTICS. may be rendered a verjr beautiful object by means of the solar microscope. The most perfectly plane glasses are those which are used for Hadlcy's quadrants : one of these may be ground in the direction of the diagonal of its transverse section, so as to make a thin wedge or prism ; and the surface of the lens employed must be a portion of a sphere of from five to ten ■feet radius. The two glasses must be retained in their po- sition by means of three screws ; for, as soon as the pressure is remoTcd, they repel each other with considerable force ; and, for this reason, neither of them ought to be very thin, otherwise they will bend before they are sufficiently near. For adjusting the glasses of the microscope, it is conve- nient to fix them in a cylinder of sufficient size to project beyond the glasses and their screws, in order that they may be readily turned so as to reflect the light coming from the speculum, into the direction of the axis of the microscope : it is obvious, that in this case, they must be somewhat in- clined to the light, so that the focus of the whole image will never be equally perfect ; and, instead of being circular, like the rings themselves, their images on the screen will be oval. In this manner, eight or ten alternations of co- lours may easily be observed ; but their order and sequence is too complicated to be easily understood ; for they are really composed of an infinite number of series of rings of different magnitude, each series being formed by each of the gradations of light in the prismatic spectram, which, near the centre, are sufficiently separate to form distinct appear- ances, either alone or in combination ; but, after eight or ten alternations, are lost in the common effect of white light. For, when the glasses are illuminated by homoge- neous light only, separated from the rest by the refraction of a prism, or otherwise, the rings of each colour occupy, together with the dark spaces, the whole visible surface, their number being only limited by the power of the eye ,in perceiving objects so minute as the external ones be- come, in consequence of the rapid increase of the thick- ness of the plate of air near the edges of the curved surface. This circumstance being once understood, it is also capable of being illustrated in a manner still more elegant, by placing a prism a few feet from the microscope, leaving only a narrow line of its surface exposed to the incident rays, and then throwing the rings of colours on it, in such a direc- tion, that this line shall pass through their centre. Care being taken to exclude from the prismatic spectrum thus formed all extraneous light, it exhibits a most interesting analysis of these colours ; for the line consists of portions of the rings of all possible gradations of colour, each form- ing a broken line, but not of the same dimensions ; and, by tjie prismatic refraction, all these broken lines are sepa- rated and placed parallel to each other, on account of th« different refrangibility of the light of which they consist. Thus the broken line of the eiueme red, which consists of the longest portions, is least refracted ; the other reds fol- ' low, and are placed in contact with the first, and with each other, but, on account of the different magnitude of the portions, somewhat obliquely. The dark spaces also are in contact, and form a separation between each portion of light. In the same manner, the green follows the red, with little or no visible yellow. The blue and violet are , somewhat mixed : for these two colours are much less widely separated by thin plates than by the prism : for this reason, each portion of light formed by the contiguous lines of the different colours is bounded not by straight but by curved lines. It is evident, that, by drawing a line across this compound spectrum at any part, we may learn the component parts of the light constituting the rings at that part ; for the prism only spreads the colours in a direction transverse to this spectrum : and it may be observed, that after tlie eighth or tenth alternation, the light transmitted at each point is so mixed, that we may easily understand how it appears white. The colours of thin plates, as seen by transmission, are also easily exhibited in the solar microscope ; but, since it is utterly impossible to exclude the very great proportion of the light which does not appear to be concerned in their formation, they are never so brilliant as the colours seefi by reflection. Account of Dr. Young's Experiments and Calculations relative to Physical Optics. From the Journals of the Royal Institution, II. Dr. Young divides this paper into six sections. 1 . Ex- perimental demonstration of the general law of the inter- ference of light. 2. Comparison of measures, deduced from various experiments. 3. Application to the supernumerary rainbows. 4. Argumentative inference respecting the na- ture of light. 5. Remarks on the colours of natiual bodies, 6. Experiment on the dark rays of Ritter. The object of the first section is to demonstrate in a sim- ple and elementary manner, by the direct evidence of the senses, the truth of the genera! principle, which appears to connect an extensive class of phenomena by a clear analogy. This principle is, that where two portions of light arrive at any point by different routes very nearly in the same di- rection, they sometimes destroy and sometimes corroborate each other, according to the different lengths of their re- spective paths. This is proved by placing a slip of card in a sun beam admitted through a small aperture, its shadow being divided by alternate lines of light and shade w^ep CATALOGUE. — NATURE OF LIGHT. 319 the light is atlowcd to pass by both of its parallel edges : but when the light on either side is intercepted, the fringes dis- appear. The crested fringes observed by Grimaldi within the rectangular termination of a shadow, are also shown to depend on the mixture of the two portions of light inflected at the two edges of the object, which form the angle. In the second section, the appropriate interval for the brightest light is calculated from experiments of Newton, and from others which are new, and made under a variety of circumstances ; and the measure deduced from each ob- servation agrees with the mean without an error of more than a fourth or a fifth : if the principle had been erroneous, there is no reason why this distance should not have varied at least as much as the measures of the fringes, which were changedinthe ratio of 7 to i, or even in a much greater ratio. There is still, however, some doubt with respect to the cause of the slight difference observed, the measure of the interval being always a little larger in these experiments than in the observations of Newton on thin plates ; and the error is the greater as the tracis of the light is the more rectilinear. The proportions of the intervals for the different colours are also shown to be the same here as in the colours of thin plates : and it is observed that the form of Grimaldi's crested fringes, ought according to the calculation to be that of an equilateral hyperbola. The law, being thus established, is in the third place ap- plied to the supernumerary rainbows observed by Dr. Lang- with and others, which Dr. Pemberton has attempted to explain by a comparison with the colours of thin plates. The advantage which Dr. Young's explanation possesses is this, that he refers the colours to the light regularly re- flected, and Dr. Pemberton employs the light irregulariy dissipated, of which the effect must be perhaps some hun- dred times weaker. Comparing the two portions of light of which the extreme terminations constitute the common rainbow, he finds that they must cause, by their interfe- rence at other parts, rings of colours, agreeing perfectly with those which were observed in a particular instance by Dr. Langwith, if the drops of rain concerned were all between ■j^ and^Lj of an inch in diameter. Hitherto, Dr. Young observes in the fourth section, he has advanced in this Paper no general hypothesis ; and he attempts to infer, by a chain of experimental arguments, that refraction is not produced by an attractive force : since from the smaller length of the appropriate intervals of in- terference in a denser medium, it may be concluded that light moves more slowly as the medium has a greater re- fractive density. He remarks that the existence of the in- tervals of interference in an arithmetical progression, agrees so well with the nature aad properties of a musical sound, which consists in the succession of motions in contrary di- rections, at intervals which are also in arithmetical progres- sion, that we can scarcely avoid concluding that the nature of sound and of light must have a very strong resemblance. It was conjectured by Newton that the colours of all natural bodies are similar to some of the series of colours produced by thin plates. In this case, as Dr. Young has ob- served in a former paper, they ought to be divided into two, three, ormore portions, by prismatic refraction, as the colours of thin plates necessarily are ; and he has pointe€roth. M.V.ii. 171. :', :.,rhU^.<.n , ■ \i. V Deguignes's Chinese planispheres. Fig. S. E. 1785. X. App. . .< *^'Fo//as^ Si' >N 3 X 'C. * 2 X / Xk i '* x ;' :' X 1 A -B / c . X D :e F Ursa major Ursa major Cassiopeia Capella Algenib Algol Cygnus Lyra Draco Cepheus B, C, 5. C, 5. E, 5. D, 4. D, 4. E, 4. D, e. D, 8. C, D, 5, 6. D, 5. Andromeda E, 4, F, 3, 7 . Pleiades E,3. Arcturus B, 7- Aldebaran D, 3. Scorpio C, 9. Mcnkar ^ E,a. Libra B. 9, 0. (Cane pus) Corona borealis B,7. Aries F,3. Hercules C,7. Orion D, 2. Serpentarius C, 7. Castor C, 3. Aquila D,8. Procyon C. 2. Pepfasus F,7. Sirius C, 1. Fomalhaut F,9 Regulus B, 2. (Centaurus *•). Spica A, 8. (Crux t). 328 CATALOGUE. — ASTROXOiAIY, SYSTEMS OF STARS. When a spherical surface has been projected on a plane, it has been usual to consider it as viewed from a particular point, either infinitely remote, as in the orthographical projection, or situated in the opposite surface of the sphere, as in the sterecgraphical. The latter method produces the least distortion, and is the most commonly used, but even here, at the extremities of the hemisphere, the scale is twice as great as in the middle. Sometimes, another prin- ciple is employed, and the hemisphere is divided into seg- ments, by omitting portions in the directions of their radii' as if the paper were intended to be fixed on a globe ; and in the same form as if a spherical surface were cut in the di- rection of its meridians, and spread on a plane. If the number of these divisions be increased without limit, the result will be the projection, which is employed in the cir- cular part of this diagram, and in the same manner the zone on each side the equinoctial, being cut open by innumera- ble divisions, so as to be spread on a plane, will coincide with the two remaining portions. By these means the distortion becomes inconsiderable. In the common stereo- graphical projection indeed, the distortion would be of no consequence, if it represented always those stars only, which are at once above the horizon of a given place, for we actually imagine the stars in the zenith to be much nearer together, than when they are nearer the horizon, and the picture would appear to agree very well with the original : but their positions being continually changing, -the inconve- nience remains. It is not. however necessary, in projections of the stars, to refer them in any instance to a spherical surface. Among Doppelmayer's charts, published at Nuremberg, there are six, which represent the sides of a cube, on which the va- rious parts of the constellations are represented : the eye being probably supposed to be situated in the centre. Funck and others have represented the stars as projected on the inside of two flat cones. But the most convenient representation of this kind, and which would approach very near to the projection here employed, would be to con- sider the eye as placed 4n the centre of a hollow cylinder, so proportioned that all the circumpolar stars should be re- presented on one of its flat ends, and all those which rise and set on its concave surface ; or if it were desired to have a division without referring to any particular latitude, the circular part might extend to the limits of the zodiac, and the parallelogram, into which the cylinder unfolds, might comprehend all the stars to which the planets approach. The horizon, and other great circles, would form lines of :<;'arious and contrary curvatures. Systems of Stars, Nebulae, and Double Stars. BuUialdi monita duo. Ace. Ph. tr. 1665—6. 1. 387. On the nebulosa Andromedae. Account of nebulae lately observed. Ph. tr, 1716. XXIX. 390. Halley. Ph. tr. 1720. XXXI. '22. Says, that it would be hard to place 13 points on a sphere at the distance of the radius. Kaestner shows, that it would be impossible. Dissertat. Math. Derham on nebulous stars. Ph. tr. 1733. XXXVIII. 70. Wright's theory of the universe. Kants Allgemeine naturgeschichte. Lambert Photometria. §. 1139. 1140. Thinks the milky way as it were the ecliptic of the fixed stars. That the greater stars belong to the solar nebula, the other nebulae being confused together in the milky way. Figure of the nebula in Orion, by Messier. A. P. 1771. 458. A figure of the nebula in Orion, supposed to be changed. Roz. XXII.34. I'igotton a nebula, and on double stars. Ph. tr. 1781. 82, 84. Herschel's catalogue of double stars. Ph. tr. 1782. 112. Herschel on the construction of the heavens. Ph. tr. 1784. 437. 1785. 213. 1802. 477. Nich. 8. V. 75. Magnified figures of ne- bulae. 1784. 1785. Conjectures, that the milky way is the projection of our nebula, and that the sun has a motion towards its node, near Cepheijs, and Cassiopeia, 1784. In acircle of is' dia- meter 588 stars were counted ; if these wen; at equal dis- tances in a cone, the length of the cone must have beea 497 times their distance. From calculations of this kind a figure of the nebula is drawn, showing a section passing through its poles at right angles to the line of the nodes. The right ascension of the pole is 166°, its polar distance i8°; 1785. CATALOGUE. ASTRONOMY, STARS. 329 Iterschel's second catalogue of double stars. Ph. tr. 1783. 40. Herschel's 1000 new nebulae. Ph. tr. 178G. 457. Herschel's second thousand of new nebulae. Ph.tr. 1789. 212. Herschelon nebulous stars. Ph.tr. 1791-71. Stars surrounded by a faint light, which Dr. Herschcl thinks must be a shining fluid. Herschel. Ph.tr. 17<)5.46. Found 600 stars in a circle 15' in diameter. This state- ment has been much mistaken by some authors. Herschel's 500 new nebulae. Ph.tr. 1802. 477. Herschel on the changes of double stars. Ph. tr. 1803. 339. 1804. 353. Nich. VII. 210. Cassini's verification of Herschel's double stars. A. P. 1784. 33 i. Asks if they are satellites. Differs a little from Herschel respecting the colour of the stars. Michell. Ph. tr. 1784. 35. Conjectures that some stars revolve round others. Lenionnier on the nebula in cancer. A. P. 1789.610. A catalogue of the stars. The double star zeta lyrae some- times appears accompanied by several little stars. Account of Dr. Herschel's paper on llie changes thai have happened, during the last twenty five years, in the fetative situation of double stars ; tcith an investigation of the cause to which they are owing. From the Juur- ' vals of the Royal Institution. II. Dr. Herschel devotes this paper principally to the con- sideration of the second class of the systems into which he has divided the sidereal world. After cursorily remarking, with respect to the solar system, as a specimen of the first class, which, among the insulated stars, comprehends the sun, that the affections of the newly discovered celestial bodies extend our knowledge Of the construction of this insulated system, which is best known to us ; he proceeds to support, by the evidence of observation, the opinion, which he has before advanced, of the existence of binary sidereal combinations, revolving round the conimon centre of gravity. Dr. Herschel first considers the apparent effect of the motion of either of the three bodies concerned, the two stars, and the sun with its attendant planets ; and then states the arguments respecting the motions of a few only VOL. II. out of the fifty double stars, of which he has ascertained the revolutions. The first example is Castor, or alpha Geminorum : here Dr. Herschel stops to show how accu- rately the apparent diameter of a star, viewed witli a con- stant magnifying power, may be assumed as a measure of small angular distances ; he found that ten different mir- rors, of seven feet focal length, exhibited no perceptible dif- ference in this respect. In the case of Castor no change of the distance of the stars has been observed, but their angular situation appears to have varied somewhat more than 4:)° since it was observed by Dr. Bradley, in 175Q ; and they have been found by Dr. Herschel in intermediate positions at intermediate times. Dr. Herschel allows that it is barely possible that a separate proper motion, in each of the stars and in the sun, may have caused such a change in the re- lative situation, but that the probability is very decidedly in favour of the existence of a revolution. Its period must be a little more than 342 years, and its plane nearly per- pendicular to the direction of the sun. The revolution of gamma leonis is supposed to be in a plane considerably inclined to the line in which we view it, and to be per- formed in about 1200 years. Both these revolutions are re- trograde ; thatofcpsilon Bootis is direct, and is supposed to occupy 1081 years, the orbit being in an oblique position with respect to the sun. In zeta Herculis Dr. Herschel ob- served, in 1802, the appearance of an occultation of the small st.-ir by the larger one : in 1782 he had seen them separate ; the plane of the revolution must therefore pass nearly through the sun ; and this is all that can at present be determined respecting it. The stars of delta serpentis appear to perform a retrograde revolution in about 375 years : their ajiparent distance is invariable, as well as that of the two stars which constitute gamma virginis, the last double star which Dr. Herschel mentions in this paper, and to which he attributes a periodical revolution of about 708 years. Y. Distance and magnitude of the Stars. See Practical Astronomy. Gregory on the annual parallax of the stars. Birch, in. 225. Suggests the observation of the distance of two neigh- bouring stars. Roberts ou the distance of the fixed stars, after Hugens. Ph. tr. l694.XVni. 101. Flamstead. Ph. tr. 1701. XXII. 815. I' u 330 CATALOGUE. — ASTRONOMV, STARS. Faneied he had foundan annual parallax of 40" or 45" ; tlie polar distance being greatest in June. Cassini on the magnitude and distance of the fixed stars. A. P. 17 17^ 256. H. 62. Halley. Pli.tr. 1720. 1. Says, that the apparent diameter of Sirius cannot be seve- ral seconds, as Cassini makes it. Halley on the infinity of the sphere of fixed stars. Ph. tr. 1720. XXXI. 22. Asserts that the equilibrium could not be maintained without an infinite number. Bradley. Ph. tr. 1728. XXXV. 637. Tliinks he would have perceived an annual parallax if it had amounted to 1". Clairaut on the hest determination of the parallax of the stars. A. P. 1739. 3o8. H. 42. Maskelyneon finding the annual parallax of Sirius. Ph. tr. 1760.889. Conjectures, from La Caille's observations, that it may be 8" or 0". Lambert's Photometria. Supposing Saturn to reflect i of the Kght that falls on him, ' and to be equal in brightness to a star as large as the sun, the distance of the star will be 425100 times as great as that of the sun, and its apparent diameter 0"' 16"". Hence we may assume the distance about 500000. Michell on the probable parallax of the stars. Ph. tr. I767. 234. From their light. jVlichellon the distance and magnitude of the fixed stars. Ph. tr. 1784. 35. Observes, that a star of 500 times the diameter of the sun ought to recall the particles of light from an infinite distance, and thinks that a sensible eflect might be produced by a star 22 times as large in diameter as the sun : tlie attraction of the sun ought to retard it -xi^r,^ in an infinite distance. The light of a stsr of the sixth magnitude is to that of the sun as one to 100 billions. Herschel on the parallax of the fixed stars. Ph. tr. 1782. 82. With figures of their telescopic appearances. Makes Lyra subtend 3553". Herschel on the sua and fixed stars. Ph. tr. 1795. 46. Some stars, if as remote from each other as Sirius is from the sun, should be 42000 times as far off as Sirius. At this distance Sirius would scarcely be visible. Herschel on the power of penetrating into space by telescopes. Ph. tr. 1 800. 49- Nich. IV. 496. A cluster of 5000 stars barely visible as a mass, by the 4» feet telescope, must be above 11 millions of millions of miU lions of miles off. Proper motion of the Star^. Bernard's chronology of the places of the stars. Ph. tr. 1684. XIV. 567. Delisle on the proper motion of the stars; A, P. 1727. 19- Cassini on the proper motion of the stars-. A. P. 1738. 273. H. 70. Hornsby on the proper motion of Arcturus. Ph.tr. 1773.93. Mayer de motu fixarura proprio. Op. ined. I. 175. Herschel on the motion of the sun and solar system. Ph. tr. 1783. 247. Supposes the motion, not slower thaathat of the earth iiv its orbit. Changeable Stars and new Stars. Hevelius's new star in theswan. Ph.tr. l665i I. 372. A second of the third magni- tude. Ph. tr. 1670. V. 2087. Further accounts Ph. tr. I67I. VI. 2197,2198. BuUialdi ad astronomos monita duo. Acc.Ph.tr. 1665-6. I. 381. A new star in the whale. Anthelme's new star in the swan. Ph. tr» 1670. V. 2092. A. P. I. 87. Cassini on the changeable star in the whale's neck. A. P. I. 87. X. 422. Kirchiiis de Stella nova in collo cygni. Misc. Berl.Ph.tr. 1715.226. CATALOGUE. ASTROVOSir, STARS. 331 History of ^new stars observed wilbin 150 Pigott on the changes of two stars. Ph. tr. years. Ph. tr. 1715. XXIX. 354. Maraldi on the changeable star in the whale. A. P. 1719-94. H.eei. Maupertuis on the changesofstars.Ph.tr. 1732. XXXVII. 240. A. P. 1732. H. 85. Barker on the mutations of stars. Ph. tr, 1760. Produces 5 authorities to show that Sirius was formerly leddish, and even redder than Mars, and proves that it is now white. Herschel on the periodical star in the whale's neck. Ph.tr. 1780. 338. The change was before obserred to happen about seven times in six years. Herschel on changeable stars. Ph. tr. 1792. 24. Herschel on the changes of stars. Ph. tr. 1795. 166. Herschel on the changes of alpha Herculis, and on the rotation of stars. Ph. tr. 1796. 452. Its period flo i days. Goodricke on the variation and period of the light of Algol. Ph. tr. 1783. 474. 1784. 287. The period 2d. 20h. 4S' S6". Goodricke on the changes of beta lyrae. Ph. tr. 1785. 153. Varies from the 3d magnitude to the 4th or 5th : the period isd.ioh. '■' i Goodricke on the changes of delta Cephei. Ph. tr. 1786. 48. It vurici from 31 to 41 or the sth magnitude. The pe- riod 5d. 8h. 37'|. The variation of Algol is not always equal in degree. Englefield, Palitch, and Bruhl on the star Algol. Ph. tr. 1784. 1,4,5. Pigott on the changes of eta Antinoi. Ph. tr. 1785. 127. From. the third or fourth to the fourth or fifth magnitude : period 7d. 4h. as'. Pigott on changeable stars in general. Ph. tr. 1786. 189. 1797. 193. In Sobiesky's shield^ and in the northern crown. Huber on the star Algol. N. Act. Helv. I. 307. Lalande on the star Algol. A. P. 1788. 240, Assigns 2d. 20h. 49' 2" as its period. Wurmon Algol. Zach. Ephem. II. 210. Its period 2d. 20h. 48'. 58".? from 15 yeai^ observation. •Twinkling of the Stars. Garcin on the twinkling of the stars. A. P. 1743. H. 28. Observes, that at Bender Abassi in Asia, where the air is very pure and dry, the stars have a light absolutely fixed. Michell. Ph. tr. 1767. 234. Attributes the twinkling to the irregularity of the emis- sion of light. Sun. Joh. Fabricius de maculis in sole observatis. Wittemb. I6II. M.B. The discoverer. Epistolae ad Velserum de solis maculis. 4. Augsb. 1612. Sc/ieineri rosa ursina. f. l6S0. M. B. Cassini on the sun's motion. Boloirna. Ace. Ph. tr. 1672. VII. 5001. Derham on the solar spots. Ph. tr. 171I. XXVII. 270. Thinks them the clouds of volcanos, afterwards becom- ing faculae. Crabtrie, in 1840, calls them e-^halations like clouds. 281. Jiauseft Theoria motus solis. 4. Leipz. 1726. Krafftde distantia inacularuma soIq. Comm. Petr. VII. 279. A. Elder de motu solis determinando. C. N. P. XII. 273. f Horsley on the sun's atmosphere. Ph. tr. 1767. 398. 332 CATALOGUE. — ASTRONOMY, PLANETS. Kaestner formulae ad motum solis. C. N. Gott. I. 1 10. Spots. A, P. Index. Art. Soleil. A. Wilson on the solar spots. Ph. tr. 1774. 1. 1783. 144. Maintains, that they are excavations, against Lalande. Marshall on the solar spots. Ph. tr. 1774. 194. Wollaston on the solar spots. Ph. tr. 1774. 329. Lalande on the sun. Brugnatelli Bibliot. fisic. I. 55. Lalande's answer to Wilson. Ph. tr. 1776. Bode Anicitung. Sect. 6l6. Mayer on the sun's motion. Ac. Palat. IV. Herschel on the sun's motion. Ph. tr. 1783. 247. Herschel on the sun and fixed stars. Ph. tr. 1795. 4f). Nich. I. 8. Ph. M. V. Thinks the sun an opaque body, possibly inhabited, covered with an atmosphere in which clouds of a luminous matter are floating, and the spots interruptions of these clouds ; of these clouds he thinks there are two strata, of which the upper only is luminous, and the under stratum he supposes to protect the body of the sun from their heat. Herschel on the nature of the sun. Ph. tr. 1801. 265, 354. Endeavours to show that the variation of heat of diflerent years is owing to the more or less copious supply of fuel in the sun, which constitutes his spots. Pi'evost on the motion of the whole solar system. A. Berl. 1781. 418. Towards the corona borealis. The idea was first sug- gested by Mayer. King's morsels of criticism. 4. Lond. 1736. R. S. On the sun, as surrounded by luminous matter. Schroter liber die sonne. 4. Erf. 1789. Fischer on the sun's spots. Bode.. Jahib. 1791. Wurm on the degree of certainty of the sun's motion. Bode. Jabrb. 1795. lichtenberg. Erxleb. naturl. Appears to doubt of the sun's motion. Von Hahn on the sun and its light. Bode. Jabrb. Ph. M. XI. 39- JVoodward on the substance of the sun. 8. Washington. 1801. R.S. Dr. Herschel thinks,' that the motion of the sun is proba- bly directed towards a point, of which the right ascension is 243° 52' so", and the north polar distance 40° 22', 1805. Solar Atmosphere, or zodiacal Light. Cassini. A. P. VII. II9. VIII. 193- Derham on a glade of light. Ph. tr. I706, XXV. 2220. March 20. Moving with the heavens. Mairan Traite de 1' aurore boreale. 1731. A, P. 1747. 371. H. 32. Lemonnier. A. P. 1757. 88. Lalande. Astronom. Sect. 845. Dicquemare on a zodiacal light. Roz. III. 330. Murhard on the atmospheres of the sun and planets. Ph. M. VI. 166. Melanderhielm on solar and planetary at- mospheres. Gilb. HI. 96. f Regnier on the zodiacal light. Zach. Mon. corr. VI. 14. Planets, in general. Kepleri astronomia nova. f. Prag. I609. Lays down his great laws. Cassini on the atmospheres of the heavenly bodies. A. P. VIII. 193. Maupertuis on the figures of planets. Ph. tr. 1732. XXXVII. 240. A. P. 1732. H. 85. Euler on the contraction of the orbits of the planets. Ph. tr. 1749. 203. 1750. 357. Maintains that such a contraction has taken place, attri- butes it to resistance, hence argues, that the world has had a beginning, and must have an end. Lemonnier on the planetary atmospheres. A. P. 1757.88. CATALOGUE. ASTRONOMY, PLANETS, 333 Herschel on the rotation of the planets. Ph. tr. 1781. 115. Ducaila on the rings of the planets. Roz. XIX. 386. Ximenes on the density of the planets. Soc. Ital. III. 278. Sclnoter on the planetary atmosphere^. Bode Jahrb. 1793. Getting. Anz. 1792. n. 86. *Murhard on the planetary atmospheres. Ph. M.VI. 166. Melanderhielm on planetary atmospheres. Gilb. m.96. fVoigt on the rotation of the planets. Gilb. VII. 232. tOnOphion.Gilb. XI. 482. Supposes that the comet of 1759 may be considered as a planet beyond the Georgian planet. Benzenberg on a law of planetary dis- tances, Gilb. XV. 169. On the progressive distances of the planets. Zach. Mon. corr. VII. 74. Particular Planets. Mercury. Wallot sur le passage deMercure. Ph.tr. 1784. 312. Attributes a horizontal refraction of .276" to Mercury, equivalent to 2fl".4 in time. Gibers on Schrbter's observations of Mercury. Zach. Mon. corr. I. 574. Schrotet thinks it revolves in 24h. or 24h. 5'. Lalande on the motion of Mercury. M. Inst. V. 442. In the transit of Nov. 1802, Mr. Bugge could find no traces of an atmosphere. Journ. R. I., I. Von Zach says, that the mean apparent diameter of Mercury is not so much as 7", probably little more than 5". Venus. Bianchini Hesperi phaenomena. f. Ro:ti. 1728. Ace. Ph. tr. 1729 XXXVI. 158. Makes the period of diurnal rotation 25 days. Lurcher Memoire sur Venus. 8. R. S. Maskelyne. Ph. tr. 1768. 355. Distinct marks of an atmosphere, or of inflection, or of both. Wallot. Ph. tr. 1784.312. Attributes to Venas a horizontal refraction of .205", equi- valent to 8" or o" in time. Schrbter on the atmosphere of Venus. Ph. tr. 1792.309. Ph. M.I V. Asserts, that Venus has a twilight of more than 4° ; and mountains 4 or 5 times as high as ours. Schroter iiberdie Venus. 4. Erfurt. 1793. Schrbter's further observations on Venus. Ph. tr. 1795. 117. Seems to have made very numerous observations ; per- sists in the rotation of 23h. 2i' ; says, that the mountains are generally obscured by the atmosphere. Schruters Aphroditographische fragmenten. 4. Helmst. 1796. R. S. Schrbter's plate of the height of the moun- tains in the earth, the moon, and Venus. Journ. Phys. XLVIII. 459- Herschel's observations on Venus. Ph. tr. 1793. 201. Denies the existence of high mountains, and the accuracy of Schroter's observations on this planet in general. Al- lows that Venus revolves, and not slowly ; that its atmo. sphere must be considerable, from the excess of its cusps above a semicircle, which Schroter first observed ; but re- marks, that Schroter, in considering it, has neglected the effect of the sun's penumbra. Thinks Venus a little larger than the earth : her disc appears brightest at the margin. Lalande on the motion of Venus. M. Inst. ,V. 350. The Earth, in its relations to the Celestial Bodies. Figure of the earth . See Geograph v. Precession of the equinoxes.' See Laws of Gravity. Gregory on the controversy of A ngelis and Riccioli, respecting the motion of the earth Ph. tr. 1668. III. 693. 334 CATALOGUE. — ASTROJTOMy, PXANETS. Bernard's history of the obliquity of the ecliptic. Ph. tr. 1684. XIV. 721. Louville on the change of place ,#f the eclip- tic. A. P. 1716.1-1. 48. Act. Lips. 1719. •281. Halley on the change of latitude of some stars. Ph. tr. 1718. XXX. 736. Most stars indicate a change of about 20' since the time of Hipparchus. Godin on the diminution of the obliquity of theechptic, A. P. 1734. 491- Legentil on the obliquity of the ecliptic. A. P. 1743. 67. H. 121. 1757. 180. Lemonnier on the nutation of the earth's axis. A. P. 1745. 512. H. 58. Bradley's discovery. Bradley on an apparent motion of the stars. Ph. tr. 1748. XLV. 1. The nutation of the earth's axis. ■Euler on the approach of the earth to the 5un.Ph.tr. 1749. XLVI. 203. Euler. Ph. tr. 1750. XLVI. 357. Queries if the earth's rotation is uniform : says, that the action of Jupiter accelerates its motion in its orbit, and infers, that its rotation must probably also be accelerated. . Lalande on the change of latitude of the stars. A. P. 1758.339- H. 87. Lalande on the obliquity of the ecliptic. A. P. 1762. 267. H. 130. 1780. 285. Diminishing about 66" in a century-. Lalande. Pli. M. IX. II. Makes the secular change 36", 38", or 4l", the obliquity 1 Jan. 1800, 23° 27' 58". Smeaton and Maskelyne on the menstrual parallax. Ph.tr. 1768. 154. Maskelyne on the nutation of the earth's axis. Astron. obscrv. 1776. Ilornsby on the obliquity of the ecliptic. Ph. tr. 1773. 93. Dimmishing about 58" in acetitury. K'asiner on the obliquity of the ecliptic. Astron. abh. iii. JVallot sur i'oDliquite de I'e.liptique. 4. R. S. Mars. Herschel. Ph. tr. 1781. 115. Siderial rotation of Mars 21 h.39' 22". Herschel on Mars. Ph. tr. 1784. 223. Juno. Harding's Juno is supposed to be somewhat nearer to the sun than Ceres. Dr. Herschel finds that neither this body nor either Ceres or Pallas^ subtends any measurable angle- Dec. 1804. It was discovered i Sept. 1S04. Pallas. Olbers's planet, . discovered 28 March 1802. Ph. M. XII. 287. Lalande on Olbers's planet. Journ. Phys. LV. 65. Ph. M. XIII. 279- Nich. VIII, 222. Burckhardt's parabolic orbit of Pallas. Ph. M. XII. 371. Burckhardt's elements of Pallas. Ph. M. XIV. 186. ' On Olbers's Pallas. Nich. 8. II. 20. Journ. R. I., L93. See Ceres. Ceres. On a new planet. Zach. ^Jon. corresp. IV. 53. Discovered 1 Jan. 1801. On the planet Piazzi. .Tourn. Phys. LIV. 165, 469. On the nature of Ceres and Pallas. Zach. Mon. corn VI. 290. Olbers thinks they may be fragments of some larger planet. Von Zach on Ceres. JNich. 8. II. 213. Ph. M. XVI. 49. Accounts of Piazzi's Ceres. Nich.,8. I. 72, 193, 284, 317. I|,48.'Ph, M. X^I. 62. Bode on Piazzi. A. Bqrl., 1801. M. 132. Herschel on the two lately discovered celes- tial bodies. Ph. tr. 180.'. 213. Nich. 8. IV. 126. Lalandc's orbits of the new planets. Nich. VIII. 222. Journ. R. 1., I. 69, 93. / eATALOGUE.- Jupiter, ASTRONOMY, PLANETS. Cassini on Jupiter's rotation. Ph. tr. 1665-6. I. 143. Period 9h. 58'. Maclaurin on the changes of Jupiter. Ed, ess. I. 184. Herschel. Ph. tr. 1781. Schroteron Jupiter. Beytrage. I. ' Schroter on the rotation of Jupiter. Roz. XXXII. 108. Saturn. Pound.Ph.tr. 1718.773. Observed that the ring was double. Maupertuis. Ph. tr, 1732. 240. Derives Saturn's ring from the tails of cornels. Heinsius de annuio Saturni. 4. Leipz. 1745. Varelaz on the disposition of Saturn's ring. Ph. tr. 1774. 113. The west end appeared always the more luminous : some bright points were seen at the extremities. Messier's observation of points in the ring of Saturn. A. P. 1774. 49> H. 55. On the ring of Saturn. Roz. XI. 77. 38 f. Bugge on the node of Saturn. Ph. tr. 1787. 37. Laplace on Saturn's ring. A. P. 1787- 249. A figure of Saturn with his ring. Herschel. Ph.tr. 1790. 1. Herschel on the rotation of Saturn's ring. Ph.tr. 1790. 427. Herschelon the ring of Saturn. Ph. tr. 1792. 1 . A good figure of the ring with its division. Herschel on a quintuple belt of Saturn. Ph. tr. 194. 28. Fig. Herschel on the rotation of Saturn. Ph. tr. 1794. 48. In lOh. 16' o". 4. Herschel. Ph.tr. 1805. Makes the figure of Saturn not an elliptic spheroid; but a little inclined to a cylindrical form. Dciuc on the ring of Saturn, Roz. XL. 101, Robison. Enc. Br. Observes, that the inner edge of the ring of Saturn should revolve in iih. 16', the outer in I7h. lo'. Schroeter doubts the rotation of the ring. Georgian Planet. Herschel's account of a planet. Ph. tr. 1781. 492. Herschel on the magnitude of the Georgian planet. Ph. tr. 1783. Apparent diameter 4". Herschel on the Georgian planet and its satellites. Ph. tr. 1788. 364. Boscovich on the new planet. Soc. Ital. 1.55. Bode von dem peu entdeckten planelen. 8. Berl. 1784. Lexell Recherches sur la nouvelle planete". Petersb. Wurm, Geschichte des neuen planeten. 8. Gotha, 1791. Secondary Planets. Supposed SattMite of Venm, Short.Ph.tr. 1741. 646. A.P. 1741. H. 124. ' Mairan. A. P. 1762. l6l. Lambert. Ac. Berl. 1773. "^22. ' Bode Jahrbuch. 1777, 1778. Chambers's Cyclopaedia, by Rees, Moon. Lunar atmosphere. Sec eclipses. Hooke's miciographia. Ch. 70. Hevelii selenographia. f. Dantz. 1667. R. I; Cassjiii Carte de la lune. Paris. R. S. Is 19 inches in diameter. Remained long unpublished. Louville on a lunar atmosphere. A. P. 1715.- 89. Cassini. 137. H. 54. Delisle. 147. H. 47. Liesmann Bresl. Samml. 1722. Goth. Mag.. I. i. 189. On a perforation. 336 CATALOGUE. ASTRONOMY, PIANETS. Fouchy. A. P. 1734. H. 68. Fouchj de atmosphaera limaii. Ph. tr. 1739. XLI. 261. Thinks that there is not enough to produce a refraction of l"ot2". Lcniarinier Seleiiographie. Ace. A. P. 17^5. H. 65. Weidler. Ph. tr. 1739. XLI. 228. •Observed lightning in a lunar eclipse. After Halley. Ml/lilts Gediinken uber die atmosphare des nioudes. 4. 1746. Mayers cosmographische nachrichten. 1748. 379- On the lunar rotation and atmosphere. Mayer von den Niirnbergischen moudkugeln. 4. 1750. Nuremb. Mayer's map of the moon. Op. ined. I. Euler on the moon's atmosphere. Ac. Berl. 1748. 103. Dunthorne on the acceleration of the moon's motion. Ph. tr. 1749. XLVI. l62. About 10" in 100 years. Short on a gap in the mountains surround- ing the lunar spot Phito. Ph. tr. 1751. 164. Boscovich de lunae atmosphaera. 4. Rom. 1753. Vienn. 1766. Dunn on a lunar atmosphere. Ph. tr. 1762. 578. Infers an atmosphere from a haziness, seen about Saturn emerging from behind the moon. Rlurdocli's comparison of the sun and moon. Ph. tr. 1768. 24. Attributes great density to the moon. Uiloa on a perforation in the moon. Ph. tr. 1779. 105. Rozier 1780. See eclipses, Herschel on the mountains in the moon. Ph. tr. 1780. 507. Makes the highest only a mile and three quarters. Herschel on lunar volcanos and other changes. Bode Jahrbuch, 1782, 1789- Herschel on three volcanos in the moon. • Ph.tr. 1787. 229. Looking like a coal coreted wiih a thin coat of ashes : one of them 3 miles in diam::ter. The inequalities-of (he moon are easily visible by the light reflected from the earth. Herschel. Ph. tr. 1792. 27. Luminous points in the moon seen in an eclipse. Herschel. Ph. tr. 1794. 39. Few or no signs of a lunar atmosphere in an eclipse. Beccaria on Ulloa's eclipse. Roz. XVH. 447. Thinks the spot volcanic : himself observed a spot in 1772. Aepinus on volcanos in the moon. N. A. Petr. 1784. II. H. 50. Goth. mag. I. iv. 155. Quotes Hooke. Girtanner on Herschel's lunar volcanos. Roz. XXX. 472. Schrtiters Beytrage. 8. Berl. 1788. Schroter on a spot in the moon. Roz. XXXIII. 313. Schroters Selenotopographische fragmenteu. 2. V. 4, Gott. 1791. 1802. R. S. Schroter on the lunar atmosphere. Ph. tr. 1792.309. Observed a very faint appearance of twilight. Schroter on the mountains of the moon. Roz. XLVIII. 459. Fig. Ph. M. IV. 393. Schroter. Ph. M. XV. Finds lunar mountains 4000 toises, or nearly 5 miles high, and such a twilight as indicates an atmosphere 300 toises high. Bode on a luminous point in the dark part of the moon. A. Berl. 1788. 204. On lunar volcanos. Bode Jahrbuch, 1792. Lichtenberg on the lunar spots. Goth. Mag. I. i. Kant on the lunar spots. Berl. Monathschr. Marz, 1793. *Russers globe of the moon. Lond. R. I. Maskelyne on Wilkins and Stretton's obser- vations of a light in the dark part of the moon. Ph. tr. 1794. 429. Stretton might have seen only Aldebaran, which was eclipsed by the moon at the time ; Wilkins could scarcely have been so much mistaken. CATALOGUE. — ASTRONOMY, COSIETS. 337 K'astner. Hind. Arch. II. 8. Averroes and Bacon thought of the moon, as Euler did of »U opaque bodies, that its substance was made luminous by the sun's rays. Mr. Leslie has lately advanced the same opinion. *xVlurhard. Ph. M. VI. l66. Rather inclines to suppose a very rare lunar atmosphere. Laplace and Delambre have found from the latest calcu- lations that the moon's mass is of the earth. Zach. OS. 5 Mon. corr. Lapl. Mec. eel. The moon's distance varies from 54 to 7 8 semidiameters. Satellites of Jupiter. Galilei nuntius sidereus. Op. II. i. Mrtm niundus Jovialis. 4. Niiremb. 1614. Herschel on the magnitude and rotation of Jupiter's satellites. Pli. tr. 1797. 332. The third is by much the largest, the first and fourth equal, the second a little smaller. They all present the same face to Jupiter throughout their revolutions. Satellites of Saturn. For the ring, see Saturn, Hugenii systema Saturninum. 4- Hague, 1659.. Cassini's discovery of two of Saturn's sateUites. Ph.tr. 1673. VI II. 5073. Pound on the satellites of Saturn. Ph. tr. 1718. XXX. 768. A sixth satellite announced. Herschel. Ph. tr. 1789. Herschel on a sixth and seventh satellite of Saturn. Ph.tr. 1790.1. -Herschel on Saturn's satellites and ring. Ph. tr. 1790.427. Herschel on the rotation of Saturn's fifth sa- telHte. Ph.tr. 1792. 1. I'resents always the same face to Saturn. .», Satellites of the Georgian Planet. Herschel on two satellites of the Georgian planet. Ph. tr. 1787. 125. 1788. S64. VOL. 11. Herschel on four additional satellites of the Georgian planet. Ph. tr. 1798. 47. Comets. Senecae quaestiones naturales. vii. Bartholinm de cometis. 4. Copenh. 1665. M. B. Lubinietz Theatrum cometicutn. f. Anist. 1668. M.B. Jiew/u cometographia. f. Dantz. 1668. M.B. Hooke's lectures and collections. 4. lG78. Cometa. Figures, p. 2, 3. Halleii astronomiae cometicae synopsis. Ph. tr. 1705. XXIV. 1882. Lord Paisley on the comet of 1723, with fi- gures. Ph. tr. 1724. XXXni.50. Hein&iuinher den comelen. 4. Petersb. 1744, Mairan on the tails of comets. A. P. 1747- 411. Dunthorne against the identity of the comets of 1106 and l680. Ph. tr. 1751. 281. Winthrop on the tails of comets. Ph. tr. 1767. 132. Wiedeburg Ubcr den cometen. Jeua, 1769. Williamson on comets. Am. tr. I. 133. Oliver on comets. 8. Salem, 1772. Laplace on the orbits of comets. S. E. 1773. 503. Dionis du Sejour sur les cometes. A. P. 1774. H. 78. Dionis du Sejour Essai sur les cometes. Par. 1775. R. S. Euler on the effects of comets. N. C. Petr. XIX. 499. Lexell on the comet of 1770. A. P. 1776. 638. Ph. tr. 1779- 68. Calculates that it moves, as Prosperia supposed, in an elliptic orbit, its period about 5i years, its aphelion a little beyond the orbit of Jupiter. *Pingre cometographie. 2 vol. Par. 1783. R. L X X 338 CATALOGUE. — ASTRONOMT, LAWS OF GRAVITY. Deguignes. S. E. X. 1785. App. 39. Enumerates two or three hundred comets mentioned by- Chinese authors. Maskelyne on the comet expected in 1788. Ph. U-. 1786. 426. Hallcy admitted doubts lespecting this comet in hif se- cond edition. Bode. Ac. Bcrl. 1786. 1787. Borfe on comets, with a map. 8. 1791. R-I- Bode's Jahrbuch. 1795. Bode's plate reduced. Rees's cyclop. I. Art. Astronomy. K'dstner's gedichte. Vermischte Schriften. 69. Miss Herschel and Dr. Herschel on a new comet. Ph. tr. 1787- 1, 4. Miss Herschel on a comet. Ph. tr. 1794. I. Olbers on the comet expected in 1788. Leipz. Mag. 1787. iv. 430. Von Zach on the expected comet. Goth. gel. zeit. 1788. xiii. Delucon comets. Journ. Phys. LIV. 25?. Rudigeron the tails of comets. Gilb. II. 99. O. Gregory's astronomy, c. 21. The comet of 1680 had a tail at least lOO milKons of miles long. Laws of Gravity in GeneraL See Centra] Forces. Hooke on gravity in wells. Birch. II. 70^. **Newtoni piincipia. Keill de legibus virium centripetarum. Ph. tr. 1708. XXVI. 174. De maximis et minimis in motibus coelesti- bus, secundum Demoivre. Ph. tr. 1719- XXX. 952. Cassini on vortices. A. P. 1/20. Biilfinger on bodies moving in a vortex. C. Petr. I. 245. Moli^res on the resistance of ether. A. P. 1731. H. 66. Maupertuis on the law of attraction. A. P. 1732. 343. H. 112. Sigorgne on the impossibility of vortices. Plu tr. 1740. XLI. 409. • Boscovich on attraction to a centre, C. Bon. II. iii. 262. Euler de resistentia aetheris. Opusc. I. 295. Euleron perturbations. A. Berl. 1763. 141. Elder on the problem of three bodies. A. Berl. 1763. 194. Euler on the motion of three bodies in aright hne. N. A. Petr. 1785. III. 126. Clairaut on the system of the world accord- ing to gravitation. A. P. 1745. 329. Clairaut on the law of attraction, in answer to Buffbn. A. P. 1745. 529, 578, 583, Buffon on the law of attraction. A. P. 1745. 493,551,580. A. P. 1745. 557. Clairaut fancied, from the motion of the moon's apogee,, that a part of the force of gravitation varied inversely as the fourth power of the distance. BufTon endeavoured to con- fute the opinion. Clairaut afterwards found his mistake, by a more accurate calculation. Kratzenstein's spring steelyard, for measur- ing the force of gravity. N. C. Petr. II. 210. Lalande Exposition du calcul astronomique^ 8. Par. 1762. Ace. A. P. 1762. H. 136. Simpson's miscellanies. Dalembert Opuscufes. BossiU sur la resistance de I'ether. 4. Char- leville, 1766. Condorcet on the motions of three attractive bodies. A. P. 1767. H. 93. Frisi on the laws of gravity. C. Bon. V, i. ii. Frisi de gravitate universali. 4. R. S. Lambert on the problem of three bodies. A. Berl. 1767.353. CATALOGUE. — •ASTRONOMY, LAWS OF GRAyiTT. 339 Laplace on the system of the world. A. P. 1772. ii. 267. H. 87. 1775. 75. H. 39. Berthier's opinions. Roz. Intr. I. 658. IV. 310., 433, and elsewhere. His retraction. Roz. IX. 460. On gravitation. Roz. I. 245. Mayeri opera inedita. R. S. Lexell on Lambert's theorem respecting cen- tral force. N. A. Petr. 1783. I. 140. Ximenes on the de'nsity of the planets. Soc. Ital. III. 278. Melanderhielui on the diminution of the sun and the resistance of ether. N. Act. Helv. 1.98. Supposes that they compensate each other. Hellins on a problem in physical astronomy, wuh an appendix. Ph. tr. 1798. 527. On perturbations. Hellins's second appendix. Ph. tr. 1800.86. Benzenberg on falling bodies. Gilb. XI. I69, 470. XIV. 222. XVII. 476. Found that 144 feet, Fr. were described in 116'". 85, in- stead of 1 86'".86. Woodhouse on problems in physical astro- nomy. Ph. tr. 1804.219. €ee Primary Planets. Equilibrium and Figure of Gra- vitating Bodies. Maupertuis sur les figures des astres. 8. Par. 1732. Clairaut Traite de la figure de la terre. 8. Paris. M. B. Ace. A. P. 1742. H.86. Clairaut's explanation in answer to Frisi. Ph. tr. 1753. 77. St. Jatjues de Silvabelle on the solid of the greatest attraction. S. E. I. 175. D'Arcy on the attraction of spheroids. A. P. 1758.318. Canterzano on the attraction of a sphere. C. Bon.V. ii. 66. Laplace on the equilibrium of a gravitating fluid in rotation. S. E. 1773. 524. La|ilace on the attraciion of spheroids and the figures of the planets. A. P. 1782. 113. H. 43. Lagrange on spheroids. A. Berl. 1773. 121. 1775. 273. 1792. 258. Hutton's determination of the point of great- est attraction of a solid. PIi.tr. 1780. 1. Lcgendre on the figure of the planets. A. P. 1784. 370. Legendre on the attraction of homogeneous spheroids on a distant point. S. E. X. 1785.411. Legendre's example of the attraction of a spheroid. A. P. 1788. 463. Legendre on the figure of the planets. A. P. 1789. 372. Krafft upon Lagrange's researches on elliptic spheroids. N. A. Petr. 1784. II. 148. Euler on the centrifugal force of the earth. N.A. Petr. 1784. II. 121. Says, that if the whole earth were fluid it could not re- main at rest without intestine motion. But would there not then be friction, and must it not be retarded? ATaring on infinite series. Pli. tr. 1791. 146. Examples of the attraction of circles and spheroidj. Gtrlach on the figure of the earth, and oa the motion of its axis. 8. R. S. Trembley on the attraction of spheroids. A. Berl. 1799. 68. Pasquich on the effect of ellipticity on pen- dulums. Zach. Mon. corr. II. 3. ' See also Geography. Orbits of the Primary Planets. Ilalley's direct mode of determining the pla- netary orbits. Ph. tr. I676. XI. 683. Varignon on the central forces of the planets. A. P. 1700. 224. H. 78. 540 CATALOGUE.' — ASTRONOMV, LAWS OF GRAVITV. Gregory de orbita Cassiniana. Ph. tr. 1704. XXIV. 1704. Keill problematis Kepleriani solutio. Ph. tr. 1713. XXVIII. 1. Cassini on the reconciliation of vortices with the Keplerian laws. A. P. 1720. Machin's solution oi' Kepler's problem. Ph. tr. 1738. XL. 205. Eukri theoria motuum planetarum. 4. Beil. 1744. Dalembert on the planetary orbits. A. P. 1743. 365. Determination of the apsidal angle. Ph. tr. 1748. XLV. 333. Silvabelle on the nodes and inclinations of the planetary orbits. Ph. tr. 1734. 383. •f-Maclaurin on the variation of the obliquity of the ecliptic. Ed. ess. I. 173. Walmesley on perturbations. Ph. tr. 1736. 700. 1761. 273. Stewart's solution of Kepler's problem. Ed. ess. II. 105. J. A. Euler on the planetary perturbations. A.Berl. 1739.338. Jeaurat's directdetermination of the place of a planet. S. E. IV. 601. liagrange on Kepler's problem. A. Berl. 1764. 204. Lagrange on the secular variations of the nodes and inclinations. A. P. 1774. 97. H^ 39. The obliquity of the ecliptic has diminished for i2000 years, and will diminish for at least 2000 more, reckoning from 17 CO. Laplace on the secular equations of the pla- nets. A. P. 1772. i. 343. H. 67. 1784. 1. 1787. 267. Laplace on the theory of Jupiter and Saturn. A. P. 1785. 33.1788.201. Lalande on the diminution of the obliquity of the ecliptic. A. P. 1780, 285. H. 38. M»ket it f^" annuaUj. Fuss on finding the true anomaly. N. A. Petr. 1783. III. 302, Robison on the orbit of the Georgian planet. Ed. tr. I. 305. Duscjour on Kepler's problem. A, P. 1 790, 401. Schubert on the obliquity of the ecliptic. N. A. Petr. 1792. X. 433. Schubert finds the mean obliquity of the ecliptic 24° 1 1'; its limits 20" 34', and 27° 48': thatitwill continue to di- minish for 4900 years, and will then be 22° 53' ; but he observes that some little inaccuracy has been introduced into the calculation, the mass of Venus having been made too great. Wurm on the perturbations of Mars. Zach. Mon. corr. VI. 549. Ivory on Kepler's problem. Ed. tr. V. 203. Brinkley's series for the Kejilerian problem. Ir. tr. VI. 349. Brinkley on the Keplerian problem. Ir. tr. IX. 83. A new mode of calculation, and a comparison of all former methods. Robison thinks, that Laplace's data are determined to* arbitrarily, in his calculations respecting the Georgian planet. Orbits of the Secondary Planets. Ciairaut on the lunar orbit. A. P. 1743. 17. H. 123. 1748. 421. C/azVfltt^Theorie de la lune. 4. Petersb. 1752. M. B. Dunthorne on the moon's motion. Ph. tr. . 1747. 412. A correction for the sun's anomaly. Walmesley on the effect of ellipticity on a satellite. Ph. tr. 1758. 8O9. The distance of the sun deduced from the theory of gravity, Edinb. 1763. JBy Stewart. Euler on. the lunar motions. A. Berl. 1 7^3. 180,221. CATALOGUE.' — ASTRONOMY, LAWS OF GRAVITT. 341 Euler on the satellites of Saturn. A. Berl. 1763. 311. Jlioycr Theoria lunae. 4. Lend, 1767. R. S. Eukri iheoria motuum lunae. 4. R. S. J. A. Euler on the variation of the moon. A. Berl. 1766. 334. Lunar motions. Emerson's miscellanies. 139- Pemberton on the computation of the lunat paralia-Y. Ph. tr. 1771. 437. Lagrange's prize memoir on the secular equa- tion of the moon. S. E. 1773. 1. Rather doubts the fact ; thinks an ether would explain it) if it existed. Laplace suspects a small irregularity in the action of gravity, p. 37. Laplace on the secular equations of the planets and satellites. A. P. 1784. 1. 1783. Enata page. 1786. 235. Shows the true cause, 1785. Laplace on the satellites of Jupiter. A. P. 1788.249.1789.1,237. Laplace on the lunar motions. Zach. Mon. corr. IL 157- IV. 113. VL 272. Ph. M. IX. 7. Laplace has deduced a nutation of the lunar orbit, from the oUate figure of the earth, amounting to 6" or 7 *, and an inequality of 6" depending on the longitude of the node. Note of Laplace's two lunar equations of 180 years. Ph. M. XIL 278. Kraftt on Eukr's lunar tables. N. A. Petr. 1787. V. 289. Biirg on the lunar motions. Zach. Mon. corr. IV. 275. The sun's place difTers about 9" at the moon's quadra- tures. Orbits of Comets. Halleii astronomiae cometicae synopsis. Ph. tr. 1705. XXIV. 1882. Bouguer. A. P. 1733. 331. H. 71. Clairaut Th^orie du mouvement des cometei. Clairaut on the planetary perturbations of comets. A. P. 1760. H. 128. Dalembert Opuscules. II. Boscovich on the orbits of comets, S. E. VI. 198,401. Laplace on the orbits of comets. S. E. 1773. 503. A. P. 1780. 13. H.41. Fuss on the perturbations of comets. S. E. X. 1785. 1. Lagrange on the perturbations of comets. S. E. X. 1785. 65. Sir II. Eiiglejield on the orbits of comets. 4. Lond. 1793. R. S. Projectiles from the Moon. Biot on the velocity of bodies falling from the moon. B. Soc. Phil. n. 68. Poisson on the velocity of a body thrown from the moon. B. Soc. Phil. Giib. XV. 329. Rotation of the Earth and Planets. Wallis on the possible change of the meri- dian. Ph.tr. 1699. XXI. 285. -f-Parent on the direction of rotation to the left. A. P. 1703. H. 14. Euler on the precession of the equinoxes. A. Berl. I. 749, 289. Euler on the rotation of the heavenly bodies. A. Berl. 1759- 265. St. Jacques de Silvabelle on the precession of the equinoxes. Ph.tr. 1754.385. Dalembert on the effects of a dissimilitude of meridians. A. P. 1754. 413. H. II6. 1768. 1.332. H. 95. Dalembert on the motion of heavy bodies, combined with the rotation of the earth. A. P. 1771. H. 10. Dalembert sur la precession des equinoxes, Walmesley on precession. Ph.tr. 1756.700. Walmesley on the effect of the tides on the earth's rotation. Ph. tr, 1758, 809. 342 CATALOGUE.— -ASTaONOMY, TIDES. Simpson on the horary displacement of the earth's equator. Ph. tr. 1757. 486. Correcting Silvabelle and Walmesley. Lalande on the change of hilitude of the stars. A. P. 1758. 339- H. 87- Darcy on the precession of the equinoxes. A. P. 1759. 420. J. A. Euler on perturbations from want of sphericity. A. Berh 1765. 414. Murdoch's comparison of the sun and moon. Ph. tr. 1768. 24. Makes the moon very dense. Precession of the equinoxes. Emerson's miscellanies. 180. Gerlach on the figure of the earth, and on the motion of its axis. 8. R. S. Laplace on the precession of the equinoxes, A. P. 1777.329 Laplace on the rotation of the heavenly bo- dies. M. Inst. L 301. Laplace on the fall of a body from a great height. B. Soc. Phil. n. 75. See Practi- cal astronomy. Milner on the precession of the equinoxes. Ph. tr. 1779- 505. Finds it by a simple method 2l" fl"' for the effijct of ttie sun. There seems to be some confusion respecting compound rotation. Heniiert et Frisius de uniformitate motus diurni terrae. 4. Petersb. R. S. Ace. N. A. Petr. 1783. L 132. Vince on the precession of the equinoxes. Ph. tr. 1787.363. The solar portion 2i" 6'", supposing the earth of uni- form density, and the ellipticity ^J^ ; but in reality about Bode on the displacement of the earth's axis. A. Berl. 1797. 100. Ph. M. XL 310. Trembley on tlie precession of the equinoxes. A. Berl. 1799. 131. M. Young on Uie precession of the equinoxes. Iv. tr. Vn. 3. Vou Zach on the precession of the equinoxes. Zach. Mon. corr. IL 500. The lunisolar precession so'.aagg, the real observed pre- cession 50".o5i or rather 50".0982. Robison doubts the accommodation of the period of the moon's rotation to that of her revolution, and principally because her axis is not perpendicular to her orbit. Ele- ments, 518. Theory of the Tides. Aerial Tides. See Meteorology. For the particular phenomen;-., see Practical Astronomy. Hydrology. Ph. tr. abr. IL IV. VI. VIII. X. fWallis on the tides. Ph. tr. 1665-6. I. 263,297. 1668. III. 652. Deducing the tides from the earth's centrifugal force, in revolving round the common centre of gravity of the earth and moon. Wallis's answer to Childrey. Ph. tr. 1670. V, 2068. Philips. Ph.tr. 1668. III. 656. Observes, that the monthly variations of the tides are is the versed sines of the times. Childrey 's remarks on Wallis's theory. Ph. tr. 1670. V. 2061. Hooke. Birch. II. 475. Illustrated the ascent of a tide in a narrow channel by the agitation of mercury in a triangular vessel. Newtoni Principia. Halley's Newtonian theory of the tides. Ph. tr. 1697. XIX. 445. Observes, that great variations in the time of the tides may be produced by shoals. Prize essays on the tides, by Cavalleri, Ber- noulli, Maclaurin, and Euler. A. P. Prix. IV. vi. . . ix. The la«t three are also in Le Seur's Newtoo. Elder on a new kind of oscillations. C. Petr. XI. 128. Euler on the equilibrium of the sea. A. Petr. 1780. IV. i. 132. Wargentin on the tides. Schw. abh. 1753. 165, 249. 1754. 83. CATALOGUE. — ASTRONOMY, TIDES. 343 Waltnesley on the effect of the tides upon the earth's rotation. Ph. tr. 175S. 8O9. Lalande on the tides. A. P. 1772. i. !297. H. 1. Lalande Trait6 du flux et reflux. Printed in the Astronomy. Note. Ph. M. VII[. 134. Lalande Astronomic. Laplace on the tides. A. P. 1775.73. 1776. 1790. 45. Mecan. celeste. Laplace on some high tides. Nich. VL 239. Agreeing with the theory. fSaint Pierre Etudes de la nature. Deduces the tides from the melting of the circumpolar ice. Suremain's remarks on St. Pierre. Roz. XLT. 239- Villelerque on St. Pierre's hypothesis. Journ. Phys.XLIV.(L)99. Chiminelli's researches on the tides. A. Pad. IL 204. Robison. Enc. Br. Art. Tides. Observes, that the smallest solar retardation of the tides is »o the greatest, as the difference of the solar and lunar influ- ence is to their sum : that is, from Dr. Maskelyne's obser- vations at St. Helena, as 37 to 87 ; and the sun's effect is therefore to that of the moon as 2 to 4.96. Woods on St. Pierre's hypothesis. Ph. M. VIIL 134. A Simple Tlieory ofihe Tides. Y. It has been sufficiently demonstrated by different authors, that the form which the sea would assume, in consequence of the moon's attranion, if the earth were at rest,is thatof anob- longellipticspheroid.ofwhichtheaxiswouldexceedtheequa- torial diameter by :ibout 10 feet, the whole height of the tides being 5 feet ; but when the effects of the earth's rotation are considered, the investigation becomes much more difficult. The spheroid of equilibrium, revolving continually, causes the position of the horizon of any place to vary periodically, so as to perform, in the course of a lunar day, two complete oscillations, resemLling those of aeycloidal pendulum; and the surfac* of any detached portion of the sea, so inclosed by perpendicular and parallel shores, as to be capable of permanent oscillations, is drawn after this variable horizon, in the same manner, as a pendulum suspended from a cen- tre, which is itself performing its own vibrations ; the midtjl* of the sea, or lake, remaining nearly at rest. Now it may easily be shown, that a pendulum suspended from a centre, which performs regular small vibrations of its own, may vibrate in the same time with the centre,, provided that the extent of its vibrations be to that of the vibrations of the centre, as the length of the thread carrying the centre is to the difference of the lengths of the two threads ;. for, in this case, the situation of the thread of tha pendulum will be always the same as that of a simple pen- dulum of the length of the thread carrying the centre. When this thread is the longer, the vibrations will agreo in direction, but, when shorter, their directions must be contrary to each other ; and, it appears to be in the latter case only, that the pendulum will always tend to acquire such a state of permanent vibration, wi.atever may have been its original situation, although it may sometimes ap- proach rapidly to it, even when the thread of the pendulum, is the shorter. If the breadth of a lake, or sea, from east ta west in miles, be I, and its depth d, the time required for its complete oscillation, or the time, in which a wave might b pass over twice its breadth, will be in hours, and the lengths of the synchronous pendulums being as the squares of the times, the extent of the oscillations of the lake will be to the extent of those of the temporary horizon, as the square of half a lunar or solar day, to the difference be- tween that time, and the time required for. the oscillation of . the lake ; the motions either agreeing or differing in direc- tion, accordingly as tiie oscillation of the lake would occupy, more or less time than half a day. Supposing the luminaiy vertical, the extent of the oscillation of the temporary sphe- roid will be, for the lunar tide 5 s.c, c being half the breadth of the lake in degrees ; and for the solar tide, 2 s.c ; whentc. .the height of the tides at the eastern and western shores will 3030000rf , 2830000;/ . , be 3 s.c -— ,and2s.c ; — —respectively, 3030000ci— /'i 283000Ud — bb ■' These become infinite, when i=:i7-!0v'<'. and lfi82v'(/, and in these cases, the magnitude of the tides would be only limited by the resistances; this must hajipcn, ifrfzrl, when bzzi 1740, or 2 5° for the lunar tide ; if dzzg, when ir:5220, and if d^, or 100 fathoms, when i:=s8^, or betweerr %° and g°. If d were 1> and i 6000, the lunar tide would be about ,48 feet, and if b were 8216, or go' of the equator, it would be ,42, At the eastern and western shores of a sea or lake, 90" irt- diameter, the ascent and descent of the water would be pre- cisely the same as in every par< of an open ocean, of the same depth ; and the tides of such an ocean may, th '.refore, be calculated, by making 6^8216, and the height, A wijt 3-ii CATALOGUE. ASTRONOMY, CELESTIAL APPEARANCES. be 303ii id id 3U3(/ — 3953 d — 13'"'(i — 14 I4A ; whence d zz 13A meiit apparens des corps celestes. 2 v. 4. Par. 1786. . . R. S, j—^; andif rf is less than 13, h being negative, the Euler on the degrees of light of the heavenly place of low water itiust be immediately below the lumi- nary. , . \3h 14/1 and d:z or h+3 fe+a The same conclusion may be obtained by very different means ; considering the tide, in comparison with the sur- face of the spheroid ot equilibrium, as a wave, which is 10 produce by its propagation, a sufficient velocity of ascent and descent, for the actual motion of the tide upon a sphere. Thus, if d were 52, the height of the tide would be 6= feet, that is li feet above the spheroid ; and such a wave being naturally propagated with a velocity twice as great as that of the tide, the water would ascend or descend, with a velo- city sufficient for its propagation with a velocity twice as great as the velocity of rotation, and, since it is actually ex- posed to the same force, for a time twice as great, a qua- druple velocity will be generated, which will be equal to the relocity of ascent, or descent, required for the tide of 6| feet, which is four times as much elevated as the supposed wave. It appears, therefore, that for any given magnitude of the elevation h, there are two values of rf, accordingly as we sup- pose the time of high water, or of low water to coincide with that of the moon's southing : thus, if /i^a, d must be either gl or 3i ; and it is difficult to determine for the open ocean whether the time of high or of low water, is nearest to the transit of the luminary. For a sea 4000 miles broad, the depth must exceed S miles, in order that the time of high water may coincide with that of the greatest elevation of the horizon ; and, if it be less than this, the time of high water must be that of the greatest depression, that is, on the eastern shore, about 5 hours after the moon's southing ; on the western, about 7 ; and, if the sea were narrower, these times might vary from the fifth to the third, and from the seventh to the ninth hours, respectively. The effects of re- sistance will also accelerate the tides of the latter kind, and in this manner, tlie theory may be perfectly reconciled with observation. Celestial Appearances in general, with reference to the Earth. Baxter's matho. Hugeuii cosiiiotheoios, 4. Hag. I69B. Foiitaielle sur la pluralite des mondes. 12. 1686. ParLalande. 1800. Diunh du SejourTTa'iic analiiiqiie des motive- bodies. A.Berl. 1750.280. Makes the light of the sun equal to that of 6560 candles at 1 foot distance, liiat of the moon to a candle at 71 feet, of Venus, to a candle at 421 feet, and of Jupiter to a candle at 1620 feet : partly from Bouguer's experiments. Hence the sun would appear like Jupiter, if removed to 131 000 times his present distance. Appearances of the Stars. Twinkling. See Fixed Stars. Bradley on a newly discovered motion of the fixed stars. Ph. tr. 1728. XXV. 637. The aberration. It was observed by Flamstead, but not understood. Lalande on the change of latitude of the stars. A. P. 1758. 339- H. 87- Lagrange on the variations of the earth's or- bit. A. P. 1774.97. H. 39. On the changes of latitude and longitude of the stars, p. 164. The change of obliquity affects the right ascension a little, but not the declination. Appearances of the Sun. Seasons, Day and Night, Twilight. La Caille on the length of twilight at the Cape. A. P. 1751. 544. H. 158. Bergmann on twilight. Schw. Abh. 1760. 237. Opusc. V. 331. VL 1. Lambert Photomelria. §. 987. The limit of visible twilight is when the sun is a"i belovr the horizon. In order to find the time when the twilight is shortest, as Rad : Sin. X.at : ; S. 6° is" : S. Sun's declina- tion, south. Appearances of the Primary Planets. Halley on the appearance of Venus in the daytime. Ph.tr. 1716. XXIX. 466. Godin on the apparent motions of the planets in epicycloids. A. P. 1733. 285. H. 67. CATALOGUE. — ASTEOXOMV, CELESTIAL APPEARAXCES. 345 Kieson the greatest brightness of Venus. A. Berl. 1750. 218. Ubsher on the disappearance of Saturn's ring. Ir. tr. 1789. III. 135. Bode on the disappearance of Saturn^s ring. Ph. M. XV. 219. Calkoen ou the disappearance of Saturn's ring. Ph. M. XV. 222. Appearances of the Secondary Planets. Moon. Cassini on the libration of the moon. A. P. 1721. 168. H.53. Lalande on the lunar Ubration. A. P. 1764. 555. H. 112. Dionis du Sejour on the faint light of the new moon. A. P. 1776. This light is a minimum at 43" elongation, a maximum at 0° and at 69° ; at 90° about half the greatest quantity. Kastner on the phases of the moon. Com- mentat Goit. 1780. III. M. I. Harvest moon. O. Gregory's astronomy, C. .\vi. Cavallo. IV. 143. Appearances of the Sun and pri- mary Planets jointly. ' Transits. See Practical Astronomy. Appearances of the fixed Stars and Moon. Occultations, Vince's Astronomy. O.Gre- gory's Astronomy. Appearances of the Sun and Moon jointly. Eclipses. Flamstead's method of calculating eclipses. Moore's system of Mathematics. I. VOL. II. Plantade and Clapiers on a lunar eclipse from the earth's penumbra. A. P. 1702. H. 73. PIi. tr. 1706. XXV. 2240. In a total eclipse ol the sun, 12 May, 1706, a streak of light was observed 0" or 7" belbre the sun's disc : hence Flamsfead infers a lunar atmosphere jJjth of the moon's diameter in height : but this might have been from oblique reflection. Duillier on a total eclipse of the sun. Ph. tr. 1706. XXV. 2241. A whiteness was seen round the moon, one twelfth of her diameter in extent ; and a white halo 4 or 5 degrees in diameter beyond it : this vanished soon after the sun re- appeared : hence he hifers a lunar atmosphere of 130 geo- graphical miles in height, and deduces the halo from the solar atmosphere. Many stars were seen during the eclipse. Halley on a total eclipse of the sun seen in London. Ph. tr. 1715. XXIX. 245. A ring of light surrounded the moon, onesixth of her dia- meter in extent, which seemed to proceed rather from a lunar than from a solar atmosphere : and a line of light was seen lingering behind. Some lightning too was seen. Lahire on the ring seen in total eclipses of the sun. A. P. 1715. 161.H.47. Delisle's experiment on a ring of light like that which appears in eclipses. A. P. 1715. 166. H. 47. Delisle and Lahire produced an appearance nearly of th same kind, by interposing an opaque substance, as a ball of stone, between the eye and the sun : but here it might be objected, that the earth's atmosphere supplied the light. Louville's geometrical mode of calculating eclipses. A. P. 1724. 63. H. 74. Gersten methodus calculi eclipsium. Ph. tr. 1744. XLIII. 22. Ph. tr. 1748. XLIV. 490. C. Bon, I. 267. A brown light was seen beyond the sun's casps, in an eclipse nearly annular. Lalande on the effect of ellipticity in eclipses. A. P. 1756. 364. H. 96. 1763. 413. Lalande on a kinar eclipse. A. P. 1783. 89. Adds 36" to the earth's shadow for the effect of tl?e at- mosphere. Y y 346 CATALOGUE. — TRACTICAL ASTRONOMY, Boscovich de solis ct lunae defectibus. 4. 1760. R. I. Jeaural on the projection of ecli|)ses. S. E, IV. 818. Witchell on the shadow of a spheroid. Ph. tr. 1767. 28. Dionis du Sejour. A. P, 1775. Attributes a refraction of about i" to the lunar at- mosphere. Dionis du Sejour on the quantity of light falling on the moon in eclipses. A. P. 1776. Lemonnier on the eclipse of 24 June 1778. A. P. 1778. 62. H. 34. With a good figure of UUoa's spot, and of the yfhole lu- minous appearance. Lemonnier on total eclipses of the sun, and on the lunar atmosphere. A. P. 1781. 243. H. 47. Finds a refraction of 24" i. Marcorelle on the heat of the sun in an echpse. Roz. XIV. 352. Ulloa on a total eclipse of the sun. Ph. tr. 1779. 105. There was a great appearance of light round the moon, which seemed to be agitated, and emitted rays to the dis- tance of a diameter ; it was reddish next the moon, then yellowish. Stars of the first and second magnitude were seen, those of the first for about 4 minutes. A minute and a quarter before the emersion, a small point was visible near the disc of the moon. From the ruddy colour of the light, the ring is referred to the moon's atmosphere : the spot to a fissure in the moon's substance. Such a fissure must have been above 40 miles in depth. Herschel on an eclipse of thesun.Ph.tr. 1794. 39. Schroter on the solar eclipse. Ph. tr. 1794. 262. Goudin sur les eclipses du soleil. 4. Par. 1800. On calculating eclipses. Vince's Astronomy. Irradiation and diffraction in eclipses. See Physical Optics. The nodes coincide with the syzygies in 6890 lunations, witii an angular error of only s' \ in pooo years. Cavallo, from Gregory. The nodes and apsides return to the same position, after about 83 revolutions of the nodes. Appearances of the primary and secondary Planets conjointly. Eclipses of Jupiter's Satellites. Short. Ph. ir. 1753. 268. Lalandeon the effect ofellipticily in eclipses. A. P. 1756. 364. H. 96. 1763, 413. Appearances of Comets. Euler on the effects to be apprehended from a comet. N. C. Petr. XIX. 499. Lambert on the apparent orbit of comets. A. Berl. 1771. 35'i. Flanetary Worlds, Appearances with respect to different Planets. Buffon and others on the heat of the celes- tial bodies. Roz. IX. 7. Ducarla on the rings of planets. Roz. XIX. 386. Practical Astronomy, in general. Cassini on the precautions necessary in astro- nomical observations. A. P. 1736. 203. Simpson's calculation of the advantage of a mean of several observations. Ph. tr. 1755. 82. Geography. Emerson's cyclomathesis. IX. Lalande on the use of interpolations in prac- tical astronomy. A. P. 1761. 125. H.ga. Lalandt Exposition du calcul astronomique, 8. Paris, 1762. Ace. A. P. 1762. H. 136. Rosters handbuch der practischen astrono- niie. CATAtOGJJE. — PRACTICAL ASTRONO^T. 347 Lagrange on taking the mean of observa- tions. M. Taur. 1770. 3. V. ii. 167. Lagrange on the simplest mode of express- ing a given number of facts. A. P. 1772. i. 513. H. S3.. Euler on Lagrange's mode of taking a mean of observations. N. A. Petr. 1785. III. 289. Bergmann on interpolations in astronomy. Opusc. VI. I. Lcrgiia Principi di geografia astronomico- geonietrica. Verona, 1789- K. S. Vince's practical astronomy. 4. Lond. 1790. R. S. Treinbley on taking a mean of observations. A. Berl. 1801. M. '29- Astronomical Apparatus, in gene- ral. See Geometricallnstruments. Htvelii organographia astronomica. f. Ghent, 1G73. Acc.Ph.tr. 1673. 6150. Hooke's animadversions on Hevelius's ma- china coelestis. 4. London, 1674. Lect. Cutl. Maskelyne's remarks. Ph. tr. 1764. 348. Due de Chaulnes on the improvement of astronomical instruments. A. P. 1765. 411. H. 65, Magellan Trait^ sur dcs in&trumens d'astro- mie. E. M. PI. Vn. Astronomic. PI. 15. Ludlam on Bird's method of dividing. 4. Lond. Montucla and Lalande. IV. 334. Troughton on some astronomical instru- ments. Zach. Mon. corr. II. 907 Obscrvatorin. Godin's convenient observatory. Mach. A. VI. 49. Bouin's trap door for an observatory. A. P. 1763. H. 148. Barker's account of tlie observatory at Be- nares. Ph. tr. 1777.598. Schulze on the situation of an observatory. A. Berl. 1777- 223. Williams's particulars of the observatory at Benares. Ph.tr. 1793.45. Ussher on the observatory in Dublin. Ir. tr. 1787.1.3. *Piazzi della specola astronomica de'regi studi di Palermo, f. Palermo, 1792. 4- R. S. Ace. Hind. Arch. I. 257. Time. Equation of time. Lalande on the equation of time. A. P. 1762- 131. H. 120. Maskelyne on the equation of time. Ph. tr. 1764. 336. Pemberton. Ph. tr. 1772. 434. A problem relative to the calculation. K'astner on reductions of time, A. Gott. D. Schr. 101, 194. Equation Clocks, for Solar Time. P. Lahire's clock, showing true ti.ne. A 1717-238. Leroy's solar clock. A. P. 1717. H. 85, Mach. A. III. 151. A. P. 1728. H. 110. Mach. A, V. 63, 348 CATAT.OGUE. -PRACTICAL ASTRONOMY. Williamson's claim to the invention of equa- ted elocks. Ph. tr. 1719. XXX. 1080. Made one in 1693 or 1694 ; another with an elliptic roller raising the pendulum, which went 400 days : this is still in the palace at Hampton Court. Made one by cora- jiarison of the sun's motion with another clock ; this of course included a general equation for temperature. Lebon's solar clock. A. P. 1722. H. IIQ. Mach. A. Ilf. 21. A. P. 1726. H. 70. Mach. A. IV. 45. Meynier's solar clock. A. P. 1723. H. 122. Mach. A. IV. 59. Thiout's solar clock. A. P. 1724. H. 93. Mach. A. IV. 67, 69, 173. Dufay's machine for showing true time. A. P. 1725.67. Kriegseisen's equation clock. A. P. 1726. H. 69. Mach. A. IV. 155. A. P. 1732. H. 117. St. Cyr's solar clock. Mach. A. IV. 149. Duchesne's equation clock. Mach. A. IV. 153. Leroy's equation applied to a striking part. Mach. A. V. 67, 71,73. Duterew's equation watch. A. P. 1742. H. 163. Mach. A. VII. 153. Berthoud's equa tion clock. A. P. 1752. H. 147. 1754. H. 140. Mach. A. VII. 425, 473. Going 13 months. Biesta's equation clock. A. P. 1757. H. 179. Biesta's equation by a moveable dial plate. A. P. 1770. H. 115. Ferguson's astronomical and equation clock. Ferg. inech. ex. 11. Schulze on an equation clock. A. Berl. 1782. 322. Observations of Time, in general. Bernoulli on finding the time at sea. A. P. Prix. VI. i. Delambre oa finding the time from cor- responding distances. Zach. Mon. corr. IV. 93. Dialling, or Gnomonics. Account of dials in the garden at Whitehall. 4. Lond. 1624. By Guntcr. Hooke's instrument for making dials. Birch.. II. 155. Piciird on dialling. A. P. VII. i. 183. Lahire on dialling. A. P. X. 444. Parent's instrnment for shewing tbt true shadow. A. P. 170). H. II6. Clapies on the angles of dials. A. P. 1707., 569. Delisle's gnomon for the sun's transit. A, I*". 1719.54. Gnomonic instruments. Leup. Th. M. G. t. 10, 11. Mean's compound dial. A. P. 1731. H. 92. Gensanne's transit instrument and dial. A. P. 1736. H. 120. Mach. A. Vil. 55. Krafft on dialling. C. Petr. XIII. 'Zo5. Leraonnier's obelise for shewing the time of noon. A. P. 1743. 36l. H. 142. 1762.. 263. Emerson's cj'clomathesis. IX. Wenz's dial. Ace. Helv. V[. 167. La Condamine's gnomonical cane. A. P. 1770. H. 114. Bertier's globes serving for dials. A. P. 1770. H. 117. Ferguson's mechanical exercises. 95. Lalande on a vertical linear gnomon, A. P. 1757.483. Ferguson on dials. Ph. tr. 1767. 389, E. M. PI. V. Marine. I. E. M. PI. VIII. Amusemens degnomonique. Carayon's sun dial with wheelwork. Roz. XXIV. 312. Mignon on Carayon's dial. Roz. XXV. 377. Castillon on gnomonics. A. Berl. 1784. 259. CATALOGUE. — PRACTICAL ASTRONO-MY. 349 Wollastnn on a universal meridian dial, 4. Lond. 1793. R. S. Montucla and Hutlon's recreations, Lefrangois on dialling. Journ. polyt, IV. xi, 261. See Transit Instruments. ChronologVj and Calendar. Cassini on the calendar. A. P, II. 198, X. 433, 520. 1701. 367. 11. 105. Eichaud on the calendar of the Siamese. A. P. VII. part. 2. iii. 154.* Wallis on altering the calendar. Ph. tr. I699. XXI. 343. , ^ Prefers the Julian reckoning. Lord Burleigh and Greaves on the calendar. Ph. tr. 1699. XXI. 355, 356, Observations on the calendar. A. P. 1700. H. 127. 1703. H. 91. Jackman on the rule for finding, easier. Ph. tr. 1704. XXIV. 2123. Newton on a French publication of his chro- nological index. Ph. tr. 1725. XXXIII.. 315. Halley's defence of Newton's chronolog\', . Ph. tr. 1726. XXXIV. 205. 1727. ■ XXXV. 296. Sauveiir's perpetual calendar. A. P. 1732. H.94. *Lor Norwood's seaman's practice. Lond. 1636. M. B. Contains an account of his measurement of a degree. Ph. tr. abr. I. vii. 546. IV. vi. 449. VI. vii- 3C)3. Vin. vii. 324. X. vi. 250. Mercator's problems in navigation. Ph. tr. 1665-6.1.215. Instructions for the use of pendulum watches at sea. Ph.tr. I669. IV. 937. Cassini on the use of astronomy in naviga- tion. A. P. VIII. 1. Duillier's navigation improved. 1728. Maupcrtuis on a loxodromic circle on the surface of the sea. A. P. 1744. 462. Maupirtuis Astronomic nautique. Douwes Haarl. Verb. 1754. I. Bernoulli on finding the time at sea. A. P. Prix. VI. i. Bouguer Trait^ de navigation, par Lacaille. JVI.B. Emerson's cyclomathesis. IX. Emerson's navigation. 12. Lemotinitr Astronomic nautique. 8. Par. 1771. Aoc. A. P. 1773. H. 95. Lemonnier Questions dans la navigation. 8. Par. 1772. *Jua)i Examen mariiimo. 2 v. 4. Madr. 1771. French, Par. 1783. Bezout Coursde math^matiques. Ltveque Guide du navigateur. Rodin^ Wbrterbuch der marine. Borda on the operations on board the Flora. A. P. 1773. 258. H. 64. Pezenas Astronomic des marins. CATALOGUK. — ASTRONOMY, NAVIGATION, 371 Murdoch's Mercatoi's sailing. 4. *Robertson's elements of navigation, by Wales. 2 vols. 8. Lond. R. 1. Maskelyne's British mariner's guide. 'Nautical sAmanac, with appendices. §. Lond. Tables to be used with the nautical almanac. 8. Lond. 1802. B. B. Bode Jahrbijcher. Schubert on tlie loxodromic curve. N. A. Petr. 1786. IV. H. 95. Betteswoith's naval mathematics. 8. *KeUy's spherics and nautical astronomy. Lond. Moore's seaman's daily assistant, 8. 1785. R. L Moore's practical navigator. 8. 1796. R- L Nichoho7i's navigator's assistant. 8. Mendoza y Rios Tratado de la navegacion. 2 V. 4. Madr. 1787. B. B, Mendoza y Rios sur les principaux problemes de I'astronomie nautique. Ph. tr. 1797. 43. Mendoza y Rios's tables for nautical calcu- lations. 4. Lond. 1801, B,B. Mendoza' s nevf iahhs. 4. Lond. 1805. Caluso on navigation upon a spheroid. M. Taur. 1788. IV. 325. 1790.V. 100. Schubert on navigation upon a spheroid. N. A. Petr. 1790. VII L 140. Lalande Abrege de navigation. 4. Par. 1793. Ace. Roz. XLIII. 218. Mackay, Enc. Br. Art. Navigation. Mackai/s navigation. 2 v. 8. Lond. South's marine atlas, f. M. S. R. I. Rochon on nautical astronomy. Journ. Phys, XLVII. (IV.) 85. " ' Cooke's instrument for calculations in navi- gation. Ir. tr. Repert. IV. 38. Instruments for navigation. Montucla and Lai. IV. 509. Collections of Observations and Tables. Lalande on the use of interpolations in prac- tical astronomy. A. P. I76I. 125. H. 92. Lagrange on forming tables from observa- tion only. A. P. 1772. i. 613. H. 83. Observations made in Cook's voyage. 4. Lond. 1782. R. S. Bugge Observationes astronomicae. 4 Co- penh. 1784. R. S. * Bradley's observations. 2 vols. f. Oxf. 1798, 1805. R. S. Corrections, Tables for correcting refraction and pa- rallax. 4. R. 1. Elements and Epoilm. See fixed Stars. Mercator on Cassini's determination of the apogee. Ph.tr. I67O. V. IIG8. Messier. A. P. 1774. 93. Saturn's ring 3 leagues thick or less : exterior diameter 66737 leagues : breadth 9534. Burckhardt's elements of Pallas. Ph. M, XIII. 91. Distance 21 to 35. That of Ceres 27 to 28. Sun. Short makes the sun's apparent diameter 3l'28" to 32' 33": mean Si'f. The radius of a sphere equal to the earth is 636937* metres. Laplace. That is 69658OO yards, the "diameter. 7915.69 miles. Lalande says, 3268159 toiscs, that Is 6966338 yards, which is the radius at 52" J latitude. 372 CATALOGUE. — AS'fROJiOMV, SOLAR SYSTEM. ELEMENTS OF THE SOLAH. SYSTEM. The tun, Q, revolves on his axis in 25d. loh. The inclinition of his equator is 7° so'. The place of its ascendinf node, J3, 2s 18°, or 78° from the equinoctial point Aries. His diameter is 883,000 English miles, and his density, to that of the earth, as .255 to 1. His mean apparent diameter is 3l' 57" ; his mean parallax 8". 75. Mercury g Venus J Earth Q Mars ^ Juno fl Pallas ^ Ceres P Jupiter Tl Saturn ^ Georgia* 1801, Jan. 1. 1805. Jan. I. isoi. Jan. 1. planet ^ -^ -J< , , A ^ "A r- 7O I 3° 44' I IS 15° 58' I 2S14°58' | INCLINATION OF THE ORBIT. 1 l°5l'l 13° 4' I 34° 38' I 10°38'1 1° lo' PLACE or THE ASCENDIHG NODE. I IS 18° 2' I 5S21° 4' I 5S22°3l' | 2S 21° 7' | 3S 8° 25' MEAN DISTANCE. r 3871 I 7238 I 10000 I 15237 I 26640 | 27650 | 27070 | 5202S J ECCENTRICITY. C 794 I 50 I 168 1 1418 1 6770 | 6800 [ 2170 ] 2*01 MEAN DISTANCE IN MILLIONS OF MILES. 37 I «8 I 05 I 1^4 1 253 I 263 | 263 | 490 PLACE OF THE APHELION. 8S 14° 22' 1 lOS 8° 37' I OS 9°30'|5S 2° 25' | 7s 23° 11' | lOS 1° 3'| 108 22° l6sll° 9' MEAN PLACE OF THE PLANET. 5S11°54'|0S 9°S7'|SS 9°40'|2S S° 51' I is 12° 33' I 18° 13' | IS 0°12'|3S22° 9' MOTION OF THE NODE IB LONGITUDE IN 100 YEAKS. 1°12'| 52' I I 47' I II I 1° MOTION OF THE APHELION IN LONOITUDE IK 100 YEARS. l034'l l°ai'| l0 44'| l"'52'| I I I 1°35' TROPICAL SEVOIIITION. 87d 23h I 224d ish I ly 5h I ly 32ld I 4y 128d 1 4y 2l9d I 4y 22ld | lly 3l5d ] 29y I6id I 83y 294d 14' 33" I 41' 27" I 48' 48" ] 22h 18'.5 | I ' I I l*h39' j 19hl6' | 8h 39' 2° 30' 3S21°57' 95497 5364 900 8S 29° 5' 4S15° 18' SS' 40' 2sl2°4l' lgl83C -8956 1800 llsl7°2l' 5S27°47' 26' l°i28' SIDEREAL REVOLUTION. I I 1 87d 23h I 224d 16h I ly 6h I ly32ld I 15'44" I 49' 11" I 9' 8" I 23h30'.6 I DIAMETER IN MILES. 3180 I 7600 I 7916 I 4120 j | | DIURNAL ROTATION. 1 23h 31' I S3h56'4"|24h39'2l"| | [ PROPORTION OF DIAMETERS. ] I 300:301 I 15:16 | | | MASS, THAT OF THE SUN BEING UNITY. 7nis» I Tihzs I iste I II I DENSITY. I I 1000 I I I I MEAN APPARENT DIAMETER. le; I s" I I I lly 3i7d I 29y i74d I 84y agd I4h27' I ih 5i' I 29' 86000 I 79000 I 34200 gh 5i' I loh 16' I 12:13 I 10:11 I Ton I Tib I ttJw 258 I 104 I 220 40" I 18" I 4" CATALOGUE. — ASTROXOMY, TABLES. 373 The cbiiquily of the earth's equator to the ecliptic h 23" 28' ; its secular diminution 5o"; its periodical change in a revolution of the moon's nodes, 6" each way ; the an- nual precession of the equinoxes is 50.23"; the greatest apparent change of place of the stars from the aberration of light, 20" each way. The mean inclination of the orbit of the moon, 5, is 5° o'; the place of the ascending node 13° 56'; the mein distance 240000 miles ; the eccentricity 13700 miles ; the place of the apogee 2s 26° 7' ; the moon's place as 15° 2'; the diurnal motion of the node 3' 10", its tropical revolution I8y 228d 4h 52' 52", its sidereal revolu- tion I8y223d7h 13' 17"; the tropical revolution of the apoge* 9y and 8h 34' 57" ; its sidereal revolution 8y 31 2d llh 11' ; the moon's tropical revolution 27d 7h 43' 5" ; her synodical revolution with respect to Q, 29d 12h 44' 3"; her diameter 2163 miles; her mass ^ of the earth's ; her density .742 ; her apparent diameter 29' 22" to 33'S4"; her horizontal parallai 53' 46" to 61' 26"; at the mean distance 57' 1". 1 Jan. I801, The sidereal periods of the satellites, and their distances In semidiameters of the planets are, Jupiter's \. id 1 8h 27 ' 33". D. 5.67. n. 3d I3h 13' 42". D. p. III. 7d3h 42' 33". D. 14.3S. IV. I6d ish. 32' 8". D. 25.3. The third, which is the largest, is about the size of the moon. Saturn's Ring loh 32' 15". D. 2.33. I. or VII. 22h 37' 23". D. 3.7. II. or VI. Id 8h 53' 8". D. 4.2. III. or I. id 2lh 18'26". D. 4.9. IV. or If. 2d I7h 44' 5i". D. 6.3. V. or III. 4d I2h 95' n" V. 8.75. VL or IV. I5d 22h 4l' Ifl". D. 20.3. VII. or V. 79d 7h 53' 43". D. 59.15. The longitude of the nodes of the ring 5s 17° 13', retreating about 35° in a century. The Georgian planet's I. sd. D. 12.7. II. 8d. D. 16.5. III. lod. D. 19.5. IV. 13. 5d. D. 22. V. 38d. D. 44. VI. 108d. D. 88. Tables of places of the Heavenly Bodies. Kepleri tabuljj,e Rudolphinae. f. Ulm, 1^27. *Connaissance des temps. 8. Paris. I679. .. Flamsteed's circle for finding the place of Jupiter's satellites. Ph. tr. 1685. XV. 1262. Lahire Tabulae astronomicae. 4. Paris. Ace. Ph. tr. 1686. XVII. 443. Wood's ahnanac. Hooke Ph. coll. ii. 26. Halley on Albategtji's tables. Ph. tr. IG93. XVII. 913. Pound's tables of Jupiter's satellites. Ph. ti. 1718. XXX. 776. 1719. XXX. 1021. Wargentin tabulae satellitium Jovis. Act. Upsal, 1741. 27. M.iyer's solar and lunar tables. C. Gott. 1752. n. 383. *Mai/cr tabulae niotuum solis et lunae. 4. London, 1770. R.S. Maker's lunar tables. 4. Lond. 1787. R. S. • Ephcmerides astromonicae. 8. Vienna, 1 757. . . Lacaille tabulae solares. 4. Paris, 1758. By Hell. 8. Vienn. I763. Elements of new tables of Jupiter's satellites. Ph. tr. 1761. 105. 7JfZ/ tabulae lunares. 8. Vienn. 1763. Euleri novae tabulae lunarcs. 8. Petersb. R.S. A. P. Index. Art. Tables. *Nautical almanac. 8. Lond. Bailly on the satellites of Jupiter. Ph. tr. 1775. 185. Bode Astronomisches Jahrbuch. 8. Berlin, 1776... R.S. Recueil de tables astronomiques. 8. Berlin. R.S. Englefield's tables of the expected comet. 4. Lond. 1788. R. S. Laplace et Delambre Tables de Jupiter et de Saturne. 4. Paris, 1789. R. S. Zach Tabulae moluum solis. 4. Goth. 1792. Supplementa, 1794... Von Zach on the place of Ceres. Ph. M. XII. 360. Report on Burg's lunar tables. Ph. M. XIIL 183. Greatest error about 12". Ephemeris of the new planets for 1803. Ph. M. XV. J 90. 374. CATArOGUE. ASTRONOMY, ILLUSTRATIONS. Projections, Charts, Globes, Orreries, and other Instruments, illustrative of Astronomy and Geography. See Asuonomiciil Instruments, Navigation. *Hugenii descriptio automati planetarii. Opp. lel. II. 175. Wallis on the construction of sea charts. Ph.tr. 1685. XV. 1193. Also on the figure of secants. Ilalley on the meridional parts, or the sum of the secants. Ph. tr. XIX. 1696. 202. Roemer's planisphere. Mach. A. T. 81. Roemer's planisphere for eclipses. Mach. A. I. 85. Roemer's wheel for unequal motion. Mach. A. L 89. Mich. IV. 404. Cassini's planisphere. Mach. A. I 133. Cassini's globe to show the precession of the equinoxes. A. P. 1708. H. 93. Allemand's celestial globe. Mach. A. I. 157. Chazelles on hydrographical charts. A. P. 1702. 150. H. 86. Lagny on reduced maps. A. P. 1703. Q5. H. 92. Chevalier on taking a map by amplitudes. A. P. 1707. H. 113. Perks on the meridional line. Ph. tr. 1715. XXIX. 331. lladus de projectionibus sphaerarum. 4. Leipz. 1717. Meynier's sphere of paper. A. P. 1723. H. 121.Mach. A. IV. 55. ileynier's clock, showing the solar motion. A. P. 1723. H. 122. Mach. A. IV. 59- Meyer's planisphere. Mach. A. IV. 61. Desagulier's experiment illustrative of the form of the earth. Ph. tr. 1725. XXXIII. 344. Brouckner's globe of copper. A. P. 1725. H. 103. Mach. A. IV. 143. Outhier's celestial automaton. A. P. 1727. H. 143. Mach. A. 15, 19, 21. Mauny's sphere. Mach. A. VI. 89. Graham's globular instrument for comput- ing latitudes. Ph. tr. 1734. XXXVIII, 450. Colson on spherical maps, or segments of globes. Ph. tr. 1736. XXXIX. 204. Latham and Senex on making the poles of the celestial globe revolve. Ph. tr. 1738. XL. 201. 1741. XLI. 730. Harris's improvement on the terestrial globe. Ph. tr. 1740. XLI. 321. Placing the horary circle under the meridian. Segneri machina ad eclipses repraesentandas. Ph. tr. 1741. XLI. 781. Maclaurin on the meridional parts of a sphe- roid. Ph. tr. 1741. XLI. 808. Richmann on maps. C. Petr. XIII. 300. Maupertuis on a loxodromic circle on the surface of the sea. A. P. 1744. 462. Ferguson's orrery for the phenomena of Venus. Ph.tr. 1746. XLIV. 127. Ferguson's improvement of the globe. Ph. tr. 1747. XLIV. 535. By msuksi for the sun and moon. Ferguson's mechanical illustration of eclipses. Ph. tr. 1751.520. Ferguson's orreries. Mach. exerc. 72. Sur la construction des grands globes, f. Nuremberg, 1746. Mrs. Senex on Senex's globes for showinc; the precession. Ph. tr. 1749. XLVI. 290. Passement's moving sfjhere. A. P. 1749. H. 183. Lowitz sur les grands globes. 4. Naremb. 1749, 1753. Robertson's explanation of Hallcy on the analogy of the logarithmic tangents and CATALOGUE. — ASTRONOMY, ILLUSTRATIONS. 975 the meridional line. Ph.tr. 1750. XLVI. 559. Murdoch on the best form of maps. Ph. tr. 1758. 553. Mountaine on maps and charts. Ph. tr. 1738. 563. Dunn and Mountaiue's defence of Mercator against West. Pii. tr. 176'j. 66, 69. Chabert on forming charts. A. P. 1759. 484. H. 127. 1766, .'384. Projections of the sphere. Emers. cyclom.VIT. King's electrical orrery. Ferg. Mech. exerc. 132. Castel's moving sphere. A. P. 1766. H. 162. K'astner on slereographical projections. N. C. Gott. 1769- 1. 138. Diss. phys. 88. Lowitz and K'astner on covering globes. Commentat. Gott. 1778. 1. M. 1. Append. The common way. K'astner on celestial maps. Zach. Eph. II. 401. Bertier's globes serving for dials. A. P. 1770. H. 117. Rittenhouse's orrery. Am.tr. I. 1. Euleron projections for maps. A. Petr. 1. i. 107. Elder on covering globes. A. Petr. Ii. i. 3. By 12 pentagons inscribed in a circle having its radius .5l96lr, with segments of circles, of which the radius is 3.4841 r. Jeaurat's asterometer, for showing the rising and setting of a given object. A. P. 1779. 502. H.37. Castillon on a moving globe. A. Berl. 1779- 301. Van Swinden's planetarium. Roz. XVI. 456. Globes. E. M. A. III. Art. Globes. Slereographical projection. E. M. PI. V, Marine 27. 1 Ducuila Expression des nivellemens. 1782. Ace. Zach. Mon. corr. 11. 148. By marking out horizontal lines at different heights on a map. Fuss on the stereographic projection. A. Petr. 1782. VI. ii. 170. Shows that the projections of all circles are circlet. Harrison on the Globes. 8. 1783. R. I. Grenet's new spheres. Roz. XXIV. 319. Schubert on the projection of a sphere on -a. cone. N. A. Petr. 1784. II. 84. Schubert on the projection of a spheroid. N. A. Petr. 1787. V. 130. 1788. VI. 123, 1789. VII. 149. Mackay. Enc. Br. Art. Projection. Cannebier'sgeocyclic machine. Roz.XXVII. 192. Kiugcl Geometriscbe entwickelung der ste- reographischen projection. 8. Berl. I788. Smeaton's improvement in the quadrant of altitude. Ph. tr. 1789. 1. Made more solid and accurate. Lorgna on maps. Soc. Ital. V. 8. Lorgna proposes that circles be drawn with their radii equal to the chords, from a given point, so that the artas may every where be true. B. Soc. Phil. n. 29. ilfflyer liber charten und kugeln. 18. Erlang. 1794. Ace. Hind. Arch. I. 236. Pearson's satellitian instrument. Nich. II. 122. Forster's instrument for placing globes by the sun. Ph. M. XII. 83. Alison's globe timepiece. Am. tr. V. 82. Alison's pendent planetarium. Am. tr. V. 87. Repert. ii. III. 331. The balls hanging by threads. Pattrick on an improved armillary sphere, and on the patent nautical angle. Nich. 8. V. 143. Delambre on the stereographic projection. M. Inst. V. 393. 376 CATALOGUE. HISTORY OF ASTBONOMY. Shows, that all the circles intersect each other in the same angles as those which they represent. After Ptolemy. A planisphere. R. I. Equation clocks. See Astronomical Time. Mr. Arrowsmith generally employs for his maps a glo- bular projection, in which the meridians and parallels are portions of circles, cutting the circumference and diameters of the projection at equal distances; they appear also to cut each other into equal portions, so that the dis- tortion principally arises from their not being perpendi- cular to each other near the poles, besides the inequality of the scale in different parts, which is perhaps nearly as small as possible. History of Astronomy and Geography. Ph. tr. \m5-Q. I, 3. Hooke found in 1864 that Jupiter revolved in about 8 hours. Cassini on the rotation of Venus. A. P. X. 324. Observed in ifla?. Ph. tr. 1725. Newton thinks that the constellations were arranged by Chiron when the solstitial and equinoctial points were in the middle of the respective constellations. Mairan. A. P. 1727. 63. H. 117. Alexandre and Baliani thought the earth turned round the moon, Molieres on vortices. A P. 1729. 235. H. 87. Against Newton. Frisch on astronomical characters. M. Berl. 1729. Latham on the antient sphere. Ph. tr. 1741. XLI. 730. 1742. XLII. 221. Costard on the Chinese chronology and astronomy. Ph. tr. 1747- XLIV. 476. Against its antiquity. Costard's history of astronomy. 4. 1767. R.I. JBaiUy Histoire de I'astronomie. 4 v. 4. Par. 1781. R. I. Ace. A. P. 1775. H.44. Bailly Traite de rastronomie Indienne. 4. Par. 1787. R. I. 4 Raper and Lalande on Norwood's measure- ment. Ph. tr. 1761.366, 369. Hassencamp Gescliichte der bemiihungendie nieereslange zu finden. 8. Rinteln. 1774. Liilande on Herschel's planet. A. P. I779. 520. H. 31. / Legentil on the origin of the zodiac. A. P. 1782. 368. H. 51. Legentil on the antiquity of the constella- tions. A. P. 1789. 506. ^ Herschel on his Georgium sidus. Ph. tr. 1783. I. V/all on astronomical symbols. Manch. M. I. 243. Derives if from the caduceus, J from the sistrum, ^ from the shield and spear, i; from Jr, ^ from the sickle. Frisch deduces 11 from lightning with the eagle. Blair's history of geography. 12. Lond. 1784. Otto on the discovery of America. An>. tr. IL 263. Nich. L 73. Zach on Harriot's observations of the solar spots. Bode Jahrb. 1788. On the knowledge of the earth's motion. Eberhard Neue vermischte schriften. 8. Halle, 1788. 67. Playfair on the astronomy of the Brahmins. Ed.tr. H. 135. Supposes some observations 5000 years old. Davison the astronomy of the Hindoos. As. res. n. 225. Davis on the Indian cycle of 60 years. As. res. III. 209. Jones on the Indian zodiac. As. res, II. 289. Jones on the lunar year of the Hindoos. As. res. III. 257. Cavendish on the civil year of the Hindoos. Ph. tr. 1792. 383. Lalande's history of astronomy for 1795 and 1796. Journ. Phys, XLV. (II,; 325. CATALOGUE. PROT>ERTIES OF MATTEU. 377 Lalande Histoire celeste. Modern Greek tetrastich on Lalande. Zach. Eph. III. Bentley on the antiquity of the Hindoo as- tronomy. As. res. VI. 537. Makes the principal tables, the Surya Siddhanta, about 731 years old. Piazzi's planet. Ph. M. X. 285. Note on the antiquity of the earth. Ph. M. XI. 280. Piazzi on the new star. Ph. M. XII. 54. Dehic on the zodiacs found in Egypt. Ph. M. XIII. 371. V Henley on the zodiac at Dendera. Ph. M. XIV. 107. History of astronomy, geography, and navi- gation. Montucl. and Lai. IV. *Smatrs history of the discoveries of Kepler. 1803. R. I. Account of Gail's memoir onSynesius's astro- labe. M. Inst. V. 34. Maps are attributed to Anaxiirander, 600 A. C. According to Plutarch, Heraclides and Ecphantus attri- buted to the earth a diurnal motion only. Astronomy was introduced into Spain by the Moors, 1201. The Mexicans, when discovered by the Spaniards, had years of 365 days, and added is days at the end of 52 years. Robison. PROPERTIES OF MATTER IN GENERAL. The opinions of the ancients are found in Aristotle and Plato. Descartes Princ. phil. II. x. On a vacuum. Boyle on the principles of natural bodies. *Hooke's lectures of spring. L. C. 1678. A curious theory of vibrations. Bernoulh de gravitate aetheris. 12. Amst. 1683. Op. I. 4.5. Bernoulli Nouvelle physique celeste. A. P. Prix. III. i. vot. II. Newtoni Principia. L. 2. On a vacuum. Newton's Optics. Queries at the end. Desaguliers's experiment to prove a vacuum, Ph.tr. 1717. XXX. 717. Woodward's natural history of the earth. Mazieres on the vortices of the subtle mat- ter. A. P. Pr. I. vi. Iloldsworth and Aldridge's short hand. Contains a hypothesis resembling that of Le Sage. Musschenbroek Elem. Phys. §. 61, 83, 383. Musschenbroek Introductio. I. iii. Of a vacuum. On the cause of gravity. M. Berl. 1743. VII. 360. Maupertuis on laws of nature supposed in- compatible. A. P. 1744. 417. H. 53. On Fermat and Leibnitz's minimum. On atoms. A. Berl. 1745. H. 28. Eller on elements. A. Berl. 1746. 1, 25. 1748. 3. Keill's introduction to natural philosophy. Lect. viii. Cadwallader Golden on the primary cause acting on matter. 1745. M, B. Euler de resistentia aetheris. Opuscul. I. 245. Euler on the origin of forces. A. Berl. 1750. 418. Knight on attraction and repulsion. 4. Lon- don, 1748. R. I. Bossut sur la resistance de I'ether. 4. Charle- ville, 1766. Chambers's cyclopaedia. Art. Element. Hiotzeberg on the cause of attraction. R02. Jntr. 1. 527. On union. Roz. II. 173. Comus on motion, and on the elements of matter. Roz. VI. 420. VII. l62. Higgins on light. 3 c^ 378 CATALOGUE. — DIVISIBILITY OF MATTER. Lam6tlierie on the elements. Roz. XVIII. 224. - Lametherie on the Kantian system of forces. .Tourn. Fhys. XLVII. (IV.) 383. Ph. M. , II. 277. Le Sage Lucr^ce Newtonien. A. Berl. 1782. 404. In favour of the impulse of atoms. L'huilier Exposition des principes des cal- culs. 4. Berl. 1786. 1«7. DeUic Idees sur la meteorologie. Wall on attraction and repulsion. Manch. M. II. 439. In most cases considers apparent repulsion as elective attraction, Ilutton's mathematical dictionary. Art. Ele- ment. Selle on elements. A. Berl. 1796. ii. 42. Gilbert on attraction. Gilb. II. 63. Les causes materielles do ['attraction devoilees. 12. Lond. 1801. Cavallo's natural philosophy. Divisibility of Matter. Boyle on effluvia. Halley on the thickness of gold on wire. Ph.tr. 1G93. XVII. 540. Calculates that it is i of an inch. Reaumur on ductility. A. P. 1713. 199. H.9. Keill de materiae divisibilitate infinita. Ph. tr. 1714. XXIX. 82. Keill's natural philosophy. Bohault's physics. S'Gravesande's natural philosophy. Musschenbroek Introductio. Hutton's recreations. IV. 80. Nicholson. Ph. tr. 1789. 286. Gold leaf Ph. M. IX. In gilding buttons 5 grains of gold are allotted by act of parliament to 144 buKons ; but they may be tolerably gilt by half the quantity. The thickness in this case would be about jyiora °f ^" inch. Musschenbroek says, that a workman of Augsburg drew a grain of gold into a wire 500 feet long. Its diameter must have been only j^ of an inch. Of a silkworm's thread 360 feet weigh a grain ; of a spider's web only ^ as much, consequently 12800 feet weigh only a grain. In drawing gilt wire, 4 5 marcs or 22l pounds of silver are covered to the thickness of j|o of an inch with 6 ounces of gold : but one ounce is sufficient for the purpose : this is drawn into a wire 06 leagues long, and when flattened it becomes 1 1 0 leagues : the gold is then j^^^ of an inch thick; if one ounce only has been used, j^jfedoj and pro- bably in some parts jjcfe^ : this may still be flattened again and reduced to the thickness of —515535 of an inch in all parts, and in some to still less, not exceeding one ten raillionth. Montucla and Hutton. A sphere of this thick- ness would contain about one two thousand million million millionth of an inch. Repulsion, or Impenetrability. See Collision. Hooke on the compression of glass. Birch. I. 129. Hooke's Lectures of spring. L. C. 1678. With fundamental experiments. On the compressibility of water. A. P. I. 139. Varignon on hardness A. P. II. 70. X. 49. Romberg on the change of volume of li- quids in a vacuum. A. P. II. 183. Hauksbee on the degree of contact of a body immersed in a fluid. Ph. tr. 1709- XXVI. 306. Finds that it is very intimate. Euleron pneumatics. C. Petr. II. 347. • Euler on the nature of the air. A. Petr. III. i. 162. Supposes molecules of air to revolve within vesicles of water more rapidly as the temperature is higher. Euler. A. Petr. 1779- i. CATALOGUE. REPULSIOX, INERTIA, CRAVITATIOX. 379 Desaguliers on the cause of elasticity. Pii. tr. 1739. XLl. 175. Moli^reson elasticity. A. P. 1726. 7. II. 53. Hausen programmata de reactione. Leipz. 1740, 1741. Lomonosow on the elasticity of the air. N. C. Petr. I. 230, 305. Derives it from heat or gyration only. Richmann on the force of water in freezing. N. C. Petr. I. 276. Remarks on Hales's experiments, in which air is said to have been reduced to J,, of its bulk. Richmann doubts the accuracy of the estimate, but the force of the ice must have been equal to 1435 atmospheres, if not to 2871. NoUet on a glass vessel appearing to be filled by its pores. A. P. 1749. 460. H. 15. Zanotti on elasticity. C. Bon. IV. O. 233. Cossigny on the supposed penetration of glass by water. S. E. III. 1. Hollmannus de experimento Florentino. Sylloge. 34. Canton on the compressibility of water. Ph. tr. 1762.640. 1764.261. Herbert de aquae elasticitate. 8. V^ienn. 1774. Zimmermann Traite de I'elasticite de I'eau et d'autres fluides. 8. Leipz. 1779- U. S. Mongez on the compressibility of fluids. Roz. XI. 1. J. Bernoulli on elasticity. Roz. XXI. 463. Deluc on expansible fluids. Roz. XLIII.'iO. Barruel on elasticity. £xtr. Journ. Phys. XLIX. 251. Ann. Ch. XXXIII. 100. Journ. polyt. IV. xi. 295. Ph. M. VI. 51. Libes on elasticity. Journ. Phys. XLIX. 413. Ann. Ch. XXXIII. 110. Palton's theory of gases. See Meteorology. Emerson says, that springs are weakened by use, but re- cover their strength when laid by. Inertia. Hansen programmata de reactione. Euler. Ac. Berl. 1750. 428. Kratzemtein amolitio vis inertiae et vis repul- sivae. 8. Hanov. 1770. Franklin's miscellanies. 4. Lond. 1779. 479. Kaestner Anfangsgriinde. I. xxi. II [. 125, 129. Diss. math. x. 75. Nature of Gravitation. See Properties of Matter in general. On the space described by falling bodies. A. P. I. 49. Varignon on weight. A. P. I. 63. II. 45. Huygens on the cause of gravity. Op. rel, 1.93. Keill de legibus attractionis. Ph. tr. 1708. XXVI. 97. Saurin on the Cartesian system of weiglit. A. P. 1709. 131. 1718. 191. H. 7. Ilambergerus de experimento Hugenii. 4. Jen. 172.J. Hamberger on the direction of bodies in a vortex. Com. Petr. 1.245. Mazieres on ethereal vortices. A. P. Pr. I. vi. Bulfinger on motion in a vortex. C. Petr. IV. 144. Bulfinger's experiment on the physical cause of gravity. A. P. Pr. If. iii. Nollet on the motion of fluids within a sphere. A. P. 1741. 184. Kratzenstein's spring steelyard for measur- ing gravity. N. C. Petr, II. 210. Berthier on terrestrial attraction and repul- sion. A. P. 1751. H. 38. Berthier's comparison of attraction with ethereal impulse. A. P. 1764. H. 148. 380. CATALOGUE. COHESION. Van Swinden de attractione. 4. Leyd. 1766. Hollmann on attraction. Comm. Gott. IV. 215. CAi/rco/ Attractioad impulsionem revocata. 4. R. S. Thoughts on general gravitation. London, 1777. E. M. Pliysique. Art. Attraction. Bergmann on universal attraction. Opusc. VI. 38. Beluc on gravity. Roz. XLII. 88. Cohesion in general. Leibnitii theoria motus. 12. Lond. I67I. Ace. Ph. tr. 1671. VI. 2213. Deriving cohesion from motion. Desaguliers's experiment on the cohesion of lead. Ph. tr. 1725. XXXIII. 345. A circle of contact, about one tenth of an inch in dia- meter, supported more thac 40 pounds. Triewald's queries respecting cohesion. Ph. tr. 1729. XXXVI. 39. }{nmber"erus et Suessmilch de cohaesione et attractione. 4. Jena, 1732. llamberger Naturiehre. Vorrede. IVinkler de causis conjunctionis. 4. Ijcipz. 1736. Felice de attractione cohaerentiae causa. 4. 1757. Dehic on cohesion and on affinities. Roz. XLII. 218. fLibeson molecular attraction. Journ. Phys. LIV. 391. Referred to gravitation. Hitter on cohesion. Giib. IV^. 1. Thinks the cohesive force is as the capacity for heat and the distance from the point of fusion conjointly. fBenzenberg on cohesion. Gilb. XVI. 76. From gravitation, a blunder. fiobison says, that the strength of gold is tripled by draw- ing it into wire. Physiol, disquis. Adams's lect. I. Jones deduces cohesion from the pressure of caloiic' ■ ^ 5 , Cokeiion and Capillary Action of Fluids, Fabri Dialogi physici. 8. Lyons, 1669. Ace. Ph. tr. I670. V. 2058. Walhs on the suspension of quicksilver at a great height. De motu. xiv. Ph. tr. 1672. VII. 5160. Huygens on the suspension of quiciisilver at 75 inches, and on the siphon running in a vacuum. Ph. tr. 1672. VII. 5027. *Boyie on the figure of fluids. Ph. tr. I676. XI. 775. On the common surface of different combinations of fluids, sometimes concave, sometimes convex. Hooke and Papin on the suspension of mer- cury and of water in a vacuum. Birch. IV. 300,301, 307. Lahire on the contraction of moist ropes. A. P. IX. 157. Carre on capillary tubes. A. P. 1705. 241. H. 21. Hauksbee on the effect of capillary tubes remaining in a vacuum. Ph. tr. 1706. XXV. 2223. A capillary siphon must have one leg at least as much longer than the other as the length appropriate to its bore, in order to run. Hauksbee on the ascent of water. Ph. tr. 1709. XXVL258. Hauksbee on the motion of a drop between two plates. Ph. tr. 1711. XXVII. 395. Hauksbee on the force of attraction of two plates.'Ph. tr. 1712. XXVII. 413. Measured' by the angular elevation at which a drop of oil was held in equilibrium. The force appears to be nearly as the square of the distance inversely. Newton mentions the same law in his queries. At 18 inches from the line of contact the elevation was 15', at 16, 25', at 8, 1'' 45', at 4, 6", at 2, 22°. Hauksbee on the ascent of water between two plates. Ph. tr. 1712. XXVII. 539. Hauksbee on the ascent of fluids. Ph. tr. 1715. XXVIir. 151. CATALOGUE. — COHESION. 381 The height of spirit of wine was exactly in the inverse ratio of the distance of the plates. When the line of con- tact of the {)lates was parallel to the surface of the water, the fluid contained between them bent inwards as the plates were raised, half way between the line of contact and the surface. This curvature may be considered as the vertex of a hyperbola, and the circumstance will be explained. The force of attraction of a drop of spirit was observed more ac- curately than that of the oil ; the inclination of the plates beingis'.at 18^ inches, the elevation was 45', at Oj, 1°46', at 4j, 6°, at 2^, 15°, the inclination being 10', the distance 18^, the elevation was 1" 30', at g~, 3" 30', at 4', 14°. Taylor on the ascent of water between two glass plates. Ph. tr. 1712. XXVII. 538. The curve is very nearly a hyperbola. Taylor on the attraction of wood to water. Ph.tr. 1721. XXXI. 204. An inch square required 50 grains to raise it ; the weight was always directly as the surface: the elevation 16 hundredths of an inch, or perhaps more. Homberg on a capillary siphon running in a vacuum. A. P. 1714. H. 84. Jurin on capillary tubes. Ph. tr. 1718. XXX. 7S9. Denies Haiaksbee's remark on a capillary siphon. But both may be right in different circumstances. Jurin on the action of glass tubes on water and quicksilver. Ph. tr. 17 19- XXX. 1083. Suggests, after Huygens, the pressure of a medium. .Turin's essay in Cotes's lectures. Ditton's discourse on the new law of fluids. Petit's new hypothesis. A. P. 1724. 94. H. 1. •j-Petit on the adhesion of the particles of air. A. P. J731. 50. H. 1. Biilfinger on capillary tubes. C. Petr. II. 233. III. 281. With Jurin's experiments. *Musschenbroek de tubis vitreis. Diss. phys. 271. De speculis, 334. Weitbrecht on capillary tubes. C. Petr. Vlll. 261. IX. 275. Gellert on lead melted in capillary tubes. C. Petr. XII. 293. "243." . The appearances resemble those of mercury. Gellert on prismatic capillary tubes. C. Petr. XII. 302. Thinks that the height is inversely as the square root of the area. Lemonnier on fluidity. A. P. 1741. H. ] I. HoUmann on the difference of barometers. C. Gott. 1751. 1.227. Thinks that in small tubes the nature of the glass has some effect. *Segner on the surfaces of fluids. C. Gott. 1751. I. 301. Proceeds on true physical principles, but commits a ma- terial error in neglecting the effect of a double curiature : appears also to have made some other mistakes in his cal- culations. Says that the height of mercury on glass or paper was .1357848 E. i. j half of this he calls the modulus for mercury. On Taylor's measure of attraction. Misc. Taur. I. Tetens de fluxu siphonis in vacuo. 4. Blitzow. 1763. Lalande Journ. des sav. 1768. Lalande sur la cause de I'elevation des li- qiteurs. 12. Par. 1770. Morveau on the attraction of water and oils> and on the adhesion of surfaces. Roz. I. 172, 460. Morveau on apparent adhesion, (^himie de I'Acad. de Dijon. 1. 63. E. M. Chimie. I. Art. Adhesion. *Lord C. Cavendish's table of the depression of mercury. I'h. tr. 1776. 382. Achard on the adherence of solids to fluids. A. Berl. 1776. 149. Schriften I. 355. *Dutour on capillary tubes, and on adhesion. Roz. XI. 127. XIII. Suppl. 357. XIV. 216. XV. 46, 234. XVI. 85. XIX. 137, 287. The mean adhesion of a disc of 72 square lines Fr. to water, was 31 gr. Fr. to wine 29, to brandy 22 J, to olive oil a2, to spirit of wine 18. A disc of glass, 11 lines in dia- 38^ CATALOGUE. — COHESION. meter, adhered to mercury with a force of 194 grains, a disc of talc with 119, of tallow 49, of paper i7j, of wax 11, of box, waxed, with a force of i onl)". Godaixl on apparent attractions. Roz. XIII. 473. ^leister on oil swimming on water. Coiu- menlat. Gott. 1778. I. 35. Besile on the cohesion of liquids. Roz. XXVIII. 171. XXIX. 287, 339. XXX. 125. Gives 82 gr. Fr. for the cohesion of 25 square lines of mercury, 8^ for water. In some cases the apparent ad- hesion was diminished under the air pump. But this was probably the effect of the extrication of air bubbles. *Monge on apparent attractions and repul- sions. A. P. 1787. 506. Nich. HI. 269. Supposes that the superficial particles of the fluid only act in producing the effects of cohesion, and infers that the curve must be a lintearia. But he has not filled up this true outline with equal success. Spirit of wine, when not too hot, forms floating globules when dropped through a capillary tube. Two dry bodies floating approach each other from an inequality of pressure ; even under the sur- face, as the fingers under mercury. A dry and a moist body repel each other in the same manner as an inclined place and a body placed on it would separate. Two wet bodies are drawn by the fluid between them as by a chain. But these explanations do not agree with the supposition of the lintearia, which is vertical at its origin. The distance of two plates being ^ of a line, the height of the water was 15j lines, at^, the height was 33J, at Jj, 74 lines. Bennet on attraction and repulsion. Manch. M. III. 116. Shows that the undulations observed by Franklin do not depend on the mutual action of matter. Banks on the floating of cork balls. Manch. iM.UI. 178. Explains the phenomena pretty correctly, after S'Graves- ande. Waterproof cloth. Ph. M. X. 370. Impregnated with some substance not highly attractive of water. See cloth. Carradori on the superficial adhesion of fluids. Journ. Phys. XLVIII. 287. Ph, M. XI. 27. Gilb.'xil. 108. Considers it as a mechanical atuaction between oils and water. Otto on the effiect of oil on waves. Zach. Eph. II. 516. III. 242. Ph. M. IV. 225. Leslie on capillary action. Ph. M. XIV. 193. Hassenfratz on the eflfcct of adhesion in de- termining specific gravities. Ann. Ch. Gilb. I. 396,515. Pounded glass appearing to be specifically lighter. Schmidt on Hassenfratz'is experiments. Gilb.. IV. 194. Denies their accuracy. B. Prevoston the motions of floating bodies. Ann. Ch. XI. 3. Milon on capillary tubes. Journ. Phys. LIV. 128. Gilb. XII. Repert. XVI. 427. Found that the cleanest mercury, when hot, would not rise even in red hot lubes. Von Arnim. Gilb. IV. 376. Finds an effect from the length of a capillary tube. H'allstrom on the rise of water in tubes. Gilb. XIV. 425. Attributes the apparent effect of the length of a capillary tube to the circumstance of its being sucked with the lipt, which, even when the lips were perfectly clean, appeared to produce a depression. In general it is probable that in- equalities in the dimensions of the bore have been the cause of the irregularity, which has never been perceptible in ex- periments with flat plates. Water rose 11.7 lines Swedish in a tube .2 line in diameter. Cavallo's Nat. Phil. II. 135, 139. A small globule of mercury will be drawn away from paper by glass, and from glass by more mercury. An iron ball floating on mercury is surrounded by a depression. A drop of mercury recedes from the line of contact of two glass plates. A needle floats on water when dry, but if any water gets over it, it sinks. Robison observes that insects, which walk on water, have their feet wetted by a spirituous solution, and sink. The equation of the surface of a drop of water is aaxx + aajiy ~ xyyi, where x z: o. Or thus, a*x'x' + la*xif'x + (a' — x'y') t/* — x'y'i'ir* 3; o, Y. The series given by Euler, A. Petr. III. 188, for the clastic curve, might be applied to the simple lintearia, which is a species of it. Catalogue. — heat and cold. 383 Fluidity of Liquids, and Firmness of Solids. See heat. Ductility. See Divisibility. Boyle fluiditatis et firmitatis historia. Works!. I. 240. Reaumur on the ductility of different sub- stances. A. P. 1713. 199- H. 9. Reaumur. A. P. 1726. 243. Lead is rendered less sonorous by hammering. Fluidity. A. P. 1741. H. 11. Beguelin on hard bodies. A. Berl. 1751.331. On the explosion of grindstones. A. P. 1762. H. 37. 1768. H. 31. Attributed to the efFect of the centrifugal force, and to the expansion of the wooden wedges. Fontana on solidity and fluidity. Soc. Ital. 1.89. On hammering. Sickingen liber die platina. 115. Coulomb on the force of torsion. A. P. 1784. 229. The force varies as the angle of deviation, and as the biquadrate power of the diameter of the wire ; a weight of half a pound vibrating twice as fast as a weight of two pounds. Steel wire was 3^ times as stiff as brass ; its direct cohesive strength as 12 to 7 ; it was 18 or 20 times as stiff as a thread of silk : brass wire was less easily deranged by great torsion. The elasticity of annealed wire was the same in quantity as that of unannealed, but its extent of action was reduced from 11 to 6 or 7 , in copper : the time of oscillation was exactly the same in both «ases. P. 26», Coulomb's physical theory of friction. S. E. X. 1785. 254. Lambert on the constitution of fluids. A. Berl. 1784. 299- *Delangez on the statics and mechanics of semifluids. Soc. Ital. IV. 329. llutton on the flexibility of the Brazilian stone. Ed. tr. III. 86. Fleuriau on elastic stones. Roz. XLI. 86, 91' On Fleurlau's mode of making marble fle.v- ible by heat, producing partial separations. Ph. M. X. 277. Link on fluidity. Ann. Ch. XXV. 113. On springs. Ph. M. II. 67. Springs of metal soon break, or take a set, if suffered to vibrate; wooden springs break if stopped and not suffered to vibrate. Red deal is the best wood for springs. Cr}stals slowly formed are the hardest. See Higgins on light. The cohesive strength depends much onsoliditj. See cohesion. HEAT AND COLD. Boyle on cold. Works II. 228. Ace. Ph. tr. 1665-6. I. 3. Boyle de frigore. 4. Lond. l6S3. Petit sur le froid et le chaud. Par. I67I. M. B. Ace. Ph. tr. 1671. VI. S043. Dodart on heat and cold. A. P. I. 143. Mariotte on heat and cold. A. P. I. I74. Oeuvr. I. 183. Varignon on fire and flame. A. P. II. 171. Malebranche on fire. A. P. I699. 22. H. 17, f Geoffrey on cold. A. P. Ace. Ph. tr. 1701. XXII. 951. Lemery on the matter of fire. A. P. 1709. 400. H. 6. Boerhaave de igne. Elementa chemiac. I. 116. Winkler de frigore. 4. Leipz. 1737. Martine's medical and philosophical essays. Chatelet Dissertation sur le feu. 8. Par. 1744. Euler, Du Fiesc, Crequi, Chastelet, and Vol- taire on fire. A. P. Prix. IV. Kraft on cold and heat. C. Petr. XIV. 218. Bikkcr de igne. 4. Utrecht, 1756. Hillarij on fire. 8. Lond. 176O. Belgiado del calore e dtil freddo. Parma, 1764. Inqiiirj/ into the effects of heat. 8. Lond. .1770. Herbert de igne. 8. Vieun. 1773. 384 CATALOGUE. — HEAT AND COLD. Bordenave on fire. Roz. IV. 104. Changeux on heat and cold. Roz. VI. 299, 357. Marat decouvertes sur le feu. 8. Par. 1779. Marat lecherches sur Ic feu. 8. Par. 1780. Donnsdorf uber Electricii'at. Magellan Essai sur la nouvelle theorie du feu elementaire, 1780. Magellan on hre. Roz. XVII. 375, 411. Lavoisier and Laplace on heat. A. P. 1780. 355. H. 3. Scheele Traite de Tair etdufeu, par Dietrich. 12. Par. 1781. R. S. Hopson on fire. 8. Lond. 178). Fontana on light, flame, and heat. Soc. Ital. I. 104. Scopoli, Volta, and Fontana on heat. Crell. ■ N. Entd. XII. 2. Annalen, 1784. Erxleben on the laws of heat. N. C. Gott. Physik. chem. abh. I. 330. Experiments on light and colours, with the analogy between heat and motion. 8. Lond. 1786. Baader \om w'armestofF. 4. Vienn. and Leipz. 178(5. Thompson (Count Rumford) on heat. Ph. tr. 1786, 1787, 1792. Rumford's institution of a prize. Ph. tr. 1757.215. Ducarla sur le feu. R. I. Carradori Teona. del calore. 2 vol. Flor. 1787. Extr. Roz. XXXIV. 271. Marne iiber feuer, licht, und warme. 1787. Weber iiber das feuer. 8. Landshut, 1788. La Serre theorie du feu. Avignon, 1788. Berlinghieri on heat. Roz. XXXV. 113, 433. Seguin on heat. Roz. XXXVI. 417- Segnin sur les phenomfenes du calorique. 8. R. S. Deluc's Letters, cxli. *Crawford on animal heat. 2 ed. 8. Lond. 1788. R. I. Lesanelier sur I'air et le feu. 2 v. 8. Par. ^1788. R. S. *Pictet Essais de physique. 8. Gen. 1 790. Pictet on ti\e. 12. 1791. R.I. <. Annales de Chimie, in many parts. Saussure on heat. Roz. XXXVI. 193. *Mai/er iiber die gesetze des warmestofls. 8. Erlang. 1791. R. I. Lampadius iiber electricitat und warme. 8. , Berl. 1793. Dalton's meteorol. obs. 115. Voigt Theorie des feuers. 8. Jena, 1793. Lampadius iiber das feuer. 8. Gott. 1793. Franklin on light and heat. Am. tr. III. 5. Gottliug Beytrag zur antiphlogistischen chemie. 8. Weimar, 1794. Gehler's phys. wbrterb. II. 207. Harrington on fire on heat. 8. Lond. 1796, 1798. R. S. Socquet sur le calorique. Journ. Phys. LII. 214. On Parr's theory of light and heat. Nich. II. 547. Mangin Theorie du feu. 8. Paris. 1800. R. S. Aslley on the doctrine of heat. Nich. V. 23. Von Arnim on heat. Gilb. V. 57. Prize questions on heat. Ph. M. I. 323. *LesUes inquiry into the nature and pro- pagation of heat. 8. Lond. 1804. U. I. CATALOGUE. — HEAT. 385 Sources of Heat and Cold. Sources simply mechanical; fric- tion, compression. See Capacity for Heat. Philo Belopoiica. Says that fire came out of Ctcsibius's airgun. Friction. Pliny Hist. nat. §. 76, 77. Of heat and cold in a vacuum. C. Bon. H. i. 312. Of cold from expansion in the machine at Schemnitz. Ph. tr. ]762. Darwin's frigorific experiments on the ex- pansion of air. Ph.tr. 1788.43. An effect of 4" or 5° was produced in some experiments. Pictet on heat from friction. Ess. ix. Picteton cold produced by exhaustion. Journ. Phys. XLVn. (IV.).186. Baillet on ice produced by the expansion of air. Journ. Phys. XLVIH. IG6. Rumford on the heat excited by friction. Ph. tr. 1798. 80. Ess. 11. ix. Nich. H. 10(3. On heat from compression. Ph. M. VHI. 214. Dalton on the heat produced by mechanical condensation. Manch. M. V. 515. Nich. 8. ni. 160. Repert. ii. H. 118. Ph. M. XUl. 59. Gilb. XIV. 101. Estimates, that air under the pressure of two atmo- spheres absorbs 50° of heat in expanding ; and that some- thing more than iO° is produced when air is admitted into an exhausted receiver. See Capacity. Davy on the collision of steel. Journ. R. I. I. Nich. 8. IV. 103. On heat in the condenser. Ph. M. XIV. 3G3. B. Soc. Phil. n. 87. Tow was inflamed in an air gun ; and light was seen through a strorg glass fixed in the substance of the ma- chine. VOL. II. Combustion. See Economy of Heat. Sage on fuel. A. P. 1785.239- Roz. XXVIII. 57. Fordyce. Ph. tr. 1787- Suspected that fuel difFerently burnt gave diflferent quan- tities of heat. Sometimes indeed much is wasted iu smoke. Thomson on combustion. Nich. 8. II. 10. Spontaneous Combustions. Albiniis et Kletwich de phosphoro. 8. Frankf. an der Oder 1688. Lefevre on a' spontaneous inflammation of serge in a fulling mill. A. P 1725. H. 4. The Empress and Georgi on spontaneous in- flammations with oil, soot, and other sub- stances. A. Petr. III. i. H. 3. Carette. Roz. XXVII. 92. Morozzo on spontaneous inflammations. M. Tur. 1786. III. 478. Repert. II. 4l6. Humfries on a spontaneous inflammation. Ph.tr. 1794. 426. From linseed oil poured on cotton cloth. Spontaneous inflammations at Spalding and ' elsewhere. Repert. III. 19, 21, 95. Supposed s])ontaneous combustion of a black silk stocking. Ph. M. XVI. 92. Bartholdi on spontaneous inflammation. Ann. Ch. Nich. VIII. 216. Effects of Heat. Temporary Effects and Measures of Heat. Expa?uion. Pyrometers, Thermometers, * See Meteorology. Experiments of the Academy del Cimento. i. With Musschenbroek's additions. Spicit thermometers described. 3 D 386 CATALOGUE. HEAT, EXPANSION. Hooke's statical tTiermometer. Birch. II. I. Waliis and Beale on thennoscopes. Ph. tr. ]65y. IV. 1113. *Croune on the expansion of water before it freezes. Birch. IV. 26. With Hooke's objections, and Croune's further experi- ments. Dated 2? Feb. 1684. Picard on the effect of cold on stones and metals. A. P. I. 77. Lahire on the effects of heal and cold. A. P. II. 36. IX. 316, 322. Lahire on thermometers. A. P. 1706. 432. 1710. 546. H. 13. 1711. 144. H. 10. Lahire on the expansion of air by boiling water. A. P. 1708. 274. H. 1. Amontons on the effects of heat on air. A. P. 1703. 101. H, 6. Amontons assumes, that his thermometer is the natural measure of absolute heat : Lambert and Dalton afterwards advanced nearly the same opinion. Amontons on the appaient fall of the ther- mometer. A. P. 170o. 75. H. 4. Hauksbee on the weight of water in different ' circumstances. Ph. tr. 1708. XXVI. 93. 221. Brook Taylor on the expansion of fluids in the thermometer. Ph. tr. 1723. XXXII. 291. He found the expansion proportionate to the increments of heat by mixture. Leupold. Th. Aerostaticum. Musscheubroek's pyrometer. Tentam. Exp. and in Desagul. Phil. I. 421. Leutmann Traite des barometres. Bulfinger de thermometris. Comm. Petr. III. 196, 242. IV. 216. Reaumur on thermometers. A. P. 1730. 452. 1'731. 250. H. 6. Reaumur's degrees are thousandths of the bulk of his diluted alcohol. Delisle on thermometers. M. Berl. 1734. IV. 343. * Delisle on the mercurial thermometer. Ph. tr. 1736. XXXIX. 221. Delitle sur Tastronomie et la geographic physique. 4. Petersb. 1738. Delisle's degrees are ten thousandths of the bulk of the mercury, neglecting the expansion of glass. Fahrenheit's are nearly ten thousandths, without this inaccutacy. Eilicott's pyrometer. Ph. tr. 1736. 297. Braun's comparison of scales. C. Petr. VII. Weitbrecht on thermometers. C. Petr. VIII. 310. Krafft on thermometers. C. Petr. IX. 241. Marline on thermometers, heating and cool- ing. 12. Segner de aequandis thermometris aereis. 4. Gott. 1739. Bernoulli's air thermometer was like a barometer,' with the reservoir hermetically sealed. Clayton on the elasticity of steam. Ph. tr. 1739. XLI. 162. A digester exploded. Ludolff on thermometers. M. Berl. 1740» VI. 255. Grischow's comparison of 1 7 thermometers, M. Berl. 1740. VI. 267. Description d'un thermometre universel. 8. Par. 1742. M. B. Celsius on thermometers. Schw. Abb. 1742. 197. Makes lOO degrees between the freezing and boiling points of water. Bouguer on the expansion of metals. A. P. 1745. 230. H. 10. Wheler on the rotation of tubes near the fire. Ph. tr. 1745. XLIII. 341. By the curvature. Mortimer on thermometers, and on a metal- line thermometer. Ph. tr. 1747. XLIV, 672. n. 484, 485. Halley suggested mercurial thermometers ; Fahrenheit introduced them. A metalline thermometer for multiply- ing the expansion by means of bars. CATALOGUE. HEAT, EXPANSION. 387 Johnson on Fotheringham's metalline ther- mometer. Ph. tr. 1748. XLV. 128. Stancari's thermometer of air and mercury. B. Bon. I. 209. Galeati on an air thermometer. C. Bon. II. ii. 201. Tabarrani on thermometers. C. Bon. II. iii. 233. ■f-Miles on thermometers. Ph. tr. 1749. XLVI. 1. Wargentin on thermometers. Schw. Abh. 1749. 1G7. Bourbon's thermometer, with a concave bulb. 1752. II. 148. Richmann on heat, as measured by ther- mometers and lenses. N. C. Petr. IV. 277. Finds the expansion greater in greater heats. *Smeaton's pyrometrical experiments. Ph. tr. 1754. 598. Errata. Lamljert on expansions. Act. Helv. II. 172. *Lambert Pyrometrie. 4. Berl. 1779- Lord Charles Cavendish on thermometers for particular uses. Ph. tr. 1757- 300. For showing the majcimum and minimum. Hecueil de diverses ]/ieces sur le thermometre et barometre. 4. Bale, 1757. Act. Helvet. m. Bergen de thermometris. 4. Nuremb. 1757. Essays on the thermometer. Act. Helv. III. 23. Sulzer on thermometers. Act. Helv. III. 259. Roz. XI. 371. Zeiher's metalline thermometer. N. C. Petr. IX. 305. Zeiher on mending thermometers, N. C. Petr. IX. 314. By a bulb of iron, adjusted by a screw to the scale. Fitzgerald's metalline thermometer. Pli. tr. 1760. 823. 1761. 146. Compound bars. Titii descriptio thermometri, Loescri. Leipz. 1765. Musschenbroek. Intr. II. Copper and brass appear to have expanded more when drawn into wire ; lead somewhat less. Hennert Traite des thermoraetres. Hague, 1768. DonnsdorfFs Electricitat. Soumille's thermometer of four parts, for en- larging the degrees. A. P. 1770. H. 1 12. Hauhold de thermometro Reaumuriano. 4. Leipz. 1771. Meister on the scales of thermometers. N. C. Gott. 1772. [II. 144. Perica's thermometer. Roz. II. 512. Herbert de igne. Vienna, 1773. Pasumoi's thermometer. Roz. VI. 230. Strohmej/er uber die thermometer. S Gott^ 1775. Fontana on the Grand Duke's cabinet. Roz. IX. 41. *Roy's experiments subservient to the mea- surement of heights. Ph. tr. 1777. 653. Roy on Ramsden's pyrometer. Ph. tr. 1785. 461. The fixed parts were of cast iron, and were kept at the freezing temperature : the object glass of the micrometer was fixed exactly over the ends of the expanding bars, mov- ing with them, and showing a difference of ^^ of an inch. When the adjustment was perfect, the expansion was found not to vary in dilferent parts of the scale. Report of a committee of the R. S. on ther- mometers. Ph. tr. 1777. 816. *DeIuc on pyrometry and areometry. Ph. tr. 1778.419. Measured the proportions of expansion by asocrtaining the quiescent point of a compound bar. Finds a tardiness in most metals to return to their original dimensions after having been heated, when slowly cooled. Attributes an irregularity to the expansion of glass, which later obser- vations have not confirmed. Deluc observes, that all fluids begin to expand more ra- pidly as they approach their boiling points. Rech. sur I'atm. II. It appears from Wedgwood's exjerimenis on a silver 388 CATAtOGUE. — HEAT, EXPANSION. piece, that in mercury the inequality cannot be very great. Deluc on expansions. Roz. XLTII. 422. Fan Smndtn sur la comparaison d5 .003379 .00000625 .00001875 .001150 .0034 54 .00000639 .00001917 Steel .0011574 .003475 .00000642 .00000661 .00001928 .00001985 Hard steel .001225 .003679 .00000681 .00002042 Annealed steel .00122 .00367 .0000068 .0000204 Tempered steel .00137 .004)1 .0000076 .000022 8 Iron .001156 .003472 .00000642 .00001926 .001258 .003779 .00000699 .00002097 Annealed iron .00133 .00400 .0000074 .0000222 Hammered iron .00139 .004 1 7 .0000077 .0000231 Bismuth .001392 .004180 .00000773 .00002320 Annealed gold .00140 .00438 .0000081 .0000243 Gold .0015 .004 5 .0000093 .000025 Gold wire .O0167 .00502 .0000093 .0000279 Copper hammered .001700 .005109 .00000944 .00002833 Copier .00191 .00573 .0000106 .0000318 Brass .001783 .005359 .00000091 .00002973 Wedgwood says, th«t ear&eBware made porous by charcoal, expanded only \ as much as when solid. Much less than glass. Rittenhouse. Roy. Ph. tr. 1785. He had before found a glasi tube expand 4 times as much as a rod. Smeaton. Ph. tr. 1754. Deluc's mean. Ph. tr. 1778. Roy. The same glass as the tube. Roy, 1777. As glass. Borda. Berthoud. Smeaton. Roy. Lavoisier. Roy. Ph. tr. 1795. 428. Smeaton. Lavoisier. Troughton. Nich. IX. Smeaton. Musschenbroek. Musschenbroek. Borda. Smeaton. Musschenbroek. Musschenbroek. Smeaton. Musschenbroek. Ellicott, by comparison. Musschenbroek. Smeaton. Musschenbroek. Borda. If glass expanded equally, the expansion of brass at 90° would be about 07 parts for l", the mean of the whole scale being 108 ; but if the inequality of the expansion of glass is so great, as appears from De Luc's experiments, the expansion of brass, al 90°, can be but about fiO pa;ts for !». 5 CATALOGUE.'— HEAT, EXPANSION. 391 Solids. For J 80 «,?. For J^ '.F. In length. In bulk. In length. In bulk. Brass scale, supposed fromHarobws ..0018554 .005575 .00001031 .00003092 Roy. Cast brass .001875 .005635 .00001042 .00003125 Smeaton. English plate brass rod .0018928 .005689 .00001052 .00003156 Roy. English plate brass trough ,001S»49 .005695 .00001053 .00003159 Roy. Brass .00001066 .00003200 Troughton. Nich. IX. Brass wire .001033 .005811 .00001074 .00003222 Sraeaton. Brass .00216 .00648 .0000120 .0000359 Musschenbroek, Copper e, tin I *OJ817 .005461 .00001009 .00003028 Smeaton. Silver .00189 .005681 .00001050 .0000315 Herbert. .0021 .0063 .00001167 .000035 EUicott, by comparison.. .002 la .00636 .0000118 .0000354 Musschenbroek. Brass 16, tin I .001908 .005736 .00001056 .00003168 Smeaton. Speculum metal .001933 .005811 .00001074 .00003222 .Smeaton. Spelter solder, hiass 2, zinc I .002058 .006187 .00001148 .00003430 Smeaton. Fine pewter .002283 .U06866 .00001230 .00003714 Smeaton. Grain tin .003483 .007469 .00001379 .00004137 Smeaton. Tin .00384 .00852 .0000159 .0000474 Musschenbroek. Soft solder, lead 2, tin 1 .002508 .007545 .00001393 .00004170 Smeaton. Zinc e, tin I, a little hammered .003692 .008095 .000014 96 .00004388 Smeaton. Lead .002S67 .00862 5 .00001592 .00004776 Smeaton. .00344 .01032 .0000191 .0000573 Musschenbroek* Zinc .003942 .008850 .00001634 .00004902 Smeaton. Zinc,hammeredouthalf aninch per ft. .003011 .009061 .00001673 .00005019 Smeaton. Liquids. Mencujty OJS88S .0000855 Cotte. Probably in glass. .016» .0000917 Mean of several experi- iji«nls. Lichtenberg. Sp. gr. I3.eat45''. .016*9 .000092 Achard, in glass. .0185 .000103 Deluc and Laplace. From 82°'to 104" .00010415 .000108 Deluc, corrected by Roy. Roy. Sp. gr. 13.61 at 68" .000104 ,00010985 Id. Ch. Cavendish. Mean of Shuckburgh's cxpe- liments. Rosenthal. .9i7iS3 .000097 Hallstrom. Seems to al- low too little for the glass. It may be inferred from'Deluc's experiments, that the mercurial thermometer may be reduced to anatural scale by adding to jnti the temperature that it indicates .07 ' m beiivg the number of degrees above the freezing point, and n the number below the boiling point, m + n of course 180, 80 or 100, according to the scale employed. These experiments ought, however, to be repeated by mixing various fluids, before we can be confident that their results are perfectly natural. Besides Dr. Crawford, another most able philosopher has found the mercurial scale less at variance with the natural one. According to this correction, 650" would be reduced to 540° for the boiling point of mercury on the natural scale j Hut Wedgwood's silver gage makes it about 607". TABLE OF THE NATUBAt SCALE, ACCORDING TO DELUC. MODIF. DE l'aTM. 30p. Merc. R. Nat. R. Form. R. Merc. R. Nat. R. Form. R. 0 0 0 45 -46.37 46.35 5 4.43 5.33 50 51.26 51.31 10 . 10.74 10.61 55 56.15 56.20 15 15.94 15,85 60 6O.96 61.05 SO 31.12 21.05 65 65.77 65.85 25 26.22 36.20 70 70.56 70.61 30 81.32 31v31 75 75.28 75.33 35 36.40 36. S5 80 80.00 80.00 40 41.40 41.40 Richraann also found the expansion greater than in proportion to the heat ; and if the apparent difference in his expe- riments had arisen from this circumstance only, it would have indicated an inequality more than twice as great as is' shown in those of Deluc. 39'2 CATAtOGUE. — HEAT, EXPANSION. Water. The degrees of Fahrenheit's thermometer, reckoning either way from 39", being called /, the eitpansion of water is nearly expressed by .000 0025!/"' — .000 000 00435/', or* more shortly, 22/' (l — .OO'if], in ten millionths; and the diminution of the specific gravity by .000 002!$/"' — .000 ooo 004? s/'. 10^ so Specific gravity. Diminution of sp. gr. Observed. Obsen'cd. Calculated. As 69°. Dalton corrected. .99980 Gilpin, 20 34 39 44 48 49 54' 59 04 69 74 77 79 (82) 90 100 102 122 142 162 J67 182 202 213 1794. • 99988 -G. •99994 G. 1.00000 G. .99994 G. .99982 G. .99978 G. .99951 G. •99914 G. .99867 G. .99812 G. .99749 G. .99680 G. .99612 Kirvran. .99511 G. 1790. .99313 G. ,99246 K. .98757 K. .98199 K. .97583 K. .96900 K. .96145 K. .95848 K. 12 0 6 18 22 49 8fi 133 188 251 225 DeLuc.by comparison. 320 388 489 687 754 1243 1128 Dr Luc. 1801 2417 2520 De Luc. 3100 3855 4152 4400 De Luc, by 18 11 5 o 5 18 22 48 S4 130 186 SSO 322 368 509 711 753 1247 1818 2443 3109 3802 4140 comparison. Expansion. Observed. Calculated. .00020 .00018 For 1°, .00004 .00012 .00011 -OOOJ {•oooi44M.Inst.) .00006 .00005 .00002 .00000 .00000 .00000 .00006 .00005 .00002 .00018 .00018 .00004 .00022 .00022 .00004 .00049 .00048 .OOOOS .00086 .00O84 .00008 .00133 .00130 .00010 .00188 .00186 .10012 .00251 .00251 .00014 .00299 Achard. .00321 .00328 .00016 .003 89 .00372 .00017 -00491 .00513 .00020 .00692 .00720 .00024 .00760 .00763 .00025 .01258 .01264 .00029 .00949 Achard, .01833 .01859 .00031 .02481 .02512 .00034 .03198 .03219 .00036 .04005 .03961 .00037 .04333 .04332 .00038 De Luc's experiments were only comparative ; hence the point of coincidence with Gilpin and Kiiwan is assumed upon a mean. His expansions vary more nearly as f*. Hauksbee says, that water freed from air expands one third less by heat. Ph. tr. 1708. 22T. Saturated brine. One fifth more than water. Robison. Sulfuric acid Sulfuric acid, sp. gr. 1.7 Sulfuric acid, sp.gr. 1.84 Muriatic acid, sp. gr. 1.1 9» Nitrous acid, sp. gr. 1.43 Spirit of turpentine For 1° F . .00031 Achard .00026 At 60° Kirwan. Ir. tr .00021 At 55° Kirwan. .00029 At 60° Kirwan. .00037 At 65° Kirwan. .00035 At 50° Kirwan. •00037 At 53° Kirwan. •00055 At 60° Kirwan. .00070 At 65° Kirwan. .00052 Achaic CATALOGUE. HEAT, CHANGES OF FORM. 593 Comparative Specific Gravity. Expansion, supposing the unit at 32'. _ By Obser- By For- For each tpirit highly rectified. vation. inula. Degree. •pecifiegr.at60''.8a5. oOF. 1.0326 oOF. — .0162 .00047 10 1.0275 12 — .0105 .00050 30 1.0223 32 .0000 .00054 so 1.0169 1.0168 52 .0110 .00057 35 1.0142 1.0141 .0132 Achard. 40 1.0114 1.0114 72 .0229 .00061 45 1.0087 1.0086 92 .035 5 .00065 50 1.0058 1 0057 112 .0489 .00069 S5 1.0029 1.0029 132 .0633 .00074 60 1.0000 1.0000 152 .0784 .0007s 05 .9971 .9971 172 .0946 .00083 70 .9942 .9941 175 .0971 75 .9913 .9912 . 80 Gilpin. Ph, tr. 171)4. .9882 .9882 100 .9758 120 .9630 140 .9496 160 .9358 180 .9214 The temperature being/", the comparatire specific gravity is 113456 — (i/+ 101 60°, 1 — .00058/ — .000000 625/». According to Gaussen's comparison of Deluc's experiments, the expansions constitute a /+ vh./ '> which becomes nearly .00053/ + .000 000 6001/*. Vitriolic ether .00072 Achard. Linseed oil .0009 About 32". Achard. Olive oil .0007 About 100°. Achard. Deluc found the expansion of olive oil, at 32° to its expansion at 212° as 47 to 54 somewhat less difference in proportion. Gases. Dry air, i.at 32» or reckoning the degrees front series, varying nearly as in middle temperatures there was For 180°. For 1°. .376 .00209 .377- .370 .00206 .388 .00216 .381 .00212 .00214 .00210 (.484) . (.00243) .357 .00198 .400 .00222 •.378 .00210 .393 .00218 .00224 .00212 (.434) (.00241) Mean of 6. LacaiUe giving .04, Mayer .046, Bonne .0477, Shuckburgh .0505, Bradley 0544, and Deluc .047, for the expansion. From 32° to 54.8° : the mean .0476. Deluc. Mayer's refractions. Gilbert. l.ambert. ' Deluc, reduced by Gilbert. LuE. About 95°. Luz. About 172°. Luz. Roy : but moisture was admitted. Schmidt: thinks it perfectly uniform, becom- ing .7 at 392°. Laplace. Syst. du monde. Gay Lussac, corrected for the expansion of glass, =: .003 or .003 5. Dalti n, reduced by Gilbert. About 95°. Dalton. About 172°. Dalton. Air, 2^ times as dense as usual (.434) (.00241) Roy. Moist air, as dry air. When additional moisture is excluded. Saussure. Hydrogen gas. ' Oxygen gas. Azotic gas. Carbonic acid gas. Muriatic acid gas. Sulfureous gas. Nitrous gas. VaiJour of sulfuric ether All as lif. Gay Lussac, and Dalton. The inequality of the mercurial scale, as observed by Deluc, is more than equivalent to the inequality of the expansion «f air, as observed by Luz, but only half as much as that which is assigned by Dalton. Robins found that air was expanded by a red heat to 4 timet iU bulk. This would indicate, according to Schmidt, a temperature of about 1580°. TOL. II. 3 X J9+ CATALOGUE. HEAT, CHANGES OF FORM. ¥ff(cti of Heat on the Form of Aggregation. Freezing, Thawing, and Melting. Merrct on freezing. Birch. I. 330. Rinaldini on ice made without air. Ph. tr, 1671. VI. 2169. Says that it is heavier than common ice. On the expansion of water in freezing. Ph.tr. 1698. XX. .S84. Desmasters on freezing water. Ph. tr. l698. . XX. 439. Lahire on the effect of cold on water in a pistol barrel. A. P. I. 14. Lahire on the figure of ice. A. P. II. 144. Lahire on ice and on cold. A. P. IX. 313. Buot on the expansion of water in freezing, A. P. 1.76. Varignon on ice. A. P. II. 70. Perrault on the effects of cold on water, boiled or not boiled. A. P. I. 77. Perrault on congelation. A. P. I. 252. Homberg on ice. A. P. II. 105. X. 173. 17O8. H. 21. Observes, that it thaws faster in a vacuum than in the air. Homberg on ice free from air. A. P. X. 173. Thinks that it is as dense as water. Mariotte on the congelation of water. A. P. X. 352. Newton's table of temperatures. Ph. tr. 1701. XXIII. 824. Amontons on the apparent fall of the ther- mometer. A. P. 1705. 73. H. 4. Hauksbee on freezing water freed from air. Ph. tr. 1709. 302. Found no difference in the density. Fahrenheit de congelatione in vacuo. Ph. tr. 1724. XXXIII. 78. Middleton found that the ice of sea water contained _L of salt, in Hudson's bayi Triewald on congelation. Ph. tr. 1731. XXXVII. 79. Produced suddenly by pressure. NoUet on ice. Ph. tr. 1738. XL. 307- Gmelin on the cold of ice. C. Petr. X. 303. Hollmann de subita congelatione. Ph. tr. 1745. XLIII. 239- Sylloge comm. 138. Experiments on steam. Desaguliers's lect. H. 333. Bertier on a knife projected from a lump of frozen snow. A. P. 1748.29- Richmann on the force of water in freezing. N. C. Petr. I. 276. Mairan on ice. Ace. A. P. 1749- H. 53. On the thawing of ice into crystals. A. P. 1751. H. 37. Braiin de frigore artificial!. 4. Petersb. 1760. Braun on the freezing of fluids. N. C. Petr. VIII. 339. Braun on the freezing of mercury by artifi- cial cold. N. C. Petr. XI. 268, 302. Watson's extract. Ph. tr. 1761. 156. Poissonnier on the congelation of mercury^. A.P. 1760. H.26. Wilke on freezing. Schw. Abh. XXXI. Lavoisier on freezing. Roz. Intr. II. 510. Black on the congelation of boHed water. Ph. tr. 1775. 124.' Takes place at 31°, perhaps from the entrance of air. Cherna de aqua intra aquam. 4. Groning. 1775. Hutchins on freezing quicksilver. Ph. tr. 1776. 174. Hutchins's experiments on the congelation of quicksilver. Ph. tr. 1783. 303*. Nairne on the freezing of sea water. Ph. tr. 1776.249. Roz. IX. 361. Van Smnden sur le froid de 1770. 8. Amst. 1778. On freezing. Flauguergues on congelation. Roz. XV. 477- CATALOGUE.^^HEAT, CHANGES OF FORM. 595 De Luc Tdees sur la met^orologie. I. ccvii. II. dcvi. On freezing. Pure boiled water may be cooled to 14" without freezing. Wilson's e.vperiments on cold. Ph.tr. 1781. 386. Snow was observed to evaporate at 27" F. without being perceptibly cooled by it. It adhered firmly to glass at 3" ; perhaps the contact of air may cause snow to melt more readily, producing the increased cold which is sometimes observed in it. ♦Cavendish on Hiitchins's experiments. Ph. tr. 1783. 303. Makes the point of congelation of mercury — asj" of the Royal Society's thermometer. Cavendish on Macnab's experiments in Hudson's bay. Ph. tr. 1786. 241. Finds that the sulfuric and nitric acids may be cooled mach below their freezing points without congelation ; that their strength rather raises than depresses their freezing points, but that when diluted they seem to have two freezing points, one for the acid, the other for the water, both of which however depend on the strength. Thus the nitric acid, its strength being .56, freezes at — 30°, .53 at 19°; .437 at — 4j°; the nitrous acid, strength .54, freezes at— 3li°, .411 at— li», .38 at — 45^", ,243 at 44i», .91 at— 17°: the sulfuric acid, strength .98 at— 15", .629 at— 36°, .41 at— 78j°, .35 at — 68^°, .34 at — 6S°, .33 at— 55^°. Diluted alcohol is also similarly af- fected. Mr. Macnab produced a cold of 7 g^". Cavendish on Macnab's further experiments. Ph. tr. 1788. 166. Confirms his former conclusions, and those of Mr. Keir, respecting the sulfuric acid ; this has a second point of difficult congelation about the strength of .92, freezing at about — 26°. Thus at .977 the freezing point was + 1°, at .918, — 26°, at .846, + 42°, at .75S, — 45°. In Keir's eiperiments the acid of the density of .848 was frozen at 46". Blagden's history of the congelation of mer- cury. Ph.tr. 1783.329. Blagden on the cooling of water below its freezing point. Ph.tr. 1788. 125. Boiled water is only more readily frozen when it is ren- dered turbid. Sand, or broken glass, did not promote the congelation, nor even agitation, unless it was minute, as when the inside trf the vessel was rubbed with \Tax, a little water being interposed. A thin film was more easily- frozen. The access of air only promotes congelation when it is loaded with frozen particles ; the smallest particle of ice producing the effect instantaneously. The contact o£ metals seems to facilitate congelation, and the rapidity with which the water Is cooled. Water expands considerably when thus cooled. The greatest cold supported without freezing was 20°. Blagden on the congelation of aqueous so- lutions. Ph. tr. 1788. 277. The point of congelation of water with - of salt was 112 " 32° ; thus, with 1 it was 4°, with ^, 2Sf. Other salts followed also similar laws. Crystallization did not seem immediately to promote congelation. The maximum of density of water with Jf of salt was about 8° above its freezing point. Euler and Krafft on the congelation of mer- cury. N. A. Pelr. 1785. III. 60. At about — 36" or — 40*. Guthrie sur la congelation du mercure. 4. Petersb. 1785. Keir on the congelation of the vitriolic acid. Ph.tr. 1787. 267. Found that the sulfuric acid of the specific gravity 1.7 so, fieezes at 45° F. into crystals, which are more dense than 1.924, perhaps more than 2, while solid, but which thaw into acid of the specific gravity 1.7 80, whether the acid was originallj- a little more or less dense. But when the specific gravity varies as far as 1.75 or 1.81, it will not freeze at 1 8° F. Chaptal on the congelation of sulfuric acid. Roz. XXXr. 468. Walker. Ph. tr. 1788. 395. Cooled water to 10° without freezing it. Walker on the congelation of quicksilver in England. Ph. tr. 1789. I99. Saussure on liquefaction. Roz. XX-XVI. 193. Williams on the expansive force of freezing- water. Ed. tr. IL 23. Makes the expansion ^', or J^-. From the difference of refractive power it might be expected to be ,', or f . Priestley on the air evolved in freezing. Am. tr. V, 36. ' 596 CATALOGUE,— HEAT, CHANGES OF FORM.; Heller on the freezing of water. Gilb. 1.474. + Dickson on water freezing. Ph. M. VII. 69. t Blandiet on explosions. Ph. M. VII. 71. Weber on the strength of ice. Gilb. XI. 353. Driessen on the congelation of water. Ph. M. XV. 249. Crichton on the melting point of lead and tin. Ph. M. XVI. 48. Sir J. Hall of the effects of heat with com- pression. Nich. IX. 98. See Tables of the Effects of Heat. Degrees of Fluidity. 'Gerstner on the fluidity of water of differ- ent temperatures. Bohm. Gesellsch. 1798. Gilb. V. 160. AYith a tube .0074 inch Fr. in diameter, 33 long, a re- s«rvoir was half emptied in 35' 34" at 30" Reaum. in 60' 56" at 10°, in -6' 19" at 4°, the remaining half in 157' ■io", 201' 40", and 38l' respectively. With a tube .136 in diameter, 7.9 long, the times of the discharge of the first half were q' 31", 2' 42", and 2' 44" : of the second half 7' 16", 7' 5j", and s' 22". Boiling, Simple Evaporation, Sublimation, Volatilisation and Deposition. Boyle on fixedness. Birch. III. 144. ' Hooke discovered the permanency of the temperature of boiling water in 1684. Papin on distilling in vacuo. Birch. IV. 427. Homberg on the heat of boiling water. A. P. 1703. H. 25. Fahrenheit de calore llquorum ebullientium. Ph.tr. 1724. XXXin. 1. Reaumur on the evaporation of snow. A. P. 1738. H. 36. Ludolff on the evaporation of mercury. M. Berl. 1741. VI. 109. Nollet on ebullition, A. P. 1748. 57. Richmann on evaporation. N. C, Petr. I. 198, 284. II. 134, 145. On the effect of Ch« depth of t«3««1s, and on tht cold fioduced. Baron on the evaporation of ice. A. P. 1753. 250. H. 194. Cullen on evaporation. Ed. ess. 11. 145. Leide7ifrost de aquae qualitatibus. S.Duisburg. 1756. On evaporation at low temperatures. Franklin's letters. I. 303, 398. Roz. II. 276. On cold from evaporation. M. Taur. I. Cigna on evaporation. M. Taur. II. 143. Cigna on ebullition. Roz. III. 109. Fourcroy de Ramecourt on the vapour of mercury. A. P. 1768. H. 36. Wistar on the vapour of melting ifce. Roz. VI. 183. Gilb.V. 354. On water thrown into melted glass. Roz. XI. 30, 411. >4ji:ll Grignon on the effects of a drop of water on hot substances. Roz. XII. 288. Lavoisier on elastic fluids. A. P. 1777. 420. H. 20. Lavoisier on fluids becoming aeriform at low temperatures. Roz. XXVI. 142. Deslandes, Bosc d'Antic, and Grignon on. evaporation at low temperatures. Roz.. 1778. Shuckburgh on the temperature of boiling water. Ph. tr. 177iJ. 362. Fontana on evaporation in quiescent air. Roz. XIII. 22. Finds that evaporation does not take place in closed vessels when the heat is communicated from above. But perhaps the heat was not conveyed to the fluid. Milon on evaporation in a vacuum. Roz. XIII. 217. Achard. Berl. Naturf. I. 1 12. Koz.XVI. 174. Achard on the heat of boiling fluids. A. Berl. 1782.3. 1783. 84. Achard on measuring heights by the boiling point of water. A. Berl. 1782. 54. Achard on the effect of diflisrenl substances upon the temperature of boiling water. A. Berl. 1784. 58. With a copious table. ^ \ CATALOGUE. — HEAT, CHANGES OF FORM. 397 ■fhe whole effect of any insoluble subsKmce seldom amounted to a degree of Reaumur. Metallic filings gene- rally lowered the point of ebullition. Achaid on the boiling point of water. A. Bed. 1785. 3. Finds some irregularities from the nature of the vessels. Aciiard on the effect of salts upon the boil- ing point of water. A. Berl. 1785. 67. Wilson on cold. Ph.tr. 1781. 386. Snow was found to evaporate at a?", but was not per- ceptibly cooled by it, yet the thermometer was always lower on the snow than in the air, unless very deeply immersed. Cotte on the evaporations from different vessels. Roz. XVIII. 306. Cavallo on cold from evaporation. Ph. tr. 1781. 511. Delessert on the heat of steam. Iloz. XX VIII. 170. Saussure on evaporation. Gren. I. iii. 460. Roz. XXXIV. 443. Betancourt siu' la force expansive de la ^ vapeur de I'eau. 4 Paris, R. S. Journ. polyt. Prony Arch. hydr. I. 157. Hut- ton's dictionary II. 755. Ph. M. I. 345. Deluc on the heat of boiling water. Roz. XLII. 264. Dalton on the force of steam. Meteor, essays. * Dalton on the force of steam and on eva- poration. Manch. M. V. 53. Repert. ii. I. 22. Gilb. XV. 1. Crichton on the boiling point of mercury. Ph. M. XVI. 48. Lichtenberg. Erxleb. Natnrl. Observes, that pure water may be heated to 234° be- fore it boils, and that it Will then sink to 212°. Table of temperatures. Erxleb. Natiirl. 401. Volta's apparatus for experiments on etherial vapour. Ann. Ch. XII. 292. Volta's notes. Gilbert. XV. B. Prevoston the motions of odorous bodies, and on rendering their emanations visible. Ann. Ch. XXII. 31. XL. 3. B. Soc. Phil. n. 8. S. E. to he printed. Guyton on odorous emanations. Ann. Ch. XXVH. 218. Canadori on heat, evaporation, and inevapo- rable fluids. Ann. Ch. XXIX. 93. XLII. 65. Gilb. XII. 103. Carradori on Prevost's expansion of odours, Ann. Ch. XXXVII. 38. Biot on Prevost's experiments. B. Soc. Phil. 11. 54. Klaproth on the evaporation of a drop of water at a high temperature. Journ. Phys. LV. 61. Nich. 8. IV. 202. Van Maruni on the conversion of licjuids into gases in a vticuum. Gilb. I. 145. On the specific gravity of steam. Repert. IX. 249. Correcting a blunder of Desaguliers. Messier on the sublimation of mercury. M. Inst. IL 473. Gilb. XII. 96. Says, that heat would not produce the efTect without light, and that bubbles were seen rising, with a glass. *Bikker and Rouppe on the force of steam. Haarl. Verb. Gilb. X. 257. The steam was made to press on hot quicksilver ; great care was taken toexpel the air. Journ. R. I., I. 179. Von Charpentier Gilb. XII. S65. Denies the influence of light on the barometer, and the ascent of visible globules ; but he does not appear to have excluded all light. Gilbert's remarks on Dalton's experiments. Gilb. XV. 25. Soldneron Dalton'slaws of expansion. Gilb. XVII. 44. Mr. Giddy has favoured me with an account.of some very accurate observations on the quantity of water em- ployed for supplying a steam engine, by which it appears, that the specific gravity of steam under a pressure of about 30. is nearly .5^, or a little more than one third of that of air; which agrees very well with Desaguliers's experiments. Professor Robison observes, that, in his experiments, the addition of 30° to the temperature, in most cases, nearly doubled the elasticity both of steam and of the vapour of 398 CATALOGUE, HEAT, CHANGES OF FORM. alcohol. Hence he obseiTcs, that the logarithm of the elasticity should vary as the temperature. Encycl. Br. Art. Steam Engine. He could, however, discover no sensible elasticity in ilcohol at 32° ; nor could Betancourt Molina. Dalton pursues Robison's idea of the logarithmic, with some alterations: he made experiment? both under the air pump and with the Torricellian column ; he found that a difference of ll^" increased the elasticity 1.4925 times at 3J°, and 1.2425 times at 212", hence he infers that .015 is to be deducted from the ratio for every such inter- val, and continues his table both ways. But it is certain that this cannot bs the law of nature, since about 394° th« elasticity would become uniform, and then decrease, if the law were true. He says that Betancourt and Robison make the elasticity too great in high temperatures from the e.\trication of air: but the fact is, that when the greatest care has been taVen to avoid it, the elasticity has appeared nearly the same, and the circumstance, if it had taken place, would have been very immaterial. Indeed, the only support of Dalton's measures above the boiling jx«nt is the law, which he has imagined for the expansion of other vapours ; he tays, that their" elasticity is always equal to that of steam, at a given difFerence of temper- ature above or below them : and some experiments, that he adduces, agree exactly with the law j but it is utterly incredible that an expansive force of 7 tenths of an inch vihich thevapourof alcohol ought to have at the freezing point, should have entirely escaped both Betancourt and Professor Robison. Still, however, his rule for the force of different vapours must be allowed to be a very valuable approximation at temperatures between 50° and 220°. A much simpler formula will agree extremely well with all Dalton's experiments on water, and with the mean of all the best experiments that have been made by others in higher temperatures. It is this, the elasticity of steam in atmospheres of 30 inches of mercury is rf:r:(l-f-.002(}/")', y being the degrees of Fahrenheit above a 1 -a", whence we .1 have /iz ' for the elevation of the boiling point with .0029 an increase of pressure. If we reckon f from 32", we shall have the elasticity in inches of mercury nearly .1781 (i-f-.ooe/)' ; and for the ejevation or depression of the boiling point, if e be the elevation of the barometer above 30 in inches, we shall have for small variations /zi * e »^ r: ).642e. Deluc makes ih* cor- 7 X .10 X -oo'^g .009 rection 1.59c, Shuckburgh l.7oe, the mean is i.64 5e, which agrees very singularly with the calculation. Ac- cording to Dalton's principles the formula may be ac- commodated to any other vajiour, by reckoning / from some other constant point of the scale ; as —5° for alcohol, 50° for muriate of lime. I.4113-f.005r Schmidt's formula is c-=.r in hundredths of a French inch of mercury, r being the temperature in degree* of Reaumur. This is nearly equivalent to 1.163-f.002l/ / in hundredths of an English inch,/ being the degrees of Fahrenheit reckoned from 32° ; or to 1.33S8-I-.004C c for the degrees of the centigrade ther- mometer. Prony's formula for Bctancourt's experiments, is ri- diculously complicated, and yet not at all accurate. Soldner gives, for expressing Dalton's numbers, the for- (■6f)2— /). (212— /■) ,. mulaen:l. 30.13. ■—^ — .He accommodates 52042 similar formulae to other scales, and deduces from them others for the determination of the heat of boiling water under different pressures. , This however is only an approximation to Dalton's principle, which from the properties of the logarithmic curve, leads to a formula of this kind, eiz.016l373 — (1.0365 — .00008/). I. (1.0365— .00008/) .4343 (.00008/). I have also found several expressions which for particular purposes may possibly be of some use, although thejr arc all superseded in general by the formula first mentioned ; 1.5 these are, reckoning / always from 32°, c— 003/ , .006788/ *0«7e8/ e=:io /, e=:io (/+.000329/*— .oooooooi (.0551/— .000019^\ 10 /e— numb. 1. .3 0103 -f- .01541/— .000017/'— .000 000 008/', in tenths; and for atmospherical temperatures ez:.2-}-.007/4-.00016/', which is deduced from Dalton's table, but may perhaps be improved by making e^.ls4-.007/4- .000l({/"*. Comtruction of Thermometers. Braun's comparison of the scales of thermo- meters. IN. C. Petr. VIl. pi. 18. VV'entz on dividing tlieniiometers with un- equal tubes. Act. Helv. III. 105. Report of the committee of the R. S. Ph. tr. ■ 1777. 816. The stem of a thermometer being 1 00° colder than the bulb, the mercury will be about ij° lower in 180°. It ought always to be of the same temperature. The bulb being immersed an inch under water, the boiling point is raised .08°, which is about half as much as the same pressure would occasion if exerted by the air. CATALOGUE. HEAT, CHANGES OF FORM. 399 The thermometer it a medium stands about .48°, higher immersed in water, than in st«am only, >yhich corres- ponds to a difference of about .3 in the height of the barometer. The rapidity of boiling makes little difference in the keat, there are, however, sometimes irregularities of half a degree or more, notwithstanding all possible precautions. The standard thermometer is graduated by immersion in steam, when the barometer is at 29.8 : its boiling point is ' " higher than that of De Luc's, who employs 28.75 for the height of the barometer, immersing the bulb in water. A vessel with a chimney is employed, loosely covered for steam, the bulb being held 2 inches above the water. When the bulb is immersed, the barometer ought to stand at 49.5, but when an open vessel is used, the baro- meter must be at 29.8, and the thermometer must be wrapped in cloths, and held upright, and hot water must be frequently poured over it. Rain water or distilled water must be employed. Corrections are given for the expansion of the scale, and for the coldness of the stem ; and a diagonal scale for re- ducing the effect of the height of the barometer. For each inch ^j^ of the interval between the freezing and boiling points must be allowed. • Six on the division of thermometers. Ph, tr. 1782. 72. Biot's thermometer. See Communication of Heat. It is simplest and most usual to reduce thermometers to SO. of the barometer. Comparative Table of Thermometers. Degrees from Freezing freezing to boiling, point. Wedgwood Poleni Amontons Newton Old Edinburgh Del Cimento sometimes Reaumur Sauvages Celsius, centigrade Delisle Del Cimento sometimes Sulzer nearly as De- lisle, about Hales Delahire Obs. Par. Fahrenheit Ac. I'ar. old. R. S. old 1.48« 15.« 21.5 34. 38.8 .8i SO 87 100. 150 154 156 163 17li 180 214 ai».s — 8.142 47.3 51.5 O. 8.2 13.5 0. 0. O. 150 20. 0. 28 32 25 — 73i Boiling point. — fl.fiSS 62.9 73- 34 4; 8 If 80 87 100 0. !?♦ 163 199i 2ia as 9 14U Degrees from freezing to boiling. Freezing point. Boiling point. Fowler Rosenthal 284^ 344 — 34 928 250; 1272 Cruquius Hawksbce 440 490 1070 0 1510 490 Hawksbee's was a spirit thermometer; he found the ex- pansion of air at the freezing point .j,^ for each of his degrees : hence his greatest summer heat, of 130°, be- comes 80°, F. if we make it 84°, we shall have 450° for the boiling point. Gaussen's comparison of the thermometers of mercury and alcohol, from the experiments of Dcluc and Micheli. Merc. 5° R. Ale. 3.9 Merc. 4 5° Ale. 40.1 10 7-9 50 45.3 15 12.1 5* 50.7 20 16.4 60 56.2 25 20.9 65 ai.9 30 25.5 70 07.8 35 30.2 73 73.8 40 33.1 80 80.0 160 156 150 135 130 W. 17977 F. This agrees with the formula i r -f- ^;„rr. Micheli found 20° of the spirit thermometer agree to 26.4° of the mercurial, 30° to 36.?°, 40° to 46.4°, JO* to 56.6°, 60° to 64.3°, and 70° to 72.4. Table of the Effects of Heat. Wedgwood's greatest heat 240° W. Nankeen porcelain withstands Best Chinese porcelain softened Pig iron melts completely Bristol porcelain withstands Pig iron begins to melt W. Iron, pure nickel, and pure cobalt melt, Bergman Smith's forge Plate glass furnace Bow porcelain vitrifies Inferior Chinese porcelain softens Flint glass furnace Derby porcelain vitrifies Chelsea porcelain vitrifies Storre ware, pots de gres, baked. Welding heat of iron Worcester porcelain vitrifies Welding heat of iron begins Cream coloured ware baked Flint glass furnace, weak. Working heat of plate glass Delft ware, baked tcoi 125 124 121 120 1 14 I 12 lO.'i 102 85 94 00 30 JO 57 41 400 CATALOGUE. — HEAT, CHANGES OF FORM. Fine gold melts, W. Bergman Settling heat of flint glass Fine silver melts, W. Bergman Swedish copper melts, W. Bergman Bra« melts Enamel burnt on Red heat, visible by daylight. W. Bergman Red heat, visible in the dark Antimony melts, Bergman 7.inc melts, Bergman Mercury boils Expressed oils boil Sulfuric acid boils Steel becomes deep bins Oil of turpentine boils a2°W.S237°F- 1301 19 28 ■•717 1000 97 4587 14S0 SI 6 oW. 1077 1050 -iW. 047 809 699 0SOor 653 600 {530 546 f 560 \324.5 Lead melts 510 Biot 504 Bergman 595 Bismuth melts 460 Bergman 494 Steel becomes straw coloureerate air 62 Sulfuric acid. See Cavendish. Ice melts Wedgwood thinks the freezing point of va- pour a little higher. Milk freezes Sea water freezes Alcohol 10, water 14, by weight, freezes Wine freezes Alcohol 1, water 3, freezes Alcohol 1 , water 1 , freezes Alcohol 2, water 1, freezes Mercury freezes, contracting about ^j, tt°r. so 3( 31 30 7 - r - 11 -39 Table of the Elasticily of Steam, in Liche% of Mercury. The best formula is e = .i78l (i +.006/)'; or, Se- condly, for low temperatures «:=: .18 + .007y+ .OOOl?/"', reckoning / from 32°. Formula. Dalton. 2° 12 32 33 34 25 26 27 28 29 3i) 31 32 33 34 35 36 37 38 39 40 41 42 43 44 43 46 47 48 49 50 51 52 53 54 55 J>6 .044 .073 .115 .120 .126 .132 .138 .144 .150 .147 .164 .171 .178 .186 .193 .202 .210 .219 .228 .237 .247 .257 .268 .278 .290 .301 .313 .326 .338 .351 .365 .379 .394 .409 .424 .440 .456 .068 .096 .139 .144 .150 .156 •162 ■168 .174 .180 .186 .193 .200 .207 .214 .321 .229 .237 .245 .254 .263 .273 .283 .294 .305 .316 .328 .339 .351 .363 .375 .388 .401 .415 .429 .443 .458 ,0 Schmidt. .1( Form. 2. .iRobison. .0? Schmidt's formula. .369 Form. 2. ,12 Betancourt. .396 Form. 2. Muriate of lime .82. D. as water 1 8" lower. .4 Van Marum. Ale. 1.5, as wa- fer 36" higher. Ammonia 7.7, as water 95° higher. Ether 13.3, as water ii8° higher. CATALOGUE. — HEAT, CHANGES OF FOHXr. 401 Formula. Dalton. '57° 58 59 00 61 02 03 64 65 66 67 68 69 70 71 72 73' 74 75 76 77 78 79 80 81 82 83 84 85 «0 • 7 • 8 «9 , 00 01 03 03 04 95 S6 97 08 09 ]00 101 103 103 104 105 106 107 108 109 110 111 113 113 114 115 .474 .491 .509 .528 .547 .567 .587 .609 .630 .653 .676 .700 .724 .750 .776 .803 .830 .858 .888 .918 .949 .980 1.013 1.047 1.082 1.117 1.154 1.192 1.231 1.270 1.311 1.353 1.396 1.442 1.487 1.533 1.580 1.629 1.680 1.732 1.785 1.839 1.895 1.B53 2.012 2.073 2.135 2.199 2.264 2.331 3.400 2.470 2.542 2.616 2.692 a. 7-0 2.830 2.931 '3.015 .474 .490 .507 .524 .542 .560 .578 .597 .616 .635 .655 .676 .698 .721 .745 .770 •798 .833 .851 .880 .910 .940 .971 1.000 1.04 1.07 1.10 1.14 1.17 1.31 1.24 1.28 1.33 1.36 1.40 1.44 1.48 1.53 1.58 1.63 1.68 1-74 1.80 1.8S 1.93 1.98 3.04 2.11 2.18 2.25 2.32 2.39 2.46 2.53 2.60 2.68 2.78 2.84 3.93 .407 Schm. Ale. 1.45 D. as water 30* higher. Ammonia 4.3 D. as waler 69° higher, .661 Form. 2. Ether 12.75, as water 110" higher. Dalt. Muriate of lime .3 D. as wa- ter 19° lower. .65 Bet. .653 Schm. .55 Rob. Muriate of lime .4 D. as water 18° lower. .764 Form. 2. Cavendish. .75 Lord C. .96 Bet. .o6i Schni. Muriate of lime .g D. as wa- ter 18° lower. 1.61 Rob. Ether 30, as water higher. Dalton. 3.38 Bet. 110" 116' 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 133 133 134 135 136 137 138 139 140 141 142 143 144 145 148- 147 149 150 151 152 153 154 155 156 157 158 159 160 161 163 163 164 165 166 167 168 169 170 171 173 173 174 175 Formula. Dalton. 3.100 3.188 3.378 3.369 3.463 3.580 3.658 3.760 3.863 3.969 4. 078 4.188 4.361 4.418 4.538 4.657 4.781 4.9O8 5.037 5.171 5.307 5.446 5.583 5.732 5.880 6.031 6.186 6.344 6.506 6.671 6.840 7.012 7.189 7.369 7.553 7-740 -7.983 8.128 8-328 8.532 8.740 8.953 9-170 9-391 9.617 9.84a 10-08 10-32 10.57 10-82 11.07 11.33 11.60 11.87 12.14 13.43 12.72 13.01 13.30 13.61 3,00 3.08 3.18 3.25 3.33 3.42 3.50 3.39 3.69 3.79 3.89 4.00 4.11 4.23 4.34 4.47 4.60 4.73 4.88 5.00 5.14 5.29 5.44 5.59 5.74 5.90 6.05 6.21 6.37 6.53 6.70 6.87 7.05 7.23 7.42 7.61 7-81 8-01 8-20 8.40 8.60 8.81 9-02 9-24 gAS 9-68 9-91 10-15 10-41 10-68 10-98 11-25 11.54 11.83 12.13 - 12.43 13-78 1302 13-32 13.63 Ale. as water 6° higher. Rob. 3.90 Bet. 3.9 Schm. Ale. as water 29* higher. Ach. Ale. aswater 30° higher. Rob. Ammonia 30, as water 72* higher. Dalton. Ale. as water 31.5* higher. Ach. Ether 64. 7. s, D. m water 105° higher. 6.72 Rob. 6.8 Achard. 11.73 Schm. A.lc. M watw 33° higher. Ach. Ale. as Ach. water 36" higher. 14. Achard. Ale. so. a> water 37° higher. Dalt. TOL. II. S F 403 CATALOGUE. HEAT, CHANGES OF FORM. Formula. Dal ton. Biker. Formula. Dal ton. Biker. 176° 13.92 13.93 937' 48.81 177 14.24 14.22 14. Kirwan from Dcluc. 238 49.76 178 14.56 14.52 Is.Schm. l4.9Achard. 239 50.71 S1.45 Schm. 179 14.89 14.83 240 51.66 52.2 54.9 Rob. Ale. as watet 180 15.23 15.15 14.05 Rob. 15.5 Schm. form. Ale. as water 37° 241 52.64 46° higher. Rob. higher. Rob. 242 53.63 (51.34) 53,9 181 15.57 15.50 243 54.63 182 15.92 15. S6 244 55.66 183 IS. 27 16.23 245 56.70 1 184 16.64 16.61 246 57.75 185 17.00 17.00 247 58.82 186 17.38 17.40 248 59.91 60.76 Schm. 187 17.76 17. 80 249 61.01 , 188 18.16 18.20 250 62.14 62.7 66.8 R. 189 18.55 18.60 951 63.28 190 18.96 19.00 19.4 Schm< 252 64.43 (60.05) 64.8 191 19.37 19.42 353 65.61 192 19-79 19.86 954 66.80 193 20.22 20.32 255 68.02 194 20.66 20-77 21.47 Achard. 256 69.25 195 21.10 2 1 -22 257 70.49 71.57 Schm. 76.9 Bet. 196 21.55 21.68 258 71-76 197 22.01 22.13 259 73.05 198 22.48 22.69 260 74.36 75.0 S0.3 Rob. 199 22.96 23.16 261 75.69 900 23.44 23.64 22.62 RoK 262 77.04 (69.72) 77.0 SOI 23.94 24.12 24.0 Schm. 263 78.41 902 24.44 24.61 264 79-80 203 24.95 25.10 265 81-21 904 25.47 25.61 266 82-65 83.81 Schm. 90. Bet, 905 26.00 26.13 267 84.10 300 36.55 26.66 263 85.58 , 907 27.10 27.20 • 269 87.08 908 27.66 27.74 270 88-60 88.6 94.0 Rob. 909 28.23 28.29 271 90-14 910 28.81 28.84 272 91-70 (79.94) 92.3 911 99.40 29-41 273 93.29 912 30.00 30.00 Ether 137.6 D. as water 84" higher. Ale. 58.5 D. as water » 5° higher. 274 275 276 94.91 96.55 98.21 S8.i3 Schm. 913 30.61 31.3 277 99-90 914 31.23 31.9 278 101 -a 105.2 915 31.87 32.5 279 103.3 916 32.51 33.3 280 105.1 ~ 109 Schm. 105.9 Roi) 217 33.16 33.7 106 Ber. 918 33.83 34.6 281 106.9 919 34.50 35.1 282 108.7 (90.99) 220 35.19 35.9 35.8 Rob. Ale. as water 42° higher. Rob. 283 284 110.6 112.4 116.98 Schm. S21 35.89 36.4 36.41 Schm. 285 114.3 222 36.60 (36.25) 37.0 286 116.9 120.5 Schm. 223 37.33 287 118.3 924 38.07 288 120.1 225 38.83 289 122.1 926 39-58 2go 124.3 126. Schmt 227 40.35 291 126.3 928 41.14 292 128.3 (102.45) 929 41.94 293 130.5 930 42.7s ' 43.2 43.11 Schm. 44.7 Rob. 394 132.6 231 43.58 Muriate of lime 30, D. as water 18° lower. 295 298 134.8 137-0 933 44.42 (48.34) 44.8 297 189-2 933 45.28 298 141-5 934 46.15 . 299 143.8 935 47-03 300 146.2 230 47.9s 301 148.6 eATALOGUE. — HEAT, PERMANENT EFFECTS, *m Formula. Dalton. 808° 150.9 (114. is) 303 153.4 304 155. S 305 158.S 308 160.9 307 163.5 308 166.0 30y 168.7 310 1/1.4 311 174.1 312 176.2 The vapour of sulfuric acid ousht to have a force of .1 at 390", that of mercury at 460", the one boiling at 590", the other at 660" Dalton. Chemical and Physiological Efects. See Economy of Heat. Richinann on solutions at different tempera- tures. N. C. Petr. IV. 270. Blagden's observations made in a heated room. Ph.tr. 1773. 111. Supported a heat of about 300" in air ; and there was no evaporation from the skin to assist in cooling, on the con- trary, water was deposited. TiUet found two girls that supported a heat of 2Soa in an oven. Mercury could not be borne at 120", nor water at 125"; oil was sup- portable at 129", and spirits of wine at 130". Harniss on the chemical action of light and heat. Nich. V. 245. Journ. de phys. LVII. 66. An account of a Spaniard who washed his hands and face in oil at 224", put his foot on a red hot iron, and held a lighted candle to his leg. His pulse was 130" or 140". See Physiology. Soda and potash are said to exchange their acids at dif- ferent temperatures. In general a bath is pleasantly warm from 90" to 1 1 0° ; we drink tea about 11 5 " or more, coffee sometimes at 130» Permanent Effects of Heat and Cold. *Hooke on glass drops. Micrographia. Homberg on the Batavian drops. A. P. II. 85. X. 146. Wolf on brittle bottles. A. P. 1743. H. 43. Brur.ion the Bologna bottles. Ph. tr. 1745. XLIII. 272. Watson on unannealed glass vessels. Ph. Ir. 1745. XLIII. 505. Casali on unannealed glass. C. Bon. II. i. 321,328. III. 40G. V. ii. I69. Lecat on glass drops, and on the tempering of steel. Ph. tr. 1749. XLVI. 175. Observes, that a drop may sometimes be ground away by emery and oil without breaking. Compares tempering to annealing. Hanovv on the Bologna jars. Danz. Gesell. I. 584. III. 328. Hawoz» Veisuchemit den Springkolbchen. 4. Danz. 1751. Bosc d'Antic on glass drops. S. E. IV. Kaestner de lacrymis vitreis. Dissert, viii. 59. 125. Maupetit on the glass drop. lloz. VI. 394. *Coulomb. A. P. 1764. 'ZQ5. Found that the force of tonion is equally powerful in wires annealed and unannealed: they perforaed their vibra- tions in equal times. A tempered bar required also as much force to deflect it to a given angle, as a hard one of the same dimensions. A soft bar, a spring tempered, and a hard one, were bent to equal angles by 5 pounds ; with 6 the hard bar broke, with 7 the soft one bent, but returned as far from its new position upon the removal of the weight, as if it had not bent. The elastic bar was broken by 18 pounds. Chladni also found the sound of soft iron and steel similar to that of the hardest, and I have observed the same in a tuning fork. This may be inferred from the theory of annealing ; the whole cohesive force not being affected by the partial extensions of some strata and the consequent condensation of others, Nicholson. Manch. M. II. 370. Observes, that the specific gravitj' of lead and tin varies in the third figure of the number expressing it, accord- ing to the different modes of cooling. Guyton on tempering steel. Ann. .Ch. XXVII. 186. From Nicholson. See Cutlery. Cavallo. Nat. Ph. II. 27- A piece of steel, whicli measured 2.769 inches when soft, was found, by Mr. Pennington, to measure after hardening, 2.7785, and when again tempered so as to become blue, 2.768. The specific gravity of hammered steel is 7.84, that of hardened steel 7.816. The difference 404 CATALOGUE.— HEAT, COMMUNICATION. of the length is ^L, that of the specific gravity from tem- pering consequently ^ ; but the hammering increases it to Jj. The expansion of water by freezing presents a similar phenomenon. On the flexure of wax and metal in cooling. Nich. 8. IV.- 176. Hatchett. Ph. tr. 1803. 118. Found that gold debased with impure copper became brittle when cast in moulds of sand, but was rendered ductile when cast in moulds of iron. The specific gravity of standard gold when cast in iron was also greater than when cast in sand, in the ratio of 290 to 289, and in one experiment of 61 to 60. The mefal cooled more rapidly in sand. In some cases the evolution of gas may, perhaps, be concerned in affecting the specific gravity. Communication of Heat by contact and in general. La Chapelle on a bar of steel becoming hot when withdrawn from boiling water. A. P. II. 25. Romberg on the increased heat of the bot- tom of a vessel when removed from the fire. A. P. 1703. H. 24. This appears to be a fallacy : with a clean surface it may easily be detected. Martine's essay on the heating and cooling of bodies. Richmann on the laws of the decrement of heat. N. C.Petr. I. 174. II. 172. Makes its decrement as the surface exposed and as the difference of temperature conjointly. Richmann on the cooUng bodies in air. N. C. IV. 241. Insists that a ball of metal 4 inches in diameter cannot be heated by boiling water beyond 207° : and the ex- periments seem to indicate, that even in cooling its tem- perature is always lower, which indeed is the only point that can affect the theory. Brass and copper retain heat longer than iron, iron than tin, and tin than lead. Lambert on heating and cooling. Act. Helv. II. 172. Lambert Pyrometrie. Darwin. Ph. tr. 1757. 240. Supposes steam to float in air, and retain its heat. Musschenbroek's table of the time of heatina: of different bodies. Introd. II. 678. Euler on the motions of fluids from heat. N. C. Petr. XI. 232. XIII. 305. XIV. 270. XV. 1, 219. Braun on the communication of heat. N. C. Petr. XII. 289. Roz. I, l. Confirms Richmann's experiments on boiling water and alcohol : but finds the result different with wine and oils. For these, however, the boiling point must be variable, and the result is of no value. Roy. Ph. tr. 1777. 720. Observes, that water is a very bad conductor of heat. Erxleben on the laws of heat. N. C. Gott. 1777. VIII. 74. Exceptions to the law of Newton, Richmann, and Lambert. Achard on the conducting powers of gases. A. Eerl. 1783. 84. Achard's comparison of heat and electricity. Roz. XXII. 245. Achard on the cooling of bodies in air of different densities. A. Berl. 1785. 24. Makes no general conclusions. The difference betvvee* the rates of cooling in air exhausted to | and to \ was some- times imperceptible, and scarcely in any case jL. Fordyce's experiment on heat. Ph. tr. 1787. 310. Two equal cylinders of pasteboard were inclosed in eider down under glass, one was covered with iron, the other with pasteboard, both painted with the same black paint, which was exposed to the sun's rays : th« pasteboard never transmitted a heat of more than nop the iron 121°: the iron also retained its heat much the longest. Sir B. Thompson on heat. Ph. tr. 1786. 273. Ess. II. viii. Repert. IV. 30. Gilb. V. 288. The conducting power of mercury being 1 000, that of moist air was 230, of water 313, of common air 80.41, of air \ as dense 80.23, of air ^ as dense 78, of a vacuum 55. The two last numbers, compared with the conducting power of common air, appear to indicate a formula of this kind, 55-J-25.4(fJT, d being the density, compared with that of the atmosphere. CATALOGUE.-— HEAT, COMMUNICATIOTST. 405 Sir B. Thompson's experiments on heat. Ph. tr. 1792. 48. Maintains that the attiaction of loose substances for air is the principal cause of thtir impeding the passage of heat : thinks that elastic fluids do not conduct heat like solids and liquids, from particle to particle. Count Rumford on the propagation of heat in fluids. Ess. I. vi. Ph. M. II. 343. Gilb. 244. Extends to liquids what he had before suggested respect- ing elastic fluids. Observes, that water thickened with farinaceous substances is with difficulty heated and cooled, and that fruits have the same property. Rumford on a phenomenon observed in the glaciers. Ph. tr. 1804. 23. Nich. IX. 58. The consequence of the expansion of water when it is much cooled, and of the want of conducting power of fluids. Saussure on collecting heat by glasses. Voyage dans les Alpes. ^ 932. Ingenhousz on the heat acquired by metals. Verm. Schr. II. 341. Gren. I. 154. Roz. 1789. i. Humboldt on the conducting power of vari- ous substances for heat. Roz. XLIIL 304. Lichtenberg in Erxleben. " Silver is the best conductor, platina the worst. Mayer on the conducting power of metals, Gren. IV. 22. Mayer on heat communicated by wood. Crell's Journ. Ann. Ch. XXX. 32. Guy ton on the conducting power of char- coal. Ann. Ch. XXVI. 225. Nich. II. 499. Ph. M. II. 182. Charcoal transmitted in ^ of an hour only 6oJ ° W. »n equal coat of sand 89°. Delue's remarks on Rumford's experiments. Glib. 1.404. Socquet on the conducting powers of fluids. Journ. Phys. XLIX. 441. Gilb. VI. 407. Repert. XIII. 277. - Asserts their conducting powers. Thomson on the conducting powers of fluids. Nich. IV. 529. Nich. 8. T. 81. Gilb. XIV. 129, 146. * Dalton on the power of fluids to conduct heat. Manch. M. V. 373. Nich. 8. IV. -V 56. Repert. ii. II. 282. Gilb. XIV. 184. Shows that fluids actually conduct heat when quiescent, but that their motions are usually the most concerned in its communication. Says that water conducts heat, as it does electricity, more readily than ice : that the maximum of effect of water in thawing ice must be at the maximum of density : which, by neglecting to con- sider the expansion of glass, he erroneously places at Nicholson's experiment on the conducting powers of fluids. Nich. V. 197. Murray on the passage of heat through fluids. Nich. I. 165, 242. Gilb. XIV. 158. Biot on the experiments of Count Rumford and Thomson. B. Soc. Ph. n. 53, 62. Biot on the propagation of heat in solids. B. .Soc. Phil. n. 88. Gilb. XVII. 231. Confirms Newton's law of decrements proportional to the difference of temperature. A bar of iron was dipped at one end in mercury at 21 a", and 7 holes were mada in it at equal distances, in which thermometers were placed : the last was never affected : the next, which was at the distance of 39 inches, was never raised more than 1° of Reaumur. Such a rod is recommended as a tlier- raometet for high temperatures : but it is probable that the effect of the air would produce great irregularities. Copper appeared to conduct heat somewhat more readily than iron. The temperatures of thermometers were nearly, in geome- trical proportion when their distances were in arithmetical proportion. Leslie's inquiry into the nature of heat. Maintains that heat is communicated through gases in three ways, by pulsation, by abduction, as in solids, and by regression or circulation : but in liquids he finds that there is no radiation. Parrot on the propagation of heat in fluids. Gilb. XVII. 257, 369. BerthoUet. Chem. Stat. Nich. VIII. 134. Thinks that fluids must communicate heat from particta to particle. 406 CATALOGUE. — HEAT, RADIATION. Hornblower on the nonconducting power of fluids. Nich, VIII. I69. Radiant Heat. Construction of burning lenses and mirrors. See Optical Instruments. Mariolte on the heat of a burning mirror. A. P. I. 223. Mariotte observes, that terrestrial heat is intercepted by glass, while light is transmitted. Oeuvres. I. Homberg on a burning mirror. A. P. 1705. H. 39. Little effect -was produced when the heat of the atmo- sphere was considerable. Homberg on the ancient burning glasses. A. P. 1711. H. 16. '^Lahire on the heat of the lunar rays. A. P. 1705. 340. Harris and Desaguliers on Viliette's con- cave. Ph. tr. 1719. XXX. 970. It burnt less powerfully as it grew hot. Segntr de speculis Archimedeis. 4. Jen. 1722. Dufay's catoptrical experiments. A. P. 172G. 115, 165. H.47. Courtivron's catoptrical researches. A. P. 1747. 449. Buffon on burning mirrors. A. P. 1747. 82. 1748. 305. Burnt wood at 209 feet, by 168 small plane mirrors. Richmann on the heat of a pencil of rays. N. C. Petr. 111. 340. IV. 277. It was nearly in the inverse ratio of the square of the dis- tance from the focus. See Expansion. Nollet's experiments with concentrated solar rays. A. P. 1757.551. H. 23. Zeiher on burning lenses. N. C. Petr. VII. 237. Pistoi on the heating of bodies by light. A. Sienn. II. 126. Franklin on the effect of colours in the ad- mission of heat. Letter Ivi. Roz. II. 381. Wolfe. Ph. tr. 17fi9. 4. Hoesen's mirrors melted a wheel nail in 3 seconds, a pistole in 2. Hoffman used them opposite to each other, and collected the heat radiating from a stove strongly heated. 2 Sept. 1768. Watson on the heat admitted by blackened bodies. Ph.tr. 1773.40. Found an elevation from 108° to 11 8°, by coating the glass bulb of a thermometer with Indian ink. Lavoisier on the heating of coloured bodies. 1772. ii. 614. 1773. H. 81. Trudaine on his lens. A. P. 1774. Essai. It was observed, that the wood caught fire more towards the extremity of the image than in the centre ; but this was only from aberration, 70, 71. The diameter was 4 feet, the focal length about 1 1 . Cavallo's thermometrical experiments. Ph. tr. 1780. 585. Found that a blackened thermometer rose about 10* higher in the sun's rays, and showed some difference even in the daylight. Found no heat from the moon. When the balls of thermometers were coloured, the colours nearest the violet showed the greatest heat. Marcorelle on thermometers in different si- tuations. S. E. X. 85. In August, at Toulon, the sun's rays raised the thermo- meter 8° or e°, and twice as much when it was surrounded with other objects. Mairan found that the heat reflected on a thermometer by plane mirrors was proportionate to their number. Socin on the reflection of heat. Roz. XXVII. 268. *Pictet on the effect of colours, and on the reflection of invisible heat. Essais de physique. Pictet's further experiments. Nich. 8. III. 223. Giib. XIII. 120. The heat of a candle was intercepted by glass. *Privost sur r6quilibre du feu. 8. Genev. Gren. VI. Rozier. XXXVIII. 314. Prevost on heat and its interception. Ph. tr.- 1802. 403. Remarks on Herschel's experiments. T.Wedgwood. Ph.tr. 1792.370. CATALOGUE. — HEAT, llADIATIOK, 407 Found that a blackened wire was sooner heated and cooled than a wire not coloured. Huttons dissertation on light, heat and fire. 8. Ace. Ed. tr. IV. H. 7. Read 1794. Calls radiant heat obscure light ; observes the greater heat of the red rays, and says that a blackened thermometer is most sensible to the eflTect of obscure light, as well as to that of visible light. *Herschel on the heat of the prismatic rays, on the invisible rays of the sun, and on the solar and terrestrial rays that occasion heat. Pli. tr. 1800. <-l55, 284, 293,437. Nich. IV. 320, 360. V. 69. Ph. M. VII. VIII. Giib. VII. 137. With many experiments on the transmission of heat. fLeshe's observations on hght and heat. Nich. IV. 344, 4l6. Giib. X. 88. *Leslie on heat. Benzenberg's remarks on Leslie. Giib. X. ' '350. Hermst'adt on the effect of heat on different colours. A. Berl. 1801. 83. ^chraidtniliiler on the heat communicated to wood by the sun's rays. Giib. XIV. 30G. Kumford's experiments on radiant heat. Ph. tr. 1804. 77. B. Soc. Phil. n. 87. Giib. XVII. Sti, 218. On the effects of colours, and on the nature of the surface. Bockmann's prize essay on the heating of bodies in the solar rays. Note. Giib. XVII, 122. On the velocity of radiant heat. Ph. M. XIX. 309. Parker's was a double convex lens, three feet in diameter, 3 inches thick in the middle : it weighed 212 pounds. Its aperture when set was 32j inches ; its focal length fl feet 8 inches : the focal length was generally shortened by a smaller lens. The most refractory substance fused was a cornelian, which required 75" for its fusion; a crystal pebble was fused in a" ; a piece of white agate in 30". Cavallo. The finger might be pUced in the cone of rays within an inch of the focus, without inconvenience. Imison's elements. I. 371. But tins remark appears to require confirmation : if it were accurate, we might expect the smallest imperfection in the focal adjustment of the eye to cause a great difference in tlie apparent brilliancy of an object ; which is not the fact : indeed Count Rumford's late experiments appear wlioUy to confute it. Leslie discovered, by experiments made in 1802, that the heat emitted by radiation was affected by the natme of ths surface exposed. The action of a blackened surface of tin being 100, that of a steel plate was 15, of clean tin 12, of tin scraped bright 16, when scraped with the edge of a fine file in one direction 26, when scraped again across about 13, a surface of lead clean 19, covered with a grey crust 45, a thin coat of isinglass 80, resin 96, writing paper 98, ice 85. Heat as well as light is so projected from a surface as to be equally dense in all directions, consequently from each point in a quantity which is as the sine of the angle of inclination. The radiation is not affected by the quality of the gas, in contact with the surface, but it is not transmitted by water. For the time of cooling of a hol- low tin ball 6 inches in diameter, filled with water, in still air, take, in minutes, L.— — L. , making the t a -^ I three first decimals integers, h and i being the tempera- tures on the centigrade scale, and a being 50. And for the same ball painted, make a z:: 110, and take ^^ of the result: thus, from 100° C. to 50°, or 212° F. to 122°, metal takes 124'.9, paper or paint 83'.2, to 10° C. or 50° F. 602' and 344'. 1 respectively. For the effect of diffiirent gases and different densities, in air the discharge from a vitreous surface is -5(3^^ + ■*(i^''), from a metallic surface i J Jt 1 ^(3 <;•' + f(2") ; in hydrogen gas Kisd* 4- id'^^), and ^(12J' + Jd"). Thus, if d r: 1, theabductive power of air is |, or .4286, tlie pulsatory energy of a vitreous surface i, or .5714, of a metallic surface ,L, or .0714. In hydrogen gas the pulsatory power the same, the abductive power '-?, or 1.7143. If cir:-5^, the abductive power is .18 for air, .857 for hydrogen, the pulsatory power .48 or .06 in air, .51 or .0637 in hydrogen. If d :=^^!^, the abductive power is .1071 for air, .5655 for hydrogen, the pulsatory- power .433 or .054 for air, .475 or .0594 for hydrogen. It would be easy to make an experiment on the velocity with which radiant heat is conveyed to a distance, and there is little doubt but that such an experiment would confute Mr. Leslie's hypothesis of the transmission of heat by a pulsation of the air propagated with the velocity of sound. 408 CATALOGUE. — HEAT, CAPACITIES. Capacity for Heat. See Natural History. Compression. See Sources of Heat. •fDesaguliers's experiments on quicksilver and water. Ph. tr. 1720. 81. Makes the quicksilver contain most heat in the same b«.ilk. Richmann on the heat of mixtures. N. C. Petr. 1. 152, lG8, 174. Hichmann on the heat of quicksilver. N. C. Petr. HI. 309. Richmann on the cooling of bodies. N. C. Petr. IV. 241. Braun on the phenomena of heat. N. C. Petr. X. 309. Musschenbroek's table of the time of heat- ing. Introd. II. 678. Baume on col3 from evaporation. S. E. V. 405, 425. *B!ack's experiments on heat. Ace. Roz. Intr. II. 428. Irvine's essays. Lavoisier and Laplace on a new mode of measuring heat. A. P. 1780. 355. H. 3. By the melting of ice. Cavendish. Ph. tr. 1783. 312. Says, that heat is " generated" in freezing, and " dis- appears" in thawing. *Wedgwood on the calorimeter. Ph. tr. 1784.371. *Crawford on animal heat and combustion. 8. Lond. 2ed. 1788. Wilke on specific heat. Roz. XXVI. 256, 381. The capacity of water being i, that of an equal weight of agate is .195, glass .187, iron .126, brass .116, copper ,114, zinc 102, silver .082, .antimony .063, tin .06, gold .05, bismuth .043, lead .042. But for equal volumes, the proportions are, copper 1.027, water 1, iron .993, brass .971, gold .966, ver .833, agate .517, lead .487, glass .448. Carette Soyer on the heat excited by lime. Roz. XXIX. tm. Kirwan's table in Magellan's essay on fire. Berlinghieri esame della teoria di Crawford. 4. Pisa, 1787. Espr. des Journ. Mars. 1790. Gren on Crawford. Journ I. Morgan on Crawford. Seguin. Ann. Ch. lit. 148. V. J9I. Table of specific lieats. Cavallo. N. Ph. HI, 70. From Crawford, Kirwan, and Lavoisier. Specimens. Water l.ooo Nitrous acid L. .661 Oxygen C. 4.749 K. .844 K. 37. Spermaceti oil C. .500 Atmospheric air C. 1.700 K. .399 K. 18.6/0 Iron C. .127 Aqueous vapour C. 1.790 K. .125 * Pictet (8.5) L. .101 Carbonic acid C. 1.045 Mercury L. .029 K. .027 K. .03* Table of capacities for heat. Thomson's chemistry. I. R. I. According to the doctrine which derives many of the variations of sensible heat from the variations of capacity of the substances concerned, the heat extricated by compres- sion, and absorbed in dilatation, must be referred to such a change of capacity, and every substance must have its ca- pacity diminished in proportion as it occupies less space. We may endeavour to ascertain in what ratio this diminu- tion of capacity takes place, supposing, as the most pro- bable ground of calculation, tfcat a condensation in a given degree diminishes the total capacity in a given ratio, what- ever the initial density may have been : the capacity must therefore be supposed to vary as a certain power of the rarity; and taking — 1400° as the natural zero, we may inquire what that power is. In Mr. Dalton's experiments, 50 degrees of heat, or somewhat more, were produced when the air was readmitted into a space partially exhausted: now it is evident that this cannot be the whole change of temperature of the air so compressed, since it is mixed with the air admitted, which is left in its original state of equili- brium. Suppose the density of the air in the receiver at so" F. to have been diminished x times, then its capacity will be diminished by compression x" times, and its temperature will be increased I450ct'' — 1450; but this increase of CATALOGUE. HEAT, CAPACITIES. 409 temperature is to be diffused through x times as much air, audit will then become ax"-' — ax—', callmg 14 JO a, which becomes a maximum when (» — l).ai''-'i + o«-'i = o, or (n — l).i"+ 1 :=o, ot x — (l — ri) ", which, as n becomes small, approaches to 2.718 as its limit. Consequently the greatest heat that can be pro- duced in this manner is when the air has been exhausted to about I of the atmospheric density, wherever we place the natural zero. Putting then 50 X 2.7 1450 X2.7'' — 1450 2T7 -=50, we have 2.7"=:- 1450 + 1 =: l.ogs, whence n i« about , and the heat produced by compression to x = 1450 V'^'*"'^— 1/, ' times the density should be 1450 \x "•"■'— i/, which, if x r: 2, becomes 93° ; and such should have been the de- gree of cold produced by the return of air of double the natural density to the state of equilibrium. Whether this effect was lost by the difficulty of making the observation with accuracy, or whether the friction produces some heat which is confounded with the sffect of expansion, may perhaps be determined by future experiments : but in this case Mr. Dalton observed only a heat of so°, at in the former experiment. We may, however, deduce from that experiment an acceleration of about f to be added to the calculation of the velocity of sound ; and since the results of experiments on sound require an acceleration of J, or only i more, which has been ascertained with great accu- racy, it may be feir to allow the supposition of I^place and Biot, that the whole acceleration of sound is owing to this cause, and we may at least assume that acceleration, as affording a limit, which the heat produced by condensation, certainly cannot exceed. We may therefore make the ex- • ponent of the density J, for expressing the change of ca- pacity, and the heat produced 1450 V^x — 1/, which, when ttie density is doubled or"'haIved, becomes 131.2°. A compression of |ig will produce a heat of 1°. Now it appears from experiments on the sounds of dif- ferent gases, and from the sound of a pipe in air of densities the most various, tha,t the correction of the velocity of sound is nearly the same in all ; hence it may be inferred that the heat produced by condensation follows nearly the same law with respect to all gase?. This principle may therefore probably be extended to steam. Supposing the conversion of water into steam to absorb as much heat as would raise its temperature 940', we may call its capacity at 212° 1. 00, and may calculate a table for other tempe- ratures, assuming, with Mr. Dalton, that its simple ex- pansion by heat is equal to tlia,t of air. Mr. Watt' has VOL. II. shown, by direct experiment, that steam has a greater ca- pacity as its temperature is lower. Specific Capacity. gravity. Isa'F. .50 1.72 103 .OS i.oa 303 .S3 1.04 313 1.00 1.00 332 1.21 . 1.50 333 1.44 1.53 342 1.71 1.50 352 2.03 1.47 303 3.38 1.44 373 3.S0 1.41 Hence, if a steam engine work with double atmo- spheres, the heat being about 247°, it will require 1.87 times as much water, of which the capacity is 1.4 8, its excess above that of water i as much as at 212°, it will therefore absorb about 752°, and the heat required for raising water from 100 will be as 1.87 (147 + 752), to 112 -f 940, or nearly as 8 to 5, while the effect is doubled. Robison says, that four ounces of water at 100°, will condense in a second nearly 200 cubic feet of steam, re- ducing its expansive force to one fifth. If this is correct, it sets at defiance all theories of capacity. The only dis- tant analogy that can be found for it, is the facility with which rarefied air is found to carry off heat, which would induce us to suppose that the capacity of a given bulk of air is nmch less affected by its density than this calculation appears to demonstrate. Natural Zero. Opinions of Amontons, Lambert, and Dalton. See Expansion. Seguin on heat. Ann. Ch. III. 148. Ac- count of the theories of specific heat. V. 191. Nich. 8. IV. 221. Observes, that from experiments on the mixture of sul- furic acid and water, it might be inferred that the natural zert) is 7292° below the zero of Fahrenheit, but from Kirwan's experiments on ice only 1350°. Other experi- ments on ice give 1401°, Dalton 1547°. Dalton on the iiatuial zero. Gilb. XIV. 287. Gay Lussac's experiments on Dalton's supposition give IbiO^. Gilb. Heat denominated latent. Landriarii. Opusc. fisicoch. viii. Roz, • -XXVI. 88, 197. 3g 410 CATALOGUE. — ECONOMY OF HEAT. Soycomt against latent beat. Roz. XXXII. 143. Germ. Quedlinburg. Young in Higgins's minutes of a society. 8. Lond. 1795. Tilloch against latent heat. Ph. M. VIII. 70. Leslie on heat. Against latent heat. Economy of Heat and Cold. Internal fire places in boilers. Birch. I. 173. Pefargues's remedy for smoke. Mach. A. I. 211. On making ice in the torrid zone. A. P. IX. 320. Chaumette's mode of preventing smoky chimnies. A. P. 1715. H. 65. Mach. A. III. 47. Ganger's fire places and stoves. A. P. 1720. H. 1J4. Mach. A. IV. 11. Gavger Mecanique du feu. Smoke Jacks. Leup. Th. M. G. t. 51. Aeolipile. Leupold. Th. M. G. t. 52. Fresneau's culinary stove. A. P. 1 739. H. 58. Lagny's fire place with a valve for putting out the fire at pleasure. A. P. 1741. H. 165. Mach. A. VII. 115. Volckamer on putting out fires in chimnies by gunpowder. Coll. Ac. VI. 281. Cooke on warming rooms by steam. Ph. tr. 1745. XLIII. 370. Vanni^res's portable fire place. A. P. 1752. H. 148. Pigage's boiler, with a fire in the centre. Mach. A. VII. 307. Nollet on producing cold withoat ice. A. P. 1756. 82. H. 1. Gennet6's cover for a chimney. A. P. 1759. H. 232. Smoke jack. Emers. mech. f. 235. Montalembert on the conversion of open fire places into stoves. A. P. 1763, 335. H. 7. J. A. Euler on ovens. A. Berl. 1766. 302. Euler on the equilibrium of fluids. N. C. Petr. XIII. 305. XIV. i. 270. XV. 1, 219. With the effects of heat. SiVg/erdedigestore Papini. B&le, I769. Gramont on the Chinese stove. Ph. tr. 1771. 59. Henry's self moving register for a flue. Am. tr. I. 350. Franklin on smoky chimnies. Am. tr. II. 1, Franklin on chimnies. Am. tr. II. 231. Franklin's stove consuming its smoke. Am. tr. II. 57. Roz. XXXV. 356. The draught going down. Acc. A. P. 1773. H. 77. Franklin on smoky chimnies. Lond. Stoves and fire places. Roz. Introd. I. 615. IX. 49, 162. Barker on the mode of making ice in the East Indies. Ph. tr. 1775. 252. By evaporation. Natural ice unknown there. The water perforates through earthen ware pans placed on sugar canec in straw. On heating rooms. Roz. XV. 148. Clements's oven. Bailey's mach. II. 55. Lavoisier on fuel. A. P. 1781. 379. Furnaces. E. M. PI. II. Fer. Glaces. E. M. A. 111. Art. Fournaliste. Smoky chimnies. E. M. A. III. Art. Fumiste, E. M.A. III. Art. Glaci^re. Stoves. E. M. A. VI. Art. Poelier. A Prussian oven for coals. Roz. XXIII. 433. Sanches on the v.apour baths of Russia. Ro«. XXV. 141. Sage on fuel. A. P. 1785. 239. 1789. 548. Roz. XXXV. 385. Repert. V. 418. Says that coal gives 1 times as much heat as an equal weight of wood. Beddoes's account of Vk'^alker's experiments on freezing mixtures. Ph. tr. 1787. 282. Walker on artificial cold. Ph. tr. 1768. 39H. 1795. 270. 1801. 120. CATALOGUE. — ECOVOMT OF HEAT, 411 Equal parts of muriate of ammonia and nitre, dissolved in water, sink the thermomclcr about 40", and may be dried again. Phosphate of soda 9, nitrate of ammoniac, dilute nitrous acid 4, depress the temperature from so" to — 21°. Muriate of lime 3, snow 2, sink it from 32° to- -^50"; caustic potash 4, snow 3, to — si". Ice ground to powder with a centrebit is better than snow, frozen vapour than either. Rumford on the preparation of food. Ess. I. iii. *Rumford on fire places. Ess. T. iv. Rumford on the management of fire and the economy of fuel. Ess. II. vi. Gilb. III. 309. IV. 85, 330. One pound of pine wood burnt raised the temperature of 20.1 pounds of water 180 degrees : from Kirwan's com- parison the same quantity of pitcoal would raise 36 pounds of water in the same degree, and a pound of charcoal 57.6 pounds. According to Lavoisier, equal heats are produced by 403 pounds of coke, 600 of pit coal, 600 of charcoal, and 1089 of oak wood. In general | of the heat of the fuel employed are wasted. Runiford's perpetual hme kiln. Ess. Journ. Phys. XLIX. 65. Rumford on increasing the heat of fires by balls. Journ. R. I., I, Repert. XV. 248. Ph. M. X. 42. Rumford on conveying heat by steam. Journ. R. I., I. Nich. V. 159. Repert. XV. 186. Ph.M. X.46. Gilb. XIII. 385. On the cold produced by tattees. Asiatic mirror. May 1789. See Meteorology, Observations of Climates. Anderson on smoky chimnies. *Fossorabroni on salt works. Soc. Ital. VII, 57. Wood produces heat enough in its combustion to eva- porate twice its weight of water, and to prepare f of its weight of salt. Saint Julien on warm baths. Roz.XXXII.51. Miche on reverberating furnaces. Roz. XXXII. 385. Descharmes on a glass house. Roz, XXXVIII. 341. Williams on the mode of making ice at Benares. Ph. tr. 1793. 56, 129. It K made when the thermometer is between Sb" and 42°. Blakeif on fire machinery. 8. Lond. 1793* Enc. Br. Art. Furnace. Brown's evaporator. S. A. XII. 257, Green's patent for wanning rooms. Repert. I. 21. Stratton's patent kitchen range.- Repert. I. 289. Hoyle's patent for heating buildings. Repert; I. 300. Ward's patent for employing smoke. Repert. I. 373. Percival's chamber lamp furnace. Repert. III. 24. Conway's patent coke oven. Repert. III. 75. Mode of sweeping chimnies by machinery. Repert. lU. 322. Lowitz on the production of cold. Ann. Ch.. XXII. 297. Percival's lamp furnace. Ir.tr. IV. 91. Smith's kettle for inflammable fluids. Am. tr. IV. 431. Repert. XV. 327. On artificial cold. Gilb. I. 479- H. 107. Pepys on artificial cold. Ph. M. III. 76. Froze sa pounds of mercury ; produced a cold of —62°. Walker's greatest cold was — 63°. Watt's patent furnaces. Repert. IV. 226» For burning smoke. Braith'waite's patent smoke jacks, Repert. VI. 1. Brodie's patent ship's stove. Repert, VII, 22. Blast machine at Carron. Smeaton's reports, Russian stoves. Repert. VII. 63. Redman's patent portable kitchen. Repert. VII. 105. Lasterie on the alcarrazas, for cooling li- quors. B. Soc. Phil. n. 13. 412 CATALOGUE. ECONOMT OF HEAT. CoUins's patent grate. Repert. VIII. 36l. Peak's improved fireplace. Am. tr. V. 320. Repert. ii. II. 436. With a sliding frontispiece. f rearson's patent for evaporation. Repert. IX. 217. Hassenfralz on the best form of boilers for evaporation. Journ polyt. II. vi. 364. Chaptal on Schmidt's stove. Ann. Ch. XXXII. 270. Claveriug on chimnies. London. *Clavelin on chimnies and fire places. Extr. Ann. Ch. XXXIII. 172. Gilb. VI. 293. Howard's improved air furnaces. Ph. ]M. V. 190. *Roebuck on blast furnaces. Ed. tr. V. 31. Nich. IV. 110. Ph. M. VI. 324., Repert. XIII. 19. Recommends a Urge quantity of air, lupplied with a moderakte velocity. Burns's stoves and grates. Ph. M. V. 204. Burns's patent grates. Repert. XII. 225. Ph. M. VII. 264. For preventing accidents. Blundell's patent machine for saving fuel. Repert. X. 84. Howard's patent pneumatic kitchen. Repert. X. 147. Raley's patent furnace. Repert. X. 155. Kirwan on the carbon in coals. Ir. tr. Re- pert. XIII. 171. Fabbroni on the alcarrazas. Gilb. III. 230. Repert. XIII. 274. Crosbey's patent fire places. Repert. XII. 73. With tubes, and a false back. Whittington's patent baking stove. Repert. XII. 78. Marquard's vapour blowpipe. Repert. XIII. 274. Rowntree's patent application of fire to boilers. Repert. XIV. ]. On Rumford's principles, making the smoke descend. Holmes's family oven, without flues. S. A. XVIII. 230. Repert. XIV. 186. Heated by a piece of iron projecting into the fiie. Wakefield's steam houses for pines. S. A. XVIII. 398. Power's patent portable oven. Repert. XIV. 365. Guyton on Carcel's lamp. Ann. Ch, XXXVIII. 135. It produced a heat of 7" W. or 505.0° C. 942° F. Guyton's Swedish stove. Ann. Ch. XLI. 97. Repert. XVI. 254. Nich, 8. II. 24. With apertures emitting heated air. Sir G. O. Paul's stoves for ventilating hos- pitals. S. A. XIX. 330. Repert. ii. II. 268. Robertson's stove consuming its smoke. Ph. M. XI. 65. Berard's stove. B. M61anges. 57. Edelcrantz's digester. Journ. Phys. LVI. 147. Nich. VII. 161. Ph. M. XVII. l62. Anderson's patent hothouses for saving fuel* Anderson's Recreations. Repert. XV. 298. Cadet de Vaux on cooking with steam. Gilb. XI. 244. Smith's patent vapour bath. Repert, ii. I. 411. Thilorier's stove without smoke. Gilb. XI. 241. ' Woolf on heating by steam. Gilb. XIII. 395. A blowpipe by alcohol. Nich. 8. III. 1. Stephens's patent lime kiln. Repert. ii. III. 89. On sweeping chimnies. Repert. ii. III. 156. Wyalt's evaporator. Repert. ii. III. 360. Hooke's blowpipe by alcohol. Nich. 8. IV. 106. Black's furnace improved. Nich. VI. 273. Gilbert on heating fluids by steam. Gilb. XVI. 503. CATALOGUE. — NATURE OF HEAT. 41S A furnace for smelting iron. Rees cyclop. II. PI. Revolving apparatus for distilling. Rees cy- clop. II. PI. Art. Chemistry. Hornblower on sweeping chimnies by a blast. Nich. VII. 246. A mode of heating boilers at Meux's brewery. Ph. M. XVII. 275. Aikin's portable blast furnace. Ph. M. XVII. 166. Accum's chemical lamp. Nich. VIII. 2l6. Greenough on Melograni's blowpipe. Nich. IX. 25, 143. Curaudau's evaporating furnace. Nich. IX. 204. An improved maltkiln. Ph. M. XX. 71. A good freezing mixture is muriate of lime i, water l ; or nitrate of ammonia 1, water 1 ; or muriate of ammonia i, nitrate of potash 5, water IS. Alcohol and snow pro- duce great cold. Extinction of Heat. Bertholon on extinguishing fires. M, Laus. III. 1. Van Marum's portable pump for extinguish- ing fires. Repert. ii. III. 46 1. Nich. 8. V. 103. Nature of Heat. Homberg. A. P. 1700. H. 11. Mentions some efTects of motion analogouj to thoje of heat, fixing a vessel-to the clapper of a mill. Lomonosow on the cause of heat and cold. N. C. Petr. I. 206. Supposes heat to consist in motion. Whitehurst on the weight of ignited sub- stances. Ph.tr. 1776.575. Euler on the nature of the air. A. Petr. III. i. 162. Supposes the particle* of air to revolve within vesicles of water with a velocity of 2150 feet in a second, at 412°; that this velocity varies as the square root of the exp&Bsive force, becoming 1790 at 100° of Delitle's ther- mometer, 1330 at 200". This variation is however some what too great. Cavendish. Ph. tr. 1783. 312. Thinks Sir Isaac Newton's opinion of heat much the most probable. Achard's comparison of heat and electricity. Roz. XXII. 245. Achard on the tendency of heat to ascend. A. Berl. 1788. 3. Printed 1793. The experiments are not conclusive. Fordyce on the loss of weight in heated bo- dies. Ph. tr. 1785. 361. Probably the effect of an ascending current of air. Fordyce's experiment on heat. Ph. tr. 1 787. 310. Is persuaded that heat is a quality and not a substance. Rome de I'isle and Marivetz on the matter of heat. Roz. XXXII. 63, 71. Henry on the increase of weight in heated bodies. Manch. M. III. 174. Explains it from oxidation. Henry on the materiality of heat. Manch. M. V. 603. Ph. M. XV. 45. Nich. 8. HI. 197. Thinks that the heat excited by friction may be borrowed from without. But to borrow heat from another body is to be colder than that body, and to cool it. // ^\ i^ - i ""' 'TJ ^N. Reynieron the nature of fire. Roz. XXXVI*,: ^^iVy'^,. ^-T! 94. Beddoes. Ph. tr. 1791. 173. Observes, that heat and flame are produced by oxyge» already fixed, in the manufacture of iron. *Pictet Essais de physique. 8. The tendency to ascend, which he attributes to heat, may perhaps be partly understood from the great compa- rative capacity for heat of air highly rarefied. *Prevost sur I'equilibre du feu. 8. Genev. Roz. XXXVIII. 314. Young's remarks on the manufacture of iron. Gentl. Mag. 1792. T.Wedgwood. Ph.tr. 1792.270. Air not visible made a wire red hot. Dize on heat as the cause of shining. Journ. Phys. XLIX. 177. Gilb, IV. 410. 414 CATALOGUE. — ELECTRICITY. Rumfoid on the heat caused by friction. Ph. tr. 1798. 80. The capacity of chips did not difier from that of any- other iron. Runjf'ord on the weight ascribed to heat. Ph. tr. 1799: 179- Repert. XII. 151. Nich. in. 381. Ph. M. IV. 162. Weighed water against mercury at different tempera- tures, and found no difference. Rumford on the nature of heat. Ph. tr. 1804. 77. Supposes a radiation of positive cold. Tilloch on the weight of heat. Ph. M. IX. 158. Tilloch on the nature of heat. Ph. M. XII. 317. For caloric. Leslie on heat. J. T. Mayer on the nature of heat. Com- mentat. Gott. 1803. XV. M. 1. In favour of the existence of caloric. On the chemical effects of tremors. Mch. VII. 122. Higgins slacked lime in vessels hermetically sealed, and found no difference in their weight. LITERAIUKE OF ELECTKICITY. Gralath Electrische bibliothek. Danz. Ge- sellsch. I. 23. B. B. Copied in Priestley's Hist. Electr. at the end.^ Kriinitz Verzeichniss der vornehmsten schrif- ten von der electricitat. 8. Leips. I769. Weigels Grundriss der Chemie. feLECTEICITY IN GENERAL. Gilbertus de magnete. Guerike experimenta Magdeburgica. Ph. tr. abr. X. i. i. 269. Homberg on the electricity of sulfur. A. P. II. 145. Hauksbee's electrical experiments. Ph. tr. 1706, XXV. 2277. 1707. XXV. 23J3, 2372. 1708. XXVI. 82, 87. ITOg.XXVI. 391,439. 1711. XXVII. 328. Fr. byDesmarets. Abstr. A.P. 1754. H. 34. Stephen Gray's electrical experiments. Ph.. tr. 1720. XXXI. 104. 1731. XXXVII. 18. 17.'J2. XXXVII. 397. Dufay's eight memoirs. A. P. 1733, 1734, 1737. Dufay's letter on electricity. Ph. tr. 1734. XXXVIII. 258. On vitreous and resinous electricity. Acknowledge- ments to Hauksbee and Gray. Schilling on electricity. M. Berl. 1734. IV. 334. Desaguliers on electricity. Ph.tr. 1739. XLI. 186, aOO. 1741. XLI. 634. 1742. XLII. 14, 140. DesaguUers on electricity. Lond. 1742. Martenson de electricitate. 4. Upsal, 1740, J 742. Bosc on electricity. A. P. 1743. Kf. 45. fVinklers Gedanken von der electricitat. 8. Leipz. 1744. Winklers Eigenschaften der electrischen materie. 8. Leipz. 1745. Winkler Electricitatis recens observata. Ph.. tr. 1745. XLIII. 317. Ro&c Tentamina electrica. 4. Witteb. 1744. NoUet on electricity. A. P. 1745, 1746, 1747, 1748, 1749, 1753, 1755, 176O,. 1761, 1762, 1764, 1766. Nollet EssaJ sur I'electricite. 12. Par. 1746. Nolkt Recherches sur I'electricite. 4. Par.. 1749. Nollet on electricity. Ph. tr, 1748. XLV.. 187. Hollet lettres sur I'electricite. 12, Par. 1753, 1760. M.B. Extract by Watsoa. Th. tr. 1753. 201.. 1761. S^Q. CATALOGUE. — ELECTRICITY. 415 Watson on electricity. Ph. tr. 1745. XLIII. 481. Elementary. Mentions fixed inflammable air. Watson. Ph.tr. 1746. XLIV.41. 1747. 695, 704. Observes, after NoUet, that electricity is derived from the ground, Watson on Franklin's theory. Ph.tr. 1751. 202. fVaiz Abliandlung von der electricitat. 4. Berl. 1745. HoUmann de igne electrico. Ph. tr. 1745. XLIII. 239. Piderit de electricitale. Marburg, 1745. -[•Miles's electrical experiments and obser- vations. Ph. tr. 1746. XLIV. 27, 53, 78, 158. Mulkr Ursach und nutzen der electricitat. 1746. Boze Recherches sur r61ectricit6. 1746. M.B. Bozt Tentamina electrica. 4. Wittemb. 1747. M.B. fHales on some electrical experiments. Ph. tr. 1748. XLV. 409. Martin on electricity. 8. Bath, 1748. Recueil de traites sur I'electricite. 8. Par. 1748. Jallabert sur I'electricit^. 8. Par. 1749. M.B. Bouhnger traitfi de I'electricite. 12. Par. 1750. Secondat observations physiques. 12. Par. 1750. Veratti sur r61ectricit6. 12. Montpel. 1750. Dutour's researches on electricity. S. E. I. 345. II. 246, 516, 537. HI. 244. Bina Electricorum effectuura explicatio. 1751. Wilson on some electrical experiments made at Paris. Ph. tr. 1753. 347, 1763. 436. Wilson's short view of electricity. 4. London, 1780. R. L Canton's electrical experiments. Ph. tr. 1753. 350. 1754. 780. Leroy on the species of electricity. A. P. 1753. 447. H. 18. 1755. 264. H. 20. Franklin's electrical experiments. Ph. tr. 1755. 300. Franklin's letter on electricity. Ph. tr. 1755. 305. 1760. 525. ♦Franklin on electricity. 4. Lond. 1769, 1774. R. L Klingenstierna Tal om de nyaste rbn vid electricitaten. Stockh. 1755. Lovett's subtile medium. 8. 1756. R. I. Lovett's philosophical essays. 8; Worcest. 1766. R. I. Lovett's electrical philosopher. 8. 1777. R. L ♦Aepinus on some electrical experiments. A. Berl. 1756. N. C. Petr. VII. 277. Musschenbroek Introductio ad Ph. Nat. Euler junior on electricity. A. Berl. 1757. 125. Beccaria Lettere dell' elettrismo. f. Bologna, 1758. Beccaria's experimentJ. Ph. tr. 1760. 514, 525. Beccaria dcU' elettrismo artificiale. 4. Tur, 1772. ' '' t Beccaria on artificial electricity. 4. 1776. R.L ^ Symmer's electrical experiments, with a let- ter of Mitchell. Ph. tr. 1759- 340. " Egelin de electricitate. 4. Utrecht, 1759. Wesley's electricity made plain. 12. Lond, 1760. Cigna's electrical experiments. M. Taur. If. 77. in. 31. V. i. 97. Dalibard Histoire abreg€e de l'61ectricil<^» 2 V. 12. Par. 1766- Al6 CATALOGUE. ELECTRICITY. Saussure de electricitate. Genev. 1766. LuUhi de electricitate. 8. Genev. 1766. Hartmami's Versuche in leeren raiime. 8. Hanov. 1766. Priestki/'s introduction to electricity. 8. Lond; 1769. R.I. Priesiky's history and present state of elec- tricity. 4. Lond. 1769- Experiments made in 1760. 49. Bauer von der theorie und dem niitzen der electricit'at. 1770. Ferguson's introduction to electricity. 8. Lond. 1771. R.S. Sigaud de la Fond Iraki de I'electricit^. 12. Par. 1771. R. I. Ace. Roz. Intr. I. 83. Sigaud de la Fond Precis des phenomfenes electriques. Par. 1781. Brydone on some electrical experiments. Ph. tr. 1773. l63. Jacqmt Precis de I'electricite. Vienna, 1775. Becket on electricity. 8. Berdoe on the electric fluid. 8. Gross Electrische pausen. 8. Leips. 1776. Dubois Lettre sur I'electricit^. Tableau des sciences. Par. 1776. 143. Weber Electrische versuche. Socin Anfangsgriinde der electricitat. 1777. Gallitzin's letters on electricity. A. Petr. I. ii. H. 25. Le Prince Gallitzin sur I'electricite. 4. Pe- tersb. 1778. Herbert Theoria phaenomenorum electrici- tatis. Vienna, 1778. *Lord Mahon's principles of electricity. 4. Lond. 1779. R- I- Lord Mahon Principes d'felectricit^. 8. Lond. 1781. R. L Lyons's new system of electricity. 4. Lond. 1780. Lyons's further proofs. 4. Marat's electrical discoveries. Roz. XVIL 317, 459. Marat Recherches physiques sur I'electri- cite. 8. Par. 1782. Germ. 1784. On electricity. Roz. XVIIL 157. La CepMe sur I'electricite. 2 v. 8. Par. 1781. R.S. Achard's electrical experiments. Roz. XIX. 417. XXIL 245. XXV. 429. Cuthbertson Eigenschappen van de electri- citat. 2 parts. Amst. 1782, part 3, 1794. Germ. 8. Leips. 1786. Cuthbertson uber die versuche von Deimann und Troostwyck. 8. Leipz. 1790. Milner's experiments and observations on electricity. D'Inarre Anfangsgriinde der naturlehre. 8- Frankf. 1783. 1. Kiihn Geschichte der electricit'at. Leipz. 1783. Van Marum Experiences sur I'electricite. Harl. R. S. Roz. XXXL 343. Gilb. I. 239, 256. X. 121. Kunze Neue electrische versuche. 4. Donndorffs Lehre von der electricitat. 8. Erf. 1784. Tressan snrie fluide electrique. 2 v. 8. Par. 1786. R.S. Beck Entwurf der lehre von electricitat. 1787. Vassalli and Zimmerman's electrical experi- ments. Soc. Ital. IV. 264. Nicholson's experiments. Ph.tr. 1789. 265. Sennet's new experiments. 8. Derby, 1789. R.S. On Charles's electrical experiments., Roz. ; XXX. 433. Briefe iiber die electricitat, von C. L. 8. Leips. 1789. CATALOGUE. ELECTRICITY. 417 Deluc on electricity. Roz. XXXVI. 450. Brook on electricity. 1790. Peart on electricity and magnetism. 8 Gainsborough, 1791. R. S. Peart on electric atmospheres. 1793. R. S, Adams on electricity, by Jones. 8. London, Lampadim iiber electricitat und warme. 8. Berl. 1793. Cavallo's electricity. 3 v. 8. Lond. 1795. R. I. Morgan's lectures on electricity. 2 v. 12. Lond. Acc.Ann.Ch. XXXIV. 93. Enc. Br. Art. Electricity. Robison. Enc. Br. Suppl. Art. Electricity. Von Arnim's electrical experiments. Gilb. V. 33. VI. 116. Clos on electricity. Journ. Phys. LIV. 3I6. Remer's electrical experiments. Gilb. VIII. 323. Theory of Electricity. Gray. Ph. tr. 1732. XXXVII. 397. Found electric attraction in and through a vacuum. Gordon Versuch einer erklarung der electri- citat. 8. Erf. 1745. Rosenberg von der ursachen der electricitat. Breslau, 1745. Kratzenstein Theoria electricitatis. 4 Hal. 1746. Kratzensteins Vorlesungen. 4. ed. Copenh. 1781. For two fluids. Ellicott on the laws of electricity. Ph. tr. 1748. XLV. 195. An approach to a theory. J. Enter de causa electricitatis, 4. Petersb. 1755. J. Elder on the physical cause of electricity. A. Berl. 1757. 125. Symmer on two electric fluids. Pb. tr. 1759. 340. VOL. II. Cigna on the analogy of magnetism and electricity. M. Taur. I. , *Aepim tentamen theoriae electricitatis et magnetismi. 4. Petersb. 1759. R. I. Aepinus's comparison of magnetism and electricity. N. C. Petr. X. 296. Dutour sur la matiero electrique. 12. Par. 1 760. Bergmann on the existence of two fluids. Ph. tr. 1764. 84. *Cavendish on the principal phaenomena of electricity. Ph. tr. 1771.584. Herbert Theoria phaenomenorijm electrici- tatis. Vienna, 1778. Elder's letters. II. 34. On the identity of the electric fluid with his ether. Wilke on the existence of two fluids. Scluv. Abb. XXXIX. 68. *Lord Mahon's electricity. On the law of the force. Achard on the elasticity of electrified air. A. Berl. 1780. Perceived no effect. Achard on the similarity of the excitation of electricity and of heat. Goth. Ma*. II. ii. 139. Achard on the efl^ectof surface. Roz. XXVI. 378. Karstens Anleitung. ccccxcvii. For two fluids. Barletti's theory of electricity. Soc. Ital. I. 1. II. 1. Laurentii Beraud Theoria electricitatis. Pe- tersb. Donndorf iiber electricitat. 1783. Forster. CrelJs JN. Entd. XII. 154. For two fluids. *Coulomb. A. P. 1784. A. P. 1785. 578. Shows that the force varies inversely as the square Of the distance. Coulomb's fourth memoir on electricity. A. P. 1786. 67. 3 H 418 CATALOGUE. — ELECTRIC IT V, The distribution of electricity is npt regulated by elective attractions. The fluid in conductors is accumulated at the surface, and does not penetrate the body, as Cavendish had before observed. Cor.lomb on the distribution of the electric riiiid. A. P. 1787. 421. With experiments. Coulomb on the distribiltion of the electric fluid in diflercnt parts of conductors. A. P. 1788. 617. With experiments. In order to avoid the supposed electric repulsion of mat- ter, Coulomb, imagines two fluids possessed of equivalent properties, neutralising each other's elasticity like oxygen and hydrogen combined. Account of Coulomb's memoirs. Roz. XXVII. 1)6. XLIII. 247. Journ. Phys. XLV.(It.)235, 448. Weber Theorie der electricitat. Naturf. Fr. xlvi. Prevost Traite du raagnetisme. Preface. Haiii/ Theorie de I'electricite et du mag- netisme. 8. Par. 1787- R. S. Hauy Traite de physique. Extract of Haliy's account of Aepinus's the- ory. Roz. XXXI. 401. DeLuc Idees sur la meteorologie. R. I. De Luc Journ. de Physique. Juin, 1790. Gehlers physicalisches worterbuch. Art. Flasche. Chajjpe on the electric properties of points. Roz. XL. 329. Voigt Theorie des Feuers. Schmidt on the weight of the electric fluid. Abhandl. 8. Giessen, 1793. 163. Biot on the disposition of electricity in a spheroid. B. Soc. Phil. n. 51. Heidmarm Theorie der electricitat. 2 v. 8. Vienn. 1799- R- S. *Robison. Euc. Br. Suppl. Art. Elec- tricity. From Aepinus and Cavendish, with his own additions. Account of Deluc's theory, near the end. Tremery against two electric fluids. B. See. Phil. n. 63. Journ. Phys. LIV, 357. Woods on the Franklin ian theory of elec- tricity. Ph. M. XVII. 97. Equilibrium of Electricity. ^ Induced Electricity. Guericke Exp. Magdeb. iv. c. 15, art. 3. Aepinus. N. C. Petr. VI. Beccaria. Ph. tr. 1770. 277. Charge. Gray on the electricity of water. Ph. tr. 1732. XXXVII. 227. Winkleis electrische kraft des wassers in glasernen gefasgen. 8. Leips. 1746. f Miles on the electricity of water. Ph.tr. 1746. 91- Wilson's retractation on the Leyden phial. Ph. tr. 1756. 682. *Wilkt de electricitatibus contrariis. 4. Ros- tock, 1757. Wilke. Schw. Abb. 1758. 241. 1762. 213, 253. Beccaria's electrical experiments. Ph. tr. 1767.297. On combinations of glass plates. Cavendish. Ph. tr. 1776. The quantity of electricity is inversely as the thickness of the glass. Achard on the charge of electricity in pro- portion to the surface of a body. A. Berl. 1780. 47. Roz. XXVI. 378. E. W. Gray on the charge of glass. Ph. tr. 1788. 121. Observes, that glass may receive a certain portion of electricity without discharging any from the other side ; and that the capacity of a body is proportional to its sur- face only. CATALOGUE. ELECTRICITY. 419 Barletti on the laws of charged glass. Soc. Ital. IV. 304. VII. 444. Nicholson. Ph.tr. 1789. 285. ' Observes, that some uncompensated electricity is neces- sary to a charge : that the intensity of the charge, and the explosive distance with a given quantity of electricity, js directly as the thickness of the substance ; he found that a piece of Muscovy talc, ^^ inch thick, received ten times as much electricity as an equal surface of common glass. Hence a solid inch of such matter must contain at least as much electricity as would charge a conductor 7 inches in diameter, and 135 feet long, so as to give a spark of nine inches ; and the bulk of a man more than 5000 times as much. Wilkimon on the Leyden phial. 8. Lond. 1798. A double plate of glass takes a higher charge than a sin- gle piece of the same thickness. Electric Attractions and Repulsions. Gray. Ph. tr. 173^. XXXVIl. 397. Finds that the attraction operates in and through a vacuum. Dufay on electric attraction and repulsion. A. P. 1733.475. 1734. 341. Wheler's experiments on electrical repulsion. Ph.tr. 1739. XLI. 98. Mortimer on \V heler's experiments. Ph. tr. 1739. XLI. 112. Desaguliers. Ph. tr. 1742. XLII. 140. Thinks the attraction between air and water may be electrical, causing the rise of vapour. Symmer on electrical cohesion. Ph.tr. 1759. 340. Lichtenberg's figures delineated on electrics by the attraction of dust. N. C. Gott. 1777. Vlir. IG8. Commentat. Gott. 1778. I. M. 65. Dcluc Idces. xii. Troostwyck en Krayenhoffs verhandllng. 8. Germ. Leipz.Samml. xlvi. Goth. Mag. I. iii. 76. V. iv. 176. Cavallo. Ph. tr. 1780. 13. Sanmartini on the effect of electricity on hydrometers. Soc. Ital. VI. 120. When the fluid was electrified the hydrometers some- times rose a few degrees. Carmoy on the motion of electrified fluids in capillary tubes. Journ. Phys. XLV. (II.) lot). Thinks the mere presence of electricity has no general effect on this motion. Miller on electric attraction and repulsion. Ir.tr. VII. l.'39.Nich. IV.461. Giib. IV. 419. V.73. Aldini attributes regular forms, like those of snow, to Lichtenberg's figures. Von Arnim denies their regularity. On the phenomena of powder thrown on glass. Journ. Phys. LW. 237. Von Arnim on terrestrial electricitj'j as tend- inf» to the discovery of springs. Gilb. Xm. 4()7. Ritter on an electric polarity. Gilb. XV. 106. Conducting Powers. Plot's catalogue of electrics. Ph. tr. XX. 1698. 384. Gray on the electricity of water. Ph. tr. 1732. XXXVIL 227. Dufay. A. P. 1733. 73, 233. Desaguliers. Ph. tr. 1741. XLI. 661. Watson. Ph.tr. 1746. XLIV. 41. Found ice a conductor. Watson on insulation. Ph. tr. 1747. XLIV. 388. Watson on electricity in a vacuum. Ph. tr. 1751. 362. Bosc on healed glass. Ph. tr. 1749. XLVI. 189- Lemonnicr on the electricity of the air. A. P. 1752. 233. II. 8. Dutour on the action of flame upon electrical bodies. S. E. II. 246. 420 CATALOGUE. — ELECTRICITY. Mazeas on the electricity of the air. Ph. tr. 1753. 377. Ammerdn de eleclriciiate lignorum. 24. Lucern. 1754. Delaval on electricily. Ph. tr. 1759. 83. Delaval oa the effects of heat. Ph. tr. 17GI. 353. fWilson and Bergman on the permeabihty of glass. Ph.tr. 176O. 896,907. Canton on Delaval's experiments. Ph. tr. 17G2. 457. Ascribes the increase of conducting power to moisture rather than to cold. Kinnersley's experiments. Ph. tr. 1763. 84. fKinnersley on the conducting power of charcoal. Ph. tr. 1773. 38. A line drawn by a black lead pencil conducts. Leroy on the transmission of the spark under different circumstances. A. P. 1766.451. Priestley on the conducting power of char- coal. Ph. tr. 1770. 211. Cotte. A. P. 1772. i.H. 16. Snow serves as a conductor in storms. Henley's experiments. Ph. tr. 1774. 389. Shows that vapour is a conductor, and that an imperfect ♦acuum conducts. Henley on the impermeability of glass. Ph. tr. 1778. 1049. Cavendish. Ph.tr. 1776. Iron wire conducts 400 million times better than pure water; sea water, with one thirtieth of salt, loo times better ; a saturated solution of salt 720 times better. Achard on the electricity of ice. Roz. VHI. 364. Acliard on the celerity of electrization. A. Berl. 1777.25. Achard on the analogy of conductors of heat and of electricity. A. Berl. 1779. 27. Roz. XXII. 245. With an instrument for measuring the conducting power. Achard on the distinction of conductors and electrics. Roz. XV. 117. Achard Schriften. 246. Bergman on the conducting power of water. Roz. XIV. 192. Cavallo. Ph. tr. 1783. 495. Pith balls electrified did not diverge in the vacuum of an air pump, whether much or little electricity was commu- nicated to tliem. Perhaps from the perfection of the con- ductor. Cavallo on a vacuum. Electr. ed. 4. part 4. c. 8. Lavoisier and Laplace on the electricity absorbed by vapours. A. P. 1781. 292. H. 6. Coulomb on the loss of electricity in a given time. A. P. 1785. 612. Morgan on a vacuum. Ph. tr. 1785. 272. When the mercury has been boiled for some hours in a gage, neither light nor charge can be procured in it. Air conducts best when the light streaming through it is bluish violet. Acids conduct better than water, and hot water than cold. Vassalli and Zimmerman's experiments on water and ice. Soc. Ital. IV. 264. Eandi. M. Tur, 1790. V. 7. Says that light may be seen in the dark, even when the vacuum is perfect. But it may be said that some mercurial vapour is present. Volta on the use of the electrometer in hy- grometry. Soc. Ital. V. 551. Volta. Gilb. XIV. 257. Says that wire conducts a million times better than water. Repeats some of Cavendish's experiments. Tremery on conductors of electricity, and on the emission of the electric fluid. B. Soc. Phil. n. 19. Journ. Phys. XLVIIL 168. Bressy on the electricity of water. Gilb. I. 375. Wood on the permeability of glass. Ph. M. II. 147. Heller on the conducting power of water. Gilb. VI. 249. CATALOGUE. ELECTRICITY. 421 Erman on conducting powers. Gilb. XII 143. Shows that ice is a nonconductor. A thread of gum lac insulates ten times as well as silk. A needle of sealing wax retains for some days its electric polarity. A capillary bore lessens the insulating power of glass. According to Saussure's hygrometer, the dissipation of electricity by the air is nearly in the triplicate ratio of its moisture. A jar will be discharged if sounded like a harmonica. Robison. Table of Conductors, in order, chiefly from Cavallo. Conduclors. Gold. Silver. Copper. Platina. Brass. Iron. Tin. Mercury. Lead. Semimetais. Metallic ores. Charcoal. Animal fluids. Acids. Saline solutions. Hot water. Cold water. Liquids, excepting oils. Red hot glass. Melted resin. Flame. ~Ice, not too cold. Metallic salts. Salts in general. Earths and soft stones. Glass, filled with boiling water. Smoke. Steam or vapour. An imperfect vacuum. Hot air. In Henley's experiments, the same charge melted of gold wire 4 inches, of brass 6, of silvered copper 8, of silver lo, of iron lo or more. Copper is allowed to conduct much more readily than irotj. Nairne. Platina is said by some to be a bad conductor. Seems to be placed too low. Snow. Cotte. Kinnersley. Yet the electrical machine works in a vacuum. Read denies that hot air is a conductor. Nonconductors. Ice, at — 13° F. Achard. Powders, not metallic. Delaval. Soft stones, when heated. Delaval. Hard stones. Dry vegetable substances. Baked wood requires to be varnished. Ashes. Dry and complete oxids. Oils. Common air, and other gases. White sugar and sugar candy. Paper. Dry and external animal sub- stances, as feathers, wool, and hair. Cotton. Silk. Wax. Resins. Sulfur. Amber. Transparent gems. Glasi of all kinds. A pel feet vacuum. Morgan. White hair conducts less perfectly than black. __ Henley. Ph. tr. 1770. Glass often heated is best fSr electrical purposes. Bosc, Motions of the Electric Fluid. Velocity. Watson. Pli. tr. 1748. XLV.49, 491. No perceptible time was occupied in a circuit of 12273 feet : but the report was not so loud when the circuit was so much extended. Simple Communication. Nairne. Ph. tr. 1774. 79. Observes, that a ball was struck at the distance of nine inches by the same charge that reached a point oply at six. Perhaps, however, the point had very rapidly diminished the charge. On the direction of the electric current. Henley, Ph. Ir. 1774. 389. ii. Flame is driven by a weak charge towards the negative side. Henley on the long continuance of exci- tation. Ph. tr. 1777. 85. 422 CATALOGUE. — ELECTRICITY. Iiigenhousz on the motions of electricity. Roz. XVI. 117. Coulomb on the loss of electricity in a given time. A. P. 1783.612. Cavallo's experiments on the escape of elec- tricity. Ph. tr. 1788. 1. Nicholson found, that a point, projecting more or less from ' a large ball, produces more or less the effect of a smaller ball, or of a point, and that a smaller projeciion has the effect of a small ball when it receives than when it emits electricity. Cuthbertson observes, that when the flame of a can(J[e is placed between two balls, the one positive, the other negative, the negative ball only is heated. It may be questioned whether every spark is not rather to be con- sidered as resembling the breaking of a charged jar than as a simple communication. « Lateral Explosions. *Priestley. Ph.tr. 1769. 57, 63. 1770. 192. Henley. Ph. tr. 1774. 389- iii- Cavendish. Ph. tr. 1776. Electricity spreads even from a wire. Discharge. ' Lemonnier on the communicatidn of elec- tricity. Ph. tr. 1746. 290. A. P. 1746. 497. H. 10. Bergmann's electrical experiments. Opusc. V. 587. Immediate Effects. Mechanical Changes. On powdering glass by the spark. Roz. XV. 334. Vacca Berhnghieri. Roz. XL. 133. Observes, that the electrical fluid has no perceptible mo- mentum. On Lulliii's card. Nich. 8. III. 223. When the experiment of perforating a card is made in air much rarefied, the perforation is near the negative in- ' stead of the positive point. Perhaps these effects are ultimately referable to heat and expansion. Light. See Galvanic Electricity. Picard on the light of barometers. A. P. II. 125. X. 393. Bernoulli on the light of barometers. A. P. 1700. 178. H. 5. 1701. 1. H. 1. Hauksbee on the mercurial phosphorus. Ph. tr. J 705. XXIV. 2129. The phenomenon is best seen when the air is exhausted to half its density, but is visible in some measure without exhaustion. Lahire on the barometric light. A. P» 1705. 22G. Wall on the light of diamonds. Pli. tr. 1708. XXVI. 69. Dufay on electrical light. A. P. 1723. 293. H. 13. 1734. 503. II. 1. 1735. 347. H. 1. 1737. 86, 307. Beccari on the light of diamonds. Coll. Acad. X. 197. Gray on electrical light. Ph. tr. 1735. XXXIX. 16. Opinion respecting thunder. 24. Miles on luminous emanations from friction. Ph.tr. 1745. XLIII. 441. Trembley on the electric nature of the baro- metrical light, 1745. Ph. tr. 1746. XLIV, 58. Waiz on barometrical light. Lohier on electric light upon clothes. A. P. ^ 1746. H. 23. Winkler descriptio pyrorgani electrici. Ph. tr. 1747. XLIV. 497. A plaything. Cooke on the sparkling of flannel and hair. Ph. tr. 1748. XLV. 394. Doppdmayer iiber das electrische licht. 1749. Canton's figures of sparks. "Ph. tr. 1734. 780. Fayol on the illumination of a plant. A. P, 1739. H. 36. CATALOGUE. ELECTRICITY. 423 Nollet on the illumination of ice. A. P. 1766. H. 2. Lane. Ph. tr. 1767- 451. A shock passing through water is visible. Nairne. Ph. tr. 1777. 614. Observes that the light is verj- faint In a moist vacuum. Deluc Modif. I. Ixxxv. On barometrical light. Morgan. Ph. tr. 1785. 272. The more readily a body conducts, the more difficult it is to make it luminous. Gold leaf may be made luminrus. The light produced by electricity streaming through very rate air is green : when the air is denser it becomes blue, and then violet, till the air no longer conducts. Crellon electrical light. Rozier, Feb. 1717. Good figures of sparks. Nicholson. Ph. tr. 1789. 265. A ball I*,, of an inch in diameter, highly electrified, was surrounded by a steady faint light ; a ball of an inch and a half was rendered luminous, with a bright speck moving on its surface. Eandi. M.Tur. 1790. V. 7. Says that a faint light may be seen in the dark, in the most perfect vacuum that can be procured, lirxleben by Lichtenberg. dxxiv. The lock of a pistol gives light under water. fJnch on the light of sugar. Ph. M. V. 207. Electric Heat. See Galvanic Electricity. Winkler onfiring spirits. Ph.tr. 1744.XLIII. 166. -f-Winkler on electrical combustions. Ph. tr, 1754.772. Miles on firing phosphorus. Ph. tr. 1745. XLm.290. Roche on a frock set 6n fire. Ph. tr. 1748. XLV. 323. Kinnersley on an electrical air thermometer, and on the extension of wire. Pb. tr. 1763. 84. Priestley on the rings made on metal by explosions. Ph.tr. 1768. 6S. The metals were held near the point of a needle. The battery contained 21 square feet. Ingenhousz on lighting a candle by electri- city. Ph. tr. 1778. 1023. Employs cotton, with powdered resin. Nairne on the effect of electricity in shorten- ing wires. Ph. tr. 1780. 334, Wolf on firing gunpowder. Goth. -Mag. II. ii. 70. Van Marum on the effects of electricity. Nich. II. 527. Bertholiet's comparison of electricity and heat. Nich. VIII. 80. Thinks that electricity produces heat only by means of chemical changes. Cuthbertson has observed, that gunpowder is readily fired by a discharge passing through an interrupted circuit, by means of wet tubes and wet twine. He says that a dou- ble charge melts a quadruple length of wire. Ehrmann's electrical lamp consists of an electrophorus, giving a spark, which sets on fire a stream of hydrogen gas. Congelation. Robert on the supposed effect of electricity in congelation, lloz. XXXVI. 222. Supposed Transmissinn of Odours. Nollet. Ph. tr. 1750. 368. Winkler. Ph. tr. 1751. 231. With Watson's experiments. Watson against the transmission of odours. Ph. tr. 1756. 348. Chemical Effects. Priestley, vii. Electricity often discolours the leaves of delicate flowers. Pearson on the gas produced by electricity. Ph. tr. 1797. H"?. Wollaston. Ph.tr. 1801. Van Marum on decomposing water by electricity. Gilb. XI. 220. 424 CATALOGUE. — ELECTEICITY. On oxidation by electricity. Gilb. XI. 400. See Galvanism. Physiological Efi'ects. On Vegetables and Animals. De BOzes on the effect of electricity on an insulated person. Ph. tr. 1745. XLllI. 419. That it quickens the pulse. Lallamand's experiment on a glass of water.. Ph. tr. 1746. XLIV. 78. The first time the shock deprived him for some mo- ments of the power of breathing. Musschenbroek repeated his experiment, and says he felt a most terrible pain. Winkler on the effects of electricity. Ph. tr. 1746. XLIV. 211. Says, that a shock gave him and his wife convulsions and cpistaxis. Winkler Rei medicae utile electricitatis in- ventum. Ph. tr. 1748. XLV. 262. Browning on electrifying trees. Ph. tr. 1747. XLIV. 373. Perceived no effect from electricity in the operation of phlebotomy. Watson. Ph.tr. 1751.231. Kits et Koestlin de effectibus electricitatis. 4. Tubing. 1775. Henley on a bullock struck by lightning. Ph.tr. 1776.463. The skin was only affected where the hair was white, being there the least perfect conductor. Cavendish. Ph. tr. 1776. Says, that the sensible shock depends rather more on the quantity of the electricity than on its force : a double force with half the quantity, producing a shock rather less powerful. Ingtnhomz Versuche niit pflanzen. 3 v. 8. Vienna, 1778.. 1790. Ingenhousz. Koz. XXXII. 321. XXXV. 81. Found no effect on vegetation. Achard on hatching eggs. A. Berl. 1778. 33. Schrjften. 241. Schwankhardt on the influence of electricity upon vegetation. Roz. XXVII. 462. Remarks. XXVIII. 93. Carmoy on shocks. Roz. XXIX. 194. Carmoy on the effects of electricity on ve- getation. Roz. XXXIII. 339- Troostlcyck et Krayenhoff de I'application de I'electricite. 4. Amst. 1788. Roulandj Dormoy, Bertholon, and Derozi^rcs on the effect of electricity on vegetation. Roz. XXXV. 3, 161, 401. XXXVIII. ■ 351,427. Effects of electricity on the hedysaruni gyrans. Goth. Mag. V. iii. 13. Van Marum on death by electricity. Roz. XXXVIII. 62. Van M arum's experiments. Ph. M. VIIl. 193. A machine capable of fusing 24 inches of wire, -i^ of an inch in diameter, produced no effect on the pulse, nor on the perspiration ; and did not appear to promote evaporation. Chappe and Mauduyt on the supposed ef- fects of electricity on the growth of ani- mals. Roz. XL. 62, 241. Volta. Gilb. XIV. 257. Says, that only a little more electricity is required to produce an equal shock from a larger surface. A surface 16 times as large required an elevation of the electrometer to one tenth of the number of degrees. But the degrees of the electrometer cannot be an immediate measure of the quantity of electricity, without having regard to its situa- tion with respect to the tlectiified bodies. On an insensibility of electricity. Gilb. XIV. 423. A small charge of a large surface gives a less unpleasant shock than a larger charge of a small one, and may per- haps be fitter for medical purposes. The spark from a long wire is sharper than from a large body. Robison. Secondary Effects of the communication of Electricity. Streams of Aax. Lord Mahon's electricity. Mayer in Gren. VI. vii. §. 208. CATALOGUE. — ELECTRIC ITT. 425 Gray on the revolutions of pendulous bodies. Ph. tr. 1736. XXXIX. 280. . ■^-Gray's last experiment on revolutions, re- lated by Mortiiner.Ph.tr. 1730. XXXIX. 400. Gray fancied the motions were naturally directed from west to east. Wheler on Gray's experiments of revolu- tions. Ph.tr. 1739. XLI. 118. According to Lichtenberg, some similar observations have keen made by Miiller, Delaperriere, Hartmann, and Schaffer. Henley. Ph. tr. 1774. SSQ. ii. Flame is driren by a weak charge towards a negative ball. A tube of glass, surrounding a point, prevents the current ef air, and the escape of the fluid. Robison. Excitation, or Destruction of the stable Electric Equilibrium. Richmann on excitation. C. Petr. XIV. 299. Bergmann on the excitation of glass plates, and of ribbons. Opusc. V. 370, 391. Aubert on electric permutations. Roz. XXXIX. 194. On excitation. Nich. II. 43. Vassalli on excitation. Gilb. VII. 498. Haiiy on the excitation of metals. B. Soc. Phil. n. 85. Gilb. XVII. 441. Beonet found that no electricity was excited by flame, by the explosion of gunpowder, nor by the expansion of condensed air. Excitation by simple Contact. Perhaps Webers Erfahrungen idioelectrische kijrper ohne reiben zu electrisiren. 1781. Bennet's experiments on excitation. Ph. tr. 1787. 26. Bennet's new experiments on electricity. 1739. Nich. 8. 1. 144, 184.Gilb. XVII.428. Cavailo's electricity. VOL. II. Volta's papers on galvanic electricity. See Galvanism. Excitation by Friction. See Electrical Machines. Hauksbee's experiments on attrition in a va- cuum. Ph. tr. 170j. XXIV. 2165. Amber rubbing a woollen cloth produced light and heat : flint and steel only a faint lambent light. Glass rubbed with woollen cloth became electric in'a vacuum. Glass rubbed with glass shone both in the open air and in a va- cuum, as well as under water. Gray's experiments on worsteds of dif- ferent colours. Ph. tr. 1735. XXXIX. 166. Ludolffon the electricity of barometers. A. Berl. 1745. 1. Cooke on the electricity of new flannel. Ph. tr. 1747. XLIV. 457. Symmer. Ph. tr. 1759- 308. Dutour from Symmer. A. P. 1767. H. 34. Beccaria dell' elettrismo. 4. 1753. Ph. tr, 1766. 105. Cigna. Misc.Taur. III. Bergmann. Schw. Abh. XXV. 344. Ph. tr. 1764. 84. Finds that a body becomes more disposed to negative electricity as it becomes more heated. Aepinus on the electricity of barometers. N. C. Petr. XV. 303. On a cat that gave smart sparks. A. P. 1771. H. 37. Henley. Ph. tr. 1774. 389- v. *Henley. Ph. tr. 1777. 122. Socins anfangsgriinde der electricitat. Ha- nau, 1778. 66. Herbert on the excitation of metals. Theoria phaenom. electr. Vienna, 1778. 15. On metals as electrics. Heuimer in Rozier. XVI. 50, 74. 3 1 426 CATALOGUE. — ELECTRICITY. Nicholson. Ph. tr. 1789. IVi/ke de electricitatibus contrariis. Auf- satze. 8. Gott. 1790. Finds that the friction of a quill, in different directions, produces different species of electricity. Lichtcnberg in Erxleben. §. 514. Wilson on the electricity of shavings. Nich. 8. IV. 49. Gilb. XVII. 205. Gersdorf on the electricity of powder. Gilb. XVII. 200. Haijy on the electricity of metals. Ph. M. XX. 120. Lichtenberg's Table of Excitation, transposed. The marks denote the electricity of the substances under which they stand. Polished glass Hair Wool Feathers Paper Wood Wax Sealing wax Ground glass Metals Resin Silk Sulfur Polished glass. 0 + + + + + + + + + + + Hair. Wool. Feathers. Paper. Wood. Wax. Sealing Ground Metals. Resin. Silk. Sulfur. wax. glass. + + + + + + + o + + + o + + It appears that any substance in this table, rtibbed with any of the following substances, becomes positively electric j with any of the preceding, negatively. This proposition is, however, liable to some modifications, according to the mode of applying friction, and the degree of heat ; the table requires also some further subdivisions. Mr. Henley says, that " a smooth glass mbe maybe made negative by drawing it crosswise over the back of a cat, or by exciting it with a dry, warm rabbit's skin." Henley made a great number of experiments with a variety of sub- stances rubbed on wool and silk : there are only two instances where the wool produced a positive and the silk negative electricity, and these were probably owing to the greater heat of the wool. There were, however, very great irregularities in the effects produced upon different substances of the same class ; thus a guinea, a sixpence, and a piece of tin, became negative ; a piece of copper, a steel button, and a silver button, positive, at least when the cloth was warm : animal sub- stances, excepting shells, generally positive : vegetables almost always negative, but the smooth skins of beans positive ; common pebbles, marble, coal, and jet, negative : gems and crystals positive : glazed wares and writing paper positive; tobacco pipe, clastic gum, a tallow candle, oiled silk, Indian ink, and blue vitriol, negative. Mr. Errington and Mr. Cavallo extended the list to almost looo articles. Excitation bi/ Change of Form of Aggregation. Gray on melted substances. Ph. tr. 1732. XXXVII. 285. Kinnersley. Ph. tr. 17G3. 84. The vapouf of electrified water did not carry up elec- tricity. Henley on the positive electricity of cooling chocolate. Ph.tr. 1777.85. Lavoisier and Laplace on the electricity ab- sorbed by vapours. A. P. 1781. 292. H. 6. Bennet. Ph. tr. 1787- Water running through a heated tobacco pipe showed a strong electricity. Liphardt on the electricity of chocolate. Roz. XXX. 434. CATALOGUE. — ELECTRICITY, GALVANISM. 427 Van Marum and Troostwyck on electricity from melting. Roz. XXX [II. 248. On electricity from evaporation. Ph. M. XIII. 231. Eltctricity from Chemical Changes, . Galvanism. Gardenii dissertatio de electrici ignis natura. Water evaporating from clean iron leaves it negative, from rusty iron, positive. Al. Galvani de viribus electricitatis in motu musculavi connnentarius. Boiogn. 179 J. C. Bon. VII. O. 363. Mayer Abhandlungen von Galvani und an- dern.'iv, 8. Prague, 1793. Balbo and Valli on Galvani's animal elec- tricity. Roz. XLI. 57, 6Q, 185... Vacca Berlinghieri on animai electricity. Roz. XLI. 314. *Volta on Galvani's discoveries. Ph. tr. 1793. 10. Ph. M. IV. 163, 306. The involuntary muscles, even the heart, appeared to Volta to be insensible of the stimulus of Galvanism ; in- sects vcere affected by it, but not worms. When a piece of zinc was laid on the point of the tongue, and a silver spoon was applied to the tongue further back, and made to touch the zinc, a sour taste was produced by the zinc at the instant of contact. Volta's remarks. Gren. III. 4. IV. 1. VIII. 303. Ann. Ch. XXIII. 270. *Volta on electricity excited by contact. Ph. tr. 1800. 403. Ph. M. VII. 289. Journ. Phys. LI. 344. Account of the Galvanic pile and series, which he con- eiders as actually producing a perpetual motion from the mechanical powers of electricity. Volta's letter on the causes of Galvanic effects. Journ. Phys. Nich. 8. I. 135. Volta's memoir. M. Inst. IV. B. Soc. Phil, n. 58. Ann. Ch. XL. 225. Gdb. X. 421. Volta's answer to Nicholson's remarks. Bibl. Brit. n. 150. Volta on charging a battery by the pile. Gilb. XIII. 257. Volta. Gilb. XV. 86. Says, that a battery may be strengthened' by the interpo- sition of plates, without a fluid. Gilbert could not, how- ever, succeed in the experiment. Fowler on animal electricity. 8. Edinb. 1793. R. L Desgenettes on animal electricity. Roz, XLI I. 238. On animal electricity. Soc. Philom. Roz XLII. 292. Laney on animal electricity.Roz.XLIII.46l. Gren. VI. Creue Beytrag zu Galvanis versuchen. 8. Frankf. 1793. P/«^'deelectricitate animali. 8. Stutg. 1790i Ace. m Gren. VIII. 196. Note of Pfaff 's galvanic experiments. Ann. Ch. XXXIV. 307. Pfaff on Volta's galvanic theory. Gilb. X. 219. Fabroni on the mutual action of metals. Read, 1793. Nich. Ph. M. V. 268. Gilb. IV. 428. Achard on the irritation of the nerves by contact. A. Berl. 179O. 3. Monro's experiments on animal electricity. Ed.u. III. 231. Ph. tr. 1794. Read finds all noxious vapours in a negative state. Aldiiiide animali electricitate.4.Bologu.R.S. 1794. R. I. Aldini sopra I'elettricita anijnale. 8. Pad. 1795. R.S. Aldini sul galvanisnio. 8. Boiogn. 1802. R. S. Aldini on galvanism. 4. Ijond. 1803. K. I, Aldini's experiments. Ph. M. XIV. 88, 191, 364. Wells on the galvanic contraction of the muscles. Ph. tr. 1795. 246. 428 CATALOGUE. — ELECTRICITV, GALVANISM. On excitation produced by the union of metals and fluids. Observes, that charcoal has a power like that of the me- tals; and that silver acquires the power of exciting by- touching moisture. E.xperiinents and observations on galvanism, b\' Nicholson, Cruickshank, Carlisle, Davy, and others. Nich. I. . V. Halle's report on galvanism. 13. Soc. Phil, n. 17. Journ. Phys. XLVII. (IV.) 302. Report on galvanism. Ph. M. I. 319. Vassalli Eandi on galvanism. Journ. Phys^ XLVIII. 336. Ph. M. VIH. 171. XV. 38, 310. Nich. 8. V. lOQ. Vassalli Eandi on animal electricity. Journ. Phys L. 148. Remarks on galvanism and chemical electri- city by *Ritter, Bockmann, Pfaff, Hebe- brand, Treviranus, Erman, Huet, Simon, Reinhold, Gerboin, Jager, and others. Giib.H. vn. Ritter's galvanic experiments. B. Soc. Phil. n. .53, 76, 79- Ann. Ch. XLI. 208, *Ritter on galvanism. Glib. VIH. 386. IX. 1. Positive electricity gives oxygen, negative hydrogen. Ritter on the denomination of galvanic poles. Gilb. IX. 212. . Calls the oxygen, or positive side, the true zinc side. Ritter's experiments with a battery of 600 pieces. Glib. XIII. 1, 265. Ritter's galvanic experiments and remar"ks. Gilb. XVI. 293. Places conductors in this order of excitation. Some amalgams of zinc and mercury, zinc, lead, tin, iron, bis- muth, cobalt, arsenic, copper, antimony, platina, gold, mercury, silver, coal, plumbago, tin crystals, nickel, pyritical substances, palladium, graphite, crystals of man- ganese. Some experiments on the sensible effects of gal- vanism. Hitter's passive battery. Journ. Phys. LVII. 345. Nich. VIII. 176, 184. ' Ritter on galvanic phenomena. Nich. VI. 223, VII. 288. Nicholson, Carlisle, Cruickshank, and others, on galvanic electricity. Ph. M. VII. 337, 347. Cruickshank on galvanic electricity. Journ. Phys. LI. 164. On Perkinism. Journ. Phys. XLIX. 232. Perkins's patent for a mode of curing dis- eases. Repert. ii. 11. 179. One of the tractors is made of copper, zinc, and gold ; the other of iron, silver, and platina. Hemmer on animal electricity. Ph. M. V. 1. Davy on galvanic comlHiiations. Ph. tr. ISO 1.397. Ph. M. XI. 202. *Davy's outlines of a view of galvanism. Jomn. R. I., I. 49. Ph. M. XI. 326. Dcivy'* charcoal battery. Journ. R. I., I. Niclr. 8. 1. 144. Davy's galvtMuc experiments. Inst. Nat. B, Soc. Phil. n. 62. Davy's galvanic experiments. Nich. 8. Ilf. 135. Wollaston on tlie chemical production and agency of electricity. Ph. tr. 1801. 427. Gilb. XI. 104. E.xperiments made at the Ecole de medecine, B. Soc. Phil. n. 45. Galvanic experiments. B. Soc. Phil. n. 50. Robertson's galvanic experiments. Ann. Ch. XXXVII. 132. Dcsormes's galvanic experiments. Ann. Ch. XXXVn. 284. Desormes and Hachette on the principles of galvanism. Ann. Ch. XLIV. 267. Hachette on galvanism. Journ. Polyt. IV. xi. 284. Von Arnim. Gilb. V. 465. Observes, that electricity is only develbped by oxidatioa when no light is produced. Cuvier's report on galvanism. Journ. Phys.. LII.318. CATALOGUE. — ELECTRICITY, GALVANISM. 4v9 Report on galvanism. Ph. M. X. 87, 93. Biot and Cuvier's galvanic experiments. B. Soc. Phil. n. 53. Ann. Ch. XXX[X. 242. Biot on the motions of the galvanic fluid. B. Soc. phil. n. .^4. Journ. Phys. LIII. 264- Gilb. X. 24. Notes of Biot's experiments. Ph. M. XI. 272, 283. Biot's reports to the National Institute on Volta's experiments. M. Inst. V. 195. Journ. R. r., I. Ph. M. XI. 301. Gilb. X. 389. Biot on the effect of oxidation on the pile. B. Soc. Ph. n. 76. Gilb. XV. 90. Makes the effect little or nothing ; but the arguments are inconclusive. Galvanic experiments by Volta, Nicholson, Carlisle, Grimm, Ritier, Hermbstadt, He- bebrand, Pfaff, Bourguet, Davy, Ileid- mann, Reinhold, Ciirtet, Bouvier, Erman> Aldini, Pepys, Buntzen, Brugnatelli, and others. Gilb. VIL.XVII. Galvanic apparatus, by PfafF, Simon, Hauff, Davy, and others. Gilb. VII. VIII. XI. XII. XV. Remarks on Volta's galvanic pile, by Gilbert Griiner, Pfaff, Von Arnim. J'ager, Ernian, Desormcs, Priestley, Biot, Cuvier, Rein- hold, and others. Gilb. VII. .XV. Van Marum and Pfaff's comparison of Vol-, ta's pile with the Teylerian machine. Nich. 8. I. 154, 173. Ph. M. XII. iGl. Van Marum charged a battery of jars with a pile; its shock was only half as intense as that of the pile. Van Marum on Pfaff's galvanic experiments. Ann. Ch. XL. 289. Van Marum on Ritter's experiments. Nicli. VIII. 212. Frie&tley on Volta's pile. Ace. Nich. 8. I. 198. Sue Histoire du galvanisme. 2 v. 8. Par. 1802. R. I. Nauche Journal de galvanisme. Paris. Lehot on galvanism. Ann. Ch. XXXVIII* 42. Gilb. IX. 188. Friedlander on some galvanic experiments. Journ. Phys. Lll. 101. Friedlander on the pile. Ph. M. IX. 221. On medical galvanism. Journ. Phys. LII. 391, 467. *Fonrcroy's galvanic experiments. Ann. Ch. XXXIX. 103. Gautherot on galvanism. Ann. Ch. XXXIXj 203. Gautherot on galvanism. Extr. Journ. Phys. LVI. 429. Adopts the chemical theory. Moyes on the pile. Ph. M. IX. 217- Cuthbertson on Volta's fundamental galva- nic experiments. Nich. 8. II. 281. ' Cuthbertson's distinction between galvanism' and electricity. Ph. M. XVII1.358. Nich. Vni. 97. Thinks that the length of wire, ignited by galvanism, is simply as the charges ; by electricity, as the square of the charge. Cuthbertson's galvanic experiments. Nich" VIII. 205. Gerboin's galvanic experiments. Ann. Ch. XLI. 197. Pepys on the galvanometer. Ph. M. X. 38. The zinc end of the pile, commonly so called, is positive. Pepys's galvanic apparatus. Ph. M. XI. 94. XV. 94. Pictet on some experiments of Volta. Ph. M. XI. 149. Gilb. VIII. 166. Gilbert observes, that a simple chain is formcd.by zinc, a liquid, and silver ; the addition of dry metals makes no difference in its nature, so that if silver and zinc be added beyond the zinc and silver, the silver end will be the true zinc pole of the chain, which is negative, and the zinc end', or the silver pole positive, giving oxygen, while the sUve' end or zinc pole gives hydrogen gas. Liidicke on a cheap battery. Gilb. IX. 1 ig., Tourdes on the galvanic irritation of the 430 CATALOGUE. — ELECTRICAL APPARATUS. fibrine of the blood. B. Soc. IJliil. n. 71. Gilb. X. 499. Bostook on galvanism. Nicli. 8. 11. 296. III. 3. Gilb. XII. 476. Note of Bonaparte's galvanic prize. Ph. M. XIII. ]88. Gilb. XI. 492. Erman's theory of the pile. Gilb. XI. 89. Journ. Phys. LIII. 121. Erman supposes, that two heterogeneous metals in con- tact become electrical piincipally by induction ; that the silver is positive where it touches the zinc, and negative on the other side ; the zinc the reverse ; that more alternations of dry metals have no further effect ; but that a communica- tion with a different conducting substance, on each side, favours the effect of induction ; that moist conductors in- terposed, divide themselves by induction into different states of electricity ; that the middle of a pile is the neutral point ; and that a communication produces a discharge like that of a charged jar. Sprenger on galvanism in deafness. Gilb. XI. 334, 488. Einhof on galvanising the deaf and dumb. Gilb. XII. 230. Parrot's galvanic tlieory. Gilb. XII. 49. From a combination of induction and chemical action. Medical galvanism. Gilb. XII. 450. Galvanic experiments. Journ. Phys. LIV.. .LVII. Lagrave's galvanic experiments. Journ. Phys. LVI. 361. Nich. 8. V. 62. Compares the transmission of the galvanic fluid through water to the propagation of sound. Wilson on the galvanic effect of minute par- ticles of zinc and copper. Nich. 8. III. 147. AlizeiTii's pile. Nat. Inst. Ace. Journ, Phys. LVn. 74. JVilkhisori's elements of galvanism. 2 v. 8. 1804. R, I. Wilkinson on burning wire by galvanism. Nich. VII. 206. Wilkinson on galvanism. Nich. VIII. 1^ 70. IX. 175, 240. Haliy Traite de physique. II. 1 . On galvanic apparatus. Nich. VII. 269. VIII. 79. Experiments by Dyckhoff and others. Nich. VII. 303, 305. Dyckhoff asserts, that the strata of a pile may be separated by bits of glass with air intervening ; thi» Wilkinson denies. Nich. VIII. I. Rossi's experiments. Ph. M. XVIII. 131. Pownall on the theory of galvanism and the Newtonian ether. Ph. M. XVIII. 155. On the theory of galvanism. Ph. M. XVIII. 170. Galvanic experiments. Nich. VIII. 84. On galvanism. Nich. VIII. I71. 'Ihicknesse on galvanism. Nich. IX. 120. Sylvester on the galvanic power. Nich. IX. 179. Harrison and Gough. Nich. IX. 241. Make the igniting power of plates as the sixth power of their diameter, from Wilkinson's experiments. - Electrical apparatus in general. Leupold Th. Aerostat, t. 9. E. M, PI. VIII, Amusemens de physique. Bohaeitbergers Electrisirmachinen. Stuttg. 17H4..I791. Giitk Instrumenten kabinet. 1790. Kunze Schauplatz der gemeinniitzigen mas- chinen. II. Weber Electrische versuche. Galvanic apparatus. See Chemical Electri- city. For a cement take 7 parts lac, 4 resin, 2 amber, and 4 Venice turpentine, 12 lac, 16 resin, I amber, 3 Venice turpentine, 24 pitch. Kunze. Sealing wax may be employed for varnishing glass, either by heating the glass, or by dissolving the wax in spirits : but amber varnish is better. Cavallo. Such a varnish makes the insulating power of the glass oioxe perfect. See Machines. CATALOGUE. ELECTRICAL APPARATUS. 431 Excitation. Electrical Machines for applying Friction. Hawksbee on a globe lined with sealing wax. Ph. tr. 1708. XXVI. 219. Winkler Beschreibung einer electrisirma- schine. 1"44. Faure Coiigeuure intorno alia machina elet- trica. 4. Rome, 1747. Plate machines used by Planta, 1760. Epinasse on electrical machines. Ph.tr. 1767. 186. Lines the cylinder with a resin. Leroy on an electrical machine for produc- ing both species of electricity. A. P. 1772. i. 499. H. 9. Leroy's electrical pump. A. P. 1783. 6l5. Nooth on the cushion and flap. Ph.tr. 1773. 333. Schmidt Beschreibung einer electrisirma- schine. 1778. Larigenbiicfier Beschreibung einer clectri- sirmaschme. 1778. Ingenhousz on the plate machine. Ph. tr. 1769. 659. Varnished pasteboard succeeded well in dry rooms. Brilhac on an electrical plate machine. R02 XV. 377. Bertholon's electrical machine. Roz. XVI. 74. An electrical machine, moved by clock- work. Roz. XIX. 149, Goth. Mag. I. i. 83. Kohlreif on the cushion. Goth. Mao-. I. iii. 101. Ron/and description des machines a taffetas. 8. Amst. 1785. Van Marum Description d'une tr^-s grande machine electrique. 4. Haarl. 178j. R. S. Roz. XXVII. 148. Fan Marum Lettre sur un,e machine elec- trique. 4. R. S. Van Marum Continuation d'experiences. 4. Haarl. 1787. R. S. Van Marum description des fiottoirs elec- triques. 4. Haarl. 1789. R. S. Roz. XXXIV. 274. On a mode of applying the silk, before praciiscd in Ens- land. ^ Van Marum on the Teylerian machine. Roz XXXVIII. 109. Van Marnm's new and simple plate machine. Roz. XXXVIII. 447. Imitating Nicholson's improvements. Van Manim on the electrical machine. Roz. XL. 270. Van MarumSeconde continuation. 4. Haarl 1795. R. S. Van Marum and Pfaff's comparison of Vol- ta's pile with the Teyleiian machine. Ph M. XII. 161. Prieur's extract on the Teylerian machine Ann. Ch. XXV. 312. Tries's claim to Van Marum's machine. Roz. XL. 1 16. Leroy's electrical machine. Roz. XXIX. 129. Nairne on his patent electrical machine. 8. Lond. 1787. R. S. Repert. VH. 380. SeiferhMs electrisirmaschine. Nuremb. 1767. Cavallo's remarks on the rubber and flap. Ph. tr. 1788. i. Attributes the effect to a compensation. Saint Julien's electrical plate machine. Roz. XXXIII. 367. Fig. ♦Nicholson's experiments and observations in electricity. Ph. tr. 1789. 26o. Nicb. I. 83. The hand was the first rubber, then the simple cushion was applisd, and a flap was added to it, then the rubber 432 CATALOGUE. — ELECTRICAL APPARATUS. was moistened ; next the amalgani was applied, and lastly Nooth invented the silk flap. The surface of a plate imme- diately opposite to the cushion attracts the electric fluid ; nothing therefore is gained by applying a cushion to it. A piece of metal projecting forwards over the edge of the cushion of a cylinder, considerably increased the intensity ofaction, probably by increasing the capacity of the glass in.its neighbourhood. If a piece of silk be applied closely to the cylinder, it will attract the electricity on one side, and emit it on the other, according to the direction in which the cylinder is turned : but such an arrangement is not prac- tically advantageous. If a cylinder be well greased, so as to become opaque, and the silk flap be made semitranspa- rent with the grease, the amalgam be then applied with leather to the cylinder, and pressed against it as long as the friction continues to increase, the action of the machine will be very powerful. When a nine inch cylinder had been tl-.us treated, the conductor gave flashes to the table on which it stood, at the distance of 1 4 inches. A square foot of a jar was fully charged by the friction of 1 8 or 1 9 feet of the cylinder : the machine at Haarlem required at first the friction of 00.6 feet, and with a single cushion would have required half as much. This cylinder was equal in effect to the great Teylerian machine, whifh was thirty times as ex- pensive -, but afterwards Van Marum tripled the effect of the Tevlcriao raachiae. Ctithbertson iiber die veisuche von Dei- man n und Troostwyck. Pearson's portable electrical machine. Nich, I. 50G. An electrical macbine of silk. Nich. II. 4eO. Fell's pocket ribbon machine. Nich. HI. 4. Cirinini on a large electrical machine. Gilb. IV. 3.39. Wolff's electrical machine. Nich. VII. 124. With improved rubbers. Galvanic batteries. See Chemical Electricity, Gcuan applied liquid mercury as a rubber. Ingenhousz's portable machine is a varnished ribband, hung on a fixed pin or nail, and rubbed with a cat's skin : the little jar which is charged is held near the rubber, and collects negative electricity from the ribband Lichtenbcrg's drum machine is of wood, covered with black woollen cloth. Gutle's electrical machine o f woollen is said to be cheap and powerful. The best cement for a cylinder consists of 5 parts of resin, 4 of bees wax, and a of powdered red ochre. The silken flap is made of black mode. Cavallo. Amalgams. Woulfe on the aurum mosaicum. Ph. tr- 1771. 114. It was made of mercury, tin, sulfur, and muriate of am- monia. Higgins's amalgam. Ph. tr. 1778. 861. Four parts of mercury with one of zinc. Kieniueyer's amalgam. Rozier XXXHI. 96- Two parts of mercury, one of zinc, and o.ie of tin. Neret's amalgam consists of equal parts of tin and mer-. cury : Cuthbertson uses mercury with tin filings and a little oil. The amalgam of tin is made with two parts of mercury and one of tinfoil, adding a little powdered chalk. Cavallo. For the amalgam of zinc, melt one part of zinc, and shake it in a wooden box with 4 or 5 parts of mercury, heated above the temperature of boiling water : then triturate it with a little tallow and a very little powdered wniting; and add one fourth of the amalgam of tin. Cavallo. Elect rophorus. -Wilke. Schw. Abh. 1762. XXXIX, 54, II6, 200. Beccaria Electricitas vindex. Gr'az. Volta. Scelta di opusc. Milan. X. 37. Roz. Vlll. 21.Sept. 1776. Ph. tr. 1782. llozier, 1783. Brugnatelli bibl. fis. Volta on the passage of electricity through imperfect conductors. Soc. Ital. V. 551. Henley. Ph. tr. 1776. 513. Achard A. Berl. 1776. 122- Achard. Schr. 226. Cavallo. Ph. tr. 1777. II6, 388. On the electrophorus. A. Petr. I. i. H. 70. Kiafft's theory of the electrophorus. A. Petr> 1. i. 154. Ingenhousz Elements of electricity, liigonhousz. l"h. tr. 1778. 1027. Socin Anfangsgrlinde. iian. 1778. 1792- Picket Expenmenta physicomedica. 8. Wuiizb. 1778. CATALOGUE. — ELECTRICAL APPARATUS. 433 Klindwoith. Goth. Mag. I. ii. S5. Obert. Goth. Mag. V. iii. 96. -Minkeler. Goth. Mag. V. iii. 110. •f-Sch'dffer AbbWduog des electricit'atstiagers. 4. Ratisb. 1776. K. S. iS'cAa^erkr'attedeselectiophors.4. Rat. 1776. Schuffers f'ernere versuche. Ratisb. 1777- Adanison electricity. 8. London, 1784. 181. Robert on the electrophorus. Roz. XXXVII. 183. Nich. I. 355. The barrier, which the surface of the electrophorus pre- sents, seems to be analogous to the operation of the galva- nic battery. "Nicholson's revolving doubter is somewhat similar in its operation to the electrophorus. See Microelectrometer. Conductors. Volta on a shock from a conductor. Roz, XIII. 249. Sulla capacity dei conduttori elettrici. 4* R.S. Nicholson. Ph. tr. 1789. Never uses points for a conductor, but a ball brought near to the cylinder, or the cushion without a rubber. Coated Jars and Batteries. See Charge. Kleist discovered the effect of charged glast in 1745. [Needham on some experiments made at Pa- ris. Ph. tr. 1746. XLiV. 247. Lcmonnier discovered the permanency of the charge- NoUet gave a shock to 180 guards at once. Dutoiir on charged talc. A. P. 1753. H. 76. Wilson's experiments. Ph. tr. 1778. 995. Found that a point was struck at the greatest distance. On the advantage of paper under the coatj- ins;. Brooks, c. iii. Says, that it prevents the jats breaking. Van Mai urn's battery. Gilb. i. 68. Halriaiie on the force of a battery. Nich. I. 156. Giib. m. 22. VOL. II. Cuthbertson's improvement on batteries* INich. 11.525. Gilb. III. 1. A battery of talc. Nich. 8. V. 2l6. Robison says, that a globe is the best form for a jar. Partisil damp is said to make a battery capable of a great intensity of charge. Electrical Measures in general. Achard on the force of electricity. Berl. Naturf. fr. I. 53. Robison. Enc. Br. Suppl. Art. Electrometer. Measures of Tension. Simple Electrometers, Darcy's electrometer. A. P. 1749. 63. H. 7. Richmann's electrometer. N. C. Petr. IV. 301. Hd^ley's quadrant electrometer. Ph. tr. 177i. 359. Comus's electric platometer. Roz. VII. 520. Cavallo's electrometers. Ph. tr. 1777. 388. 1780. 15. For the pocket, and for atmospherical observations, Brooks's electrometer. Ph.tr. 1782.384. An electrical balance. Terry's electrometer. Roz. XXIV. 315. An electrometer. Roz. XXV. 228. *Coulomb's electrical balance. A. P. 1785. 569. Employs the torsion of a wire. Saussure's electrometer. Voyage. IFI. Ixxviii. Boyer Brun's electroscope for a conductor, Roz. XXVllI. 183, Deluc's fundamental electrometer. Idees. I, cccxcvii. Gren. I. iii. 380. Rennet's electrometer. Ph.tr. 1787.26. Nich. II. 438. Of gold leaf. Chappc's electrometer. Roz. XXXIV. 370. Vassalli's elcctrometrical experiments. M. Tur. 1790. V. 57. Improved electrometer. Nich. I. 270. . 3K 434 CATALOGUE.— EX-ECTRlCAt APPARATUS. Cadet's electrometer. Ann. Ch. XXXVII. 68, Nich. V.31. Marechaiix's delicate electrometer. Gilb. XV. 98. Microelectrometers. Condensers, Multipliers, and Galvanometers. Volta on rendering sensible small degrees of electricity. Th. tr. 1782. 237- Volta on the advantage of an imperfect in- sulation. Roz. XXII. 325. XXIII. 381. Soc. Ital. V. Bennet's electrometer with a condenser. Ph- tr. 1787. 32. A plate of marble on the electrometer, and on this a imall plate of metal. Bennet's doubler of electricity. Ph. tr. 1787. 288. Merely varnished plates laid on each other. Liable to the inconvenience of contracting a permanent charge. Dumotiez's condenser. Roz. XXXI. 431. Cavallo on measuring small quantities of electricity. Ph. tr. 1788. 1. Found many accidental errors from permanent charges, even when the plates of the instruments had been untouched for a month. To illustrate this, he made experiments on the decreasing progression of the vslocity with which the Huid escapes. Cavallo's multiplier. Nich I. 394. Cavallo's collector. Ph. tr. 1788. 255. Roz. XXXIV. 258. Consisting of a fixed plate between two moveable ones. Nicholson's revolving doubler. Ph. tr. 1788. 403. Nich. II. 370. IV. 95. Some thin plates at the distance of -^ of an inch from each other had their capacity augmented lOO times. This instrument was intended for producing electricity from the charge which is almost inseparable from the plates, and usually gave a spark when turned lO or 20 times. It pumps out positive or negative electricity from a ball into two fixed plate s,by means of a revolving plate; the redundant electricity contained in either of the fixed jlates is attracted to one of them by the revolving plate, con- nected with the ball; all the communications are then de- stroyed, and the revolving plate, with a charge equal and opposite to that of the first fixed plate, is brought opposite to the second, while this is connected with the ball, and acquires from the ball a charge nearly equal to that of the first plate : so that the redundant electricity of each of the fixed plates is now nearly equal to what they both contained at first, and the charge is nearly doubled by each turn. On the doubler of electricity. Journ. Phys. XLV. (II.) 463. A Microelectrometer. Nich. I. l6. Read on the invention of the doubler. Nich. II. 495. Cuthberlson on Read's condenser. Nich. Gilb. XIII. 208. Pepys's galvanometer. Ph. M. X. 38. Of gold leaf. Gilbert and Bohnenberger on microelectro- meters. Gilb. IX. 121,158. Weber's glass condenser. Gilb. XI. 344. Indicated the electricity of ice on the Danube. Hacliette and Desormes's improved doubler. B.Soc. Phil. n. 83. Gilb. XVII. 414. Marechaux's electromicrometer. Gilb. XV. 98. XVI. 115. With a screw and silver leaf. Wilson's condenserand doubler. Nich. IX. 19. Regulators and Dischargers. Lane's electrometer. Ph. tr. 1767. 451. Cuthbertson's measurement by explosion. Nich. II. 215. Lawson's discharging electrometer. Ph. M. XI. 251. Von Hauch's discharging electrometer. Ph. M. XI. 267. Gilb. XIV. 257. Volta says, that Lane's electrometer agrees with Henley's in all its indications. Distim'uhhers. Chappe on a mode of distinguishing electri- city. Roz. XXXIV. 62. Nicholson on instruments for the distinctioD of electricity. Nich. 8. HI. 121. CATALOGUE. — SPONTANEOUS ELECTRICITY. 435 One from a projecting point which gives sparks at diffcr- ont distances, according to the kind of «i«etricity : the •ther from the decomposition of water. Cuthbertson on the distinction of electricities. Nich. 8. III. 188. Ph. M. XIX. 83. From the heat of a candle communicated to the negative bail. Spontaneous Electricity. Of Inanimate Substances. Atmospheric Electricity. See Meteorology. Mineral Eltctriciltf. Tourmalin and other Crystals. Due de la Noya Caraffa surla tourmaline. 4. Par. 1759. M. B. Wilson. Ph. tr. 1759. 302. 1763. 436. On some similar gems. Ph. tr. 1762. 443. fWatson on the lyncurium. Ph. tr. 1 759. 394. Aepimis Recueil de memoires sur la tourma- line. 8. Petersb. 1762. Aepinus on the Brasilian emerald. N. C. Petr. XII. 351. Bergmann. Ph. tr. 1766. 236. Schvv. Abh. XXIII. 286. Finds, that one pole of the tourmalin becomes positive by expansion, and negative by contraction, the other the reverse. Bergmann on the electricity of Iceland crys- tal. Opusc. V. 36G. On the tourmalin. 401. Wilke. Schw. AbH. XXVIII. 95. XXX. 1, 105. Franklin. A. P. 1773. H.78. Miiller an Born. 4. Vienna, 1773. Zallinger vom turmalin. 8. Vienna, 1779. Gerhard. Roz. XXI. Suppl. 1782. Ddaunay Lettre sur la tourmaline. 4. R, S. Werner in Cronstedt's mineralogy. Hauy. A. P. 1785. 206. On the tourmaline and on electricity as a test. Haliy on the boracite. Ann. Ch. IX. 59. Roz XXXVIII. 323. Gren. VII. 87. Haliy on the electricity of some crystals. M. Inst. I. 49. Haiiy Traite de physique. I. Haiiy has observed, that electrical crj'stals are notsj'mme- trically formed at the corresponding angles : thus in the bo- rate of magnesia the 4 intire angles became negative, and the 4 truncated angles positive. Beckmann. Erfind. 2 ed. I. 248. Napione sul lincurio. 4. Rom. 1795. R. S. Ritter on electrical polarity. Giib. XV. 106. On terrestrial electricity. Gilb. XVll. 482. Animal Electricity. See Chemical Electricit}'. On electric fishes. Roz. Intr. II. 432. Oseretskovsky on a preternatural electricity.. A. Petr. III. i. 2.33. The person was Michael Puschfcin of Tobolsk ; the rela- tor was not an eye witness. Lovens on electricity as a living force. 1779. Geoffrey on the anatomy of electric fishes. B. Soc. Phil.n. 70. Journ. Phys. LVI.242. Ph. M. XV. 126. Gilb. XIV. 397. Haiiy on electric animals. Traite de'Phys. 4 1 . Raia Torpedo. Authors on the torpedo. Krlinitz. Abhandl. xvii. Reaumur. A. P. 1714. 344. H. 19. TewpZeOTflM in Nouvelliste. 1759. Schilling de morbo yaws. Utr. 1770. Walsh. Ph.tr. 1773. 461. 1775.46.5. Hunter. Ph. tr. 1773. 481. Pringle's discourse on the torpedo. 4. Lond. 1775. 't-Ingenhousz. Ph. tr. 1775. 1. *Gavendish. Ph. tr. 1776. 196. The shock of the torpedo resembles that of a lar^-e battery weakly charged; such a shock will pass but a little way through the air. An artificial torpedo was made so as 435 CATALOGUE. -MAGNETISJI. to imitate all the effects of the natural one. One hand re- ceived alinost as great a shock from it as could be obtained by both hands. Roz. IV. 205. Ac. Brux. III. H.5. Spallanzani. Goth. Mag. V. i. 41. Girardi and Walter on the torpedo. Soc. Ital. in. 553. Biyant on the torpedo. Am. tr. If. 166. VassalU Eandi on the torpedo. Journ. Phys. XLIX, 69. Nich. I. 355. Gyninotus Electricus. Richer. A. P. I. Il6. VII. i. part 2. 92. Duhamel Hist. Ac. Sc. l68. Berkel Reise nach Rio de Berbice. 1680. 1689. Allamand. Haarl. Verb. II. 372. Gronovius. Act. Helv. IV. 26. Basle, 1760. Mussch^nbr. A. P. 1760. H.21. SchilUng. A. Berl. 1770. 68. *Williams. Ph. tr. 1775. 94. Garden. Ph. tr. 1775. 105. *Hunter. Ph.tr. 1775. 395. Anatomical. Ingenhousz. Phys. scbr. I. 273. Flagg. Am. tr. II. 170. Bryant and Collins. Amer. trans. II. Goth. Mag. V. ii. 171. Block Fische. 4. Berl. 1786. II. Fahlberg. Gilb. XIV. 4i6. Silurus Electricus. Broussonet. A. P. 1782. 692. Roz. XXVII. 139. After Adanson and Forskal. Trichiinus Indicus; * Gmel. Linn. 1.1142. 'Nieuhoff. It. ind. II. 270. Jiaii syn. pise. Anguilia marina. Wilhtgkbj/. Ichth. aj)p. t. 3. f. 3. Tetrodon, as supposed. Paterson. Ph. ir. 1786. 382. MAGNETISM IN GENERAL. *Gilbertus de magnete. f. Lond. l600. M. B. Cabaei philosophia magnetica. f. Ferrar. 1629. M. B. Kirchtri magnes. 4. Cologne, 1643. M. B. Nortnan's new attractive. M. B. Ph. tr. abr. II. iv. 601. IV. 2 p. iv. 286. VI. 2 p. iv. 253. VIII. 2 p. iv. 740. X.2 p.iv.678. Lister on magnetism. Birch, iv. 26l. Derham's magnetical experiments and ob- servations. Ph. tr. 1704. XXIV. 2036. Some experiments on dividing magnets. Eberhai-ds uiagnetische theorie. 4. Leipz. 1720. Dufay on the magnet. A. P. 1728. 355. 1730. 142. 1731.417. Mu.sschenbroek de magnete. Diss. Phys. ] . *Serviugton Savery's magnetic observations. Ph.tr. 1730. 295. Pieces sur I'aiman. 4. Par. 1748. A. P. Prix. V. , , D. and J . Bernoulli. A. P. Pr. V. xii. Euleri nova theoria magnetis. Opusc. in. Schwigkardi ars magnetica. Penrose on magnetism. 4. Lond. 1753. Description des couraas magnetiques. 4. Strasb. 1753. Germ. Hamb. Mag. XII. i. 579. *Aepini tentainen theoriae. 4. Aepinus. N. C. Pet'r. IX. 340. Scarella de magnete. 2 v. 4. Brescia, 1759. Cooper's experimental magnetism. 8. 1761. Lalande on the magnet. A. P. 1761. Rinman Geschichte des eisens, von Georgi.iii. Wilke Tal om magneten. 8. Stock. 1764. CATALOGUE. THEORY OF MAGNETISM. 437 Wilke uber der magneten. Germ, by G ro- iling. 8. Leips. 1794. Brugman de materia magnetica. 4. Franeq. 1765. R. S. Germ.by Eschenbach. 8. Leips. 1784. JBrugmunni magnetismus. 4. Leyd. 1778. Lovett on electricity and magnetism. 8. 1766. R.I. *Lambert on magnetism. A. Berl. 1766. 22, 49. Lemonnier Loix du magnetisme. 2 v. 8. Par. 1776. Ace. A. P. 1776. H. 51. Lacam's thoughts on magnetism. 8. R. S. Fraiik/in in Sigaud de la Fond Precis expe- rimental. Franklin on magnetism. Am. tr. III.. 10. Van Swindell Tentamen de phaenomenis magneticis, specimen 1. 4. R. S. Gai/er Theoria magnetis. 8. Ingolst. 1781. Rittenhouse on magnetism. Amer. tr. j^rfa/HS on magnetism. 8. Loud. 1784. Cavallo on magnetism. 8. Lond. 1787. 1800. R. L Cotte's magnetical observation. Roz. XXX. 349. Feart on electricity and magnetism. 8. Gainsbor. 1791. R. S. Dalton's meteor, obs. 61. Walktr on magnetism. 8. Lond. 1-794. R.S. Larimer on magnetism. 4. 17957 R. L Kirwan on magnetism, h. tr. VL 177. Giib. VL391. Magnetical observations. Gilb. IIL 43. VL 170. Ritteron magnetic attraction. Gilb. IV. I. Madison on m;ignetisni. Hepert. XV. 329- HuiiyTraite de Physique. II. 58. Theory of Magmthm. Hausksbee on the law of magnetic attiaction. Ph. tr. 1712. XXVIl. 506. Taylor. Ph. tr. 1714. XXIX. n. 344. Musschenbroek de viribus magneticis. Ph. tr. 1725. XXXIII. 370. Failed in the attempt to discover the law. Knight's experiments. Ph.tr. 1747. XLIV. 656. In favour of magnetic currents. Euleri nova theoria magnetis. Opusc. 4. Berl. 1750. III. Euler supposes, that the direction of the currents is regu- lated by a kind of valves. jiepinus de similitudine vis electricae etmag- neticae. 4. Petersb. 1758. N. C. Petr. X. 296. *Aepinus Tentamen theoriae electricitatis et magnetismi. Aepinus's further comparison of magnetism and electricity. N. C. Petr. X. 296. Aepinus on Mayer's theory of magnetism, N. C. Petr. XII. 325. Cigna on the analogy between electricity and magnetism. Misc. Taur. I. Brti^mann de materia magnetica. Kraftt on the force of magnetism. C. Petr. XII. 276. Gabler theoria magnetis. Donndorir Uber electiit ilat. Van Swiitden llei;ueil de memoires sur I'ana- logie de I'electricite et du magnetisme. 3 v. 8. Hague, 1784. *Coulomb on the law of the magnetic and electric forces. A. P. 1785. Finds, that they vary as the squares of the distances in- versely. A needle is urged by a constant force in the direc- tion of the quiescent position. Coulomb's seventh memoir. A. P. 1789. 455. Roz. XLIII. 247. Particular consideration of the separation of a magnet. Coulomb on the ft)rces of needles. M. Inst. III. 176. Ph.M.XI. 18.3. When the form is similar, the force is as the weight. Coulomb supposes the existence of two magnetic fluids, which are only displaced in each molecule. 438 CATALOGUE. — MAGNETIC SUBSTAKCES.. Abridgment of Coulomb's theory. Journ. Phys. XLV. (II.)448. Silberschlag. A. Berl. 1786. Deduces magnetic attraction from currents. Rittenhouse, Am. tr. II. 178. HauyTheoriede I'etectricite at du magnet- isme. Prevost de I'origine des forces magnetiques. 8. Genev. 1788. Viallon's theory of magnetism. Roz. XLIII. 208. On supposed magnetic currents. Nich. 8. 1. 234. Arnim on the theory of magnetism. Gilb. III. 48. VIII. 84. The magnetic arrangement of filings may be imitated by strewing powder on a coated plate of glass placed on two electric balls. Robison. Magnetic Substances. Pa"-et and Hooke on the effect of heat on the magnet. Birch. IV. 256, 264. Musschenbroekonthe Indian magnetic sand. Ph.tr. 1734. XXXVllI. 297. Galeationthe iron found in different bodies. C. Bon. II. ii. Arderon on giving pohirity to brass. Ph. tr. 1758. 774. Lehmann on the magnetism of copper and brass. N. C. Petr. XII. 368. On the universality of magnetism. TBrug- mann by Eschenbach. Leipz. 1781. Coulomb. A. P. 1784.266. Found that wire, when twisted, received 9 tijnes as much ■magnetic force. Coulomb on universal magnetism. B. Soc. Phil. n. 61, 63. Journ. Phys. LIV. 240, 267, 454. Journ.R. I., I. Ph. M.XII. 278. XIII. 401. Gilb. XI. 254, 367. XII. 194, A metal is affected if it conuins only y^^ part of iron. Kohl on pure cobalt. Crell. N. E. VII. sg. Cavallo on the magnetism of various sub- stances. Ph. tr. 1786. 62. Finds, that a smaller quantity of iron will affect the needle than can be detected by any chemical test. Some pieces of nickel were not magnetic, but they were found to contain cobalt. Some brass, but not all, becomes magnetic by ham- mering, and loses its power by heat ; and this effect could not be produced by an artificial mixture of iron with brass. Cavallo's experiments. Ph.tr. 1787.6. Almost all substances attracted needles floating on a very clean surface of quicksilver. The brass which was least mag- netic was not rendered magnetic by hammering. Iron while dissolving in an acid, disturbed the needle 1°. Red hot iron is not attracted. This Gilbert had before observed. Brisson. A. P. 1788. l6l. Cast steel is unfit for magnetic use ; English and German steel best. Bennet. Ph.tr. 1792-81. Thinks that Cavallo's experiments on solution and on hammering may be explained from the production of pola- rity in the substances. But is difficult to conceive, that po- larity in this sense can increase the attraction. Landriani in Mayers sammlung. 8. Dresd. 1793. III. 388. Humboldt on a magnetic serpentine. Ann. Ch. XXII. 51. Journ. Phys. XLV. (II.) 314. Von Arnim on magnetic substances, Gilb. V, 384, With a catalogue, Yourtg on Coulomb's experiments. Journ. R. I., I. Carradori on Coulomb's universal magnel- isni. Journ. Phys. LV. 450. Sage on the magnetism of nickel. Ph. M. XIII. 58. Thenard on nickel. B. Soc. Phil. n. 68. Chenevix on the magnetism of nickel. Nich. 8. III. 286. Gilb. XI. 370. Hatcheit on magnetical pyrites. Ph.tr. 1804. 315. The smallest mixture of antimony destroys the polarity of iron. M. Young. CATALOGUE. — MAGNETICAL EXPERIMENTS. 439 From the Journals of the Royal Inslilulion. I. 134. Extract from the Decade Philosophique, No. 21. National Institute. Experiments showing that all bo- dies are subject to the magnetic influence, even in a degree which is capable of being measured. These experiments were made by Mr. Coulomb, and re- peated by him before the Institute. He employed all the substances that he examined in the form of a cylinder, or a small bar J he suspended them by a thread of silk in its na- tural state, and placed them between the opposite poles of two magnets of steel. Such a thread can scarcely support more than two or three drachms without breaking ; it was therefore ruicessary to reduce these needles to very small di- mensions. IVIr. Coulomb made them about a third of an inch in length, and about a'thirtieth of an inch in thick- ness ; and those of metal only one third as thick. In making the experiments, he placed the magnets in the same right line. Their opposite poles were separated about a quarter of an inch more than the length of the needle which was to oscillate between them. The result was, that of whatever substance the needles were formed, they always ranged themselves accurately in the direction of the magnets ; and if they were deflected from this direction, they returned to it with oscillations, which were often as frequent as thirty or more in a minute. Hence, the weight and figure of the needles being given, it was easy to deter- mine the force that produced these oscillations. The experiments were made in succession with small plates of gold, silver, copper, lead, and titi; with little cylinders of glass, with a bit of chalk, a fragment of bone, and different kinds of wood. In the course of his lecture on magnetism on the 3oth of April, Dr. Young repeated some of these experiments with wires of different kinds : one of them was of tin, and sus- pended within a cylindrical glass jar by a single silk worm's thread : its oscillations were so slow as to occupy several minutes, and it was scarcely affected by turning the cross barto which the thread was attached ; so that the suspension «iust have been sufficiently delicate : under these circum- stances the opposite poles of two strong magnets were ap- plied close to the jar, and at the distance of about twice the length of the suspended wire : but the effect was absolutely imperceptible : in the morning indeed, there had been an appearance of oscillations occupying about a minute, and tending to the direction of the magnets, perhaps derived from some superficial particles of iron which had lost their magnetic property by oxidation in the course of the day. There must at any rate be a doubt whether the presence of a quantity of iron, too small to be ascertained by chemical tests, might not have been the cause of the effects described by Mr. Coulomb, although they indicate a force something greater, upon a rough calculati6n, than one 2000th of the weight of the substance, Y. P. 217. Note on Mr. Coulo.mb's Experiments on Mag- netism. We find in No. 3, Tome 3, of the Bulletin de la Societe Philoraathique, an account of Mr. Coulomb's further experi- ments on magnetism. They appear to have been made with great precaution, and they tend to confirm the opinion already advanced in these Journals, p. 135, that the greater part, if not the whole, of the effect observed was owing to the presence of iron. For it appears that, according to the method employed in the purification of the metals exa- mined, their apparent magnetic power was very materially different. Mr. Coulomb observes that, upon this founda- tion, we may make.the action of the magnet, upon a needle thus suspended, a very useful instrument in chemical exa- minations ; for he finds that the attractive force is directly as the quantity of iron in any mixture ; and, according to its magnitude, we may estimate that quantity, when it is so small as wholly to elude all chemical tests. Supposed Magnetism of Animals. Schilling on the magnetism of the gymnotus electricus. A. Berl. 1770. 68, Against Schilling. Ingenhousz Verm. schr. 271. Spallamani a Lucchesini. Pav. 1783. Three essays in VanSvvintien's Recueil. Andry and Thouret. Mem. de la Soc. de Med. Saurine on animal magnetism. Roz. XXXVI. SOS. Particular Experiments and Pheno- mena. Desaguliers's experiments. Knight's experiments. Ph. tr. 1747- XLIV. 6.56. Waddel and Knight on the destruction of polarity by lightning. Ph. tr. 1740. XLVl. 111. 440 CATALOGUE, — TERRESTRIAL MAGNETISM. Colepress on heating a magnet. Pli. tr. I667. 11.50. Effects of iron on the needle. Ph. tr. lG85. XV. 1213. Leeuwenhoek's magnetical experiments. Pli. tr. 16J7.X[X. 512. Ballard on the magnetism of drills. Ph. tr. 1608.417. Taylor's experiments. Ph. tr. 1721. XXXI. 204. Savery's observations. Ph.tr. 1780. XXXVI. 295. Marbel. Ph. tr. 1732. XXXVII. n. 423. Middleton on the effect of cold on the nee- ,dle. Ph.tr. 1738. XL. 310. Eames on a plurality of poles. Ph. tr. 1738. XL. 383. Desagiiliers. Ph.tr. 1738. XL. 385. On an experiment of Diifay. 386. A blow fixing the temporary polarity and again destroy- ing it. Bremond on a file made magnetic by light- ning. Ph. tr. 1741. XLI. 614. Knight's experiments. Ph. tr. 1744. XLIII. 161. 1747. XLIV. 656. With very powerful magnets. Aepinus on a magnetical experiment. N. C. Petr. IX. 340. Lafollie's magnetical experiments. Iloz. III. 99- Van Swinden sur un ph^nomfene paradoxe. Recueil. III. Veratti's magnetical experiments. C. Bon. VI. 31. Cavailo on magnetism as affected by effer- vescence, Ph.tr. 1786. 1787. Ilittenhouse's magnetical experiments. Am. tr. II. 178. Madison's magnetical experiments. Am. tr. IV. 323. Magnetical phenomena. Ph. M. I. 426. Liidicke's experiments. Gilb. XI. 114. Kilter's experiments.Journ.Phys. LVII. 406. Terrestrial Magnetistn. Declination, Dip, and Variation, For particular observations^ see various nau- tical and meteorological journals, Gellibrand on the variation of the needle. Petit on aterrella, and on the change of de- clination. Ph. tr. 1667. [I.n.28. , DecUnation in l66s. Ph. tr. I668.III. 725. Bond's prediction of the variation to 17 16. Ph.tr. 1668.111. n. 40. Makes it 9°. 1?' W. in 1? 16. It was actually about 10°. Auzout on the declination at Rome in 1670. Ph.tr. 1670. V, 1184. It was 21°. W. Hevelius. Ph. tr. 167O. V. 2059- Halley. Ph. tr. l683. XIII. 208. Halley's hypothesis. Ph. tr. I693. XVII. 563. Bound with XVI. in the copy of the R. X.. Halley. Ph. tr. 1714. I65. Heathcote. Ph. tr. 1684. XIV. 578. In Guinea. At Nuremberg. Ph. tr. l685. XV. 1253. Valkmont sur I'aimant qui s'est fait a Char- tres. 12." Par. I692. M. B. *J. C. on the polarity of iron. Ph. tr. I694. XVIII. 257. Molvneaux on an error from the change of variation. Ph.tr. l6y7. XIX. 625. Ballard on the magnetism of dulls.. Ph. tr. 1698. XX. 417. Cunningham on the dip. Ph. tr. 1706.XXII. 507. Cunningham. Ph. tr. 1704. XXIV. l639. In China. Ph. tr. 1700. XXII. 725. CATALOGUE. — TERRESTRIAL MAGNETISM. 441 Ship! are sometimes carried into the Bristol channel in- stead of the British, by mistalting the variation, not by a current. Wallison Halley's chart. Ph.tr. 1702.XXIII. 1106. Saunderson. Ph. tr. 17'20. XXXI. 120. In the Baltic. Rogers and Halley. Ph. tr. 1721. XXXI. 173. Cornwall. Ph. tr. 1722. XXXII. 55. In the Ethiopic ocean. -[-Leeuwenhoek on the magnetism of an iron cross. Ph. tr. 1722. XXX FI. 72. Graham. Ph. tr. 1724. XXXIK. 96. Observes a diurnal change of variation, Graham on the dip. Ph. tr. 1725. XXXIII. 332. About 74° 40' in 1 723. Notes the frequency of vibration. Graham. Ph. tr. 1748. XLV. 279- Middleton. Ph.tr. 1726. XXXIV. 73. 1731. XXXVII. 71. 1730. XXXIX. 270'. 1742. XLII. 157. In Hudson's Bay. Robin's tables from Middleton. Ph. tr. 1731. XXXVII. 69. 1733. XXXVIII. 127. Hoxton on an agitation of the needle in a storm. Ph. tr. 1731. XXXVII. 53. Hoxton. Ph. tr. 1739. XLI. 17 1. Atlantic. Musschenbroek. Ph.tr. 1732.XXXVII.428. At Utrecht. Musschenbroek's chart for 1744. Introd. II. At the end. On board the Hartford. Ph. tr. 1732. XXXVII. 331. Harris. Ph. tr. 1733. XXXVIII. 75. Elvius. Sdnv. Abh. 1747-89. Wargentin on the effect of an aurora borea- lis. Ph.tr. 1751. 126. Mountaine and Dodson on the magnetic chart. Ph.tr. 1754.875. ♦Mountaine and Dodson's tables of 50 000 observations. Ph. tr. 1757. 329. *OL. II. For 1700, 1710, 1720, 1730, 1744, and 1750. Con- clude that no calculations can extend to all the changes. Mountaine on maps and charts. Ph. tr. 1758. 563. *Mountaine and Dodson's chart. R. I. Mountaine on the variation from 176O to 1762. Ph. tr. 1766.216. Williams on ascertaining the longitude by the variation. Load. 1755. Engl. Ital. Written by Dr. Johnson. Euler's theory of the magnetic declination. A. Berl. 1755. 117. 1757. 175. I766. 213, Strmncr et ZegoUstroni de declinatione. Ups. 1755. Euler's theory. A. Berl. J 755. 107. 1757. 175. 1766. Canton on the diurnal variation. Ph. tr, 1759. 398. With tables. Mayer's theory. GiJlt, Anz, 176O. 633. 1762, 377. Lichtenberg in Er.xleben. Mayer Op. posth. Confused and inaccurate. Kobison. Mtindert Sorrey Beschaffenheit der erdkugei aus der wirkung des magnets. 1744. Bdlin Carte des variations. Par. 1765. Lambert. A. Berl. 1766. Wilke's chart. Schw. Abh. XXX. 209. A, P. 1772. ii. 464. Wilke iiber den magneten. Eckeberg's observations. Schw. Abh. XXX. 238. Mallet's observations in Lapland. Ph. tr. 1770. 363. Cook.Ph.tr. 1771.422. Lemonnier. A. P. 1771.93. H.29. 1772. ii. 457. H. 56. 1773. 440. H. 1. 1774. 237. H. 5. On the dip. 1777- 89. H. 4. Lemonnier Loix du magnetisme. On the line of no declination. Lemonnier. A. P. 1777. 168. St 44S CATALOr.UE. TKUKESTEIAL iMAGNETISM. Hutchins on the dip in the north seas. Ph. tr. 1775. 129. 1776. 179. Douglass's observations made about 1735. Ph. tr. 1776. 18. Known to Mountaine. Dunns magnetic atlas. Lond. 1776. Legentil. A. P. 1777. 401. H. 5. Diilryniple. Ph. tr. 1778. 389. Easrlndics. Pickersgiil. Ph. tr. 1778. 1057- Davis's straights. Miller. Koz. XIII. 391- Lacepede. Roz. XV. 140. J?ode Jahrbuch. 1779. VunSwindcn. S. E. Vlll. Thinks the diurnal variation owing rather to a change in the needle than in the earth, the effects in different places and with different needles varying considerably. The de- clination increases before an aurora borcalis. Van Swinden on the affection of the needle in the aurora borealis. A. Petr. J780. IV. i.H.lO. Coulomb. S. E. VIII. ' , , . . Attributes the diurnal Tarijition to the action of»the ,sun with his atmosphere, like the aurora bprealis, driv- ing the magnetic fluid from the parts of the earth nearest lo him : the action continuing in these climates an hour or two after noon, till the sun reaches the meridian of the magne- tic pole. runcks N. und S. Erdoberflache. Leip.z. . 1781. Sho\vs the variation and the dip. Cassini on the dailv vaikition. Koz. XXIV. 2.37. Po'ister in Svvinbiirne's Travels. II. Several observations of variation. Am. Ac. I. Chart of the magnetic equator and meridian. A. P. 1786. 4:). Journ. Phys. XLVI. 84. Silberschlag's theory. A.Berl. 1786.87. Makes the lines of equal dip parallel. Cavallo. Ph.tr. 1787. 6. Deduces the diurnal variation from the effect of heat. Btiffon Mineralosrie. V. Cotteonthediurnal variation. R02. XLr.204. Makes the needle undergo several vicissitudes in the year, becoming four times stationary. From January to March it retires from the meridian, then approaches it till May, is stationary in June, retires in July, approaches till October, and retires from it in November and December. Churchman's magnetic atlas. II. 1. Churchman on the magnetic atlas. 4. R. I, Dalton's meteor, observ. 61. *llobison. Enc. Br. Art. Variation. Suppl. Art. Magnetism. Macdonald on the diurnal variation of the needle in Sumatra. Ph. tr. 1796.340. The variation about 1° s' E. at 7 in the morning, 1" 11' at 5 in the afternoon; diminishing again till 7 the next morning. Supposes the strongest pole to the south. Macdonald on the variation of the needle at St. Helena. Ph.tr. 1798.397. Nov. 1796, the variation was 15° 40' 311" W.; in- creasing 3' 55" from 6 in the morning to 8, then dimi- nishing till 6 in the evening, and remaining stationary all night. Haiiy on natural magnets. B. Soc. Phil. n. .5. Journ. Phys. XLV. (II.) ,'309. Rennel's variation chart of Africa. Fark's travels. Zach. Ephem. IV. 192. Harding on the variation.' Ir. tr. IV. 107. Thinks the change at Dublin is 1 2' 20 " every year. Nugent on the magnetic poles. Ph. M. V. 378. Heller on the magnetic effects of the sun and moon. Gilb. IV. 477. Humboldt. B. Soc. Phil. n. 37. Found the number of vibrations in tqual times at Paris 245, at Valcntia 235, atCumanaSig. But what was the temperature ? Humboldt. Ph. M. XI. 3.55. Finds the lanishing point of declination lat. 29°. N. Ions'. .66° 40'VV. probably of Paris : this is further W. than in Lambert's chart in Bode. 1779. Humboldt's letters. Ph. M. XVI. l65. Burckhardt on the law of declination at Pa- ris. Zach. Mon. corn III. 161, 546. Note. Ph. M. IX. • Gives for the declination at Paris T. dccl. = .449 Csin. ^ CATALOGUE. — TERRESTRIAL MAGNETISM. US ,465 gr. t) 4- .0425 (sin. .03 gr. t) * + .0267 (sin. l.oe gr. 0* ; 'being the number of years elapsed since 1863, the degrees, gr. being decimal. In 1799 the declination at Paris was 2s.26fl", in 183?, according to the formula, it will be a maximum at 24°. 2S'. The complete period is 860 years. On a magnetic globe floating in mercury. Ph. M. XIII. 404. Hitter on magnetism. Gilb. XV. 206. Supposes a lunar period. Lalande on Churchman's north pole. Ph. M. XIV. 249. Account of Gay Lussac and Biot's aerosta- tic voyage. Ph. M. XIX. S74. They found little or no difference in the foice at the height of above 4 miles. The eruption of Hecla considerably affected the needle. Robison. It has been observed, that the variation is certainly affected by atmospherical causes, as in the aurora borealis ; but not certainly by terrestrial, and that it is fair to con- clude that itscause is wholly atmospherical : the argument appears however to be a weak one. Table of the change of Declination observed in London. Cavallo. Progress of the diurnal Variation. 1576 11° 15'E. 1730 13° o'W. 1586 11 11 1735 14 10 1612 6 10 1740 15 40 J622 6 0 1745 16 5S 1633 4 5 1750 17 54 1634 4 5 1700 ig 12 1657 0 0 1765 20 0 1665 I 221 W. 1770 20 35 1666 1 351 1774 21 3 1072 2 30 J775 21 30 1083 4 30 1780 22 10 1692 6 0 1783 22 50 1700 8 0 1790 23 34 1717 10 42 1795 23 52 1724 11 45 1900 24 7 1725 11 50 Mean diurnal Variation, according to Canton Jan. 7' 8" May 13' 0" Sept, Feb. . » 58 March 11 7 April 12 2fi June July Aug. 0" 13 21 13 14 IS 19 11' 43" Oct. 10 30 Nov. 8 9 Dec. 6 5 8 June 27, 175S 1. Decl. .W. Temperature, Morning, oh .18'. 19". , 2'. 62° K 0 4 18 58 62 8 30 18 5 5 65 9 2 18 54 67 10 20 18 57 69 11 40 19 4 6SJ Afternoon. 0 50 19 9 70 1 38 19 8 70 3 10 19 8 68 7 20 18 59 61 9 12 19 0 50 •11 40 18 51 57i Canton I Table of the Dip. Cavallo. N. lat. E. : long. N. end S. lat. W. long. N. end below. belou . 17? 6. 1776. 53° 55' 193' ' 39' 09° 10' 7° 3' 33"2l' . 17°57' 49 36 233 w. 10 long. 72 29 n 25 34 2 4 E. long. 9,15 S. end 44 5 8 10 71 34 below. 38 53 12 1 70 30 16 45 208 12 29 28 34 57 14 8 66 12 19 :i8 204 11 41 0 29 18 16 7 62 17 1777. 24 24 IS 11 59 0 21 8 185 0 39 J 20 47 19 36 56 15 1774. 15 8 23 38 51 0 35 55 18 20 45 37 12 1 23 35 48 26 1777. 10 0 22 52 44 12 41 5 174 13 03 49 5 2 20 10 37 25 1773. 0 3 27 38 30 3 45 47 166 18 70 5 4 40 30 34 22 15 The mean dip observed by Nairne in London, 1772, was 72° 20'. Ph. tr. 1772. 476. In 1570, Norman found the dip 71° 50', in 1670, Bond 73°47', in 1720, Whiston 75° lo', in 1723, Graham 7S^°, or 75°, in 1776 Cavendish malies it 72" 3o': the maximum was therefore about 1720. Ph. u. if 70. 375. Magnetical Apparatus. E. M. PI. VIII. Amusemens de physique. Artificial Magnetism. A. P. Index. Art. Aimant. Reaumur on making magnets. A. ]\ 1723. Marcel. Ph. tr. 1732. XXXVII. 294. Diihamel fa^on d'aimantcr. A. P. 1735. 1745. 181. H.I. U\ CATALOGCE. — MAGNETIC AL APPARATUS. Strength of Knight's magnets. Ph. tr. 1744. XLIII. 161. Knighton the poles of magnets. Ph. tr. 1745. XLIII. 361. Mitchell on artificial magnets. 8. Lond. 1750. Cambr. 1751. M.B. Canton's method, with Folkes's report. Ph. tr. 1751. 31. Klingatstierna el Brander de magnetismo ar- tificial!. Stoch. 1752. liiviere sur les aimansartificiels. Par. 1752. Richmann on malving magnets. N. C. Petr. IV. 235. Wenlz on artificial magnets. Act. Helv. II. 264. Nebel de magnete artificiaii. 4. Utr. 1756. Antheauime. A. P. 1753, 1761. jintktaulme sur les aimans artificiels. Par. 1760. Le Noble's artificial magnets. A. P. 1772. i. H. 17. Lemonnier Loix du niagnetisme. Fothergiil oq Knight's machine. Ph. tr. 1776. 591. Fuss on artificial magnets. A. Petr. II. ii.H. 35. Roz. 1782. On artificial magnets. Roz. IX. 454. Wilson on Knigiit's artificial loadstones. Ph. tr. 1779-51. Made of elutriated iron filings, and linseed oil. E. ]M. A. VI.694. E. M. Piiysique. Art. Aimant. Ingenhousz's paste. Venn. Schr. 1.409. Brisson on the best steel for magnetical uses. A. P. 1788. 169. Repert. III. 276. Cast steel bad. English or German best. Tremery on elliptic magnets. B. Soc. Phil. n. 6. A complex horseshoe magnet. Isich. 8. V. 216. Sjostcen on making magnets. Gilb. XVIF. 325. Touching them in a cirde. A bar rubbed from both ends to the middle, has both ends of the same quality with the pole employed ; the mid- dle of the contrary quality. Oil somewhat impedes the communication of mag- netism. Robiscn. Compasses and dipping Needles. See Navigation. Lahire on an annular needle^ Ph.tr. I6B6. XVI. 344. Lahire's variation compass. A. P. 1716.6. Mean's compass. A. P. 1731. H. 92. Buachc's compass. A. P. 1732. 377. For the dip and declination. Quereineuf's azimuth compass. A. P . 1734. 11.105. Mach.A.VII. 3. Middleton's azimuth compass Ph. tr. 1738. XL. 395, With a telescope. Lemaire's variation compass. A. P. 1747. H. 126. Mach. A. VII. 361. Magny's compass. A. P. Bernoulli on dipping needles. A. P. Prix. V. viii. Act. Helv. III. 233. Trombelli and Collina on the invention of the compass. C. Bon. II. iii. 333,372. Knight.Ph.tr. 1749. iii. Rhomboidal needles are bad. *Kuight's compass, with Smeaton's remarks. Ph. tr. 1750. 505, 513. Duhamel on the improvement of the com pass. . A. P. 1750. 154. H. 1. 1772. ii. 44. H. 58. Zeiher's needle and compass. N. C. Petr. VII. 309. VIIL 284. Kotelnikovv's suspension for a needle. N. C. Petr. VIII. 304. Nairneon Mitchell's dipping needle. Ph. tr. 1772. 476. ."5> CATALOGUE. — MAGXETICAL OESERVATIOXS. US Marine compass. A. P. 1773. 320. Lemonnier on removing friction from com- passes. A. P. 1773. 440. H. 1. A compass. Roz. Intr. I. 422. Lorimer's needle for the dip and the varia- tion. Ph. tr. 1775. 72. Cavendish. Ph. tr. 177fi. 375. The needle is capable of inversion : the dipping needle on Mitchell's construction. Gaule's variation compass. A. P. 1777. Krafft on the dipping needle. A. Petr. II. ii. 170. Ingenhousz on suspending needles. Ph. tr. 1779. 537. Proposes to have them made hollow, so as nearly to float on a fluid, and then suspended by a magnet, with a cavity below to prevent their being shaken off. Lac6p^de on compasses, Roz. XV. 140. *Van Swinden on magnetic needles. S. E. VIII. 1780. Prize memoir. Proposes flat needles, turning on a pro- jecting point. *Coulomb on magnetic needles. S. E. IX. 1780. Prize memoir.Thinks the form of a needle of little conse- .quencc •. perforating them has scarcely any effect. Divided needles act most powerfully. Found the circle of contact of the needle with its support, in a particular case, -Jj of aline, supposing it to be equally pressed, which is nearly true. Coulomb's needle suspended by a thread of silk. A. P. 1785.560. Coulomb's mode of measuring the dip, M. Inst. IV. 565. B. Soc. Phil. n. 31. Compares the weight required to keep the needle hori- 2nntal with the time of its horizontal vibration ; and thinks that the dip may be thus determined within lo'or 12'. Coulomb. Ph. M. XV. 186. Prefers long and broad needles magnetized by Aepinus's method . Gattey on guarding needles from electricity, Roz. XVII. 296. Rmnouski on observing the dip. A. Petr. 1781. V. i. 191. E. M. A. VI. 7 14. E. M. PI. V. Marine. III. E. M. Physique. Art. Aimant. Boussole. Degaulte sur un compass azimuthal a reflec- tion. 8. R. S. Cavallo.Ph.tr. 1786.65. Recommends for delicate purposes suspension by a chain of horse hair. Cotte's variation compass. Roz. XIX. 189. Romans's improved compass. Am. tr. 11.396. Repert. IV. 178. The box hung on a centre. Report on M'Culloch's sea compasses. Lond. 1788. Drury on cased needles. Ir. tr. 1788. II. IIQ. Repert. I. 111. Rennet's suspension of the magnetic needle. Ph.tr. 1792.81. Repert. XII. 311. Aspider's thread, which, after 1 8000 revolutions, showed no tendency to untwist, and broke at last. Prony's instrument for observing the varia- tion. Journ. Phys. XLIV. (II.) 471. Cassini's azimuth compass. M, Inst, V. 145. Magnetical Observations. Howard on a reversion of the needle. Ph. Ir. 1676. XI. 647. Reversion of a compass. Ph. tr. 1684, XIV, 520. Middleton. Ph. tr. 1738. XL. 310. Found the needle afiected by cold so that it could not traverse. Bouguer on marine observations of declina- tion. A. P. Pri.x. II. vi. Remark on the disturbance of the nee'dle by the electricity of the glass. Ph. tr. 1746. XLIV. 242. ' The electricity may be removed by a wet finger. Waddel and Knight on the destruction of polarity by lightning. Ph, tr, J749. XLVI. 111. 446 CATALOGUE. — METEOROLOGY. The needles were rhomboidal, there was iron about the compass, and in the binnacle. Magnetic Measures. See Terrestrial Magnetism. Graliam. Ph. tr. 1725. XXXIII. 3.32. Observed the frequency of the vibrations of the dipping needle. Coulomb. A. P. 1785.578. Shows, that a horizontal needle is urged by a force which is constant if reduced to the direction of the meridian. Saussure's magnetometer. Voyages, cccclv. METEOROLOGY. Literature of Meteortdogj-. " Weigels Chemie.' ^. 398. Meteorology in general. Zahn on the economy of tlie world. Lycosthenes on meteors. J)cs Cartes Meteora. Opp. II. Ph. tr. abr. II. i. 1 . IV. 2 p. J. 1 . VI. 2 p, i. 1. Vni. 2 p. i. 377. X. 2 p. i. 269. Fritscfi on meteors. Jurin invitatio ad observationes metcorologi- cas. Ph. tr. 1^23. XXX 11. 422. Greenwood on the method of meteorologi- cal observations. Ph. tr. 1728. XXXV. 390. *Polem observationes meteorologicae Paia- vianae. Ph. tr. 1731. 201. Cyrilli aeris terraeque historia, 1732. Ph. tr. 1733. 184. On the causes of a dry and wet summer. Ph. tr. 1740. 519. A frosty winter producing a diy summer. HoHmann on meteorological observations. C. Gott. 1751. 1. 41. And elsewhere. Bernoulli on the atmosphere. Act. Heir. T. 35. U. 101. Ellis on wind and weather. Ph. tr. 1755. 124. Franklin's physical and meteorological ob- servations, read 1756. Ph. tr. 1765. 182. Milk's essay on the weather. 12. Musschenbroek's cautions on observations. N. C. Petr. VIII. 367. Richard llisto'ue natureile del'air et des me- teores. 10 v. 12. Par. 1770, 1771. Lambert on meteorology. A.Berl. 1771- GO. Lambert on meteorological observations. A. Berl. 1772. 60. Defuc Modifications de I'atmosphere. 4. Gen. 1772.8. Par. 1784. R.I. *Df/uc Idees sur la meteorologie. 2 v. 8. Lond. 1786, 1787- R. L Deluc on meteorology. Roz. XXXVII. 120. Deluc'ri answer to Monge. Ann. Ch. VIlI. 73. Colte Traite de meteorologie. 4. Par. 1774. Suite. 2 V. 1789. Cotte on meteorology. Roz, VII. 93. Cotte's general results or axioms. Journ. Phys. XLIV.(l.)23l. Ph. M. VI. 146. Note of Cotte's memoirs. Journ. Phys, XLV.(II.)431. Fdhiger liber die witterung. 4. Sagan. 1773. Toaldo on meteorology as affecting vegeta- tion. Roz. X. a49. Toaldo la meteorologia applicata all' agri- eoltura. 8. Ven. 1786. R. S. Toaldo Saggio meteorologico. 4. R. S. Busch Vermischte abhandlungen. Hamb. 1777. II. 225. Van Sieiitdfh sur les observations faites a Franeker. 8. Leyd. Extract of a memoir of Van Swinden, by Cotte. Roz. XII. 297. Dionis du Sejour sur les phenom&nes. 8. R.S. CATALOGUE. METEOROLOGY. 447 Gatterer's meteorological year. Commeii- tat. Gott. 1780. III. Ph. 82. Gatterer Goth. Mag. I. ii. 1. Horrebow tractatus historicometeorologicus. 4. Copenh. 1780. Jones on the natural philosophy of the ele- ments. 4. R. 1. , Rosent/ial iiber meteorologische beobachtun- gen. 4. Erf. 1781. Ephemerides societatis meteorologicae Pala- tiiiae. 1781. . . Manh. B. B. Extracts from the memoirs of the Palatine society^ by Cotte. Roz. XLIH. 294. Joiiru. Phys. XLIV. (I.) Mouitum ad observatores societatis meteoro- logicae. 4. R. S. Achard on the imperfections of meteorology. Roz. XXIII. 282. *Hube iiber (lie ausdlinstung. lioiiland Tableau des proprietes de I'air. 8. Par. 1784. II. I. *Senebier on the improvement of meteoro- logy. Roz. XXVII. 300. XXX. 177, 24o, 328. *Saussure Voyages. Saussure Relation abregee d'un voyage a la cime du Mont Blanc. 8. Gen.R.S. Account of Saussure's journey. Roz. XXXI. 317, 374. Saussure's observations. Roz. XXXIV. l6l, *Saussure liygrometrie. Madison on meteorological observations. Am. tr. II. 123. Filgrams VVetrerkundc. Vienna, 1788. 4. Marsham's indications of spring. Ph. tr. 1789- 154. Rdtnond Observations faites dans les Pyre- nees. 8. Par. 1789. U. S. Ramond's ascent of Mont Perdu. Nicb VI. 230. Meteorological remarks. Roz. XXXIV. 321. Monge on the principal phenomena of me- teorology. Ann. Ch. V. 1. Garnett's collection of meteorological ob- servations. Manch. M. IV. 234, 521. Copland and others on the weather. Manch. M. IV. 243. Dalton's meteorological observations and essays. 8. Lond. 1793. Rules for judging of the weather. 195. Enc. Br. Art. Weather, Six on meteorology. 8. 1794. R.I. Kirwan on the weather. Ir. tr. V. 3, 31, 39. Kirwan on the variations of the atmosphere. Ir. tr. Vlll. 2G9. Pouchet Meieorologie terrestre. 8. Rouen, 1797. R. S. Locliead on the natural history of Guiana. Mich. II. 297. Humboldt's letter from South America. Journ. Phys. XL1X.433. Lamarck on meteorological registers. Journ. Phys. LI. 419. Coupe's meteorological remarks. Journ. Phys. LIII. 262. Bcddoes on prognostics of the weather. Nich.8. I. 98. Capper on the weather in England. Nich. 8. I. 275. Parrot on meteorology. Gilb. X. 1G7. Bockmann's meteorological remarks. Gilb. XIV. 112. Cordier's journey to the summit of Teneriffe. Ph. M. XVII. 31. Menzies's journey to the summitof Whararai. Journ. R. I., 1.311. Prognostics of the weather. Nich. VII. 148. Aerostatic voyage by Gay Lussac and Biot Ph. M. XIX. 374 448 CATALOGUE. — METEOROLOGICAL JOURNALS. IMeleorological Apparatus, and Modes of Observing. Leutmanni inslrumenta meteorognostica. 8. Wittenberg, 1725. Nollet. A. P. 1740. 385, 567. 1741. 338. H. 145. Pickering. Ph. tr. 1744. n. 473. *Cavendish on the meteorological instru- ments of the R. S. Ph.tr. 1776.375. Fontana's account of the Grand Duiic's cabi- net. Roz. IX. 41. Changeux's meteorographic instruments. Roz. XV. 74. XVI. 325. TIemmtr Descriptio instruuientoruni societa- tis Palalinae. 4. Manh. 1782. Monitum ad observatores societatis Palatinae. Rosenthal Meteorologische werkzeuge. 2 v. 8. Gotha, 17S2, 1784. Landriani Descrizione di una machina me- teorologica. 4. R. S. *Moscati's description of a meteorological observatory. Soc. Ital. V. 356. On Lazowsky's long wire. Nich. II. 11. Toaldo on the prognostications of animals. Ph. M. IV. S67. Schweighauser on the sound of a long wire. Ph. M. IX. 285. A very long wire was supposed to emit a sound upon the approach of any change of weather : it was probably from an alteration of temperature. Bossi suHa dottrina di QuatremereDisjonval. 8. Tur. 1803. R. S. Meyer on the presensations of animals. Ph, M.XI.211. Nouveau traite sur les barometrcs. 8. Par. 1802. Meteorological Journals. A. P. Numerous observations may be found by the inde.\. Plot. Ph. tr. 1685. XV. 930. At Oxford. A barometrical diagram. Garden. Ph. tr. 1685. XV. 991. Hillier. Ph. tr. l697. XIX. 687. Cape Corse in Guinea. Derham. Ph. tr. I698. XX.41.AtUpminster. 1699. XXI. 45. 1700. XXII. 527. 170s. XXIIi. 1443. 1707. XXV, 2378. 1709. XXVI. 309, from Irelandf ; 342. Switzer- land and Upminster.1732. XXXVIT.26I. 1733.XXXVIII. 101. 1734.XXXV1II. 334, 405, 458. Cunningham. Ph.tr. l699- XXI,323. 1704. XXIV. 1639. China. Townley. Ph. tr. 1699- XXI. 47. 1705. XXIV. 1877. Locke.Ph.tr. 1705. XXIV. I917. Cruquius. Ph. tr. 1724. XXXIII. 4. Middieton. Ph. tr. 1731. XXXVII. 76. *Poleni. Ph. tr. 1731. XXXVII. 201. 1738. XL. 239. Pavia. *Musschenbro€k. Ph. tr. 1732. XXXVII. 357,428. Utrecht. CyrilU. Ph.tr. 1733. XXX VIU. 184. Weidler. Ph. tr. 1736. XXX IX. 238, 260. Hadley. Ph. tr. 1738. XL. 154. Abstr. 1742. XLII. 243. Abstr. Lynn. Ph. tr. 1741. XLI. 686. Synopsis. Revillas. Ph. tr. 1742. XLII. 193. Rome. Linings. Ph. tr. 1748. XLV. 336. South Carolina. T. Heberden. Ph.tr. 1751.357. 1754.617. Madeira. Watson. Ph.tr. 1753. 108. Siberia ; abstract. CATALOGUE. — METEOROLOGY, CELESTIAL INFLUENCES. 445 Simon. Ph. tr. 1753. 320. 17o6. 759. Dublin. Borlase. Ph. tr. 1763. 27. 1770. 230. 1772. 365. Rose. Ph. tr. 1766. 291. Guebec. Huxham Ph. tr. 1767. 443.PI. Carlyle. Ph.tr. 1 768. 83. Wolfe. Ph. tr. 1768. 151. Warsaw. Wargentin. Ph. tr. 1768. 152. Stockholm. Farr. Ph. tr. 1769. 81. 1775. 194. 1776. 367. 1777.353. J778. 567. Bristol. Miller. Ph. tr. 1769. 155. 1771. 195.' Ph. tr. 1770.228. At Bridgewater. Pigott. Ph.tr. 1771. 274. Rouen. Barker. Ph. tr. 17 72.. 1802. From 1736. Lyndon. Woilaston. Ph. tr. 1773. 67. Cotte. S. E. 1773. 427. From Messier, for 10 years. ♦Journals kept at the house of the R. S. Ph. tr. 1775. . . ♦Horsley. Ph. tr. 1775. 167. Abriged 1776. 354. Barker. Ph. tr. 1775. 202. Allahabad. Roxburgh. Ph. tr. 1778. 180. 1780.246. Manuscript continuations. R. S. Fort St. George. Dalryniple. Ph. tr. 1778. 389- East Indies. Barr. Ph. tr. 1778. 560. 1780. 272. Montreal. M'Gouan. Ph. tr. 1778. 564. Edinburgh. Lloyd. Ph. tr. 1778. 571. Leeds. VOL. II. Pickersgill. Ph. tr. 1778. 1057. Davis's Straights. Latrobe. Ph.tr. 1779-657. )781. 197- Several manuscript continuations. R. S. Nain and Okak. Diary kept in Hudson's bay. f. R. S. Chandler's meteorological diary- f. R^ S. Robertson's journal kept on board the Rain- bow. 4. R. S. Schotle. Ph. tr. 1780. 478. Scnegambia. *Ephenierides ^ocietatis Palalinae. Cotte's extracts; Roz. Aikins. Ph. tr. 1784. 58. Minchead. At the Royal Observatory of Paris, A. P. 1784. 631. Bent, for several years, M.S. R.S^ London. Pcarce. M.S. R. S. Fort William. '^t^f/'="0'RNIA. Kirwan. Ir. tr.V.VI. Dublin. Observations in Greenland, Labrador, and Africa. Gilb. XIL 206. Mourgue Essais de siatistique. Ace. Jonrn. Phys. LII. 118. Several other manuscript journals. R. S. General effects of the Sun and Mooii. Kratzenstein von dem einflusse des mondes. 8. Halle, 1746. 1771- Lambert on tl^e moon's influence upon the atmosphere. Act. Helv. IV. 315. A. Berl. 1771.66. Toaldo della vera influenza degli astri. 4. Pad. ' 1770. R.S. Frencb by Jacquin. Toaldo Tabulae barometri aestnsque maris. 4. Pad. 1773. Toaldo Saggio meteorologico. 4. R. S. 3M 450 CATALOGUE. — METEOROLOGV, CLIMATE. Toaldo Oil the lunar influence. Roz. XIII. 442. Toaldo Saros meteoiologique. 4. R. S. Roz. XXI. 176. Toaldo's 24 aphorisms. Rozier. 1785.388. Toaldo's system and observations. Ph. M. III. 120. IV. 417. Gr. Fontana on the hinisolar influence on the atmosphere. Ac. Sienn. V.' llG. Fabri Geogr. Ma^,. II. i. 72. Horsley. Ph. tr. 177fi. 354. Cotte on lunar periods. Roz. XX. 249- Cotte on the lunar period of 19 years. Roz. XXVIII. 270. XLII. 279. Journ. Piiys. L. 358. Mann on aerial tides. Roz. XXVU. 7. Ph. Mag. V. 104. Chiminello on atmospheric tides. A. Pad. r. 195. IV. 88. Lamarck on the lunar influence on the atmo- sphere. Journ. Phys. X LVI. (III.) 428. LII. 296. LIII. 277. B. Soc. Phil. n. 15. JSich. III. 488. Ph.M. IX. 373. Gilb. VI. 204. Against Cotte. Howard on the variation of the barometer from solar and lunar influence. Ph. M. VII. 355. Finds a mean elevation of .1 at the quadratures. Lamanon on atmospherical tides. Gilb. VI. 194. Hemmer on the sun's influence upon the ba- rometer. Ph. M. XI. 151. Climate in general. Halley on the heat of different latitudes. Ph. tr. 1693. XVII. 878. From computation. ■{•Lahire on the thermometer covered with snow ascending in a frost. A. P. IX. 318 Effect oi the wind on the thermometer. Ph. tr. 1710, XXVU. 644. H. 13. Mairan on the causes of heat and cold. A. P. 1719. 104. H. 3. 1721. 8. H. 16. 1765. 143. H. ]. • Mairan Recherches sur le chaud et le froid. 4. Par. 1768. Weitbrechl on the heat of running water. C. Petr. VII. 235. Euler on climates. C. Petr. XI. 82. Merely mathematical ; supposing the sun to cool the earth at night. Nollet on the freezing of large rivers. A. P. 1743. 51. H. 8. Krafft Oratio declimatibus borealibus. Segner de caloreet frigore. 4. Golt. 1746. Ellis on the temperature of the bottom of the sea. Ph. tr. 1751. 211. Kaestner on Halley. Hamb. Mag. II. 426. Simpson's fluxions. Sheldrake's causes of heat and cold. 8. Lond. 1756. Wargentin on climate. Schw. Abh. 1757. 159. Marline's essays. Lomonosow on the ice in the North sea. Schw. Abh. 1763. 37. On mean temperatures. Act. Helv. IV. 1. Gr'uners Eisgebirge des Schweizerlandes. 8. Bern. 17 60. 36. Heberden on the heat at diflJerent heights. Ph. tr. 1765. 126. Finds 1" depression for each 1 90 feet of height. Barrington on the clianges in the climate of Italy. Ph. tr. 1768. 58. Douglas on the temperature of the sea at ditterent depths. Ph. tr. 1770. .S9.^ Emerson's miscellanies. 490. Williamson on the change of climate in America. Am. tr. I. 277, 336. On chmates. Roz. III. 245. IV. 174. X. 148. Bourrit des glacieres de bavoye. 8. Gen. 1773. CATALOGUE. — METEOROLOGT, CLIMATE. 451 Bourrit des Alpes Pennines. 8. Gen. 1781. Phil. tr. 1775. 459. Roebuck suggests the estimation of climates by the tem- perature of springs. Saussure Voyages dans les Alpes. - Observes, that there is sometimes a sense of heat on these mountains. Wilson on local heat. Ph. tr. 1780. Hassenfratz on the free heat of the atmo- sphere. Roz. XIX. 337. Goth. Mag. I. ii. 19- Six on local heat. Ph. tr. 1784. 428. 1788. 103. In cloudy weather there is little difference In the tempe- rature at different heights ; in clear weather the lowest station is coldest at night, and hottest by day. When the heat is below 40° there is liltle difference in the day time. !n general the difference is 1° or 2', sometimes 4° at night. The ground is sometimes 1° or 2° colder than the air a few feet above it, and was found even 1 0° colder than the highest station. In a well at Dover, 360 feet deep, with 21 feet of water, the water was 56" at the surface, 52° in the middle, 48|" at the bottom, in September. At Sheerncss in a well with ISOfeet of water, wholly below the level of the sea, the ther- mometer was 51° in the middle, 56° at the bottom: but perhaps the pressure of six atmospheres disturbed the ther- mometer a little. Pugh on European climates. 8. Lond. 1784. U.S. Deluc Idees. Il.dccxcvii. On the sense of heat upon high mountains. Forster's works. Proves that ice may be formed at sea. *Kirwan's estimate of the temperature of dif- ferent latitudes. 8. Lond. 1787. K. I. Pr. --by Adet. 8. Exir. Ptoz. XXXVir. 410. Kirwan on the variations of the atmosphere. Extr. Ph. M.XVI. 21'>. On tliC heat of summers and winters. Darvviu. Ph. tr. 1788. 43. The air ascending from t..e vallies towards the hills, must expand, and thence become cooler : thus the thermometer often rises with the barometer. Hamilton on the climate of Ireland. Ir. tr- 1783. II. 143. VI. 27. Nich. 11. 381. Morozzo on tlie temperature of the sea and • lakes at diftereut depths. M. Tur. 1788, TV, 309. Guthrie on the climate of Russia. Ed. tr. If. 213. Mann on the changes of climates. Comm- Ac. Theod. Pal. 1790. VI. 82. Gi:eu. I. 231. Ph. M. IV. 357. V. Mann sur les grandes gelees. 8. Ghent, 1792. R.S. Mayer de variationibus thermomeri. Op. ined. I. 1. Toaldo on the hejit of the lunar rays. C. Bon. VII. 0.9,471. Toaldo on climates. Ac. Pad. III. 2l6. Pictet Essais de physique. I. viii. On the warmth of the strata of air. Picteton mean temperatures. Roz.XLII. 78. Williams on the use of the thermometer in soundin;?. 4. Phllad. 1792. Am. tr. III. 82. Dalton on climates. Meteor, observ. 1 1 8. Cotte on temperatures. Roz. XLII. 282. Cotle on lunar constitutions. Roz. L. 358. *Prevost sur I'equilibre de la chaleur. Roz. XLII. 81. Lamarck on the variations of the heavens in mean latitudes. Note. Ph. M. XV. I89. Cassini on the equinoctial variation of tem- perature. Roz. XL. 295. Rittenhouse on the temperature of the air and of the sea. Am. tr. 111. \Qi. ■ Strickland on the use of thermometers in naviqat.on. Am. tr. V. 90. - Van Svvinden on hard winters. Journ. Pliys. L. 277. Playfair. Ed. tr. Says, tl.at the temperature diminishes 1° for about so« feet of elevation. 4^2 CATALOGUE.. — METEOROLOGY, CLIMATE. HiiniSoldt on the temperature of the sea. B. Soc. Fhil. n.57. Says, that the water becomes much colder in shallow places, Prony on the declination of the columns of the I^intheon. B. Soc. Phil. n. 37- Probably the effect of a change of temperature. Beddoes on foretelling the temperature of summers. Nich. V. 131. Nich.8.1.98. On the temperature of springs. Gilb. III. 217. Lamarck on the cliniate in middle latitudes. Journ. Phys. LVI. 118. Note. Ph. M. XV. 189. Voliinj on the climate and soil of America. 8. 1804. R. I. Esmark on the height of the snow line. Ph. M. XVII. 374. ' Perrln's register of the heat of the sea, in the East Indies. Nich. VIII. 131. CoUe's fieneial aphorisms, from Gren. 111. 5. There is little variation of heat between the tropics : it be- comes greater on plains than on hills : it is never so low near the sea as in inland parts: the wind has no effect on it ; its maximum aad minimum are about six weeks after the solstices : it varies more in suiamer than in winter : it is least a little before sunrise:' its maxima in the sun and shade are seldom on the same day : it decreases more rapidly in the autumn than it increases in summer. A cold winter docs not forebode a hot summer. Kirwan says, that the mean heat at the sea side is 84" — 53 (sine lat.) *. From this we must deduct for elevation, i" for each 800 feet that wc ascend perpendicularly, wheVe the declivity is about 6 feet per mile ; where 7 feet, 1" for 600 feet ; where 13 feet, for 500 ; where 1 5 or more, 1" for 400. For the distance from the sea, we must add 1° for each 50 miles, between 10° and 20° latitude ; between 2.5° and 30", 1° for 100 miles : between 30° and 35°, we must deduct 1" for 400 miles; between 35" and 70" for 150. It seldom freezes in latitudes below 35°, and seldom hails beyond 60° ; between these limits it generally thaws when the sun's alti- tude is above 40°. The greatest cold is usually half an hour before sunrise ; the greatest heat at the equator about 1 •'clock ; further north it is later : in latitude 50° about half past 2. In latitudes above 48° July is warmer thanAugust: in lower latitudes colder. At Petersburgh the greatest sum- mer heat is usually 79°- In every habitable climate there is a heat of 60° or more, for at least 2 months. According to Cavallo, the greatest heat of the day in July is before 3 o'clock; according to others, about half way between noon and sunset. Particular Observations of Tem- perature. Account of a frost in Somersetshire. Ph. tr. 1672. VII. 5138. Derham on the great frost of I7O8 — 9. Ph. tr. 1709. XXVI. 454. Derham on a frost. Ph. tr. 1731. XXXVII. 16. *Cossigni and Reaumur. A. P. 1733. . 1740. Isle of Boutbon and Paris. Miles. Ph. tr. 1742. XLII. 20. 1747. XLIV. 613. 1749. XLVI. 208. 1750. XLVI. 571. 1754. 507, 525. 1755. 43. Middleton. Ph. tr, 1742. XLII. 157. Linings. Ph, tr. 1743. XLII.49I. In Carolina. Ardeion. Ph. tr. 1750. XLVI. 573, 1754* 507. Stedman. Ph. tr. 1751. 4. Deniidoir. Ph. tr. 1753. 107. In Siberia. Trcmblcy. Ph. tr. 1757. 148. Hague. Huxham. Ph.tr. 1757.428. 1758.523. Smeaton. Ph.tr. 1758. 488. Edystone and Plymouth. Ellis. Ph. tr. 1758. 754. In Georgia : greatest heat 105°. Brooke. Ph. tr. 1759. 58, 70. Maryland. Pallas. PI), tr. 1763.62. Bcilin. Howard. Ph. tr. 1764. 118. Bedfordshire. Martin. Ph.tr. 1764. 217- Bengal. CATALOGUE. — METEOROLOGY, CLIMATE. 45$ Whitehurst. Ph. tr. 17^)7. 265. Apr. 1 8, at J past 9, p. m. — 1 ° F. Bevis and Short. Ph. tr. 1768. 54, 55. Byres. I'h. tr. 1768. 336. At Rome, gg''. Watson. Ph. tr. 1771.213. Wilson. Ph. tr. 1771.326. Glasgow. Van Swinden. Ph. tr. 1773. 89. De Caifi.S. E 1773.541. On the cold in Canada from the N. W. winds. Barker. Ph.tr. 1775. 202. Allahabad. The heat often 109" in the shade, once 114°. Roebuck on the heal of London and Edin- burgh. Ph. tr. 1775. 459. Roz, IV. 82. A heat of34i R. or lOo" F. was fatal to more than l»000 persons at Pekin. Brisson and Duluc. A. P. 1777- 522. The cellar or well of the observatory varied from ol" to IQl" R. or from 53'' to i5|" F. Wilson on cold at Glasgow. Ph. tr.' 1780. 45 I . Blagden. Ph. tr. 1781. The mean temperature in Jamaica is about 81°. CullumOn a hardfiosi 23 June 1783. Ph. tr. 1784.416. Cassini. A. P. 1786. 507- Roz. XXXV. 140. Cassini on the greatest heat at Paris. M. Inst. IV. 338. In 1701, 104° F. Hunter. Ph. tr. 1788. 53. Found the springs at Kingston in Jamaica, about 80° ; after a gentle ascent of two miles 79° ; cold spring, nearly 1400 yards above the sea, was 61 j"; the variation is 1" for SSOfeet.Theextremes atKingston weresg and gi° :theusual height in the cold season from 70' to 77' , in the hot from «5° to 90°. At Brighthelmstone the heat of a well was 50", at Bromley, in November 491", and the mean between the heat in London, at sunrise and at 2 o'clock, is about 49". 2. Kirwan gives 52" for the mean heat of London, The wrclls at New York vary from 54° to 50°. Heberden's table of the mean heat from 1763 to 1772. Ph. tr. 1788. 66. P. Wilson on cold attending a hoar frost. Ed. tr. I. 146. Pingie on some severe winters, A. P. 1789. 514. Philotattee. Jsiatic Mirror. Mag. 1789. An account of the heat at Cawnpore, from 7 th April t« 6th May 1789. For 21 days from 14th April to 6th May, the mean heat without doors at 2, p. m. was 127°, the greatest heat, lath April, 144"; the mean heat at night U3": behind a tattee, or wet mat, tlie mean heat, at 2, was 79", 48 ' lower than in the open air. *Cotte's table of temperatures. Roz- XXXIX. 27. Agrees in general with Kirwan. Cotte malies the mean temperature of Paris 9;° R. or 53".4 F. Cotte on some severe winters. Journ. Phys. XLVIII. 270. Toaldo on the temperatures of 50 places. Roz. XXXIX 43. Toaldo on some sudden heats. Soc. Ital. VI. 85. A copious table of temperatures by Heinsius. Erxleb. §.761. From Winkler's physik. Rumford on the saltncss of the sea. Ess. If. vi. Manch. M. IV. 601. The sea varies at Liverpool from 36° to 68''. Messier on the heat of 1793. Ann. Ch. XVIII. 310. Messier on the heat at Paris. M, Inst. IV. 501. Manch. M. IV. The thermometer at Kendal is about 47° at a mean. • Kirwan's rules give 4 8i°. Ph. M. X. 172. The mean temperature at Columbo is 79^.5, the utmost variation 13". The mean of the greatest cold and heat at Paris is 54*^.5. Lalandt mentions a heat of 113° in Senegal. In the sum- mers of 1753, 1765, and 179s, it was 104" in France. The mean temperature in London is 50°, 5 from the ob- 454 "CATALOGUE. — METEOROLOGY, WINDS. servations of the R. S. varying in different years from 48° to 52® : the mean of the greatest cold and greatest heat is 50" or 4g°. A t the equator, the line of congelation is about 1 5 600 feet above the sea; near the tropic, 13 430; at Teneriffe, lat. 28°, 10 000 ; in Auvergne, lat. 45°, 6740 ; lat.51° to 54" 5800 ; lat. 80° n. about 1200. Bouguer says, 2434 tois»s in the torrid zone ; in France 1300 or 1600. Meteorological Tliermometers. See Heat. Self registering thermometer. Leupold. Th. Aerostat, t. 23. Van Swinden surla comparaison des thermo- metres. 253. On thermometers showing the maximum. Lord Charles Cavendish on thermometers showing the maximum. Ph.tr. 1757. 300. Gaussen. Itoz. XV II. 61. Six's thermometer. Ph. tr. 1782. 72. Six on a thermometer. 8. Maidstone, 1794. K.I. Hutchins's thermometgrs. Ph. tr. 1783.303*. Rutherford's thermometer. Ed. tr. III. 247. Consisting of two horizontal thermometers, one of spirit, with a little cone of coloured glass within the fluid, the other of mercury, with a bit of ivory in the empty part : the one marking the greatest heat, the other tne least. Keith's self regiitcriiig thermometer. Ed.tr. IV. 203. Nich. HI. 264. Ph. M. IE. 61. Glib. XVII. 319. Wiih a float leaving a mark, or writing on a wheel. Enc. Brit. Art. I hermomeler. Lemaistre on Six's thermometer. Gilb. II. 287. Von Arnim's thermometrograph. Gilb. II. 289. Crichton's self registering thermometer. Ph. M XV. 147. Glib. XVI[ 317. A thermometer of metal showing the ma.iimum and mi- nimu-n. A oaroscope is sometimes made of a solution of 6 parts of camphor, 2 nitre, and l sal aramoniacj in common malt spirits ; this is said to crystallize in bad weather, especially in windy weather : but it is probably mote atfectcd by eoH than by wind. Winds. Winds in general. Bacon de ventis. 1664. Works. III. 441. Bohun on winds. 8. Oxf. l671. Ace. Ph.tr. 1672. VII. 5147. Garden's causes of wind. Ph. tr. l6S5. XV. 1148. Morhofi Polyhistor. II. ii. c. 33. D'Alembat sur la cause geuerale des vents. 4. Berl. 1747. Ace. A. P. 1750. H. 41. Relating to gravitation. Musschenbioek Introductio. II; 1090. VVargentin. Schw. Abh. 1762. 173. Elder on the motions of fluids from he?it. N. C.Petr. XI. XIII. XIV. XV. Leipz. Samuil. zur Physik. II. 575. Coudvaye Theorie des vents et des ondes. 8. Fontenay, 1786. Copenh. 1796. R.S. Par. 1802. Ducarla on winds. Roz. XXXII. 89. Kirwan on the variations of the atmosphere. Ir. tr. Darwin's botanic garden. Notes. Observations on winds. Manch. M. IV. 601. Capper on the winds and monsoons. 4. Lond. 1801. U. S. Regular Winds. Garden on the cause of several winds. Ph. tr. 1685. XV. 1148'. *Halley on the trade winds, with a map. Ph. tr l.iSG. XVI. 1>3. / *Wailis'bOi)jeitions to Ilalley. Birch. IV.5I9. * Had ley on the cause of trade winds. Ph. tr. 1735. XXXIX 58. On the rotatory momentum of the air. CATALOGUE. METEOROtOGY, WINDS. 455 Musschenbroek's chart of the trade winds. Introd. at the end. *Semeyns Haarl. Verh. III. 183. La Nux on the trade winds. A. P. 1 760. H. 17. Franklin. Ph. tr. 1765. 182. Derives the N. W. wind from the current of air descend- ing from the upper regions : in America theN. W. wind is a land breeze. Forrest on the monsoons. 4. Calc. 1732. B. B. 8. Lond. 1784. Bad theory. Atkins. Ph. tr. 1784. 58. The N. W. wind prevails at Minehead. Legentil. A. P. 1784. 480. The wind is inclined to W. at Paris. On trade winds. Leipz. Mag. fur Oekon. 1786. i. ♦Prevost on the trade winds. Roz.XXXVlII. 365, 370. Kirwan on the variations of the atmosphere. Extr. Pli. M. XV. 311. Incline to Halley's theory in preference to Hadley's. On the monsoons at Bombay. Ph. M. XiV. 328. Mafich. M. IV.601. At Liverpool the S. E. wind prevails, probably from local circumstances. In other places, S. W. or N. E. winds are most usual. Particulars of the trade winds, from Roherlson. \. For 30° on each side of the equator, there is almost con- stantly an easterly wind in the Atlantic and Pacific oceans : it is called the trade wind : near the equator it is due east, further off it blows towards the equator, and is N. E. or S. E. 2. Beyond 30° latitude, the wind is more uncertain. 3. The monsoons are, perhaps erroneously, deduced from a superior current in a contrary direction. 4. In the Atlantic, between 10° and 28° N. latitude about 300 miles from the coast of Africa, there is a con- stant N. E. wind. 6. On the American side of the Caribbee islands the N. E. wind becomes neatly E. 6. The trade winds extend 3° or 4° further N. and S. on the W. than on the E. side of the Atlantic. 7. Within 4° of the equator^ the wind is always S. E. : it 3 is more E. towards America, and more S. towards Africa, On the coast of Brasil, when the sun is far northwards, the S. E. becomes more S. and the N. E. more E. and the reverse when the sun is far southwards. 8. On the coast of Guinea, for 1 500 miles, from Sierra Leone to St. Thomas, the wind is always S. or S. W. pro- bably from an inclination of the trade wind towards the land. g. Between lat. 4" and 10°, and between the longitudes of Cape Verd and the Cape Verd islands, there is a track of sea very liable to storms of thunder and lightning. It is called the rains. Probably there are opposite winds that meet here. 10. In thelndian ocean, between 10° and ao°S. latitude, the wind is regularly S. E. From June to November, these winds reach to within 2'^ of the equator ; but from Decem- ber to May the wind is N. W. between lat. 3° and 10° near Madagascar, and from 2° to 12° near Sumatra. 11. Between Sumatra and Africa, from 3^ S. latitude to the coasts on theN. the monsoons blow N.E. from Septem- ber to April, and S. W. from March to October : the wind is steadier, and the weather fairer in the former half year. 12. Between Madagascar and Africa, and thence north- wards to the equator, from April to October there is a S.S. W. wind, which further N. becomes W. S. W, 13. East of Sumatra, and as far as Japan, the monsoons are N. and S. but not quite so certain as in the Arabian gulf. 14. From New Guinea to Sumatra and Java, the mon- soons are more N. W. and S. E. being on the South of the equator ; they begin a month or six weeks later than in the Chinese seas. 15. The changes of these winds are attended by calms and storms. 10. At Liverpool the wind is said to be westerly two thirds of the year. In the south of Italy the S. E. scirocco is the most frequent. 17. Winds passing over land become dry and dense: over the sea, warm and light. 18. In some countries the dry winds produce dreadfully scorching effects, as the solanos in Arabia. Others, as in China, are inconvenient from their extreme moisture. Measures of Wind. Wren's weather clock. Birch. I. 341. Fi". Croun's anemometer. Bird'. \\. 257- Giegory on wind. Ph. tr. 1 J75. X. 307. The wind broke down «n obelise la feet high, 3 feet tbi«k. i56 CATALOGUE. METEOROLOGT, WINDS. Derham on sound. Ph. tr. XXVI. Leupold Tb. aerostat, t. 18, 20, 22. Plagos- copium et plagographium. t. 39) 48, 49- Anemometers. Bouvet's machine for measuring the force of the wind at sea. \]ach. A. VI. 153. D'onsen Bray's self registering anemometer. A. P. 1734. 123. Wilke's anemobaiometer. Schw. Abh. III. 85. Kraffr. C.Petr.XIIt. Lomonosow's anemometer. N. C. Petr. II. 128- Smealon. Ph. tr. 1759. 100. Plagoscope. 'Emerson's mech. F. 253. Gadoiin el Hiolte de anemometro novo. Abo, 17G0. Brice on the velocity of the wind. Ph. tr. 1766. 226. Found it 63 miles in an hour. BouguerManoeuvre des vaisseaux.l5 1 .Traite du navire. 359. One of the best anemometers. Noilet Art des experiences. III. 62. Zeiher's measurement of the wind. N. C. Petr. X. 302. Brunings on the velocity of the wind. Haarl. Verhand. XIV. 609. Lind's portable wind gage, with a table of the wind's force. Ph. tr. 1775. 353. An inverted siphon ; the connexion is formed by a narrow tube to prevent oscillations ; in frosty weather salt may be •dded to the water. Stedman on the degrees of wind required for machines. Ph. tr. 1777. 493. Heavy machines can work about ^ of the year. Van Swiuden sur le froid de I77(}. Lambert on observing the wind. A. Berl. 1777. 36. Dahlbcrg Description d'un anemometre. 4. Erf. 1781. Hoz. XVII. 438. Demenge's anemometer. Roz. XV. 433. Woltraann Theorie des hydrometrischea flUgels. Ximenes on the velocity of the wind. Goth. M. Ill.iii. 191. On Knowles's machine for weighing the force of the wind. 8. R. S. A wind fane with an index. Roz. XX. 416. Saussure's anemometer. R. S. Rochon Voyage a Madagascar. Par. 1791. A wind that went iso feet in i", or 102 miles in an how. Manch. M. 1V.602. Hutchinson measured the velocity of the wind by run- ning with a handkerchief, till it remained flat against a stick. Hermans windbeobachter. Freiberg. 1793. *Ludicke on the ancient denominations of the winds. Hind. Arch. III. 38. Benzeuberg on wind gages. Gilb. VIII. 240. Ph. M. XIII. 194. Garnerin went with Mr. Sowden 60 miles in ^of an hour* with Mr. Locker 9 miles in ^ of an hour. VVeatherbottle. bee Meteorological thermo- meters. CATALOGUE. — METEOROLOGT, WIND. ^57 Intensity of Wind. Comparison of Rouse's Table, published by Smeaton, with that of Lind. -i lid's Force on a square Feet Miles age. foot in pounds i IV. in 1" in ih. Character. by calculation. 0.005 1.43 1 Hardly perceptible. R. 0.020 2.93 2 Just percfptiblc. K. 0044 4.40 3 1 0.070 5.87 ♦ ■• Gentle winds. H. 0.123 7. as 5 J ' 0.025 0.130 A gentle wind. L. o.oso 0.260 Pleasant wind. L. 0.492 14.67 10 I'Isasant brisk gale. R. 0.10 0.521 I'resli breeze. I.. 1.107 22.00 15 Brisk gale. R. i.gos 29.34 20 Very brisk. R. 0.5 2.604 Brisk gale . L. 3.075 30.07 25 Very brisk. R. 4.429 44.01 30 High wind. R. 1.0 5.208 High wind. L. a.027 51.34 35 7.873 58.08 40 Very high. R. 9.963 66.01 45 Great storm. Derham. 2 10.416 Very high. I.. 12.300 73.35 50 Storm, or tempest. R. s 15.625 Storm. L. 17.715 88.02 60 Great storm. R. 4 20.833 Great storm. L. 21.435 96.82 66 Great storm. La Condamine. 5 26.041 Very great storm. L. 31.490 117.36 80 Hurricane. R. 0 31.250 Hurricane. L. 7 36.548 Great hurricane. L. t 41.667 V/ery great hurricane. L. 9 46.875 Most violent hurricane. L. 49.200 146.70 100 Hurricane that tears up trees and 10 52. 083 throws down birtldings. R. 11 57.293 5S.450 160.00 109 Observed by Rochon. 18 63.5 » Particular Observations of Storms. A storm at Oundle. Ph.tr. l6y3. XVII. 7 10. Scarburgh on a storm in Virginia. Ph. tr. 1697. XIX. 659. Southwell on the damage done to Portland island. Ph. tr. I697. XIX. 6o9. AVallis on a storm in Northamptonshire. Ph. tr. 1698. XX. 5. Fuller on a storm. Ph. tr. 1704. XXIV, 1530. Salt blown 10 or ao miles. VOL. II. Derham on a storm. Ph. tr. 1704. .Leciuvcnhoek on a storm. Ph. tr. 1704. XXIV. 1535. Bridcnian on a storm at Ipswich. Ph. tr. 1708. XXVI. 137. Nelson on a storm at Colchester. Ph. tr; 1708. XXVI. 140. Thoresby on a storm. Ph. tr. 1709- XXVI. 289. 1711. XXVIL S'.>0. 1722. XXXII. 101. Fortli on a storm. Ph. tr. 1736. XXXIX. 288. S N 458 CATALOGUE. — METKOKOIOG Y, TVIND. Degeer's exiilanation of a shower of insects. A. P. 1750. H. 30. Borlase on a storm. Ph. tr. 1753. 80. Miller on a storm in Cumberhind. Ph. tr. 1757. 194. ^ Griffith on a storm at Oxford. Ph. tr. 1765. 273. Particular kinds and effects of Wind. Waterspouts. See Atmospherical Electricity. Pliny xi. c. 103. Says, that waves are stilled by oil. Quoted by Cayallo. Boyle's relations about the bottom of the sea. Says, that storms have little effect at 20 feet below the surfsce of the sea, and probably none at 30 feet, Wright on a sand flood in Suffolk. Ph. tr. « 1668. III. 722. Templer on two hurricanes in Northampton- shire. Ph. tr. 1671. VI. 2156. Langford on hurricanes. Ph. tr. I698. XX. 407. Abr. II. 105. Thinks, that hurricanes are connected with the moon. Before a hurricane the skies appear turbulent, the sun looks red, although the hills are free from clouds or fogs. All hunicanes begin between N. and W. their course is gene- ■ rally opposite to that of the trade winds. Tornados come from several points. Bocanbrey. See Waterspouts. Derby on a whirlwind. Ph. tr. 1739. XLl. 229. Fuller on a hurricane in Huntingdonshire. Ph.tr. 1741. XLI. 851. Lord Lovell on a fiery whirlwind. Ph. tr. 1742. 183. A flash of fire, or lather more than a flash, with a jmell oftulfur. On a whirlwind. C. Bon. II. i. 453. Henry on a stream of wind. Ph. tr. 1753. XLII. Franklin and others on stilling waves by oil. Ph.tr. 1774.445. The success was partial only, as might be expected. Franklin. Am. tr. 11. Says, that one side of a piece of water, 3 feet deep and 10 miles wide, has been raised 10 feet by the wind, the other - being left bare. .Servieres on a singular wind. Roz. XIII. Suppl. 132. Dobson on the harmattan. Ph. tr. 1781. 46. An extremely dry wind in Africa, coming from the N. E. drying even potash. It generally brings a fog of soraeunknowTH nature. On the harmattan. Goth. M. I. iv.41. On the Samum. Goth. M. IV. iii. 38. Ducarla on winds cooled by evaporation. Roz. XXII. 432. Saussure on cold winds. Nich. I. 229. Gilb. III. 201. Dalton on bottom winds on Derwent lake. Meteor, obs. 52. No theory. A violent tornado in Berwickshire. Ph. M. IV. 219. Lamarck on a hurricane. Journ. Phys. LII. 377. Clos on partial winds. Journ. Phys. LIV. 259. Mitchell on a N. E. storm in America. Ph. M. XIII. 273. Franklin observed, that such storms generally begin I© leeward : they advance 100 miles in an hour. Currents of the Sea. Smith's conjecture respecting an inferior cur- rent in the Straights. Ph. tr. l684. XIV. 564. Says, that an inferior current was found in the Baltic so strong as to carry a boat against a superior current, by m«ans of a bucket sunk with a cannon ball. CATALOGUE. — METEOROLOGY, BAROMETERS. 459 Ph.tr. 1?00. XXII. 725. The entrance of ships into the Bristol channel, instead of the English, has been attributed to a current, but was sup- posed to be rather owing to a mistake of the variation. Vossius on currents. On the currents at the mouth of the Sliaighls. Ph.tr. 1724. XXXIII. igi. The current runs 2 miles an hour where the breadth is 5 leagues ; 1 mile, where it is 18 leagues : but at the sides there is a current outwards, especially on the south side. In 1712, Mr. L'aigle sunk a Dutch ship, laden with brandy and oil, in the middle between Taiiffa and Tangier ; a few days afterwards the sunk ship rose 4 leagues to the west- wards : the relater was at Gibraltar at the time, and saw the brandy brought from Tangier, and conversed with the cap- tain and other eye witnesses. The straights aie unfathom- able. D. Bernoulli on the cause of currents. A. P. Prix. vir. Belidor. Arch. hydr. II. ii. 19. Waiz on the current at the Straights. Schw. Abh. 1775. 28. ♦Peyssonnel on the currents in the West In- dies and elsewhere. Ph. tr. 1756. 624. More on the tides in the Straights. Ph. tr. 1762. 447. Maintains, that the currents run in contrary directions on the opposite coasts. *Blagden on the heat of the water in the gulf stream. Ph. tr. 1781. S34. The stream is about 20 leagues broad, and warmer thaa the neighbouring water. Its heat at its commencement in. the gulf of Florida is about 82°, and it loses 2° for every 3° of latitude in going northwards : it continues sensible ofF Nantucket. Franklin's maritime obseivations. Am. tr. II, 314. With a chart of the gulf stream, and an account of its heat. It extends to 4*" N. lat. FownalVs hydraulic and nautical observa- tions. 4. Lond. 1787. R. S. On the currents of the Atlantic. On the agitations of Derwent water. Ph.M. XI. 1G3. Possibly from gas under the mud. But whence are the " bottom winds .'" Rennel on a current prevailing to the west of Scilly. Ph. tr. 1793. 1S2. Supposed to come out of the bay of Biscay, towards the N. W. by W. and to have been collected by the westerly winds of the Atlantic. Robisonsays, that the current at the Straights sometimes runs outwards in the middle. ^m'ometers. Mercurial Barometers, and Baro> meters in general. Schotti technica curiosa. Wallis and Beale. Ph. tr. 1669. IV. 1113. Hooke's wheel barometer. Ph. tr. \C\Q5, 1666. 1.218. Hooke on a barometer with spirits. Ph. tr. 1686. XVI. 241 Traite des barometrcs. Amst. 1686. Derham on a svhcel barometer, with a rack. Ph.tr. 1698. XX. 41. Sturmii collegium experimentale. Gray's microscopic baromettr. Ph.tr. l69t{. XX. 176. Comparison of barometers of mercury and of water. A. P. I. 234. Amontons on barometers. A. P. II. 2.'). V704. 264,271. H. 1. 1705. 232. H. 16. 229. Huygens on a new barometer. A. P. X. 375. Journ. Sav. 1672. 139. Lahire on barometers. A. P. 1706. 432. Lahire's new barometer. A. P. 1708. 154. H. 3. Maraldi on an irregtilariiy of some barome- ters. A. P. 17O6. H. 1. . From the accidental introduction of a fluid. •Hallcy.l'h.ti. 1720. XXXI. Patrick's barometer is a tube sliglid.y tapered without k bulb, like Bernoulli's. 460 CATALOGUE. — METEOHOtOGY, BAROMETERS. Fahrenheit's new barometer. Ph. tr. 1724. XXXIII. 179. From the heat at Which water boils. Cavallo estimates, that such a barometer will determine the density within .1 of quicksilver. Self registering barometer. Lciipold. Th. acrostaticum. t. 23. Deslantles on a barometer which stood still for 7 montiis. A. P. 1726. H. 14. Saurin on the rectification of barometers. A. P. 1727.282. liulfinger on barometers. C. Petr. 1.317. Rowning's barometer. Ph. tr. 173". XXXVIII. 59. The barometer floats in a fluid, with a small prominent stem : it must therefore rise and fall very rapidly. Middleton. Fh.tr 173;l.XXXVIIl. 127. Commends Patrick's marine barometer. Beigliton onOrme's barometer. Ph. tr. 173S. XL. 248. A diagonal barometer, the mercury well boiled. Saul on the" vveatlier glass. 8. Lond. 1730. 1748. M. B. Ludolff's baror.ieter scale, corrected for tem- perattne. A. Berl. 1749.33. Richmann's barometers. N. C Petr. If. 181. Various nioies of reading off: some of them suspended siphons, nearly like Magellan's. Kollet's obervations on barometers. A. P. 17J1.275. H.23. Bourbon's poitable barometer. A. P. 1751. H. 173. Brisson's portable barometer. A. P. 1755. H. 14f). Rccueil de p ^ces sur Ic thermonietre et sur le barometre. 4. Basle, 1757. Act. Ilelv. JII.94. Sulzci's portable b.tvomcter. Act. Ilelv. III. 259. Boistissandeau's portable barometer. A. P. - 1758. H. 105. S€g»er Baromctruin navale. Gott. On correcting barometers for temperature. M. Taur. I. Fitzgerald's wheel barometer. Ph. tr. 1761. 146. 1770. 74. With friction wheels. Leslie on barometers. Schw. Abb. 1763. 89. Spry on a portable barometer. Ph. tr. 1765. 83. Dciuynes on the effect of tubes of different diameters. A. P. 1768 247. H. 10. On this subject see the properties of matter. Sho\vs the great effect of boiling the mercury. Portable barometers by Bourbon and Perica. A. P. 1771. H. 68. Perica's barometer. Roz. XVIII. 39I. Cigna on barometer tubes. Koz. Iiitr. II 462. Changeu.x on the barometer. Roz. IV'. 85. •|-Changeux's barometer. Roz. XXII. 387. With appendices which receive small portions of mercury, and mark the height. It is said, however, to be difficult oi impossible to empty these appendices. Deluc. Ph. tr. 1777. 401. Recommends siphon barometers as alone to be depended on. Ramsdeii's portable barometer. Ph. tr. 1777. 658. Described by Roy. Fonchy's statical barometer. A. P. 1780. 75. H. 1. ITdseler vom Ludolffischen barometer. 4. Holzmiindcn, 1780. Lamanon's barometer. Roz. XIX. 3. Magellan's barometer. Roz. XIX. 108, 194 257, 341. Magellan Bcschreibung neuer barometer. Leipz. 1782. R. L E. M. A. VI. Art. Procedes. 762. E. M. Physique. Art. Barometre. Moscati and Landriani on the improvement of the barometer. Soc. Ital. I. 225. Moscati Ricerche sopra il barometro. 4. R, S^ On the barometer. Roz. XXI. 436, 449. CATALOGUE. — METEOROLOGY, BAROSCOPES. 46 1 Lw uber die barometer. Leipz. 1782. R. I. Rosenthal Meteorologishe werkzeuge. Hurler's new baroiiieier. iloz. XXIX. 346. Portable. Acliard on barometrical measures. A. Berl. 1786. 3. M'Guire's portable barometer. Ir. tr. 1787. 1.41. M'Guire's self registering barometer. Ir. tr. IV. 141. .idfrfams on the barometer. London, 1790. Adams's leot IV. 430. When a tube has once had mercury boiled in it, is is found, that even cold mercury will often fill it completely. Cotte on the effect ot temperature on the ba- rometer. Roz. XLIl. 441. Austin's portable barometer. Ir. tr. IV. 99. Barton's barometer with a wheel inde.\. Manth. M.IV. 547- Hamilton's portable barometer. Ir. tr. V. 95. Bfylr'age zur verferligung des barometers. Frankf. J 795. Humboldt'^s portable barometer. Journ. Phys. XLVII. (IV.) 468. Ph. M. IV. 304. Cont^'s portable barometer. B. Soc. Phih n. 14. Prony's barometrical balance. B. Soc. Phil. n. 20. Guerin on a portable barometer. Journ. Phys. LIU. 444. Fh. iVl.XI. 362. Klugel on Magellan's barometer. Hind. Arch. III. 182. Per|>etual motion by barometers. Nich. III. 126. Keith's self registering barometer. Ed. tr. IV. 209. "Von Arnim on barometers by Prony, Conte, Humboldt, Godekiiig, Brander, and Voigt. Gilb. 11.311. Some statical, others portable. Voigt on Haas's barometer. Gilb. IV. 456. Mullei's barometer. Gilb. V. 17- Corrected for temperature. R 'dig's sim,>le barometer. Gilb. VI. 445-. Wilson on increasing the sensibility of the ba- rometer. Nich. 8. III. 21. Schmidt on the double biuometer of Hny- gens. Gilb. XlV. 199. Recommends it strongly, and makes it correct itself for tompeiaturc. Without such a correction the eipansion and the vapour of the spirits would produce great irregularity. Maigne's portable barometer. Gilb. XV. 463. A barometrical perpetual motion. Nich. IX. 212. Rees's Cyclop. III. Plates. Pneumatics. When the mouth of a barometer is much contracted, a friction is produced. Some preserve the surface of the re- servoir level, by letting it spread on a horizontal surface : and if the surface is large enough, the method must be a good one, but the mercury ought not to be confined to a height less than one seventh of an inch. The specific gravity of mercury, once distilled, is frora 13.55 to 13.57, but Boerhaave foundit after 511 distillations 14.11. The density of the mercury usually employed is 13.6. Roy found that the expansion of 30 inches of mercury is the barometer, including the effects of its vapour, from 32" to 91°, was .1922. The results of his experiments are expressed very nearly by the formula e^: .00011 182 / — .000 000 0913/* — .000 000 000 OjJ^ ^ which gives .1926 for 92°. Some authors assert, that Roy's results are a little too great : and if any dependence can be placod on Dalton's analogies, the effect of the vapour must be extremely incon- siderable. Statical Baroscopes, Air Barome- ters and Manometers. Schotti technica curio^a. I. c. GI. Boyle's statical baroscope. Ph. tr. 1660 — 6. I. 231. Hooke on a statical barometer. Birch. III. 384, 387. *Hooke's marine barometer. Ph. tr. 1701, XXII. 791. 462 CATALOGUE. — METEOROLOGY, VARIATrONS OF THE BAROMETEU. Described and much commended by Ilalley. With a spi- rit thermometer and a sliding scale. • Chapelle on a barometrical fish. A. P. I. 274. Caswell's baroscope. Ph. tr. 1704. XXIV. 1597. A floating manometer. Amontons's marine barometer without mer- cury. A. P. 1705. 49. H. 1. Varignon's manometer. A. P. 1705. SOO H. 26. Manometers. Leupold. Th. aerostat, t. 9. Zeiher's marine barometer. N. C. Petr. VIII, 274. Measuring the force by a spring. Fouchy's dasymeter. A. P. 1780. 73. Roz. XXV. 345. A beam resting on a cun'ed surface, answering the pur- pose of Guerike's manometer, which was a thin ball sup- ported by a bent lever balance ; but perhaps no improve- ment. Manometer. E. M. A. VI. 734. Gerstner's air balance. Gren. IV. 172. Kramp's manometer. Hind. Arch. III. 233. Like Caswell's, an open hemisphere, to be depressed to a given mark, by weights put in a dish. •fSay's areometer, with Arnim's remarks. Gilb. II. 230. Journ. Phys. LVI. 366. Berger brought portions of air from different heights in well stopped bottles, and compared the quantities of mer- cury that was forced into them. But the method does not appear to be very accurate. Berard Melanges. l63. Davy on the manometer. Journ. R. I., I. INich. 8. IV. 32. Gilb. XVI. 105. On eudiometry and manometry. Gilb. XV. 61. Variations of the Barometer in general. *Beaieon the barometer. Ph. tr. 1665— G. I. 153, 163. Boyle on the barometer. Ph. tr. l665 — 6. I. 181. Halley. Ph. tr. 1686. XVI. 104. The mercury is commonly low in calm weather before rain, higher in serene settled weather ; lowest in high winds, even without rain ; highest in E. and N. E. winds ; high in calm frosty weather : it rises fast after storms of wind ; it varies most in high latitudes, within the tropics very little. It has been observed by others, that N. and N. E. winds are heavier than S. and S. W., as being colder. Lister on the barometer. Ph. tr. 1 684. XIV. 790. Leibnitz on the cause of the changes. A. P. 1711. H. 3. Leibnitz invented a machine to illustrate the variations of the barometer by the effects of the fall of a body upon the equilibrium of a balance. Desaguliers on the variation of the barome- ter. Ph. tr. 1717. XXX. 570. In answer to Leibnitz. Gersten de mutationibus barometri. 8. Frankf. 1733. M. B. Ace. Ph. tr. 1733. XXXVin.43. Beighton's remarks on the barometer. Ph. tr. 1738. XL. 248. Hollmannus de difterentiis altitudinum baro- metri. Ph.tr. 1742. XLIL 116. Hollmannus de barometrorum cum tempesta- tum mutationibus consensu. Ph.tr. 1749. XLVI. 101. On the various heights of the barometer. M. Taur. I. C. Bon. II. i. 307, 353. Fourcroy de Ramecourt on oscillationsof the barometer. A. P. 1768. H. 36. Beguelin. A. Berl. 1773.47. 1774.119. Montaigne. Roz. II. 26l. Changeux. Roz. VII. 459. Deluc Idees. II. 590. Modifications. I. iii. 223. Saussure Hygromelrie. §..294. Voyti^es. IV. Lambert on the density of the air. Ro/.. XVIIL 126. CATALOGUE. — SIETEOROLOOY, WEIGHT OF THE ATMOSPHERE. 463 *Ephemeiides Soc. Palat, Toalcio on a variation of die barometer. Roz. XX. 83. Dangos on tiie periodical variation of the ba- rometer. Roz. XXX. 260. Kirvvan. Ir. tr. 1788. 11.43. Roz. XXXIX. 100. Legentil. Vo^-age. I. 526. The barometer does not vary at Pondicherry. Fontana dalle altezze barpiiietriche saggio analitico. 4. R. S. Fontana on the mass of the atmosphere. Ac. Sienn. V. 76. Cotte on the variations of the barometer in different places. Roz. XLI. 54. XLII. 340. At Bourdeaux and at Montmorency, 12 changes out of 19 were the same wa) , 7 the contrary way. Cotte on the barometer. Ph. M. I. 208. Franceschini on the height of the barome- ter. Soc. Ital. V. 294. As. Res. IV. 195. Ed tr. IV. H. 25. Balfour found the barometer in April, at Calcutta, rise a little from 6 in the morning to lo, then fall till 6, rise till 10, and fall till 6 again. The difference is sometimes .1, but generally less than .05, depending probably on some reci- procation of winds. Due la Chapelle on the diurna;! variations of the barometer. B. Soc. Phil. n. 21. Gilb. II. 361. Pugh sur la pesanteur de I'atmosphere. 4. Rouen, 1800. R. S. Biich on the variations of the barometer. Journ. Phys. XLIX. 85. Gilb. V. 10. Humboldt on the barometer in South Ame- rica. Ph. M. IX. Q.85. From g in the morning it falls till 4, then rises till 11, falls till J past 4, and rises till g again, in all weathers. ZachMon. corr. III. 6Q, 543. Burckhardt finds the mean height of the barometer greater by .23 when the wind is E. than when S. Accountof the diurnal variations of the baro- nictefj from Peyrouse's Voyages. Ed. tr. V. 3. Dalton. Manch..M. V. 666. Thinks that the same barometrical variations generally extend over all Europe without a day's difference. But Cotte's observations seem to be inconsistent with this opi- nion. In these climates, the barometer is generally lowest at noon and at midnight. The mean height is greatest at the equinoxes, but greater in summer than in winter. Cavallo. The usual scale of the barometer is, 31 , very dry or hard frost; 30.5, settled fair or frost ; 30, fair or frost ; 29. 5, changeable ; 29, rain or snow ; 28.5, much rain or snow ; 28, stormy. Any rapid change is said to foretel bad weather. The diurnal variation of the barometer has been found to be more sensible at sea than on shore, especially in inland places. It is possible that currents of air from heat may be concerned in its production. Particular Barometrical Obser- vations. Plot on the weather at Oxford, with a baro- metrical diagram. Ph. tr. 1685. XV. 930. Beeston on the barometer in Jamaica. Ph. tr. 1696. XIX. 225. Variation only .3. Cunningham on the barometer in China. Pb. tr. 1699. XXI. 323. Variation .0 or .7. Latitude 24° 20'. Toaldo novae tabulae barometri aestusque maris. 4. R. S. Roxburgh. Ph. tr. 1778. 180. At Fort St. George. Variation .3. Fleuriaii on the mean height of the barome- ter at the sea side. Journ. Phys. XLVII. (IV.) 158. Variation at Columbo. 36. Ph. M. X. 172. 28 ia^.lFr. or .7644.™ Manch. M. V. The surface of the mercury moves annually about 8d inches at Kendal ; in London much lees. 454 CATALOGUE. METEOROLOGY, EVAPORATION. Mean Height of the Barometer, from Erxle- only isa; millions. But the experiment c„ evaporation ivican 111.1^,111. ui iiii. . ^^^ ^^^^ ^^ ^ ^^_.j^^^ j^g ^^j,,l for jhe comparison. ben and others. ,. » tj iv ou; Lanire. A. r. JA.3I5. Height once observed at Middlewich.Manch. M. V. 31.00 Hawksbee on the absorption of air by water. Greatest observed height. Shuckb. - - 30-957 Ph. tr. 1707. XXV. 2412. Upsal- - - " l°'\l Leibnitz and others on vapours. M.Berol, ^.Carolina - - * 30.09 ^ it ■■ o^ Mean level of the sea. Fleuriau - - 30.095 ] 7 10. 1. 123. Op. II. U. 82. Atlantic. Burckhardt - - " 3o°9 Dcsaguliers on the rise of vapours. Ph. tr. Mediterranean. Burckhardt ^ - 30"* 1729. XXXVI. 6. Mean in England and in Italy. Shuckb. - 30.04 ^^^^^ ^^^ specific gravity of steam ^feo f™™ observations Mean level of the sea, as usually estimated - 30.00 ^y jjeighton and himself: or ^yW from Nieuwentwy t's ex- , Tort St. George - - " 30.00 p„iments on the eolipilc: hence infers, that vapour in sura- Columbo. Ph. M. X. - - - 29.98 mej heat should be about 5J55 as dense as water, and should Dover - - " ^°^° therefore float in air. But from his own experiments, the London. R. S. - - ■ ^S'^' specific gravity should be above five times as great. Repcr- «1 feet above the level of low water. The mean of ^^^^ ^^ ^^^^^ any yea. scarcely differing 0.5. DesaQuherS. Ph. tr. 1742. XLII. 140. - - , - • - 29. SI -^ Leyaen . - - Thinks, that vapour maybe raised by an electric attraction Kendal - - - ' - - 29.80 in the air. Padua ^^-^^ TT I ir c^ ^ Manama =9 80 Hales. Veg. Stat. „ ^ „ . .>n 60 Makes the annual evaporation from the earth in England Porto bello . . - - - ^y.ou ... _ on. 7 4 clinches. Liverpool - - -" ' * "i „ i • 1 • Turin . . . - - 29.62 NoUet on the vapour found m the air pump. Petersburg - • - " 29.57 A. P. 1740. 243. Gottingen - - - " ^^•^'' Wallerius and Ericson's experiments. Schw. ^"'" - ' ' ' '"'" Abh. 1740. 27. 1746. 3, 153. 1747. 235, Bile '*•** Nuremberg - - - - "'"^ 272. Zurich - - - - 28.29 Kratzemtein von diinsten und dampten. 8. Clausthal - - - - 27-89 j^^^jj^^ j^^^^ t^hur - - - " '^'•^* Kra/f? de vapoium generatione. 4f Tubing. M.St.Gothard - . - - 23.0s -if * a ■, - - - 21-37 1745. Eichmann. C. Petr. XIV. 273. N. C. Petr. , • 7 T- 4- I- 198. II. 121. Atmospherical ±.VapOratlOn, or Thinks the evaporation nearly proportionate to the tem- ' Ilygrology. perature. Leroy on the suspension of water. A. P. 1751. Simple Evaporation. See Effects of Heat. 48 1. Halley on the evaporation of the sea. Ph. tr. Eeles. Ph. tr. 1755. 124. 1686 XVI. 368. Against the existence of vesicular vapour ; in favour of Halley on the evaporation in 1693. Ph. tr. electrical atmospheres. 1694 XVIII 183 Franklin's observations, read 1756.Ph.tr. In a place not exposed, 8 inches. Calculates, that the 1765.182. evaix>ration of the Mediterranean in a summer's day, is Thinks that either water or dust may be supported in the i280 million tuns, and that the 9 principal rivers furnish air by adhesion: that evaporation is a solutum in air. CATALOGUE. METEOROLOGY, EVAPORATIOK, 465 Darwin's remarks on Eeles's opinions. Ph. tr. 1757. 240. Supposes that the particles of vapour are real steam, but incapable of communicating their heat, perhaps on account •f some motion. Hamilton on evaporation. Pli. tr. 1765. 146. Objects both to vesicles and to fixed fire, and maintains the doctrine of solution in air. Lambert on hygrometry, with experiments on evaporation. A. Berl. 1769. 68. 1772. 103. Roz. XVIIF. 126. Makes the quantity of vapour as the square of the den- sity. Lord Karnes on evaporation. Ed. ess. IIL 80. Cigna on evaporation. Roz. Intr. IL 232. Dobson on evaporation. Ph. tr. 1777.244. The mean annual evaporation, in an exposed situation at Liverpool, was 38.79 inches ; the rain 37.43. Fontana on evaporation in quiescent air. Roz. XII 1.22. +Servieres on the refraction of moist air. Roz. XIII. Suppl. 130. On a phenomenon respecting ice. Roz.XIII. Suppl. 252. Dobson on the harmattan. Ph. tr. 1781. 46. The usual annual evaporation at Whydah is 04 Inches ; when the harmattan blows, it is at the rate of 133. Achard on the cause of vapours. Rozior. XV, •163. *Saussure Essai sur I'hj'gromctrie, Saussure. Roz. XXXVI. 193. Eason on the ascent of vapours. Manch. Mem. I. 395. Attributes their suspension to electricity. Williams on evaporation. Am. tr. II. 1 18. Monge. A. P. 1787. Denies the existence of vesicular vapour, Werner on evaporation. Goth. M. VI. i. 111. Against Deluc. Hube liber die ausdlinstung. 8. Leipz. I790, Against Halley. VOL. II. Deluc on vapours and rain. Roz. XXXVI. 276. *Deluc on evaporation. Ph. tr. 1792. 400. Maintains, that vapour exists in air precisely as in a va- cuum, the distance at which its particles can remain with- out uniting with each other being determined only by the temperature, and not being affected by the interposition of air. Deluc finds that the hygrometer stands at the same height in a moist vacuum as in moist air. VVistar oa evaporation in cold air. Am. tr. 111.125. IV. 72. Repeit. XIV. 375. Volta in Gren. III. 479- Found by many experiments, that the presence of air is indiflferent to the quantity of vapour. Aug. 1798. Gilb. XII. 394. Kirwah on the variations of the atmosphere. Ir. tr. Vill. Extr. Ph. M. XIV. 143. Nich. 8. V. 287- Contains much valuable matter, but the theory is com- plicated and improbable. Heller on the effect of light in evaporation. Gilb. IV. 210. Thinks it very considerable. Effect of light in the sublimation of phospho- rus. Ph. M.XI.89. Von Arnim on the principles of hygrology and hygrometry. Gilb. IV. 308. Dalton on rain ,ind evaporation. Manch. M. V. 346. Gilb. XV. 121. Compared the rain with the quantity of water that ran out of a vessel of earth three feet deep, sunk into the ground. At Manchester, where the rain was 33.5 inches, the evapora- tion was 25 inches of rain, besides 5 allowed for dew. But the rain was here prevented from running off the surface of the earth, and there were probably some other causes that increased the evaporation. . From the mean of many ac- counts of rain, which appears to be about 31 inches for all England and Wales ; adding 5 inches for dew, and deduct- ing 13 for the water carried offby rivers, we have 23 inches for the mean evaporation from the surface of England and Wales. Dalton on the constitution of mixed gases, and on evaporation. Manch. M. V. 535. Gilb. XII. .085. Nich. VI. 257. VII. 5. Maintains, that there is no mutual repulsion betv/ecn the particles of different gases. 3o 466 CATALOGUE. — METEOROLOOr, EVAPORATION. Dalton's elucidations of his theory of mixed gases. Nich. 8. III. 267. Ph. M. XIV. ' 169. Gilb. Xni. 438. Nich.Vrn. 145. .Dalton's answer to Gough. Nicii. IX. 89, 2S9. Biot on Dalton's theory. B. See. Phil. n. 72. Quotes Laplace as ha-ving compared Dalton's theory with Saussure's experiments ; btjt Dalton had done the same. The comparison is however still imperfect. Parrot's theory. Gilb. X. ii. XIII. 244. - Professor Parrot considers the moisture contained in air as existing in two distinct states, of chemical and of physical vapour: he thinks the chemical vapour is sustained merely by the oxygen gas contained in the air, and that it is preci- pitated in consequence of the diminution of the oxygen ; and the physical vapour he supposes to be merely interposed be- tween the interstices of the elastic particles of air, and re- .tiined-in its situation by heat : that the chemical solution of water orice resembles oxidation, but that no physical eva- poration can take place under the freezing point. Mr. Par- rot builds his theory principally on eudiometrical experi- ments with phosphorus, which are attended with a copious precipitation, while the absorption of oxygen seems also to be much accelerated by the presence of water ; but these experiments do not appear to be, by any means, decisive in favour of Mr. Parrot's theory. The same paper contains a proposal for inoculating the clouds with thunder and light- ning, by projecting a bomb to a sufficient height. Parrot's remarks on Dalton. Gilb. XVII. 82* Wrede's remarks on Parrot. Gilb. X. 488. XII. 319. Bockmann's remarks on Parrot. Gilb. XI- 66. Mitchill on vapour from cold. Gilb. XI. 474. Sea water smokes when 25» warniet th«n the air: rain water when j 9°. Desormes on the water contained in gases. Gilb. XIII. 141. Finds the quantity independent of the nature of the gas, agreeing with Deluc, Volta, and Dalton. Henry. Ph. tr. 1803. 29. 2~4. Fmds, that equal volumes of the same gas, under differ- ent pressures, are absorbed by water. See Springs. Henry on Dalton's theory of gases. Nich. Vlll. 297. IX. 126. Remarks on Dalton. Berthollet's chemical statics. I. 346. Haiiy Traite de physique. Adopts Dalton's calculations, but reduces his theory to the ideas which were originally Deluc's. Accum's apparatus for drying. Nich.VI.212. Gough on the solution of water in the at- mosphere. Nich. VIII. 243. Gough on Dalton's theory. Nich. IX. 52 107, 160. " ' The few experiments, adduced as objections to Dalton'* theory, agree, in fact, very accurately with it. Remarks on the Quantity of Moisture contained in Air. If we examined the progression of M. Saussure's resultt alone, we might conclude, that the presence rfair increases the capacity of any space for vapour, nearly in the subdu- plicate rario of the density, and that air of the usual density enables it to contain five times as much vapour as could re- main in it when free from air. But it agrees almost as well with these experiments, and much better with those of Schtnidt, to suppose that the presence of air increases the capacity of a space for moisture in the simple ratio of its den- sity, enabling it to contain, under the common pressure, about twice as much as it could contain in its total absence. These experiments ought to be repeated, but until they are confirmed, they scarcely authorise us to reject the ppl- nion of Deluc. CATALOGUE. — METEOROLOGY, EVAPORATl'ON. 46r Comparison of ihe expansion of drj' Air, alnd Air saturated witli moisture, from Schmidt. Tlie Barometer being at 29.84. Elasticity of steam Temperature. Dry Air. Moist Air. Elasticity of vapour. at the same tem- perature. 32° 1.0000 34i 1.0045 1.010(5 .IB .10 50 1.0357 1.04B5 .37 .30 59 1.0538 1.07§5 .SO .51 08 1.0715 1.11^2 1.13 .08 77 1.0893 1.1528 1.05 .95 80 1.1072 1.1980 2.28 1.20 gs 1.1251 1.3771 5.40 i.ao 101 1.1430 1.8050 11.90 2.20 loei 1.1474 1.P834 13.60 3.S5 •212 1.3574 It is however very improbable that the expansion of moist air in high temperatures was so great as Schmidt makes it, and in the lower temperatures his experiments agree witli Deluc and Dalton. Dalton says, that he found, by numerous experiments, that the expansion of moist air was exactly proportional to the effect of the elasticity of the vapour. Still, however, the best experiments on the speci- fic grayity of steam make it not more than -^^ as dense as water, and the specific gravity of vapour at 212°, appears from the experiments of Saussure, Schmidt, and Dalton to be about -pLj, or about -^ at 50°, so that it is difficult to re- concile these results with the opinion of the perfect inde- pendence of vapour ; unless we suppose steam to be much more expanded by heat than air. Pictet found the specific gravity of pure steam, at the common temperature of the atmosphere, about yj^j. Chi Evaporation. Dalton asserts, that the quantity of any liquid, that evapo- rates in agiven time in the open air, is directly as the force of vapour at the same temperature, deducting only the pressure of the vapour of the same kind which is already in the at- mosphere ; that the atmosphere does not contribute to pre- serve liquidity, that it only retards evaporation a little, but does not diminish its quantity ; that the evaporation of alco- hol and ether requires no deduction for pressure. He found the evaporation of a disc, 3 J inches in diameter, from ao to 45 grains in a minute, at 212'' ; in a high wind it would probably have be«n 60 grains ; at 180°, from 18 to 22 ; at 152°, from 8 to 12 grains, being always proportional to the •lasticity of steam at the given temperature. Hence he calculates a table for a disc of 6 inches, making 120,154, and 189 grains the least, mean, and greatest evapo- ration in a minute, at 212° ; taking 35, 45, and 55 as the evaporation, under similar circumstances, from his disc of 3| inches. But it is much simpler and more convenient t» estimate the depth of the water evaporated in a day, aiyl i* happens that the column of mercury, equivalent to the elas- ticity of the vapour, expresses accurately enough the mean evaporation in 24 hours: for 45 X 60 X 24 := 64800 grains, or 256.6 cubic inches, which would make a cylin. dcr 30.9 inches in height, on a base scinches in diameter' and this differs only Jj from the height of the column of rrtercury : we may therefore assume, that the mean daily evaporation is equal to the tabular number expressing the elasticity of the vapour ; sometimes exceeding it or falling short of it about one fourth ; and we may readily allow for the effect of the moisture of the atmosphere, by deducting the number corresponding to the temperature of deposition. Mr. Dalton says, that the annual evaporation at Manches- ter, from avessel kept full, was 44.4, from the ground 23.5 : that the point of deposition for any time may be calculated from the evaporation, when the temperature is given. In July 1800 and 1301, the mean point of deposition was 53", the highest 62°; in August 1800, the mean about 55°: 1801, 54.5°; in September 1301, the mean was 54°; in December, the highest 44", the lowest is". We may also infer, that at Liverpool, where Dr. Dobson found the annual evaporation from water 36.78 inches, » that is, a tenth of an inch daily ; the mean temperature be- ing, according to Dr. Dobson, 54°, but more probably somewhat lower ; the mean temperature at which the air began to deposit its moisture was about 7" lower than that of the air; or considering the exposed situation of the vessel, perhaps nor more than 6", so that the mean temperature of deposition wag 47 or 48°. Mr. Dalton says, that the point of saturation is generally trom I to 10° below the mean heat of the 24 hours. Mr. Dalton found that ice lost, at 32", 33 grains in ami. 458 CATALOGUE. — METEOROLOGY, HYGROMETERS. nute, correspon^^ng to vaponr deposited at 2 1 .5 : it was ac- tually at 22°. Gilbert says, that Schmidt's experiments agree perfectly with Dalton's theory. Gilb. XV. 25- Lambert's experiments, reduced to English measure, give 5.95,5.53, 3.51, 1.53, asd .77, at 169°, 167°, 142°, m". and 84° ; instead of 11.83, 11.25, 6.19, 2.68, and 1.14; which are nearly in the same proportion, although almost twice as great. Hygrometers. A hygrometer of transverse deal, turning a wheel. Ph. tr. 1676. XI. 647i Conier's hygroscopes. Ph.tr. 1670'. XL 715. Both of deal. '"Gould on oil of vitriol used as a hygroscope. Ph. tr. 1684. XIV. 496. ■ Also on a hygroscope of lute string. Molyneux on a hygroscope. Ph. tr. 1685. XV. 1032. Of whipcord. Amontons's hygrometer. A. P. II. 13. Lahire on the abbreviation of moist ropes. A. P. IX. 157. Leupold. Th. Aerostat. 1. 13. . 17. Arderon's hygroscope. Ph.tr. 1746. XLIV. 95. A sponge counterpoised. Arderon on the weathercord. Ph. tr. 1746. XLIV. 169. A whipcord a little inflected, drawing transversely as it straightens itself. Arderon's hygrometer. Ph. tr. 1646. XLIV. 184. Of cross grained deal, acting on levers. Ferguson's hygrometer. Ph. tr. 1764. 259. A transverse slip of white deal, with cords and pullies : it requires to be changed every four years. Lambert's essay on hygrometry. A. Berl. 1769. 68. 1772. 65. With diagrams. Smeaton's hygrometer. Ph. tr. 1771, 198. A cord impregnated with salt. Deluc's hygrometer. Ph.tr. 1773,404. A tube of ivoiy filled with mercury. Deluc Idees sur la m^teorologie. I. Deluc on the hygrometer. Roz. XXX. 437. XXXII. J 32. *Deluc on hygrometry. Ph. tr. 1791. 1. 389. A transverse slip of whalebone, held by pincers, attached at one end to a thin flattened wire of silver gilt, of which the other end is fixed to a weak spring. Lowitz's hygrometer. Gott. Mag. III. 491, Senebieron his hygrometer. Roz. XI. 421. Inochodzow's hygrometer, A. Petr. II. ii. 193. A schistus which is weighed. Copineau on the hygrometer. Roz. XV. 384. *Saussure Essai sur I'hygronietrie. 8. Neuch, 1783. R. I. Saussure's defence of the hair hygrometer, Roz. XXXII. 24, 98. Says, that Deluc's hygrometer is irregular : objects to Chiminello's quill with mercury, and to Jean Baptiste's ribband. Schreber on the oculus mundi. Naturforsch. xix. Halle, 1783. Gedda sur les hygromStres. Copenh. 1784. Cazalet on Casbois's hygrometer of the silk worm's intestine, Roz. XXIX, 344, Seems to have little advantage. Achard. A, Berl. 1786. 3, Denies that hygrometers indicate the true quantity of va- pour not precipitated. Franklin on a hygrometer of mahogany. Am. tr. II. 51. Kriinitz Encyclopadie, XXVII, Sir B. Thompson on the moisture absorbed by various substances. Ph.tr. 1787.240. Re- pert. IV. 247. The weight of wool was increased from 1 to 1.084 in 4« hours, in 72 to 1.IS3, the thermometer being at 45°, and the air saturated with moisture : of other substances exa- mined, the most absorbent was fur, then eider down, silk linen, and cotton : the cotton was increased to 1 .043 and 1.089. Hence woollen clothes next the skin are recom- mended. Silver wire acquires no additional weight. Ricke's hygrometer, Gren, I, i. 150, Pilgrams wetterkunde. CATAtOGUE. — MET EORO LOGY, II VGROMETERS, 469 Sflge on Ulcke's hygrometer. Roz. XXXIV. 58. Geoffrey on the hair hygrometer. Roz. XXXIV. 255. Attributes to it some irregularities. Volta on the use of the electrometer in hygro- nietrv. Soc. Ifal. V. 551. Ascertaining the velocity of the dissipation of electricity. Leslie's hyjirometer. Nich. UI. 401. Gilb. V. 23(5. X. no. Leslie on moisture absorbed by earths and stones. Glib. XII. 114. Says, that rarefaction lessens the action considerably. Heated flannel dries the air very effectually. Hofhheimer's hygrometer. Ph. M. 1.36?. Weighing a plate of glass, to which the moisture is sup- posed to adhere. Ludicke on hygrometers. Gilb. I. 282. II. 70. V. 70. X. no. Mr. Ludicke considers the result of his experiments as very favourable to Mr. Leslie's hygrometer. He proposes to improve it, by employing two mercurial thermometers with very fine tubes, fixed to the same support, and having their bulbs very near together ; one of the tubes is to be curved; and the bulb, being first blown larger than is necessary, is to have a portion depressed, so as to form a dish for the re- ception of water, which it will supply for many hours, without the interruption occasioned by renewing it: the eold produced by the evaporation is then considered as the measure of the dryness of the air. It would however be «asy to supply the quantity of water necessary, without giv- ing the bulb a form so peculiar. The hair hygrometer ap- peared, in the comparison, to indicate the maximum of moisture too early. Voigl's hygrometer, of a quill cut spirally. Gilb. III. 126. Quill hygrometer. Gilb. IV. 477. Zylius on the hygrometer, and in answer to remarks. Gilb. V. 257. VIII. 342, Remarks in answer to Zylius. Gilb. VI. 236. - Forster's hygrometer. Ph. M. XI. I67. From the beard of the avena sterilis. Dalton. Manch. M. V. Parrot on hygrometry. Gilb. XIII. 244. Bockmann's comparison of the hygrometers of Leslie, Saussure, and Deluc. Gilb. XV. 355. The wind affects Leslie's hygrometer very materially : the others do not agree well with each other. Deluc's seems to be a Tittle less depressed by an elevation of temperature than Saussure's. On the Indications of Hygrometers. Deluc observes, that when the grass is covered with dew, the air above it is often far from the state of extreme mois- ture, the hygrometer standing at 50" or 55" ; that extreme moisture, as indicated by the hygrometer, seldom, but sometimes, exists in the open transparent air; that at great heights the air is very dry, excepting the clouds. The mean moisture in London, as indicated by Deluc's hygro- meter, is 79", or -,'5^ of the extreme moisture. The whole expansion of the vv-halebone is about |. Deluc says, that substances immersed in alcohol and ether were expanded almost as much as when immersed in water. Ph. tr. 1791. Saussure found that no vapours except that of- water affected his hygrometer. Hygrometrie. Deluc produces extreme dryness in a vessel accurately closed, with hot lime in it ; extreme moisture by a wire cage covered with cloth, having a reservoir at the top to keep it moist, which is enclosed in a jar over water : here the whalebone hygrometer rises slowly but certainly to 100°, the hair falls to 98°. Slips of substances cut across the grain, preserve a march more consistent with the increase of weight than threads. Glass becomes wet when Deluc's hygrometer stands at 80°, metals and other substances, at 100°. Cnventry's hygro- meter, of paper weighed, is a very delicate test. According to Mr. Deluc, air in a vessel with water does not attain the maximum of moisture, except in very low temperatures ; the whalebone hyi^rometer usually standing at 80", Saussure's at 100°. There is generally an atmo- sphere of extreme moismre an inch or two above the surface of the water in a close vessel, the glass becoming clouded by the slightest change of temperature. Deluc found the expansion of a hair corresponding to the degrees of his hygrometer thus : 15.6 at 5° 88.8 at 55' 09.4 . — . 10 91.6 — 60 40.9 — 15 93.8 — 65 50.5 20 95.6 — 70 59.2 — 25 97.2 — 75 68.8 — 30 98.0 — 80 73.0 — S5 1000 — 85 ?8.3 — 40 100.0 — 90 82.1 — 45 99.3 — 95 86.1 — 50 98.3 — 100 Bockmann found 10° of Deluc correspond to about 3S' 470 CATALOGUE. — METEOROtOG V, HYGIiOMETER*, of Saussure, 20° to 54° ; 30° to 65°; 40° to 80° ; 45° to 86° ; in atmospherical observations : the greatest heights were Deluc's 56°, when Saussure's was 85° ; and Saussure's 00°, T.hen Deluc's was 4 8°. Height of Deluc's hygrometer in London, from the Journal of the R. S. Lowest. Hiehest. Mean. 1794 40° 85° 1793 43 85 1794 45 89 C6.8" 1795 47 Oi 71.8 1796 59 90 74.6 1797 60 01 79.3 1798 30 05 J799 45 9i 1800 41 95 69-2 (not " 79-2") 1801 50 95 72.5 1802 55 94 76.3 1803 58 99 79.8 It is observable, that in this table the mean height of the hygrometer was gradually increased 10° or more in three years, from 1794 to 1797, and thatthesame happened from 1800 to 1803, the instrument having been repaired, and a new slip probably inserted. It would therefore he advise- able that every hygrometer shouhi be annually submitted to the tests of extreme dryness and extreme moisture, other- wise an allowance must be made for the expansion probably produced by exposure to the air, which appears to amount, in the beginning at least, to three or four degrees annually. If we apply this correction, the mean heights will become 66.8, 67.8, 66.6, 67.2, and 69.2, 68.5, 68.3, 67.8, for the eight years that are compared, and the mean of these is 67.8. We may therefore call the mean height of the hygro- meter in London 68°, or at most 70", and not 79". Accord- ing to Deluc's comparison, this corresponds to 95.6° of Saussure's hair hygrometer ; but it does not seem probable that Saussure's hygrometer would make the mean moisture of London so near the extreme, much less that it would stand above 97°, which would be inferred from 79" of Deluc. Mr. Deluc seems to consider the weight acquired by any hygrometrical substance as the most natural test of the de- gree of moisture ; but it does not appear that this is a very correct criterion ; theproportions may vary greatly in different substances, and they certainly do vary greatly with the time of exposure. The true natural scale appears to be that which expresses the proportion of moisture in any space to that which would so far saturate it as to begin to be depo- sited : and Saussure's experiments show, that his hygrome- ter indicates this proportion inasimilar manner at two differ- ent temperatures, yet not correctly with respect to either, except in particular parts of the scale. Deluc's hygrometer indicates the proportion pretty accurately through half the scale, but the mean between the height of his hygrometer andthat of Saussure, agrees tolerably well throughout. It is obvious, that the height of the natural hygrotjieter may be found directly on Mr. Dalton's principles, by ascertaining the point of deposition, since it is expressed by the elasticity of vapour at the point of deposition divided by the elasticity at the actual temperature, or by the seventh power of the quotient of the temperatures reckoned from a point 133" be- low the zero of Fahrenheit; and, from the height of the na- tural hygrometer, we may deduce the depression necessary to produce a precipitation, by multiplying its seventh root by tlie temperature expressed in the same way. For Saus- sure's experiments on the moisture in air, the degrees of the natural scale appear to be obtained pretty correctly, by taking 2 I — U, I being the degree of Deluc divided by 100; but this seems to make the mean moisture of London too great, since it would become .91 of the natural scale, which im- plies adepression of 2.4° only to produced deposition of m«is- ture. Saussure found, that a cubic foot Fr. of air at 15.16° R. absorbed 11. 069 gr. Fr. of moisture, expanding 5'j ; at 6.18°, 5.655 grains; the hair hygrometer standing at 98°; at other heights of the hygrometer, the quantities of moisture were in the proportions expressed in the table here deduced from tlicse experiments, which consequently show the degrees of the natural hygrometer : the degrees of Deluc's hygrometer are inferred from his experiments, and to these degrees the approximation 2 I — U is also applied. issure. Deluc. Mean. Fonn. Exper. at 6.18°. R. Exper. at 15.16°. R. Mean 10 3.3 6.7 .065 .045 .043 .043 20 6.7 13.8 .130 .113 .099 .106 so 10.3 30. 1 .195 .101 .163 .177 40 14.4 27.S .267 .271 .233 .252 SO 19.9 34.9 .358 .370 .316 .343 60 25.1 42.5 .440 .480 .423 .451 70 31.4 55.7 .530 .597 .578 .588 80 42.3 61.1 .667 .720 .726 .723 00 57.1 73.5 .812 .871 .883 .877 98 80 80. .960 1.000 1.000 1. 000 CATALOGUE. JIETEOKOLOGY, IiyCROMETERS. 471 These experiments agree well enough with the formula, as far as their evidence goes, to make us adopt the ex- pression 2 Z — llzzn, and I'^l^.^ (l — n.) Upon this ground the depression required for producing deposition may. be calculated as in the table. at.hygr. n Form, for Deluc. n S .7107 10 7943 10 .8420 21 .8773 30 .9057 37 .9296 45 .9503 55 .0688 69 .9851 1.0 100 1. 0000 1 Depre ssion required Form. 2 1— n7 for deposi tion at for Deluc 42" 52° 62" 72° .2 803 49 52 55 57 7 .2054 30 38 40 42 14 .1580 28 29 31 .^2 22 .1227 21 23 24 25 30 .0943 16 17 18 19 3 8 .0704 12 13 14 14 4 8 .0497 9 9 10 10 58 .0314 ■ 5.5 5.8 6.1 6.4 70 .0149 2.8 2.7 2.9 3.0 83 .0000 0.0 0.0 0.0 0.0 100 Novf, since the mean height of Deluc's hygrometer is tbove 70 in London, and thepoint of deposition cannot, in general, be supposed to be less than 5 or 6 degrees below the mean temperature, it appears that the formula for re- ducing Deluc's to the natural scale requires sonie alteration; we may therefore make it 1.5/ — 5 U^ln, Sind Izzi.s •1/ (s.25 — n) whence we obtain the numbers in the last co- lumn, where 70° corresponds to a depression of about 6", required to procure a deposition. To raise the natural hygrometer 1°, or .01, the tempera- ture must be depressed as many degrees as the quotient of the temperature reckoned froni — 133° divided by700»: thus, at 62°, if n= .50, i?J =: .56°, if n = .30, .28°, which is nearly the difference of the depression corresponding to the different degrees of the hygrometer. For Deluc's scale the inequality is greater ; a depression of .44° being required to raise the hygrometer from 50° to 51", and of only .1 4° to laise it from 99° to 100". Saussure's experiments on this subject, must, as DaUon observes, have been affected by considerable inaccuracy. On the specific gravity of Air. We may now attempt the solution of a problem, which is of some practical importance; that is, to determine the spe- cific gravity of common air for any given state of the baro- meter, thermometer, and hygrometer. Let the height of the barometer, the temperature of the mercury being re- duced, if necessary, to 32°, be b, that of Fahrenheit's ther- mometer, reckoned from 32°,/, the height of the point of deposition of raoismre above 32° g, the specific gravity of vapour being to that of air as 1 toti.and thespecific gravity of dry air to that of water, at 32°, when the barometer stands at 30, as 1 to a. Now the space occupied by the vapour "'11 1^' — > " being -is+.oo? f + .00010 B*> and the quantity of matter contained in it • , at 32" 30av the re- maining space being 1 — will contain — '—( 1 -) 30 30a ^ 30/ and the sum of these will be ~ — l\ ) ^ iOa \ 30 / 30 a j; which must be reduced in the ratio of 1 to 1 -f .0021 yi and will become ■ • ( .( 1 ) -4 |. 1 + .0021/ \ 30 a V 30/ 3000/ And if we employ Deluc's hygrometer, on the most proba- ble supposition of the nature of its scale, its height in de- grees divided by 100 being /, we have e^ (r. 5/ — ill). (.18 -t- .O07/-t--000l9/'). By comparing this formula with Sir G.Shuckburgh's experiments, from which thespecific gra- vity appears tohave been -|j when b was 30,/z:2 1 ,and I proba- bly about 80°, taking 11— 1 .4 from Saussure's experiment, in which 7. sE. grains occupied j'jofacubicfootjor perhaps alittle more, at 66", we have azi770; and the formula becomes (i *- i '" +i ' ) = ^"' + '■""•^^ '""'="'' °f which, we may employ, in common cases, l:781-f-i.C4y + .05 f -J- .0014 i'S which gives, in the circumstances of the experiment, where g is about is. 816.8 At 55°, with vapour deposited at 50", the specific gravity becomes -\^, which may be assumed as the mean at the sea side for . England and France : at 80°, with vapour deposited at 62°, the barometer being at 28 ; ^ : at 2°, when the air is dry, and the barometer at 31, ^, ; so that the greatest pos- sible variation at anyone place, is nearly in the ratio of 3 to 4 : and the height of the atmosphere, supposed homogeneous, is 820X2.5X13.6=27880 feet. The weight of a cubic inch of air will be .308 grains. This estimation of the air's va- rying density is applicable both to barometrical measure- ments, and to atmospherical refraction. 3 472 CATALOGUE. — METEOROLOGV, BAROMETRICAL MEASUREMENTS. Barometrical Measurements. Hooke on the constitution of the atmosphere. 1652—.'}. Birch. I. 141, 181. Hooke on the weight of air. Birch. I. 379. Makes it ^ as heavy as water. Pascal de I'^quilibre des liqueurs. 12. Par. 166S. Sinclair Ars gravitatis et levitatis. Halley on the height of the barometer at dif- ferent elevations. Ph. tr. 1686. XVI. 104. Makes the mean density of air j^, of mercury 13.5: the height 30 at the sea ; 29, 915 feet above it. Halley's barometrical observations on Snow- don. Ph. tr. 1697. XIX. 565. A fall of 3.8 for 3720 feet. Halley on barometrical measurements. Ph. tr. 1720. XXXI. 116. Proposes to employ Patrick's barometer. Derham on the height of the barometer on the monument. Ph.tr. 1698. XX. 1. Finds a difference of .2 in 164 feet. Cassini on the condensation of the air. A. P. 1705.61,272. H. 10. Lahire on the density of the air, and on the height of the atmosphere. A. P. 1705. 110. H. 10. 1708. 274! H. 11. 1713. 53. H.6. Hauksbee on the weight of the air. Ph. tr. 1706. XXV. 2221. Found it Jj; in May, the barometer 20.7- Maraldi. A. P. 1708. H. 26. Scheuchzer on the expansion of the air. A. P. 1711. 154. H.6. Scheuchzer Experimenta barometrica de aeris elasticiiate. Ph. tr. 1715. XXIX. 266. Scheuchzer on the height of mountains. Ph. tr. 1728. XXXV. 537, 577- Allows 73.6 feet to .1. Varignon on the densities of the air. A. P. 1716. 107. H. 40. Desaguliers's contrivance for taking levels. Ph. tr. 1724. XXXIII. 165. A manometer, to be brought to a given temperature. Ph.tr. 1725. XXXIII. 201. Some mercury, from the East Indies, was 14 times as heavy as water. Nettleton. Ph. tr. 1725. 308. Allows 85 feet for .1 at 30. Celsius Experimentum in argentifodina. Ph. tr. 1725. XXXIII. 313. Gives 106 or 112 feet for .1, Swedish measure. Bernoulli. Act. Helv. I. 33. II. 101. *Bouguer on the expansions of the atmo- sphere. A. P. 1753, 515. H. 39. Sulzer on barometrical measurements. A- Berl. 1753.114. Lambert. Churbayerische Abh. III. ii. 75. Kaestner Markscheidekunst. cciv. *De Luc Modifications. §. 263. Logarithms give fathoms at 39-74° ; reducing for toiscs the air to 69.32°; the mercury to 54^°. Deluc's barometrical observations on the depth of mines. Ph. tr. 1777- 401. Deluc's second barometrical measurement in the Hartz. Ph. tr. 1779- 485. Confirms his own rules. Deluc. Roz. XLII. 264. « Deluc on refractions and expansions. Roz. XLIII. 422. Maskelyne on Deluc's rule. Ph. tr. J 774. 158. Hbrsley on Deluc's rules, with investigations. Ph. tr. 1774. 214. Lavoisier on the weight of the air. A. P. 1774. 364. A cubic inch weighs .48 grains. Fr. ; hence a cubic inch E. .325 gr. E., which seems to be too much. Hennert de ahitudinum mensuratione. 8. Utrecht, 1776. 1788. *Shuckburgh's observations for ascertaining the height of mountains. Ph.tr. 1777. 513. Thespecific gravity of air at 53°, when the barometeris at 29.27, is Jj, consequently J,^ when the barometer is at 30°. CATALOGUE. — METEOROLOGY, BAROMETRICAL MEASUREMENTS. 473 Barometrical experiments give ^ and j^. The specific gravity of mercury at fl8° is 13-61. The decrease of gravity in ascending from the earth's surface produces no percepti- ble effect. Logarithms give fathoms at 31.24°. *Shuckburgh's compaiisoti of his rules with GenPi-al Roy's. Ph. tr. 1778. 681. Thinks, that either Roy's rules or his own are sufficiently accurate. *Roy on the measurement of heights. Ph. tr. 1777. 653. Finds, that logarithms give fathoms about 31.7° in Eng- land, but at Spitzbergen about 01°, and at the equator near 0° : the difference may perhaps depend on moisture : the .same cause appears to require a correction for the mean height above the sea, of which a table is given, the cor- rection for temperature being diminished about ^j for each inch that the mean height of the barometer is below 30°. After all possible corrections, the height of Moel Eilio came out near ^ij too great : if Dcluc's rules had been employed, the error would have been greater. Chiminello on barometrica] measurements. Roz. XIII. 457. Fouchy on the weight of the air. A. P. 1780. S. Magellan's description of barometers. Magellan's barometer. Roz. XIX. 108,194, 257,341. Achard on measuring heights by boiling water. A. Berl. 17«2. 54. Roz. XXV. 287. Dawie?i demoniium altitudine. Hague, 1783. Pasumot. Roz,. XXIX. 13. Trembley in Saussure Voyages. III. Tieinbiey's remarks on Deluc. Roz. XXXII. 87. XLII. 181. Maifcr iiber das hohenmessen 8. Frank f. 1787. Mayer iiber die warme in lucksicht auf dem barometer. 8. Frankf. 1796. *Playfair. Ed. tr. I. 87. Accurate calculations. Saussure on the density of the air at different heights. Roz. XXXVI. 98. Morozzo on the constitution of the air. Soc. Ital. VI. 221. vot. II. for Gerstner and Gruber on the density of the air. Roz. XLI. 110. Robison. Enc. Br. Art. Pneumatics. Hamilton. Ir. tr. V. 117. Wild on the influence of the wind. Zach, Eph. IV. 385. Laplace Exposition da systeme du monde. Follows Deluc. Laplace Mecanique celeste. IV. Rhode liber die berechnung der berghohen nacli Laplace. Halle, 1803. Berger's mode of bringing down air in bot- tles, Journ. Phys. LVI. 366. ,. ■ ■ , s» i3.(iie—y) . . Lambert gives A =10 000 1. — — — ■-- for the y SI 583 — y height in toisej, y being the height of the mercury in inches Fr. Deluc s rule is ft — 10 000 1. - | l -^ I l^ \ 484 / toises, / being the degrees of Fahrenheit. Maskelyne's rule deduced from Deluc'i is ft =: (10 000 1. (-\'^.ii'igj ( 1+'^^ )» «■ being the difference of the temperatures. Or, if we use a thermometer on which the freezing point is at 0° and the boiling point at 81.4°, for measuring the temperature of the meicury, and another with the freezing point at —9°, and the boiling point at 191' for that of the air, we shall have A iz (10000 1. ( -qzi ). (*^ + '\ 1 -I ), i being the difTerence of the mercurial tem- 1000/ peratures, and k and I the temperatures of the air. Shuckburgh says, that for common practice, when the height is lessthana mile, it is sufficient to allow 91.72 feet for every tenth of an inch of difference, adding .211 f. for each degree above 55", and increasing the whole in the ra- tio of 30 inches to the mean height of the barometers. One ten thousandth may also be added for each degree ot dit- fcrence in the temperature. Robison's formula is nearly similar, ft~ (87X.21/) 30 — d ±: 2.83 e; /being the mean temperature reckoned from the freezing point, \j the mean height of the mercury, d the difference of the heights, in tenths, and e the differ- ence ot the temperatures. Or we may take ft r= (2810±0/} d:yit 2.8c.) It is said, that where the barometer rises or sinkt in the course of the operation, the alteration is generally less at Sp 474 CATALOGUE. — METEOROLOGT, CLOUDS AND MISTS. the greater height than in the proper proportion, acircum- itance which adds to the difficulties. The hygtotneier might perhaps be employed in these re- searches with considerable advantage. Clouds and Mists. Bernoulli on the heights of the clouds. Act. eiud. 1688. 98. Opp. I. 336. Stilling on a darkness in America. Ph. tr. 1763. 63. A sulfureous cloud continuing all day, on the igth of Oct. i;62. Meister on the form of the clouds. Gott. Mag. I. i. 38. Marsden on a dry fog at Sumatra, killing the fish.'Ph.tr. 1781. 383. E. M. Physique. Art. Brouillard. Deluc Idees. II. On the mist of 1783^ which affected the smell. Gedanken liber den nebel, von Beroldingen. Brunsvv. 1783. Christ von der nierkvvlirdigen wilterung von 1783.^0?* der cntstehung des nebels. Vienna, 1783. Lausnitz Provinzial blatter, Gorlitz, 1783. VI. Deutscker Mercur. Oct. 1783. To- aWo sulla nebbia. 1783. Goth. Mag. II. ii. Wiedeburg uber erdbeben und nebel. 8. Jen. 1783. Cotte. Roz. XXIII. 201. Papers in Roz. XXIV. Melanderhiehn. N. Schw. Abh.'V. Ilobii voni erdbchen ;Hif Island. 8. Cop. 1784. Goth. M ag. V. iii. 1'28. Torcia to Toaldo. Deutscher Mercur. Apr. 1784. Verdeil on the elec- tric mists of 1783. Mem. dc Lausanne. I. no. Lamanon. Ph. M.V.80. HUbners phys. tageb. I. i. Franklin. Manch. M. II. See Igneous Meteors. Ducarki on parasiiical clouds. Roz. XXIV. 39c, 450. XXV. 31,94. • On the attraction of mountains to mists. Roz. XXV. 303. Saussure's cyanometer. M Tur. 1788. IV. 409- Roz. XXXV II I. 199- A circle of shades of blue, for estimating the colour of the sky. Saussure's diaphanometer. M.Tur. 1788.1V. 42.5. Hube uber die aasdiinstung. Poisse on a mist at Maestiicht. Ann. Ch. XXXIIl.217. Nich. V. 326. Murhard on Saussure's diaphanometer, for measuring the transparency of the air. Ph. M. III. 377. Kirwan on the variations of the atmosphere. B. Prevost on Saussure's cyanomctrical ob- servations. Journ. Phys. LVII. 372. L. Howard on the forms of the clouds. Ph. M. XVI. 97, 344. XVII. 11. Dalton's correction of a mistake of Kirwan respecting the clouds. Nich. VI. 118. It is said, that in 1791, 230 persons were drowned at Amsterdam, by falling into the canals in a great fog. Lucfcorabe. Dew. A. P. II. 13. llosee et serein. Gersten de mutationibusbarometri. S. Frankf. 1733. Extr. Ph. tr. 1733. XXXVIII. 43. Some experiments on dew. Observe.-;, that honey dew is derired from insects. Dufay. A. P. 1736. 332. Remarks, that metals protect glass from dew. Also wa- fers and paper. Hales's vegetable statics. Found, that 3.28 inches of dew fall annually on the earth. Leroy. A. P. 1751. 481. Macfait on foggy weather. Ed. ess. I. 197. t^wrcr Kleine schriften. 8. Reuteln, 1766.1 .15. Ek on dow. Roz. Intr. I. 383. E.\pcriments and observations on light and colours. 8. London. 1 786. 78. It is said, that dew attaches itself to the inside of a bottle partly full of water, on the side opposite to the colai light. CATALOGUE. — METEOROLOGV, DEW, 474 but nearest to the light of the sky. But probably a differ- ence of temperature was concerned. Hube iiber die ausdiinstung. 211. On honey dew. See the Author^ quoted by Lichtenberg in Eixleben.§. 730. Prieuron dew. Joiirn. Polyt. II. vi. 409. Ann. Ch. XXV1II.317. Nich. IV. 86. Hassenfratz on the evening and morningdew. Jouru. de I'Ecole Poiytechn. Ph. M. VII. 114. *B, Prevost on dew. Ann. Ch. XLIV. 75. Jomn. K. I., I. Nich. 8. III. 290. Gilb. XV. 485. Most of the facts may perhaps be explained by means of Mr. Leslie's discoveries. Pallon on rain and dew. Manch. M. V. Makes the dew falling on grass about 5 inches annually, or somewhat less. Account of a Mtmoir on Dew. By Benedict I'revost. ' Ahridgtd from the Annalet de Chimie. No. 130. Journ. R. I. I. 292. It is well I;nown that dew is often deposited on glass, when metals in its neighbourhood remain dry ; Mr. Prevost has however discovered some new and curious facts relative to this deposition. When thin plates of metal are fixed on pieces of glass, it sometimes happens that they are as much covered with dew as the glass itself: but more frequently they remain dry ; and in this case they are also surrounded by a dry zone. But when the other side of the glass is ex- posed to dew, the part which is opposite to the metal re- mains perfectly dry. If the metal be again covered with ' glass, it will lose its effect in preventing the deposition. These experiments may be very conveniently made on the glass of a window, when moisture is attaching itself to cither of its surfaces ; Mr. Prevost remarks that it often happens that dew is deposited externally, even when the air within is warmer than without. A plate of metal fixed internally on a window receives a larger quantity of moisture than the glass, while the space opposite to an external plate remains dry : and if the humidity is deposited from without, the place opposite the -internal plate is also more moistened, while the external plate remains dry: and both these cir- cumstances may happen at once with the same result. A small plate fixed externally, opposite to the middle of the ' internal plate, protects this part of the plate from receiving moisture, and a smaller piece of glass, fixed on the external plate, produces again a cential spot^ of moisture on the in- ternal one: and the same changes may be continued for a number of alternations, until the whole thickness becomes more than half an inch. Gilt paper, with its metallic sur- face exposed, acts as a metal, but when the paper only is exposed, it has no effect. When a plate of metal, on which moisture would have been deposited, is fixed at a small dis- tance from the glass, the moisture is transferred to the sur- face of the glass immediately under it, without affecting the metal : if this plate is varnished on the surface remoje from the glass, the effect remains, but if on the side next the glass, it is destroyed. The oxidation of metals renders them also unfit for the experiment. When glasses partly filled with mercury, or even with water, are exposed to the dew, it is dei)Osited only on the parts which are above the surface of the fluid. But in all cases when the humidity is too copious, the results are confused. ■ In order to reduce these facts to some general laws, Mr. Prevost observes, that when the metal is placed on the warmer side of the glass, the humidity is deposited more copiously either on itself or on cither surface of the glass in its neighbourhood : but that, when it is on the colder side, it neither receives humidity nor permits its deposition on the glass : that a coat of glass, or varnish, destroys the efficacy of the metal, but that an additional plate of metal restores it. Mr. Prevost was at first disposed to attribute these pheno- mena to the effects of electricity; but he thinks it possible to explain them all by the action of heat only : for this pur- pose he assumes, first, that glass'attracts humidity the more powerfully as its temperature is lower ; secondly, that me- tals attract it but very little ; thirdly, that iglass exerts this attraction notwithstanding the interposition of other bodies • and fourthly, that metals give to glass, placed in their neiglibourhood, the power of being heated by warm air, ani being cooled by cold air, with greater rapidity ; hence that the temperature of the glass approaches more nearly to that of the air on the side opposite to the metal, and attracts the hu- midity accordingly more or less, either to its own surface, or to that of the metal. We should indeed have expected a contrary cffi;ct ; that the metal would rather have tended to communicate to the glass the temperature of the air on its own side : but granting that the assumptions of Mr."Prevost serve to generalise the facts with accuracy, their temporary utility isas great as if they were fundamentally probable. Y. Kuin in general. Labile on rain water. A. P. 1703. 5(5. Wargentin. Schw.Abh. XXV.3. Leche. Sdiw. Abh. XXV. 16. 476 CATALOGUE. — METEOROLOGV, KAIN. Schenmark. Scliw. Abh. XXVI. 159. UIloii's voyages. 11. It never rains in Peru, but for a part of the year the at- mosphere is obscured by thick fogs, called garuas. Franklin. 1756. Ph.tr. 1765. 182. Observes, that a small black cloud portends rain, denoting the beginning of a current of cold air from above. Franklin and Percival on the difference of rain at different heights. Manch. M. II. No satisfactory theory. *Heberden on the rain falling at different heights. Ph.tr. ntHj. 359. In 1706, li.l inches fell at the top of Westminster abbey, below the houses, 22.fi. Barringlon on the rain on mountains. Ph.tr. 1771.294. Not much less than on the plains. Dobson. Ph. tr. 1777.255. Confirms Meberden's remark. Bertholon Nn a cause of rain. Roz. XIV. 482. Ducarla on rainy winds. Roz. XVIII. 446. Deluc Idees sur la meteorologie. Deluc on vapours and rain. Roz. XXXVI. 276. Letter to Hutton in the Monthly Review. 1789. Chiminello on the fall of rain in different centuries. A. Sienn. VI. 1. Hutton's theory of rain. Ed. tr. 1. 41. II. SQ. Observes, that since the capacity of air for moisture in- creases faster than the temperature, there must he a deposi- tion of moisture when two saturated portions of air at differ- ent temperatures are mixed. liibes on rain. Roz XL. 85. Erxleben. II. 735. It is said, that the drops of rain, .at the equator, are some- times an inch in diameter. Ijichtenberg's reraarkson rain. Gilb. II. 121. Hassenfratz on snow and rain. Journ. Polyt. I. iv. 570. Repert. XIV. 64. Saussure on dryness preceding rain. Gilb. 1.317. Nich. I. 511. Zylius on rain. Gilb. V. '257- Kirwan on rain. In tr. Nich. 8. V. 120. Electric theory. Gough. Manch. M. IV. Observes, that the quantity of rain at different heights i« nearly as the height of the point of perpetual cong«lation above the gage. Dalton on rain and dew. Manch M. V. 346. Nich. 8. IV. 159. Repert. ii. I. 203. Dalton found the rain of a gage, so yards high, in sum- mer i, in winter i as much as that of a gage below. Howard on Hutton's theory of rain. Ph. M. XIV. 55. It has been remarked, that the largest quantities of rain fall on the hills, where they arc the most wanted, since they soon run off, from the inclination of the ground. Rain Gages. register. Hooke's statical rain gage and Birch. III. 477. Perrault. A. P. II. 25. Loup. Th. Aerostat, t. 17, 18. Grischow's hyetometer. M. Berl. 1734. IV. 349. Pasumot's rain and snow gage. Roz. VIII. 43. Landriaiii's chrouhyometer. Soc. Ital. I. 205. Roz. XXII. 280. Registering the time and quantity. Garnctt on rain gages. Ir. tr. V. 357. Some of these gage? measure the quantity by wheelwotk. Particular Registers of Rain. See MeteorologicalJournals. Townley on the rain at Townlcy, in Lanca- shire. Ph. tr. 1694. XVIII. The average of ) 5 years was 41.518. Ph.tr. 1696. XIX. 357. At Grcsham College. Derham. Ph. tr. 1714. XXIX. ISO. At Upminster. Hoisley. Ph. tr. 1723. XXXII. 328. In Nonhumberland. Grischow. M. Berl. 1734 . . IV. . Linings. Ph.tr. 1745. XLIII. 330, 1753.284. At Charlestown, CATALOGUE. — HETJCO HOLOGY, RAIN. 477 Hagpn. Ph.tr. 17ol. 360. At Leydcn. Byam. Pli. tr. 1755.295. In Antigua. Anieron. Ph. tr. 17G3. 9. At Norwich. Borlase. Ph. tr. 17G4. 59. In Cornwall. Continued. Barker. Ph. tr. 1771. 221. At Lyndon. Continued. Hutchinson on the dryness of the year 1788. Ph. tr. 1789. 37. A caution respecting the rain gage of the R. S. Ph tr. 1792. Erxleben. ^. '38. At various places. An annual table printed by Burbage at Nottingham. AtExeter,Chichester,London,Diss,Chatsworth, W.Bridg- ford, Ferriby, Lancaster, and Kendal. It appears that De- cember was the wettest month in 4 places ; June in 2 ; May and November each in one, and April and December in one instance equally wetter than the rest. 1804. Annual fall of Rain, from Erxleben, Dalton, and others. Upsal ... Inches 18.7 West Bridgford, Netting. - - - 17.O Wittenberg - - - - 17.O St. Petersburg - - . - 17.2 Lund ... . 18.5 Diss, Norfolk - . - - 18.7 Upminster, Essex - - 19.5 Carlisle, 1 y. - - - 20.2 Paris .... 20.2 Berlin ... _ 5Q,g , Widdrington, North. 1 y. - - 31.2 Rome . - - - 21.3 Edinburgh ... . jj.q Dublin - - - - 02.2 South Lambeth, 0 y. - - 02.7 London, 7 y. - - - 33.0 ~ Near Oundle, North. 14 y. - - 23.0 Lisle - . - - 24.0 Lyndon, Rutl. 21 y. • - - 24.3 Utrecht ..... 34.7 Haarlem ... . 24.7 Youngsbury, Hartf. 5 y. - - 25.0 Kimbolton, Hunt. ... 95,0 Noprich, 13 y. Fyfield, Hampsh. 7 y. Ferriby, Yorksh. Chichester Ulm Algiers Barro.vby, Yorksh. 6 y. Chatsworth, Derbysh. 15 y. Hague Delft Harderwyk A place in Cornwall, 1 y. Bristol, 3 y. Bridgwater, Somers. g Abo Leyden - » Madeira Minehead, Somers. Inches. 2S.5 25.9 26.6 36.8 27.0 37.0 27.5 27.S 38.4 28.6 28.6 29.1 29.3 29-3 29.3 30.2 31.0 ai.a Dalton's mean for all England, taking first a mean of the counties - - . 31.3 Mean of 16 places in Great Britain, Enc. Br. 32.5 Dalton's immediate mean of 32 places, mostly rainy 35.2 Manchester, 9 y. - - - 33.0 Middleburg - - - - 33.0 Zurich .... 33.1 Exeter - ... asjj v Liverpool, 18 y. - - - 34.4 Padua .■'... 34.5 Cotte's mean of 147 places ... 34.7 Sieima ... - . 35.2 Venice - - - - 36.1 Selbourne, Hampsh. - - 37.2 Dover, 5 y. - - - - 87. 5 Lyons .... 39.* Kirkmichael, Dumfr. - - 40.8 Ludgvan, Cornw. - - - 41.0 Dordrecht - - - s 41.0 Townley, Lane. 15 y. - - 41. s Pisa - .... .43.2 Lancaster, 10 y. - - - 4.i.o Waith Sutton, Weslm. 5 y. - - 40. 0: Plymouth, 2y. - - - " 46.5 Charlestown - - ... 50.9 Garsdale, Westm. 3 y. - - - 52.3- Fellfoot, Westm. 3 y. - - - 55-7 Kendal, Westm. 11 y. - - - 59. » Kendal, in 17S2 ... 53.5 Crawshawbooth, Lane. 2 y. - - - 60.0 Keswick, Cumb. 7 y. - - - 67.5 East Indies, sometirasj - - - - 104.0 478 CATALOGUE. METEOROLOGY, SNOW AND HAIL. For rain and dew together Dalton makes the mean for England and Wales 36 inches, amounting in a year to 28 cubic miles of water. Storms of Rain. Ph. tr. 1698. XX. 382. In Yorkshire. Derliain and Leeuweiihoek, Ph, tr. 1704. XXIV. 1530, 1535. Chiefly wind. Sloane. I'h. tr. 1706. XXV. 2342. At Denbigh, Thoresby. Ph.tr. 1711. XXVII. 321. 1722. XXXII. 101. Near Halifax; fifteen persons were drowned. Luckoinbe's tablet of memory. A flood in Spain, nny, destroyed 2000 persons, Campbell. Maiidi. M. IV. 265. Six inches of rain fell in a storm at Lancaster. Snow and Hail. Figures of snow. See Physical Optics. Kepler on the se.xangular figure of snow. Dornav. amphitheatr. 751. Figures of snow. Hooke's micrographia. 88, 91. Exir. Ph. tr. 16/4. IX. Fairfiix on a hailstorm. Ph. tr. 1667- II. 481. Grew on the nature of snow. Ph. tr. l673. VIII. 5193. Bart/wliiiwi de naturae mirabilibus. 4. Co- penh l!i74. ii. Ace. Ph. tr. 1674. IX. , Hailstones of more than a pound in Flanders. I'h. tr. 1693. XXIV. 858. Halley on a hail storm. Ph. tr. I697. XIX. 570. On a hail storm. Ph. tr. l697. XIX. 577, 579. fWallis on hail. Ph. tr. 1697- XIX. 653, 7£9. Cassini on the figure of snow. A. P., II. 87i X. 25. Hail stones weighing l^^lb., the least two fingers thick. A. P. 1703. H. 19. Thoresby on a hail storm. Ph. tr. 1712. XXVII. 514. Langwith on the figures of snow. Ph. tr. 1723. XXXII. 298. Musschenbroek on some figures of snow. Ph. tr. 1732. XXXVII. 357. Mussch. Intr. II. pi. 61. Lulofs on the figure of snow. M. Eerl. 1740. VI. 83. Stocke nivls figurae. Ph. tr. 1742. XLII. 114. Engtlmati Verhandeling over de sneewfigu- ren. Haarl. 1747. Monesier sur la gr^le. 4. Bourd. 1752. *Netti3 on the configuration of snow. Ph. tr. 1756.644. Bruni on the mass of snow that fell upon Berg.nmoletto. Ph.tr. 1756.796. Fauquier on a hail storm in Virginia. Ph. tr. 175S. 746. Wilke on the forms of snow. Schw. Abh. 1761.3, 89. lloz. I. 106. The forms are shown by freezing soap bubbles. Messieron a number of globules passing over the sun's disc. A. P. 1777- 464. H. 3. Probably large hail stones. f Ciiamboa on hail. Roz. X. 301. A letter on hail. Rozier. Sept. 1778. Mongez on hail. Kox. XII. 202. Hailstones of above two pounds. Mourgue de Montredon. A. P. 1781. 754. With a dry fog supposed to be volcanic. Barberet. Acad. Dijon. 1. Pasumot on prisms of ice. Roz. XXIII. 62. Franklin. Maiich. M. II. 357. Suspects that hail is formed in a very cold region, high in the atmosphere. But this is not the most probable hypo- thesis. Tessier's account of a hail storm extending 200 leagues. A, P. 1789- 6I8. 1790.263. 5 CATALOGUE. — METEOROLOGY, SPRINGS AND RIVERS. 479 Lichtenberg on hail. N. Hannov. Mag. Jan. 1793. Eixl. Naturl. Thinks, that hail depends on" electricity, perhaps as promoting evaporation and cold. Observes, that it very sel- dom hails at night ; that in wiiuer snow is much more common than hail ; that it often snows or rams for some days, and then hails with thunder ; and that hail often at- tends volcanic explosions. Most of these circumstances ire easily understood, if we consider that much of the cold which congeals the hail is probably produced by evapora- tion. Hassenfratz on snow and rain. Journ.Polyt. I. iv. 570. Rcpeit. XIV. 64. Hassenfratz on the air contained in snow. Journ. Phys. XLVIII. 375. Hail stones of 8 pounds. Mann. Ph. M. II. 216. Saussure on a red snow. Ph. M. III. 168. Driessen on the congelation of snow water. . Ph. M. III. 249. Gilb. IV. 246. ■ Aldini attributes the form of snow to electricity. Von Arnim denies the observation on which the opinion is grounded. Gilb. V. 73. Account of a iiail stone whicli fell in Hungar}', 1803, and which eight men could not lift. Gilb. XVI. 75. From newspapers only. On snow. Nich. VIII. 73. Hailstones 14 inches in circumference are said to have fallen in Hartfordshire, 4 May, 1697 ; some of as ounces weight in the Pyrenees, 1784. In 1710 a storm of snow destroyed 7000 Swedes in their march against Drontheim. Springs, Rivers, Lakes, and Seas: liattr and Ice. See Theory of Hydraulics, and Hydraulic Architecture. On ebbing and flowing wells. Plin. Epia. iv. SO. Danubius illustralus. Boyle on the saltuess of the sea. Works. Ill, 357. Hydrology. Ph. tr. abr. II. ii. 257. TV. 2 p. ii. 18.1. VI. 2 p. ii. 163. VIII. Sp.ii. 641, . X.2p. ii. 567. Vossius de Nili origine. 4. Hague, I666. Ace. Ph. tr. 1655—6. 1. 304. Brown on the lakeof Zircknltz in Carniolia. Ph. tr. IV. 1669. 1083. A lake several miles long, which abounds with fish in the winter, but is dry from June to SejJtember, yielding grass and hay. It empties itself by a subtc^raneous channel, Mariotte du nicuveinent deseaux. clxxix. X/'or/g/nedes fontaines. Par. 1674. Ace. Ph. tr. 1675. X. Southwell on water. Birch. HI. 196. Valvasor on the lake of Zircknitz, with a map, Ph.tr. 1686. XVI. 411. Young on fountains and springs. Hooke. Lect. Cutl. Thinks they originate from the sea, since large springs are sometimes found in small islands. Hooke docs not ac- cede to the opinion. Halley on the lake of Zircknitz. Birch. IV. 558. Halley &n the cause of springs. Ph. tr. 1692. XVII. 468. Halley on the saltness of the sea and of lakes. Ph. tr. 1715. XXIX. 29fi. Oliver on an ebbing well in Torbay. Ph. tr. 1693. XVII. 908. Bartholiitus de origine fontium. 4. Copenli. 1689. Sedileau on Springs. A. P. I693. 117. On the origin of rivers. X. 221. Diodati on an inundation in Mauritius. Ph. tr. 1698. XX. 268. Dodart on the wells at Calais, fluctuating with the tides. A. P. I. '^34. H. 87. Borelli and Lahire on reciprocating springs. A. P. II. 25. Heariie de lacu Vettero. Ph. tr. 1705. XXIV. I9S8. Thoresb\ 011 an eruption of waters in Craven. Ph. tr. 1706. XXV. 2236. 480 CATALOGUE. — METEOROLOGY, SPRINGS AND RIVERS. Vailimrri Lezzione intorno alle fontane. Ve- nice, 1715. M. B. Robelin on wells aliernating with the tides. A. P. 1717. H. 9. Ph tr. 1722. XXXIf. The height of the falls of Niagara is 186 feet. Desaguliers on the rise and fall of water in ponds. Ph.tr. 1724. XXXIII. 132. On the principle of Hero's fountain. Gunltieri sopra le fontane. 8. Lucca, 1728. M. B. Atwcll on reciprocating springs. Ph.tr. 1732. XXXVII. 301. On the principle of the siphon. Ilttmberger et Dankwerts de fontium origine. 4. Jen. 1733. Sfgner Progammata duo. Gott. 1737. On reciprocating springs. On rivers. S'Gravesande. Nat. Ph. iii. c. 10. Lucas on the cave of Killarney, which some- times overflows with reciprocating water. Ph. tr. 1740. XLI. S60. Marsigli Storia del mare. <}hezzi deJIe fontane. 12. Ven. 1741. M. B. Jallabert on the alternations of the lake of Geneva. A. P. 1742. H. 26". Kii/m vom ur.^prunge der quellen. 8. Berl. 1746. On an inundation in Cumberland, which un- oermi..ecl a mountain. Ph. tr. 1750. 362. 'l>eparcieux on a pipe that gives more water by night than by day. A. P. 1750. H. 153. 1754. H.33. Probably from iacluded air. On springs. Belidor. Arch.Viydr. II. i.SSQ. Speed de aqua marina. 4. Oxf. 1755. Guettard on the disappearance of some rivers. A. P. 1758.271. H. 13. Wallcrius et Sv. W. de origine fontium. 176I. Milbourne on a decrease of the river Eden. Ph. tr. 1763. 7. Perhaps from frost. Baciiilli on the mouths of rivers. C. Bon. V, ii. 99. Barbieri on the saltness of the sea. Raccolta d'opusc. xlvii. On the divining rod. Roz. Intr. II. 231. Montucla. Math. recr. Baumer on springs. Roz. I. 177. On springs. Roz. VI. 435. Lengths and heights of rivers. Roz. VII. 292. fMaison neuve on the saltness of the sea. Roz. XII. 392. Rennel on the lengths of rivers. Ph. tr. 1781. 90. Fraula on thawing. Roz. XXI. 390. Desmaretson ice. Roz. XXII. 50, 165. Page on the wells at Sheerness. Ph.tr. 1784. 6. A well being dug 330 feet deep, the water rose in it to within 18 feet of the surface. Allut on periodical springs. Roz, XXVI. 295. Robert and Meyerotto on the Hautes Fag- nes, a marsh on an elevated plain. A. Berl. 1788. 94,577. Ribbach on the Hautes Fagnes. A. Berl. D, Abh. 17»8. 177. Pott on ice at the bottom of rivers. Roz. XXXIII. 59. Besson on subaqueous ice. Roz. XXXIV. 387. Godart on subaqueous ice. Roz. XXXV» 205. Brunelli on the river of Amazons. C. Bon. VII. O. 39. Rumford on the saltness of the sea. Ess. II. Observes, that it tends to prevent the expansion of the water in cooling, and to equalise the temperature of the air, by causing the circulation of the water to continue in low tem- peratures. The lake of Eichen in Baadcn haa some remarkable Tari- ations. Lichtenberg. CATALOGUE. — METEOROLOGV, ATMOSPHERICAL ELECTRICITY. 481 Trembley on rivers, and on the lake of Ge- neva. A. Berl. 1794. 3. Baillet on wraters in mines. Journ. Phys. XLVIII. 164. Grimm and others on the origin of subterra- neous water. Gilb. II. 336. TrauUe on new springs. Journ. Pliys. LV. 346. Edelbrooke on the Ganges in Bengal. As. res. VII. 1. Cousin on the height of the Seine. M. Inst. IV. 334. Lamarck Hydrogeologie. 8. Par. 1802. K. S. Pearson on the wells at Brighton. Nich. 8.111.65. The high water prevents the efflux of the springs, and Raises the wells. Dalton. Manch. M. V. 346. Gilb. XV. 244. Observes, that a foot of wet soil contains 7 inches of water, that is j? . Thinks that the Thames carries off i of the rain and dew that fall in England ; other rivers 8 times as much, making together 13 inches, and leaving 23 for evaporation. Henry. Ph. tr. 1803. 29, 274. Nich. 8. V. 229. Report, ii. HI. 255. Finds, that equal volumes of any gas are absorbed by wa- ter under any pressure. Hence we may understand why the water of the deepest wells contains the most air. Sweetening Sea Water, and pre- serving Fresh. Hauton. Ph. tr. 167O. V. 2048. Lister. Ph. tr. 1685. XV. 836. Boyle. Ph.tr. 1691. XVII. 627. Watson. Ph.tr. 1753.69. Chapman. Ph.tr. J 758. 635. On Irwin's mode of sweetening sea water. A. Gott. D. Schr. 202. Roz. XVI 1 1. l64. Lorgiia. Soc. Ital. HI. 375. V. 8. Lorgna intorno alia dolcificazioncdell acqua del mare. 4. R. S. Bay ley's machine, llepert. V. 320. VOL. II. Lowitz on freshening putrid water. N. A. Petr. 1792. X. 187. Montucla and Lalande. IV. 507. Trotter's medical and chemical essays. 8. 1795. Recommends casks charged within. Bentham's metallic tanks for preserving fresh water at sea. Repeat. XVI. 238. Atmospherical Electriciiy in general. ' v St. Gray. Ph. tr. 1735. XXXIX. 24. Observes, that " the electric fire (si licet magnis com po- nere parva) seems to be of the same nature with that of thunder and lightning." •[-Logan on the form of lightning. Ph. tr. 1736. XXXIX. 240. Winkler Abhandiung von der electrischen ursprung deswetterleuchtens. 1746. Geh- lers worterb. Art. Blitz. *Franklin's letters. Maffei della fonnazione dei fulmini. 4. Ve- rona, 1747. Wilke. Schw. Abh. 1750. 81, 155. Eeles on the cause of thunder. Ph. tr. 1751. 524. Nollet and Mylius on the electricity of the clouds. Ph. tr. 1751. 553, 559. Nollet on the effects of thunder. A. P. 1764. 408. Watson on thunder clouds. Ph. tr. 1751. 567. Watson on the effects of lightning. Ph. tr. 1 762. 6^9. Macfaiton thunder. Ed. ess. I. I89. Lemonnier on the electricity of the air. A. P. 1752. 233. H. 8. Mazeas on the electriciiy of the air. Ph. tr. 1753. 377. Birch's remark on the light seen on spear points. Ph. tr. 1754. 484. Bittsc/taiizAc fnlgureet tonitru. Gotting.1757. Hartniann von lufterschcinungen. 8. Hanovt 1759. 3Q 48'Ji CATALOGUE. — METEOROLOGY, ATMOSPHERICAL ELICTRICITY. Bergman on horizontal lightnings. Schw. Abh. 1760. 62. Po/?cf/c< de la nature du tonnerre. 12. Par. 1766. Ronayneon atmospherical electricity. Ph. tr. 1772.137. Cotte. A. P. 1772. i. H. 16. Snow serves as a conductor in storms. Beccaria dell' elettricita atmosferica. 4. R. S. Bertliolon on thunder. Roz. VII, 258. Bertholon on atmospherical electricity. Roz. XX. 224. Jicrthulon de I'electricite des meteores. Par. 1787. Cavallo on the electricity of the atmosphere. Pii.tr. 1776.407. 1777. 48. Mako vom donner. 1778. , Rebnarus vom blitze. 2 v. 8. Hamb. 1778. 1794. Changeux on the effects of electricity on tlie barometer. Rozicr. Apr. 1778. Gallitzin on an electrical kite. A. Petr. II. ii. 76. Fig. With precautions to prevent accidents. Mourgiie on thunder. Roz.XIlI. Suppl. 459. Poll sopra il tuono. 8. R. S. Deiuc Idees. II. Delucon lightning. Roz. XXXIX. 262. Deiuc to Lanietherie. Roz. Aug. 1790. Peluc on lightning without thunder. Roz. Oct. 1791. Rozier on the cause of thunder. Roz. XVI. 309. Rozier on a phosphoric cloud. Roz. XVIIf. 276. Acliard on atmospherical electricity. A. Berl. 1780. 14. Achard on terrestrial electricity, k. Berl. 1786. 13. In contradistinction to atmospherical. Uucarla on rainy winds. Roz. XVIII. 446, Ferris on ascending thunder. Roz. XXII. 197. Electric mists of 1783. See Clouds and Mists. Baldwin on the appearance of an electrical kite. Am. Ac. I. 257. Diwisch Meteorologische electricitat. 1786. Oliver on lightning. Am. tr. II. 74. Bennet's account of atmospherical electri- city. Ph. tr. 1787. 288. Finds, that a candle collects more electricity than any point. Sen6bier. Rozier. March and April 1787. Lightning without thunder. Senebier in Ro- zier. 1787. Gronau. Naturf. Fr. IX. Bergmann on lightning. Opusc. V. 348. Hervieu on a remarkable light in a storm. Roz. XXXIV. 386. Aepinus's letter on atmospherical electricity. Ed. tr. II. 213. Read's instrument for collecting atmospheric electricity. Ph.tr. 1791. 185. Read's apparatus and journal of electricity. Ph. tr. 1792. 225. Read's summary view of the electricity of the earth and atmosphere. Lond. 179,5. Read's meteorological journal of atmospheri- cal electricity. Ph. tr. 1794. 185. Finds, that out of 404 observations in a year, theairwas positively electric in 241, negative in 156, and neutral in? only. Read's experiments with the doubler. Ph. tr. 1794. 266. Attributes the uncertainty of the doubler wholly to at- mospheric electricity ; finds all noxious and putrid ex- halations,.{ind the air of close rooms, in a negative state. On fairy rings. Withering's bot. arr. III. 335. Monthly Mag. XV. 2 19- Gilb. XVII. 3 51, They are formed by the agaricus orcades, or fairy rin g agaric, becoming larger as the roots of the fungus spread. Volta to Liclitenbeig. Brugnatelli Bibl. fisi- ca. Germ. Meteorologische briefe. Lei])2- 1793. CATALOGUE. — METEOROLOGY, ACCOUNTS OF STORMS. 4B3 Lampadius uber electricitat und w'anne. 8. Berl. 1793. Lichtenberw. Erxl. Nat. o Thinks, that thunder is less frequent but more violent in winter, because the air is less disposed to conduct. Robison. Enc. Br. Suppl. Art. Thunder. Tcaldo on thunder. Ac. Par. III. 212. On the clouds in a thunderstorm. Nich. 1. 265. fOn fairy rings. Nich. I. 546. Heller on the returning stroke. Gilb. TI. 223. Aldini's opinion of snow. See .Snow. Priestley on an igneous meteor. Gilb. XI. 76. A particular kind of lightning, supposed to be about 20 miles high. Kirwan on rain. Ir. tr. Nich. 8. V. 120. Erman on atmospherical electricity. Gilb. XV. 385. 502. Bilitoro asserts, that lightning generally strikes the S. E. side of a house, sometimes the S. W. but never the north. Particular Accounts of Storms. Instances of lightning without audible thun- der. Homer. Odyss. xx. 139. Virg. Georg. I. 487. Cicer. de divin. I. xviii. Hor. Od. I. 34. Waller. Ph. tr. 1665—6. 1. 222. At Oxford. Neale. Ph.tr. 1665—6. 1. 247. Ph. tr. 1^70. V. 2084. At Stralsund. Kirkby. Ph. tr. 1673.V1II. 6092. Effects on grain. Howard. Ph. tr. I676. Xf. 647. Effects on the compass, a complete reversion. Ph.tr. 1(596. XIX. 311. Near Aberdeen, 4 persons killed. Mawgridge. Ph. tr. I697. XIX. 782. Effects on a galley. Thoresby. Ph. tr. 1699. XXI. 51. Ph.tr. 1700. XXII. 507. At Leeds. Molyneux. Ph. tr. 1708. XXVI. 36. Chamberlayne. Ph. tr. 1712. XXVII. 528. Wasse. Ph.tr. 1725. XXXIII. 36?. At Mixbury. Probably an igneous meteor. Mr. Jessop attributes the fairy rings to lightning. Bocanbrey on a vortex of fire rolling on the earth. A. P. 1725. H. 5. Seems to have been a whirlwind or dry spout. Beard. Ph. tr. 1726. XXXIV. 118. - Davies. Ph.tr. 1730. XXXVI. 444. In Carmarthenshire. Cookson. Ph. tr. 1735. XXXIX. 75. Magnetic effects. Clark. Ph. tr. 1739. XLI. 235. Lord Petre. Ph. tr. 1742. XLII. 136. Ph.tr. 1745. XLIII. 447. Miles. Ph. tr. 1748. XLV. 383. 1757. 104. Waddel and Knight. Ph. tr. 1749. XLVI. 111. Effects on the compass. Chalmers on a fire ball. Ph. tr. 1750. XLVI. 366. On board the Montague, in lat. 43" 48', 4 Nov. 1749, a ball of fire as large as a millstone w^ai seen rolling three or four miles along the sea with the wind; it struck the main topmast, rent the whole mainmast, and knocked down 6ve men. It has been supposed that this was an electrical cloud. Franklin. Ph. tr. 1751.289- Palmer.Ph.tr. 1751. 330. At Southraolton. Account of the death of Richmann. A. P. 1753. H. 78. Ph.tr. 1754. 7o7. 1755.61. Hatiow Nachricht aus St. Petersburg. Kratzcnstcin says, that the stroke which destroyed Hich- mann was not conducted by his apparatus. Hiixham. Ph.tr. 1755. l6. At Plymouth. Brander. Ph. tr. 1755.298. In Wellclose Square. Child. Ph. tr. 1755. 309. At Darking. Dyer. Ph. tr. 1757. 104. In Cornwall. Smeaton. Ph. Ir. 1759' 198. At Lestwithitl. 484 CATALOGUE. METEOROLOGY, ACCOUNTS OF STORMS. Cooper. Ph.tr. 1759. 38. At Norwich. Mrs. Whitfield. Ph. tr. 1759. 282. Mountaine and Knight. Ph. tr. 1759. 286, 294. Borlase. Ph. tr. 1762. 507. Watson. Ph.tr. 1762.629. On ships. Bergmann. Ph. tr. 1763. 97. Delaval. Ph. tr. 1764. 227. St. Bride's church. Lawrens. Ph. tr. 1764. 235. Essex street. Heberden. Ph.tr. 1764. 198. At S. Weald. Veicht. Ph. tr. 1764. 284. On ships in the East Indies. Paxton. Ph. tr. 1769. 79- Devonsliire. A noise equal to lOO cannon. Williams. Ph. tr. 1771.71"." Cornwall. A whole congregation, except 5 or 6, were stiuclv senttlcss. Cornwall seems to be the most exposed to thunder of any county in Britain. Henly.Ph.tr. 1772. 131. Kirkshaw. Ph. tr. 1773. 177. A person struck dead in bed. King. Ph.tr. 1773.231. Wilts. Hamilton. Ph.tr. 1773. S24. Lord Tylney's house at Naples. Ivichoisou. Ph. tr. 1774. 350. A horse's ears were luminous : there was a light stream- ing from cloud to cloud like an aurora borealis; Henley. Ph. tr. 1776.463. A bullock was struck by lightning, which affected the skin where the hair was white : probably because the skin was here a less perfect conductor than elsewhere, and the least perfect conductors are most affected. Cooper. Ph. tr. 1779- l60. On the ship Atlas. *Brereton. Ph. tr. 1731. 42. East Bourne. A ball was, seen to burst against the house; two persons were killed. Roz. XVni. 45. Leroy. Roz. XX. 82. Lorgna. Roz. XX. 365. Poll sopra alcuni fultnini. 8. R. S. Nairne on wire shortened by lightning. Ph. tr. 1783.223. Buissart on an ascending stroke of thunder. Roz. XX lU. 279. Verdeilon a stroke of thunder al Lausanne. M. Laus. I. 158. Geschickte einer ausserordentlichen begeben- heit. 8. Frankf. 1785. Lightning without thunder. Lee on a stroke of lightning. Am. Ac. T. 253. Brydone on a thunder storm in Scotland. Ph. tr. 1787.61. No flash appeared to strike the men, and the lowest point only of the iron of the wheels was melted. Lord Stanhope on Mr. Brydone's account. Ph.tr. 1787. 130. Explains the circumstance from the effect of the return- ing stroke. Lavoisier on a stroke of lightning on St. Paul's church. A. P. 1789. 6l3. Hervieu on a storm. Roz. XXXIV. 386. Kl'ugel Beschreibung eines heftigen gewitters. 8. Halle, 1789- Withering on some effects of lightning. Ph. tr. 1 790. 293. A man was struck dead under a tree ; a hole 2 J inches in diameter was made, and some quartzose sand and peb- bles were vitrified in it. Haldane on the cause of accidents from lightning. Nich. L 433. Effect of lightning. Nich. HL 432. Lichtenberg on a thunder cloud. Ph. M. VL 41. Toscan on a stroke of lightning, preceded by the appearance of a globe of light on an iron bar. Gilb. XHl. 484. Storms of th\inder. Gilb. XV. 227. Gough and Wilson on some effects of light- ning. Nich. IX. 1. CATALOGUE. METEOROLOGY, PRESERVATION FROM LrOHTNING. 485 Measures of Atmospherical Elec- tricity. Franklin's electrical kite. Ph. tr. 1751. 565. Romas. S. E. II. 393. Hartmann liber die erforschung der electri- cit'iit. 4. Haiiov. 1764. Gallitzin. A. Petr. II. ii. 76. A kite. Lichtenberg's meteorological electroscope. Goth. Mag. I. i. 157. Boyer Brun on an electroscope for a conduc- tor. Roz. XXVIII. 133. Read. Ph. tr. 1791 185. 1792. 225. Read on the electricity of the earth and at- mosphere. Preservation from Lightning. Con- ductors and Precautions. W'mkler dc avertendi fulminis artificio. 4. Leipz. 1753. Watson on conductors. Ph. tr. 1764. 201. Delaval. Ph. tr. 1764. 227. Recommends a conductor 6 or 8 inches by J for St. Bride's church. Wilson on blunt conductors. Ph. tr. 1764. 24.6. Wilson's dissent from a committee, witU ex- periments. Ph. tr. 1773. 48, 49. Wilson says, that points attract discharges, which are eften dangerous. A bat, near 4- inches by ^ an inch, was probably heated red hot in St. Paul's, March 177*. Wilson's experiments in the Pantheon and elsewhere. Ph. tr. 1778. 232, 999- A point was struck at a greater distance than a ball. Proposal of a committee for securing St. Paul's. Ph. tr. 1769. l60. Recommends 4 bars not less thai* an inch squaie, to se- cure the lantern. Winn on a conductor for a ship. Ph. tr. 1770. 188. Leioy on con-liictors. A. P. 1770. 53. H. 14. 1773. 599. H. 3. 1790. 472, 588. Roz. XLIII. 94. Franklin. Ed. ess. III. 129. Franklin on electricity. Fdbiger Kunst gebaiide zu bew'ahren.S.BresI. 1771. *Keport of a committee on securing powder magazines. Ph. tr. 1773. 42. Consisting of Cavendish, Watson, Franklin, and \ odiers. They recommend pointed conductors ; ar.d adhere to theiropinion. Ph.tr. 177«, Henley on conductors. Ph. tr. 1774. I3S. In favour of points. Henley and Haffenden on a house with a conductor that was struck. Ph. tr. 1775. 336. Henley. Ph. tr! 1777. 85. Observes, that lampblack and tar act as a pres^atife from lightning. Tetein iiber die sicherung seiner person, 8. Biltzow, 1774. Gudcn von der sicherheit wider die donner- strahlen.B. Gott. 1774. Swift on conductors. Ph. tr. 1778. 155. 1779* 454. In favour of points. Papers relative to an accident at Purfleet. Ph. tr. 1778. 232. Musgrave's dissent from the committee. Ph. tr. 1778. 801. Observes, that other things being equal, points are struck farther off than balls. *Nairne's experiments in favour of pointed conductors. Ph. tr. 1778. 823. Says, that other things being equal, balls are struck fur- ther otf than points. Thus a point, moving swiftly under a conductor, approached nearer to it without being struck than a ball. Peihaps, however, there was time for a par- tial discharge in silence ; if sp, 3 point must have great power in producing such a discharge. 486 CATALOGUE. METEOROT.OGT, WATERSPOUTS. Verhaltungsregehi bey doniierwittern, von Lichtenberg. 8. Goiba, 1778. Rosenthal. Goth. Mag. IV. i. 1. Reimarus von blitz ableilungen. 8. Hamb. 1778. Reimarus on conductors. Gilb. VI. 377. Barbier du I'inan on conductors for build- ings. Roz. XIV. 17. Latourette on conductors at Lyons. Roz. XIX. 382. Camus on ringing bells in storms. Roz. XIX. 398. Camus on conductors. Roz. XXII. £23. Bartaloni on a conductor at Sienna. A. Sienn. VI. 253. Blagden and Nairne on tlie accident by lightning at Heckingham. Ph. tr. 1782. 335. There were eight pointed conductors of iron ; but the communication with moisture in the earth was perhaps im- pared, the conductors were rusty, and perhaps they were too distant ; there was at the time a very heavy rain. A woman said she saw three balls of fire strike the house. The wall was injured, and a saddle hanging in a stable was da- maged. E. M. A. V. Art. Paralonnerre. Buissart on a multiplicity of conductors. Roz. XXI. 140. Gallitzin and Achard on conductors. Roz. XXII. 199. Conductors for a powder magazine. Roz. XXII. 477. ^lichaelis and Lichtenberg on conductors. Roz.. XXIV. 320. XXV. 297. XXVI. 101. Showing, that the bars which were fixed on the temple of Solomon, tokeepoff the birds, must have served as conduc- tors. iMTidriani dell' utilita dci conduttori. 8. Milan, 1784. R. S. Breitingcr on a conductor. Roz. XXIX. 90. JJemmerubev wetterleiter. Manh. 1786. II. I. iif;nOTt7i verhaltungsrcgeln. 8. Manh. 1791. A conductor, with means for extinguishing fire. Goth. Mag. V. iv. 148. Lord Stanhope. Ph. tr. 1787. 130. Recommends a number of conductors not far apart. Geanty on conductors. Roz. XXXI. 286. Bergmann on conductors. Opusc. VI. 110. Leipz. Samml. zur Phys. II. 583. The church at Genoa was struck, notwitstanding a con- ductor. Bonnin on conductors. Roz. XXXII. 26l. Patter.son on conductors. Am. tr. III. S21. Repert. I. 1 14. Employs black lead for the points. Nicholson. Ph. tr. 1789. Observes, thata point, projecting frotn a ball, only modi- fies its effect, and concludes, that a sharp conductor pro- jecting from a building can seldom act as a point, especially when the cloud is negative. Gross Ableitungskunst. Leipz. 1796. Regniei's conductor approved. M. Inst. IV. Haldane on conluctors. Nich.Gilb. V. 115, Wolff on conductors. Gilb. Vlil. 69. Von Arnim on conductors. Gilb. VIII. 290. Gilbert on relief from a stroke of lightning. Ph. M. XVII. 300. A person struck by lightning in bed at Augusta, a Jan. 1803, and left senseless, was recovered by some pails of cold water, which his wife threw on him. The point of a conductor ought to be of copper, not only as being less liable to rusf, but as conducting equally well with iron of twice the dimensions. Reimarus recommends, that all the highest parts of a house should be protected by slips of lead communicating with the ground. And this method is preferred by many to a pointed conductor. Conductors have sometimes been fixed to sticks and um- brellas, connected with a chain which is dragged along tht ground, but they can afford little or no protection. Waterspouts, perhaps of Electrical Origin, generalli/ accompanied by Electrical Phenomena. Mayne on a waterspout on the river at Tops- ham. Ph.tr. 1695. XIX. 28. CATALOGUE. — METEOROLOGY, AFATEUSPOUTS, 487 An appletree s inches in diameter was cut off and thrown contrarily to the direction of the spout : an anchor was also carried several feet. Gbidon on a waterspout in the Downs. Ph. tr. 1701. XXII. 805. Delapryme on a spout. Ph. tr. 1702. XXIII. 281. It seemed to be produced by a concourse of winds, turning like a screw, the clouds dropping down into it : it threw trees and branches about with a gyratory motion. Delapryme on a second spout in Lincoln- shiie. Ph. tr. 1703. XXIII. 1331. It was like the first, taking thatch from the houses and lead from the church : the tube seemed to fill at both ends. *Stuart's description of waterspouts, with figures. Ph. tr. 1/02. XXIII. 1077- Some appeared to be hollow, with water ascending in them: they began from above and from below nearly at the same time. Ricliardson on a fall of water from a spout. Ph.ir. 1719- XXX. 1097. The spout does not appear to have been seen, but 10 acres of ground were destroyed, and a cavity seven feet deep was left. Bocanbrey on a vortex of fire rolling on the earth. A. P. 1725. H. 5. Perhaps a waterspout with some electric light. Harris on a waterspout. Ph. tr. 1733. XXXVIII. 75. By estimation of the distance, its thickness must have been about 60 yards, its height J of a mile. It wasted first at the lower part. Lord Lovell. Ph.tr. 1742. A phenomena like Bocanbrey's. Barker on a meteor like a waterspout. Ph. tr. 1749. XLVl.248. A black whirling cloud that carried up water, and tore off an ash 8 inches thick : it surrounded some persons like a thick mist, whirling about and dividing itself. Ray on a watcispout in Deeping fen, Lin- colnshire. Ph. tr. 1751.477. It was first seen moving across the land and water of the fen : it raised the dust, broke some gates, and destroyed a field of tuimps : it vanished with an appearance of fire ; it was accompanied by three others. Franklin. Ph. tr. 1765. 182. Read 1756. Franklin on electricity. Thinks a vacuum is made by the rotatory motion of the ascending air, as when water is running through a funnel, and that the water of the sea is thus raised. But no such cause as this could do more than produce a slight rarefaction of the air, much less raise the water to above 30 or 40 feet. At the same time the force of the wind thus excited might carry up much water in detached drops, as it is really ob- served to exist in waterspouts. Swinton on a meteor seen at Oxford. Ph.tr. 1761.99. Forster's voyage. L 19I. Dubourdine on a waterspout seen near the Seine. A. P. 1764. H. 32. Brisson on a waterspout. A. P. 1767. 409. H. 11. On a terrestrial spout. Roz. VII. 70. Butel on a terrestrial spout. Roz. VII. 334. Fig. Mentions a fiery cloud. Wilke. Schw. Abh. 1780. Goth. Mag.V. iv. 90. Oliver on waterspouts. Am. tr. II. 101. Observes, that water may be sucked up by a quill held at some distance above it. Perkins on waterspouts. Am. tr. II. 335. Michaud on a waterspout. M. Tur. 1788. IV. App. 3. Roz. XXX. 284. Nith. I. 577. Gilb. VII.49. Spallanzani on some waterspouts. Soc. Ital. IV. 473. Wild on a waterspout on the lake of Geneva. Journ. Phys. XLIV. (I.) 39- Gilb. VII. 70. Baussard on a waterspout. Journ. Phys. XLYl. (IU.)346. Gilb. VII. 73. Wolke on a waterspout. Gilb. X. 482. Professor Wolke gives an account of a waterspout, which passed immediately over the ship, in which he was sailing, in the Gulph of Finland : it appeared to be about 25 feet in diameter, consisting of drops about the 488 CATALOGUE. — METEOROLOGY, AURORA BOEEALIS. size of a cherry ; the sea was agitated round iti base through a space of about 130 feet in diameter : the relator rather supposes that the water was ascending than descending. Cavallo. III. 306. Thinks electricity rather a consequence than a cause of waterspouts. They sometimes vanish and reappear. Murhard on some waterspouts. Gilb. XII. 239. Destiiption of a JValerspout. In a letter Jrom William UiCKETTS, Esij. Captain in the R»yal Navy, to the Right Hon. Sir Joseph Banks, Bart. K.B. P. R. S. Read to the Royal Society sth May, 1803. From the Journals of the Royal Institution. II. 75. In the month of July 1800, Capuin Rickctts was sud- denly called on deck, on account of the ra^jid approach of a waterspout, among the Lipari Islands : it had the appear- ance of a viscid fluid, tapering in its descent, proceeding from the cloud to join the sea : it moved at the rate of about two miles an hour, with a loud sound of rain : it passed the stern of the ship, and wetted the after part of the mainsail : hence Captain Ricketts concluded that water- spouts were not continuous columns of water : and subse- quent observations confirmed the opiirion. In November 1801, about twenty miles from Trieste, a waterspout was seen eight miles to the southward ; round its lower extremity was a mist, about twelve feet high, nearly of the form of an Ionian capital, with very large vo- lutes, the spout resting obliquely on its crown. At some distance from this spout, the sea began to be agitated, and a mist rose to the height of about four feet : then a projection descended from the black cloud which was impending, and met the ascending mist about twenty feet above the sea ; the last ten yards of the distance were described with a very great rapidity. A cloud of a light colour appeared to ascend in this spout like quicksilver in a glass tube. The first spout then snapped at about one third of its height, the inferior part subsiding gradually, and the superior curling upwards. Several other projections fiom the cloud appeared, with corresponding agitations of the water below, but not always in spots vertically under them : seven spouts in all were formed ; two other projections were reabsorbed. Some of the spouts were not only oblique but curved : the ascending cloud moved most rapidly in those which were vertical; they lasted from three to five minutss, and their dissipation was attended by no fall of rain. For some days before, the wea- ther had been very rainy with a south easterly wind ; but no rain had fallen on the day of observation. Aurora Borealis. Account of authors, Weigels Chemie. I. 324. M. Berl. 1710. I. 131. Seen in 1707. Halley. Ph. tr. 1716. XXIX. 40G, The first that he had seen. Halley. Ph. tr. 1719. XXX. 1099. Barrell. Ph. tr. 1717. XXX. 384. Folkes. Ph tr. 1717. XXX. 586. Ph. tr. 1719- XXX. IIOI. In Deyonshire. 1719. XXX. 1104. At Dublin. Hearne. Ph. tr. 1719- XXX. 1107. Percival. Ph. tr. 1720. XXXI. 21. At DubUn. Ph.tr. 1721. XXXI. 180. In Devonshire. Ph. tr. 1721. XXXI. 186. Linnae regis. Ph. tr. 1723. XXXII. 300. Binman. Ph. tr. 1724. XXXIII. 175. Langwith, Huxhani, Hallet, Halley, and Calandrini. Ph. tr. 1726. XXXIV. 132.. 150. Langwith. Ph. tr. 1727- XXXV. SOI. With a good figure. Dobbs. Ph. tr. 1726. XXXIV. 128. Huxham. Ph. tr. 1750. XLVI. 472. Meyer. C. Petr. I. 351. Derham. Ph.tr. 1727. XXXIV. 245. 1729. XXXVI. 137. At Lynn. Ph. tr. 1727. XXXV. 253. llestrich. Ph. tr. 1727. XXXV. 255. Ph.tr. 1728. XXXV. 453. Maier. C. Petr. IV. 121. Cramer. Ph. tr. 1730. XXXVI. 279. Hoxton on an agitation of the needle. Ph tr. 1731. XXXVII. 53. It lasted an hour. Greenwood and Lewis. Ph. tr. 1731. XXXVII. 55. Mairan Trait^ de 1' aurora boreale. 4. Par CATALOGUE. — METBOROLOGY, AURORA EOREALIS. 469 1733, 2. ed. 1754. A. p. 1731: Suite. 1751. Suite. Ace. A. P. 1732. H. 1. Ph. tr. 1734. XXXVIII. 243. by Eames. Thinks the aurora borealis about 200 leagues above the earth : in one instance, Cramer computed the height to be 160 leagues. Supposes it derived from the sun's atmo- sphere, extending in some directions beyond the earth's orbit ; attributes the nebulae of stars and the tails of comets to a similar substance. Mairan's explanations. A. P. 1747.363..423. H. 32. Account. 17j1- H. 40. On Euler's system and on his oven. Mairan observed the direction of the dipping needle to the pole of the aurora borealis. M. Young. Wcidler. Ph. tr. 1734. XXXVIII. 291. Wtidler de aurora boreal). 4. Celsius. Ph. tr. 1736. XXXIX. 241. Short. Ph. tr. 1740. XLI. 368. Ph.tr. 1741. XLI. 583. Various accounts, with a good figure. Hevelius. Ph. tr. 1741. XLI. 744. Mortimer, Martyn, and Neve. Ph, tr. 1741. XLI. 839, 840, 843. Martyn. Ph. tr. 1750. XLVI. 319, 345. Nocetus de iride et aurora boreah, cum notis Boscovich. Rom. 1747. Miles. Ph. tr. 1750. XLVI. 346^ Baker. Pii. tr. 1750. XLVI. 499. Winkler de vi vaporum solarium in lumine boreali. 4. Gabrius. Ph.tr. 1751.39. *Wargeiitin. Ph. tr. 1751. 126. Observes the effect on the compass. VVargentin's history. Schw.Abh. 1752. I69. 1753. 85. Bartram and Franklin. Ph. tr. 1762.474. Franklin's works. II. Franklin. Roz. XIII. 409. Bergmann. Ph. tr. I7G2. 479. Bergmann. Sehw,. Abh. 1764.. 200, 251. On the height of the lights, VOL. II. Bergmann. Opusc. V. 272. Swinton. Ph. tr. 1764. 326, 332. I767. 108. A luminous arch. Ph. tr. 1769. 367. 1770. 532. Messier. Ph. tr. 1769. 86, Wiedeburg iiber die nordlichter. 8. Jena, 1 77 1 • Am. tr. I. 404. Fdbiger Wie nordlichter zu beobachten. 4, Sorau, 1772. Winn. Ph, tr. 1774. 128.. Observes, that the lights are generally followed the day after by a storm from the S. or S. W. Hell. Ephem. Vienn. 1777. Hupsch Untersuchung des nordlichts. 8. Co- logn, 1778. Van Swinden. S. E. VIII. 1780. Roz. XV. 128. A. Petr. 1780. IV. i. H. 19- Observes, that the variation of the needle increases wrhen the aurora borealis is approaching. Fan Swinden Recueil de memoires. Hague, 1784. IIL 173. Cavallo on an arch which lasted more than an hour, and eclipsed the sUirs. Ph. tr. 1781.329. Peyrouse de la Coudicre. Goth. Mag. I. i. 10. E. M. Physique .Art, Aurore boreaie,,. VVilke von den neuesten erklarungen des nordfichts. Schwedischcs Museum. 8. Wis- mar, 1783. I. 31. Kiinig. Goth. Mag. III. ii. 175. Blagilen and Gmelin. Ph. tr. 1781. 228. Several testimonies of a rustling noise heard with these lights. Cramer iiber die entstehung des nordlichts. S.Brem. 1785. Ace. Goth. Mag. IV. ii. l63. Gannei. Am, Ac. I. 237. Eggers Bcschreibung von Island. 8. Copenh, 178G, Viano. Roz. XXXIIL 153. Ginge. NvoSamling. Copenh. III'. Hey, Wollaston, Hutchinson, Fj^nklin;, Pi- 3 K 490 CATALOGUE.— JIETEOROLOGrY<«A»BUQUAKES. god and Cavendish on lunoinous arches. Ph. tr. 1790. 33 . . 47,101. Cav'cndish thinks, tliat the height wis between 52 and 71 miles; observes, that the diffused nature of the light may make the appearance different in different places, and thus make distant observations fallacious ; says, that the common aurora borealis has been supposed to consist of parallel streams. Libes in Rozier. June 1790. Febr. 1791. XXXVIII. 191. Lichtenberg in Erxleben. Compares the aurora borealis to th^ excitation gf the tourmalin by heat. Dalton's meteorological observations. 8. 1793. 54, 153. Thinks that the apparent beams of the aurora borealis are the projections of cylindrical portions of a magnetic fluid which are actually parallel to the dipping needle, and therefore appear to converge to the magnetic pole, that the light is produced by the transmission of electricity through them, which somewhat disturbs their magnetic properties. TTie arches are always perpendicular to the magnetic meri- dian,and, being more pcrmanentin their form, afford an op- portunity of determining the height, which from one observ- arion on a base of B-2 miles, appears to be about i so miles. Ciiimincllo 011 a luminous arch. Soc. Ital. VIL 153. Ritter on the hinnr periods of the aurora bo- realis. Gilb. XV. 206. ' Earthquakes and Agitations. In order of time. Account of authors. VVeigels Chemie. §. 369. An earthquake in the year 17 destroyed 12 cities in Asia. Herculaneum destroyed in 79. Earthquakes at Antioch in 115,458^526, 528,581 and 1159- The Thames ebbed for a whole day, 1214. St. Paul's injured in 1580. Boyle. Ph. tr. 1665— 6. 1. 179. Near Oxford. Pigot, Ph.tr. 1683- XIIL 311. At Oxford. Listeronearll^qijakps.Ph. tr.l684. XIV.511. Deduces them from pyrites. Lima nearly destroyed in 1689 : a hundred thousand perished. Hartop and Burges. Ph. Ir, l69.^. XVII. 8?7, 830. In Sicily. Bonajuto. Ph. it. 1694. XVI II. o. la Sicily, 60 menkilled. Sloane. Ph. tr. 1694. XVIII. 78. In Peru, 168". Ph. tr. 1700. XXII. Effects on tlie rivers about Batavia. Lem6ry. A. P. 1700. 101. H. 54. Thoresby. Ph. tr. 1704. XXIV. 1555. An overflow of the sea near Avranches, A. P. 1716. H. 16. Barrel. Ph. tr. 1727. XXXV. 305. Colman. Ph. tr. 1729- XXXVI. 124. At Boston. Cyriili historla terraemotusNeapoiitani, 1733. Ph. 1731.tr. XXXVIH. 79. Cyriili aeris terraeque historia, 1732. Ph. tr. 1733. XXXVIII. 184. Lewis. Ph. tr. 1733. XXXVIII. 120. Dudley. Ph. tr. 1735. XXXIX. Q3. In New England. Duke of Richmond and others. Ph. tr. 1736. XXXIX. 361. Sussex and elsewhere. Temple. Ph.tr. 1740. XLI. 340. At Naples ; the shock was slight, but it was attended by a remarkable agitation of the nervous system in all who felt \U This seems to favour the supposition that electricity i« concerned. Johnson. Ph. tr. 1741. XLI. §01. At Scarborough. Plant.Ph.tr. 1742. XLII. 33. In New England. Ph. tr. 1742. XLII. 77- Leghorn. A great earthquake at Lima in 1746. Forster. Ph. tr. 1748. XLV. 398. Taunton. CATALOGUE. — lAf ETEOROLOG Y, EARtHQU AKES. A91 A collection of 56 letters and papers relative , to earthquakes in England and elsewhere, in. 1750. Ph. tr. 1750. XLVJ. 601. Stukely on the causes of earthquakes. Ph. tr. 1750. XLVI. 657, 731. Attributes them to electricity, prindpally from the rapidity with which they affect extensive tracts of country. 6'fMAe/y's philosophy of earthquakes. 8. Lond. J 756. M, B. Hales on the causes of earthquakes. Ph. tr. 1750. XLVI. 669. Thitjks them sulfureous and electrical. Tressan on the overflow of the brook Sirkes. A. P. 1750. H. 34. Baker. Ph. tr. 1754. 564. At York. At Cairo 1754. Destroyed " 40 000." Porter.Ph.tr. 1755. 115. At Gtmstantinople. Accounts of the great earthquake, 1 Nov. 1755, and of the earthquakes of 9 and 18 Nov. in 49 letters. Ph. tr. 1 755. 35 1 . . 436. Destroyed the city of Lisbon. Pye. Ph. tr. 1756. 458. ■ Frequent at Manilla. Whytt. Ph. tr. 1756.501. At Glasgow. A shower of dust in the N. Sea. Bonnet. Ph. tr. 1756.511. The I4lh Nov. 1755. Allemand. Ph. ir. 1756. 512. The 26 Dec. 1755. Stevenson. Ph. tr. 1756. 521. An agitation of a lake in Dumfriesshire for 4 hours. Feb. 1756. Accounts of the irregularities of the tides in the Thames, Feb. 1756. Ph. tr. 1756. 523. 530. Mrs. Belcher. Ph. tr. 1756. 344. An agitation of lake Ontario, Feb. 1756. Grovestiiis. Ph.tr. 1756.^544. Hague, Feb. )756. Allemaad. Ph. tr. 1756. 545. Pringle. Ph. tr. 1756. 546. At Brussels. Ph. tr. 1756. &oO. Agitations. Warren. Ph. tr. 1756.579. Donati. Ph. tr. 1750. 6 1 2. At Turin. Ph. tr. 1756. 6 16. At Brigue, by the Rector of the college. Condainine's inferences from earthquakes. Ph. tr. 1756. 622. Prince. Ph. tr. 1756. 642. An agitation at llfracorabe. Holdsworth. Ph. tr. 1756. An agitation at Dartmouth. 643. Vernede. Ph. tr. 1756. 663. Maestricht. Affleck. Ph. tr. 1756. 668. An agitation at Antigua. Rutherforth. Ph. tr. 1756. 681. Agitations inHartfordshire. Trembley. Ph. tr. 1756. 893. On a shock and agitations. Ed. ess, 11.423. Hannov. nlitzi. Samml. 1756. xix. Mayer refers earthquakes to a change of the direction of gravitation. Bertrand Recueil de traites sur les tremble- , mens de terre. 8. 1756. M. B. Bertrand Meinoire sur les tremblemens de terre. 8. Hague, 1757. Winthorp. Ph. tr. 1757. 1. In America, 18 Nov. 1755. An earthquake in the Azores, 1757. Buried " 10 000" persons. Perry. Ph. tr. 1758. 491. In Sumatra, 1756. Borlase. Ph. tr. 1758.499- 1762. 418, 507. In Cornwall. j. Burrow. Ph. tr. 1758. 614. Paderni. Ph.tr. 1758. 619. At Herculaneum. Peyssonei. Ph. tr. 1758. 645. Russel. Ph. tr. 176O. 529. In Syria. *Michel[ on the cause of earthquakes. Ph. tr. 1760. ob6. Explaining the operation of subterraneous fires at differ- ent depths : and attributing the explosions to steam. 493 CATALOGUE. — METEOROLOGY, EARTHQUAKES. Salvador and MoUoj. Ph. tr. 176I. At Lisbon, 30 March 1761. Heberden. Ph. tr. 176I. 155. In Madeira, 3 1 March. Mason. Ph. tr. 1762. 477. An agitation at Barbadoes, 31 March. Weymarn. Ph. tr. 1763. 201. Id Siberia. Gulston, Hirst, and Verelst. Ph. tr. 1763. 251.. 265. At Chattigaan. Saussure. A. P. 1763. H. 18. An elevation of waters at Geneva. Tucker. Ph.tr. 1764.83. An irregular tide at Brisitol. Ph. tr. 1765. 43. At Lisbon, l"84. Bevts's Iiistory and philosophy of eartii- qufikes. 8. Devisme. Ph. tr. 1769. 71. At Macao. Ilollmann Sylloge Comm. 1. W ark's method of measuring earthquakes. Ed. ess. III. 142. Koz. 1.376. By powdeiing the inside of a vessel partly filled witli water. A great earthquake in Guatimala. 1774. Henry. Ph. tr, 1778. 221. At Manchester, 1777- It extended 140 miles : the bells tolled twice ; it was observed that most noise was heard in the neighbourhood of conductors of electricity, and some shocks were felt. AtTauririn Persia in 1780. Threw down 15 OOO houses. Pennant. Ph. tr. 1781. 193. In Wales. Lloyd. Ph. tr. 1781. 331. At Hafodunos : the barometer was not affected. lioyd. Ph. tr.l783. 104. In Wales. *Hamilton. Ph. tr. 1783. 169. Calabria. Ippolito. Ph. (r. 1783. 209. Calabria. Leone Giornale de' tremuoti. 2 v.8.Nap].1783. VivenzioStoria. de' tremuoti. 4.Napl. 1783.II.S. Pira sulla causa de'tremuoti. 4. Catan. 1783. Sarti Congeturresu i tremoti. 8. Luce. 1783. X)o/o»iteMsurletremblement deterrede 1783. Holm vom Erdbeben auf Island. 8. Copenh. Goth. Mag. V. iii. 128. Wiedeburg liber erdbeben nnd nebel. On the fog of 1783. See Clouds and Mists. Bartels briefe liber Calabrien. 2 v. Gott. 1784. - Seybold vom erdbeben. Hubnen phys. ta- geb. I. ii. Salzb. 1784. Rozier Aug. and Sept. 1785. Williams on earthquakes. Am. Ac. I. 260. Stepkensens schilderung von Island. Alt. 1786. More on an earthquake in the north of Eng- land. Ph.tr. 1787.35. Le/imann Gedanken vom erdbeden, 8. Berl. 1787. Fleming on an agitation of Loch Tay. Ed. tr. I. 200. fBertholon on a paratremblement and a pa- ravolcan. lloz. XIV. 111. Cunductors. Bej/trdge zur kenntniss beyder Sicilien. 8. Zur. 1790. II. ' ' Voglio on an earthquake, 1779. C. Bon. VII. o. 27. In Cuba, 1791, vvith a storm. Destroyed 3000. Turner. Ph. tr. 1792. 28S. Lincolnshire. Taylor on some shocks. Ed. tr. III. 240. An earthquake in Turkey, April 1794. Destroyed 6000. Gray. Ph. M. 1796. 353. The 18 Nov. I7fl5. The extreme places aflfected were Leeds, Bristol, Norwich and Liverpool; the centre, Derby- shire and Leicestershire. A very dark cloud was seen be- fore the shock, and at the moment, a blast of wind, some- what like an explosion, was heard. Gray thinks, the causes of earthquakes sometimes subtenancous and sometimes at- mosphcrLcaL CATALOGUE. — METEOROLOGY, SUBTERRANEOUS FIRES. 493 Cavanilles. Nich. III. 377. Ph.M. V. 318. Gilb. VI. 67. In Peru, 1797. CourrejoUes on earthquakes. Journ. Phys. LIV. 103. LVH. 119. Ph. M. XII. 337. Ph. M. X. 368. In Scotland. Ph. M. XV. 90. In Transylvania. Subterraneous Fires and Vokanos. Account of authors. Weigel Chemie.§.369.c. Eruption of Vesuvius that destroyed Pompeii, described by Pliny. Epist. Hcrculaneura was accessible by a well in 1730, it$ ruins having been discovered the year before. Robinson on a rain of ashes in the gulf of Volo. Ph. tr. 1665—6. I. 377. Eruptions of Elna.Ph,tr.l669.IV. 909, 1028. Bordli hisloria incendii Aetnaei, anni 1669. 4.Reg, Jul. 1670. M.B, Acc.Ph.tr. 1671. VI. On a volcano in the island of the Palma in 1677. Hooka. Lect. Cutl. 52. Nine or ten houses vrere burnt, and 300 acres of land spoiled. Palma is one of the Canaries. Paragallo Istoriadel monle Vesuvio. 4. 1689- M. B. Account of vokanos in Ternate and else- where. Ph. tr. 1695. XIX. 42. Moluccan volcanos. Ph. tr. 1697- XIX.529. Bianchini on a fire in the Apennines. A. P. 1706. 336. Hear Firenzuola. Valletta de incendio Vesuvtano, 1707- Ph. tr. 1713. XXVni. 22. Berkeley on the eruptions of Vesuvius. Ph. tr. 1717. XXX. 708. Forster on a burning island raised but of the sea near Tercera. Ph. tr. 1722. XXXII. 100. Kesbitt on a subterraneous fire in Kent Ph. tr. 1727. XXXV. 307. Three acres of a marshy field vpere burnt by a slow and spontaneous combustion, like that of a hay rick. Cyrilius on an eruption of Mount Vesuvius. Ph.tr. 1732. XXXVII. 3.36. Prince Cassano on an eruption of Mount Ve- suvius. Ph. tr. 1739- XLl. 237. Another account. 252. *Serao on the eruption of Vesuvius in 1737. Naples. Shepherd on the boiling of a canal. Ph. tr. 1739. XLI. 289. Merely from inflammable air. Histoire du mont V^suve. 12. Par. 1741. Supple on the eruption of Vesuvius. Ph. tr, 1751.315. Another accoun t. 409. Parker on tl>e eruption of Vesuvius. Ph. tr. 1751.474. Jamineau on the eruption of Vesuvius. Ph, tr. 1755. 24. Account of an eruption of Etna. Ph. tf. 1755.209. Delia Zbrre Istoria del Vesuvio. 4. Napl. 1755. Mitchell on a shower of black dust in Zet- land. 1757. 297. Stiles and Mackinlay on an eruption of Ve- suvius. Ph. tr. 1761. 39,44. ♦Hamilton oh an eruption of Vesuvius. Ph. tr. 1767. 192- 1768. 1. I769. 18. 1780.42. Hamilton's journey to Etna. Ph. tr. 1770. 1. Hamilton on the soil of Naples. Ph. tr. 1771. 1. Hamilton's letters on vokanos. Germ. 8. Frankf. 1784. Hamilton i Campi Phlcgraei, with asupple- menu f. R. S. Hamilton on tiie present state of Vesuvius. Ph. tr. 1786. 365. Hamilton on the late eruption of Vesuvius. Ph. tr. 1795. 73. With coloured plates. The eruption was as violent as any on record, excepting those of 7 9 and 1631. It was expected ; the crater having been nearly filled ; the water had also 494 CATALOGUE. — METEOROLOGY, SUBTEURAN EOU-S FIRES. subsided in the wells. Ashes wet wiih salt water were thrown out: the ashes were very thick at Taranto, 250 miles off : a stone ten feet in diameter was thrown to an imniense height, and eighteen hours afterwards, a shower of stones fell at Sienna, 250 miles off. The electricity of the atmosphere was positive ; there was violent lightning, with the appearance of balls of fire bursting. A stream of lava 1300 feet wide and 24 deep destroyed Torre del Greco, and covered 3000 acres of vineyards. Twenty seven ounces of ashes were deposited on a fig branch which weighed only three ; the ashes appeared to be phosphoric. A mofete, or carbonic acid gas, was emitted by the earth, and destroyed vineyards ; but was in one instance successfully drained off. Much sal ammoniac was sublimed. Notwithstanding these devastations, the inhabitants of Torre del Greco, 1 8000 in number, unanimonsly refused the offer of another situation for rebuilding their town. Hamilton and others on the eruption of 1 794. Gilb. V. 40S. VI. 21. Ferbershriek aus Walschland. 8. Prag. 1773. liaspe Beschreibung der Niederhessischen al- ien vulkanen. 8. Cassel, 1774. Mairan on the central fire. A. P. 1765. H. 13. Catani della Vesuviana eruzzione di 1767. Catana, 1768. Bartaloni on volcanos. Ac. Sienn. V. 301. A volcano in Ferro broke out in 1777. Threw out a quantity of red water, which discoloured the lea for several leagues. Faujas de St. Fond sur les volcans. f. Par. 1778. R. I. Faujas de St. Fond Mineralogie des volcans. 8. Par. 1784. R. I. t-Bertholon on a paravolcan. Roz. XIV. 111. A conductor. Mourgue de Montredon on hailstones sup- posed to be volcanic. A. P. 1781. 754. _ Gioeni on ashowerof ashes. Ph. tr. 1782. 1. Gioeni Saggio di litologia Vesuviana. 8. Napl. 1790. R.S. Ducarlaon volcanic inundations. Roz. XX. 113. Volta on terrestrial fires, and on the Pietra mala near Florence. See. Ital. II. 662, QOO. Dolomieu Voyage aux isles de Lipari. Germ. S. Leipz. 1783. Dolomieu on the antiquity of lava. Goth. Mag. III. i. 175. Borch Briefe liber Sicilien. fiO. On the antiquity of lava. Dcluc's letters on the history of man. II. ColUni on volcanos. Germ. 4. Dresden, 1783. Knoll iiber die feueispeyenden barge. 8. Erf. 1784. Anderson's account of Morne Garou, in St. Vincent. Ph. tr. 1785. I6. Fig. Probably a recent volcano. Williams on a remarkable darkness. Am. Ac. I. 234. Jones and Alexander on a mountain sup- posed volcanic. Am. Ac. I. 312, 3)6. Beroldingen Uber die vulkane. 8. Manh. 1791. Arduino on an ancient volcano. Soc. Ital. VI. 102. On the origin of basaltes. Authors quoted by Lichtenberg in Erxl. §. 787. Stanley on the hot springs in Iceland. Ed. tr. III. 127. Three views of the Geyser. R. S. Cassan and RoUo on a volcano in St. Lucia. Ph. M. III. 1.256. Holm on the eruption in Iceland, 1783. Ph. M. III. 113. See Earthquakes. Patrin on volcanos. Gilb. V. I9I. *On the explosion of a blast furnace at Colncbrook Dale. Ph. M. XI. 92. A curious illusliation of volcanic eruptions. Fortis on a shower of mud at Udina. Nich. 8. V. 101. Ph.M. XVI. 374. Probably from dust which had been carried up. Humboldt on mountains and volcanos. Nich. VI. 242. See Earthquakes. " A considerable eruption of Vesuvius happened in 1 104 : a sUU greater in I SOS. CATALOGUE. — JIETEOROI.OGV, GEOLOGT. A9o Geology. See Geography. Goodwin sands overflowed in 1 100. Dollort sea, between Groningen and E. Friesland, formed 1277. Irruption of the sea at Dort, 1421. Destroyed 72 villages and looooo persons. Pleurs in Italy buried by a piece of the Alps. 1618. Mineralogy and geology. Ph. tr. abr. II. iii. 267. IV. 2 p. iii. 205. VI. 2 p. iii. 185. VIII. 2 p. iii. 655. X. 2 p. iii. 587. Steno on a solid within a solid. Engl. Lond. 1671. Acc.Ph.tr. IG71. VIII. 2180. Leibnitii protogaea. Opp. II. ii. 81. Burneti telluris theoria sacra. 4. Lond. 1081. R.I. Wkiston's new theory of the earth. 8. Camb. R.I. Southwell on Pen park hole. Ph. tr. 1683. XIII. Le monde naissant. 8. Utrecht, 1686. Ray^s three physicotheological discourses. 8. Lond. 1692. 1713. R. I. Woodwardi historia naturalis telluris. 8. Lond. 1695. R. I. Woodnard's natural history of the earth. 8. Lond. 1733. Horsham on an irruption of a bog. Ph. tr. 1697. XIX. Keil de theoriis Burneti et Whistoni. 8. Oxf, 1698. R. I. Lister on coal borings. Ph. tr. IG99.XXI.73. fWallis on the original junction of Dover and Calais. Ph. tr. 17OI. XXII. 967. Trees found infens.Th.tr. 1701. XXII. 986. Sinking of Borge, a seat in Norway, 1702. Became a lake 100 fathoms deep. Sherard on a new island in the Archipelago. Ph. tr. 1708. XXVI. 67. Bourguignon on a new island near Santerini. M. Trcv. Ph. tr. 1 70S. XXVI. 200. Scheuchzer on the origin of mountciins. A. P. 1708. H. 30. Buttncri ruderadiluvii testes. 4. Leips. 17 10. M. B. Lord Cromartie and Sloanc on mosses. Ph. tr. 1711. XXVII. 296. Goree on the new island in the Archipelago, with a figure. Ph. tr. 1711. XXVII. 353. Derham on subterraneous trees found near the Thames. Ph.tr. 1712. XXVII. 478. •f-Bishop of Clogher on the sinking of a hole. Ph.tr. 1713. XXVIII. 267. Sachette on the earth sinking in Kent. Ph. tr. 1716. XXIX. 469. Musgrave de Britannia olim peninsula. Ph. tr. 1717. XXX. 589. Le Neve on the sinking of three oaks. Ph. tr. 17 18. XXX. 766. Halley on the universal deluge, read 1 694. Ph. U-. 1724. XXXIU. 118. Refers it to a comet. fOn the ground sinking in Kent. Ph. tr. 1728. XXXV. 551. Mairan's conjectures on the diurnal motion of the earth. A. P. 1729. 41. H. 51. Bourguet Lettres sur les sels et les cristaux. 12. Amst. 1729. M. B. Kluvers Geologia. 4. Hamb. 163O. R. I. Marsigli Storia del mare. Pardines on the ground sinking at Auvergne. Ph. tr. 1739. XLI. 272. Moro dei marini corpi che si trovano su mon- ti. 4. Ven. 1740. M. B. Linnaeus on the increase of the habitable globe. Am. Acad. II. 402. Arderon on the ground sinking in Norfolk. Ph.tr. 1745. XLIIL 52. A hole 12 feet deep, 12J in diameter; probably undei- rained by water. 496 CATALOGUE. METEOROLOGY, GEOLOGY. fRichmond on a moving moss. Ph.tr. 1745. XLIII. 282. Manfredini on the increased depth of the sea. Comm. Bon. II. ii. i. Kriigers geschichte dererde. 8. Halle, 1746. Stther vom uisprunge der berge. 4. Zur. 1746. Sulzer's geological conjecture. A. Berl. 1762. 90. Manfredi on the increase of the sea. C. Bon. II. ii. 1. Buffon. Hist. nat. I. X)ow«/« Storia deir Adriatico. 4. Ven. 1750. Hx)llmann on marine fossils. Comm. Gott. III. 285. Syll. Comm. 170. Borlase on the changes in the Scilly isles. Ph. tr. 1753. 55. Borlase on submarine trees in Mount's bay. Ph. ir. 1757.51. Three hundred yards below the present high water mark : some rootc also remtin in a marshy earth. £ertrand sur les usages des montagnes. 8. Zurich, 1754. R. I. Bertrand Recueil sur Thistoire naturelle de la terre. 4. Avignon, 1766. Maitlet Telliamed, sur la diminution de la mer. 2 v. Hague, 1755. R. I. BPowallius ooi wattu minskningen.8.Stockh. 1755. Germ. Untersuchung von der verminderung des wassers. 8. Stockh. 1756. Matthews on the sinking of a river near Pon- tipool. Ph. tr. 1756. 547. Lehmann Geschichte von Flotzgebirgen. 8. Berl. 1756. Bruun de terrae mutationibus. 4. Petersb. 1756. M. B. Walltrim et Ecjkstrand de origine montium. Ups. 1758. Walhrius et Rude de geocosmo senescente. Ups. 1758. Walhrius et Petharlin de diluvio universal!, Ups. 1761. WalUrius et Murbert de tcllure olim non fluida. 4. Ups. 176I. Traite du deluge. 4. Bale, I76I. Fiichsel. Act. Acad. Mogunt. II. Raspe Specimen historiae naturalis globi. 8. Amst. 1763. Silbenchlag Theorie der erde. 8. Berl. 1764. Silberschtags Geogenie. 3 v. 4. Berl. 1780. Beylag Gott. 1784. (Geogenie). King on the deluge. Ph. tr. 1764. 44. King on a descent of ground near Folkstoue. Ph. tr. 1786. 220. , King's morsels of criticism. Dalrymple on the formation of islands. Ph. tr. 1767.394. Abhandlung von dem ursprunge der gebirge. 8. Leipz. 1770. Lavoisier on the nature of water. A. P. 1770. 73,90. Jmti Geschichte des erdkbrpcrs. 8. Berl. 1770. Lloyd and King on Elden Hole, Ph. tr. 1771.250. Walker on an eruption of the Solway moss. Ph. tr. 1772. 123. . Surprised the inhabitants of 12 villages in theit beds. Ferner on the diminution of the sea.. Roz. Intr. I. 5. Beytr'dge zur physischen erdbeschreibung. 5 V. 8. Brandenb. 1773 . '. 1785. Collected by Otto. Pouget on the changes upon the coasts of Languedoc. A. P. 1775. 56l. Dicquemare on the bottom of the sea. Roz. Vf. 438. Saussure on the physical geography of Italy. Roz. VII. 19. Saussure's geological hints. Ph. M. III. 33. Wiedtburg Neue muthmassungen. 8. Goth. 1776. CATALOGUE, — METEOROLOGY, GEOLOGT. 497 BnfFon Histoire naturelle. Pallas sur la formation des montagnes. 4. Peteisb. 1777. A. Petr. I. H. 21. Remarks. Leipz. Samml. zur Physik. Deluc Lettres sur I'liistoire tie la terre et de I'homme. 5 v. 8. Hague, 1779. K. I- *Deluc's essa\'s, xi. Deluc's letters to Lam6tlierie. lloz. , XXXVII. 290, 332, 441. Roz. XLI.221. 414. Deluc's letter ia the Monthly Review enl. June 1790. 20fi, and II. Append. Deluc's letters to Blumeubacli. Goth. Mag. VIII. 4. IX. 1. Christ Geschichte des Erdkorpers. 8. Frankf. 1785. Barbieri Storia del mare. 8. Ven. 1782. MeisterCommentat. Gott. 1782. V. M. 28. 1783. VI. M. 102. On mountains and on the deluge. Derived from a sup- posed change of the earth's axis. Forster on physical geograpli}'. Fragment iiber die geogonic. 4. Bresl. 1783. Strange de' monti colonnari. 4. R. S. Recherclu's sur la generation des etres or- ganises. 12. Par. 1784. By Serain. On the cavern at Gailenreuth. Schr. Berl. Naturf. V. 56. Ferber on the antiquity of the strata of the earth. N. A. Petr. 1784. Ferber on petrefactions, A. Berl. 1790. 148. Ferber's travels. R. I. Darwin. Ph. tr, 1785.5. Says, that water rises highest from tht lowest strata of the earth ; and infers, that the strata, which arc the highest in the hills, arc the lowest in the plains. J}ouglas on the antiquity of the earth. 4. Lond. 1785. R. S. Trebrayom innern dergebirge.f.Dessau,1785. Trebra sur I'interieur des montagnes. Par. 1787. R.S. Kant's theory. Berl. monatschr. 1785. i. 210. VOli. 11. Spallanzanis travels. R . I. Lincoln's geological observations. Am. Ac. I. 372. Camper on some petrefactions. Ph. tr. 1786, 443. Whit.ehurst on the original state of the earth. 4. Lond. 1786. 1792. R. I. Fossombroni on alluvions. Soc. Ital. III. 533. Brighton blockhouse carried away by the sea in 1786. Ileidiiigcr Eintlieilung der gebirgsarten. 4. Dresden, 1787. Limbirdon a well at Boston. Ph.tr. 1787. 50. JVerner Kurze classification der gebirgsarten. 4. Dresd. 1787. *JVerner iiber die gHnge. 12. Werner on metallic veins. Roz. XL. 334. 46y. Separate. R. I. Thcori/ of the earth. 8. R. S. Lainetherie Theorie de la terre. 5 v. 8. Lametherie's answer to Deluc. Roz. XLI.437. //erc^ers ideenzurgescliichtedermenscheit.il. Hutton's theory of the earth, Ed. tr. I. GOQ. Hutton on some appearances near Arthur's seat. Ed. tr. II. 3. Hutton's system. Roz. XLIII. 3. Ousley on the moving of a bog. Ir. tr. 1788. XL 3. Lavoisier on the strata deposited by the sea. A. P. 1789.351. A geological question. Roz. XXXIV. 401. Mills on the strata in Ireland and Scotland. , Ph. tr. 1790. 73. Pini's geological essays. Soc. Ital.-V. l63. VI, 389. The Neptunian theory. Pini sopra i monti. 4. R. S. On fossil bones. Blununbach Beytrage zur naturgeschichte. 8. Gott. 1790. 1. B. B. Walch on the deluge. Blumenb. Beytr, zur naturgeschichte. 1. 17- 8. Burrows's theory. As. res. II. App. 3s 498. CATALOGUE. — METEOUOLOGy, GEOLOGY. Calcott on Penpark hole. 8. Bristol,! 792. U.S. Dolomlcu on Egypt. Roz. XLII. Ott(^ Naturgescliichte des meeres. 2 v. 4. Bcrl. 1792. Franklin's conjecture on the earth. Am. tr. III. 1, 10. Eiirop. Mag. Aug. 1793. Got- ting, taschent'iilender, 1795. Sinking of the ground in Finland, 1793. Apiece, of the extent of 1000 square ells, sunk 15 fathoms. Outran! on some singular balls of limestone. Ph. tr. 1796. 350. Account of the bones found in the caves of Ba3'reuth, witli Hunter's observations. Ph, tr. 179-i. 402. Taiton peatmosses. Ed. tr. III. 266. ■ _ Latrobe on sand hills, Aui. tr. IV. 439. Pallas on an eruption of mud. N. A. Petr. 1794. XII. 44. Gough on the decrease of the lakes. jNlandi. M. IV. 1. Thinks that many vallies and bogs have formerly been lakes. Tkddoes on flints. Manch. ]\I. IV.fiOS. Wilse on a fall of earth in Norway'. Zach. Ephcm. I. 545. With a map. Aikin's geological observations. Nicli. I. 220. III. 285. Kij-vvan on the primitive state of the globe. Ir. tr. VI.233. *iC/rz£;o?<'s geological essays. 8. Lond. 1799. R. I. Kirwan on the Huttonian theory. Ir. tr. VIII. 3. Nich. IV. 97. Gilb. VIII. 109. Kirwan's remarks on the declivities of moun- tains. Ir. tr. VIII. 35. Ph. M. VIII. 29- ISich. S. IV. >lbG. Observes, that the direcMon of most mountains is from E. to \V. that the S. and S. E. sides are steepest ; and sup- poses that the primitive forms were traced by a current run- ning from W. to E. and that these were modified by a cur- rent running from N. to S, Kirwan's reply to Playfair. Ph. M. XIV. 1, 14. Correa de Serra on a submarine forest. Ph. tf. 1799. 145. On the east coast of England. Bertrand on the theory of die earth. Jom-n. Phys. XLIX. 120. L. 88. Lowenorn on a new island near Iceland. Ph. M. V. 286. On a new island in the sea of Azof. Ph. M. VII. 91. Howard's letters on the creation and deluge. Lond. 1797. H. I. Humboldt's geological sketch of South Ame- rica. Journ. Phys. LIII. 6I. Ph. M. :^VII.347. riai/faii''s illustration of theHuttonian theory. 8. Edinb. 1802. R. I. Lamarck Hydrogeologie. 8. Par. 1802. R.S. Wrede on the supposed remains of the city Vineta. Zach. Mon. corr. V. VI . Reimarus ubcr die bilduug des erdbodens. Hamb. 1802. Ace. Zach. Mon. corr. VII. 180. Remarks on Dcluc's opinion. lleim on the primitive state of the earth. Zach, Mon. corr. VI. 528. Jameson on deposits and petrefactions.'Nich, 8.111. 13. Gy'sgeological ideas. Journ. Phys, LVII.IO9. Hall on whinstoue. Ed. tr. V. 43. Gr. Watt on the texture of basalt. Ph. tr. 1804. 279. Ptfr/f2«son's organic remains. 4. Lond. 1804. R.I. On a hill raised in a lake. Gilb. XVI. 384. In a mossy soil in llolstein. Richardson on the Huttonian theory. Ir. tr. IX. 429. CATALOGUE. — METEOROLOGY, LUMINOUS METEORS. 499 Luminous Meteors. Account of authors. Wcigel Chemie. 1.327- Exhalations. Spontaneous light from decomposition. See Physical Optics. Lhvvd. Ph. tr. 1694. XVIII. 49, 223. Account of some ricks of hay burnt in December 1S93, at Dolgelly, by a vapour like a weak blue flame coming from the sea. Bianchini on a fire in the Apennines. A. P. 1706.336. *Derham and Beccaria on the ignis fatuus. Ph. tr. 1729. XXXVI. 204. Derham thinks it a vapour on fire ; he saw one frisking about a dead thistle, it was disturbed by the slightest mo- tion of the air. Beccari says, that in the neighbourhood of Bologna, they sometimes divide and meet again, and give out sparks ; that they are most common in rain or snow, which may perhaps be because the vapour is forced out of the earth as the water sinks into it ; that they are not actu- ally on fire, but are rather of the nature of cold phosphori ; that when a horse is crossing a muddy place in hot weather, a flame often rises in his footst«ps : that the meteor often appears near brooks and in clayey soils ; and that one in particular seemed fixed to a certain spot, about two feet above some stones near a river, but disappeared when the observer came close to it, nearly in the same manner as a mist is seldom seen where it is very near to us. More. Ph. tr. 1750. XLVI. 466. On the fire at Firenzuola. See Volcanos. Shaw's travels. 4. Lond. 1754. 334. Trebra. Deutscher Merkin-. Octob. 1783. Atmospherical Meteors and Shootino; Stars. Wallis on an igneous meteor. Pli.tr. 1677. Xn. 863. Thoresby.' Ph. tr. 1711. XXVII. 322. Halley on some extraordinary meteors. Ph. tr. 17 14. XXIX. 159. Account of a phenomenon seen in the sea. Ph.tr. 1716. XXIX. 429. Halley on a meteor seen throughout England. Ph.tr. 1719- XXX. 978. It exploded wiih a great report ; it must have been 60 mi!es high, and have passed over300 geographical miles in. a minute. Cotes on a great meteor. Ph. tr. 1720. XXXI. 66. Vievar on an explosion in the air. Ph. tr. 1739. XLI.288. Crocker, Bevis, and Breintnall on meteors. Ph.tr. 1710. XLI. 346,359. Short on several meteors. Ph. tr. 1741. XLI. 625. Lord Beauchamp, Fuller, and Gostling on a fire ball. Ph. tr. 1741. XLI. 871, 872. Gostling. Ph.tr. 1742. XLII. (iO. Mason on a fire ball. Ph. tr. 1742. XLII. 1. Cooke. Ph. tr. 1742. XLII.25. Gordon and Gostling. Ph. tr. 1742. XLII. 58, 60. Milner. Ph. tr. 1742. XLII. 138. A luminous track remained long after the meteor ; there was also a black cloud. Lord Loveli on a fiery whirlwind. Ph. tr, 1742. XLII. 183. See Waterspouts. Cradoek on a fiery meteor. Ph. tr. 1744. XLIII. 78. Costard on a fiery meteor. Ph. tr. 1745. XLIII. 522. Smith and Barker on a fire ball. Ph. tr. 1751. 1,3. Hirst on a fire ball. Ph. tr. 1754. 773. Forster, Colebrooke, and Dutton. Ph. tr. 1759-299,301. *Prlng!e on the accounts of a meteor. Ph, tr. 1 759. 259- Eirch. Ph. tr. 176I.6. In New England. Silberschlag Thcorie dcr feuerkugcln von 1762.4. Magdeb. 1764. Winthrop. Ph. tr. 1764, 185. Very high, as usual. Swinton. Ph.tr. 1764.326. *Leroy on a meteor. A. P. 1771. 668. II. 30. It appears to have been formed over the coasts of En 5- 500 CATALOGUE. — WETIOROLOGY, LUBIINOUS METEORS. laud: it was at first more than 18 leagues high : it described ill 10" more than Oo leagues. Dees not think the ap- . pearances electric. Pringle thought they vrere substances revolving round the earth. Biyclone on a fiery meteor. Pli.tr. 1773. l63. *Caviillo on a meteor seen 13 Aug. 1783, at Windsor. Pli. tr. 1784. 108. With a figure. From the time at which the report was heard it was supixjscd to be 58| miles high, 10*0 yards in diameter, and over Lincolnshire. C/appan meteors abovetIieiUinosphere.4.T{.S. Auhertoii two meteors. Pli. tr. 1784. 112. The first, Ig Aug. moved in a waving line, and from con- curring observations seemed to be 40 or io miles high. Cooper and Edgewortli on a meteor, 18 Aiig.Ph.tr. 1784. 116, 118. *Blag(len on some late fiery meteors. Ph. tr. 1784. 201. The meteor seemed to deviate to the E. and to resume its direction ; its height was about 50 miles : it was observed by many persons that a whizzing was heard at the instant that it passed. It moved at least 20 miles in a second : a velo- city too great for a revolving body ; hence there is reason to luppose its nature electrical. jMore than half the igneous meteors .that have been observed, have moved nearly in the direction of the magnetic.meridian. The author conjectures thatW. Greenland, having become more icy in the course of ye^rs, has had an eflcct on the distribution of the electric fluid, and the electric fluid on the place of the magnetic meridian. Pigott on the meteor of 18 Aug. seen near York. Ph.tr. 1784. 4,)7. Makes its height about 41 miles, its distance about no, S. S.E. Bernstorff. Roz. XXIV. 112. The 18 Aug. 1783. Ilittenhouse. Amer. tr. K. Barletti. Soc. Itiil. HI. 331. Seen 11 Sept. 1784. Franklin. iManch. M. If. S.i7. Suspects that the fog of 1783 may possibly have been produced by smoke " from the consumption by fire of some of those great burning balls or globes vi-hich we happen to meet with in our rapid course round the sun, and which ate sometimes seen to kindle and be destroyed in passing our atmosphere." Letttrt fisicometeorologiche. 8. Turin, 1789. Llidicke on large igneous meteors. Gilb. I. 10. Baudin. Ph. M. 11.225. Gilb. XHI. 346. Fulda. Ph.M. III. 60. Benzenberg and Brandes on the height of falling stars. Gilb. V'"1.224. X. 242. They were observed from a base of 46200 feet F. or 2.1 German geographical miles, 1 5 of which make a degree ; their height was from 4 to 30 of those miles ; the mean height about 11, or near 50 English miles. The velocity of two of them was from 4 to 0 miles, or about 22 English miles in a second. One was brighter than Jupiter, and was 450 miles distant. In the second paper Dr. Benzenberg gives two instances indctail. Scptem. 15. Ashooting starof the fifth magnitude. Elevation of the beginning 7.7 geographical miles, of the end 8.2. Length of the path 1.5 miles. Longitude of the place of disappearance 28" 3' ; Latitude 53'' 22'. Observed by Brandes, in Ekwarden, and Benzenberg, in Ham, near Hamburg : length of the base 14 miles. October 3. An- other of the fourth magnitude observed by the same persons. The termination 7.1 geographical miles above the earth. Ix)ngitude 27" "' ; Latitude 53° 5'. These observations show, says Dr. Benzenberg, that a long base will furnish as accurate a comparison as a shorter one ; that even me- teors of the fourth and fifth magnitude may be seen at places distant above fourteen geographical miles from each other; and they confirm the former observations made at Gottingen with a base of but one or two miles. Dr. Pott- giesser, in Elberfeld, forty iniles distant from Hamburg, saw a meteor on tiie 2nd of October, in the zenith, which appears to have been the same as was scsn at Hamburg in the horizon; its height is estimated at 25 German miles. It was intended to continue these observations with unremit- ting assiduity. Benzenberg on the nature of falling stars. Gill). XIV. 46. Thinks them too numerous to be bodies revolving inde- pendently of the earth. An igneous meteor preceded by a cloud, Gilb. XI. 47s. Hardcnberg on igneous meteors. Gilb. XIII. 250. Droysen on a meteor. Gilb. Xlfl. 370. Wrede on igneous meteois. Gilb. XIV. 55. XV. 111. CATALOGUE. — METEOROLOGY, FALLEN METEORS. 501 A meteor seen at once in Cumana and in Gernumy. Gilb. XV. 109. Account of a meteor seen 13 Nov. 1803. Nich. VI. '279. To me this meteor appeared smaller than is icpresented in most of the accounts of it. Faieyon a meteor, 13 Nov. Nich. VII. 66. Firmiiigcr on a meteor. Pli. M. XVII. 279- With a good figure. Prevost on a meteor. To be published, S. E. Meteors which have fallen to the Ground. Barham on a fiery meteor in Jamaica. Ph. tr. 1718. XXX. 837. It struck i[itc the earth and made several deep holes. Halley's conjectures. Ph. tr. 1719. XXX. n. 360. Wasse on the effects of lightning. Ph. tr. 1725. XXXiH.367. At Mixburg in Northamptonshire, a fire ball was seen to burst, and two holes were made about a yard deep and five inches in diameter, in a gravelly soil : an iron ball shot per- pendicularly from a mortar did not make a greater impres- sion. Mr. Wasse's nephew searched ihe holts, and it) one he found avcry hard glazed slone, ten inches long, six wide, and four thick, cracked into two pieces : a man was killed by what is called the lightning; he was much wounded, with some appearance of electric effects. Cook on a ball of sulfur supijosed to be gene- rated in the air. Ph. tr. 1738. XL. 4'27. It was found in a meadow after thunder ; it was covered ■with crystals. Falconet on the boetilia. Mimoires de I'Aca- d^mie des Inscriptions. 4. Paris. Zahn specula physicomathemalicohistorica. Gemma fisica soiterranea. De Celis on a mass of native iron found in South America. Ph. tr. 1788. 37. At Otumpa, in the chaco Guulamba, far from any mines ©r rocks ; weighii>g about 300 quintals : supposed to be of volcanic origin. There was another piece of an iuboiescent form. Account of a mass of iron in South Ame^ rica like the Siberian. A. P. 1787. H. 8. Nine feet by 6, and 1 foot thick. *Chladni on the Siberian iron. Riga, 179'1. Ph. M. II. 337. Chladni on meteoric stones. Gilb. XIII. 350. Chladni's chronology of fallen stones. Gilb. XV. 307. Agrees with Benzenberg, that shooting stars must be of a different nature, since these sometimes appear to ascend. Hamilton. Ph. tr. 1795. 103. A shower of stones fell at Sienna 1 8 hours after the erup- tion of Vesuvius. King's remarks on stones said to have fallen- from the clouds. 4. Lond. 1796. Sottt/ifi/s travels. Mentions stones that fell in Portugal, Feb. iJgB. Baudin. Ph. M. II. 225. *Fulda on fireballs. Ph. M. IH. 66, 171. Tata on the shower of stones at Sienna. Gilb. VI. 156. Howard on stony and metalline substances which are said to have fallen on the earth. Ph. ir. 1802. 168. Nich. 8. II.216. Gilb. XIII. 291. On stones that have fallen. Gilb. X.502. Grevilleon stones that have fallen in France, and a lump of iron that fell in India. Ph. tr. 1803. 200. Nich. VI. 187. Izarn Lithologieatmospherique. Paris, 1803.' Ace. Gilb. XV. 437. Lalande. Journ. Phys. LV. 451. Gilb. XIIF. 343. Account of a meteor that fell near the Mis- sissippi. Ph. M. XI. 191. Laplace'.'! conjecture on the lunar origin of stones. Zach. Mon. corr. VI. 276. Gilb. XIII. 353. Olbers on the fall of stones. Zach. Mon. corr. VII. 148. Gilb. XIV. 38. Ph. M. XV. 289. Had suggested Laplace's idea in 1795. 502 CATALOGUE. XATURAL HISTORY. fPatiiii's remarks on Howard. Glib. XIII. 328. Klaprotli's analysis of meteoric stones. Gilb. XIH.337. Confirms Howard's conclusions. Finds that terrestrial native iron contains no nickel. Biot on meieoric stones. B. Soc. Phil. Gilb. XIII. 353. Ph. M. XVI. 217. Biot on stones that Tell near Aigle. B. Soc. Phil. n. 7f). Nich. VI. 135. Gilb. XV. 74. XVI. 44. Beauford. Ph. M. XIV. 148. Salverte and Vauqueiin. Ann. Ch. XLV. 62, 225. Ph. M. XV. 346, 354. Gilb. XV. 419. Vauqueiin confirms Howard's conclusions. Foinrroy on the stones which fell near Aigle. Ph. M. XVI. 2iJ9. St. Aniand on stones that fell in Gascony in 1790. Gilb. XV. 429. On a stone that fell in Provence, Oct. 1803. Gilb. XVI. 72. Dree. Journ. Phys. LVI. 380, 405. Ph. M. XVI. 217, 289. G. B. on the lunar oiiarin of meteors. Nich. 8. III. 255. V. 201. Poisson's calculations. Extr. by Biot. B. Soc. Phil. n. 71. Iiitleron the terrestrial origin of stones that have fallen. Gilb. XVi. 221. Infers it from tlie meteorological phenomena : observes ill analojcy with tlic aurora borcalis. Lalande on stones which have fallen. Ph. M. XVII. 228. Bourdon on a showerof stones. Ph. M.XVII. 271. Account of a stone which fell near Glasgow. Ph. M. XVI II. 371. It was seen and heard to fall into a drain ; splashed about the water and mud ; penetrated 1 3 inches, and made a hole 14 inchet in diameter; forcing its way into a sand stone rock ; no warmth could however be perceived in it. From the Journals of the Royal Institution. If. :6. It had long been conjectured by several persons in this country, that the stones said to have fallen from the air, on different parts of the earth, and lately analysed by Mr. Howard, might originally have been emitted b) lunar vol- canos facing the earth ; and meeting with little or no resist- ance from the moon's atmosphere, might have risen to such a height, as to be more powerfully attracted by the earth than by the moon, and of consequence, to be compelled to continue their course, until they arrived at the confines of our atmosphere, and were again retarded by its resistance. The idea has been lately renewed in France by Laplace ; and the inflammation and combustion of the stones has been attributed to the intense heat, which must necessarily be extricated, by so great a compression of the air, as would be produced by the velocity with which these bodies must enter the atmosphere. Mr. Biot has calculated, that an initial velocity, about five times as great as that which a cannon ball sometimes receives, would be suflBcient for the projection of a body from a lunar volcano into the limits of the earth's superior attraction, which are situated at nearly one ninth of the dis- tance of the earth from the moon. A body, entering the atmosphere with such a velocity, would soon experience a resistance many thousand times greater than its weight,and the velocity would therefore soon be very considerably lessened. It has already been shown (Journals I. 152), that a stone of moderate dimensions could scarcely retain a velocity of above 200 feet in a second. With respect, however, to the actual probability of tht stones in question having been projected from the volcanos of the moon, there will, perhaps, long be a diversity of opinions. N.'irURAI. HISTORY IN GENEHAL. ♦Account of authors. Dryander Catalogus Bibliothccae historiconaturalis Joseph! Banks. 5 v. 8. Loud. 1798. Ph. tr. and A. P. Particular references in na- tural history are omitted. Bonnet sur Ics corps organises. 2 v. 8. Amst. 1768. Abrege des transactions philosophiques. Ilts- toiro n.ttureilf. 2 v. 8. Par. 1787. *Liimaei systema naturae. R. I. CATALOGUE. NATURAL HISTORY, SPECIFIC GRAVITIES, 503 Buff'on Histoire naturelle, par Sonnini. 96 v. 8. R.I. Shaw's naturalist's miscellany. 8. Lontl. R. S. Transactions of the Liiineaa society. 4. Lond. 1791... R. I. Dictionnaire d'histoire naturelle.-Par. 1803... R.I. Density of particular Substances. Tables of specific gravities. Ph. tr. 1685. XV. 926, 927. 1693. XVII. 694. Ellicott on the specific gravity of diamonds. Ph. tr. 1745. XLIII. 468. " Leutmann on the specific gravity of fluids. C. Petr. V. 273. *Davies's tables of specific gravities. Ph. tr. 1748. XLV. 418. Abr. X. 206. Vcty copious, with an account of the authors. Musschenb. Introd. II. 536. Brisson on the specific gravities of metals. A. P. 1772. ii. 1. H. 30. Brisson Pesantenr specifique des corps. 4. Par. 1787. K. I. Watson on the specific gravities of salts and solutions. Ph. tr. 1770. 336. Hoy on compressed air. Ph.tr. 1777. Kirwanon the specific gravities of saline sub- stances. Ph. tr. 1781. 7. 1782. 179. Kirwan's mineralogy. Ed. 2. Gilpin on the mixtures of spirit and water. Ph.tr. 1794. 275. Prony Architecture hydraulique. Cavallo's Natural Philosoph}'. II. 74. A Table of Specific Gravities. Principally from Davics and Lavoisier. Davies's table is compiled with great diligence from many different authors ; Lavoisier's is chiefly extracted from Brisson ; it is carried to four places of decimals, but little dependence can be placed on the last. Mineral Productions. Solids Platina, purified 19. 5000 hammered 20.3368 Platina, wire " 21.04)7 Platina, laminated 22.0090 Pure Gold, cast 19-2381 hammered 19-3617 Gold 22 carats fine, of the standards of London and of Paris, cast ■ 17-4863 hammered 17-i69t French gold coin 2 1 u carats fine. cast 17.4022 coined 17-6474 French trinket gold, 20 carats'fine, cast 15-7090 , hammered 15.7746 Mercury 13.5681 Lead, cast 11.352S Litharge 6.30 Pure silver, cast JO.4743 hammered 10.4107 Parisian silver, 11 den. logr. fine, , cast 10.1752 hammered 10.3765 French silver coiji, 10 den. 2 igr- fine, cast 10.0476 hammered 10.4077 Bismuth, cast 9.8-227 Copper, cast 8.7880 wire 8. 8785 Brass, cast 8.3953 Brass wire 8.5441 Cobalt, cast 7-8119 Nickel, cast 7.807O Iron, cast 7-2070 Bar iron 7-7880 Steel, hard, not screwed 7-8103 screwed 7. 8180 soft, not screwed 7-8331 screwed 7-84 04 Loadstone 4.80 Haematite 4.20 Tin, cast 7-2914 screwed 7.2994 Zinc, cast 7.1908 Antimony, cast 0-7021 Glass of antimony 4-9404 Crude antimony 4-0043 Tungstein 6.000.-, Arsenic, cast 5.7633 Molybdena 4.7385 Ponderous spar 4.4300 Jargon of Ceylon 4..4161 Oriental ruby 4.2833 Spindle ruby 3.7SOO Ballas ruby 3.6158 Brasilian ruby 3-5311 Pseudotopaz 4-27 Bohemian garnet 4.1881 504 CATALOGUE.— NATURAL HISTORY, SPECIFIC GRAVITIES. Syrian garnet 4.0000 Jasper, red SapphirofPuy ' 4.07<59 White antique alabaster Oriental sapphir 3.0941 Rhombic calcarious spar Sappliir of Brasil «.1307 Pyramidal calcarious spar Oriental topaz 4.0108 Slate Saxon topas 3.5640 Pitch itone,red Brasillian topaz. ».53(JS blackish Emerjr 4.00 yellow Hyacinth S.087S black Beryl, er oriental aquamarine 3.5489 Onyx pebble Occidental aquamarine 1.722 Transparent chalcedony liiimond, rose coloured 3.5310 Red Egyptian granite white 3.5212 Pure rock crystal lightest S.501 Amorphous quarti Manganese, crude 3.53 Agate onyx Black schorl, crystallized 8.3852 Carnelian amorphous ».«225 Sardonyx Flint glass 3.3293 Purbeck stone White glass Q.8922 White flint Hottle glass 2.7325 Blackish flint Green gla-s 2.64-23 Oriental agate Glass of St. Gobin 2.4882 Prase Fluor, red > S.1011 Portland stone green 3.1817 Whetstone of Auverpie violet 3.1757 Red zeolithe blue 3.16S9 Crystallized zeolithe white S.1'555 Millstone Black and white hone 3.1311 Paving stone White hone 2.8763 Touchstone GranitsUo S.062S Chinese porcelain Green serpentine of Dauphini 2.9883 Porcelain of Limoges Green serpentine 2.8900 Porcelain of Sevet Ophite 2.0722 Lapis obsidianus Green jade 2.9660 Selenite White jade 2.9502 Sulfate of potash Black mica. 2.9004 Sulfate of »od» Basaltes, from the Giant's causeway 3.8642 Grindstone Basaltes from Auvergne S.415S Salt White Parian marble 2.8376 Native sulfur Green marble 2.7417 Melted sulfur Red marble 2.7242 Transpirent sulfur White marble of Carrara 9.7I68 Nitre Jasponyx / S.SlflO Brick Chrysolith 2.7821 Alabaster Chrysolith of Brasil 2.6023 Plumbago Peruvian emerald 9.7755 Sulfate of zinc Red porphyry ».765I Alum Jasper, grey 2.7640 Borax violet 1.7111 Sulfate of iron yellow a.7101 Asphaltura fcrown 2.6911 Scotch coal 9.6612 2.7302 9.7151 9.7141 3.671* 9.660t 2.3191 2.0600 3.049* 9.6644 2.6640 2.6541 3.6530 S.6471 2.037* a.aisr 3.609 » 9.601 9.5041 9.S8ir 9.»901 3.5S0i 2.5^0 2.563* S.486* 9.0(33 9.4aS( 2.415* 2.4153 9.3847 9.3410 9.1457 3.3480 9.322 9.250 9.200 9.149* 9.130 9.0339 1.0907 1 05O 9.000 9.ooe 1.874 1.86 i.sse J. 720 1.71s 1.700 1.400 1.300 N. CATALOGUE. NATURAL HISTOUY, SPECIFIC GRAVITIES. Newcastle coal 1.270 Aloes, hepatic Staifordshlre coal 1.240 Bdellium Jet 1.238 Myrrh Ice, probably .930 Pomegranate tree Pumice stone i . ;. .9145 Cocoa shell Liquids, Opium Sulfuric acid. 1.8409 Lignum vitac Ph. Lond. 1.850 Box, Dutch Nitrous acid, Ph. Lond. 1.550 French Nitric acid 1.2175 Asafoetida Solution of salt 1.244 Tragacanth Water 27, salt 10 1.240 Ivy gum Water 3, salt 1 1.217 Scaihmony, ftohi Smyrna Water 12, salt I 1.060 from Aleppo Water of the dead sea 1.2403 Sarcocolla Sea water 1.0263 Myrrh Solution of caustic soda 1.200 Guaiacum Muriatic acid 1.1940 Gamboge Water of the Seine, filtered 1.0015 Resin of jalap Naphtha .708 Galbanum Substances partly Mineral. Solids. Gum ammoniac Acetite of lead 2.700 Dragon's blood Tartrite of antimony 2.100 Sagapenum Muriate of ammonia 1.400 Lignum nephriticum Ebony Liquids. Olibanum . Sulfuric ether .7394 Heart of oak, 60 years old Nitric ether .9088 Dry oak Muriatic ether • 7298 Pitch Elastic Fluids. Copal, opaque Kirwan. Lavoisier. transparent Barometer 30. Euphorbium Therraora. 52®. Storax Sulfureous acid gas a.203 Oil of sassafras Carbonic acid gas 1.500 .00176 Benzoin Nitrous gas 1.194 Sandarac Hepatic gas 1.106 Yellow amber Oxygen gas 1.103 .00137 Mastic Atmospheric mr l.OOQ .00128 Yellow resin Nitrogen gas .gss .00120 Frankincense Ammoniacal gas .600 Mahogany Hydrogen gas .084 .000096 Acetic acid yegetalle Productions, Oil of cinnamon Crystals of tartar 1.850 Anirae, occidental Extract of liquorice 1.7228 oriental Opopanax 1.6226 Malmsey Madeira White sugar 1.606 Oil of cloves Solution of potash 1.570 G.1II nuts Gum arable 1.4523 Elemi Honey 1.450 Cider Catechu 1.3980 Distilled vinegar Aloes, socotrine 1.379s Water at 60" VOL. 11. 1.3586 1.3717 1.3600 1.3540 1.345 1.3366 1.3330 1.328 .912 1.8275 1.3161 1.2948 1.2743 1.2354 1.2684 1.250 1.2280 1.2210 1.2185 1.2130 1.2071 1.2045 1.2008 1.200 1.177 1.1732 1.1700 .932 1. 150 1.1398 i.0452 1.1244 1.1098 1.094 1.0924 1.0920 1.0780 1.0742 1.0727 1.071 1.063 1.0620 ^0439 1.0426 1.0284 1.0382 1.0363 1.034 1.0182 1.0181 1.0095 1.0000 3 T 506 CATALOGUE. NATURAL HISTORY, SPECIFIC GRAVITIES. Extract from Mr. Gilpin's Table. Ph. tr. 1794. Water. Alcohol, at 30". 40". 50'. 60°. 70». 80°. 10 0 1.00774 1.00094 1. 00068 1.00000 .99894 .99759 10 1 .98804 .98795 98745 .98654 .98527 .98367 10 2 .gsios .98033 .97920 •97771 .97596 .97385 10 • 3 .9?635 .97-172 .97284 .9:074 .968,16 .96568 10 4 .97200 .96967 .967O8 .96437 .96143 .95826 10 5 .96/19 .96434 96126 .958v<4 .95469 .95111 10 6 .96209 .95879 .95534 .95)81 .94813 .94431 10 7 .9.i681 .95328 94958 .94579 .94193 .93785 10 8 .951/3 .94802 .94414 .94018 .93616 .93201 10 9 .94675 .94295 .93897 .93493 •93076 .92646 10 10 .94222 .93827 .93419 .93002 •92580 .92142 9 10 .93741 .9334 ^ .92910 .92199 .92069 .91622 8 10 .93191 .92783 .92358 .91933 .91493 .91046 , 1 10 .92563 .9-2 1. ■■1 •91723" .91287 •90847 .90385 0 10 .91847 .9)428 .90997 .90549 .90104 .89639 i 10 .91023 .90596 .90160 .89707 .89252 .88781 4 10 .90054 .89617 .89174 .88720 .88254 .87776 3 10 .88921 .88481 .88030- .8/569 .87105 • .86622 2 10 .87,585 .87134 .86O78 .86208 .85736 .85248 1 10 .85957 .85507 .85042 .84568 .84092 .83803 0 10 .83896 .83445 .82977 .82500 .82023 .81530 Bouideaur wine .9939 Alder .800* Burgundy wine .9915 Elm .800 Liquid turpentine .9910 to .600 Camphor - .9887 Apple tree .7930 Oil of mint .975 Plumb 1 tree .7550 Oil of nutmeg .948 > to .663 Medlar tree .9440 Indigo .7690 Linseed oil .9403 Maple .7550 Oil of caraway- .940 Cherry tree .7150 Oil of marjoram .940 Quince tree .7050 Oil of spike .936 Orange tree .7050 Oil of rosemary .934 Walnut .6710 Elastic gum .9335 Pear tree .6610 Oil of poppy seed .9288 Fir, yellow .637 Olive wood * .9270 white .569 Oil of beech mast .9176 Male fir .5500 Oil of almonds .9170 Female fir \ .4040 Olive oil .9153 Cypress .6440 Logwood .913 Lime tree .6040 Rape oil .' .913 Filbert wood .6009 Balsam of Tolu .898 Arnotto .5956 Oilof lavender / .8938 ' Willow .5850 Oil oj^ranges .838 Cedar .5608 Essential oil of turpentine .869/ Juniper wood •sso Acetic ether •866* White Spanish poplar .5294 Beech •«*20 Poplar .3830 Ash .8450 Sassafras wood .482 Yew, Spanish •«°?o Cork .3400 Dutch t. .7880 CATALOGUE. — NATURAL HISTOET, SPECIFIC GRAVITIES. 507 Animal Substances, Pearl Coral Sheep's bone, recent Oyster shell Ivory Stag's horn Ox's horn Blade bone of an ox Lac Isinglass Egg of a hen Human blood Blood, buff coat serum red globules Ewe's milk Asses milk Mare's milk 2.?50 Goat's milk 2.680 Cow's milk 2.222 Woman's milk 2.092 Whey of cow's milk 1.917 Wax, white 1.875 yellow 1.840 Lard 1.65a Spermaceti 1.1390 Butter 1.111 Tallow 1.090 Fat of hogs 1.053 of veal 1.058 of nwtton 1.028 of beef 1.126 Ambergrease 1.0409 Lamp oil 1.03SS Solution of pure ammoniji 1.0340 1.0341 1.0324 1.0203 -.0193 .968S .-0648 •9478 .9433 .9423 .9419 .gacs .9842 .9235 .9!232 .9263 .9233 .W7» 508 CATALOGUE. NATURAL HISTORY, SPECIFIC HEAT. A Table of the Capacity of different Substances for Heal. Taken principally, with corrections, from Dr. Thomson's Heat in Heat in table, which was compiled and reduced from Crawford, equal wts. equal vol Kirwan, Wilke, Lavoisier, Bergmann , and others. Pear tree .50 .30 Heat in Heat in Spermaceti oil .500 e( jual wts. equal volumes. Kirwan .399 Hydrogen gas. 21.400 .0021 Beech wood "^ .49 .34 Oxygen gas 4.749 .0065 Oil of turpentine .472 .468 Kirwan .87 Elm •*7 . .30 {Carbonate of amhionia 1.85) Plumb tree .44 .30 Atmospheric air 1.790 .0021 Vinegar .387 .397 Varying nearly as the 8th Distilled vinegar .103 .104 root of the density. Y, Pit coal .278 Nitrogen gas .704 .0008 Charcoal .263 Steam 1 .550 .0000 Chalk .256 Arterial blood 1.030 Quicklime .22 Venous blood .893 Water 9, quicklime 16 .335 Water 1.000 1.000 Agate .195 .503 Cow's milk 1.000 1.033 Glass, without lead .193 Sulfuret of ammonia .994 .813 Flint glass .174 .58 Ice .900 Ashes of cinders .188 Nitric acid .844 Sulfur .183 .364 Nitrous acid .578 .780 Iron .126 .995 Sulfate of magnesia l, water 8 .844 Sheet iron .110 Salt 1, water 8 .833 Rust of iron .250 Nitre 1, water 8 .817 Rust nearly freed from air .167 Nitre l, water 3 .640 Brass .114 .954 Muriateofammonia 2, waters, .779 Copper .112 .985 Solution of potash, sp.gr. 1.348 .759 1.013 Oxid of copper .227 Sulfate of iron 2, water 5 .734 Zinc .098 .703 Sulfate of soda 10, water 29 .728 Ashes of charcoal .091 Oil of olives .710 .650 Silver .083 .83 Ammonia .708 .706 Tin .066 .49 Muriatic acid, sp. gr. 1.122 .680 .763 Antimony .064 .39 Alum 100, water 445 .649 Antimony, Kirwan .086 Lime tree wood .62 .253 White oxid of antimony Fir wood .61 .37 washed .227 Alcohol .003 .504 Oxid of antimony, nearly Sulfuric acid .597 freed from air .167 Kirwan .718 Gold .050 .95 Sulfuric acid 4, water 5 .663 Lead .042 .49 Apple tree .57 .364 Crawford .035 Alder .53 .256 Kirwan .050 Linseed oil .528 .496 " Bismuth .043 .42 Oak .51 .37 . Mercury- .031 .43 Ash .51 .33 ii. - =r a s r* Q f^ 3 r :?> !I? re CD 3" "J cr a- 3- o '^ — ti 3 S' §■ 3 x-s »5 S Water Ice — _ Steam at 212° Hydrogen gas Nitrogen gas Atmospheric air Oxygen gas Carbonic acid gas Fir wood — Elm — — Alcohol — — Ash — — Beech — — ' Olive oil — — White wax — Oak — _ Box — _ Solution of potash Sulfuric acid — Ivory — — Crown glass — Free stone — Plate glass — Flint glass — Diamond — Zinc — — Tin — _ Iron and steel Brass — — Copper — — Silver — — Lead — _ Mercury — — Gold — _ Platina — — A Comparative Table of the Pliysical Pro- perties of Vari- ous Substances H- K- -. fc." 0 0 0 ^ w ^ t- w 4w 0» ^J QO Specific Gravity. 0 2250 10000 5000 5760 3240 to § 0 0 0 0 c 0 c 0 0 ' ' w CC "^ OO'-'t0*'l0W»'iOl/'tn ococ?. 00000000 Height of the modulus of elasticit)-, in thousands of feet. ^« 0 r to Superficial cohesion of an inch, in grains, when liquid , to Lateral adhesion of a square inch, in pounds. to Co to o> 2.5 6 40 to 150 - - Ok ^ ■vr to Co CO Cohesive strength of 0 square inch, in thousand.s of pounds. 01 en 0 0 0 - to 0 - •-4 X ce oi Repulsive strength of a square inch, in thousands of pounds. to h- .^ OD — A. M -^ ci b» O' H- 1-. h- -^ c*; Co 4^ 01 b b 0 0 Simple re fraciive power. 1 o»io«oaou.«ooo OD OJ -^ to 0> Cd CO 0. lb. to 0 (0 10 0 ^ 1.000 .840 .0006 .0021 .0008 .0021 .0065 Heat in a given measure. 510 CATALOGUE. — NATURAL HISTORV, MINERALOOr. General effects of Mixture. Mixed gases. See Metereology. Pearson. Ph. tr. 1796. Aristotle mentions the imrosusception of tin. Hooke on the mutual penetration of mixtures. Birch. III. oil. IV. 11. Hauksbee's experiments on mutual penetra- tion. Ph.tr. 1711. XXVII. 325. Leutmann on the specific gravity of mixed metals. C. Petr. III. 138. Gellert on the density of alloys. C. Petr. XIII. 382. Krafft on the density of alloys. C. Petr. XIV. 252. K'iistner on the specific gravity of mixtures. N. C. Gott. 1775. VI. 102. A mode of comparing the curves expressive of the densi- ties. Achard on the bulk of solutions. A. Berl. 1785. 101. Pouget on mixtures of alcohol and water. Jr. tr. 1789. III. 157. *Blagden ;ind Gilpin on the excise of spiritu- ous hquors. Ph. tr. 1790. 321. 1792. 425. 1794. 275. Sanmartini on the areometer. Soc. Ital. VII. 79. Pearson on some alloys. Ph. tr. 1796. 422. Hassenfratz on saline mixtures. Ann. Ch. XXXI. 285. Hassenfratz on measures of spirit. Ann. Ch. Repert. XIII. 45. Hassenfratz and von Arnim on mixtures. Gilb. IV. 364. The alcoometrical curve. Walker's philoso- phy. Lect. vj. ' Schionbachon the condensation of mi.xtures. Gilb. XI. 175. Ilatchett on the alloys of gold. Ph. ti 1803. 43. Nich. 8. V. 286. Jtkim on specific gravities. 4. Lond. 1803. Ace. Nich. 8. IV. 285. Ph. M. XVI. 26, 305. The bulk of water is diminished by the addition of Jj of sal ammoniac: 40 parts of platina, 5 of iron make but 39 by measure. Robison. Enc. Br. Affinities and Combinations. The proper subject of Chemistry. Beccariaon the internal motions of fluids. C. Bon. I. 483. Le Sage Essai de chimie mecanique. R. S. *Kirwap on the attractive powers of the mi- neral acids. Ph.tr. 1783. 15. Deduces a numerical measure of the elective attraction from the quantity of the substance required to neutralise the acids, and thence explains other phenomena with apparent success. Kirwan on the real acids in salts. Ir. tr. IV. Sc.3. VII. 163. Elliot on affinities in alcohol. Ph. tr. 1786. 155. Audebat on attraction acting in solution. Roz. XXXIII. 198. BerthoUet on the laws of affinity. Extr. Ann. Ch. XXXVI. 278. Venturi on the solution of camphor in wa- ter. Ann. Ch. XXI. 262. Gilb. II. 298. B. Prevost on spontaneous motions in mi.x- tures. Ann. Ch. XL. 3. Uraparnaud on the inutual actions and mo- tions of fluids. Nich. VIII. 201. On the chemical effects of tremors. Nich. VII. 122. In some cases, soda and potash exchange their acids with their temperatures. Ann. Ch. Mineralogy in General. Ph.tr.abr.II.IV.VI.VIII.X. See Geology. CATALOGUE. — NATURAL HISTORY, BOTANY. 511 Systems. KirwarCs mineralogy. 2 v. II. I. Haliy on methods of mineralogy. Ann. Ch. XVIII. 225. Philosophy of Mineralogy. Forms of Primari/ Aggregation. Cri/stal- Ihation. Musschenbroek. Intr. I. pi. 1. Baume and Lavoisier on crystallization, lloz. I. 8, 10. Haliy on the forms of crystals. Roz. XIX. 366. XXIV. 71. XLIII. 103, 146, l6l. A. P. 1784. 273. 1785. 213. 1786. 78. 1787.92. 1788. 13. 1789.519. 1790-27. Ann. Ch. HI. 1. X Vll. 225. Ph. M. I. 1 13. II. 398. Traite de physique. I. K'astner on the fracture of crystals. Commen- tat. Gott. 1783. VI. M.52. Eason on crystallization. Manch. M. I. 29. Wall. Manch.M. II.4t9. Says, that large crystals are formed when the liquid is much exposed to the air, and that in salt works, a little re- sin or oil is thrown in, inorder to make the salt fine. Antic on the crystallization of lee. Roz. XXXIII. 56. Regnier on the crystallization of organized bodies. Roz. XXXIII. 215. Chaptal on the effects of air and light in cfy- stallizalion. Roz. XXXIII. 297. Dorthes on the effects of light. Ann. Ch. II. 92. Kramp. Hind. Arch. II. 80. Denies Hauy's principleof the decrements of crystals pro- ceeding always according to integer numbers. Journ.Phys. LVI. 237. It has been asserted, that powder thrown on electric glass assumed a regular crystalline arrangement ; but further ex- periments have confuted the assertion. Clifford and Buee on the system of Delisle and Hauy. Nich.IX. 26. Ph. M. XIX. 159. Haiiy considers all calculations of forms of crystals as re- ducible to arrangements of parallelepipeds, but he more com- monly refers them to three species of primitive molecules, the tetraedron, the triangularprism, and the parallelepiped, mak- ing by their combinations, first, 6 primitive forms of crystals, which are only divisible in planes paraUeJ to their surfaces, the tetraedron, parallelepipeds, oclaedrons, tegular or irregu- lar, hexaedral prisms, the dodecacdron of equal rhombi, and the dodecaedron of two hexagonal pyramids. These, as they are built up in various orders, decreasing by regular steps, which begin either at the side, or at the angles of a crystal, serving as a nucleus, form all the immense variety of crystalline figures. A dodecaedron of rhombi is sometimes composed of cubes ; a dodecaedron of pentagons may be produced by the same elements with a difierent law of de- crement : a cube is sometimes the nucleus df an cctaetlroa of which the sides correspond to the angles of ihe cube. The molecules of ice are supposed to be either cubes or tetraedrons ; the diagonals of the surfaces of the calcarious rhombus, or the Iceland crystal, are as the square roots of 3 and 2, the obtuse angle of the surface 101° Si' I3'',"that of the contiguous planes 104° 28' 40'. A. P. 1789. and Tr. Phys. Botatiy in General. Abreg6 des transactions philosophiques.Bota- nique. 2 v. Par. 1790. R. I. Ph. tr. abr. II. v. 623. IV. 2 p. v. 29^. Vt.'^ p. V. 307. VIII. 2 p. V. 747. X. 2 p. v. 699. Lirmaei philosophia botanica. Mawe's dictionary of gardening and botany. 4. 1798. R. I. Miller's gardener's dictionary, by Martyh. f. 1798. R.I. Htdwig Descriptio niuscorum. Leipz. fl. I. Gaertnerde fructibus et seminibus. 4. Slutg, 1798. B. B. Smith Flora Britannica. 3 v. 8. Lond. B. B. Wildenouh introduction to botany. 8. Edinb. 1805. R.I. Systems. *Linnaei systema naturae. GenCTa planta-- rum. Species plantarum. sn CATALOGUE. — NATURAL HISTORY, BOTANY. *Jiissieu on the arrangement of plants. A. P. 1773. 214. H. 34. 1774. 175. H. 27. Withering's botanical arrangement. Lamarck on the classification of vegetables. A. P. 1785. 437. Ventenat Tableau du regne vegetal selon la methode de Jussieu. 4 v. 8. B. B. Guiart on the method of Tournefort. Ann. Ch. XLV. 149. Vegetable Anatomy and Phy- siology. Colours of plants. Aristotle on colours. Quoted. Roz. XLI. 470. A. P. Index. Art. Plantes. Tonge. Ph. tr. l669.IV. 913. 167O. V. Il65, 1168,1199,2067. Beale on the seed of plants. Ph. tr. 1669. IV. 919. 1671. VI. 2143. Willoughby. Ph. tr. 1669. IV. 963. 167O. V. 1165, 1168, 1199. 1671. VI. 2119. Found that willows and osiers would grow when in- verted. Wray. Ph. tr. 1669- IV. 963. Lister. Ph.tr. 1670. V. 2067. I671. VI. 2119, 3051. 1672. VIL 5132. 1673. VIII. 6060. Gnw on the anatomy of vegetables. 12. 1671. B.B. Acc.Ph.tr. 1671. VI. 3037. Grew's anatomy of the trunks of plants. 8. Lond. Ace. Ph. tr. 1675. X. 486. Wallis. Ph. tr. 1673. VIII. 606O. Leeuwenhoek. Ph. tr. I676. XI. 653. 1683. XIII. 197. Adds little to Grew and Malpighi. Woodward. Ph. tr. 1699.XXL 193. Huygens on vegetation in a close bottle. A. P. I. 130. Lahire. A. P. 11. 114. 1708. 231. H. 67. Dodart on the direction of branches. A. P. 1700. 47. H.6I. Delapryme. Ph.tr. I7O2. XXIII. 1214. Morland. Ph. tr. 1703. XXIII. 1474. On the use of the flower. Grew had observed the farina lo be seminal ; Morland supposes it to pass to the seed. Perrault. A. P. 1709. 11.44. Parent on the motions of plants. A. P. 17 10. H. 64. Bradley. Ph.tr. 1718.XXX.486. Bradlei/ on the gvovfth of plants. 8. 1733. Fairchild! Ph. tr. 1724. XXXIII. 127- Dudley. Ph. tr. 1724. XXXIII. 194. On the multiplication of plants. *ifaZ£s'svegetable Statics. 8. Lond. 1731.11. 1. Extract by Desaguliers. Ph. tr. 1727. XXXV. 264, 323. Mairan. A. P. 1729. H. 35. On the sensitive plant. ISicholIs. Ph. tr. 1730. XXXVI. 371. Seba. Ph. tr. 1730. XXXVI. 441. On vegetable preparations. Biilfingeron the tracheae of plants. C. Petr. IV. 182. Logan on the farina foecundans. Ph. tr. 1736. XXXIX. 192. Dufay.A.P. 1736.87. H. 73. On the sensitive plant. Duhamel and Buffon on the woody strata of trees. A. P. 1737- 121. H. 65. 1751. 23. H. 147. *Duhamel Physique des arbres. Klein on letters found in the middle of a beech. Ph. tr. 1739- XLI. 231. Clark on substances found within trees. Pb. tr. 1739. XLI. 235. A tree 13 feet in diameter. f Baker on a perfect plant in the seed. PJj.tr. 1740. XLf. 448. Miles on the seed of fern^. Ph. tr. 1741. XLI. 770. CATALOGUE. — NATURAL HISTORY, VEGETABLE PHYSIOLOGY. 513 Hollmannus Jesceletofolioium. Ph.tr. 1741. XLI. 79(), 789. Cook. Ph. tr. 1745. XLIII. 525. Effects of the farina of a different plant. Kraffiou vegetation. N. C. Petr. II. 231. Watson on the sex of flowers. Ph. tr. 1751. 169. .Bonnet sur I'usage cles feuilies. 4. Gott. 1751. B.B. Riville on caprification. S. E. II. 369. H. 4. Alston on the sejjes of plants. Ed. ess. I. 205. Collet on a peat pit. Ph. tr. 1757- IO9. Pulteney on tlie sleep of plants. Ph. tr. 1758. 506. Marshall! on the growth of trees. Ph. tr. 1759-7. Marsham on the measures of trees. Ph. tr. ■ 1797. 128. Adanson on the motions of the tremella. A. P. 1767. 5fi4. H. 75. Murray on fallen leaves, N. C. Gott. 1770. II. 27. Fordj/ce's elements of agriculture and vegeta- tion. 8. 1771. 1796. R. 1. A cross formed in the wood, and a corre- sponding cross in the bark, of diiferent di- mensions. A. P. 1771. 491. Mustel. Ph. tr. 1773. 1?6. Against the existence of any circulation in the sap, after Hales. Mustel Traite de la vegetation. 8. Hunter on the heat of vegetables. Ph. tr. 1775.446. E. M . Forets et Bois. Tessier on the effects of light upon plants. A, P. 1783. 133. Broussonet on the motions of plants, and on the hedysarum gyrans. A. P. 1784. 609. Saussure on the electricity of vegetables. Roz. XXV. 290. Bruce on the sensitive quality of the aver- ihoa carambola. Ph. tr. 1785. 356. VOi. 11. Percival on the perceptive power of vegeta- bles. Manch. M. II. 114. In favour of its existence. Henry on the effect of fixe^ anon vegetation. Manch. M. II. 341. Shows, after Percival, that it is favourable, when the plants are exposed at the same time to the atmosphere. Bell on the physiology of plants, translated by Currie. Manch. M. II. 394. Observes, that Hill discovered the existence of a green co- rona between the wood and the pith : he also asserts, that the cuiicle contains vessels, which the author thinks are in- tended for admitting air into the tracheae. Bell thinks, that the sugar of the maple is not contained in the sap, but is de- rived from some proper vessels. Hope found, that the sap flowed first from the superior orifices of the lowest of several horizontal incisions. Bell concludes, that the proper juice descends, and that in its descent the wood acquires its growth. Guettard shows, that perspiration takes place from the upper surface of the leaf ; and, as well as Duhamel and Bonnet, that absorption is performed by the lower surface. The motions of plants show, that they possess other powers than those of inanimate matter, and these are probably con- cerned in propelling the sap : for the discharge from an in- cision proves, that the humidity is not imbibed merely by capillary action. Bell thinks, that plants have even a degree of sensation. Ingenhousz Nuuvelles experiences. 8. Pa- ris, 1785. R. S. Extr. Roz. XXXIV. 436. Ingenhousz's experiments on vegetables. 8. Lond. Ingenhousz on germination. Roz. XXVIII. 81. Ingenhousz on the nourishment of plants. Journ. Phys. X1.V. (II.) 458. Fongeroux on the formation of the ligneous strata. A. P. 1787- 110. Desfoutaines on the irritability of the orn-ans of plants. A. P. 1787. 468. Desfontaines on the organization of mono- cotyledonous plants. M. Inst. I. 478. Rcgnier on the generation of plants. Roz. XXXI. 321. 3u 514 CATALOGUE. — NATURAL HISTORY, VEGETABLE PHYSIOLOGY. Smith on the irritability of vegetables. Ph. tr. 1788. 158. Thinks, that they do not possess at once both irritability and spontaneous motiorf. Wallier on the motion of sap. Ed. tr. I. 3. Says, that the sap ascends in the wood, and that in the spring the lower part of the bark receives it before the upper. Maj'er on the vessels of plants. A. Berl. 1788. 54. Mayer on the impregnation of seeds. A. Berl. 1790.61. Kolreuter on the" irritability ofthe stamina of the barberry. N. A. Petr. 1788. VI. 207- St. Martin on the perspiration of plants. Es- prit des Journ. Apr. 1 790. Achard on the nourishment of vegetables. A. Berl. 1790.49. Senebieron the heat of vegetables. Roz. XI. 173. Sen^bier on the green matter found in water. Journ. Phys. XLVUI. 155. Senebier's vegetable physiology. 5 v. 8. Ge- nev. Ace. Journ. Phys. LI. 354. Hassenfratz on the nutrition of vegetables. Ann. Ch. XIII. 178. Rossi on the fecundation of plants. Soc. Ital. VII. 369. Tait on peal mosses. Ed, tr. III. 266. Humboldt on the physiology of plants. 8. Leipz. 1794. Noticed. Ph. M. IX. Knight on grafting trees. Ph. tr. 1795. 290. Knight on fecundation. Fh. tr.'1799. 195. Nioh. III. 458, 519- Ph. M. VII. 97. Could not produce hybrid plants. Knight on the ascent ofthe sap. Ph. tr. 1801 . 333. Knight on the descent of the sap. Ph. tr. 1803. 277. Knight on the motion of the sap. Ph. tr. 1804. 183. Correa de Serra on the fructification of sub- mersed algae. Ph. tr. 1796. 494. Gough on the vegetation of seeds. Manch. M. IV. 310, 488. Showing the effect of the air on it. Gough on the nourishment of succulent ve- getables. Nich. III. 1. Gough on the use of oxygen in vegetation. Nich. IX. 217. Chaptal on the juices of vegetables. Ann.-Ch. XXI. 284. Peschier on the irritability of animals and plants. Journ. Phys.XLV. (II.) 343. Hooper on the structure and economy of plants. 8. Oxf. 1797. On the irritability of the pollen of plants. Nich. I. 471. Delametherie on the respiration of plan-ts. Journ. Phys. XLVII. (IV.) 299. Delametherie on the irritability and organiza- tion of plants. Journ. Phys. LVI. 281, 355. LVII. 283. With some figures. Brugman de lolio. Join-n. Phys. XLVII. (IV.) 388. Ph. M. IIL321. Asserts, that plants excrete. Barton on the stimulant effects of camphor. Am. tr. IV. 232. Refreshing flowers when put into the water in which they are kept. Fabricius on the virinter sleep of animals and. plants. Ph. M. III. 156. Rafn on the physiology of plants. 8. Leips. 1798. Ace. B. Soc. Phil. n. 28. Ph. M. V. 233. Ph. M. IX. Decandolle on the influence of light upon ve- getables. B. Soc. Phil, n, 42. Journ. Phys. LII. 124. Decandolle on the structure of leaves. B. Soc. Phil. n. 44. Journ. Phys. LII. 130. Ph. M. IX. 170. CATALOGUE. NATURAL aiSTORY, VEGETABLE PHYSIOLOGV. 515 Vastel on germination. Extr. B. 3of. Phil. n. 66. I'll. M. Vlir. 1S7. Gilb. XIV. 364. Coulomb on the circulation of sap. M. Inst. 11.246. Journ. Phys. XLIX. 392. Ph. M. VI. 310. Repert. XII. 356. Says, that it ascends, with some air, near the axis of the tree. *Mirbel on vegetable anatomy. B. Soc. Phil. n. 60. Journ. Phys. LII. 336. . . With many figures. Ph. M. XIII. 36. MiVie/ An atomic et physiologic vegetales. 2 v. 8. B. B. Darwin's phylologia. 4. Lond. 1800. R.I. Th. de Saussure on the influence of the soil on vegetables. Journ. Phys. LI. 9. Gilb. VI. 459. Seems to think, that plants generate some calcariom earth. Ik. de Saussure Recherches chimiques sur la vegetation. 8. Par. 1804. R. I. Ace. B. Soc. Phil. n. 86. Thinks, that all the solid contents are derived from the soil. Miclielotti. Ph. M. IX. 240. Velley on the food of plants. Repert. XII. 32. Carradori on germination in oxygen. Journ. Phys. Llll. 253. On the effect of light on germination. Journ. Phys. LIV. 3iy. Solom^ on the temperature of vegetables. Ann. Ch. XL. 114. Fairman engrafting. S. A. XX. 181. Nich. VI. 124. Hunter on the nourishment of vegetables. Repert. ii. III. 349. Jurine on the organization of leaves. Journ. Phys. LVI. 169. Ph. M. XVI. 3, 147. With figures. Edelcrantz's plaster for trees. B. Soc. Phil. n. 82. B. Prevost on the tracheae of plants. Journ. Phys. LVII. 112. Account of Mr. Knight's Experiments on the descent of the Sap in Trees. From the Journals of the Royal Jnsluy- tution. I J. 71. The principal object of this paper is to point out the causey of the descent of the sap from the leaves through the bark, and of the consequent formation of wood. These causes Mr, Knight supposes to be gravitation, agitation, and capillary attraction, combined with some peculiar structure of the vessels. From experiments on vine leaves, it appears that the per- spiratory vessels of the leaf are confined to its under surface : the upper part Mr. Knight considers as serving to receiv« the influence of light, andas probably emitting oxygen gas; and he quotes Boniiet'sexperiments, as showing that this sur- face of the leaf, when detached from the plant, is capable also of absorbing moisture. Mr. Knight removed a portion of the bark of the branch of a vine which was in an inverted position, and he found that new bark and wood were generated at the lip of the wound which was actually uppermost ; and from a comparison of this with his former experiments, he infers, that the force of gravitatien is materially concerned in the circulation of the sap. By means of bandages, Mr. Knight prevented the agita- tion of some young apple trees in Some parts of their stems, and in particular directions, while their motion was per- mitted in other parts : and it was found that their growth was the most considerable in the parts, which were freely agitated, and that the diameter of the section was greater by about one sixth in the direction of the motion. Hence we may understand the greater thickness of the lower parts of the trunk, and of single trees in exposed situations, while the trees that form a wood, and shelter each otljer, are higher and more slender. If a large tree has been deprived of motion, by cutting off its foliage or otherwise, its growth is promoted by removing the dry external layers of the bark, which appear to impede the motion of the sap. Mr. Knight supposes that the expansion and contraction of the alburnum, from changes of temperature, are partly communicated to the bark, and assist in propelling its sap : but that the principal cause of this motion is gravitation, which operates more completely in the perpendicular parts of the tree, than in the horizontal branches; hence these branches are not liable to become top large for their strength, in an unfavourable position. Leaves of the vine were succesfuUy grafted on the fruit- stalk, the tendril, and the succulent shoot ; and a branch was nourished by the leafstalk, the tendril, and the fruit- 516 CATALOGUE. — NATURAL HISTORY, PHYSIOLOGY. stalk. The wood of a leafstalk, supporting a shoot," was de- posited on the external sides of the vessels, called by Mr. Knight, central vessels, and on the medulla ; but the me- dulla appeared to be inactive in the deposition, nor did any processes originate in it. When abud is inserted on a stock, the new wood appears to be generated above the line of union, and to be produced by the bud. When new bark grows over an exposed surface of albur. num, the processes called medullary, which constitute the silver grain of the wood, are seen clearly to originate in the bark, and to ttrminate at the lifeless surface of the albur- num. Mr. Knight is still of opinion, that the sap acquires its power of generating wood, from its exposure to light and air in the leaves ; but he thinks it possible that the young bark may in a slight degree supply the place of the leaves, when they are removed : and he concludes from some ex- periments, that when a small part of the wood is deprived of bark, it may be able to transmit a small quantity of sap from the leaves downwards, through its superficial parts, so that a little wood may be generated below ; but that this power is confined within narrow limits. By immersing the running roots of a polatoe in a coloured fluid, Mr. Knight traced a great number of vessels, pro- ceeding, from the parent plant, to lamify minutely between the cortical and internal parts of the young tuber : these he supposes to convey nourishment, prepared by the leaves, for the support of the internal parts, conceiving these parts to be analogous to the alburnum of woody, vegetables, which always appears to require the operation of the leaves for its complete organization. Zoology. In General. Ph. tr. abr. II.vi.73G. V. i. l. *Bufi'on Histoire naturelle. Systems. Fabricii philosophia entomologia. Fabricii entomologia systematica. Hunter on the identity of the wolf, jackal, and dog. Ph. tr. 1787.253. Pinel's classification of animals from the lovverjaw. Roz. XLI. 401. Brongniart on the classification of reptiles. B. Soc. Phil. n. 35. Lac6p^de on an arrangement of birds and mammalia. M. Inst. III. 454, 469. Dumeril on the classification of insects. B. Soc. Phil. n. 44. Journ. Phys. LI. 427. Distinguishes the genera by the subdivisions of the tarsus. Physiology. Charlton Physiologia. f. 1654. Account of 4 men that lived 24 days in a mine without food. Ph. tr. 1684. XIV. 577. Robinson's account of Jenkins, a fisherman, aged 169. Phil. tr. l6yf>. XIX. 265. Seigue on a toad found in an oak 100 years old. A. P. 1731. H. 24. Another found in an elm 171a. JHa/fs's Statical essays. 2 v. 8. 1731. R. I. Miles on the globules of the blood in the water eft. Ph. tr. 1741. XLI. 725. Jurin and Leeuwenhcek found 4 globules of the blood equal in diameter to a wire which measured ^ inch : some were a litile larger. A Capricorn beetle found in the centre of a tree. Ph. tr. 1741. XLI.861. Mortimer thinks it was nourished by the sap. Papers on the fresh water [)olypus. Ph. tr. 1742. XLII. 281. Maclaurinon the cells of bees. Ph. tr. 1743. XLIL565. Lcca/ Traite des sens, 8. Amst. 1744. Douglas on the heat of animals. 8. 1747. A case of long fasting. C. Bon. II. i. 221. Kaan Boerhaave on the cohesion of living solids. N. C. Petr. IV. 343. llalkr Elementa physiologiae. 8 v. 4. Lau- sanne, 1757. M. B. Tillet on the power of supporting heat. A. P. 1764. 186. H. 16. Found that 130° R. or 337° F. was supported in an oven for ten minutes. Blagden says 280°. Fontanaon the laws of irritability. Ac. Sienn. III. 209. 2 CATALOGUE. — NATURAL HISTORY, PllYSIOLOGV. 517 BraiiQ on the heat of animals. N. C. Petr. XIII. 419. lillis on the division of animalcules. Ph. tr. I7G9. 138. Hewson on the red particles of the blood. Ph. tr. 1773.303. Asserts the existence of central particles, perhaps from an optical deception. See Cavallo on factitious airs. Macbride and Stuckey Simon on the revivi- scence of snails, after being dry 15 years or more. Ph. tr. 1774.432. Blagden's observation in a heated room. Ph. - tr. 1775. 111. The power of bearing heat owing to life only. Hunter found a carp surrounded by water iji the midst of ice. Mar- tine found a swarm of bees at g?". Vegetables also generate beat. Blagden's further experiments. Ph.tr. 1775. 484. Supported 260° with clothes, 2-20" without. A beef steak was dressed in 13 minutes in the same room. Hunter on the heat of animals and vegetables. Ph. tr. 1775. 446. 1778.7. Amphibia are generally from 1° to 10° warmer than the surrounding medium, but not always. Trees may be cooled to 17" F. without being frozen. ■ Hunteron some parts of the animal economy, 4. Lond. 1786. R. S. Hunter on the extirpation of one ovarium in a sow. Ph. tr. 1787. 233. Seems to have reduced the numbers of the litters to J. Hunter on bees. Ph. tr. 1792. 128. Dobson's experiments in a heated room. Ph. tr. 1775.463. At 224°. - Changeux on the experiments of Fordyce and Blagden. Roz. VII. 57. Debravv on the sex of bees. Ph. tr. 1777. 15. Asserts, that any female bee may be made a queen by proper food, and will then breed without any other preli- minary. Bonnet on the reproduction of the heads of snails. Roz. X. 165. Bonnet on reproduction in lizards. Roz. X. 385. .Dicquemare. Ph. tr. 1775.202. The actinia may be multiplied by dividing its basis. Polhill on Debraw's culture of bees. Ph. tr. 1778. 107. Fontana sopra la fisica animale. 4. R. S. Fontana sopra i globetti rossi. 8. R. S. Crawford. Ph. tr.' 1781. Says, that venous blood drawn in the hot bath is scarlet. Spallanzani on the reproduction of the heads of snails. Soc. Ital. I. 526. II. 506. Spallanzani on respiration. Ph. M. XVIII. On a toad found in a hole. A. Beil. 1782. H. 13. In a slate quarry. A fissure was found descending towards the hole. Righy on animal heat. 8. Lond. 1785. R. S. Bell's arguments against the generation of cold in the human body. Manch. M. 1. 1. Explains the power of bearing heat by the frigorific eflfect of evaporation, joined to the small capacity of the air for heat. White on the regeneration of animal sub- stances. Manch. M. I. 325. Mentions a supernumerary thumb, which was removed and grew again. A. Fothergiil on longevity. Manch. M. I. S55, Louisa Truxo, a negrcss in South America, was said to be living in 17 80, at the age of 175, on the authoriiy of the newspapers only. Says that Galen lived to 140 ; but Blair makes him only 70. On the authority of the papers only,- a Russian is said to be living at the age of 180. Percival on the sufferings of a collier. Manch. M. 11.467. He was 7 days without food, and died. Sir W. Hamilton mentions a girl who lived 1 1 days without food. Fantonus mentions a woman who ate but twice in 50 days, and then died. Men can breathe where candles will not burn. Blumenbach's specimen of comparative phj'- siology. C.Gott. 1785. VIII. Ph. 69. 1786. IX. 108. 518 CATALOGUE. — NATURAL HISTORY, PHYSIOLOGY. Blumenbach. Ph. ISI. IT. 251. Asserts the fascination of the rattlesnake, and thinks the noise is concerned in frightening birds. Blumenbach on hereditary mutilations. Ph. M. IV. 1. Clarke on the mortality of males. Ph. tr. 1786. 349. Male infants generally weigh 71 pounds ; females 6f. twins 1 1 pounds together. Caldanii institutiones physiologicae. 8. Ve- nice, 1786. R. S. A case of somnambulism. M. Laus. III. 98. Ford^'ce on muscular motion. Ph. tr. 1788. 23. Attributes it to the attraction of life. Tordyce on digestion. 4. Lond. 1790. Peart on animal heat. 8. Gainsborough,1788. R. S. Saint Julien on the heat of warm baths. Roz. XXXir. 51. Baronio on reproduction. Soc. Ital. IV. 480. In warm blooded animals. Lavoisier on respiration. A. P. 1789. 566. Girtanner on irritability. Roz. XXXVII. 139. Seguin on respiration and animal heat. Roz. XXXVII. 467. Ann. Ch.'XXI. 225. Priestley on respiration. Ph. tr. 1790. 106. Shows that some azote is absorbed. Ferriar on the vital principle. Manch. M. III. 216. Merizies de respiratione. 8. Edinb. 1790. Ace. Ann. Ch. VIII. 211. Observes, after Jutin, that about 40 cubic inches are res- pired at once. Currie on the effects of cold. Ph. tr. 1792. 199. Darwin's zoonomia. 4 v. 8. 1804. R. I. Vauquelin on the respiration of insects. Ann. Ch. XII. 273. Monro on the action of the muscles. Ed. tr. III. 250. Olivi on the touch of marine worms. Soc. Ital. Vn. 478. Gruikshank and Haighton on the reproduc- tion of nerves. Ph. tr. 1795- 177, 190. Haighton on animal impregnation- Pli. tr. 1797. 159. Home on muscularmotion.Ph.tr. 1795.202. Home on the teeth of graminivorous qua- drupeds. Ph. tr. 1799. 237. Humboldt on the chemical process of vita- lity. Ann. Ch. XXII. 64. Nich. I. 359. Wells on the colour of the blood. Ph. tr. 1797.416. Attributes the change of colour produced by the air to the increased opacity of and XXIV. 1723). It appears, from hia descriptions and figures, that the crys- talline of hogs, dogs, and cats, resembles what I have observed in oxen, sheep, and horses ; that in hares and rabbits, the'' raK diating lines on each side, instead of three, are only two, meeting in the axis so as to form one straight line; and that in whales they are five, radiated in the same manner as where there are three. It is evident that this variety will make no material difference in the action of the muscle. I have not yet had an opportunity of examining the human crystalline, but from its readily dividing into tliree parts, we may infer that it is similar to til at of the ox. The crystalline in fishes be- ing nearly spherical, such a change as I atr tribute to the lens in quadrupeds cannot take place in that class of animals. It has been observed that the central part of the crystalline becomes rigid by age, and this is sufficient to account for piesby»- opia, without any diminution ofthehumours ; although 1 do not deny the existence of this diminution, as. a concomitant circumstance. 1 shall here beg leave to attempt the solu- tion of some optical queries, which have not beea much considered by authors. L Musschenbroek asks, What is the cause of the lateral radiations which seem to adhere to a candle viewed with winking eyes? I an- swer, the most conspicuous radiations are those which, diverging from below, form, each with a vertical line, an angle of about seven degrees ; this angle is equal to that which the edges of the eyelids when closed make with a horizontal line ; and the radia^- ^2« OBSEHVATlbNS ON VISION. tions are ver}' jusdy attributed by Musschen- broek to the refraction of the moisture con- tiguous to the eyelids. But the lateral radia- tions are produced by the light reflected from the eyelashes. 2. Some have inquired. Whence arises tliat luminous cross, which seems to proceed from the image of a candle in a lo6king- glasi? This is produced by the direction of the friction by which the glass is commonly polished : the scratches, placed in a horizon- tal direction, exhibiting the perpendicular part of ihe cross, and the vertical scratches the horizontal part, in a manner that may easily be conceived. 3. Why do sparks appear to be emitted when the eye is rubbed or compressed in the dark ? This is Mnsschenbroek's fourth query. When a hroadish pressure, as liiat of the finger, is made on the opaque part of the eye in the dark, an orbicular spectrum appears on the part opposite to that which is pressed : the light of the disc is faint, that of the cir- cumference much stronger; but when a nar- row surface is applied, as that of a pin's head, or of the nail, the image is narrow and bright. This is evidently occasioned by the irritation of the retina at the part touched, referred by the mind to the place from whence light coming through the pupil would fall on this spot ; the irritation is greatest where the flexure is greatest, that is, at the circumference, and sometimes at the centre, of the depressed part. But in the presence of light, whether the eye be open or closed, the circumference only will be luminous, and the disc dark ; and if the eye be viewing any ob- ject at the part where the image appears, that object will be almost invisible. Hence it follows, that the tension and compression of the retina tend to destroy all the irritation. except that which is produced by its flexure; and this is so slight on the disc, that the ap- parent light there is faiHter than that of the rays 'arriving at all other parts through the eyelids. This experiment demonstrates a truth, which may be inferred from many other argtiments, that the sapp6sed rectifica- tion of the inverted image on the retina does not depend on the direction of the incident rays; since th6 mind can refer the object to its true relative situation without any a«sist- tance from this direction. Newton, in his sixteenth query, has described this phantom as of pavonian colours, but I ean distinguish no other than white ; and it seems most na- tural that this, being the compound or aver- age of all existing sensations of light, should be produced when nothing determines to any particular colour. This average seems to re- semble the middle form, which Sir Joshua Reynolds has elegantly insisted on in his dis- courses ; so that perhaps some principles of beautiful contrast of colours may be drawn from hence, it being probable that those co- lours which together approach near to white light will have the most pleasing effect in ap- position. It must be observed, that the sen- sation of light, from pressure of the eye, sub- sides almost instantly after the motion of pressure has ceased, so that the cause of the irritation of the retina is a change,' and not a difference of form ; and therefore the sensa- tion of light appears to depend immediately on a minute motion of some part of the op- tic nerve. If the anterior part of the eye be repeat- edly pressed, so as to occasion some degree of pain, and a continued pressure be then made on the sclerotica, while an interrupted pres-* sure is made on the cornea ; we shall fre- quently be able to observe an appearance of OBSERVATIONS OK VISION. 529 luminous lines, branched, and somewhat connected with each other, darting from every part of the field of view, towards a cen- tre a little exterior and superior to the axis of the eye. This centre corresponds to the in- sertion of the optic nerve, and the appear- ance of lines is probably occasioned by that motion of the retina which is produced by the sudden return of the circulating fluid, into the veins accompanying the ramifications of the arteria centralis, after having been de- tained by the pressure which is now inter- mitted. As such an obstruction and such a readmission must require particular circum- stances, in order to be effected in a sensible degree, it may naturally be supposed that this experiment will not always easily suc- ceed. VOL. 11. S T 530 OBSERVATIONS ON TISION, PLATE 1. Explanation of the Figures. Fig. 1. A vertical section of the ox's eye, of twice the natural size. A. The cornea, covered by the tunica conjunctiva. BCB. The sclerotica, covered at BB by the tunica albuginea, and tunica conjunctiva. DD. The choroid, consisting of two laminas. EE. The circle of adherence of the choroid and sclerotica. EG. FG. The orbiculus ciharis. HI, HK. The uvea; its anterior surface the iris; its posterior surface lined with pigmeu- tum nigrum. IK. The pupil. HL, HL. The ciliary processes, covered with pigmentani nigrum. MM. The retina, N. The aqueous humour. O. The crystalline lens. P. The vitreous humour. QR, QR. The zona ciliaris. RS, RS. The annulus mucosus. Fig. 2. The structure of the crystalline lens, as viewed in front. Fig. S. A side view of the crystalline. t ., PiATE 1 . Tig.: t?ig. 2 Fig.S. /"u^. &K y. Johnson , Londmi i July 1 806. II. OUTLINES OF EXPERIMENTS AND INQUIRIES RESPECTING SOUND AND LIGHT. BY THOMAS YOUNG, M.D F.R.S. IN A LETTER TO EDWARD WHITAKER GRAY, M.D. SEC. R.B. FROM THE PHILOSOPHICAL TRANSACTIONS. Rtad before the RovAL Society, January 16, 1800. DEAR SIK, Xt has long been my intention to lay before the Roya! Society a few observations on the subject of sound ; and I have endeavoured to collect as much information, and to make as many experiments, connected with this in- quiry, as circumstances enabled me to do ; but the further I have proceeded, the more widely the prospect of what lay before me has been extended ; and, as 1 find that the investigation, in all its magnitude, will oc- cupy the leisure hours of some years, or per- haps of a hfe, I am determined, in the mean time, lest any unforeseen circumstances should prevent my continuing the pursuit, to submit to the Society some conclusions which I have already formed from the results of various experiments. Their subjects are, I. The measurement of the quantity of air discharged through an aperture. IL The de- termination of the direction and velocity of a stream of air proceeding from an oritice. III. Ocular evidence of the nature of sound. IV. The velocity of sound. V. Sonorous ca- vities. VI. The degree of divergence of sound. VII. The decay of sound. Vlll. The harmonic sounds of pipes. IX. The vibra- tions of different elastic fluids. X. The ana- logy between light and sound. XI. The coalescence, of musical sounds. XII. The frequency of vibrations constituting .a givea note. XIII. The vibrations of chords. XIV. The vibrations of rods and plates. XV. The human voice. XVI. The temperament of musical intervals^ I. Of the Quantity of Air discharged through an Aperture. A piece of bladder was tied over the end of the tube of a large glass funnel, and punctured with a hot needle. The funnel was inverted in a vessel of water ; and a gage, with a graduated glass tube, was so placed as to measure the pressure occasioned by the different levels of the surfaces of the water. 532 EXPEHIMEISTTS AND INQUIRIES As the air escaped through the puncture, it was sup[)lied by a phial of known dimensi- ons, at equal intervals of time ; and accord- ing to the frequency of this supply, the ave- rage height of the gage was such as is ex- pressed in the first Table. It appears that the quantity of air, discharged by a given aper- ture, was nearly in the subduphcate ratio of the pressure. The second, third, and fourth Tables show the result of similar experiments made with some variations in the apparatus. Tabic I. Table in. A B C D E F .00018 .25 3.9 30.1 4.18 7.2 .001 .045 7'. 8 10.8 1.77 6.1 .001 .2 i5.a 21.7 3.74 5.8 .001 •7 31.2 43.3 7.00 6.3 0.3 Mean. All numbers throughout this paper, where the contrary is not expressed, are to be un- derstood of inches, linear, square, or cubic. A is the area, in square inches, of an aper- ture nearly circular. B, the pressure in inches. C, the number of cubic inches discharged in one minute. D, is the observed velocity of the air in a second, expressed in feet. E, the square root of the height of a column of air equivalent to the pressure. F, the quotient of the two last columns. Table ii. A B c D E F .07 .07 1. 2. 2000. 2900. 30.7 57.5 8.37 11.84 4.8 4.9 A is the area of the section of a tube about two inches long. B, the pressure. C, the quantity of air discharged in a minute, by es- limation. D, E, and F, as in Table i. A B C D E F G- .0064 1.15 .2 46.8 9.9 3.74 2.5 .0064 10. .45 46.8 9.9 5.61 1.8 .0064 13.5 .35 31.2 6.0 4.95 1.3 .0064 13.5 •7 46.8 9-9 7.00 1.4 A is the area of the section of a tube. B,. its length. C, the pressure. D, the discharge in a minute. E, F, and G, as D, E, and F, in Table i. Table IV. A B c D E 1 F 1 .003 .2 8 46.8 21.7 4.43 4.0 1 A is the area of an oval aperture, formed by flattening a glass tube at the end : its dia- meters were .025 and .152. B, the pressure. C, the discharge. D, E, and F, as in Table i. II. Of the Direction and Velocitif of a Stream of Air. . An apparatus was contrived for measuring, by means of a water gage communicating with a reservoir of air, the pressure by which a current was forced from the reservoir through a cylindrical tube; and the gage was so sensible, that, a regular blast being supplied from the lungs, it showed the slight variation produced by every pulsation of the heart. The current of air issuing from the tube was directed downwards, upon a white plate, on which a scale of equal parts was engraved, and which was thinly covered with a coloured liquid ; the breadth of the surface of the plate laid bare was observed at diftier- ent distances from the tube, and with difler- ent degrees of pressure, caie being taken that the liquid should be so shallow as to RESPECTING SOtTNI) AND LIGHT. 535 yield to the slightest impression of air. The results are coiiectefl in Tables v and vi. (Phite -2. Fig. 4. . 15.) In order to measure, with greater certainty and precision, the ve- locity of every part of the current, a second cavity, furnished with a gage, was provided, and pieces perforated with apertures of dif- ferent sizes were adapted to its orifice : the axis of the current was directed as accu- rately as possible to the centres of these aper- tures, and the resullsof the experiments, with various pressures and distamjes, are inserted in Tables vii, viii, and ix\ The velocity of a stream being, both according to the commonly received opinion, and to the expe- riments already related, nearly in thesubdu- plicate ratio of the pressure occasioning it, it was inferred, that an equal pressure would be required to stop its progress, and that the ve- locity of the current, where it struck against the aperture, must be in the subdupllcate ra- tio of the pressine marked by the gage. Having thus ascertained the velocity of the stream at different distances from the aper- ture, we must adopt, in order to infer from it the magnitude of the stream, some suppo- sition respecting the mode in which its mo- tion is retarded, and the simplest hypothesis appears to be, that the momentum of the particles contained at first in a given small length of the stream, together with that of the particles of the surrounding air, which they drag along, remains always constant, so that the area of tlie transverse section may be inversely as the square of the velocity ; and the diameter inversely as the velocity it- self ; the particles of the stream occupj'ing a section as much wider as the velocity is smaller, and carrying with them as many more particles as will require a space still larger in the same proportion. On this sup- position, the ordinates of a curve may be taken reciprocally in the subdupll- cate ratio of the pressure marked by the se- cond gage to that indicated by the first, at the various distances represei;ted by the ab- scisses, and the solid, described by the revo- lution of thi» curve round its ax's, will nearly represent the magnitude of the current in all its parts. (Plate a. Fig. l6. . 2(i.) As the central particles must be supposed to be less impeded in their motion than the superficial ones, of course, the smaller the aperture opposed to the centre of the current, the greater the velocity ought to come out, and the ordinate of the curve the smaller ; but where the aperture was not greater ihan that of the tube, the difference of the veloci- ties at the same distance was scarcely per- ceptible. When the aperture was larger than that of the tube, if the distance was very small, of coursethe average velocity came out much smaller than that which was inferred from a smaller aperture ; but, where the ordinate of the internal curve became nearly equal to this aperture, there was but little difference between the velocities indicated with differ- ent apertures. Indeed, in some cases, where the diameter of the aperture was a little greater than that of the stream striking on it, it appeared to indicate a greater velocity than a smaller aperture : this might have arisen in some degree from the smaller aperture not having been exactly in the centre of the current ; but there is greater reason to sup- pose, that it was occasioned by some resist- ance derived from the air returning between the sides of the aperture, and the current en- tering it. Where this took place, the exter- nal curves, which are so constructed as that their ordinates are reciprocally in the subdu- plicate ratio of the pressure observed in the 53i EXPERIMENTS AND INQUIRIES second cavity, with apertures equal in semi- diameter to their initial ordinate, approach, for a short distance, nearer to the axis than the internal curve ; after this, they continue their course very near to this curve. Hence it appears, that no observable part of the motion diverged beyond the limits of the so- lid which would be formed by the revolution of the internal curve, deduced from observ- ations on a small aperture, which is seldom inclined to the axis in an angle so great as ten degrees. A similar conclusion may be made, from observing the flame of a candle subjected to the action of a blowpipe : there is no divergency beyond the narrow limits of the current ; the flame, on the contrary, is every where forced by the ambient air to- wards the current, to supply the place of that which it has carried away by its friction. The lateral communication of motion, very ingeniously and accurately observed in water by Professor Venturi, is exactly similar toitie motion here shown to take place in air ; and these experiments fully justify him in reject- ing the tenacity of water as its cause : no doubt it arises from the relative situation of the particles of the fluid, in the line of the current, with respect to that of the particles in thecontiguous strata, which, whatever mpy be the supposed order of the single particles with respect to each other, must naturally lead to a communication of motion nearly in a pa- rallel direction ; and this may properly be termed friction. The lateral pressure which urges the flame of a candle towards the stream of air from a blowpipe, is probably exactly similar to that pressure which causes the inflection of a current of air near an ob- stacle. Mark the dimple which a slender stream of air makes on the surface of water ; bring a convex body into contact with the side of the stream, and the place of the dim- ple will inmiediately show that the current is inflected towards the body ; and, if the body be at liberty to move in every direction, it will be urged towards the current, in the same manner as, in Venturi's experiments, a fluid was forced up a tube inserted into the side of a pipe through which water was flow- ing. A similar interposition of an obstacle, in the course of the wind, is probably often the cause of smoky chimneys. One circum- stance was observed in these experiments, which it is extremely difficult to explain, and which yet leads to very important conse- quences : it may be made distinctly per- ceptible to the eye, by forcing a current of smoke very gently through a fine tube. When the velocity is as small as possible, the stream proceeds for many inches with- out any observable dilatation ; it then imme- diately diverges at a considerable angle into a cone, (Plate 3. Fig. 27) ; and, at the point of divergency, there is an audible and even visible vibration. The blowpipe also affords a method of observing this phenomenon : as far as can be judged from the motion of the flame, the current seems to make something like a revolution in the surface of the cone, but this motion is too rapid to be distinctly discerned. When the pressure is increased, the apex of the cone approaches nearer to the orifice of the tube (Fig. 28, 29) ; but no degree of pressure seems materially to alter its ultimate divergency. The distance of the apex from the orifice is not proportional to the diameter of the current; it rather ap- pears to be the greater the smaller the cur- rent, and is much better defined in a small current than in a large one. Its distance in one experiment is expressed in Table x. from observations on the surface of a liquid ; 3 RESPECTING SOUND AND tlCKT. 535 in other experiments, its respective distances were sometimes considerably less with the same degrees of pressure. It may be in- ferred, from the numbers of Tables vii and VIII, that in several instances a greater height of the first gage produced a less height of the second : this arose from the nearer approach of the apex of the cone to the ori- fice of the tube, the stream losing a greater portion of its velocity by this divergence than it gained by the increase of pressure. At first sight, tlie form of the current bears some resemblance to the vena contracta of a jet of w-dter : but Venturi has observed, that in water an increase of pressure increases, instead of diminishing, the distance of the contracted section from the orifice. Table T. Table ti. A 1. 2. 3. 3.* B C c C C 1. .1 .1 .1 2. .12 .12 .2 3. .17 .25 .3 4. .2 .4 .4 S. .25 .5 e. .30 .52 7. .35 .54 .5 8- .37 .S8 9. .39 .58 10. .40 .6 .S .5 IS. .7 18. .60 20. The diameter of the tube .07. A is the distance of the liquid from the orifice. B, the pressure. C, the diameter of the surface of the liquid displaced. A 1. 2. B C c 1. .1 .1 2. .13 3. .2 .3 4. .25 .3 0. .3 .4 7. .35 .5 10. .35 .S 15. .35 •7 20. .35 •7 Diameter of the tube, .1. A, B, and C, aa in Table v. Table VII. A .5 B .06 .15 C D D .1 .083 .2 .IS .3 .25 .1 .4 .35 .5 .45 .0 .33 .2 .7 .6 .8 .3 1. .5 1.2 .4 .4 1.5 .8 2. ■07 .55 4. 1.3 .1 8. ,2 9. .3 14. .5 Diameter of the tube .06". A is the distance of the opposite aperture, from the orifice of the tube. B, the diameter ofthe aperture. C,thepressure,indicated by the first gage. D, the height ofthe second gage. 5156 EXPERIMENTS AND INQUIRIKS Table Vlll. A .5 1. 2. 4. B ,00 .15 .3 *5 .00 .15 .3 .5 .00 .15 .3 .5 .00 .15 .3 .5 C D D D D "" D D D D D D D D D D D .1 .05 .05 .03 .017 .2 .1 .1 .12 .08 .02 .034 .5 .2 .22 .1 .00 .00 1. .32 .30 .1 • 17 .1 .1 .05 .04 2. .»a .0 .2 .28 .22 .21 .08 .07 3. •8 .9 .3 .4 .36 .32 .12 .12 .1 .1 4. 1.1 1.2 .4 .58 .52 .42 .10 .18 .15 .14 5. 1.5 .5 .8 .08 .52 .2 .23 .2 .18 .04 .04 .03 6. 1.7 .6 1. .83 .03 .25 .3 .25 .22 .05 .05 .06 /• 1-9 .7 1.2 1. ./i .3 .35 .3 .20 .00 .06 .07 8. 2.1 .8 1.5 1.2 .88 .34 .4 .34 .3 .07 •07 .07 9- 2.3 • 9 1.7 1.4 1. .37 .45 ■37 .34 .08 .08 .08 10. 2.0 1. 1.9 1.0 1.1 .4 .5 .4 .37 .09 .09 .09 Diameter of the tube .1. A, B, C, and D, as in Table vii. Table IX. A B 1.15 3.3 4. .15 .3 .5 1. .06 .15 1. .06 C D D 1 D D D D D D .5 .1 .1 •1 1. .2 .2 ■2 2. .4 .35 •34 .13 .1 .1 .125 3. .6 .5 .5 .2 .15 .15 .18 .1 Diameter of the tube .3. A, B, C, and D, as in Table vii. Table x. A B •4 0. • 8 3. 1.2 1.5 1.8 1. 3. .5 4. .0 A is the pressure. B, the distance of the apex of the cone from the orifice of a tube . 1 in diameter. III. Ocular Evidence of the Nature of Sound. A tube about the tenth of an inch in dia- meter, with a lateral orifice half an inch from its end, filled rather deeper than the axis of the tube, (Fig. 30,) was inserted at the apex of a conical cavity, containing about twenty cubic inches of air, and was luted perfectly tight : by blowing through the tube, a sound nearly in unison with the tenor C was produced. By gradually increasing the capacity of the cavity as far as several gal- lons, with the same mouthpiece, the sound, although faint, became more and more grave, till it was no longer a musical note. Even before this period a kind of trembling was distinguishable ; and this, as the cavity was still further increased, was changed into a succession of distinct puffs, like the sound produced by an explosion of air from the lips; as slow, in some instances, as 4 or 3 in a second. These were undoubtedly the single vibrations, which, when repeated with sufficient frequency, impress on the auditory RESPECTING SOUND AND LIGHT. nerve the sensation of a continued sound, On forcing a current of smoke through the tube, the vibratory motion of the stream, as it passed out at the lateral orifice, was evident to the eye ; although, from various circum- stances, the quantity and direction of its mo- tion could not be subjected to exact mensu- ration. This species of sonorous cavity seems susceptible of but few harmonic sounds. It was observed, that a faint blast produced a much greater frequency of vibrations than that which was appropriate to the cavity : a circumstance similar to this obtains also in large organ pipes ; but several minute ob- servations of this kind, although they might assist in forming a theory of the origin of vi- brations, or in confirming such a theory drawn from other sources, yet, as they are not alone sufficient to aflPord any general conclusions, are omitted at present, for the sake of brevity. IV. Of the Vtlocily of Sound. It has been demonstrated, by Isl. De la Grange and others, that any impression whatever, communicated to one particle of an elastic fluid, will be transmitted through that fluid with a uniform velocity, depending on the constitution of the fluid, without refer- ence to any supposed laws of the continua- tion of that impression. Their theorem for ascertaining this velocity is the same as New- ton has deduced from the hypothesis of a particular law of continuation : but it must be confessed, that the result differs somewhat too widely from experiment, to give us full confidence in the perfection of the theory. Corrected by the experiments of various ob- servers, the velocity of any impression trans- mitted by the common air, may, at an aver- age, be reckoned 1 1 30 feet in a second. VOL. II. V. Of sonorous Cavities. M. De la Grange has also demonstrated, that all impressions are reflected by an ob- stacle terminating an elastic fluid, with the same velocity with which they arrived at that obstacle. When the walls of a passage, or of an unfurnished room, are smooth, and per- fectly parallel, any explosion, or a stamping with the foot, communicates an impression to the air, which is reflected from one wall to the other, and from the second again to- wards the ear, nearly in the same direction with the primitive impulse : this takes place as frequently in a second, as twice the breadth of the passage is contained in 1130 feet ; and the ear receives a perception of a musical sound, thus determined in its pitch by the breadth of the passage. On making the experiment, the result will be found ac- curately to agree with this explanation. If the sound is predetermined, and the fre- quency of vibrations such, that each pulse, when doubly reflected, m;iy coincide with the subsequent pulse proceeding directly from the sounding body, the intensity of the sound will be much increased by the reflection ; and also, in a less degree, if the reflected pulse coincides with the next but one, the next but two, or more, of the direct pulses. The appropriate notes of a room may readily be discovered by singing the scale in it ; and they will be found to depend on the pro- portion of its length or breadth to 1 130 feet. The sound of the stopped diapason pipes of an organ is produced in a manner somewhat similar to the note from an explosion in a passage; and that of its reed pipes to the j.esonance of the voice in a room : the length of the pipe in one case determining he sound, in the other, increasing itg strength. The frequency of the vibrations 3 z 538 EXPERIMENTS AND INQUIRIES does not at all immediately depend on the diameter of the pipe. It must be confessed, that much lemailis to be done in explaining the precise manner in which the vibration of the air in an organ pipe is generated. M. Daniel Bernoulli has solved several difficult problems relating to the subject: yet some of his assumptions are not only gratuitous, bwt contrary to matter of fact; VI. Of the Divergence of Sound. It has been generally asserted, chiefly on the authority of Newton, that if any sound be admitted through an aperture into a chamber, it will diverge from that aperture equally in ail directions. The chief argu- ments in favour of this opinion are deducetl from considering the phenomena of the pres- sure of fluids, and the motion of waves ex- cited in a pool of water. But the inference seems to be too hastily drawn : there is a very material difference between impulse and pressure ; and, in the case of waves of water, the moving force at each point is the power of gravity, which, acting primarily in a per- pendicular direction, is only secondarily converted into a horizontal force, in the di- rection of the progress of the waves, being at each step disposed in some measure to spread in every direction : but the impulse, transmit- ted by an elastic fluid, acts primarily in the direction of its progress. It is well known, that if a person calls to another with a speaking trumpet, he points it towards the place where his hearer stands. 1 am assured \>y a very respectable Member of the Royal Society, and it was indeed long ago observed by Grimaldi, that the report of a cannon appears many times louder to a person to- wards whom it is fired, than to one placed m a contrary direction. It must have oc- curred to every one's observation, that a sound, such as that of a mill, or a fall of water, has appeared much louder after turn- ing a corner, when the house or other ob- stacle no longer intervened ; and it has been already remarked by Euler, on this head, that we are not acquainted with any sub- stance perfectly impervious to sound. Many solid bodies even appear to conduct sound better than the air : as in the well known experiment of scratching a long beam with a pin; and in discovering the ap- proach of cavalry, by applying the ear to the ground. Indeed, as Mr. Lambert has very truly asserted, the whole theory of the speak- ing trumpet, supported as it is by practical experience, would fall to the ground, if it were demonstrable that sound spreads equally in every direction. In windy weather it may often be observed, that the sound of a dis- tant bell varies almost instantaneously in its strength, so as to appear at least twice as re- mote at one time as at another ; an observa- tion which has also occurred to another gen- tleman, who is uncommonly accurate in ex- amining the phenomena of nature. Now, if sound diverged equally in all directions, the variation produced by the wind could never exceed one tenth of the apparent dis- tance ; but, on the supposition of a motion nearly rectilinear, it may easily happen that a slight change, in the direction of the wind, may convey a beam of sound, either directly or after reflection, in very different degrees of strength, to the same spot. From the ex- periments on the motion of a current of air, already related, it would be expected that a sound, admitted at a considerable distance from its origin through ao aperture, would proceed, with an almost imperceptible in- RESPECTING SOUND AND LIGHT. 5S9 cfease of divergence, in the same direction ; for, the actual velocity of the pa i tides of air, in the strongest sound, is incomparably less than that of the slowest of the currents in the experiments related, where the beginning of the conical divergence took place at the greatest distance. Dr. Matthew Young has ob- jected, not withoutsome reason, to M. Hube, that the existence of a condensation will cause a divergence in sound : but a much greater degree of condensation must have existed in the currents described than in any sound. There is indeed one difference be- tween a stream of air and a sound ; that, in sound, the motions of different particles of 4Ur are not synchronous : but it is not demon- strable that this circumstance would affect the divergency of the motion, except at the instant of its commencement, and perhaps not even then in a material degree ; for, in general, the motion is communicated with a veiy gradual increase of intensity, so that there isnosudden condensation nor rarefaction. The subject, however, deserves a more particular investigation ; and, in order to obtain a more solid foundation for the argument, it is pro- posed, as soon as circumstances permit, to in- stitute a course of experiments for ascertain- ing, as accurately as possible, the different strength of a sound once projected in a given direction, at different distances from the axis of its motion. VII. 0/ the Lkcay of Soimd. Various opinions have been entertained respecting the decay of sound. M. De la Grange has published a calculation, by which its force is shown to decay nearly in the simple ratio of the distances; and M. Daniel Bernoulli's equations for the sounds of conical pipes lead to a similar conclusion. The same inference follows from a comple- tion of the reasoning of Dr. Helsham, Dr. Matthew Young, and Professor Venturi. It has been very elegantly demonstrated by Maclaufin, and may also be proved in a much more simple manner, that, when mo- tion is communicated through a series of elas- tic bodies increasing in magnitude, if the number of bodies be supposed infinitely great, and their difference infinitely small, the motion of the last will be to that of the first in the subdupiicate ratio of their respec- tive magnitudes ; and since, in the case of concentric spherical laminae of air, the bulk increases in the duplicate ratio of the dis- tance, the motion will in this case be directly, and the velocity inversely, as the distance. It may, however, be questioned, whether or no the strength of sound is to be considered as simpl)' proportional to the velocity of the particles concerned in transmitting it. VIII. Of the harmonic Sounds of Pipes. In order to ascertain the velocity with whidh organ pipes of different lengths require to be supplied with air, according to the va- rious appropriate sounds which they produce, a set of experiments was made, with the same mouth piece, on pipes of the same bore, and of different lengths, both stopped and open. The general result was, that a similar blast produced as nearly the same sound as the length of the pipes would per- mit ; or at least that the exceptions, though very numerous, lay equally on each side of this conclusion. The particular results are expressed in Table XI, and in Plate 3. Tig. 3 1 . They explain how a note may be made much louder on a wind instrument by a swell. 540 EXPERIMENTS AND INQUIRIES than it can possibly be by a sudden impres- sion of the blast. It is proposed, at a future time, to ascertain, by experiment, the actual compression of the air within the pipe under different circumstances : from some very slight trials, it seemed to be nearly in the ra- tio of the frequency of vibrations of each harmonic. Tahle xi. OPEN. STOPPED. A B c D E F A B c D E F 4.5 0.7 8.8 dk 1 4.5 0.3 1.8 T 1 4.1 8.8 2 1.2 5.0 1.7 9.0 10.0 3 5 9.4 0.3 0.9 7 1 0.8 8.0 2 9-4 0.2 0.4 ./■ 1 2.0 18.0 3 0.45 1.6 3 5.0 8.0 20.0 4 1.1 1.6 8.5 5 16.5 18.0 5 7.0 8.0 7 19.0 20.0 6 16.1 0.4 0.6 d« 3 16.1 0.4 1.0 e 2 • o.a 0.65 1.1 5 0.8 1.0 2.2 3 0.9 1.1 2.4 7 1.2 2.2 4.7 4 1.6 2.4 4.9 9 2.2 4.7 11.5 5 2.5 4.8 9.0 11 3.4 13.5 6 6.0 70 13 4.0 6.5 10.0 15.0 7 8 20.5 1.0 0.8 1.1 1.1 3.8 r» 7 9 n 1.8 3.8 11 20.4 0.6 0.8 b 3 3.2 3.8 12. 17 0.8 1.9 4 12. 0 00 1.1 1.9 5.7 5 4.5 5.7 8 • A is the length of the pipe from the lateral orifice to the end. C, the pressure at which the sound began. B, its termination,- by lessening the pressure ; D, by increasing it. E, the note answering to the first sound produced by each pipe, according to the German method of notation. F, the number showing the place of each note in the regular series of harmo- nics. The diameter of the pipe was .35 ; the air duct of the mouth piece measured, where smallest, .25 by .035 ; the lateral orifice .25 by .125. The apparatus was not calculated to apply a pressure of above 22 inches. Where no number stands under C, a sudden blast was required to produce the note. RESPECTING SOUND AND LIGHT. 541 IX. Of the Vibrations of different elastic Fluids. All the methods of finding the velocity of sound agree, in determining it to be, in fluids of a given elasticity, reciprocally in the sub- duplicate ratio of the density : hence, in pure hydrogen gas it should be ^13 = 3.6 times as great as in common air ; and the pitch of a pipe should be a minor fourteenth higher in this fluid than in the common air. It is therefore probable, that the hydrogen gas, used in Professor Chladni's late experi- ments, was not quite pure. It must be ob- served, that in an accurate experiment of this nature, the pressure causing the blast ought to be carefully ascertained. There can be no doubt but that, in the observa- tions of the French Academicians on the ve- locity of sound, which appear to have been conducted with all possible attention, the dampness and coldness of the night air must . have considerably increased its density : hence, the velocity was found to be only 1 109 feet in a second ; while Derham's ex- periments, which have an equal appearance of accuracy, make it amount to 1142. Per- haps the average may, as has been already mentioned, be safely estimated at 1 130. It may here be remarked, that the well known elevation of the pitch of wind instruments, in the course of playing, sometimes amounting to half a note, is not, as is commonly sup- posed, owing to any expansion of the instru- ment, for this should produce a contrary ef- fect, but to the increased warmth of tlie air in the tube. Dr. Smith has made a similar observation, on the pitch of an organ in sum- mer and winter, which he found to differ more than twice as much as the English and JVench experiments on the velocity of sound. Bianconi found the velocity of sound, at Bologna, to differ at different times, in the ratio of 152 to 157. X. Of the Analogy between Light and Sound. Ever since the publication of Sir Isaac Newton's incomparable writings, his doctrine of the emanation of particles of light, from lucid substances, has been almost universally admitted in this country, and but little op- posed in others. Leonard Euler indeed, in several of his works, has advanced some powerful objections against it, but not suffi- ciently powerful to justify the dogmatical re- probation with which he treats it ; and he has left that system of an ethereal vibration, which after Hu^'gens and some others he adopted, equally liable to be attacked on many weak sides. Without pretending to de- cide positively on the controversy, it is con- ceived that some considerations may be brought forwards, which may tend to dimi- nish the weight of objections to a theory similar to the Huygenian. There are also one or two difficulties in the Newtonian sys- tem, which have been little observed. The first is the uniform velocity with which light is supposed to be projected from all luminous bodies, in consequence of heat, or other- wise. How happens it that, whether the projecting force is the slightest transmission of electricity, the friction of two pebbles, the lowest degree of visible ignition, the white heat of a wind furnace, or the intense heat of the sun itself, these wonderful cor- puscles are always propelled with one uni- form velocity ? For, if they differed in velo- city, that difference ought to produce a dif- ferent refraction. But a still more insupera- ble difhcuity seems to occur, in the partial reflection from eveiy refracting surface.- 542 EXPERIMENTS AND INQUIRIES Why, of the same kind of rays, in every cir- cumstance precisely similar, some should al- ways be reflected, and others transmitted, appears in this system to be wholly inexpli- cable. That a medium resembling, in many properties, that which has been denominated ether, does really exist, is undeniably proved by the phenomena of electricity ; and the arguments against the existence of such an ether, throughout the universe, have been pretty sufficiently answered by Euler. The rapid transmission of the electrical shock shows that the electric medium is possessed of an elasticity, as great, as is necessary to be supposed for the propagation of light. Whe- tlier the electric ether is to be considered as the same with the luminous ether, if such a fluid exists, may perhaps at some future time be discovered by experiment ; hitherto I have not been able to observe that the refractive power of a fluid undergoes any change by electricity. The uniformity of the motion of light in the same medium, which is a dif- ficulty in the Newtonian theory, favours the admission of the Huygenian ; as all impres- sions are known to be transmitted through an elastic fluid with the same velocity. It has been already shown, that sound, in all probability, has very little tendency to di- verge : in a medium so highly elastic as the luminous ether must be supposed to be, the tendency to diverge may be considered as infinitely small, and the grand objection to the system of vibration will be removed. It is not absolutely certain, that the white line visible in all directions on the edge of a knife, in tlie experiments of Newton and of Mr. Jordan, was not partly occasioned by the tendency of light to diverge ; nor indeed has any other probable cause been yet assigned for its appearance. Eulcr's hypothesis, of the transmission of light by an agitation of the particles of the refracting media them- selves, is liable to strong objections ; accord- ing to this supposition, the refraction of the rays of light, on entering the atmosphere from the pure ether which he describes, ought to be a million times greater than it is. For explaining the phenomena of partial and total reflection, refraction, and inflection, nothing more is necessary than to suppose all refracting media to retain, by their at- traction, a greater or less quantity of the lu- minous ether, so as to make its density greater than that which it possesses in a va- cuum, without increasing its elasticity ; and that light is a propagation of an impidse communicated to this ether by luminous bo- dies : whether this impulse is produced by a partial emanation of the ether, or by vibra- tions of the particles of the body, and whether these vibrations, constituting white light, are, as Euler supposed, of various and irregular magnitudes, or whetjier they are uniform, and comparatively large, remains to be hereafter determined; although the opinion of Euler respecting them seems to be almost the only one which is consistent with the New- tonian discoveries. Now, as the direction of an impulse, transmitted through a fluid, de- pends on that of the particles in synchronous motion, to which it is always perpendicular, whatever alters the direction of the pulse, will inflect the ray of light. If a small elas- tic body strikes against a larger one, it is well known that the smaller is reflected more or less powerfully, according to the diflerence of their magnitudes : thus, there is always a reflection when the rays of light pass from a rarer to a denser stratum of ether ; and fre- quently an echo when a sound strikes against a cloud. A greater body, striking a smaller RESPECTING SOUND AND LIGHT. 548 one, propels it, without losing all its motion : thus, the particles of a denser stratum of ether do not impart the whole of their mo- tion to a rarer, but, in their effort to proceed, they are recalled by the attraction of the re- fracting substance with equal force ; and thus a reflection is always secondarily pro- duced, when the rays of light pass from a denser to a rarer stratum. Let AB, (Plate 4. Fig. 32,) be a ray of light falling on the re- flecting surface FG ; c d the direction of the vibration, pulse, impression, or condensation. When d comes to H, the impression will be, either wholly or partly, reflected with the $aroe velocity as it arrived, and EH will be equal to DH : the angle EIH to DIH or CIF ; and the angle of reflection to that of incidence. Let FG, (Fig. 33,) be a refract- ing surface. The portion of the pulse IE, which is travelling through the refracting medium, will move with a greater or less ve- locity in the subduplicate ratio of the densi- ties, and HE ^vill be to KI in that ratio. But HE is, to the radius IH, the sine of the an- gle of refraction ; and KI that of the angle of incidence. This explanation of refrac- tion is nearly the same as that of Rizzetti and Euler. The total reflection of a ray of light, by a refracting surface, is explicable in the same manner as its simple refraction: HE, (Fig- 34,) being so much longer than KI, that the ray first becomes parallel to FG, and then, having to return through an equal di- versity of media, is reflected in an equal an- gle. When a ray of light passes near an in- flecting body, surrounded, as all bodies are supposed to be, with an atmosphere of ether denser than the ether of the ambient air, the part of the ray nearest to the body is retarded, and of course the whole ray isinflected towards the body, (Fig. 35.) It has already been con- jectured, that the colours of light consist in the different frequency of the vibrations of the luminous ether : the opinion is strongly confirmed, by the analogy between the co- lours of a thin plate and the sounds of a se- ries of organ pipes, which, indeed, Euler ad- daces as an argument in favour of it, al- though he states the phenomena very inac- curately. The appearances of the colours of thin plates require, in the Newtonian sys- tem, a very complicated supposition,, of an ether, anticipating by its motion the velo- city of the corpuscles of light, and thus pro- ducing the fits of transmission and reflection; and even this supposition does not much as- sist the explanation. It appears, from the accurate analysis of the phenomena which Newton has given, and which has by no means been superseded by any later observa- tions, that the same colour recurs, whenever the thickness answers to the terms of an arith- metical progression, and this effect appears to be very nearly similar to the production of the same sound, by means of a uniform blast, from organ pipes which are different multiples of the same length. The greatest difficnhy in this system is, to explain the different degree of refraction of differently coloured light, and the separation of white light in refraction : yet, considering how imperfect the theory of elastic fluids still re- mains, it cannot be expected that every cir- cumstance should at once be clearly eluci- dated.^ It may hereafter be considered, how far the excellent experiments of Count Rum- ford, which tend very greatly to weaken the evidence of the modern doctrine of heat, may be more or less favourable to one or the other system of light and colours, 544 EXPERIMENTS AND INQUIRIES XI. Of the Coalescence of musical Sounds. It is surprising that so great a mathema- tician as Dr. Smith could have entertained, for a moment, an idea that the vibrations constituting different sounds should be able to cross each other in all directions, without affecting the same individual particles of air by their joint forces : undoubtedly they cross, without disturbing each other's progress ; but lliis can be no otherwise effected . than by each particle's partaking of both motions. If this assertion stood in need of any proof, it might be amply furnished by the: phenomena of beats, and of the grave harmonics ob- served by Romieu and Tartini ; which M. De la Grange has already considered in the same point of view. In the first place, to sim- plify the statement, let us suppose, what pro- bably never precisely happens, that the par- ticles of air, in transmitting the pulses, pro- ceed and return with uniform motions; and, in order to represent tlieir position to the eye, let the uniform progress of time be repre- sented by the increase of the absciss, and the distance of the particle from its original po- sition, by the ordinate, (Fig. 36. .41). Then, by supposing any two or more vibrations in the same direction to be combined, the joint motion will be represented by the sum or dif- ference of the ordinates. When two sounds are of equal strength, and nearly of the same pitch, as in Fig. 39, the joint vibration is alternately very weak and very strong, pro- ducing the effect denominated a beat, (Plate 5. Fig. 46, B and C) ; which is slower and more marked, as the sounds approach nearer to each ciher in frequency of vibrations ; and of these beats there may happen to be seve- ral orders, according to the periodical ap- proximations of the numbers expressing the proportions of the vibrations. The strength, or rather the momentum, of the joint sound is double that of the simple sound only at the middle of the beat, but not throughout its duration ; and if we estimate the force of sound by the momentum of the particles, it may be inferred, that the strength of sound in a concert will not be in exact proportion to the number of instruments composing it. Could any method be devised for ascertain- ing this by experiment, it would assist in the comparison of sotind with light : but the establishment of the fact would be no proof of a difference in the nature of sound and light ; for there is no reason to suppose the undulations of light continuous : their inter- missions may easily be a million million times greater than the duration of each parcel of undulations. In Plate 4. Fig. 36, letP and Q be the middle points of the progress or re- gress of a particle in two successive com- pound vibrations ; then, CP being = PD, KR = RN, GQ = QH, and MS = SO, twice their distance, 2 RS = 2 RN + 3 NM + 2 MS = KN -h NM + NM -I- MO =:KM + NO, is equal to the sum of the distances of the corresponding parts of the simple vibrations. For instance, if the two sounds be as 80 : 81, the joint vibration will be as 80.5; the arithmetical mean between the periods of the single vibrations. The greater the difference in the pitch of two sounds, the more rapid the beats> till at last, hke the distinct puffs of air in the experi- ments already related, they communicate the idea of a continued sound ; and this is the fundamental harmonic described by Tartini. For instance, in Plate 4. Fig. 37. . 40, the vibrations of sounds related as 1 : 2, 4 : 5, 9:10, and 0 : 8, are represented ; where RESPECTING SOUND AND LIGHT. 5^5 the beats, if the sounds are not taken too grave, constitute a distinct sound, which corresponds with the time elapsing between two successive coincidences, or near ap- proaches to coincidence ; for, that such a tempered interval still produces a harmonic, appears from Plate 4. Fig. 41. But, besides tliis primary harmonic, a secondary note is sometimes heard, where the intermediate compound vibrations occur at a certain in- terval, though interruptedly ; for instance, in the coalescence of two sounds related to each other, as 4 : 5, there is a recurrence of a similar state of the joint motion, nearly at the interval of y of the whole period, three of the joint vibrations occupying ^l and leaving ■^g : hence, in the concord of a major third, the fourth below the key note is heard as dis- tinctly as the double octave, as is seen in some degree in Plate 4. Fig. 38; AB being nearly two thirds of CD. If the angles of all the figures resulting from the motion thus assumed be rounded off, they will approach more near- ly to a representation of the actual circum- stances ; but, as the laws, by which the mo- tion of the particles of air is rvigulated, differ according to the different origin and nature of the sound, it is impossible to adapt a de- monstration to them all : if, however, the particles be supposed to follow the law of the harmonic curve, derived from uniform cir- cular motion, the compound vibration will be the harmonic instead of the arithmetical mean ; and the secondary sound of the inter- rupted vibrations will be more accurately formed, and more strongly marked: thus, in the concord 4 : 5, instead of -^ of the whole period, the compound vibration will become J, and three such vibrations, occupying |, will leave exactly y. (Plate 5. Fig. 44, 45.) The demonstration is deduciblefrom the pro- VOL. II. perties of the circle ; and in the same man- ner if the sounds are related as 7 C 8, or as 5 : 7, each compound vibration will occupy JLj or -i\^ ; and deducting 5 or 4 vibrations from the whole period, we shall have a re- mainder of y. This explanation is satisfac- tory enough with regard to the concord of a major third ; but the same harmonic is some- times produced by taking the minor sixth below the key note: in this case it might be supposed that the superior octave, which usually accompanies every sound as a se- condary note, supplies the place of the ma- jor third; but I have found that the experi- ment succeeds even with stopped pipes, which produce no octaves as harmonics. We must therefore necessarily suppose that in this case, if not in the former, the sound in question is simply produced as a grave har- monic, by the combination of some of the acute harmonics, which always accompa- ny the primitive notes. It is remarkable> that the law, by which the motion of the particles is governed, is capable of some singular alterations by a combination of vibrations. If we add to a given sound other similar sounds, related to it in fre- quency as the series of odd numbers, and in strength inversely in the same ratios, we may convert the right lines indicating a uni- form motion very nearly into figures of sines, and the figures of sines into right lines, as in Plate 4. Fig. 42, 43. XII. Of the Frequency of Vibrations consti- tuting a given Note. The number of vibrations, performed by a given sound in a second, has been variously ascertained; firet, by Sauveur, by a very in- genious inference from the beats of two sounds; and since, by the same observer and 4 A 546 tXPERIMENTS AND INQUIRIES several others, by calculation from the weight and tension of a chord. It was thought worth while, as a confirmation, to make an experiment, suggested, but coarsely conducted, by Mersenne, on a chord 200 inches in length, stretched so loosely as to have its single vibrations visible; and, by holding a quill nearly in contact with the chord, they were made audible, and were found, in one experiment, to recur 8.3 times in a second. By lightly pressing the chord at one eighth of its length from the end, and at other shorter aliquot distances, the fundamental note was found to be one sixth of a tone higher than the respective octave of a tuning fork marked C : hence the fork was a comma and a half above the pitch as- sumed by Sauveur, of an imaginary C, con- sisting of one vibration in a second. XIII. Of the Vibrations of Chords. By a singular oversight "in the demonstra- tion of Dr. Brook Taylor, adopted as it has been by a number of later authors, it is as- serted, that if a chord be once inflected info any other form than that of the harmonic curve, it will, since those parts which are without this figure are impelled towards it by an excess of force, and those within it by a deficiency, in a very short time arrive at or very near the form of this precise curve. It would be easy to prove, if this reasoning were allowed, that the form of the curve can be no other than that of the axis, since the lending force is continually impelling the chord towards this line. The case is very similar to that of the Newtonian proposition respecting sound. It may be proved, that every impulse is communicated along a tended chord with a uniform velocity; and this velocity is the same which is inferred from Dr. Taylor's theorem ; just as that of sound, determined by other methods, coin- cides with the Newtonian result. But, al- though several late mathematicians have given admirable solutions of all possible cases of the problem, yet it has still been supposed, that the distinctions were too minute to be actually observed. The theorem of Euler and De la Grange, in the case where the chord is supposed to be at first at rest, is in effect this: continue the figure each way, alter- nately on dilferent sides of the axis, and in contrary positions; then, from any point of the curve, take an absciss each way, in the same proportion to the length of the chord as any given portion of time bears to the time of one seinivibration, and the half sum of the ordinates will be the distance of that point of the chord from the axis, at the ex- piration of the time given. If the initial figure of the chord be composed of two right lines, as generally happens in musical in- struments and experiments, its successive forms will be such as are represented in (Plate 5. Fig. 50,51 :) and this result is fully confirmed by experiment. Take one of the lowest strings of a square piano forte, round which a fine silvered wire is wound in a spi- ral form ; contract the light of a window, so that, when the eye is placed in a proper po- sition, the image of the light may appear small, bright, and well defined, on each of the convolutions of the wire. Let the chord be now made to vibrate, and the luminous point will delineate its path, like a burninf' coal whirled round, and will present to the eye a line of light, w;hich, by the assistance of a microscope, nmy be very accurately ob- served. According to the different ways by which the wire is put in motion, the form of RESPECTrXG SOUND AND LIGHT. 547 tliis path is no less diversified and amusing, than the multifarious forms of the quiescent lines of vibrating plates, discovered by Pro- fessor Chladni ; and it is indeed in one re- spect even more interesting, at it appears to be more within the reach of mathematical calculation to determine it ; although liither- to, excepting some slight observations of Busse and Chladni, principally on the mo- tion of rods, nothing has been attempted on the subject. For the present purpose, the motion of the chord may be simplified, by tying a long fine thread to any part of it, and fixing tliis thread in a direction perpen- dicular to that of the chord, without drawing it so tight as to increase the tension : by these means, the vibrations are confined nearly to one plane, which scarcely ever happens when the chord vibrates at liberty. If the chord be now inflected in the middle, it will be found, by comparison with an ob- ject which marked its quiestfent position, to make equal excursions on each side of the axis ; and the figure which it apparently oc- cupies will be terminated by two lines, the more luminous as they are nearer the ends. (Plate 3. Fig. 52.) But, if the chord be in- flected near one of its extremities, (Fig. 53,) it will proceed but a very small distance on the opposite side of the axis, and will there form a very bright line, indicating its longer continuance in that place; yet it will return on the former side nearly to the point from whence it was let go, but will be there very faintly visible, on account of its short delay. In the middle of the chord, the excursions on each side of the axis are always equal ; and, beyond the middle, the same circumstances take place as in the half where it was in* fleeted, but on the opposite side of the axis ; and this apjwarance continues unaltered in its proportions, as long as the chord vibrates at all : fully confirming the nonexistence of the harmonic curve, and the accuracy of the construction of Eulcr and De la Grange. At the same tiine, as Mr. Bernoulli has justly observed, since every figure may be infinitely approximated, by considering its ordinates as composed of the ordinates of an infinite number of harmonic curves of different mag- nitudes, it may be demonstrated, that all these constituent curves would revert to their initial state, in the same time that a similar chord bent into a harmonic curve would per- form a single vibration ; and this is in some respects a convenient and compendious me- thod of considering the problem. But, when a chord vibrates freely, it never re- mains long in motion, without a very evir dent departure from the plane of the vibra- tion ; and, whether from the original obli- quity of the impulse, or from an interference with the reflected vibrations of the air, or from the inequabiiity of its own weight of flexibility, or from the immediate resistance of the particles of air in contact with it, it is thrown into a very evident rotatory mo- tion, more or less simple and uniform ac- cording to circumstances. Some specimens of the figures of the orbits of chords are ex- hibited in Plate 5. Fig. 47. At the middle of the chord, its orbit has always two equal halves, but seldom at any other point. The curves of Fig. 49, are described by combin- ing together va^'ious circular motions, sup- posed to be performed in aliquot parts of the primitive orbit : and some of them approach nearly to the figures actually observed. When the chord is of unequal thickness, or when it is loosely tended and forcibly inflected, the apsides and double points of the orbits haver a very evident rotator}' motion. The coui- 548 EXPERIMENTS AND INQUIRIES pound rotations seem to demonstrate to the eye the existence of secondary vibrations^ and to account for the acute harmonic sounds wliich generallj' attend the fundu- mentai sound. There is one fact respecting these secondary notes, which seems entirely to have escaped observation. If a chord be inflected at one half, one third, or any other aliquot part of its length, and tiien suddenly left at liberty, the harmonic note, which would be produced by dividing the chord at that point, is entirely lost, and is not to be distinguished during any part of the conti- nuance of the sound. This demonstrates, that the secondary notes do not depend upon any interference of the vibrations of the air with each other, nor upon any sympathetic agitation of auditory fibres, nor upon any effect of reflected sound upon the chord, but merely upon its initial flgure and motion. If it were supposed that the chord, when inflected into riglit lines, resolved itself necessarily into a number of secondary vibrations, ac- cording to some curves which, when pro- perly combined, would approximate to the figure given, the supposition would indeed in some respects correspond with the pheno- menon related; as the cocfiicients of all the curves supposed to end at the angle of in- flection would vanish. But, whether we trace the constituent curves of such a figure through the various stages of their vibrations, or whether we follow the more compendious method of Euler to the same purpose, tlie figures resulting from this series of vibrations are in fact so simple, that it seems incon- ceivable how the ear should deduce the com- plicated idea of a numbei of heterogeneous vibrations, from a motion of the particles of air, which must be extremely regular, and almost uniform ; a uniformity which, when proper precautions are taken, is not contra- dicted by examining the motion of the chord with the assistance of a powerful magnifier. Tills difiiculty occurred very strongly to Elder: and De la Grange even suspects that there is some fallacy in the experiment, and that a musical ear judges from previous as- sociation. But, besides that these sounds are discoverable to a ear destitute of such asso- ciations, and, when the sound is produced by two strings in imperfect unison, may be verified by counting the number of their beats, the experiment already related is an undeniable proof that no fallacy of this kind exists. It must be confessed, that nothing fully satisfactory has yet occurred to account for the phenomena; but it is highly proba- ble that the slight increase of tension pro- duced b3' flexure, which is omitted in the calculations, the elasticity or inflexibility of the chord, and the unavoidable inequality df thickness of its different parts,may, b}- disturb- ing the isochronism of the suboVdinate vi- brations, cause all that variety of soumls which is so inexplicable without them. For^ when the slightest diftierence is introduced in the periods, there is no difficulty in conceivJ^ ing how the sounds mi>y be distinguished ; and indeed, in soa>e casesi a nice ear ^^ill discover a slight imperfection in the tune of harmonic notes: it is- also often observed, in \tuningan instrument, that some of the single strings produce beating sounds, which uii- doubtedly arise from their want of perfect uniformity; the same circun»stance is the cause of the motion of the apsides, which "is often observable in the rotations already de- scribed. It may be perceived that any par- ticular harmonic is loudest, when the chord is inflected at about one third of the corre^ sponding aliquot part from one of the extre- RESPECTING SOUND AND LIGHT. 549 mities of that part. An observation of Dr. W allis seems to have passed unnoticed by later writers on harmonics. He says, that if the stringofaviohii be struck in the mid- dle, or at any other aliquot part, it will give either no sound at all, or a very obscure one. This is true, not of inflection, but of the motion communicated by a bow ; and may be explained from the circumstance of the successive impulses, reflected from the fixed poitits at each end, destroying each other : an explanation nearly analogous to some ob- servations of Dr. Matthew Young on the mo- tion of chords. When the bow is apphed not exactly at the aliquot point, but very near it, ihe correspondingharmontc is extremely loud ; / and tli€ fuudamentat note, especially in the lowestharnionics, scarcely audible : thechord assumes the appearance, at the aliquot points, of as many lucid lines as correspond to the number of the harmonic, more nearly ap- proachmg to each other as the bow ap- proaches more nearly to the point. (Plate 5. Fig. 54.) According to the various modes of applying the bow, an immense variety of figures of the orbits are produced, (Fig. 48.) more than enough to account for all the dif- ference of torte in different performers. In experiments of this kind, a series of harmo- nics is frequently heard in drawing the bow across the siime part of the chorti : these are produced by the bow ; they are however not proportionate to the whole length of the bow, but depend on the capability of the portion oftiie bowstring, intercepted between its end and the chord, of performing its vi- brations in times which are- aliquot parts of the vibration of the chord : hence we may perhaps infer, that the bow takes effecton the chord but at one instant, or for a very short time, during each fundamental vibration. la these experiments, the bow was strung with the second string of a violin. XIV. Of the Vibratiom of Rods and Plates. Some experiments were made, with the as- sistance of a most excellent practical musi- cian, on, the various notes produced by a glass tube, an iron rod, and a wooden ruler;, and, in a case where the tube was as much at liberty as possible, all the harmonics corre- sponding to the nmnbers from 1 to 13, were distinctly observed ; several of them at the same time, and others by means of difTerent blows. Tliis result seems to differ from the calculations of Euler and Count Iliccati, con- firmed as they are by the repeated experi- ments of Professor Chladni ; it is not there- fore brought forward as sufficiently contro- verting those calculations, but as showing the propriety of an inquiry into the sources of error in such experiments. Scarcely any note could ever be heard when a rod was loosely held at its extremity ; noi when it was held in the middle, and struck one seventh of the length from one end. The very ingenious method of Professor Chladni,. of observing the vibrations of plates by strewing fine sand over them, and discover- ing the quiescent hues by the figures into which it is thrown, has hitherto been little known in this country: his treatise on the phenomena is s}i Shr.ltoTt jodp. VoiJi.r. sp4. Plate 4 I'l/h. hy ./. JoTuhson .loTidon 2 July. i8o6. Joseph Skdtan, srAtlfJ. Sl-V f- TLA.TE 5. rolJ[.t•c■i.^. Ti R- . 44- • Fub.bv J.Jy^hruim .Zondan x JvJ^ 1806 ■ Josmh .STcrff^'n •ruff^. Tel.a.P.: Plate 6. Fig. 56. AJf .iy J. XifTuisim. JLondorv u. July ido6 . JoJCph Sfu'lJoiV sculp. III. AN ESSAY ON CYCLOIDAL CURVES, WITH INTRODUCTORY OBSERVATIONS. From the British Magazine, for April 1800. ON MATHEMATICAL SYMBOLS. Many of the most celebrated mathema- ticians of the present day have been disposed to pride themselves on the very great supe- riority, which they altribiUe to the mo- dern methods of calculation, over those which were known to the ancients. That, in the course of so many centuries, mathe- matical sciences, hke all others, should have been very considerably advanced, is no more than must have been expected, from the great number of persons who have employed iheir talents in the cultivation of those sciences. But, if we examine the matter impartially, we shall have reason to believe, not only that mathematics have been as slow in their real advancement as any other part of phi- losophy, but that the moderns have very fre- quently neglected the more essential, for fri- volous and superficial advantages. To say nothing of the needless incumbrances of new methods of variations, of combinatorial ana- lyses, and of many other similar innovations, the strong inclination which has been shown, especially on the continent, to prefer the al- gebraical to the geometrical form of repre- sentation, is a sufficient proof, that, instead of endeavouring to strengthen and enliglitea the reasoning faculties, by accustoming thetn to such a consecutive train of argument as can be fidly conceived by the mind, and represented with all its links by the recol- lection, they have only been desirous of spar- ing themselves as much as possible the pains of thought and labour, by a kind of mecha- nical abridgment, which at best only serves the office of a book of tables in facilitatinar computations, but which very often fails even of this end, and is, at the same time, tlie most circuitous and the least intelligible. These philosophers are like the young^Eng- 556 AX ESSAY OX CyCLOIDAL CURVES. lishman on his travels^ who visits a country by drivingAvith all possible speed from place to place by night, and refreshing his fatigues in the day time, by lounging half asleep at his hotel. Undoubtedly there are some coun- tries through which one may reasonably wish to travel by night, and uiidoubiodly there are Bome cases where algebraical symbols areniore convenient than geometrical ones : but ■when we see an author exerting all his inge- nuity in order to avoid every idea that has the least tincture of geometry,' when he obliges us to toil through immense volumes filled with all manner of literal characters, without a single diagram to diversity the prospect, we may observe with the less sur- prise, that such an "author appears to be con- fused in his conception of the most elemen- tary doctrines, and that he fancies he has made an improvement of consequence, when, in fact, he is only viewing an old object in a new disguise. It happens frequently in the description of curves, and in the solution of problems, that the geometrical construction is very simple and easy, while it almost ex- ceeds the powers of calculus to express the curve or the locus of the- equation in a man- ner strictly algebraical :, and, indeed, the astonishing advances that were n;ade, in a comparatively short time, by Euclid, by Apol- lonius, and above all, by Archimedes, are sufficient to prove, that the method of repre- sentation which they employed could not be very limited in its application : and the pre- cision and elegance, with which the method of geometrical fluxions is treated by Newton and Maclaurin, form a strong contrast to the tedious affectation of abstraction an(l obscu- rity which unfortunately pervades the writings of many great mathematicians of a later date. It would be of inestimable advantage to the progress of all the sciences, if some diligent and judicious collector would undertake to compile a complete system of mathematics ; not as an elementary treatise, nor as a mere index of reference, but to contain every pro- position, with a concise demonstration, that has ever yet been communicated to the pub- lic. Until this is done, nothing is left but for every individual, who is curious in the search of geometrical knowledge, to look over all the mathematical authors, and all the literary memoirs, of the last and present centuries.: for without this, he may very easily fancy he has made discoveries, when the same facts have been known and forgotten long before he existed. An instance of this has lately occurred to ayounggentlemanin Edinburgh, a man who certainly promises, in the course of time, to add considerably to our know- ledge ol' the laws of nature. The tractory, tractrix, or equitangential curve, was first described by Huygens, and afterwards more fully by Mr. Bomie, (Mem. Acad. ]712,)and by Mr. Perks. (Ph. tr. XIX. n. 345, Abr. IV. 456.) Bomie and Perks have shown many remarkable properties belonging to it ; and one in particular, which may be briefly demonstrated, that it is the involute of the catenaria: for since the equation of the ca- tenaria is zz r: 2«x + xx, wq have zz — ax -f XX, and x : z :: 2 : a + x, therefore the vertex of the right angled triangle, •bf which the base is the evolved radius, and the hypo- tenuse a line paralhel to the axis of the curve, describes a right hue ; and the perpendicu- lar of this triangle is always = a, and is the constant tangent of the curve described by the evolution. Cotes has also, in his Logo- metria, investigated the properties of the tractrix of the circle. Bernoulli observed in 1730, that the tractrix was one of the AN ESSAY ON CYCLOIDAL CURVES. 557 tautoclironous curves in a resisting medium. In 1736 it was the subject of a dispute be- tween MM. Clairaut and Fontaine : it is not yet entirely forgotten on that spot of acade- mic Giroiind which srave birth to the discove- ries of Newton; and its equation is to be found in a work no less common than F.nier- son's Fluxions, nearly in the same form as that which is published as new in the Philoso- phical Transactions for 17'98. We find in the same paper a new method of dividing an elliptic area in a given ratio ; but the curve which the author calls a cycloid is the' com- panion of a trochoid, and is only a distortion of the figure by which Newton had very simply and elegantly solved the same problem. It is unnecessary to compare the altenijit tode- mon'^trate the incommensuruhility of an oval with the Newtonian method ; since Dr. Waring's proof, deduced from the nature of the equation of limits, is decidedly more sa- tisfactory than any other hitherto made known. On the whole, it appears that this ingenious gentleman has been somewhat un- fortunate in the choice of those problems which he has selected as sf)ecimens of the elegance of the modern mode of demonstra- tion; whether those, which he has l^rought forwards without proof, would have furnished him with a more favourable opportunity for the display of neatness and accuracy, may be more easily determined, whenever he may think proper to lay before the public their analysis, construction, and demonstration at full length. But, allowing the superiority of the modern calculations in many cases, their great advantage appears to be derived from the methods of series and approximations ; indeed, however we may wish to adhere to the rigour of the ajicient demonstrations, it is absolutely necessary for the purposes of the higher geometry to extend, in some measure, the foundations which the ancients laid in their postulates. Perhaps the most material addition may be comprehended in this form: " Let it be granted that any curve line may be drawn whenever an indefinitely great number of points maybe geometrically found in, or indefinitely near to, that line." No. doubt it is lAathematically impossible to comply with this postulate; but it must be remembered, that it is also impossible to dr.iw, with strictly mathematical accuracy, a right line or a circle ; but in both cases we can approach sufficiently near to the truth for practice: and itappcars to be more convenient to consider such curves as arc thus described as belonging to geometry, than to limit the number of geometrical curves, according to Descartes, to those of which the ordinate and absciss are comparable by an algebraical cquiition. This postulate forms the connect- ing link between rational and irrational quan- tities, between the infinite an)5, Torricelli, in 1644, first pub- lished the quadrature and the method of drawing a tangent, both of which had been investigated by Descartes in I63'g. Wallis gave, in 1670, a perfect quadrature of a portion of the cycloid. The epicycloid is said to have been invented by Roemer : its rectification and evolute were investigated by Newton in the Trincipia, publisVied in 1&87. In 1695 Mr. Caswell showed the perfect quadrabrliiy of a portion of the epicycloid, and Dr. Halley immediately published an extension of Caswell's discovery, together with a compari- son of all epitrochoidal with circular areas. M. Varignon is also said to have reduced the rectification of the epitro- choid to that of the ellipsis, in the same year. Nicole, De- lahire, Pascal, Reaumur, Maclaurin, the Bernoullis, the commentators on Newton, and many others, have contri- buted to the examination of cycloidal curves, both in planes and in curved surfaces; and Waring, the most pro- found of modern algebraists, tias considerably extended his researches upon the nature of those lines which are gene- rated by a rotatory progression of other curves. In the pre- sent essay, the most remarkable properties of cycloidal curves are deduced io a simpler and more general manner than appears to have been hitherto done, the equations o several species are investigated, and a singular property o the quadricuspidate hypocycloid is demonstrated. Those who wish for further information respecting the history of these curves, may consult either Carlo Dati's essay on the subject, or Montucla's Historyofthe mathematics. PitoposiTioN 1. Theokem. (Plate7.Fig- 57.) In any curve generated by the rotation of antjther on any basis, the right Hnejoiningthe AN ESSAY ON CYCLOIDAL CURVES. S59 describing poinf, and the point of contact of the generating curve and the basis, is al- ways perpendicular to the curve described. If may by some be deemed sufficient to consider the ge- nerating curve as a rectilinear polygon, of an infinite num- ber of sides ; since, in this point of view, the proposition requires no further demonstration ; and, indeed, Newton and others have not scrupled to lake it for granted : but it is presumed, that a more rigid proof will not be considered as superfluous. Let M be the describing point, and P the point of contact : and let LO, MP, and NQ, be succes. sive positions of the same chord of the generating curve at infinitely small distances : then it is obvious, and easily de- monstrable, that the arcs OP and PQ,. described by the point P of the generating curve, in its passage from O to P, and from P to Q, will be perpendicular to the basis at P, and will therefore touch each other. Let the arcs L, LMK, and N, be described with the radius PM, on the centres O, P, and S. Then the curve described by M will touch IMK ; for since O and Q lie ultimately in the same direc- tion from P, if L be above IMK, N will also be above it, since these points must be in the circles L and N, and infinitely near to M ; and if L be below IMK, N, for the same reason, must be below it ;, and M is common to the circle and the curve, therefore the curve touches the circle IMK at M, and is perpendicular to the radius PM. Proposition ii. Problem. To draw a tangent to a cycloidal curve at aay given point. On the given point, as a centre, describe a circle equal to the desaribing circle of the curve, and from the intersection of this circle, with the line described by the centre of the generating circle, let fall a perpendicular on the basis ; the point thus found will be the point of contact, and the tan- gent will be perpendicular to the right line joining this point of contact and the given point, by the first proposi- tion. It will be obvious, from inspection, which of the two intersections of the circle to be described, with the track of the centre, is to be taken as the place of that centre cor- responding to the given point. Scholium. The tangents of cycloids and epicycloids may be diawn from any given point without them bj means of curves, which are described by the intersection of two lines revolving on given points, with proportionate angular velocities, and in the case of the bicuspidate epicycloid, the curve becomes an equilateral hyperbola. Proposition hi. Pkobleru (Plate 7. Fig. 38.). To find the length of an ephro- choid. Let C be the centre of the basis VP, K that of the rotat. ing circle PR, and of the describing circle GL, P the point of contact, and M the describing point. Then joining MXC, and supposing VX to be an element representing the motion of the point P, in cither the basis or the generating circle, draw the arc MN on the centre C, and join CVN : then NM will represent the motion of the point M as far as it is produced by the revolution round the centre C : take MO to VX as GR to PK, then MO will be the motion of M arising from the revolution round K, and NO will be the element of the curve produced by the joint motion. Let CII be parallel to PM, then CX or CP : CM::VX : MN, and PK:MK::CP:HM::VX:M0, therefore, CM; HM :!MN:MO, and these lines being perpendicular to CM, HM, the triangle NMO is similar to CMH, and MN r NO ::CM:CH, hence CP.:CH::VX: NO. Take PY to CP asPK to CK, thenCHtCP::PM:PY::NO:VX. On L describe the circle PfB, and draw IMLF: let FD be per- pendicular to PRB, take DE to DF as PG to PL, and E will be always in the ellipsis BEP : let AE and AF be tangent* to the ellipsis and circle at E and F ; then the increment of the arc BF will be to MO as PL to GL, and to VX as PL to PR. Join GM, and parallel to it draw PI ; then PIL is a light angle, and IL1'=AFD, and IM : ILXPG: PLXDE ; DF, by construction ; therefore the figure IPML is similar to DAEF, and as PL to PM, so is AF to AE, and so is the increment of the arc BF to that of BE ; but the increment cf BF Is to VX as PL to PR, therefore the increment of BE is to VX as PM to PR. Now it was proved that NO: VX. ::P.M : PY ; therefore the increment of BE is to NO as PY to PR, or as CP to 2 CK ; and the whole elliptic arc BE it to the whole SM as the radius of the basis to twice the dl''_ tance of the centres. C0K01.1AUY 1. The fluxion of every cycloidal arc Is proportional to the distance of the describing point from the point of contact. CoHOLLARY 2. Fot the epicycloid, the ellipsis coincides with its axis HP, and the arc BE with BD, which is double the versed sine of half the arc GM, in the describing or generating circle ; therefore the length of the curve is to this versed sine as four times the distance of the centres to the radius of the basis. Proposition iv. Problem. (Plate 7. Fig. 58, 59.) To HikI the centre of cur- vature of an epitrochoid. Let PY be, as in the last proposition, to CP as PK to CK, and on the diameter PY describe the circle PZY, cutting PO In Z : take OW a third proportional to OZ and OP, and W will be the centre of curvature.. For let QP::zVX be ;C0 AN ESSAY ON CYCLOIDAL CURVES. the space desrribed by P, while NO is described by O : it is obvious, from prop. 1, that the intersection of NA and OP must be the centre of curvature. Let QF be perpendi- cular to PO, and TA parallel to QN ; then, by prop. 3, NO : VX or QPXPO : PY, but by similar triangles QP: Or::PY:PZ; therefore NO: QFV.PO : PZ, and by division, NO : AOI'.OP : OZ, and by similar triangles;: OW : or or OP. Corolla BV 1. When Z coincides Vifith O or M, OW is infinite ; therefore whenever PZY intersects the describing ciiele, the cpittochoid vsill have a point of contrary flexure at the same distance from C as this intersection ; and the circle PZY is given when the basis and generating circle are given, whatever the magnitude of the describing circle may be. If the basis be a straight line, PY will be equal toPK. CoHOLLiRY 2. By means of this proposition, we may find the curve which will produce any given curve by toll- ing on a given basis ; or having the two curves, we may find the basis. When the basis is given, supposing NO a small portion of the given curve, of which W is the centre of curvature, VP being the circle of equal curvature with the basis at the point P, if we take OZ a third proportional to OW and OP, draw the perpendiculars PY and ZY, and take CP— PY : PY::PY : YKj then K will be the centre of curvature of the generating curve ; for by addition CP : PY::PK:YK, CP:PK::PY:YK, and CP:CK::PY: PK, as before. When the basis is a right line, Y is the centre of curvature of the curve required. Scholium. Hence we may easily find the curvature necessary in the tooth of a wheel for impelling a pallet without friction, by determining the curve which will ge- nerate, by rolling on the face of the pallet, a circle passing through the axis of the wheel ; but the tooth could never be disengaged from the pallet, without an escapement in- troduced for the purpose. Proposition v. Problem. (Plate 7. Fig. 60.) To find the evolute of an epicycloid. In the epicycloid SM, the point M being in the circum- ference of PIVIR, PZ will be to PM in the constant ratio of PY to PR, and MZ to PM as RY to PR, and PM to MW in the same ratio; hence PM:PW::RY : PYIICR: CP, therefore the point W is always in a circle PWH of which the radius is to PK in that proportion, and which touches SP in P. On the centre C describe a circle AS© touch- ing PWH in S; then, since CR : CP::PR : PH, we have by division CR ; CPX.CP ; VS, and the circle PWS being to A20 as PMR to SP, the arc PM being equal to SP, the similar arc PW will be equal to AS, and taking AS0=: PWH, 3Q will be always equal to SW, and W in a curve ©WS similar to SM, of which it is the evolute. Proposition vi. Problem. (Plate 7. Fig. Ol ) To find the area of an epitrochoid. On the centre C describe a circle touching the epitrochoid in S, take GFI to GC as PR to PC, and let the circle G*!! describe on the basis SG the epicycloid S*. Then taking GM always to G* as GL to Gn, M will be in the epitro- choid SM ; for the angular motion of the chord G, is the same as that of GM in the primary epitrochoid. Let SJi be the evolute of S, and GWS its generating circle. On diameters equal to SG, SL, and Sn, describe three circles, AD, AE, and AF, touching the light line AB in A ; let the angl» BAD be always equal to GHO, and it is evi- dent that AD, AE, and AF, will be equal respectively to WG, WM, and W*. But the angular motion of WG oft W being equal to the sum of the angular motions of GM on G and CG on C, is to that of AF, or of GM, or half that of KM, in the ratio of CIl to CG, or CR to CP ; therefore the fluxions of the areas SWG, SWM and SW* • are to those of the segments AD, AE, and AF, in the same ratio ; and that ratio being constant, the whole areas, and their differences, are also respectively to eax;h other as CR toCP. Scholium. The quadrable spaces of Halley are those which are comprehended between the arc of the epitro- choid, that of the describing circle, and that of a circle concentric with the basis, and cutting the describing circle at the extremities of its diameter. Proposition VII. Problem. (Plate 7. Fig. 62.) To find a central ecjuation for the epic^'cloid. Let CT be perpendicular to RT, the tangent at the point M, then PMR will be a right angle, and PM parallel to CT. On the centre C describe through M the circle MNO, and let MG be perpendicular to RO. Then the rectangle OQN=PQil, OQ : PG::GR : GN, by addition OQ : PQ ::0R : PN ; hence by division OP : PQ::IR : PN, and PQ ^2m-p^. But PM,=PR X PQ=^^X INP : IK. IK. and by similar triangles CT : CR : : PM : PR, whence Cfj Let MZ and RY be tan- CR(7 „ INP ^£gxPM,=CR,Xj^. gents to SP, then INP=MZ^, and IRP^RYj, CT=:CR MZ RY and CT will be to MZ in the constant ratio of CR to RY. Putting CP=a, CR=b, CMzzs, CT=u, thea uit as — aa =i:b I'L'—aa Vol.lLI.sbo Fig. 5 J. Plate 7 Fig. 60. Fig. 58. Fig.6x. Fig. 62. Fig. 69. Pub. by J. Johnson. Zondon x .^uly 16 oS. Joseph. Skelton. sculp. ' AN ESSAr OX CVCLOIDAL CURVES. 561 Peoposition viii. Problem. (Plate 8. Fig. 63.) To find a geometrical equation for tbe conchoidal epitrocboid. Let CP:=PK. On the centre C describe a circle equal to GM, cutting SC in Z. Join MZF, then the arc DZ=:GM, and MZ is parallel to CK, therefore EF is also equal to DZ or GM, CF is parallel to KM, arid MF=CK : there- fore this epitrochoid is the curve named by Delahire the conchoid of acircular basis, as was first observed by Reau- mur in 1708, and afterwards by Maclaurin, in 1720. Call CK, a, DE, b, ZII, r, HM, y, ZM, s ; and let ZI be perpendicular to CK ; then FZzza — s, CI— - and l< CIZ and ZHM being similar, CZ : Clr.ZM : ZH, or a— 5 ——:'.s:x; hence /i^as — ss, bx4-ssZlas, /I'a'+Shs'' 2 • . +j*z:dV, and by substituting for s', I'-l- it-r' — o'J^'■' + 6'I'^-2.T'J'-^- ibxy' -^ y' — a'y':ZO. Corollary 1. Join FN, and complete the parallelo- gram MFNL; then since EFzzDZizEN, FN is perpendicu- cular to EK, and ML to NL, and, NL being always equal to FM or CK, L i» always in a circle described on the cen- tre N, LM a tangent to that circle, and ZM a perpendicu- lar to that tangent drawn from the point Z. Corollary 2. (Plate 8. Fig. 64.) Tlie unicuspi- date epicycloid admits of a peculiar central equation, with respect to the point S. Call SM, s, and let ST:=u be i For IP and the trian- perpendlcular to the tangent MT, then k= { — j being half of SM, or s, SP =: v^ (—) gles SIP andMTS being similar, SP5 : SMi/XIPj • ST.?, or — : i';;— : «', and 2at/^s'. Corollary 3. The unicuspidate epicycloid is one of the caustics of a circle. For making the angle CllY = MRC = JMKP=iSCP, the triangle CRY is isosceles, and CY is constant; so that all rays in the direction of the tangent MR will be reflected by the circle QR towards Y, and consequently SM will be the caustic of a radiant point atY. Proposition i.x. Peoble.m. (Plate 8. Fig. 65.) To find a geomeliical equation for the tricuspidate hypocycloid. Let PA and MF be perpendicular to CS. Join PMB, KM, RMG, and PD. Then the angle APB is equal to the dif- ference of APC and MPR, or to that of their complements PRM, PCA : but PRM=i PKM=:|PCA, therefore AP VOL. II. = 1 PCA=ADP=:APS, and the triangles APS and APB are similar and equal. Ixt SC=o, SF=.t, FM=:y, and SB=r. Then SA ; SP::SP: SD, and SP^v' (ar). Draw PE perpendicular to BP ; then BE—SDzz'ia, BC=:o— r, £0=30— r, and by similar triangles, CP: CR'.IEC : CG =1 EC=:a— ir; therefore GB=:ii- : but BE : BG :: BP .- BM or 2a:|r:: v" [ary.r —^Z («r)=:BM ; again, BP: BM :; BA: BF, or v'(ar) : -^*/(ar):;.I- -. IL, andSF=:x=r_ 3a 2 6a rr — , 6ax=:6ar~rr, andrZZ3a± ./ {gaa — 6ax). But r' r' MFq=BUq — BVg, 0Ty'=: , and 36a'- »/«=: ' ply exercises the fa- culties, at the same time that it forms a de- sirable variety, when intermixed with lite- rary or professional employments. To call it an amusement onl}', betrays an ignorance of the nature and difliculty of the study; so far is the science of music from being of a light and superficial nature, that, in its wliole extent, it is scarcely less intricate or more easily acquired than, the most profound of the more regul.tr occupations of the schools : and even practical perfection in music re- quires so much intense and laborious appli- cation, such a minute accuracy of percep- tion, and so rapid an association of various sensitive ideas, with other ideas and mecha- 566 X.'S ESSAT ON MUSIC. tiical motions, that it is inconceivable how men, who have no appearance of superior briiliancj^inanyoUieraccompiisiimentjShould •be able to attain a conception and execution ■in music, which seem almost to require the faculties of a superior order of beings. An intemperate and dissipated attachment to music may indeed often be productive of evils; but probably the same individuals, who have been its victims, would have been equally idle and irregular if they had been destitute of this accomplishment. A consider- able share of the pleasure of practical music arises from causes perfectly distinct from the sensual perceptions : the consciousness of hav.iii"' overcome difficulties, tl>e laudable satisfaction of entertaining others, and the interest and emulation produced by a con- currence of others in the same pursuits; all these entirely outweigh the temporary Amusement of the ear, and wholly remove the objection, which might be made, to the enervating effect of a continued devotion to pleasurable sensations. Tiie ancient [ihilo- sophers, with all the manliness and dignity of character to which they aspired, were not ashamed to consider music as an indispensa- ble part of a liberal education ; and Plato devotes three of the earlier years of his young citizens entirely to the study of the lyre: nor are we without examples in modern times, of philosophers, and princes, and heroes, who have excelled as much in musical perform- ances, as in literature and in arms. U. 01- THE ORIGIN OF THE SCALE. The first lyre, with three strings is said to have been invented in Egypt by Hermes, xmder Osiris, between the years 1800 and 1.500 before Christ. The second and third string were, perhaps, the octave and fifth of the first, or more probably its fifth and fourth' as it would be easy to sing the octave with the accompaniment of the primitive note only. The melody might be either always in unison with one of the strings, resembling a very simple modem bass part; or the inter- vals might be occasionally filled up by the voice, without accompaniment. We have, in modern music, a specimen of a pleasing air, by liousseau, formed on three notes alone, the key note with its second and third ; bnt there can be little doubt that the earliest me- lodies must have had a greater compass than this; although some suppose the three strings of the oldest lyre to have been successive notes of the scale. The trumpet is said to have been invented about the same time : a little experience might have taught the Egyptians to produce from it the octaves, the 12th, 17th, 23d, and other harmonics of the primi- tive sonnd, which are related to it in the ra- tio of the integers from 1 to 9, and the same sounds might have been observed by a deli- cate ear among the secondary notes of a long chord ; and then, by descending three octaves from the 23d, and two from the 17th, they miglit have added to their lyre the se- cond and major third of the principal note. But it does not appear that this method ever occurred to the ancients : they seem rather to have attended to the intervals of the notes within the octave, than to the union of simi- lar notes in the natural harmonics; and, be- sides, the series of natural harmonics would never have furnished a true fourth or sixth, ll is uncertain when, or by whom, the fourth strimr was added : but the merit of increas- ing the number to seven is attributed to Tcrpander, about the year 700 befoi'e Christ, two centuries after Ff omer : although some persons Ixave asserted that he only brought the A^' ESSAY ON iiusrc. 667 improvement from Egypt, and that Hermes was also the inventor of the l^'re with seven strings. Pythagoras, or Simonides, about the year 500, added an eighth, and Timo- theus a ninth string : the number was after- wards extended to two octaves ; and Epigo- nus is said so have used a lyre of forty strings, or rather a harp, as he played with- out a plectrum : but the theory of the an- cient music soon became more intricate than interesting. The lyre of eight strings com- prehended an octave^ corresponding pretty accurately with the notes of our natural scale, beginning with e : the key note was a, so that tlie melody appears to have borne usually a minor third, which has also been observed to be the case in the airs of most uncultivated nations ; but there was a con- sideraljlc diversity in tlie manner of tuning the4}'re, according to the great variety of mod€8 and genera tlwit were introduced. These modes were of a nature totally differ- ent from the modern modulations into vari- oas keys, but they must have afforded a more copious fund of striking. If not of pleasing melodies, than we have at present. In some of the genera, intervals of about a qiiaiter tone were employed ; but this practice, on ac'countof its difficulty, was soon abandoned; a difficulty which is not easily overcome by the most experienced of modern singers ; al- though some great masters have been said to introduce a progression of quarter tones, in pathetic passages, with surprising effect. The tibia of the ancientsj as it appears evi- dently from I'heophrastus, although, not from the misinterpretations of his commenta- tors and of Pliny, had a reed mouth piece about three itjches long, and therefore was more properly a clarinet than a flute ; and the same performer generally played on two at once, and not in unison. Pollux, in the time of Commodus, describes, under the name of the Tyrrhene pipe, exactly such an organ as is figured by Hawkins, composed of brass lubes, and blown by bellows : nor does he mention it as a new discovery : it apjiears, from other authors, to have been often fur- nished with several registers of pipes; and it is scarcely possible that the performer, wiio is represented by Julian as having consider- able execution, should have been contented without occasionally adding harmony' to his melody. That the voice was accompanied by thorougii bass on the lyre, is undeniably proved by a passage of Plato: and that the ancients had some knowledge of singing in three puns, is evident i'rom Macrobius. Martini, who is one of die strongest oppo- nents of that opinion, which attributes to the ancients a knowledge of counterpoint, ob- serves, that " they allowed no concords bul the octave, fourth, and fifth, or at most very rarely the thin! ; yet tiiey were not without a knowledge of concord of harmonious paits. It is known with certainty, that two parts, whether vocal or instmniental, or mixed, besides unison, performed at the same time the same melody, either always in octaves or pj'obably always in fifths, or always in foiirllis ; which was called a symphony : perhaps also, they changed in the course of the performance from one interval to an- other, add this might be done by more than two parts at the same time." It is not im- probable that this statement mav be accu- rate : nor is it necessiiry to suppose a very exquisite and refined skill in the intricacies of composition,, to produce all the effects that have with any probability been altri- . buted to music. It is well known thatllousseau and others have maintained, that harmony 568 AJJ ESSAY OX MUSIC. is rather detrimental than advantageous to an iDteresting melody, in which ^true music consists ; and it may easily be observed, that an absolute solo, whether a passage or a cadence, is universally received, even by cul- tivated hearers, with more attention and ap- plause, than the richest riiodulalions of a powerful harmony. The minor scale being the most commonly used by the ancients, it was natural for Pope Gregory, who in the year 6()0 is said to have marked the notes by the Roman letters, to begin with A, the key note of that scale : al- though if, as there is some reason to suppose, the B was originally flat, A was not the key note, but its fifth, until the B natural was introdiieed, and denoted by a square b in- stead of a round one. By degrees the chro- matic scale was filled up, and the five added intervals were denoted by the letter belonging- to the note. abbve them, with the addition of the round b, or by the note below, with the addition of four lines crossing each other, im- plying a half note, as composed of four commas. A simple cross would, however, at present, be much more convenient, as more readily distinguishable from the square b, which is used to signify a natural note, in opposition to these ffotS; and siiarps. This is the historical account of the origin of the scale ; but, according to the modern theory and practice of music, the subject may be more easily understood, by beginning with an explanation of the major Bcale. III. PRACTICAL APPLICATION OF THE SCALES. The simplest proportions of two sounds to each other, next to unison, is whenr the fre- quency of their vibrations are related as one to two : such sounds bear a very strong resem- blance to each other, and when named, they are denoted by the same letter, and are only distinguished by the appellations in alt, in al- tissimo, on the one side, and double, and double double, on the other. The Germans, with great propriety, make use of small let- ters or capitals, with one, two, or more lines over or under them. The note marked by the tenor cliff is called ~, the octaves above, c, c, as far as six lines, which is, perhaps, the highest note used in music : the octaves below c, are c, C, C, C : C is probably not audible, vibrating but eight times in a se- •cond. C with six lines below it, would denote a sound, of which the complete vibrations should last precisely a second. The series of natural notes is this. A, B, C, D, E, F, G A, B, c, d. . b, c, d. . .The subjoined table will show the absolute frequency and the dimen- sions of each vibration of the octaves of c and the length of the simplest organ pipe that produces it : but, according to the dif- ferent temperature of the air, and the pitch of the instruments, these numbers may vary somewhat from perfect accuracy: and it must be observed, that the usual pitch of con- certs, in London, is somewhat higher than this standard ; and in Germany, perhaps a httle lower. AN ESSAY ON MUSIC. ■569 Sound moves in a second 1130 feet. Note. Vibrations in a second. Length of open pipe in feet. I 2 595.00 282.50 4 141.25 *- 2 audible 8 IS 32 70.(52 35.31 17.<)8 04 8. S3 c f S 128 4.41 =M 255 2.21 .» 1 * 512 1.10 A' 1024 2048 .55 .28 J 4096 .14 cyy 8192 .07 Any sound may be assumed at pleasure for the primitive or standard note of a piece of music, and is then' denominated the key note : and the idea of this note is perpetu- ally impressed on the mind in all simple compositions, both from its frequent recur- rence, and from the relation that all the other sounds bear to it. C being the key note of the scale called natural, we shall con- sider it as the foundation of the scale. The next in importance is the fifth, G, which, for various reasons, is intimately connected with the key note. The first reason is, that it constitutes the most perfect melody and harmony with C, since every alternate vibra- tion of C coincides with every third of G; the second is, that an attentive ear may almost always distinguish the fifth, at least its octave, the 12th, whenever any instrument sounds C ; it being one of those secondary sounds which are called natural harmonics, and which may generally be observed, in the pro- portion of the natural numbers, as for as twenty or more, but which have not hitherto been completely explained: thirdly, a stopped pipe, if blown forcibly, springs immediately from C to g, and an open pipe first to c, VOL. II. and then to g. The interval, between C and r G, is most naturally divided by the note E, which answers to the number 5, when C and G are represented by 4 and 6, and which is found among the natural harmonics both of chords and pipes. Tliese three notes consti- tute the harmonic triad, or common accord, in the major scale, which is the most per- fect, or rather the only perfect harmony. But the intervals are still much too largcfor melody, and require a further subdivision ; we now therefore take the fifth below instead of above the key, or its octave, the fourth above, F, which is to C as 4 to 3 : this sound is no where found among the natural har- monics of C, but C is the most distinguish- able of its harmonics, and tlicrefore the rela- tion is nearly the same. Tiie scale is com- pleted by filling up the perfect triads of G , and F : the fifth of G furnishing D, the se- . cond of the key, which is also tl^e ninth na- tural harmonic of C ; the third of G, the se- venth, B, which is the fifteenth harmonic of • C ; and the third of F being the sixtii of the ke}'. A, which is neither among the harmo- nics of C, nor has c among its harmonics. Hence we have a second table, in which the proportions of the length of a chord, or pipe, producing the various sounds, aye detailed, and the place among the principal natural harmonics of the key annexed. Notes. Proportions. Nat. harm. Key C 1 1 2d D f V 3d E \ 5, 10 4th I'- \ 0> (l) 5th G h 3, 6, 12 6th A 1 0 7th B \t 15 8th c .\. . a, 4, 8, 1(5 Now when two or more perfectly harmo- nious parts are performed together, they must necessarily be found all in the sanii? 4 » 5f0 AN'IfiSAT ON MOSIC. tiiad, C, E, G ; G, B, D : or F, A, C ; nntl the succession of these triads, in various forms, is sufficient for the accompaniment of any simple melody. A regular melody always terminates by aa ascent or descent of one degree to the key note ; the last note but one must therefore be alwa^'s B or D : ami both of tliese being in the triad of G, G is Called the governing note, or the dominant of C ; and F, being in the same manner governed by C, is called its snbdominaut. And it is usual, in all regular compositions of any length, to depart for a short time from the principal harmony of the key note, and to modulate into the key of the dominant, then to re- turn, and to modulate for a still shorter time into the subdominant, before the final close in the tonic or key note. It is necessary there- fore, 'for greater variety, to complete the scale of the dominant, as well as that of every other note which may be occasionally introduced as a principal key note ; but to do this with mathematical accuracy, in'the same proportions as have beeti explained, would be practically impossible, and even theoreti- cally inconvenient : hence arises the neces- sity of tempering some intervals, to make the others more tolerable, without too much in- creasing the number of sounds. It has been found sufficient in practice, to add five notes to the seven which have been enume- rated ; but the best proportions of these have not yet been absolutely determined : some have made all the twelve intervals equal : others have left the whole scale of C perfect : others again have taken a middle path, and have introduced a slight imperfection into this key, in order to make the neighbouring ones the less disagreeable. The least circuit- ous introduction of these notes is shown in the third table, together with the proportion that they bear to C when thus considered. They are denominated nearly in the Ger- man manner, the addition of the syllable "is" signifying what the English call sharp, and the French dike, and that of " es," flat, or bcmol. Notes. Relations. Proportions. Fis Bes Cis K<;s Gis as 7th of G as 4th ot F as 7th of D as 4 th <^Bes as 3d of E u m it But a still greater variety being required than these major scales afford, it has been found, that the interval of a fifth may be agreeably, though somewhat less harmoni- ously, divided, by placing the minor third below, instead of above, the major; so that C may be to E as E was toG, and conse- quently E to G as C was to E. The E, thils depressed to '|, diffeis but by a comma, or in the ratio of 80 : 81, from the Ees found above, as the 4th of Bes ; therefore the same string serves for both notes; and the scale becomes C, D, Ees, F, G, A, B, C ; wliich is the ascending minor scale, the A and B be- ing retained as leading best towards the key note, and the major triad of the dominant be- ing therefore necessary to the cadence. But in descending, the triad of the subdominant Fmay conform to the character of the minor mode, and Aes is substituted for A; and most frequently Bes for B, as dividing the interval from C to Aes more equally and more melodiously. Thus we have a pretty comprehensive view of the most usual practical relations of all the notes to each other. Their use as dis- cords is somewhat more complicated, and would lead further into the science of music than is consistent with the nature of so sum- 4 AV E,SSAy ON MUglC. mary a view. But it may be leujaikecl in general, that by far tbe most common dis- cord is tiie note which constitutes the dis- tinction of the scale of the key from that of its dominant ;• for instance, F with tlie triad of G, which is called the accord of the flat seventh of G ; and F, not being in the scale of G, is considered, as a regular preparative to the final accord of C ; in which that part or instrument by which the F is. introduced, must necessarily descend to E, the third of the key. The second, kind of discords are suspended discords, when one or more notes of any preceding accord are continued after the commencement of a different harmony in otber parts of the composition. The third, which is rare, and less uni|Versally adopted, consists in an anticipaiipn of a subordinate note of an accord which isj to follow, as in the case of f;he added sixth of the French school. The fourth kind are passing discords, where a note^ forming only a melodious step between two others, is inserted without any regard to its harmonious gelations. IV. OF THE TERMS- JiXPRBSSIVB-OF-TlMEi Tlie notation of music, as it, has been established for more thaii two centuries, is in general admirably adapted for its purpose: but there is one great ; deficiency, which might very easily be remedied, and that is, the total omission of any character expres- sive of the absolute duration of each note, however accurately the relative value of the , notes may be prescribed. It is true, some little allowance must be made for the execu- tion of the performer, and tor the habits of the audience ; but this is no reason why time might not be niitch more accurately noted, than by the vague terms which are usiially adopted. Tt woiiirfbe easy to prefix to each movement a munber, signifying how many bars are to be performed in a minute, whicli might at first be ascertained by.the.help of a stop watch, and would soon become perfectly familiar both to composers and performers, even without this assistaitce. According to Quanz, the nuQiber whidh should bp substi- tuted for Allegro assai, in common time, is about 40 ; .for Allegretto, (20 ; for, Lurghetto, 10 ; and for Adagio assai,_ 5. But it^ is usual to perform modern music much mord rapidly than this ; or at least the style of composition is so changed, tl^iat the terms are very differ- ently applied. An allegro, or even an alle- gretto, in common time, without semiquavers, is often performed as fast as 60;. seldom sl9wer than 30. jA very superficial attempt, to affix a deter- minate meaning to the words denoting musi- cal time, may be seen in the table subjoined . which, if it were more completely arid accu- rately filled up, might be of considerable use to young musicians ; although it will appear, from inspection of this table, that composers have hitherto employed those terms in very indefinite significations. But it must be con- fessed, that much latitude must necessarily be left for the ear and taste of a judicious per- former, and that it is impossible for human art, to describe on paper every delicacy of finished execution. 572 AN ESSAY ON MUSIC. . Terms. C ! you i i Prestissimo As fast as can. Presto 100 80, H. Presto ma non tioppo 90, H. Allegro assai 40, a 80, PI. 70, H. Allegro molto 100 H. Allegro TJvace 60, PI. 50, PI. Allegro fas. Ha. 45, M. \ 40, 50, 60, PI. 100, 120 H.75,80, PI. 65, H. Allegro non troppo 60, PI. 50, PI. Allegro moderate 40, H. 70, M. Vivace assai 100, H. 60, H. Vivace 60, H. Spiritoso 90, H. Menuetto allegro molto 75, H. 70, H. PI. 55, H. 50, H. M. Alkgretto QO, Q. 45, Pk Allegretto grgzioso 50, M. Moderate 30, PI. Maestoso 19 Larghetto 10, Q. Andante graz. Andante f35,H.Pl. \ 50, PI. 30, M. 30, M. And. cantab. 20, 25,M. Largo cant. 20, H. Adag. n. tr. 17, H. 27,30,P1. 20 Adagio 7, Cor. 14, H. 10, 12, M. Adagio molto 15, Scoz. 10, PI. Cor. Corelli. Ha. Handel. Q. Suanz. H. Haydn. M. Mozart. PI. Pleyel. If we choose to compare the time, occupied either by a bar, or by any of its parts, witli the vibrations of a pendulum, we may easily do it by means of the following table, which shows the number of vibrations in a minute, corresponding to pendulums of different lengths, expressed in inches. 4 5 6 7 8 9 10 13 'ations. Length. Vibrations 187 15 07 167 20 84 153 25 75 142 30 68 132 35 63 125 40 5t U8 SO sa 107 <0 47 -,*f. V. ON THE MECHANISM OF THE EYE. BY / THOMAS YOUNG, M.D. F.R.S. FROM THE PHILOSOPHICAL TRANSACTIONS. Read before the Royal Society, November 27, 1800. I. XN the year 1793, I had the honour of laying before the Royal Society some ob- servations, on the faculty, by which the eye accommodates itself to the perception of ob- jects at different distances*. The opinion which 1 then entertained, although it had never been placed exactly in the same light, was neither so new, nor so much forgotten, as was supposed by myself, and by most of those with whom I had any intercourse on the subject. Mr. Hunter, who had long before formed a similar opinion, was still less aware of having been anticipated in it, and was engaged, at the time of his death, in an investigation of the facts relative to it "I- ; an investigation for which, as far as physiology was concerned, he was undoubtedly well qualified. Mr. Home, with the assistance • Phil. Trans. 1793.169. t Phil. Trans. 1794. 21. jPhil. Trans. 1795. 1. of Mr. Ramsden, whose recent loss this So- ciety cannot but lament, continued the inquiry which Mr. Hunter had begun ; and the results of his experiments appeared very satisfactorily to confute the hypothesis of the muscularity of the crystalline lens J. I there- fore thought it incumbent on me, to take the earliest opportunity of testifying my persua- sion of the justice of Mr. Home's conclusions, which I accordingly mentioned in a Disser- tation published at Gottingen in 1796 §, and also in an Essay presented last year to this Society ||. About three months ago, I was induced to resume the subject, by perusing Dr. Porterfield's paper on the internal mo- tions of the eye ^ ; and I have very unex- pectedly made some observations, which, I think I may venture to say, appear to be § De Corporis humani Viribus conservatricibus, p. (58. II Phil. Trans. 1800. 148. f Edinb. Med. Essays. IV. 13*. 67 i ox THE MECPANISM OF THE EYE. finally conclusive in favour of my former opinion, as far as tiiat opinion attributed to the lens a pojver of changing its figure. At the same time, I must remark, thatever^^ per- son, who has been engaged in experiments of this nrMne, will be siwinre of ^he extreme delicacy and precaution requisite, both in conducting tliem, and in drawing inferences from them ; and will also readily allow, that no apology is necessary for the fallacies vvhiah have misled man}' others, as well as myself, in the application of 'those experi- ments to optical and physiological determi- nations. II. Besides the inquiry, respecting the ac- commodation of tlie eye to different dis- .tanees, I shall have occasion to notice some other particulars relative to its fu«ctiujis;and 1 shall begin with a general consideration of the sense of vision. I shall then describe an instrument for readily ascertaining the focal dist.%>ce of the eye ; and with the assistance ef this instr«me-nt, I shall investigate the 'dimensions and refractive powers of the human eye in its quiescent state; and the form and magnitude of the picture, which is delineated on the retina. I shall next inquire, how great are' the changes which the eye ad- mits, and what degree of alteration in itspro- fKjrtions will be necessary for these changes, on the varioussuppositions that are principal- ly deserving of comparison. • Ishall proceed to relate a variety of exi^eriments, which ap- ,pear to be the most proper to decide on the truth ofeach of these suppositions, and toexa- mine such arguments> as have been brought forwards, against the opinion which 1 shall endeavour to maintain ; and I shall conclude with some apatomical illustrations of the ca- pacity of the organs of various classes of ani- mals, for the functions attributed tothem. III. Of all the external senses, the eye is generally supposed to be by far the best uir- • derstood ; yet so complicated and so diversi- fied are its powers, that many of them have been hitherto uninvestigated : and on others, much, laborious rese^sirch has been spent in vain. It cannot indeed be denied, that we are capable of cvplaining the use and opera- tion of its different parts, in a far more satis- factory and interesting manner thata those of the ear, which is the only organ that can be strictly com{)ared with it; since, in smell- ing, tasting, and feeling, the objects to be examined come, almost unprepared, into im- mediate contact with the extremities of the nerves; and the only difficulty is, in conceiv- ing the nature of the effect produced by them, andof its communication to the sensorium. But the eye and the ear are merely preparatory organs, calculated for transmitting the im- pressions of light and sound, to the retina, and to the termination of the soft auditory nerve. In the eye, light is conveyed to the retina, without any change of the nature of its pro- pagation : in the ear, it is 'very probable, that instead of the successive motion of dif- ferent parts of the same elastic medium, the small bones transmit the vibrations of sound, as passive hard bodies, obeying the motions of the air nearly in their whole extent at the same instant. In the eye, we judge very pre- cisely of the direction of light, from the part of the retina on which it impinges; in the ear, we have no other criterion than t^e slight ' difference of motion in the small bones, according to' the part of the tyiupa- num on which the sound, concentrated by different reflectionsy first strikes ; hence, the idea of direction is necessarily very indistinct; and there is no reason to suppose, tljat dif- ferent parts of the auditory nerve axe ejcclu- ox THE JIECIIANISM OF THE EYfi. .575 sively affected by sounds in different direc- tions. Supposing the rye capable of con- veying a distinct idea of t\Vo points subtend- ing an angle of e^ minute^ which is, perhaps, nearly the smallest interval at which two ob- jects can be distinguished, although a line, subtending onl*one tenth of a minute in bre&dth, may sometimes be perceived as a single object ; there must, on this supposi- tion, be about 36O thousand sentient points, for a field of view of 10 degrees in diameter, and above 60 millions for a field of 140 de- grees. But, on account of the various sen- sibility of the retina, to be explained here- after, it is not necessary to suppose, that there are more than 10 million sentient points, nor can there easily be less than one million : the optic nerve may, therefore, be judged to consist of several millions of dis- tinct fibres. By a rough experiment, I find, that I can distinguish two similar sounds proceeding from points which subtend an angle of about five degrees. But the eye can discriminate, in a space subtending every way five degrees, about 90' thousand different points. Of such spaces, there are more than a thousand in ahemisphere : so that the ear can convey an impression of about a thousand different direetions. The ear has not, how- ever, in all cases, quite so nice a discrimi- nation of the directions of sounds : the rea- son of this difference between the eye and ear is obvious ; each point of the retina has only three principal colours to perceive, since the rest are probably composed of various proportions of these ; but there being many thousands or millions of varieties of sound audible in each direction, it was impossible that the number of distinguishable directions should be very large. It is not absolutely cer- tain, that every part of the auditory nerve is capable of receiving the impression of each of the very great diversity of tones that we can distinguish, in the same manner as each sensitive point of the retina receives a dis- tinct impression of the colour, as well' as of the strength, of the light which falls on it ; although it is extremely probable, that all the different parts of the surface, ex- posed to the fluid of the vestibule, are more or less affected by every sound, but in different degrees and succession, accord- ing to the direction and quality of the vibra- tion. Wl^ether or no, strictly speaking, we can hear two sounds, or see two objects, in the same instant, cannot easily be determined; but it is sufficient, that we can do both, with- out the intervention of any interval of time perceptible to the mind ; and indeed we could form no idea of magnitude, without a com- parative, and therefore nearly cotemporary, perception of two or more parts of the same object. The extent of the field of perfect vi- sibn, for each position of the eye, is certainly not very great ; although it will appear here- after, that Its refractive powers are calcu- lated to take in a moderately distinct view of a whole hemisphere : the sense of heaiing is equally perfect in almost every direction. IV. Dr. Porterfield has applied an ex- periment, first made by Scheiner*, to the de- termination of the focal distance of the eye ; and has described, under the name of an op- tometer, a very excellent instrument, founded on the principle of the phenomenon f. But the apparatus is capable of considerable im- provement; and 1 shall beg leave to de- scribe an optometer, simple in its construc- tion, and equally convenient and accurate in its application. • Priestley's opt. 113. t Edinb. Med. Ess. IV. I8i. 676 ON THE JIKCHANISM OF THE EYE. Let an obstacle be interposed between a radiant point (11, Plate 15. Fig. 109j) and any refracting surface, or lens (CD), and let this obstacle be perforated at two points (A and B) onl3'. Let the refracted rays be inter- cepted by a plane, so as to form an image on it. Then it is evident, that when this plane (EF) passes through the focus of refracted rays, the image formed on it will be a single point. But, if the plane be advanced for- wards (to GH), or removed backwards (to IK), the small pencils, passing through the perforations, will no longer meet in a single point, but will fail on two distinct spots of the plane (G, H ; I, K :) and, in either case, form a double image of the object. Let us now add two more radiating points, (S and T, Fig. 110,) the one nearer to the lens than the first point, the other more remote ; and, when the plane, which receives the images, passes through the focus of rays com- ing from the first point, the images of the se- cond and third points must both be double (« s, t t ;) since the plane (EF) is without the focal distance of rays coming from the fur- thest point, and within that of rays coming from the nearest. Upon this principle. Dr. Porterfield's optometer was founded. But, if the three points be supposed to be joined by a line, and this line to be some- what inclined to the axis of the lens, each point of the line, except the first jKiint (K, Fig. 1 1 1,) will have a double image; and each pair of images, being contiguous to those of the neijiibouring radiant points, will form with them two continued lines ; and the images being ntore widely separated as the point which they represent is further fron^ the first radiant point, the lines (s t, s t,) will convergeon each side towards (r) the image of this point, and there will intersect each other. The same happens when we look at any object through two pin holes, within the li- mits of the pupil. If the object be at the point of perfect vision, the image on the re- tina will be single ; but, in every other case, the image being double, we shall appear to see a double object : and, if we look at a line pointed nearly to the e3'e, it will appear as two lines, crossing each other in the point of perfect vision. For this purpose, the boles may be converted into slits, which ren- der the, images nearly as distinct, at the same time that they admit more light. The num- ber may be increased from two to four, or more, whenever particular investigations render it necessary. This instrument has the advantage of show- ing the focal distance correctly, by inspec- tion only, without sliding the object back- wards and forwards, which is an operation liable to considerable uncertainty, especially as the focus of the eye may in the mean time be changed. The optometer may be made of a slip of card paper, or of ivory, about eight inches in length, and one in breadth, divided lon- gitudinally by a black line, which must not be too strong. The end of the card must be cut as is shown in Plate 9. Fig. 71, in order that it may be turned up, and fixed in an in- clined position by means of the shoulders : or a detached piece, nearly of this form, maybe applied to the optometer, as it is here engrav- ed (Fig. 72.). A hole about half an inch square must be made in this part ; and the sides so cut as to receive a slider of thick paper, with slits of different sizes, from a fortieth to a tenth of an inch in breadth, divided by spaces somewhat broader ; so that each ob- server may choose that which best suits the aperture of his pupil. In order to adapt the ON THE MECHANISM OF IIHE ETE. 57 instrument to the use of presbyopic eyes, the other end must be furnished with a lens of four inches focal length; and a scale inpst be made near the line on each side of it, di- vided from one end into inches, and from the other according to the table here calcu- lated, by means of which, not only diverging, but also parallel and converging rays from the lens are referred to their virtual focus. If ivory be employed, its surface must be left without any polish, otherwise the regular re- flection of light will create confusion ; and in this respect, paper is much preferable. The instrument is easily appUcable to the purpose of ascertaining the focal length of spectacles required for myopic or presbyopic eyes. Mr. Gary has been so good as to fur- nish me with the numbers and focal lenu;lhs of the glasses commonl}' made ; and I have calculated the distances at which those num- bers must be placed on the scale of the opto- meter, so that a presbyopic eye may be en- abled to see at eight inches distance, by using the glasses of the focal length placed opposite to the nearest crossing of the lines ; and a myopic eye, with parallel rays, by using the glasses indicated by the number that stands opposite tlieir furthest crossing. It cannot be expected, that every person, on the first trial, will fix precisely upon that power which best suits the defect of his sight. Few can bring their eyes at pleasure to the state of full action, or of perfect relaxation ; and a power two or three degrees lower than that which is thus ascertained, virill be found sufficient for ordinary purposes. I have also added to the second table, such numbers as will point out the spectacles necessary for a presbyopic eye, to see at twelve and at eighteen inches respectively: tli« middle series will perhaps be the most proper for placing the numbers on the scale. The optometer should be applied to each eye ; and, at the time of observing, the opposite eye should not be shut, but the instrument should be screened from its view. The place of inter- section may be accurately ascertained, by means of an index sliding along the scale. The optometer is represented in Plate 9- Fig. 72 and 73 ; and the manner in which the lines appear, in Fig. 74. Table i. For extending the scale by a lens of 4 inches focus. 412.00 S 2.22 2.40 2.55 2.671 2.77 2.88 2.93 3.00 3.06 3.11 3.16 3.33 3.4 3.52 3.64 3.70 3.7 70 80 3.61 100 200 00 — 200 — 100 4.17 — 50 4.35 — 45 4.39 3.76 3.85 3.92 4.00 4.08 -40 4.44 -3S 4.51 -30 4.62 -25 4.76 -2o!5.00 -15^5.45 -14 5.60 -13|5.78 -I2|C.00i — 11 — 10 — 9.5 — 9 0 — 8.5 — 8.0 6.^9 6.67 6.90 7.20 7.5s S.OOi Table u. For placing the numbers indicating the focal length of convex glasses. Foe. VIII. XII. 00 8.00 13.00 40 10.00 17-14 36 10.28 18.00 30 10.91 20.00 38 11.20 21.00 26 11.56 22.29 34 13.00 24.00 22 12.77 26.40 20 .13.33 30.00 18 14.40 36.00 16 16.00 48.00 14 18.67 84.00 13 24.00 00 11 ■ 29.33 — 132.00 It) 40.00 — 60.00 g 72.00 — 36.00 8 00 — 24.00 7 —56.00 — 16.80 6 — 24.00 — 12.00 5 — 13.33 — 8.57 4.5 — 10.29 — 7-20 4.0 — 8. 00 — 6 00 - 3.5 — 6.22 — 4.94 - 3.0 — 4,80 — 4.00 " xvm. 18.00 32. 7J 36.00 4.^.00 50.40 58.50 72.00 99.00 180.00 00 — 144.00 — 63.00 36.00 — 28.29 22.50 18.00 14.40 11.45 9.00 5. 93 6.00 5.14 4.34 3.60 VOL. II. 4e 57S ON THE MECHANISM OF THE EYE. Ihble III. For concave slasses. Number. Focus. Number. Focus. Number. 1 24 8 7 15 2 18 g 6 10 3 Ifl 0 5 17 4 12 11 4.i 18 5 10 12 4.0 li) 0 9 13. S.i so 7 » 14 S.OO Focus. 2.7s 2. 50 a. 2 5 2.00 1.75 1.50 V. Being convinced of the advantage of making every observation with as little as- sistance as possible, I have endeavoured to confine most of my experiments to my own eyes; and Ishall> in general, ground my calcu- lations on the supposition of an eye nearlj' similar to my 'own. I shall therefore first endeavour to ascertain all its dimensions, and all its faculties. For measuring the diameters, I fix a small key on each point of a pair of compasses; and I can venture to bring the rings into im- mediate contact with the sclerotica. The transverse diameter is externally 98 hun- dredths of an inch. To find the axis, I turn the eye as much in- wards as possible, and press one of the keys close to the sclerotica, at the external angle, till it arrives at the spot where the spectrum formed by its pressure coincides with the di- rection of the visual axis, and, looking in a glass, I bring the otl^er key to the cornea. The optica] axis of the eye, making allow- »nce of three hundredths for the coats, is thus found to be 91 hundredths of an inch, from the external surface of the cornea to the retina. With an eye less prominent, this method might not have succeeded. The vertical diameter, or rather chord, of the cornea, is 45 hundredths: its versed sine, ] ] hundredths. To ascertain the versed sine, I ;:)oked with the right eye at the image of the left, in a small speculum held close to the nose, wiiile the left eye was so averted, that the margin of tiie cornea appeared as a straight line, and I then compared the pro- jection of ilic cornea with the image of a cancellated scale held in a pro[,er direction behind the left eye, and close to the left temple. The horizontal chord of the cor- nea is nearly 49 hundredths. Hence the radius of the cornea is 31 hun- dredths. It may be thought, that I assign too great a convexity to the cornea ; but I have verified it by a number of concurrent observations, which will be enumerated here- after. The eye being directed towards its image, the projection of the margin of the sclerotica is 22 hundredths from the margin of the cornea, towards the external angle, and 27 towards the internal angle of the eye : so that the cornea has an eccentricity of one for- tieth of an inch, with respect to the section of the eye perpendicular to the visual axis. The aperture of the pupil varies from 27 to 13 hundredths ; at least this is its apparent size, which must be somewhat diminished, on account of the magnifying power of the cornea, perhaps to 25 and 12. When di- lated, it is nearly as eccentric as the cornea ; but, when most contracted, its centre coin- cides with the reflection of an image from an object held immediately before the eye; and this image very nearly with the centre of the whole apparent margin of the sclerotica : so that the cornea is perpendicularly intersected by the visual axis. My eye, in a state of relaxation, collects, to a focus on the retina, those rays which diverge vertically from an object at the dis- tance of ten inches from the cornea, and the rays which diverge horizontally from an ob- ON THE MECHANISM OF THE EYE. 579 ject at seven inches distance. For, if I hold the plane of the optometer vertically, the images of the line appear to cross at ten inciies; if horizontally, at seven. The dif- ference is expressed hy a focal length of 23 inches. I have never experienced "any in- convenience from this imperfection, nor did I ever discover it till I made these experi- ments ; and I helieve I can examine minute objects wiih as much accuracy as most of those whose eyes are differently formed. On mentioning it to Mr. Gary, he informed me that he had frequently taken notice of a similar circumstance ; that many persons were obliged to hold a concave glass ob- liquely, in order to see with distinctness, counterbalancing, by the inclination of the glass, the too great refractive power of the eye in the direction of thatinclination, and finding but little assistance frotn common spectacles of the same focal length. The difference is not in the cornea, for it exists when the effect of the cornea is removed, by a method to be described hereafter. The cause is, without doubt, the obliquity of the uvea, and of the -crystalline lens, which is nearly parallel to it, with respect to the visual axis : this obliquity will appear, from the dimensions already given, to be about 10 degrees. Without en- tering into a very accurate calculation, the difference observed is found to require an in- clination of about 13 degrees; and the re- maining three degrees may easily be added, by the greater obliquity of the posterior sur- face of the crystalline opposite the pupil. There would be no difficulty in fixing the glasses of spectacles, or the concave eye glass of a telescope, in such a position as to remedy the defect. In order to ascertain the focal distance of the lens, we must assign its probable dis- tance from the cornea. Now the versed sine of the cornea being 1 1 hundredths, and the uvea being nearly flat, the anterior surface of the lens must probably be somewhat behind the chord of the cornea ; but by a very in- considerable distance, for l.he uvea has the substance of a thin membrane, and the lens approaches very near to it : we will there- fore call this distance 12 hundredths. The axis and proportions of the lens must be estimated by comparison with anatomical observations ; since they affect, in a small degree, the determination of its focal dis- tance. M. Petit found the axis almost al- ways about two lines, or 18 hundredths of an inch. The radius of the anterior surface was in the greatest number 3 lines, but oftener more than less. We will suppose mine to be 3^, or nearly -rV of an inch. The radius of the posterior surface was most frequently 2i lines, or 1^ of an inch*. The optical centre will be therefore (^^x^°—\ about one tenth \30+'22 / of an inch from the anterior surface : hence we have 22 hundredths, for the distance of the centre from the cornea. Now, taking 10 inches as the distance of the radiant point, the focus of the cornea will be llo^hun- diedths behind the centre of the lens. But the actual joint focus is (gi — 22 = ) 69 be- hind the centre : hence, disregarding the thickness of the lens, its principal focal dis- tance is 173 hundredths. For the index of its refractive power in the eye, we have 4 j4- Calculating upon this refractive power, with the consideration of the thickness also, wc find that it requires a correction, and comes near to the ratio of 14 to 13 lor the sines. It is well known that the refractive powers of the humours are equal to that of * Mam. cle I'Acad. de Paris. 1730. 6. Ed. Amst. 580 ON THE MECHANISM OF THE EYE. water; and, that the thickness of the cornea is too equable to produce any, effect on the focal distance. For determining the refractive power of the crystalline lens by a direct experiment, I made use of a method suggested to me by Dr. Wollaston. I found the refractive power of the centre of the recent human crystal- line to that of water, as 21 to 20. The dif- ference of this ratio from the ratio of 14 to 13, ascertained from calculation, is i)robably owing to two circumstances. The first is, that, the substance of the lens being in some degree soluble in water, a portion of the aqueous fluid within its capsule penetrates after death, so as sdmewhat to lessen the density. When dry, the refractive power is little inferior to that of crown glass. The second circumjtance is the unequal density of the lens. The ratio of 14 to 13 is founded on the supposition of an equable density: but, the central part being the most dense, tlie whole acts as a lens of sm.iller dimensions: and it may be found by calculation (M. E. 465.) that if the central portion of a sphere be sup- posed of uniform density, refracting as 21 to 20, to the distance of one half of the radius, and the density of the external parts to de- crease gradually, and at the surface to be- come equal to that of the surrounding me- dium, the sphere, thus constituted, will be equal in focal length to a uniform sphere of the same size, with a refraction of 16 to 15 nearly. And the effect will be nearly the same, if the central portion be supposed to be smaller than this, but the density to be somewhat greater at the surface than that of the surrounding medium, or to vary more ra- pidly externally than internally. Or, if a lens of equal mean dimensions, and equal fo- cal length, with the crystalline, be supposed to consist of two segments of the external por- tions of such a sphere, the refractive density at the 'centre of this lens must be as 18 to 17. On the whole, it is probable that the refrac- tive power of the centre of the human crys- talline, in its living state, is to that of water nearly as 18 to 17; that the water, imbibed after death, reduces it to the ratio of 21 to 20 ; but that, on account of the unequable density of the lens, its effect in the eye is equivalent to a refraction of 14 to 13 for its whole size. Dr. Wollaston has ascertained, the refraction out of air, into the centre of the recent crystalline of oxen and sheep, to be nearly as 143 to 100; into the centre of the cr^'stalline offish, and into the dried crys- talline of sheep, as 152 to 100. Hence, the refraction of the crystalline of oxen, in water, should be as 15 to 14: but the human cry- stalline, when recent, is decidedly, less re- fractive. These considerations will explain the in- consistency of different observations on the refractive power of the crystalline ; and, in particular, how the refraction which I for- me^Jy calculated, from measuring the focal length of the lens*, is so much greater than that which is determined by other means. But, for direct experiments. Dr. WoUaston's method is exceedingly accurate. When I look at a minute lucid point, such as the image of a candle in a small concave speculum, it appears as a radiated star, as a cross, or as an unequal line, and never as a perfect point, unless I apply a concave lens, inclined at a proper angle, to correct the unequal refraction of my eye. If I bring the point very near, it spreads into a surface nearly circular, and almost equably illumi- nated, except some faint lines, nearly la a • Phil. Trans. 1793. 174. OK THE MECHANISM OF THE EYE. 581 radiating direction. For this purpose, the best object is a candle or a small speculum, viewed through a minute lens at some little distance, or seen by reflection in a larger lens. If any pressure has been applied to the e^'e, such as that of the finger keeping it shut, the sight is often confused for a short time after the removal of the finger, and the image is in this case spotty or curdled. The radiating lines are probably occasioned by some slight inequalities in the surface of the kns, which is very superficially furrowed in the direction of its fibres: the curdled. ap- pearance will be explained hereafter. When the point is further removed, the image be- comes evidently oval, the vertical diameter being longest, and the lines a little more dis- tinct than before, the light being strongest in the neighbourhood of the centre ; but im- mediately at the centre there is a darker spot, -owing to such a slight depression at the ver- tex as is often observable in examining the lens after death. The situation of the rays is constant, though not regular; the most conspicuous are seven or eight in number ; sometimes about twenty fainter ones may be counted. Removing the point a little fur- ther, the image becomes a short vertical line ; the rays that diverged horizontally be- ing perfectly collected, while the vertical rays are still separate. In the next stage, which is the most perfect focus, the line spreads in the middle, and approaches nearly to a square, with projecting angles, but ip marked with some darker lines towards the diagonals. The square then flattens into a rhombus, and the rhombus into a horizontal , line unequall}' bright. At every greater dis- tance, the line lengthens, and acquires also breadth, by radiations shooting out from it, but does not become a uniform surface, the central part remaining always considerablj brightest, in consequence of the same flat- tening of the vertex which before made it faintest. Some of these figures bear a consi- derable analogy to the images derived from the refraction of oblique rays, and still more strongly resemble a combination of two of them in opposite directions ; so as to leave - no doubt, but that both surfaces of the lens are oblique to the visual axis, and cooperate in distorting the focal point. This may also be verified, by observing the image delineated by a common glass lens, when inclined to the incident rays. (Plate 12. Fig. 92. n. 28. .40.) The visual axis being fixed in any direc- tion, I can at the same time see a luminous object placed laterally at a considerable dis- tance from it; but in various directions the angle is very different. Upwards it extends to 50 degrees, inwards to 60, downwards to 70, and outwards to QO degrees. These in- ternal limits of the field of view nearly cor- respond wjjh the external limits formed by the different parts of the face, when the eye is directed forwards and somewhat down- wards, which is its most natural position ; jflthough the internal limits are a little more extensive than the external : and both .are well calculated for enabling us to perceive, the most readily, such objects as are the most likely to concern us. Dr. VVollaston's eye has a larger field of view, both vertically and ho- rizontally, but nearly in the same propor- tions, except that it extends further upwards. It is well known, that the retina advances further forwards towards the internal angle of the eye, than towards the external angle ; bi^t upwards and downwards its extent is nearly equal, and is indeed e^very way greater than the limits of the field of view, even if allowance is made for the refraction of the 582 ON THE MECHANISxM OF THE EYE. cornea only. The sensible portion seems to coincide more nearly with the painted cho- roid of quadrupeds : but the whole extent of perfect vision is little more than 10 degrees; or, more strictly speaking, the iniperfection begins within a degree or two of the visual axis, and at the distance of 5 or 6 degrees becomes nearly stationar}', until, at a still greater distance, vision is wholly extin- guished. The imperfection is partly owing to the unavoidable aberration of oblique rays, but principally to the insensibility of the retina: for, if the image of the sun itself be received on a part of the retina re- mote from the axis, the inipression will not be sufficieiitly strong to form a permanent spectrum, although an object of very mode- rate brightness will produce this effect when directly viewed. It has been said, that a faint light, like the tail of a comet, is more observable by a lateral than by a direct view. Supposing the fact certain, the reason pro- bably is, that general masses of light and shade -are more distinguishable when the parts are somewhat confused, than when the whole is rendered perfectly distinct; thus I have often obiierved the pattern of a paper os floor cloth to run in certain lines, when I viewed it without my glass ; but these lines vanished as soon as the focus was rendered perfect. It would probably have been in- consistent with the economy of nature, to bestow a larger share of sensibility on the re- tina. The optic nerve is at present very large ; and the delicacy of the organ renders it, even at present, very susceptible of injury from slight irritation, and very liable to in- flammatory afiections; and, in order to make the sight so perfect as it is, it was necessary to confine that perfection within narrow li- mits. The motion of the eye has a range of ab()uf55 degrees in every direction : so that t'le field of perfe^^t vision, in succession, is by this motion extended to 1 10 d.egrees. But the whole of the retina is of such a form as to receive the most perfect image, on ever3' part of its surface, that tlie state of each refracted pencil will admit ; and the va- rying density of the crystalline renders that state more capable of delineatiirg such a pic- ture, than any other imaginable contrivance could have done. To illustrate this, I have constructed a diagram, representing the suc- cessive images of a distant object filling the whole extent of view, as they would be formed by the successive refractions of the different surfaces. Taking the scale of my own eye, I am obliged to substitute, for a series of objects at any indefinitely great dis- tance, a circle of 10 inches radius; and it is most convenient to consider only those mys which pass through the anterior vertex of the lens; since the actual centre of each pencil must be in the ray which passes through the centre of the pupil, and the short distance of the vertex of the lens, from this point, will always tend to correct the unequal refrac- tion of oblique rays. The first curve (Plate 10. Fig. 80) is the image formed by the furthest intersection of rays refracted at the cornea; the second, the image formed by the nearest intersection ; the distance, be- tween these, shows the degree of confusion in the image ; and the third curve, its brightest part. Such must be the form of the image which the cornea tends to deli- neate in an eye deprived of the crystalline lens; nor can any external remedy properly correct the imperfection of lateral vision. The next three curves show the images formed after the refraction at the anterior surface of the lens, distinguished in the same OV THE MECHANISM OF THE EYE. 583 manner; uml t'le three following, the result of all the successive refractions. The tenth curve is a repetition of the ninth, with a slight correction near the axis, at F, where, from the breadth of the pupil, some perpen- dicular rays must fall. By comparing this with the eleventh, which is the form of the retina, it will aj)pear that notliing more is wanting for their perfect coincidence, than a moderate diminution of density in the late- ral parts of the lens. If the law, by which this density varies, were more accurately as- certained, its effect on the image might easily be estimated ; and probably the image, thus corrected, would approach very nearly to the form of the twelfth .curve. To find the place of the entrance of the optic nerve, I fix two candles at ten inches distance, retire sixteen feet, and direct my eye to a point four feet to the right or left of the middle of the space between them : .they are then lost in a confused spot of light; but any inclination of the eye brings one or the other of them into the field of view. In Ber- noulli's eye, a greater deviation was required for the direction of the axis* ; and the ob- scured part appeared to be of greater extent. From the experiment here related, the dis- tance of the centre of the optic nerve from the visual axis is found to be \6 hundredths of an inch ; and the diameter of the most insensible part of the retina, one thirtieth of an inch. In order to ascertain the distance of the optic nerve from the point opposite to the pupil, I took the sclerotica of the human eye, divided it into segments, from thie centre of the cornea towards the optic nerve, and extendedjt on a plane. I then measured the longest and shortest distances from the cornea to the perforation made by the nerve, * Cprora. Petrop. 1, 314, and their difference was exactly one fifth of an inch. To this we must add a fiftieth, on account of the eccentricity of the pupil in the uvea, which in the eye that I measured was not great, and the distance of the cen- tre of the nerve from the point opposite the pupil will be 11 hundredths. Hence it ap- pears, that the visual axis is five hundredths, or one twentieth of an inch, further from the optic nerve than the point opposite the pu- pil. It is possible, that this distance may be different in different eyes : in mine, the obli- quity of the lens, and the eccentricity of the pupil with respect to ir, will tend to throw a direct ray upon it, without much inclination of the whole eye ; and it is not improbable, that the eye is also turned slightly outwards, when looking at any object before it, although the inclination is too small to be subjected to measurement. It must also be observed, that it is very dif- ficult to ascertain the proportions of the eye so exactly, as to determine, with certainty, the size of an image on the retina ; the situ- ation, curvature, and constitution of the lens, make so material a difference in the result, that there may possibly be an error of al- most one tenth of the whole. In order, there- fore, to obtain some confirmation from ex- periment, t placed two candles at a small distance from each othei-, turned the eye. in- wards, and applied the ring of a key so as to produce a spectrum, of which the edge coincided with the inner candle; then, fixinn- my eye on the outward one, I found that the spectrum advanced over two sevenths of the distance between them. Hence, the same portion of the retina that subtended an angle of seven parts at the centre of motion of the eye, subtended an angle of five at the sup- posed intersection of the principal rays ; 584 ON THE MECHANISM OF THE EYE, (Plate 9. Fig. 75.) and the distance of this intersection from the retina was 637 thou- sandths. This nearly corresponds with tlie former calculation ; nor can the distance of the centre of the optic nerve from the point of most perfect vision be, on any supposition, much less than that which is here assigned. And., in the eyes of quadrupeds, the most strongly painted part of the choroid is further from the neiVe than the real axis of the eye, I have endeavoured to express, in four figures, the form of every part of" my eye, as nearly as I have been able 19 ascertain it ; the first (Plate 1 1. Fig. 81 ) is a vertical sec- tion ; the second (.Fig. 82.) a horizontal sec- tion ; the third and fourth are front views, in different states of the pupil. (Fig. 83 and 84.) Considering how little inconvenience is experienced from so material an inequality in the refraction of the lens, as I liave described, we have no reason to expect a very accurate provision for correcting the aberration of the lateral rays. But, as far as can be ascer- tained by the optometer, the aberration arising from figure is completely corrected; since four or more images of the same line appear to meet exuctly in the same point, which they would not do if the lateral ray.s were materially more refracted than the rays' near the axis. The figure of the sur- faces is sometimes, and perhaps always, more or less hyperbolical* or elliptical : in the interior laminae indeed, the solid angle of the margin is somewhat rounded off; but the weaker refractive power of the external parts must greatly tend to correct the aberration, arising from the too great curvature towards the margin of the disc. Had the refractive power been uniform, it might have collected the lateral rays of a direct pencil nearly as • Petit. Mem. del'Acad. 172s. 20. well ; but it would have been less adapted to oblique pencils of rays: and the eye must also have been encumbered with a mass of much greater density than is now required, even for the central parts ; and, if the whole lens had been smaller, it would also liave ad- miltod too little light. It is possible too, that Mr. Ramsden's observation-^-, on the advan- tage of having no reflecting surface, may be well founded : but it has not been demon- strated, that less light is lost in passing" through a medium of variable density, than in a sudden transition frona one part of that medium to another ; although such a con- clusion may certainly be inferred, from the only hypothesis which affords an explanation of the cause of a partial reflection in any case. But neither this gradation, nor any other provision, has the effect- of ren- dering the eye perfectly achromatic. Dr. Jurin had remarked this, long ago;}:, from observing the colour bordering the image of an object seen indistinctly, Dr, W oliaston pointed out to me, on the optometer, the red and blue appearance of the opposite inter- nal angles of the crossing lines; and men- tioned, at the same time, a very elegant ex- periment for proving the dispersive power of the eye. He looks through a prism at a small lucid point, which of course becomes a linear spectrum. But the eye cannot so adapt itself as to make the whole spectrum appear a line ; for, if the focus be adapted to collect the red rays to a point, the blue will be too much refracted, and expand into a surface ; and the reverse will happen if the eye be adapted to the bliie rays; so that, in either case, the line will be seen as a tri- angular space. The observation is confirmed, by placing a small concave speculum in dif- t Phil. Trans. 1795. a. J Smith, e. 90. OV TME MECHANISM OF THE EYE. 585 ferent parts of a prismatic spectrum; and as- certaining the utmost distances, at wliich the eye can collect the rays of different colours to a focus. B}' these means I find, that the red rays, from a point at 12 inches distance, are as much refracted as white or yellow light at 11. The difference is equal to the refraction of a lens 132 inches in focus. But the aberration of the red rays, in a lens of crown glass, of equal mean refractive power with the eye, would be equivalent to the ef- fect of a lens 44 inches in focus. ]f, there- fore, we can depend upon this calculation, the dispersive power of the eye, collectively, is one third of the dispersive power of crown glass, at an equal angle of deviation. 1 can- not observe much aberration in the violet rays. This may be, in part, owing to their faintness ; but yet I think their aberration must be less than that of the red rays. I be- lieve it was Mr. ilamsdeii's opinion, that since the separation of coloured rays is only observed where there is a sudden change of density, such a body as the lens, of a density gradually varying, would have no effect whatever in separating the rays of different colours. If this hypothesis should appear to be well founded, we should be obliged to attribute the whole dispersion to the aqueous humour ; and its dispersive power would be half that of crown glass, at the same devia- tion. But we have an instance, in the at- mos[>here, of a very gradual change of den- sity ; and yet Mr. Gilpin informs me, that the stars, when near the horizon, appear very evidently coloured ; and Dr.Herschel has even given us the dimensions of a spectrum thus formed. At a more favourable season of the year, it would not be difficult to ascertain, by means of the optometer, the dispersive power of the eye, and of its different parts, with VOL. u. greater accuracy than by the e.vperiment here related. Had the dispersive power of the whole eye been equal to that of flint glass, the distances of perfect vision would have varied from 12 inches to 7, for different ra3s, in the same state of the mean refrac- tive powers. VI. The faculty of accommodating the eye to various distances appears to exist in very different degrees in different individuals. The shortest distance of perfect vision, in my eye, is 26 tenths of an inch for horizontal, and 29 for vertical rays. This power is equivalent to the addition of a lens of 4 inches focus. Dr. WoUaston can see at seven inches, and with rays slightly converging; the difference an- swering to 6 inches focal length. Mr. Aberne- thy has perfect vision from 3 inches to 30, or a power equal to that of a lens 3^ mches in fo- cus. A young lady of my acquaintance can see at 2 inches and at 4 ; the difference being equivalent to 4 inches focus : a middle aged lady at 3 and at 4 ; the power of accommo- dation being only equal to the effect of a lens of 12 inches focus. In general, I have reason to think, that the faculty diminishes, in some measure, as persons advance in life; but some also of a middle age appear to pos- sess it in a very small degree. I shall take the range of my own eye, as being probably about the medium, and inquire what changes will be necessary, in order to produce it ; whether we suppose the radius of the cornea to be diminished, or the distance of the lens from the retina to be increased, or these two causes to act conjointly, or the figure of the lens itself to undergo an alteration. 1. We have calculated, that when the eye is in a state of relaxation, the refraction of the cornea is such as to collect rays di- verging from a point ten inches distant, to 4f 586 ON THE MECHANISM OF THE ETE, a focus at the distance of IS^ tenths. In or- der that it may bring, to the same focus, rays diverging from a point distant 29 tenths, we shall find that its radius must be diminished from 31 to 25 hundredths, or very nearly in the ratio of five to four. 2. Supposing the change from perfect vi- sion at ten inches, to perfect vision at 29 tenths, to be effected by a removal of the re- tina to a greater distance from the lens, this will require an elongation of 135 thousandths, or more than one seventh of the diameter of the eye. In Mr. Abernethy's eye, an elon- gation of 17 hundredths, or more than one sixth, is requisite. 3. If the radius of the cornea be dimi- nished one sixteenth, or to 29 hundredths, the eye must at the same time be elongated 97 thousandths, or about one ninth of its dia- meter. 4. Supposing the crystalline lens to change , its form ; if it became a sphere, its diameter would be 28 hundredths, and, its anterior surface retaining its situation, the eye would have perfect vision at the distance of an inch and a half. This is more than double the Jictiial cliange. But it is impossible to deter- mine precisely, how great an alteration of form is necessarv, without ascertaining the nature of the curves into which its surfaces may be changed. If it were always a sphe- roid, more or less oblate, the focal length of each surface would vary inversely as the .squareof the axis: but, if the surfaces be- came, from spherical, portions of hyperbolic conoids, or of oblong spheroids, or changed from moie obtuse to more acute figures of this kind, the focal length would vary more rapidly. Disregarding the elongation of the axis, and supposing tlie curvature of each surface to be cli;«)ged proportionally. the radius of the anterior must become about 21, and that of the posterior 15 hun- dredths. VII. I shall now proceed to inquire, which of these changes takes place in nature ; and I shall begin with a relation of experiments, made in order to ascertain the curvature of the cornea in all circumstances. The method, described in Mr. Home's Croonian Lecture for 1795*, appears to be far preferable to the apparatus of the pre- ceding yearf : for a difference in the dis- tance of two images, seen in the cornea, would be far greater, and more conspicuous, than a change of its prominency, and far less liable to be disturbed by accidental causes. Ii is nearly, and perhaps totally, im- possible to change the focus of the eye, with- out some motion of its axis. The eyes sym- pathize perfectly with each other ; and the change of focus is almost inseparable from a change of the relative situation of the optic axes ; so much, that, in my eye this sympa- thy causes a slight imperfection of sight ; for, if I direct both my eyes to the same object, even if it is beyond their furthest focus, I can- not avoid contracting, in some degree, iheir focal distance: now while one axis moves, it is not easy to keep the other perfectly at rest; and, besides, it is not impossible, that a change in the proportions of some eyes may render a slight alteration of the position of the axis absolutely necessary. These consi- derations may partly explain the trifling dif- ference in the place of the cornea that was observed in 1794. It appears that the expe- riments of 1795 were matie with considerable accuracy, and no doubt, with excellent in struments ; and their failing to ascertain the existence of any change induced Mr. Home *-Phil. Trans. 1798. 2. f Thil. Trans. 1795. 13. ON TirU MECHANISM OP THE EYE, 587 and Mr. Kainsdcn to abandon, in great measure, the opinion which suggested them, and to suppose, that a change of the cornea produces only one third of the effect. Dr. Olbers, of Bremen, who in the year 1 780 pub- lished a most elaborate dissertation on the internal changes of the eye*, which he lately presented to the Royal Society, had been equally unsuccessful in his attempts to measure this change of the cornea, at the same time that his opinion was in favour of its existence. Room was however still left for a repeti- tion of the experiments; and I began with an apparatus nearly resembling that which Mr. Home has described. I had an excel- lent achromatic microscope, made by Mr. Ramsden for my friend Mr- John Ellis, of five inches focal length, magnifying about 20 times. To this I adapted a cancellated micrometer, in the focus of the eye not em- ployed in looking through the microscope ; it was a large card, divided by horizontal and vertical lines into fortieths of an inch. When the image in the microscope was compared with this scale, care was taken to place the head of the observer so that the relative motion of the image on the micrometer, caused by the unsteadiness of the optic axes, should always be in the direction of the horizontal lines, and that there could be no error from this motion, in the dimensions of the image taken vertically. I placed two candles so as to e.v- hibit images in a vertical position in the eye of Mr. Konig, who had the goodness to as- sist me; and, having brought them into the field of the microscope, where they occupied 35 of the small divisions, I desired him to fix his eye on objects at different distances in the same direction : but I could not perceive * De Oculi Miitationibus intemis, 4. Gotting. 1780. the least variation in the distance of the images. Finding a considerable difficulty in a pro- per adjustment of the microscope, and being able to depend on my naked eye in measur- ing distances, without an error of one 500th of an inch, I determined to make a similar ex- periment without any magnifying power. I constructed a divided eye glass of two por- tions of a lens, so small, that they passed be- tween two images reflected from my own eye : and, looking in a glass, I brought the apparent places of the imai^es to coincide, and then made the change requisite for view- ing nearer objects ; but the images still coin- cided. Neither could I observe any change in the images reflected fiom the other eye, where they could be viewed with greater con- venience, as they did not interfere with the eye glass. But, not being at that time aware of the perfect sympathy of my eyes, I thought it most certain to confine my ob- servation to the one with which I saw. I must remark that, by a little habit, I have acquired a very ready command over the accommoda-* tion of my eye, so as to be able to view an object with attention, without adjusting my eye to its distance. I also stretched two threads, a little in- clined to each other, across a ring, and di- vided them, by spots of ink, into equal spaces, I then fixed the ring, applied my eye close behind.it, and placed two candles in proper situations before me, and a third on one side, to illuminate the threads. Then, setting a small looking glass, first at four inches dis- tance, and next at two, I looked at the images reflected in it, and observed at what part of the threads they exactly reached across in each case ; and with the same result as before. .588 ON THE MECHANISM OF THE EYE. I next fixed the cancellated micrometer at a proper distance, illuminated it strongly, and viewed it through a pin hole, by which means it became distinct in every state of the eye ; and, looking with the other eye into a small glass, I compared the image with the micrometer, in the manner already described. I then changed the focal distance of the eye, so that the lucid points appeared to spread into surfaces, from being too remote for per- fect vision ; and I noted, 6n the scale, the distance of their centres ; but that distance jvas invariable. Lastly, I drew a diagonal scale, with a diamond, on a looking glass, (Plate 9. Fig. 76.) and brought the images into contact with the lines of the scale. Tlien, since the image of the eye occupies, on the surface of a glass, half its real dimensions, at whatever distance it is viewed, its true size is always double the measure thus obtained. I illumi- nated the glass strongly, and made a perfo- ration in a narrow slip of black card, which I held between the images ; and was thus enabled to compare them with the scale, al- though their apparent distance was double that of the scale. I viewed them in all states of the eye ; but I could perceive no variation in the interval between them. The sufficiency of these methods may be thus demonstrated. Make a pressure along the edge of the upper eyelid with any small cylinder, for instance a pencil, and the op- tometer will show that ihc focus of horizontal rays is a little elongated, while that of verti- cal rays is shortened ; an eifeet which can only be owing to a change of curvature in the cornea. Not only the apparatus here described, but even the eye unassisted, will be capable of discovering a considerable change in the images reflected from the cor- nea, although the change be much smaller than that which is requisite for the accom- modation of the eye to different distances. On the whole, I cannot hesitate to conclude, that if the radius of the cornea were dimi- nished but one tvvencieth, the change would be very readily perceptible by some of the experiments related ; and the whole altera- tion of the eye requires one fifth. But a much more accurate and decisive experiment remains. I take, out of a small botanical microscope, a double convex lens, of eight tenths radius and focal distance, fixed in a socket one fifth of an inch in depth ; securing its edges with wax, I drop into the socket a little water, nearly cold, till three fourths full, and then apply it to my eye, so that the cornea enters half way into it, and is every where in contact with the water. (Plate 9. Fig. 77). My eye immediately becomes presbyopic, and the refractive power of the lens, which is re- duced by the water to a focal length of al)oul 16 tenths, is not sufficient to sup- ply the place of the cornea, rendered in- efficacious by the intervention of the water ; but the addition of another lens, of five inches and a half focus, restores my eye to its natural state, and somewhat more. I then apply the optometer, and I find the same inequality in the horizontal and verti- cal refractions as without the water ; and I have, in both directions, a power of accom- modation equivalent to a focal length of four inches, as before. At first sight indeed, the accommodation appears to be somewhat less, and only able to bring the eye from the state fitted for parallel rays to a focus at five inches distance; and this made me once ON THE MECHANISM OF THE EYE. 589 imagine, that the cornea might have some slight effect in the natural state ; but, con- sidering that the artificial cornea was about -a tentli of an inch before the place of the natural cornea, I calculated the effect of this difference, and found it exactly sufficient to account for the diminution of the range of vision. I cannot ascertain the distance of the glass lens from the cornea to the hun- dredth of an inch ; but the error cannot be much greater, and it may be on either side. After this, it is almost necessary to apo- logize for having stated the former experi- ments ; but, in so delicate a subject, we can- not have too great a variety of concurring evidence. VIII. Having satisfied myself, that the cornea is not concerned in the accommoda- tion of the eye, my next object was, to in- quire if any alteration in the length of its axis could be discovered ; for this appeared to be the only possible alternative : and, considering that such a change must amount to one seventh of the diameter of the eye, I flattered myself with the ex- pectation of submitting it to measurement. Now, if the axis of the eye were elongated one seventh, its transverse diameter must be diminished one fourteenth, and the semi- diameter would be shortened a thirtieth of an inch, I therefore placed two candles so that when the eye was turned inwards, and directed to- wards its own image in a glass, the light re- flected from one of the candles by the scle- rotica appeared upon its external margin, so as to define it distinctly by a bright line : and the image of the other candle was seen in the centre of the cornea. I then applied the tlouble eye glass, and the scale of the look- ing glass, in the manner already described j but neither of them indicated any diminution of the distance, when the focal length of the eye was changed. Another test, and a much more delicate one, was the application of the ring of a key at the external angle, when the eye was turned as much inwards as possible, and confined at the same time by a strong oval iron ring, pressed against it at the internal angle. The key was forced in as far as the sensibility of the integuments would admit, and was wedged, by a moderate pressure, between the eye and the bone. In this situ- ation, the phantom, caused by the pressure, extended within the field of perfect vision, and was very accurately defined ; nor did it, as I formerly imagined, by any means pre- vent a distinct perception of the objects ac- tually seen in that direction ; and a straight line, coming within the field of this oval phantom, appeared somewhat inflected to- wards its centre; (Plate 9- Fig. 78.) a dis- tortion easily understood by considering the effect of the pressure on the form of the re- tina. Supposing now the distance between the key and tiic iron ring to have been, as it really was, invariable, the elongation of the e3'e must have been either totally or very nearly prevented ; and, instead of an increase of the length of the eye's axis, the oval spot, caused by the pressure, would have spread over a space at least ten times as large as the most sensible part of the retina. But no such circumstance took [dace . the power of ac- commodation was as extensive as ever; and there was no perceptible change, either in the size or in the figure of the oval spot. Again, since the rays which pass through the centre of the pupil, or rather through 590 0N THE MECHANISM OF THE EYE. the anterior vertex of tlie lens, may be con- sidered as delineating the image ; and, since the divergence of these rays, with respect to each other, is but little affected by the refrac- tion of the lens, they may still be said to di- verge from the centre of the pupil ; and the image of a given object on the retina must be very considerably enlarged, by the remo- val of the retina to a greater distance from the pupil and the lens. To ascertain the real magnitude of the image, with accuracy, is not so easy as at first sight appears ; but, be- sides the experiment last related, which might be employed as an argument to this purpose, there are two other methods of es- timating it. The first is too hazardous to be of much use; but, with proper precaution?, it may be attempted. I fix my eye on a brass circle placed in the rays of the sun, and, af- ter some time, remove it to the cancellated micrometer ; then, changing the focus of my eye, while the micrometer remains at a given distance, I endeavour to discover whe- ther there is any difference in the apparent magnitude of the spectrum on the scale ; but J can discern none. I have not insisted on the attempt ; especially as I have not been able to make the spectrum distinct enough without inconvenience ; and no light is suf- ficiently strong to cause a permanent impres- sion on any part of the retina remote from the visual axis. 1 therefore had recourse to another experiment. I placed two candles so as exactly to answer to the extent of the ter- mination of the optic iierve, and, marking accurately the point to which my eye was di- rected, I made the utmost change in its fo- cal length; expecting that, if there were any elongation of the axis, the external candle would appear to recede outwards upon the 1 visible space. (Plate 9- V\g. 79.) But this did not happen : the apparent place of the obscure part was precisely the same as be- fore. I will not undertake to say, that I could have observed a very minute difference either way : but I am persuaded, that I should have discovered an alteration of less than a tenth part of the whole. It may be inquired, if no change in the magnitude of the image is to be expected on any other supposition ; aud it will ap- pear to be possible, that the changes of cur- vature may be so adapted, that the magni- tude of the confused image may remain per- fectly constant. Indeed, to calculate froin the dimensions which we have hitherto used, it would be expected that the image should be diminished about one fortieth, by the ut- most increase of the convexity of the lens. But the whole depends on the situation of the refracting surfaces, and the respective in- crease of their curvature, which, on account of the variable density of the lens, can ' scarcely be estimated with sufficient accuracy. Had the pupil been placed before the cornea, the magnitude of the image must, on any sujiposition, have been very variable : at pre- sent, this inconvenience is avoided by the situation of the pupil; so that we have here an additional instance of the perfection of this admirable organ. P'lOin the experiments related, it appears to be highly improbable that any material change in the length of the axis actually takes place : and it is almost impossible to conceive by what power such a change could be effected. The straight muscles, with the adipose substance lying under them, would certainly, when acting independently of the socket, tend to flatten the eye : for, since ON THE MECHANISM OF THE EYE. m their contraction would necessarily lessen the circumference or superficies of the mass that they contain, and round off all its pro- minences, their attachment about the nerve and the anterior part of the eye must there- fore be brought nearer together. (Plate 11. Fig. 85, 86.) Dr. Olbers compares the mus- cles and the eye to a cone, of which the sides are protruded, and would by contrac- tion be brought into a straight line. But this would require a force to preserve the cornea as a fixed point, at a given distance from the origin of the muscles ; a force which cer- tainl}' does not exist. In the natural situa- tion of the visual axis, the orbit being coni- cal, the eye might be somewhat lengthened, although irregularly, by being forced further into it ; but, when turned towards cither side, the same action would rather shorten its axis : nor is there any thing about the human eye that could supply its place. In quadru- peds, the oblique muscles are wider than in man ; and in many situations might assist in the effect. Indeed a portion of the orbicu- lar muscle of the globe is attached so near to the nerve, that it might also cooperate in the action : and I have no reason to doubt the accuracy of Dr. Olbers, who states, that lie effected a considerable elongation, b}' tying threads to the muscles, in the eyes of hogs and of calves ; yet he does not say in what position the axis was fixed ; and the flacci- dity of the eye after death might render such a change very easy, as would be impossible in a living eye. Dr. Olbers also mentions an observation of Professor Wrisberg, on the eye of a man whom he believed to be destitute of the power of accommodation in his life time, and whom he found, after death, to have wanted one or more of the muscles : but this want of accommodation was not at all ac- curately ascertiii ned . I measured, in the hu- man eye, the distance of the attachment of the inferior oblique muscle from the insertion of the nerve: it was one fifth of an inch ; and from the centre of vision, not a tenth of an inch ; so that, although the oblique mus- cles do, in some positions, nearly form a part of a great circle round the eye, their action would be more fitted to flatten than to elon- gate it. We have therefore reason to agree with VVinslow, in attributing to them the of- fice of helping to support the eye on that side where the bones are most deficient: they seem also well calculated to prevent its being drawn too much backwards by the action of the straight muscles. And, even if there were no difficulty in supposing the muscles to elongate the eye in every position, yet at least some small difference would be expectjed in the extent of the change, when the eye is ill different situations, at an interval of more than a right angle from each other ; but the optometer shows that there is none. Dr. Ilosack alleges that he was able, by making a pressure on the eye, to accommo- date it to a nearer object * : it does not ap- pear that he made use of very accurate means for ascertaining the fact; but, if such an el- fect took place, the cause must have been an , inflection of the cornea. It is unnecessary to dwell on the opinion which supposes a joint operation, of changes in the curvature of the cornea, and in the length of the axis. This opinion had derived very great respectability, from the most in- genious and elegant manner in which Dr. Olbers had treated it, and fro t;n being the last result of the investigations of Mr. * Pliil, Trans. 1794. in. 592 ON THE MECHANISM OF THE ETE. Home and Mr, Ramsden. But either of the series of experiments, which have been re- lated, appears to be sufficient to confute it. IX. It now remains to inquire into the pre- tensions of the crystalline Jens to the power of altering the focal length of the eye. The grand objection, to the efficacy of a change of ligure in the lens, was derived from the ex- periments, in which those, whohavebeen de- prived of it, have appeared to possess the fa- culty of accommodation. My friend Mr. Ware, convinced as he was of ihe neatness and accuracy of the experi- mems iclated. in the Croonian Lecture for 179.3, yet could not still help imagining, iVoin the obvious advantage ail his patients found, after the extraction of the lens, in using two kinds of spectacles, that there must, in such cases, be a deficiency in that faculty. This circumstance, combined with a consi- deration of the directions very judiciously given by Dr. Porterfield, for ascertaining the point in question, first made me wish to repeat the experiments upon various indivi- duals, and with the instrument which i have above described, as an improvement of Dr. Porterfield's optometer : and I must here ac- knowledge my great obligation to Mr. Ware, for the readiness and liberality, with which he introduced me to such of his numerous pa- tients, as he thought most likely to furnish a satisfactory determination. It is unnecessary to enumerate every particular experiment ; but the universal result is, c-ontrarily to the expectation with which lentered on the in- quiry, tliat, in an eye deprived of the crystalline lens, the actual focal distance is totally un- changeable. This will appear from a selec- tion of the most decisive observations. 1, Mr. R. can read at four inches and at six only, with the same glass. He saw the double lines meeting at three inches, and al- ways at the same point ; but the cornea was somewhat irregularly prominent, and his vi- sion not very distinct; nor had I, at the time that I saw him, a convenient apparatus. I afterwards provided a small optometer, with a lens of less than two inches focus, add- ing a series of letters, not in alphabetical order, and projected into such a form as to, be most legible at a small inclination. The ex- cess of the magnifying power had the advan- tage of making the lines more divergent, and tlieircrossingmore conspicuous; and theletters served fur more readily naming the distance of the intersection, and, at the same time, for judging of the extent of the power of distin- guisiiing objects, too near, or too remote, for perfect vision. (Plate 11. Fig. 87.) 2. Mr. J. had not an eye very proper for the experiment ; but he appeared to distin- guish the letters at 24^ inches, and at less than an inch. This at first persuaded me, that he must have a power of changing the focal distance: but I afterwards recollected that he had withdrawn his eyeconsiderablv, to look at the nearer letters, and had also partly closed his eyelids, no doubt contracting at the same time the aperture of. the pupil ; an action which, even in a perfect eye, always accompanies the change of focus. The slider was not applied. 3. Miss H. a young lady of about twenty, had a veiy narrow pupil, and I had not an opportunity of trying the small optometer; but when she once saw an object double through the slits, no exertion could make it appear single at the same distance. She used for distant objects a glass of 4i inches focus; with this she could read as far off as O'S THE MECHANISM OF THE EYE. SB'S 12 riiclies, nnd as near as five: for nearer oljects she added another of equal focus, and could then read at 7 inches, and at 2^. 4. Hanson, a carpenter, ageil 63, iiad a cataract extracted a few years since from one eye : the pupil was clear and large, and he saw well to work with a lens of 2^- inches focus; and coi;!d read at 8 and at J 5 inches, but most conveniently at 1 1. With the same glass, the lines of tlie optometer appeared always to meet at 11 inches; but he could not perceive that thev crossed, the line be- ing too strong, and the intersection too distant. The experiment was afterwards repeated with the small optometer : he read the letters from 2 to 3 inches; but the intersection was always at 24- inches. He now fully under- stood the circumstances that were to be no- ticed, and saw the crossing with perfect dis- tinctness : at one time, he said it was a tenth of an inch nearer ; but! observed that he had removed his eye two or three tenths from the glass, a circumstance which accounted for this small difference. 5. Notwithstanding Hanson's age, I consi- der him as a very fair subject for the experi- ment. But a still more unexceptionable eye was that of Mrs. Maberly. She is about 30, and iiad the crystalline of both eyes extracted a few years since, but sees best with her right. She walks without glasses ; and, with the assistance of a lens of about four inches focus, can read and work with ease. She could distinguish the letters of the small optometer from an inch to2f inches; but the intersection was invariably at the same point, about ly tenths of an inch distant A portion of the capsule is stretched across the pupil, and causes her to see remote ob- jects double, when without her glasses nor VOL. II, can she, by any exertion, bring the two- images nearer together, although the exer- tion makes them more distinct, no doubt bv contracting the pupil. The experiment with the optometer was conducted, in the presence of Mr. Ware, with patience and perseverance ; nor was any opinion given to make her report partial. Considering the difficulty of finding an eye perfectly suitable for the experiments, these proofs may be deemed tolerably satis- factory. But, since one positive argument will counterbalance many negative ones, provicjed that it be equally grounded on fact, it becomes necessary to inquire into the com- petency of the evidence employed to ascer- tain the power of accommodation, attributed, in the Croonian Lecture for 1794, to the eye of Benjamin Clerk. And it appears, that the distinction long since very properlj- made by Dr. Jurin, between distinct vision and perfect vision, will readily explain away the whole of that evidence. It is obvious that vision miiy be made dis- tinct to any given extent, by means of an aperture sufficiently small, provided, at the same time, that a sufficient quantity of light be left, while the refractive powers of the eye remain unchanged. And it is relnark- able, that in those experiments, when the comparison with the perfect eye was made, the aperture of the imperfect eye only was very considerably reduced. Benjamin Clerk, with an aperture of -^\ of an inch, could read with the same glass at If inch,' and at 7 inches*. With an equal aperture, I can read at ly inch and at SO inches : and I can retain the state of perfect relaxation, and read with the same aperture at 2|r inches, without any real change of refractive power,. • Phil.Trau». 1795. 0. 4 o 594 ©* THE MECHANISJt OF THE EYE. and this is as great a difference as was observ- ed in Benjamin Clerk's eye. It is also a fact of no small importance, that Sir Henry Englefield was much astonished, as well as 'the other observers, at the accuracy with which the man's eye was adjusted to the 'same distance, in the repeated trials that were made with itf. This circumstance alone makes it highly probable, that its perfect vision was confined within very nar- row limits. Hitherto I have endeavoured to show the inconveniences attending other suppositions, and to remove the objections to the (-pinion of an internal change of the figure of the lens. I shall now state two experiments, which, in the first place, come very near to a mathematical demonstration of the exist- ence of such a change, and, in the second, explain in great measure its origin, and the manner in which it is effected. I have already described the appearances of the imperfect image of a minute point at different distances from the eye, in a state ■of relaxation. For the present purpose, I Hvill only repeat, that if the point is beyond the furthest focal distance of the eye, it assumes that appearance which is generally described by the name of a star, the central part being considerably the brightest. (Plate 12. Fig. 92. n. 36. .39-) But, when the focal le effect. What tiuir use maj' be, cannot easily be determined : if it were necessary to have any peculiar organs for secretion, we might call them glands, for the percolation of the aqueous humour; but there is no reason to think them re- quisite for this purpose. The marsupium nigrum of birds, and the horseshoe like appearance of the choroid of fishes, are two substances which have some- limes, with equal injustice, been termed mus- cular. All the apparent fibres of the marsu- pium nigrum are, as Haller had very truly as- serted, merely duplicatures of a membrane, which,when its ends are cut off, may easily be unfolded under the microscope, with the as- sistance of a fine hair pencil, so as to leave no longer any suspicion of a muscular texture. The experiment related by Mr. Home*, can scarcely be deemed a very strong argument for attribuiing to this substance a faculty which its appearance so little authorises us to expect in it. The red substance, in the cho- roid of fishes, (Plate 13. Fig. 102.) is more capable of deceiving the observer ; its colour gives it some little pretension, and I began to examine it with a prepossession in favour of its muscular nature. But, when we recol- lect the general colour of the muscles of • Phil.TraiM. ireS. is. ON THE MECHANISM OF THE EYE. 601 fishesjthc consideration of its redness will no longer have any weight. Stripped of the membrane which loosely covers its internal surface, (Fig- 103.) it seems to have trans- verse divisions, somewhat resembling those of muscles, and to terminate in a manner some- what simihir; (Fig. 104.)but, when viewed in a microscope, tlie transverse divisions ap- pear to be craciis, and the whole mass is evi- dently of a uniform texture, without the least fibrous appearance : and; if a particle of any kind of muscle is compared with it, the contrast becomes very striking. Besides it is fixed down, throughout its extent, to the posterior lamina of the choroid, and has no attachment capable of directing its cflcct; to say nothing of the diflSculty of conceiving what that effect would be. Its use must remain, in common with that of many other parts of the animal frame, entirely' concealed from our curiosity. The bony scales of the eyes of birds, which were long ago described in the Memoirs of the Academy, by Mery *, in the Philosophi- cal Transactions, by Mr. Ranby fj -Tid by Mr. Warren ;|:, afterwards in two excellent Memoirs of M. Petit on the eye of the tm- key and of the owl ^, and lately by Profes- sor Blumenbach ||, Mr. Pierce Smith ^, and Mr. Home **, can, on any supfiosition, have butlittle concern in the accommodation of the eye to different distances : they rather seem to be necessary for the protection of that organ, large and prominent as it is, and un- «n. 15. t Phil. Trans. XXXIII. 223. Abr. VII. 435. : Ptiil. Trans. XXXIV. 113. Abr. VII. 43?. § Mem. de 1' Acad. 1735. 163. 1730. 166. Ed. Amst. II Comm. Gott. VII. 62. ^ Phil. Trans. 1795. 263. •• Phil. Trans. 1786. 14. VOL. II. supported by any strength in the orbit, against the various accidents to wliich the mode of life and rapid motion of those ani- mals must expose it ; and they are much less liable to fracture than an entire bony ring of the same thickness would have been. The marsupium nigrum appears to be intended to assist in giving strength to the eye, to prevent an J' change in the place of the lens, by exter- nal force : it is so situated as to intercept but little light, and that little is principally what would have fallen on the insertion of the optic nerve: and it seems to be too firmly tied to the lens, even to admit any consider- able elongation of the axis of the. eye, al- though it certainly would not impede a pro- trusion of the cornea. There is a singular ob- servation of Poupart, respecting the eyes of insects, which requires to be mentioned here. He remarks, that the eye of the libellula is hollow; that it communicates with an air vessel placed longitudinally in the trunk of the body; and that it is capable of being in- flated from this cavity : he supposes that the insect is provided with this apparatus, in order i'or the accommodation of its eye to the ])erception of objects at different dis- tances*. There is no difficulty in supposing that the means of producing the change of the refractive powers of the eye, may be, in different classes of animals, as diversified as their habits, and the general conformation of their organs. But an examination of the ~ eyes of libellulae, wasps, and lobsters, in- duces me not only to reject the suggestion of Poupart, but to agree with those naturalists, who have called in question the. pretensions of these organs to the name usually a[)plied to them. Cuvicr has given a very fair state- • rhil. Trans. XXII. 673. .\br. II. 762. 4H 6"02 ox THE MECHANISM OF THE EYE. ment of the case, in his valuable work on com- parative anatom3' ; and bis descriptions, as well as those of Svvamnierdam, agree in ge- neral with what I have observed. We are prejudiced in favour of their being eyes, by their situation and general apjjearance. The copious supply of nerves seems to prove, at least, that they must be organs of sense. In the hermit crab, Swamiiierdam says, that their nerves even decussate, but this is not the case in the crawfish. The external coat is always transparent; its divisions are usually more or less leniiculur. Many insects have no other organs at all resembling eyes; and wImju these eyes have been covered, the insects appear to have been either wholly or partially blinded*. Hut, on the other hand, nnany insects are without tliese eyes, and of tiiose who have them, many have others also, more unquestionably fitted for vision. The neighbouring parts of the hard skin or shell are often equallv tr;inspa- rent with these, when the crust lining them is removed. In the apis longicornis, the an- tennae, as Mr. Kirby first iiifornved me, have somewhat of the same reticulated appearance but not enough for the foundation of any argument respecting its use. This reticu- lated coat is always completely lined by an obscure and opaque mucus, which appears perfectly unfit for the transmission of light ; nor is there any thing like a transparent hu- mour in the whole structure: and the con- vexity of the lenticular portions is bv no means sufticiently great, to bring the rays of light to a very near focus; indeed, in lobsters, the cxteruid surface is perfectly equable, and tlic internal surface is only divided into squares by a cancellated texture adhering to iU There is nothing in any way analogous • Hooke Microgr. ijg. to a retina, and there can be no formation of such an image, as is depicted in the eyes of all other animals, not excepting even the vermes: nor does there appear to be room to allow with Bidloo that there is a perforation, admitting light, under the centre of each hexagon. If they are eyes, their manner of perceiving light must rather resemble the sense of hearing than that of seeing, and they must convey but an iinperfect idea of the form of objects. And it maybe remarked that beetles, which have no other eyes, fly much by night, and are proverbially dull- sighted. The stemniata, which are usually 3, 6, 8, or 12 in number, have much more in- disputably the appearance of eyes. In the wasp, they consist externally of a thick double convex lens, firmly fixed in the shell, perfectly transparent, an Dec. 1675.) " In the second place, it is to be supposed, that the ether is a vibrating medium, like air, only the vibrations far more swift and mi- nute ; those of air, made by a man's ordinary voice, succeeding one another at more than half a foot, or a foot distance; but those of ether at a less distance than the hundred thousandth part of an inch. And, as in ain the vibrations are some larger than others' but yet all equally swift, (for in a ring of bells the sound of every tone is heard at two or three miles distance, in the same order that the bells are struck,) so, I suppose, the ethe- real vibrations difter in bigness, but not in 616 ON THE THEORY OF LIGHT AND COLOURS. swiftness. Now, these vibrations, beside their use in reflection and refraction, may be sup- posed the chief means by which the parts of fermenting or putrifying substances, fluid liquors, or mehed, burning, or other hot bodies, continue in motion." (Birch, III. G51. Dec. 1675.) " When a ray of hght falls upon the sur- face of any pellucid body, and is there re- fracted or reflected, may not waves of vibra- tions, or tremors, be thereby excited in the refracting or reflecting mediuui ? — And are not these vibrations propagated from the point of incidence to great distances? And do they not overtake the rays of light, and by overtaking them successively, do they not put thein into the fits of easy reflection and easy transmission described above ? (0|)tics, Qu. 17.) " Light is in fits of easy reflection and easy transmission, before its incidence on transparent bodies. And probably it is put into such fits at its first emission from lu- minous bodies, and continues in them dur- ing all its progress." (Optics, Second Book, Part iii. Prop. 13.) Hypothesis iii. The Sensation of differ- ent Colours depends on the dijferent frequency of Vibrations, excited bj/ Light in the Re- tina. passages from NEWTON. " The objector's hypothesis, as to the fun- damental part of it, is not against me. That fundamental supposition is, that the parts of bodies, when briskly agitated, do excite vi- brations in the ether, which are propagated every way from those bodies in straight lines, and cause a sensation of ligiit,by beating and dashing against the bottom of the eye, some- thing after the manner that vibrations in the air cause a sensation of sound, by beating against the organs of hearing. Now, the most free and natural application of this hy- pothesis to the solution of phenomena, I take to be this : that the agitated parts of bodies, according to their several sizes, figures, and motions, do excite vibrations in the ether of various depths or bignesses, which, being pro- miscuously propagated through that medium to our eyes, effect in us a sensation of light of a white colour ; but if by any means those of unequal bignesses be separated from one another, the largest beget a sensation of a red colour, the least or shortest of a deep violet, and the intermediate ones of interme- diate colours ; much after the manner that bodies, according to their several sizes, shapes, and motions, excite vibrations in the air, of various bignesses, which, according to those bignesses, make several tones in a sound : that the largest vibrations are best able to overcome the resistance of a refract- ing superficies, and so breakthrough it with, least refraction ; whence the vibrations of se- veral bignesses, that is, the rays of several co- lours, which are blended together in light, must be parted from one another by refrac- tion, and so cause the phenomena of prisms, and other refracting substances; and that it depends on the thickness of a thin transpa- rent plate or bubble, whether a vibration , shall be reflected at its further superficies, or transmitted ; so that, according to the num- ber of vibrations, interceding the two super- ficies, they may be reflected or transmitted for nianv successive thicknesses. And, since the vibrations which make blue and violet, are supposed shorter than those which make red and yellow, they must be reflected at a less thickness of the plate: which is sufficient to explicate all tlie ordinary phenomena of ON THE THEORY OF LIGHT AND COLOURS. 617 those plates or bubbles, and also of all natu- ral bodies, whose parts are like so many frag- ments of such plates. These seem to be most ])1ain, genuine, and necessary conditions of this hypothesis. And they agree so justly with my theory, that if the animadversor think fit to apply them, he need not, on that account, apprehend a divorce from it. But yet, how he will defend it from other difficul- ties, I know not." (Phil. Trans. VII. 5088. Abr. I. 145. Nov. 1672.) "To explain colours, I suppose, that as bodies of various sizes, densities, or sensa- tions, do, by percussion or other action, excite sounds of various tones, and consequently vibrations in the air of different bigness; so the rays of light,by impinging on the stiff" re- fracting superficies, excite vibrations in the ether, — of various bigness; the biggest, strongest, or most potent rays, the largest vibrations; and others shorter, according to their bigness, strength, or power: and there- fore the ends of the capillamenta of the optic nerve, which pave or face the retina, being such refracting superficies, when the raj's impinge upon them, the}' must there excite these vibrations, which vibrations (like those of sound in a trunk or trumpet) will run along the aqueous pores or crystalline pith of the capillamenta, through the optic nerve into the sensorium ; — and there, I suppose, affect the sense with various colours, accord- ing to their bigness and mixture; the biggest with the strongest colours, reds and yellows ; the least with the weakest, blues and violets; the middle with green ; and a confusion of all with white, much after the manner that, in the sense of hearing, nature makes use of aerial vibrations of several bignesses, to ge- nerate sounds of divers tones ; for the ana- VOL. II. logy of nature is to be observed." (Birch. III. 262. Dec. 1675.) " Considering the lastingness of the mo- tions excited in the bottom of the eye by light, are they not of a vibrating nature? — Do not the most refrangible rays excite the shortest vibrations, — the least refrangible the largest? May not the harmony and discord of colours arise from the proportions of the vibrations propagated through the fibres of the optic nerve into the brain, as the har- mony and discord of sounds arise from the proportions of the vibrations of the air f" (Optics, Qu. 16, 13, 14.) Scholium. Since, for the reason here assigned by Newton, it is probable that the motion of the retina is rather of a vibratory than of an undulatory nature, the frequency of the vibrations must be dependent on the constitution of this substance. Now, as it is almost impossible to conceive each sensi- tive point of the retina to contain an infinite number of particles, each capable of vibrat- ing in perfect unison with every possible undulation, it becomes necessary to suf)pose the number limited ; for instance, to the three principal colours, red, yellow, and blue, of which the undulations are related in mag- nitude nearly as the numbers 8, 7, and 6 ; and that each of the particles is capable of being put in motion less or more fprcibly, by undulations difliering less or more from a perfect unison ; lor instance, the undula- fions of green light, being nearly in the ratio of 64j will afl'ect equally the particles in uni- son with yellow and blue, and produce the same efl'ect as a light composed of those two species: and each sensitive filament of the nerve may consist of three portions, one for each principal colour. Allowing this state- 4 K 618 ON THE THEORY OF LIGHT AXD COLOURS. ment, it appears that any attempt, to produce a musical eftcct from colours, must be un- successful, or at least that nothing more than a very simple melody could be imitated by them ; for the common period, which in fact Constitutes the harmony of any concord, being a multiple of the periods of the single undulations, would in this case be wholly without the limits of sympathy of the retina, and would lose its eflecl ; in the same man- ner as the harmony of a third or a fourth is destroyed, by depressing it to the lowest notes of the audible scale. In hearing, there seems to be no permanent vibration of any part of the organ. [See the Account of some cases of the production of colours.] Hypothesis iv. All mattrial Bodiesare to be considered, with respect to the Phenomena of ■ Light, as consisting oj Particles so remote from tach other, as to allow the ethereal Medium to pervade them with perfect freedom, and either to retain it in a stale of greater den- iity and of equal elasticity/, or to constitute, together with the Medium, an Aggregate, which may be considered as denser, but not more elastic. It has been shown, that the three former hypotheses, which may be called essential, are literally parts of the more complicated Newtonian system. This fourth hypothesis differs in some degree from any that have been proposed by former authors, and is, in some respects, diametrically opposite to that of Newton ; but, both being in themselves equally admissible, the opposition is merely accidental ; and it is onl}' to be inquired, which is the most capable of explaining the phenomena. Other suppositions might, per- haps, be substituted for this, and therefore I do not consider it as fundamental, yet it ap- pears to be the simplest and best of any that have occurred to me. Proposition i. All Impulses are propa- gated in a homogeneous elastic Medium with an equable Velocity. Every experiment, relative to sound, coin- cides with the observation already quoted from Newton, that all undulations are pro- p.igated through the air with equal velocity ; and this is further confirmed by calculations. (Lagrange. Misc. Taur. I. 91. Also, much more concisely, in my Syllabus of a Course of Lectures on Natural and Experimental Phi- losophy, about to be published. Article 289.) It is surprising that Euler, although aware of the matter of fact, should still have main- tained, that the more frequent undulations are more rapidly propagated. (Theor. luus. and Conject. phys.) It is probable, that the actual velocity of the particles of the lumini- ferous ether generally bears a much smaller proportion to the velocity of the undulations, than is usual in the case of sound ; for light may be excited by the motion of a body moving at the rate of only one mile, in the time that light moves a hundred millions. And if our sun's light reaches some of the re- motest fixed stars, the utmost absolute ve- locity of the particles of the ethereal medium must be reduced to less than one thousandth part of an inch in a second. Scholium 1. It has been demonstrated, that in different mediums, the velocity vaiies in the subduplicate ratio of the force di- rectly, and of the density inversely. (Misc. Taur. 1. 91. Young's Syllabus, Art. 294.) Scholium 2. It is obvious, from the phe- nomena of elastic bodies and of sounds, that tlie undulations may cross each other witli- out interruption. But there is no necessity OK THE THSOIIT OI' tieHT AN» COtOCBS. 6l^ that the vavioiw colours of white %ht should ture ; on the contrai'y, in 4 circular wave of water, every part is, usually, at the saine in- sUmt either elevated or depressed. It may be difficult to show mathematically the mode, in which this intquahty of force is pre- served: but the inlerence from the matter of fact ajipears to be unavoidable. The theory of Huygens indeed explains the cireitin- stance in a manner tolerably satisfactory ; intermix their undulations; for, supposnig the vibrations of tlie retina to continue but a five hundredth of a second after their excite- ment, a m^illion uadula^itms of each of a million colours B»ay arrive, iu distinct succes- sion, within this inteival of time, and produce the same sensiole effect, as if ail the colours arrived precisely at the same instant. Proposition ii. Jn Uudnlation, conceived he supposes every particle of the medium to' to originate from the libralton of a single propagate a distinct undulation in all direc- JPurticle, must erpaitd through a homogeneous tions ; and that the general effect is only Medium in a spherieal Form, hut zeith dif- perceptible where a portion of each undula- ferent Quantities of Motionin different Parts. tion conspires in direction at the same in- For, since every imijulse, considered as slant ; and it is easy to show that sucli a ge- potiiiive or negative, is propagated with a neral undulation, would, in all cases, proceed' constant velocity, each part of the undula- rectilineavly, with proportionate force ; but, tion must, in equal times, have past through upon this supposition, it seems to follow, equal distance-i from the vibrating point, that a greater quantity of force must be lost And, sui)posing the vibrating particle, in the by the divergence of the partial undulations, course of its motion, to proceed forwards to than apj)ears to be consistent with the pro- a small distance in "a given direction, the pagation of the effect to any considerable principal strength of the undulation will na- distance. Yet it is obvious, that some such turally be straigh' before it ; behind it, the limitation of the motion must naturally be motion will be equal, in a contrary direction; expected to take place ; for, if the intensity and, at right angles to the line of vibration, of the motion of any pai'ticular part, instead the undulation will be evanescent. of continuing to be propagated straight for- Now, in order that such an undulation wards, were supposed to affect the intensity may continue its progress to any consider- of a neighbouring part of the undulation, an able distance, there must be, in each part of impulse must then have travelled from an in- it, a tentlency to preserve Us own motion in ternalto an external circle, in an oblique di- a right line from the centre ; for, if the ex- cess of force at any part were communicated to the neighbouring particles, there can be no reason why it should not very soon be equalised throughout, or, in other words, be- come wholly extinct, since the motions in contrary directions would naturally destroy each other. The origin of sound from the ribratioa of a chord is evidently of this na- rection, in the same time as in the direction of the radius, and consequently with a greater velocity ; against the first proposition. In the case of water, the velocity is by no means so rigidly limited as in that of an elas- tic medium. Yet it is not necessary to sup- pose, nor will the phenomena of light even allow us to admit, that there is absolutely not the least lateral communication of the force of 620 ON THE THEORT OF LIGHT AND COLOURS. the undulation, but it appears that, in highly elastic mediums, this communication is al- most insensible. In the air, if a chord be perfectly insulated, so as to propagate ex- actly such vibrations as have been described, they will, in fact, be much less forcible, than if the chord be placed in the neighbourhood of a sounding board, and probably in some measure, because of this lateral communica- tion of motions of an opposite tendency. And the different intensity of different parts of the same circular undulation may be observed, by holding a common tuning fork at arm's length, while sounding, and turning it, from a plane directed to the ear, into a position perpendicular to that plane. Proposition hi. A Portion of a sphe- rical Undulation, admitted ihrough an Aper- ture into a quiescent Medium, tcill proceed to be further propagated rectilinearly in con- centric Superficies, terminated laterulhj hy weak and irregular Portions of newly diverg- ■ ing Undulations. Ax. the instant of admission, the circum- ference of each of the undulations may be supposed to generate a partial unduhilion, filling up the nascent angle between the radii and the surface terminating the me- dium ; but no sensible addition will be made to its strength by a divergence of mo- tion from any other parts of the undulation, for want of a coincidence in time, as has already' been explained with respect to the various force of a spherical undulation. If indeed the aperture bear but a small propor- tion to the breadth of an undulation, the uewly generated undulation may nearly ab- sorb the whole force of the portion admitted; and this is the case considered by Newton in the Principia. When an experiment is made under these circumstances in light, it is cer- tain that, whatever may be the cause, it by no means wholly retains a rectilinear direction. Let the concentric lines in Fig. 105. .(Plate 14.) represent the contemporaneous situa- tion of similar parts of a number of succes- sive undulations diverging from the point A ; they will also represent the successive situations of each individual undulation : let the force of each undulation be repre- sented by the breadth of the line, and let the cone of light ABC be admitted through the aperture BC ; then the principal undulations will proceed in a rectilinear direction towards Gil, and the faint radiations on each side will diverge from B and C as centres, with- out receiving any additional force from any intermediate point D of the undulation, on account of the inequality of the lines DE and OF. But, if we allow some little lateral divergence from the extremities of the undu- lations, it must diminish their force, with- out adding materially to that of the dissi- pated light ; and their termination, instead of the right line BG, will assume the form CH ; since the loss of force must be more considerable near to C than at greater dis- tances. This line corresponds with the boundary of the shadow in Newton's first ob- servation. Fig. 1 ; and it is much more pro- bable that such a dissipation of light was the cause of the increase of the shadow in that observation, than that it was owing to the action of an inflecting atmosphere, or of an attractive force, which must have extended a thirtieth of an inch each way in order to produce it; especially when it is considered that the shadow was not diminished by sur- rounding the hair with a denser medium than air, which must in all probability have OV THE THEOnV OF LIGHT AND COLOURS, 621 weakened its attractive forccj or have con- tracted its inflecting atmosphere. In other circumstances, the lateral divergence might appear to increase, instead of diminishing, the hreadth of the beam. It is said that a beam of light, even passing through a va- cuum, is visible in all directions, and if the va- cuum were as perfect as it is possible to make it, the experiment would afford a strong ar- gument against the projectile system. The whole of the phenomena described by Grimaldi, under the very proper denomi- nation " diffraction," afford us examples of the deviation of light from rectilinear motion, nor have we the slightest evidence that an attractive force is concerned in producing these effects ; on the contrary the experiment already mentioned, in which the refractive density of the substance concerned appears to be indifferent to the result, renders the supposition of such an inflecting force ex- tremely improbable. As the subject of this proposition has al- ways been esteemed the most diflicult part of thcundulatory system, it will be proper to examine here the objections which Newton has grounded upon it. " To me, the fundamental supposition itself seems impossible; namely, that the waves or vibrations of any fluid can, like the rays of light, be propagated in straigiit lines, without a continual and very extravagant spreading and bending every way into the quiescent medium, where they are termi- nated by it. I mistake, if there be not both experiment and demonstration to the con- trary." (I'hil. Trans. VTI. 5089. Abr. I. 14G. Nov. lf)72.) " Motus omnis per fluidum propagatus di- rergit a recto tramile in spatia immota." " Quoniam medium ibi," that is, in the middle of an undulation admitted, "densiu* est,quam in spatiis hinc inde,dilatabitscse torn versus spatia utrinquc sita, quani versus pul- suum rariora intervalla; eoque pacto — pulsus eiidemfere celeritate sese inmedii partes qui- escentes hinc indc relaxare debent; — ideoque spatiumtotinn occupabunt. — ^Hoc experimur in sonis." (Princip. Lib. II. Prop. 42.) " Are not all hypotheses erroneous, in which light is supposed to consist in pression or motion, propagated through a fluid me- dium?— If it consisted in pression or motion, propagated cither in an instant, or in time, it would bend into the shadow. For pression or motion cannot be propagated in a fluid in right lines, beyond an obstacle which stops part of the motion, but will bend and spread every way into the quiescent medium which lies beyond the obstacle. — The waves on the surface of stagnating water, passing by the sides of a broad obstacle which stops part of them, bend afterwards, and dilate them- selves gradually into the quiet water behind the obstacle. The waves, pulses, or vibra- tions of the air, wherein sounds consist, bend manifestly, though not so much as the waves of water. For a bell or a cannon may be heard beyond a hill, which intercepts the sight of the sounding body ; and sounds arc propagated as readily through crooked pipes as straight ones. But light is never known to follow crooked passages, nor to bend into the shadow. For the fixed stars, by the in- terposition of any of the planets, cease to be seen. And so do the parts of the sun, by the interposition of the moon, i\Iercury, or Venus. The rays, which pass very near to the edges of any body, are bent a little by the action of the body; — but this bending is not towards but from the shadow, and is performed only in the piissagc of the ray by 6«2 ©N THE THEORY OF LIGHT AND COXOURS. the body, and at a very small distance from it. So soon as the ray is past the body, it goes right on." (Optics, Qu. 28.) Now tlie proposition quoted from the Principia, even supposing it to be strictly demonstrated, does not directly contradict this proposition ; for it does not assert that such a motion must diverge equally in all directions ; and the admission of the term " almost" is sufficient to invalidate the chain of reasoning : neither can it with truth be maintained, that the parts of an elastic medium, communicating any simple motion, must propagate that motion equally in all di- rections. (Phil. Trans. 1800. lOg. .112.) All tbat can be inferred by reasoning is, that the marginal parts of the undulation must be somewhat weakened, and that there must be a faint divergence in every direction : but whether either of these effects might be of sufficient magnitude to be sensible, with re- spect to light, could not have been concluded from argument, if the affirmative had not been rendered certain by experiment. As to the analogy with other fluids, the most natural inference from it is this : " The waves of the air, wherein sounds consist, bend manifestly, though not so much as the waves of water;" water being an inelastic, and air a moderately elastic medium: but the ether being most highly elastic, its waves bend very far less than those of the air, and there- fore almost imperceptibly. Sounds are pro- pagated through crooked passages, because their sides are capable of reflecting sound, just as light would be propagated through a bent tube, if perfectly polished within. The light of a star is by far too weak to produce, by its faint divergence, any visible illiimination of the margin of a planet eclips- ing it. Such a light has, however, often been seen attached to the moon in a. solar eclipse, as could not be attributed to a lunar atmo- sphere only. What Newton here says, of in- flection, h inconsistent, as Mr. Jordan has already remarked, with some of his own ex- periments. To the argument adduced by Huygens, in favour of the rectilinear propagation of undu- lations, Newton has made no reply; perhaps, because of his own misconception of the na- ture of the motions of elastic mediums, as de- pendent on a peculiar law of vibration, which has been corrected by later mathema- ticians. (Phil. Trans. 1800. 116.) On the whole, it is presumed, that this proposition may be safely admitted, as perfectly consist- ent with analogy and with experiment. Proposition iv. When an Undulation arrives at a Surface which is the Limit of Me- diums of different Densities, a partial Re- flection takes place, proportionate in Force to the Difference oftlie Densities. This may be illustrated, if not demon- strated, by the analogy of elastic bodies of different sizes. " If a smaller elastic body strikes against a larger one, it is well known that the smaller is reflected more or less powerfully, according to the diflierence of their magnitudes : thus, there is always a re- flection when the rays of light pass from a rarer to a denser stratum of t-ther;- and fre- quently an echo when a sound strikes against a cloud. A greater body striking a smaller one, propels it, without losing all its motion: thus, the particles of a denser stratum of ether do not impart the whole of then- mo- tion to a rarer, but in their eflort to proceedj they are recalled by the attraction of the re- fracting substance with equal force ; and ON THE THEORr OF LIGHT AVD COLOims. 625 ihoB a reflection is always secondarily pro- duced, wiien the ra)'S of light pass from a denserto a rarer stratum." (Phil. Trans. 1800. 127.) But it is not necessary to suppose an attraction in the latter case, since the effort to proceed would be propagated backwards without it, and the undulation would be re- versed, a rarefaction returning in place of a condensation ; and this will perhaps be found most consistent with the phenomena. Proposition v. When an Undulation is transmitted through a Surface terminating different Mediums, it proceeds in suck a Direction, that the Sines of the Angles of Incidence and Refraction are in the con- stant Raiio of the Felocity of Propagation in tlie two Mediums. (Barrow Lect. Opt. II. 4. Huygens de la Lum. cap. 3. Euler Conj. Phys. Phil. Trans. 1800. 128. Young's Syllabus, Art. 582.) Corollary 1. The same demonstration prove the equality of the angles of reflection and incidence. Scholium. It appears from experiments on the refraction of condensed air, that the difference of the sines varies simply as the density. And the same is probably true in other similar cases. Proposition vi. When an Undulation falls on the Surface of a rarer Medium, so obliqueli/ tltat it cannot be regularly refracted, it is totally reflected, at an Angle equal to that of its Incidence. This phenomenon appears to favour the supposition of a gradual increase and di- minution of density at the surface terminat- ing two mediums, (Phil. Trans. 1800, 128.) although Hwygens has attempted to ex- plain it somewhat differently. The velocity, with which the successive parts of the undulation arris'e at the reflecting sur- face, is sufficient to determine the angle of reflection ; in the same manner as when a bird is swimming in a stagnant piece of wa- ter, we see a rectilinear wave diverging at a certain ano;le on each side. The total re- flection seems to require tiie assistance of the particles of the rarer medium, to which the motion of the preceding portion of the undulation has been partly communicated, without being able to produce any other ef- fect than that of urging them in the direc- tion of the surface, and enabling them to re- sist the force of the direct undulation, which tends to remove them from the surface. Proposition vit. If equidistant Undula- tions be supposed to pass through a Medium, of which the Parts are susceptible of perma- nent vibrations somewhat slower than (he Un- dulations, their Velocity will be somewliat lessened by this vibratory Tendency ; and, in the same Medium, the. more, as the Undula- tions are more frequent. For, as often is the state of the undulation requires a change in the actual motion of the particle which transmits it, that change will be retarded by the propensity of the particle to continue its motion somewhat longer : and this retardation will be more frequent, and more considerable, as the difference between the periods of the undulation and of the -na- tural vibration is greater. Corollary. It was long an established opinion, that heat consists in vibrations of the particles of bodies, and is capable of be- ing transmitted by undulations through an apparent vacuum. (Newt. Opt. Qu. 18.) 'this opinion has been of late very much abandoned. Count llumford and Mr. Davy, are almost the only modern authors who have appeared to favour it; but it seems to have 624 OK THE THEORY OF I-IGTIT AND COLOURS. been vejected without any good grounds, and will probably very soon recover its po- pularity. Let us suppose, that these vibrations are less frequent than those of light; all bodies therefore are liable to permanent vibrations slower than those of light; and indeed almost all are liable to luminous vibrations, either when in astate of ignition, or in the circum- stances of solar phosphori ; but much less easily, and in a much less degree, than to the vibrations of heat. It will follow from these suppositions, that the more frequent lu- minous undulations will be more retarded than the less frequent ; and consequently, that blue light will be more refrangible than red, and radiant heat least of all ; a conse- quence which coincides exactly with the highly interesting experiments of Dr. Her- schel. (Phil. Trans. 1800.284.) It may also be easily conceived, that the actual exist- ence of a state of slower vibration may tend still more to retard the more frequent undu- lations, and that the refractive power of so- lid bodies may be sensibly increased by an increase of temperature, as it actually appears to have been in Euler's experiments. (Acad. de Berlin. 1762. S28.) Scholium. If, notwithstanding these con- «iderations, this proposition should appear to be insufficiently demonstrated, they must be allowed to be at least equally explanatory of the phenomena with any thing that can be advanced on the other side, from the doc- trine of projectiles ; since a supposed accele- rating force must act in some other propor- tion than that of the bulk of the particles; and, if we call this an elective attraction, it is only veiling, under a chemical term, our incapacity of assigning a mechanical cause. Mr. Short, when he found by observation the equality of the velocity of light of all co- lours, felt the objection so forcibly, that he immediately drew an inference from it in favour of the undulatory system. It is as- sumed in the proposition, that when light is dispersed by refraction, the corpuscles of the refracting substance are in a state of actual alternate motion, and contribute to its trans- mission ; but it must be confessed, that we cannot at present form a very decided and accurate conception of the forces concerned in maintaining these corpuscular vibrations. The proposition is not advanced as adding weight to the evidence in favour of the un- dulatory system, but as explaining in some degree a difficulty wjiich is common to all systems; and there is still room for other il- lustrations of the subject. The principal ar- gument in confirmation of the system is built on the next proposition, which appears to be equally new and important. Proposition viii. JV/ien two Undula- tions, from different Origins, coincide either perfect/}/ or very nearh/ in Direction, their joint effect is a Combination of the Motions belonging to each. Since every particle of the medium is affected by each undulation, wherever the directions coincide, the undulations can pro- ceed no otherwise, than by uniting their mo- tions, so that the joint motion may be the sum or difference of the separate motions, accordingly as similar or dissimilar parts of the undulations are coincident. I have, on a former occasion, insisted at large on the application of this principle to harmonics; (Fhil. Trans. 1800. 130.) and it will appear to be of still more extensive utility in explaining the phenomena of co- ON THE THEORY OF LIGHT ANp COIOURS. €2$ lours. The undulations which are now to be compared are those of equal frequency. When the two series coincide exactly in point of time, it is obvious that the united velocity of the particular motions must be greatest; and also, that it must be smallest, and, if the undulations are of equal strength, totally destroyed, when the time of the greatest direct motion, belonging to one un- dulation, coincides with that of the greatest retrogtade motion of the other. In inter- mediate states, the joint undulation will be of intermediate strength ; but by what laws this interinediate strength must vary, cannot be determined without furthej- ,data. It is well known that a similar cause produces, inbound, that effect which is called a beat; two series of undulations of nearly equal magnitude cooperating and destroying each other alterijaitely, as they coincide more or less perfectly in the limes of performing their respective motions. CoRouhATiy i, Qf t/ie iJolours afUriattd Surfaces. J3oyle appears to hav<2 beien the first that observed the colours of scratches on po- lislred surfaces. Nicwton lias not noticed them. Mazieas and Mr. Brougham have •Blade some psperinients on the subject, yet .yrjthout deriving any satisfactory conclusion. liM »|l the vsriiejies of these jjolours are very easily deduced from this proposition. JL^t there be, in a given plane, two reflect- ing points very near each other, and let the ■plane be so situated that the reflected iuiage i)f a luminous object seen in it may appcaj- ^ocojjncide with the points; then it is obvious that the ler^ih of the incident and irefltict^d jay, taken together, is equal with respect to both points, considering them a:j capable vol.. IJ. of reflecting in all directions. Let one of the points be now depressed below the given plane ; tten the whole path of the light, reflected from it, will be lengthened by a line which is to tiie depression of the point as twice the cosine of incidence to the radius. (Plate 14. Fig. tOG.) If, therefore, equal undulations of given dimensions be reflected from two points, situated near enough to appear to the eye but as one, wherever -this line is equal to half the breadth of a whole undulation, tiifc reflection ftom the depressed point will so interfere with the reflection from the fixed point, that the progressive motion of the one will coincide with the retrograde motion of the other, and they will both be destroyed ; but, when this line is equal to the whole breadth of an undulation, the eflecc will be doubled- and when to a breadth and a half, again de- stroyed ; and thus for a considerable number of alternations ; and, if the reflected undu- lations be oi" dilfereijt kinds, they will be va-f riously aftected, according to their propori- tions to the various lengths of the line which is the difference between the lengths of their two paths, and which may b denominated ihe interval of retardation. In order that the effect may be the more perceptible, a numlier of pairs of points must be united into two parallel lines ; and, if several such pairs of lines be placed near each other, they will facilitate the observa- tion. If one of the Jines be made to revolve lound the other, ?w an .axi^, t\ie djepressioa below the given plane will be as the sine of the iuclina.,tiou ; and wijila thp eye and lu- piinous object remain £,xed, the difference of thelengthsof the paths will vary iis this sine. The i)cst subjects for the experiment aj:e 4l <)26' -ON THE THEORY OF LIGHT AND COLOURS. Mr. Co-rentry's exquisite micrometers; such •of tliem as consist of parallel lines drawn on glass, at the distance of one five hundreth t)f an inch, are the most convenient. Each of these lines appears under a micro- scope to consist of two or more finer lines, exactly parallel, and at the distance of some- what more than a twentieth of that of the adjacent lines. I placed one of these so as to reflect the sun's light at an angle of 45°, and fixed it in such a manner, that while it revolved round one of the lines as an axis, I could measure its angular mtKion ; and I found, that the brightest red colour occured at tlie inclinations 10^:°, 20^°, 32°, and 45°; of which the ^ihes are as the numbers 1, 2, 3, and 4. At all other angles also, when the sun's light was reilcclcd from the surface, the colour vanished with the inclination^' and was equal at equal inclinations on either side. This experiment affords a very strong con- firmation of the theory. It is impossible to deduce any exi)lanation of it from any hy- pothesis hitherto advanced ; and I believe it would be difficult to invent any other that would account for it. There is a striking analogy between this separation of colours, and the production of a nmsieal note by suc- cessive echos from equidistant iron palisades; which I have found to correspond pretty ac- curately with the known velocity of sound, and the distances of the surfaces. It is not improbable that the colours of the integuments of some insects, and of some other natural bodies, exhibiting in different lights the most beautiful versatility, may be found to be of this description, and not to be derived from thin plates. In some cases, a single scratch or furrow may produce similar effects, by the reflections of its opposite edges. ConoLtARY n. Of the G&lours of thin Platen. When abeam of light falls on two parallel refracting surfaces, the partial reflections coincide perfectly in direction ; and, in this case, the interval of retardation, taken' between tlie surfaces, is to. their distance as twice the cosine of the angle of refraction to the raJ- dius. For, in Plate 14. Fig. 107, drawing AB and CD perpendicular to the rays, the times of passing through BC and AD will be equal, and DE will be half the interval of retarda- tion ; but DE is to CE as the sine of DCE to the radius. Hence, in order that DE rnay be constant, or that the same colour may be reflected, the thickness CE must vary as the secant of the angle of refraction CED : which agrees exactly with ISewton's experi- ments; for the correction which he has intro- duced is perfectly inconsiderable. Let the medium between the surfaces be, riirer than the surrounding mediums ; then the impulse reflected at the second surface, meeting a subsequent undulation at the first, will render the particles of the rarer medium capable of wholly slopping the motion of the denser, and destroying the reflection, (Prop. 4.) while they themselves will be more strongly propelled than if they had been at rest; and the transmitted light will be in- creased. So that the colours by reflection will be destroyed, and those by transmission rendered more vivid, when the double thick- nesses, or intervals of retardation, are any multiples of the whole breadths of the undu- lations; and at intermediate thicknesses the eflects will be reversed : according to the Newtonian observations. If the same proportions be found to hold good with respect to thin plates of a denser ON THE THEORY OF LIGHT AND COLOURS. 527 medium, which is indeed nol improbable, it will be necessary to adopt the corrected de- monstration of Prop. 4. but, at any rate, if a thin plate be interposed between a rarer and a denser medium, the colours by reflection and transmission may be expected to change places. From Newton's measures of the thicknesses reflecting the different colours, the breadth and duration of their respective undulations may be very accurately determined. The whole visible spectrum appears to be com- prised within the ratio of tiiree to five, which is that of a major sixth in music ; and the undulations of red, yellow, and blue, to be related in magnitude as the numbers 8, 7, and 6 ; so that the interval from red to blue is a fourth. The absolute frequency expressed in numbers is too great to be distinctly con- ceived, but it limy be better imagined by a comparison with sound. If a chord sounding the tenor c, could be continually bisected 40 times, and should then vibrate, it would afford a yellow green light : this being denoted by c, the extreme red would be a, and theblued. The absolute length and frequency of each vibratioii is expressed in the table : suppos- ing light to travel in 8| minutes 500 000' 000 000 feet. Length of an Undulation Number of Number of Undulations Colours. in parts of an Inch, in Air. Undulations in an Inch. in a. Second. Extrenlfc .0000266 37640 463 millions of millions. Red .00002.16 39180 482 Intermediate - .OOO0Q16 40720 501 Orange '.---- .000024 0 41610 512. Intermediate - - - .000023.5 42510 523 Yellow - - - . - .0000227 44000 542 Intermediate - - - .0000219 45600 561 (=2 "nearly) Green - - - .0000211 . 47460 584 Intermediate. - - - .0000203 49320 607 Blue .0000)96 51110 629 Intermediate - .0000189 52010 652 Indigo .0000185 54070 665 Intermediate .0000181 55240 680 Violet .0000174 57490 707 Extreme .0000167 59750 735 Meanof.all, or White .0000225 44440; 547 Scholium. It was not till I had satisfied myself respecting all these phenomena, that I found, in Hooke's ^Iicrographia,a passage which might have led me earlier to a similar opinion. " It is most evident, that the re-, flection from tlie under or furilier side of the body, is llie principal cause of the produc- tion of these colours. — Let the ray fall ob- liquely on the thin plate, part thereof is re- flected back by the first superficies, — partr refracted to the second surface, — whence it is reflected and refracted again. — So that, after two refractions and one reflection, there is propagated a kind of fainter ray — ," and, " by reaS|On of the time spent in passing and repassing, — this fainter pulse comes behind- the" former reflected " pulse ; so that hereby (the surfaces being so near together that the ffaar .MP T1IF LIGHT A N D C 0 ItCTUTl 9, e^e cniinat dwciriminate them from one,) this contused or duplicated pulse, whose strongest part precedes, and whose weakest follows, does produce on the retina, tiie sensation of a yeUow. If tiiese surfticBs are further removed asunder, the weaker pulse may become coincident with the" reflection of the " second," or next following pulse, from the first surface, " and lagg behind thatalso, and be coincident with the third, fourth, fifth, sixth, seventh, or eighth — ; so that, if there be a thin transparent body, that from the greatest thinness requisite to produce co- lours, does by degrees grow to the greatest thickness, — the colours shall be so often re- peated, as the weaker pulse does lose paces with its primary or first pulse, and is coinci- dent with a" sub^equeiu " pulse. And this, as it is coincident, or follows from tiie first hypothesis, 1 took of colours, so upon expe- riment have I found it in multitudes of in- stances that seem to prove it." (P. 65. . 6?.) This was printed about seven years before any of Newton's experiments were made. We are informed by Newton, that Hooke was afterwards disposed to adopt his " sugges- tion" of the nature of colours ; and yet it does not appear that Hooke ever applied that improvement to his explanation of these phenomena, or inquired into the necessary consequence of a change of obliquity, upon his original supposition, otherwise he could not but have discovered a striking coinci- dence with the measures laid down by New- ton from experiment. All former attempts, to explain the colours of thin plates, have either proceeded on suppositions which, like Newton's, would lead us to ex[)ect the greatest irregularities in the direction of the refracted rays ; or, like Mr. Michell's, would reC<)tO'UK9: 02^ idteM1!tcul with tlife production of those 6f thirt plates-. It is indeed stirprisittg', that it did ribl occur to so accurate a reasoner, tliat the colours of thin plates are always lost in white light, after ten or twelve alternations, ■while, in this case,, they are supposed-to bft distinguishable itftfir utariy thousiinds. GonoLLARY IV. Of Colours by inflection. . VVhatever may be the cause of the inflec- tion of light passing through a small aper- ture, the light nearest its centre must be the least diverted, and the nearest to its sides the most: another portion of light, falling ver3^ obliquely on the margin of the aper- ture, will be copiously reflected in various directions; some of which will either per- fectly' or very nearly coincide in direction with the unreflecled light, and having taken a circuitous route, will so interfere with it, as to cause an appearance of colours. The length of the two tracks will differ the less, as the direction of the reflected light has been less changed by its reflection, that is, in the light passing nearest' to tl>e margin; so that the blues will appear in the light nearest the ihadow. The effect will be increased and modified, when the reflected light falls within the influence of the opposite edge, so as to interfere with the light simply inflected by that also. On the supposition that inflection is pro- duced b}' the effect of an ethereal atmosphere, varying as a given power of the distance from a centre, I have constructed a diagram, (Plate 14. Fig. 108.) with the assistance of calcula- tions similar to those by which the effect of at- mospherical refraction is determined, show- ing, by the two pairs of curves, the relative position of the reflected and unreflected por- tibflsof ahv MIetilidulation- at tM'0's»t?cdsst^'itf &mt>iy ai<# ri'siJ*,' hy sdind^i lisefe dravtri aertoss, the pjittfe vt'here the intervals of ret tardation are in arithmeticid pro2;ressioH, and where similar colours' will be exhibited at different distances from the inflecting sub- stance. The lesult agrees sufficiently with the observations of Newton's thiril book, and with those of later writers. But 1 do nW consider the existence of such an atmosphere as necessar}' tb the explanation of the phe- nomena; the siinple opinion ofGrimaldi andi Hooke, who supposed that inflection arises from the natural tendency of light to diverge, appearing equally probable. Proposition i.x. liadiant Light consists in Undulations of the luminifirous Ether. This proposition is the general conclusion from all the preceding; and it is conceived that they conspire to prove it, in as satisfac- tory a manner, as can possibly be exjiccted from the nature of the subject, [t is clearly granted by Newton, that there are ethereal . undulations, y6t he denies that they constitute light; but it is shown in the Corollaries oi' the last Proiwsition, that all cases of the increase or diminution of light are refer- able to an increase or diminution of such un- dulations, and that all tiie affections, to which the undulations would be liable, are distinctly visible in the phenomena of light; it may therefore be very logically inferred, that the undulations are light. A few detached remarks will serve to ob- viate some objections which may be raised against this theory. 1. Newton has advanced the singular re- fraction of the Iceland crystal, as an argu- ment that the particles of light must be pro- 630 ON THE THEORY OF LIGHT AND COLOURS. jected corpuscles ; since he thinks it proba- ble that the clifFerent sides of these particles are diRercntly attracted by the crystal, and since Hiiygens has confessed his inability to account in a satisfactory manner . for all the phenomena. But contrariiy to what might have been expected from Newton's usual accuracy and candour, he has laid down a new law for the refraction, without giving a reason for rejecting that of Huygens, which Mr. Haliy has found to be more accurate than Newton's ; and, without attempting to deduce from his own system any explana- tion of the more universal and striking ef- fects of doubling spars, he has omitted to observe, that Huygens's most elegant and in- genious theory perfectly accords with these general effects, in all particulars, and of course derives from them additional preten- sions to truth : this he omits, in order to point out a difficulty, for which only a verbal so- lution can be found in his own theory, and which will probably long remain unexplained by any other. 2. Mr. Michell has made some expe- riments, which appear to show that the rays of light have an actual momentiun, by means of which, a motion is produced when they fall on a thin plate of copper delicately suspended. (Priestley's Optics.) But, tak- ing for granted the exact peipendiculaiity of the plate, and the absence of any ascending current of air, yet since, in every such expe- riment, a greater quantity of heat must be communicated to the air, at the surface on ■which the light falls, than at the opposite surface, the excess of expansion must neces- sarily produce an excess of pressure on the first surface, and a very perceptible recession «f the plate in the direction of the light. Mr. Bennet has repeated the experiment, with a much more sensible apparatus, and also in the absence of air ; and very justly in-, fers, from its total failure, an argument in fa-i vour of the uridulatory system of light. (Phil. Trans. 1792. 87.) for, granting the utmost imaginable subtility of the corpuscles of light, their effects might naturally be ex- pected to bear some proportion, to the effects of the much less rapid motions of the electrical fluid, which are so easily perceptible. 3. There are some phenomena of the light of solar phosphori, which at first sight might seem to favour the corpuscular system; for instance, its remaining many months as if in a latent state, and its subsequent reemis- sion by the action of heat. But, on further consideration, there is no difficulty in sup- posing the particles of the phosphori, which have been made to vibrate by the action of light, to have this action abruptly suspended by the intervention of cold, whether as con- tracting the bulk of the substance or other- wise ; and again, after the restraint is re- moved, to proceed in their motion, as a spring would do, which had been held fast for a time, in an intermediate stage of its vi- bration ; nor is it impossible that heat itself may, in some circumstances, become in a similar manner latent. (Nicholson's Journal- 11- 399-) But the affections of heat may, perhaps, hereafter be rendered more intelli- gible to us ; at present, it seems highly pro- bable, that light differs from heat only in the frequency of its undulations or vibrations ; those undulations which are within certain limits, with respect to frequency, being ca- pable of affecting the o])tic nerve, and con- stituting light; and those which are slower, and probably stronger, constituting heat ON THE THEORY OF LIGHT AND COLOURS. 631 fonly ; that light and heal occur to us, each in two predicanients, ilie vibiatoiy or per- manent, and the undulatory or transient state; vibratory light being the minute mo- tion of ignited bodies, or of solar phospbori, and undulatory or radiant light, tbe motion of the ethereal medium excited by these vi- brations; vibratory iieat being a motion, to M'hich all material substances are liable, and w hich is more or less permanent ; and iindnlHtory heat that motion of the same ethereal medium, which has been shown by Hoffmann, Buftbn, Mr. King, and M. Pic- tet, to be as capable of reflection as light, ind by Dr. Herschel to be capable of sepa- rate refraction. (Phil. Trans. 1800. 284.) How much more readily heat is communi- cated by the free access of colder substances, than either by radiation or by transmission through a ([uiescent medium, has been shown by the valuable experiments of Count llum- ford. It is easy to conceive that some sub- stances, permeable to liglit, may be unfit for the transmission of heat, in the same manner as particular substances may transmit some kinds of light, while they are opaque with . respect to others. On tiie whole it appears, that the few op- tical phenomena which admit of explanation by the corpuscular system, are equally con- sistent with this tlieory ; that many others, which have long been known, but never understood, become by these means perfectly intelligible ; and that several new facts are found to be thus only reducible to a perfect analogy with other facts, and to the simple principles of the undulatory system. It is presumed, that henceforth the second and third books of Newton's 0[)tics will be con- sidered as more fully understood than the first has hitherto been ; but, if it should ap- pear to impartial judges, that additional evidence is wanting fur the establishment of the theory, it will be easy to enter more mi- nutely into the details of various experiments, and to show the insuperable dilhculties at- tending the Newtonian doctrines, which, without necessity, it would be tedious and in- vidious to enumerate. The merits of their author, in natural philosophy, are great be- yond all contest or comparison ; his optical discover}' of the com])osition of white light would alone have immortalised his name ; and the very arguments, which tend to over- throw his s}'stem, give the strongest proofs of the admirable accuracy of his experi- ments. Sufficient and decisive as these arguments appear, it cannot be superfluous to seek for further confirmation ; which may with con- siderable confidence be expected, from an experiment very ingeniously suggested by Professor Robison, on the refraction of the light returning to us from the opposite mar- gins of Saturn's ring ; for, on the corpuscu- lar theory, the ring must be considerably distorted when viewed through an achroma- tic prism : a similar distortion ought also to be observed in the disc of Jupiter ; but, if it be found that an equal deviation is produced in the whole light reflected from these planets, there can scarcely be any remaining hope to exjdain the aflTections of light, by a compa- rison with the motions of projectiles. J PLATE 14. Fig. 105. The progress of a series of undulations admitted through an aperture. Fig. 106. Tiie difference of the paths of the light reflected from two points situated near each other. Fig. 107. The difference of the paths of tlie light reflected from the opposite surfaces of a thin plate. Fig. 108. The paths of two portions of hght supposed to pass through an inflecting atmo- sphere. PLATE 14. Voi..a.p.ff3i. Pia?. io5. J*ub. by J. JohnsmL .London, ijuly i8o0'. Joseph SkeieaTt sculp. VIII. AN ACCOUNT OF SOME CASES OP THE PRODUCTION OF COLOURS, NOT HITHERTO DESCRIBED. BY THOMAS YOUNG, M. D. F. R. S. PROFESSOR OF NATURAL PHILOSOPHY IN THE ROYAL INSTITUTION. FROM THE PHILOSOPHICAL TRANSACTIONS. Read before the Royal Society, Juli/ 1, 1802.~^^ W HATEVER opinion may be entertained of the theory of light and colours which I have hitely had the honour of submitting to the Royal Society, it must at any rate be al- lowed, that it has given birth to tlie discovery of a simple and general law, capable of ex- plaining a number of the phenomena of co- loured light, which, without this law, would remain insulated and unintelligible. The law is, that " wherever two portions of the same light arrive at the eye by different routes, either exactly or very nearly in the same direction, the light becomes most in- tense when the difference of the routes is any multiple of a certain length, and least intense in the intermediate state of the interfering portions; and this length is different for light of different colours." I have already shown, in detail, the suf- ficiency of this law, for explaining all the phenomena described in the second and third VOL. II. books of Newton's Optics, as well as some others not mentioned by Newton. But it is still more satisfactory to observe its con- formity to other facts, which constitute new and distinct classes of phenomena, and which could scarcely have agreed so well with an}' anterior law, if that law had been erroneous or imaginary : these are, the colours of fibres, and the colours of mixed plates. As I was observing the appearance of the fine parallel lines of light which are seen upon the margin of an olyect held near the eye, so as to intercept the greater part of the light of a distant luminous object, and which are pro- duced by the fringes caused by the inflection of light already known, I observed that they were sometimes accompanied by coloured fringes, much broader and tnoredistinct; and I soon found, that these broader fringes were occasioned by the accidental interposition of a hair. In order to make them more distinct. 4 M. 634 ACCOUNT OF SOME CASES I employed a hmse liair ; but they were then no longer visible. With a fibre of- wool, on the contrary, they became very large and conspicuous: and, with a single silk- worni's thread, their magnitude was so much increased, that two or three of them seemed to occupy the whole field of view. They ap- peared to extend on each side of the candle, inthe same order as the colours of thin plates, seen by transmitted light. It occurred to me that their cause must be sought in the inter- ference of two portions of light, one reflected from the fibre, the other bending round its opposite side, and at last coinciding nearly in direction with the former portion; that, accordingly as both portions deviated more from a rectilinear direction, the difference of the lengths oftheir paths would become gra- dually greater and greater, and would conse- quently produce the appearances of colour •usual in such cases ; that, supposingthem to be inflected at right angles, the difference would amount nearly to the diameter of the fibre, and that this difference must consequently be smaller as the fibre became smaller ; and, the number of fringes within the limits of a right angle becoming smaller, that their angular distances would Consequently become greater, and the whole appearance would be dilated. It was easy to calculate, that, for the light least inflected, the difference of the paths would be to the diameter of the fibre, very nearly as the deviation of the ray, at any point, from the rectilinear direction, to its dis- tance from the fibre. I therefore made a rectangular hole in a card, and bent its ends so as to support a hair parallel to the sides of the hole : then, upon applying the eye near the hole, the hair of course appeared dilated by indistinct vision into a surface, of which the breadth was de- termined by the distance of the hair and the magnitude of the hole, independently of the temporary aperture of the pupil. When the hair approached so near to the direction of the margin of a candle that the inflected light was suflSciently copious to produce a sensible effect, the fringes began to appear; and it was easy to estimate the proportion of their breadth to the apparent breadth of the hair, across the image of which they ex- tended. I found that six of tlie brightest red fringes, nearly at equal distances, occupied the whole of that image. The breadth of the aperture was tIoo^, and its distance from the hair —, of an inch ; the diameter of the hair was less than-;-!-^ of an inch ; as nearly as I could ascertain, it was ^^. Hence, we have Tws^ for the deviation of the first red fringe .at the distance 4^5 ; and, as t^oI To^ro- '■•g'o-o •it-soooo*. or fxTTT '^r the dif- ference of the routes of the red light, where it was most intense. The measure deduced from Newton's experiments is t^s^- I thought this coincidence, with only an error of one ninth of so minute a quantity, suffi- ciently perfect to warrant completely the ex- planation of the phenomenon, and even to render a repetition of the experiment un- necessary ; for there are several circum- stances which make it difircult to calculate much more precisely what ought to be th^ re- sult of the measurement. When a number of fibres of the same kind, for instance, those of a uniform lock of wool, are held near to the eye, we see an appear- ance of halos surrounding a distant candle ; but their brilliancy, and even their existence, depends on the uniformity of the dimensions of the fibres; and they are larger as the fibres OF tHE PRODUCTION OF COLOURS. 63i are smaller. It is obvious that they are the immediate consequences of the coincidence of a number of fringes of the same size, which, as the, fibres are arranged in all ima- ginable directions, must necessarily surround the luminous object at equal distances on all sides, and constitute circular fringes. There can be little doubt that the coloured atmospherical halos are of the same kind ; their appearance must depend on the exist- ence of a number of particles of water, of equal dimensions, and in a proper position, with respect to the luminary and to the eye. As there is no natural limit to the magnitude of the spherules of water, we may expect these halos to vary without limit in their dia- meters"; and, accordingly, Mr. Jordan has observed that their dimensions are exceed- ingly various, and has remarked that they frequently change during the time of obser- vation. Mr. Jordan supposes that they de- pend on the joint effect of two neighbouring drops; but it has been shown that a unifor- mity of dimensions is necessary for their pro- duction, and no such uniformity can possibly exist in the distances of the drops from each other. The lines, which are seen within the shadow of a hair, are produced nearly in the same manner as these colours of fibres, or rather they are the beginning of the series, derived from two portions of light inflected into the shadow, instead of one inllected and one re- flected portion. 1 first noticed the colours of mixed plates, in looking at a candle through two pieces of plate glass, with a httle moisture between them. I observed an appearance of fringes resembling the common colours of thin plates; and, upon looking for the fringes by reflection, I found that these new fringes were always in the same direction as the other fringes, but many times larger. By examin- ing the glasses with a magnifier, I perceived th.-jt whei'ever these fringes were visible, the moisture was intermixed with portions of air, producing an appearance similar to dew. I then supposed that the origin of the colours was the same as that of the colours of halos; but, on a more minute examination, I found that the magnitude of the portions of air and Wfiter was by no means uniform, and that the explanation was therefore inadmissible. It was, however, easy to find two portions of light sufficient for the production of these fringes; for, the light transmitted through the water, moving in it with a velocity dif- ferent from that of the light passing through tlie interstices filled onlj' with air, the two portions would interfere with each other, and produce effects of colour according to the general law. The ratio of the velocities, in water and in air, is that of 3 to 4; the fringes ought therefore to appear where the thickness is 6 times as great as that which corresponds to the same colour in the common case of thin plates ; and, upon making the experi- ment with a plain glass and a lens slightly convex, I found the sixth dark circle actually of the same diameter as the first in the new fringes. The colours are also very easily pro- duced, when butter or tallow is substituted for water; and the rings then become smaller, on account of the greater refractive density of the oils : but, when water is added, so as to fill up the interstices of the oil, the rings are very mucfi enlarged ; for here the diff"erence only of the velocities 'n\ water and in oil is to be considered, and this is much smaller thaa the diifereuce between 'an- and water. 636 ACCOUNT OP SOME CASES It appears to be necessary for theproduc- toon of these colours, that the glasses be held nearly in a right line between the eye and the common termination of a dark and lu- minous object: the portion of the rings, seen on the dark ground, is then more distinct than the remaining portion ; and, instead of being continuations of the rings, they exhi- bit every where opposite colours, so as to re- semble the colours of common thin plates seen by reflection, and not by transmission. In order to understand this circumstance, we must consider, that where a dark object (as A, Plate 15. Fig. 1 1 2.) is placed behind the glasses, the whole of the light, which comes to the eye, is either refracted through the edges of the drops, (as the rays B, C,) or reflected from the internal surface, (as D, E ;) while the light, which passes through those parts of the glasses which are on the side opposite to the dark object, consists of rays refracted as before through the edges, (as F, G,) or simply passing through the fluid (as H, J..) The respective combinations of these portions- of light exhibit series of colours in diflierent orders, since the inter- nal reflection modifies the interference of the jays on the side of the dark object, in the same manner as in the common colours of thin plates, seen by reflection. When no dark object is near, both these series of co- lours are produced at once ; and since they are always of an opposite nature at any given thickness of a plate, they neutralise each other, and constitute white light. In applying the general law of interfer- ence to these colours^ as well as to those of thin plates already known, it is impossible to avoid a supposition, which is a part of the undulatory theory, that is, that the velocity of light is the greater, the rarer the medium ; and there is also a condition annexed to this explanation of the colours of mixed plates, as as well as to that of the colours of simple thin plates, wli ich involves another part of the same theory; that is, that where one of the portions of light has been reflected at the surface of a rarer medium, it must be supposed to be re- tarded one half of the appropriate interval ; for instance, in the central black spot of a soap bubble, where the actual lengths of the paths very nearly coincide, but the effect is the same as if one of the portions had been so retarded as to destroy the other. From considering the nature of this circumstance, I ventured to predict, that if the two reflec- tions were of the same kind, made at the surfaces of a thin plate, of a density inter- mediate between the densities of the me- diums containing it, the effect would be re- versed, and the central spot, instead of black, would become white; and I have now the pleasure of stating, that I have fully verified this conclusion, by interposing a drop of oil of sassafras between a prism of flint glass and a lens of crown glass : the central spot seen by reflected light was white, and surrounded by a dark ring. It was however necessary to use some force, in order to produce a con- tact sufficiently intimate ; and the white spot differed, even at last, in the same de- gree from perfect whiteness, as the black spot usually does from perfect blackness. There are also some irregularities attending the phenomena exhibited in this manner by different refracting substances, especially when the reflection is total, which deserve further investigation. The colours of mixed plates suggested to me an idea, which appears to lead to an ex- OF THE PRODUCTION OF COLOURS. 637 planation of the dispersion of colours by re- fraction, perhaps more simple and satisfactory than that which I advanced in the last Bakerian lecture. We may suppose that every refrac- tive medium transmits the unduhitions coii- stitutin*^ hght in two separate portions, one passing tlirough its ultimate particles, and ihe other through its pores : and that these portions reunite continually, after each suc- cessive separation, the one having preceded the other by a very minute but constant in- terval, depending on the regular arrange- ment of the particles of a ho:.iogeneous me- dium. Now, if these two portions were al- ways equal, each point of the undulations, re- sulting from their reunion, would always be fourid lialF way between tlie places of the corresponding point in the separate portions; but, supposing the preceding portion to be the smaller, the newly combined undulation will be less advanced than if both had been equal, and the difference of its place will depend, not only on the difference of the- lengths of the two routes, which will be con- stant for all the undulations, but also on the law and magnitude of those undulations ; so that the larger undulations will be somewhat further advanced after each reunion than the smaller ones, and, the same operation re- curring at every particle of the medium, the whole progress of the larger undulations vvill be more rapid than thatol'the smaller; hence the deviation, in consequence of the retard- ation of the motion of light in a denser me- dium,, will of course be greater for the smaller than for the larger undulations. As- suming the law of the harmonic curve for the motions of the particles, we might with- out much difficulty reduce this conjecture to a comparison with experiment ; but it would he necessary, in order lo warrant our con- clusions, to be provided with accurate mea- sures of the refractive and dispersive jjowers of various substatices, for rays of all de- scriptions. Dr. Wollaston's very interesting observa^ tions would furnish very great assistance in this inquiry, when compared with the sepa- ration of colours by thin plates. I have re- peated his experiments on the spectrum will* perfect success, and have made some at- tem[)ts to procure comparative measures from thin plates; and I have found that, as Sir Isaac Newton lias already observed, the blue and violet light is more dispersed by re- fraction, than in proportion to the differ- ence of the appropriate dimensions deduced froui the phenomena of thin plates. Hence it happens, that when a Une of the light, pro- ceeding to form an image of the rings of co- lours of thin plates, is intercepted by a prism, and an actual picture is formed, resembling the scale delineated by Newton from theory, for estimating the colours of particles of given dimensions, the oblique spectrums, formed by the different colours of each series, are not straight, but curved, the lateral re- fraction of the prism separating the violet end more widely than the red. The thicknesse?, corresponding to the extreme red, the line of yellow, bright green, bright blue, aiid ex- treme violet, I found to be inversely as the numbers 27, .30, 35, 40, and 45, lespectively. Ir» consequence of Dr. Wollaston's correc- tion of the description of the prismatic spec- trum, compared with these observations, it beconses necessary to modify the supposition that 1 advanced in the last Bakerian lecture, respecting the proportions of the sympathe- tic fibres of the retina ; substituting red, 63S ACCOUNT OF SOME CASES OF THE PRODUCTIOy OF COLOURS. green, and violet, for red, yellow, and, blue, aud the numbers 7, G, and 5, for 8, 7, and 6. The same prismatic analysis of the colours of thin plates appears to furnish a satisfac- tory explanation of the subdivision of the light of the lower part of a candle : for, in fact, the light, transmitted tlirough every part of a thin plates is divided in a similar man- ner into distinct portions, increasing in num- ber with the thickness of the plate, until they become too minute to be visible. At the thickness corresponding to the ninth or tenth portion of red hght, the number of portions of different colours is five ; and their pro- portions, as exhibited by refraction, are nearly the same as in the light of a candle, the violet being the broadest. We have only to suppose each particle of tallow to be, at its first evaporation, of such dimensions iis to produce the same effect as the thin plate of air at this point, where it is about —o Jts^ of an inch in thickness, and to reflect, or per- haps rather to transmit, the mixed light pro- duced by the incipient combustion around it, and we shall have a light completely resem- blinsthat which Dr. VVollaston has observed. There appears to be also a fine line of strong yellow light, separate from the general spec- trum, prin(;ipal!y derived from the most su- perficial combustion at the margin of the flame, iind increasing in quantity as the flame ascends. This yellow light is rendered much more conspicuous by putting a few grains of salt ou the wick of the candle, and it is, not improbably, always derived from some salt contained in the tallow. Similar circumstances might undoubtedly be found ju other cases of the production or modifi- caiion of light ; and experiments upon this subject might te«d greatly to establish the Newtonian opinion, that the colours of all natural bodies are similar in their origin to those of thin plates ; an opinion which ap- pears to do the highest honour to the saga- city of its author, and indeed to form a very considerable step in our advances towards an acquaintance with the intimate constitution and arrangement of material substances. I have lately had an opportunity of con- firming my former observations on the dis- persive powers of the eye. 1 find that, at the respective distances of 10 and 15 inches, the extreme red and extreme violet rays are si- milarly refracted, ■ the difference being ex- pressed by a focal length of 30 laches. Now the interval between red and yellow;!* about one fourth of the whoJe spectrum; conse- quently, a focal length of 120 inches ex- presses a power equivalent to the dispersion of the red and yellow, and this differs but little from 132, which was the result of the observation already described. • I do not know that the^e experiments are more accu- rate than the former one ; but I have repeated them several times under different circum- stances, and I have no doubt that the dis- persion of coloured light in the human eye is nearly such as I have stated it. It may also be ascertained very accurately, by looking, through an aperture of known dimensions, at the image of a point dilated by a prism into a spectrum, and measuring the angle formed by its sides on account of the difference of refrangibility of the rays ; and this method seems to indicate a greater dispersive power than the former. IX. EXPERIMENTS AND CALCULATIONS RELATIVE TO PHYSICAL OPTICS. BY THOMAS YOUNG, M.D. F.R.S. FROM THE PHILOSOPHICAL TRANSACTIONS. Read before the Royal Society, November 24, 1803. 1. EXPERIMENTAL DEMONSTRATION OF THE GENERAL LAW OF THE INTERFER- ENCE OF LIGHT. JLn making some experiments on the fringes of colours accompanying shadows, I have found so simple and so demonstrative a proof of the general law of the interference of two portions of light, which I have already en- deavoured to establish, that I think it right to lay before the Royal Society a short statement of the facts, which appear to me to be thus decisive. The proposilion, on which 1 mean to insist at present, is simply this, that fringes of colours are produced by the interference of two portions of light; and I think it will not be denied by the most preju- diced, that the assertion is proved by the experiments I am about to relate, which may be repeated with great ease, whenever the sun shines, and without any other apparatus than is at hand to every one. Exper, 1 . 1 made a small hole in a window shutter, and covered it with a piece of thick paper, which I perforated with a fine needle. For greater convenience of observation, t placed a small looking glass without the win- dow, shutter, in such a position as to reflect the sun's light, in a direction nearly hori- zontal, upon the opposite wall, and to cause the cone of diverging light to pass over a table, on which were several little screens of card paper. 1 brought into the sunbeam a slip of card, about one thirtieth. of an inch in breadth, and observed its shadow, either on the wall, or on other cards held at dif- ferent distances. Besides the fringes of co- lours on each side of the sh^idow, the shjidow itself was divided by similar parallel fringes, of smaller dimensions, differing in number, according to the distance at which the sha- dow was observed, but leaving the middle of the shadow always white. Now these fringes were the joint effects of the portions of light passing on each side of the slip of card, and inflected, or rather diflracted, into the sha- dow. For, a little screen being placed either '«40 EXPERIMENTS AND CALCULATIONS. before tlie cavil, or a few inches behind it, «o as either to throw tlie edge of its shadow on the margin of the card, or to receive on its own margin the extremity of the shadow of the card, all the fringes which had be- fore been observed in the shadow on the wall immediately disappeared, although vthe light inflected on the other side was allowed to retain its course, and although this light must have undergone any modi- fication tliat the proximity of the other edge of the slip of card might have been ca- pable of occasioning. When the interposed screen was at a greater distance behind the narrow card, it was necessary to plunge it more deeply into the shadow, in order to extinguish the parallel lines; for here the ligiit, diffracted from the edge of the object, had entered further into the shadow, in its way towards the fringes. Nor was it for want of a sufficient intensity of light, that one of the two portions was incapable of pro- ducing the fringes alone; for, when t:hey were both uninterrupted, the lines appeared, ijvenif the intensity was reduced to one tenth or one twentieth. iixjKr. 2. The crested fringes, described by the ingenious and accurate Grimaldi, afford an elegant variation of the preceding expe- riment, and an interesting example of a calculation grounded on it. When a sha- dow is formed by an object which has a rec- tangular terminiaion, besides the usual ex- ternal fringes, there are two or three alterna- .tions of colours, beginning from the line which bisects the angle, disposed on each side of it, in curves, which are convex to- wards the bisecting line, and which converge in some degree towards it, as they become more remote liom the angular poini. These fringes are also the joint effect of the light whigh is inflected directly towards the sha- dow, from each of the two outlines of the object. For, if a screen be placed within a few inches of the object, so as to receive only ene of the edges of the shadow, the whole of the fringes will disappear. If, on the contrary, the rectangular point of the screen be opposed to the point of the sha- dow, 60 as barely to receive the angle of the shadow on its extremity, the fringes will re- main undisturbed. II. COMPARISON OF MEASURES, DEDUCED FROM VARIOUS EXPERIMENTS. If we now proceed to examine the dimen- sions of the fringes, under different circum- stances, we may calculate the differences of the lengths. of the paths described by the portions of light, which have thus been proved to be concerned in producing those fringes ; and we shall find, that where tlie lengths are equal, the light always remains white; but that, where either the brightest light, or the light of any given colour, disap- peiurs and reappears, a first, a second, or a third time, the differences of thelengths of the paths of the two portions are in arithme- tical progression, as nearly as we can expect experiments of this kirwl to agree with each other. I shall compare, in this point of view, the measures deduced from several ex- periments of Newton, and from some of my own. In the eighth and ninth observations of the third book of Newton's Optics, some ex- periments are related, which, together with the third observation, will furnish us with the data necessary for the calculation. Two knives were placed, with their edges meeting RELATIVE TO PHYSICAL OPTICS. 641 at a very acute angle^ in a beam of the sun's light, admitted through a small aperture; and the point of concourse of the two first dark lines, bordering the shadows of the re- spective knives, was observed at various dis- tances. The results of six observations are expressed in the first three lines of the first Table. On the supposition that the dark line is produced by the first interference of the light reflected from the edges of the knives, with the light passing in a straight line be- tween them, we may assign, by calculating the difference of the two paths, the interval for the first disappearance of the brightest light, as it is expressed in the fourth line. The se- cond Table contains the results of a simi- lar calculation, from Newton's observations on the shadow of a hair ; and the third, from some experiments of my own, of the same nature ; the second bright line being supposed to correspond to a double interval, the second dark line to a triple interval, and the succeeding lines to depend on a con- tinuation of the progression. The unit of all the Tables is an inch. Table I. Obi. g. N. Distance of the knives from the aperture Distances of the paper from the knives . . \\, 3\, 8 Distances between the edges of the knives, opposite to the TJ point of concourse . Interval of disappearance .012, .020, .034, 32, .057, 96, .081 JOh 131. .087. .0000122, .0000155, .0000182, .00001G7, .0000166, .0000166. Table II. Obs. 3. N. Breadth of the hair . . ..... Distance of the hair from the aperture Distancesof the scale from the aperture (Breadths of the shadow * . Breadth between the second pair of bright lines Interval of disappearance, or half the difference of the paths Breadth between the third pair of bright lines Interval of disappearance, i of the difference Table III. Eiper. 5. Breadth of the object . . . . ; Distance of the object fiorn the aperture Distance of the wall from the aperture Distance of the second pair of darkUnjes from each other Interval of disappearance, 4- of the difference . , 150, T4» .0000151, 4 7T» .0000150, 2. To" 144 252. y) ♦ .0000173. .0000143. .4r,4. 125. 250. 1.1 67. .0000149. vol. If. 4 o 6i2 EXPERIMENTS AND CALCULATIONS Exper. 4. Breadth of the wire Distance of the wire from the aperture Distance of the wall from the aperture (Breadth of the shadow, by three measurements Distance of the first pair of darlv hues Tnterval of disappearance Distance of the secontl pair of dark lines Interval of di:^appearance Distance of the third pair of dark lines Interval of disappearance .... .083. .32. 250. .815, 826, or .827 ; mean, .823.) 1.165, 1.170, or 1.160; mean, 1.165. .0000194. 1.402, 1.395, or 1.400 ; mean, 1.399- .0000137. 1.594, 1.580, or 1.585 ; mean, 1.586. . \ . ... , .0000128. It appears, from five of the six observations of the first Table, in which the distance of the shadow was varied from about 3 inches to 1 1 feet, and the breadth of the fringes was increased in the ratio of 7 to 1, that the diiference of the routes, constituting the in- terval of disappearance, varied but one eleventh at most ; and that, in three out of the five, it agreed with the mean, either ex- actly, or within t4o part. Hence we are warranted in inferring, that the interval, ap- propriate to the extinction of the brightest light, is either accurately or very nearly con- stant. But it may be inferred, from a compari- son of all the other observations, that when the obliquity of the reflection is very great, some circumstance takes place, which causes the interval thus calculated to be somewhat greater: thus, in the eleventh line of the third Table, it comes out one sixth greater than the mean of the five already mentioned. On the other hand, the mean of two of Newton's experiments and one of mine, is a result about one fourth less than the former. With respect to the nature of this circum- stance, I cannot at present form a decided opinion ; but I conjecture that it is a devia- tion of some of the light concerned, from the rectilinear direction assigned to it, arising either from its natural diffraction, by which the magnitude of the shadow is also enlarged, or from some other unknown cause. If we imagined the shadow of tbp wire, and the fringes nearest it, to be so contracted, that the motion of the light bounding the sha- dow might be rectilinear, we should thus make a sufficient compensation for this de- viation ; but it. is difficult to point out what precise track of the light would cause it to require this correction. The mean of thfc three experiments, which appear to have been least affected by this un- known deviation, gives .0000127 for the in- terval appropriate to the disappearance of the brightest light ; and it may be inferred, that if they had been wholly exempted from its effects, the measure would have been somewhat smaller. Now the analogous in- terval, deduced from the experiments of Newton on thin plates, is .00001 12, which is about one eighth less than the former result ; and this appears to be a coincidence fully sufficient to authorise us to attribute these RELATIVE TO PHVSICAL OPTICS. 643 two classes of phenomena to the same cause. It is very easily shown, with respect to the colours of thin plates, that each kind of light disappears and re^ippears, where the differ- ence of the routes of two of its portions are in arithmetical progression ; and we have seen, that the same law may be in general inferred from the phenomena of diffracted light, even independently of the analogy. The distribution of the colours is also so similar in both cases, as to point immedi- ately to a similarity in the causes. In the thirteenth observation of the second part of the first book, Newton relates, that the in- terval of the glasses where the rings appeared in red light, was to tlie interval where they appeared in violet light, as 14 to 9 ; and, in the eleventh observation of the third book, that the distances between the fringes, under the same circumstances, were the 22d and 27th of an inch. Hence, deducting the breadth of the hair, and taking the squares, in order to find the relation of the difference of the routes, we have the proportion of 14 to 9|, which scarcely differs from the proportion observed in the colours of the thin plate. We may readily determine, from this ge- neral principle, tlie form of the crested fringes of Grimaldi, already described; for it will appear that, under the circumstances of the experiment related, the points in which the differences of the lengths of the paths described by the two portions of light are equal to a constant quantity, and in which, therefore, the same kinds of light ought to appear or disappear, are always found in equilateral hyperbolas, of which the axes coincide with the outlines of the shadow, and the asymptotes nearly with the diagonal line. Such, therefore, must be the direction of the fringes ; and this conclusion agrees perfectly with the observation. But it must be re- marked, that the parts near the outlines of the shadow are so much shaded off, as to render the character of the curve somewhat less de- cidedly marked where it approaches to its axis. These fringes have a slight resemblance to the hyperbolic fringes observed by New- ton ; but the analogy is only distant. HI. APPHCATION TO THE SUPERNUME- RARY RAINBOWS. The repetitions of colours, sometimes ob- served within the common rainbow, and de- scribed in the Pliilosophical Transactions, by Dr. Langvvith and Mr. Daval, admit also a very easy and complete explanation from the same principles. Dr. Pemberton has at- tempted to point out an analogy between these colours and those of thin plates; but the irregular reflection from the posterior surface of the drop, to which alone he attri- butes the appearance, must be far too weak to produce any visible effects. In order to understand, the phenomenon, we have only to attend to the two portions of light which are exhibited in the common diagrams ex- planatory of the rainbow, regularly reflected from the posterior surface of the drop, and crossingeach other in various duections, till, at the angle of the greatest deviation, they.coin- cide with each other, so as to produce, by the greater intensity of this redoubled light, the common rainbow of 41 degrees. Otherparts of these two portions will quit the drop in direc- tions parallel to each other ; and these would exhibit a continued diffusion of fainter light, for .23° within the bright termination which forms the rainbow, but for the general law of interference, which, as in other similar 644 iXPEHlMENTS AVD CAJXUXATIONS ping them from a phial, and it may easily be conceived that the drops, formed by natural operations, may sometimes be as uniform, as any that can be produced by art. How accurately this theory coincides with the observation, may best be deter- mined from Dr. Langwith's own words. "August the 21st, 1722, about half an hour past five in the evening, weather tem- perate, wind at north east, the appearance was as follows. The colours of the primary rainbow wer-e as usual, only the purple very much inclining to red, and well defined : under this was an arch of green, the upper ■part of which inclined to a bright yellow, the lower to a more dusky green : under this were alternately two arches of reddish purple, and two of green : under all, a faint appear- ance of another arch of purple, which va- nished and returned several times so quick, that \jc could not readily fix our eyes upon it. Thus the order of the colours was, i. Red, orange colour, yellow, green, light blue, deep blue, purple, n. Light green, dark green, purple, in. Green, purple. , is increased in the simple inverse ratio of the distance ; and the mean action, or negative pressure of the fluid, on each particle of the surface, is also increased in the same ratio. When the float- ing bodies are both surrounded by a depres- sion, the same law prevails, and its demon- stration is still more simple and obvious. The repulsion of a wet and a dry body does not appear to follow the same proportion : for it by no means approaches to infinity upon the supposition of perfect contact ; its maximum is mejisured by half the sum of the elevation and depression on the remote sides of the substances, and as the distance increases, this maximum is only dinrinished by a quantity, which is initially as the square of the distance. The figures of the solids concerned modify also sometimes the law of attraction, so that, for bodies surrounded by a depression, there is sometimes a maximum, beyond which ihe force again diminishes; and it is hence that a light body floating on mercury, in a vessel little larger than itself, is held in a stable equilibrium without touching the sides. The reason of this will become apparent, when we examine ihe direction of the surface necessarily assumed, by the mercury, in order to preserve the appropriate angle of contact; the tension acting with less force, when the surface attaches-itself tothe angular termina- tion of the float in a direction less horizontal. The apparent attraction produced between solids, by the interposition of a fluid, does not depend on their being partially immersed in it; on the contrary, its eifects are still more powerfully exhibited in other situations ; and, when the cohesion between two solids is in- creased and extended by the intervention of a drop of water or of oil, the superficial co- hesion of these fluids is fully sufficient to ex- plain the additional effect. When wholly immersed in water, the cohesion between two pieces of glass is little or not at all greater than when dry : but if a small portion only of a fluid be interposed, the curved surface, that -it exposes tothe air, will evidently be capable of resisting as great a force, as it would support from the pressure of the co- lumn of fluid, that it is capable of sustaining in a vertical situation ; and in order to apply this force, we must employ, in the separation of the plates, as great a force as is equivalent to the pressure of a column, of the height ap- propriate to their distance.Morveau found that twodiscs of glass, 3 inches French in diameter,, at the distance of one tenth of a line, appeared to cohere with a force of 47 19 grains, which is equivalent to the pressure of a colnmn 23 lines in height: hence the product of the height and the distance of the plates is 2.3 lines, instead of 2.65, which was the result of Monge's experiments on the actual ascent of water. The difference is much smaller than the difference of the various experiments on the ascent of fluids ; and it may easily have arisen from a want of perfect parallelism in the plates; for there is no force tending to preserve this parallelism. The error, in the extreme case of the plates coming into con- tact at one point, may reduce the apparent cohesion to one half. The same theory is sufficient to explain the law of the force, by which a drop is at- tracted towards the junction of two plates, inclined to each other, and which is found to ON THK COHESION OF FLUIDS. 657 vary in the inverse ratio of the square of the distance ; whence it was inferred by Newton that the primitive force of cohesion varies in the simple inverse ratio of the distance, while other experiments lead us to suppose that cohesive forces iu general vary in the direct ratio of the distance. But the difficulty is removed, and the whole of the effects are satisfactorily explained, by considering the state of the marginal surface of the drop. If the plates were parallel, the capillary action would be equal on both sides of the drop : but when they are inclined, the curvature of the sur- face at the thinnest part requires a force pro- portional to the appropriate height to coun- teract it; and this force is greater than that which acts on the opposite side. But if the two plates are inclined to the horizon, the deficiency may be made up by the hydro- static weight of the drop itsell"; and the same inclination will serve for a larger or a smaller drop at the same place. Now when the drop approaches to the line of con- tact, the difference of the appropriate heights for a small drop of a given diameter will in- crease as the square of the distance decreases ; for the fluxion of the reciprocal of any quan- tity varies inversely as the square of tliatquan- tity ; and, in order to preserve the equilibrium, the sine of the angle of elevation of the two plates must be nearly in the inverse ratio of the square of the distance of the drop from the line of contact, as it actually appears to have been in Hauksbee's experiments. VI. PHYSICAL FOUNDATION OF THE LAW OF SUPERFjIClAL COHESION. We have now examined the principal phenomena which are reducible to the sim- ple theory of the action of the superficial VOL. II. panicles of a fluid. We are next to investi- gate the natural foundations upon which that theory appears ultimately to rest. We may suppose the particles of liquids, and j)robably those of solids also, to possess that: power of repulsion, which has been demon- stratively shown by Newton to exist in aeri- form fluids, and which varies in the simple inverse ratio of the distance of the particles from each other. In airs and vapours this ■force appears to act uncontrolled; but in li- quids, it is overcome by a cohesive force, while the particles still retain a power of mov- ing freely in all directions; and in solids the same cohesion is accompanied by a stronger or weaker resistance to all lateral motion, which is perfectly independent of the cohe- sive force, and which must be cautiously distinguished from it. It is simplest to sup- ])ose the force of cohesion nearly or perfectly constant in its magnitude, throughout the minute distance to which it extends, and owing its apparent diversity to the contrary action of the repulsive force, which varies with the distance. Now in the internal parts of a liquid these forces hold each other in a perfect equilibrium, the particles being brought so near, that the repulsion becomes precisely equal to the cohesive force that urges them together: but whenever there is a curved or angular surface, it may be found, by collecting the actions of the diflerent parti- cles, that the cohesionraust necessarily prevail over the repulsion, and must urge the super- ficial parts inwards, with a force proportional to the curvature, and thus produce the efleet of a uniform tension of the surface. For, if we consider the efl"ect of any two particles in a curved line on a third at an equal dis- tance beyond them, we sludl find that the 4 p 658 ON TirK COHESION OP I'LUIDS. result of their equal attractive forces bisects the whole angle formed by the lines of direction ; but that the result of their repulsive forces, one of which is twice as great as the other, divides it in the ratio of one to two, forming with the former result an angle equal to one sixth of the whole; so that the addition of a third force is necessary, in order to retain these two results in equilibrium ; and this force must be in a constant ratio to the eva- nescent angle which is the measure of the curvature, the distance of the particles being constant. The same reasoning may be ap- plied to all the particles which are within tiie influence of the cohesive force : and the con- clusions are equally true if the cohesion is not precisely constant, but varies less rapidly than the repulsion. VII. COHESIVE ATTRACTION OF SOLIDS AND FLUIDS. When the attraction of the particles of a fluid for a solid is less than their attraction for each other, there will be an equilibrium of, the superficial forces, if the surface of the fluid make with that of the solid a certain an- gle, the versed sine of which is to the dia- meter, as the mutual attraction of the fluid and solid particles is to the attraction of the particles of the fluid among each other. For, when the fluid is surroundeareiitbo(hes on light, if liiey had ever been so fortunate as to obtain Mr. Laplace's attention. Indeed an " attraction insensible at all sensible dis- tances," would not explain the cfTects of what Newton calls inflection, which affects the rays passing at a very considerable distance, at least as much as the tenth or twentieth of an inch, on each side of an opaque sub- stance, placed in a small pencil of light in a dark room. " Clairaut is the first, and has hitherto remained the only person, that has subjected the phenomena of capillary tubes to a rigorous calculation, in his treatise on the fi- gure of the earth. After having shown, by arguments which are equally applicable to all the theories which have been advanced, the inaccuracy and iniufhciency of that of Jurin, he enters into an exact analysis of all the forces which can contribute to the elevation of a portion of water in a tube of glass. But his theory, although explained with all the elegance peculiar to the excellent work which contains it, leaves undetermined the law of the height of that elevation, which is found from experimenjt to be inversely proportional to the diameter of the tube. This great mathematician contents himself with observing, that there must be an infinite variety of laws of attraction, which, if substituted in his formulas, would ^ITord this con- 1 elusion. The knowledge of these laws is, however, the most delicate and the most important part of the theory ; it is absolutely neccssary_ for connecting together the dif- ferent phenomena of capillary action; and Clairaut would himself have been aware of this necessity, if he had wished, for example, to pass from capillary tubes to the spaces in- cluded between two parallel planes, and to deduce from calculation the equality, which is shown by experiment, between the height of ascent of a fluid in a cylindrical tube, and its height between two parallel planes, of which the distance is equal to the semidiameter of the tube ; a re- lation which no one has yet attempted to explain. I en- deavoured, long ago, to determine the laws of attraction ort which tliese phenomena depend ; some later investigations have enabled me to demonstrate, that they may all be refer- red to the same laws, whicB will account for the phenomena- of refraction, that is, to such as limit the sensible effect of the attraction to an insensible distance ; and from these laws, a complete theory of capillary action may be deduced." It is true that Clairaut was the first that attempted to lay the foundation of a theory of capillary action ; but he is by no means^ the only one that has made the attempt. Seg- ner published, in the first volume of the Transactions of the Royal Society of Gottin- gen, for 1751, an essay, in which he has gone much further than Clairaut : it is true that he has made some mistakes in particular cases: but he begins, like Mr. Laplace, from the eftiscts of an attraction insensible at all sensible distances ; he has demonstrated that the curvature of each point of the surface of a fluid is always proportional to its disttuice above or below the general level, and he has inferred, from earlier experiments, the trae magnitude of this curvature at a given height, both for water and for mercury, without ma- terial error. We shall however find, that the principles, which Clairaut, Segner, and Litplace, have successively adopted, are insuf- ficient for explaining all the phenomena ; and that it is impossible to account for them with- out introducing the consideration of a repul- sive force ; which must ijideed inevitably be <>()'. ON THE COHESIOJfx of FLUIDS. supposerlto c.vijt, even if its presence were not inferred from the effects of capillary action. " Attempts!' have certainly been made, to explain the equality of the ascent; of a fluid between the two planes, and in a tube of wiiic-h the radius is equal to their dis- tuiice-; Mr. Leslie has made sueli an attempt, and with perfect success ; but, if I am not nii'^takeii, the same explanation had been given long before. " Clatraut supposes, that a capillary tube may exert a sensible aciion on an infinitely narrow column of thefluiii, situated in the axis of the tube. In this respect, I am obliged to differ from him, and to agree with Haultsbee, and with many other philosophers, in thinking, that capil- lary action, like refractive powers, and the forces of chemi- cal affinities, is only sensible at imperceiitible distances. Hauksbee has observed, that when the internal diameters of several capillary tubes are equal, the water rises in them to the same height, whether they are very thin or very thick. The cylindrical strata of glass, which are at a sen- sible distance from the interior surface, do not therefore contribute to the ascent of the water, although each of them, taken separately, would cause it to rise above its natural level. It is not the interposition of the strata which they surround, that prevents their action on tlie water ; for it is natural to suppose, that the force of capillary attrac- tion is transmitted through the substance of all material bodies, in the same manner as that of gravitation ; this action is, therefore, only prevented, by the distance of the fluid from these strata; whence itfollows, that the attraction of glass for water is only sensible at insensible distances. " Proceedini; upon this principle, I have investigated the action of a fluid mass, terminated by a portion of a con- cave or convex spherical surface, upon a fluid column with- in it, contained in an infinitely narrow cylindrical cavity or tube, directed towards the centre of the surface. By this action I mean the pressure, which the fluid contained in the tube would exert, in consequence of the attraction of the whole mass, upon a flat ba^s, situated within the tube, perpendicular to its sidi%, and at any sensible distance from Jhe external surface, taking this basis for unity. I liave«hown that this action is either smaller or greater than if the sur- face were plane, accordingly as it is either concave or con- vex. The algebraical formula, which expresses it, consists of two terms : the first, which is mucli larger than th'e second, «*j)rsS5(;s the action of thejnass supposed to he terminated by a plane .surface ; and I coneeive that this force is the cause of the suspension of mercury in the tube of a baro- meter, at a height two or three times greater than that which is derived from the pressure of the atmosphere, of the refractive powers of transparent bodies, of cohesion, and of chemical affinities in general. The second term ex- presses that part of the attraction, which is derived from the curvature of the surface, that is, the attraction of the me- niscus comprehended between that surface and the plane which touches it. This action is either added to the fot- raer, or subtracted from it, accordingly as the surface is con- vex or concave. It is inversely proportional to the radius of the spherical surface ; and it is indeed obvious, that, the smaller the radius is, the greater is the meniscus near the point of contact. This second term expresses the cause of capillary action, which differs, in this respect, from the chemical affinities represented by the first term." It is indeed so " obvious," that the menis- cus, which constitutes the difference be- tween a curve surface and a plane one, is inversely proportional to the radius of cur- vature, that the complicated calculations, which have led Mr. Laplace to this conclu- sion, must be considered as wholly superflu- ous. The attraction of the meniscus upon the evanescent column must be confined to the edge which immediately touches the co- lumn, extending only to an insensible dis- tance on each side ; and the situation of all the particles in this infinitely thin edge of the meniscus, with respect to the column, being similar, whatever the curvature may be, it is evident that their joint action must be proportional to their number, that is, to the curvature of the surface. " From these conclusions, relating to bodies wliich are terminated by sensible portions of a spherical surface, I de- duce this general theorem. Whenever the attractive force be- comes insensible at any sensible distance, the action of a body, terminated by a curved surface, on an internal column, of infinitely small diameter, and perpendicular to the sur- face at any point, is equal to the half sum of the actions, which would be exerted on the same column by two spheres, having for their radii the largest and the smallest of the radii of curvatute at the given point." ON THE COHESION- OF FLUIDS. 6G3 Tins theorem may be very simply inferred from llie former, by considering that, ac- cording to the principle laid down in the second section of this essay, the sum of the thicknesses of the evanescent mcniscoid, in any two planes passing tiirough the axis at right angles to each other, is equal to the sum of the thicknesses of the two menisci formed by the largest and the smallest radii of curvature ; consequently the sum of the whole actions of these menisci must be twice as great as the action of the meniscoid. " By means of this theorem, and of the laws of the equi- Tibriuiii of fluids, we may determine the figure which must be assumed by a gravitating fluid, inclosed in a vessel of any given form. We obtain from these principles an equation of partial differences of the second order, the in- tegral of whidi cannot be found by any known method. If the figure is such, as might be formed by the revolution-of a curve round an axis, the equation is reduced to common differences or fluxions, and its integral or fluent may be found very near the truth, when the surface is very small. I have shown in this manner, that, in very narrow tubes, the surface of the fluid approaches the nearer to that of a sphere, as the diameter of the tube is smaller. If these segments are similar, in different tubes of the same sub- stance, the radii of their surfaces will be" directly " pro- portional to the diameters of the tubes. Now this similarity of the spherical segments will easily appear, if we con- sider that the distance, at which the action of the tube ceases to be sensible, is imperceinible; so that if, by means of a very powerful microscope, it were possible to maln1e, ami S being 50^, the term afj'- bccoines=4, and makes the negative part of tiie forimila greater thaa the positive. Wlien Mr. Lnphice investigates the relation of the curvature and of the marginal depres- sion to the diameter of tlie tuhe, he simply -considers the whole surface as spherical ; but even on this supposition his formula is by no in(>ans the most accurate tiiat may be found, and begins to be materially incorrect even when liie diameter of the tube amounts to one fifili of an inch only. The formula, which I have already given in this paper, is sufliciently accurate, until the diameter be- comes equal to half an inch ; but I shall hereafter mention another, whieii comes much nearer to the truth in all cases, " The comparison of these results shows the true causeofthe ascfiitor depression of fluid's in capillary tubes, which is inversely proportional to their diameters. If we imagine an infinitely narrow inverted siphon to have one of its branches placed in the axis of the tube of glass, and the other terminating in the general horizontal sur&ce of the w;iter in the vessel, the action of the water in the tube on the first branch of the siphon will be less, en account of the concavity of its surface, than the action of the water of the vessel on the second ; the fluid must therefore ascend in the tube, in order to compensate for this difference ; and, as it has been shown, that the difference of the two actions is inversely proportional to the diameter of the tube, the elevation of the fluid above the general level must follow the same law. " If the surface of the fluid within the tube is convex as in the case of mercury contained in a tube of glass, its ac- tion on the inverted siphon will be greater than that of the fluid in the vessel ; the fluid must therefore be depressed in the tube, in proportion to the difference, that is, inversely in proportion to the diameter of the tube. " It appears therefore, that the immediate attraction of a capillary tube has no other effect on the elevation or depression of the fluid contained in it, than so far as it de- termines the inclination of the first portion of the surface of the fluid, when it approaches the sides of the tube : and that the concavity or convexity of the surface, as well as the magnitude of its curvature, depends on this inclination. The frictionof the fluid, against the sides of the tube, may increase or diminish a little the currature of its surface, as we continually observe in the mercury of the barometer : and in this case, the capillary effects are increased or dimi- liished in the same proportion. These effects are also very sensibly modified by the cooperation of the forces derived from the concavity and convexity of two different surfaces. It will appear hereafter, that water may be raised, in a given capillary tube, to a greater height above its natural level in this manner, than when the tube is immersed in a vessel filled with that fluid." It would perhaps be more correct to say in this case "above its apparent level ": for the real horizontal surface must here be con- sidered as situated above the lower orifice of the tube, the weight of the portion of the fluid below it being as much supported by the convexity of the surface of the drop, as if it were contained in a vessel of any other kind. " The fluxional equation of the surface of a fluid, in- closed in a capillary space of any kind, which may be re- ferred to an axis of revolution, leads to this general result, that if a cylinder be placed within a tube, so that its axis may coincide with that of the tube, the fluid will rise in this space to the same height, as in a tube of which the ra- dius is equal to this distance. If we suppose the radii of the tube and of the cylinder to become infinite, we obtain the case of a fluid contained between two parallel vertical planes, placed near each other. The conclusion is con- fixmed in this case by the experiments which were made long ago in the presence of the Royal Society of London, under the inspection of Newton, who has quoted them in ■ his Optics; that admirable work, in which this profound genius, looking forwards beyond the state of science in his own times, has suggested a variety of original ideas, which the modern improvements of chemistry have confirmed. Mr. Haiiy has been so good as to make, at my request, some experiments on the case which constitutes the oppq. site extreme, that is, with tubes and cylinders of a veiy smsU diameter, and he has found the conclusion as correct in this case, as in the former." If indeed we may be allowed to place any confidence in the fundamental principle of an equable tension of the surface of the fluid, an equal length of the line of contact of the solid and fluid supporting in all cases an ON THE COHESION OF FLUIDS. 665 equal weight, these results follow of necessity, which I had already published, in ah essay without any intricacies of calculation what- not (Containing, in its original state, any one mathematical symbol, it is obvious that the inaccuracy of Newton's reasoning did not depend upon any deficiency in his tnatheilia- tical acquirements. " It may be shown by calculation, that the sine of the . inclination of the axis of the cone to the horizon will be veiy nearly equal to the fraction of which the denomi- nator is the distance of the middle of the drop from the ever " The phenomena exhibited by a drop of a fluid, moving, or suspended in equilibrium, either in a conical capillary lube, or between two planes, inclined in a small angle to each other, are extremely proper to confirm our theory. A small column of water, in a conical tube, open at both ends, and held in a horizontal position, will move towards the vertex of the cone ; and it is obvious, that this must ne- cessarily happen. In fact, the surface of the column is concave at both ends, but the radius of this curvature is summit of the cone, and the numerator the height to smaller at the end nearer the vertex than at the opposite '"^'"^^ «he fluid would rise in a cylindrical tube, of adiame- end ; the action of the fluid upon itself is dierefore less at '"^f^qual to that of the cone at tlie middle of the column. the narrower end, consequently the column must be drawn ^^ *' "^° planes, inclosing a drop of the same fluid, form towards this side. If the fluid employed be mercury, its ^'^^ '^^^^ °'^" *" angle, equal to that which is formed by surface will be convex, and the radius of curvature will still '*'* ^"'^ °f ''^^ '^""^ and its sides, the inclination of a plane, be smaller towards the vertex than towards the base of the b'secting this angle, to the horizon, must be the same as cone ; but, on account of its convexity, the action of the *^' °^ '^^ *"'* °f ^^^ <^0"c> '" °'d" that the drop may re- fluid upon itself will be greater at the narrowerend, and the "*'" '" equilibrium. Hauksbee has hiade, SWth very column must therefore move towards the wider part of the S"^*^" '^^''' *" experiment of this Icind, '♦fhich I have com- tube. " This action may be counterbalanced by the weight of the column, so as to be held in equilibrium by it, if we in- cline the axis of the tube to the horizon. A veiy simple pared with the theorem here laid down ; and the near agreement between the experiment and the theorem is amply sufficient to confirm its truth." If the height at which the fluid would calculation is sufficient to demonstrate, that if the length of Stand, in a tube of the diameter of the up- the column is inconsiderable, the sine of the inclination of per end of the Coluilin, be k ; the distance ot this end from the vertex of the cone being it, and the length of the column y, the height corresponding to the remoter end will b6 ■j-^, and the difference of the heights h — -r- =-7- 'Which must be the difference of the the axis must be inversely proportional to the square of the distance of the middle of the column from the summit of the cone ; and this law is equally applicable to the case of a drop of a fluid placed between two planes, which forma very small angle with each other, their horizontal margins being iij contact. Tlicse results are perfectly con- formable to experiment, as maybe seen in the 3 1st query of Newton's optics. This great geometrician has endea- voured to explain them, but Ms explanation, compared heights of the ends of the drop, in Ordef that with that vfhich has been here advanced, serves only to it maj'remain in equilibrium ; but this heio-ht ihow the advantages of a precise and mathematical invts- j^ to y as A to X+y, consequently the axis ligation." p , , , . 1. 1 t I . or tlie tube must be mcliiled to the horizon, Mr. Laplace's superior skill in the most re- . , . . ^ , c , „ ^u .• 1 • ^- ^- >' • u» in an angle, of which the sine is exactly » faned " mathematical investigations might . ° ' J x+y perhaps have enabled him to make still more the denominator being the distance of one essential improvements, if it had been em- end from the vertex, and the numerator the ployed on some other subjects of natural height at which the fluid would stand in a philosophy; but his explanation of these tube, of which the diameter is equal to that phenomena being exactly the same as that of the column at the other end. VOL. n. ^^ 666 ON THE COHESION OF FLUIDS. " This theory affords us also an explanation of another remarkable phenomenon, which occurs in experiments of this nature. If a fluid be either elevated or depressed b«- tween two vertical and parallel planes, of which the lower ends are immersed in the fluid, the planes will tend to ap- proach each other. It is shown by calculation, that if the fluid is elevated between them, each plane is subjected to a pressure, urging it towards the other plane, equal to that of a column of the same fluid, of a height equal to the half sum of the elevations of the internal and external lines of contact, of the surface of the fluid with the plane, above the general level, and standing on a base equal to apart of the plane included between these lines. If the fluid is de- pressed between the planes, each of them will be forced inwards, by a pressure equal to that of a column of the same fluid, of which the height is half the sum of the de- pressions of the lines of contact of the external and internal surfaces of the fluid with the plane, and its base the part of the plane comprehended between those lines." In another part of his essay, Mr. Laphice asserts, that " this force increases in the in- verse ratio of the distance of the planes ;" if this is not an error of the press, or of the pen, it can only mean that the force in- creases as the distance diminishes : for the magnitude of the force is not simply in the inverse ratio of the distances, but very nearly in the inverse ratio of their squares, as I have already observed. " Since it has been hitherto usual with natural philoso- phers, to consider the concavity and convexity of the sur- faces of fluids in capillary spaces, as a secondary effect of capillary attraction only, and not as the principal cause of phenomena of this kind, they have not attached much im- portance to the determination of the curvature of these sur- faces. But the theory, which has been here advanced, having shown that all these phenomena depend principally on the curvature, it becomes of consequence to examine it. Several experiments, which have been made with great accuracy by Mr. Haiiy, have shown, that in capillary tubes of glass, of very small diameters, the concave surfaces of water and of oils, and the convex surfaces of mercury, dif- fer very little from the form of a hemisphere." Mr. Laplace informs us that M.M. Haiiy and Tremery made at his request several experiments, in which the mean ascent of water, in a tube one thousandth part of a metre in diameter, was 13.37 thousandths, and that of oil of oranges 6.74. The product of the diameter and the height of ascent of water is .039371 X. 534 = .021 E. i., which is little more than half as much as I have assigned for this product from the best expe- riments of many other observers. Probably both these experiments, and those of New- ton or Hauksbee, were made with tubes and plates either a little greasy, or too dry ; and Mr. Haiiy might be the more readily satisfied with the first results that he obtained, from finding them agree nearly with those of Newton, which Mr. Laplace wished to com- pare with them. These gentlemen also found the depression of mercury in a tube of the same diameter .2887 E. i., the product being .01 137, instead of .015, which is the ultimate product inferred from Lord Charles Caven-r dish's experiments of a similar nature. The observation of Mr. Haiiy, on the curvature of the surface of mercury in a tube, is also far from being accurate ; Mr. Laplace himself asserts that the angular extent of the surface must fall short of that of a hemisphere more or less, accordingly as the tube has more or less attraction for the fluid ; and it is easy to show that glass has a very considerable at- traction for mercury. The method that I took to ascertain the angle, formed by the surface of the mercury, with the side of the tube, was to- observe in what position the light reflected from it began to reach the eye, and I have every reason to think, from the comparison of a great variety of experiments of difl'crent kinds, that the angle which I have assigned is very near the truth. I have lately repeated my calculations of the depression of mercury, in barometer tubes of considerable diameter, with great ON THE COHESrOK OF FLUIDS. 667 care, and by difteient methods. I had before formed a table, by means of diagrams, which I had actually constructed for each case, upon a sufficiently accurate approximation : 1 have now followed nearly the same steps in calculatint;, bv means of tables of sines and cosines, the precise form of the surface in a variet}' of cases. Beginning from the vertex of the curve, I have determined the mean curvature for every small arc, from the approximate height of its middle point; calcu- lating, with the assistance of a series of diffe- rences, the normal of the curve at each step for the same point, in order to find the trans- verse curvature. I have also pursued, in some cases, in order to confirm these calcu- lations, a method totally different, finding the mass of the quantity of fluid to be sup- ported by the tension of the surface at each concentric circle, and inferring from its mag- nitude the inclination of the curve to the ho- rizon : taking the height of the external cir- cumference of each portion, thus calculated, for the mean height; a supposition which nearly compensates for the omission of the curvature of its surface. But the accumu- lated effect of this curvature becomes very sensible in the vertical height of the surface, and I have' therefore allowed for it, upon tiie supposition of a simple curvature varying with the height; but this correction, for want of including the effect of the variation of the transverse curvature, is still a Ifttle too small; the horizontal diameter of the sur- face, however, agrees extremely well with the former mode of calculation. In order that the results of these investigations may be the more easily compared with each other, and with experiment, I shall insert some spe- cimens, by means of which, if it be required, the curves may be very correctly delineated. 1. Central depression .007. FIRST METHOD, BY THE CURVATUBI» Arc. Horizontal Depression. 0'' 1 2 , 3 4 S 6 7 8 9 10 12 14 10 18 20 3S 30 35 40 45 50 ordinate. .00000 .02444 .04758 .06651 .0S338 .09?91 .11049 .12153 .13146 .14033 .14814 .16177 .17338 .18344 .ly220 .20012 .21603 .22869 ' .23891 .2473! .25420 .25986 .00700 .00721 .00782 .00865 .00968 .01082 .01203 .0)329 .01458 .01589 .01721 .01986 .02354 .02524 .02793 .03063 .03722 .04381 .05033 .05676 .06307 .06911 SECOND M«TH0D, HT THE TENSION. Arc. Horizontal Depression, ordinate. .00 .02 .04 .OS .08 .10 .13 .14 .10 .18 .20 .22 .34 .26 .270s .00000 .02000 .04000 .05999 .07997 .09993 .11985 .13971 .15948 .17908 .19842 .21732 .23550 .25039 .25740 .00709 .00714 .00757 .00830 .00939 .01101 .01303 .0156S .01909 .02353 .02923 .03653 .04530 .05707 .06459 2. Central depression .05. Arc. 00 1 2 3 4 5 6 7 FIRST METHOD. Depression. Horizontal ordinate. .00000 .00349 .00697 .01044 .01388 .01729 .02063 .02402 .02731 .0305S .05000 .05003 .05012 .05027 .05048 .0507 » •05107 .05145 .0518* .05237 €68- 6n ths coflEsroN or fluids. Arc. Horizontal ordinate. Depressloiu 10° .03375 .05291 12 .03995 .05411 14 .04589 .05543 18 .05157 .05696 IS .05697 .05861 90 .06209 .06037 as .07363 .06515 30 .08365 .07035 35 .09214 .07583 40 .09953 .08 146 *i .10581 .08717 SO .11105 .09289 SECOND METHOD. Arc. Horizontal ordinate. Depression. .00 .00000 .05000 .01 .01000 .05025 .03 .01999 .05101 .03 .02994 .05229 . .04 .03982 .05409 •OS .04961 .05644 .06 .05926 .05938 -07 .06873 .06294 .08 .07796 .06718 •Oft .08668 .07212 .10 .09540 .077H3 .11. .10342 .08436 .12 .11080 .09170 .1214 .11173 .09280 .5. Central depression .14. riUST METHOD. Arc. Horizontal Depression, o« .00000 .14000 J .00623 .14027 10 .01234 .14108 15 .01832 .14240 90 .02405 .14421 S5 .02950 .14646 30 .03459 .14911 S5 .03931 .15211 40 .04361 .15541 45 .04749 .15897 «0 •05091 .16270 SECOND METHOD. Arc. Horizontal ordinate. Depressioi .00 .00000 .1400 .01 .01000 .1407 .02 .01990 .1428 .03 .02950 .1464 .04 .03857 .1514 .05 .04686 .1580 .0S5S .05078 .1621 For rcpresen ling the depression, thus de- termined, in a formula capable of expressing it at. once, in terms of the diameter of the tube, I have deduced an approximate determination from the supposit on of a sphe- rical surfiice, and corrected it, by compa- rison with the results of these calculations, so as to agree with them all, without an error of one two thousandth of an inch, in the most unfavourable of the five cases com- pared. The theorem is, first, c = .0\5d dd+. 16 which is nearly half the versed sine of a spherical surface, and then /=-— — |- e — 14.5e', which shows the central depression without any sensible error. I have also found a formula, which ex- presses the difference between the central and marginal depression, so that an obser- vation on the height of the barometer may " be corrected, with equal accursfcy, whe- thCT the elevation of the highest or lowest point of the surface has been measured, pro- vided that the tube be of moderate dimen- sions. This formula is s=: — 5f +100 ° 15{5d-l-100d'J + 18. If d were very large, it would require some further correction, g being ultimately too great by .OO69. The results of these for- mulas are compared, in the first of the fol- lowing tables, with those of the calculations at large ; and in the second, they are re- duced into a form more immediately appli- cable to practice, and are compared also with the table pubhshed by Mr. Cavendish. Diameter. True central depresion. Form. 1. True additi- onal depres- sion at the margin. Form. .5197 .007 .0071 .0821 .0633 .3187 .025 .0150 .0535 .0534 .2221 .050 .0498 .0429 .0432 .1468 .090 .0905 .0313 .0311 .1018 .140 .1396 .0337 .0336 ON THE COHESION OF FLUIDS. 669 3. Central depression .09. Diameter. Observed central True central True marginal depression. depression. depression. .00 .002» .90 .0023 .80 .00-29 •70 .0032 .60 .005 .004 5 ,08«0 .50 .007 .0074 .esgi .«S .0100 .0703 .40 .015 .0139 .0722 .35 .025 .oigs .0753 .30 .038 .02 80 .0798 .25 .050 .0404 .0872 .20 .06- .0589 .0989 .15 .C02 .0S80 .1198 .10 .140 .1424 .1649 .05 .29S4 .3083 By continuing the calculations of the figure of some of these curves to an arc of 90% I have adapted them to the surface of water contained in a cylindrical tube; but in this case, the scale must be supposed to be augmented in the proportion of 1 to i/2. The additional numbers stand thus in ab- stract. 1. Central depression .025. Arc. Horizontal Depression, ordinate. 0° .00000 .02500 10 .06214 .03023 so .10280 .04097 30 .12969 .05340 40 .14793 .06609 50 .15934 .07847 CO .16768 .09030 70 .17299 .10169 80 .17580 .11228 00 .17665 .12203 2. Central depression .05. Arc. Horizontal ordinate. Depression, o« .00000 .05000 10 .03375 .85291 20 .08209 .06037 so .08385 .07036 40 .09958 .08149 50 .11105 .092 89 CO .11991 .10414 70 .12494 .1)492 «0 .12769 .12518 80 .12853 .13470 Arc. Horizontal ordinate. Depression, 0» .00000 .09000 10 .01904 .09042 SO .03662 .09366 SO- .05172 .10337 40 .06397 .11192 50 .07340 .12133 CO .08022 .13109 70 .08475 .14077 80 .O8727 .15017 90 .08804 .15904 Hence, for water, we have the central ele- vation .035355, .07071, and .12728, and the marginal elevation .17258, .19050, and .22495, in tubes of which the diameters are .49964, .36354, and .2490 respectively. The difference of the elevations is expressed neary bv n=: ; — rr. r.N> which is cor- ■' •' V8+10{arent bodies, ■ provided they be less refractive than the pttsm 'employed. It may also serve as a chemical test, for example in essen- tial oils, which when adulterated are generally rendered less refractive ; and a very minute quantity is sufiicient for the experiment. Where the medium is of variable density, this is almost the only mode in which its refractive power can be ascertained ; hence it is of singular utility in exa- mining the refraction of the crystalline lens. (Phil. Trans. 1801.41.) A copious table of the refractive powers of various substances is here inserted. The dispersive powers ot different substances are inferred from similar observa- tions upon tlie fringes which usually accompany, or rather constitute, the boundary of reflection : the author observes that they are sometimes wanting, or even reversed, when the dispersion is equal at different angles of deviation, or when it is greater even with a less deviation, as when oil of sassafras is applied to a prism of flint glass, as well as in many cases of spars with fluids. Solutions of metallic salts in general are found to be very highly dispersive : by weak- ening the solution till the line of separation became colour- less, and then noting the refractive density. Dr. Wollaston has been able to compare the dispersive powers of several such substances with that of plate glass. He has also ar- ranged a number of substances in a table, in the order of their dispersive powers, at a given deviation ; an order ma- terially different from that of their refractive density. A very important observation concludes this part of the essay. Dr. Wollaston observes, that by looking tljrough a prism at a distant crevice in a window shutter, the division of tire spectrum may be seen more distinctly than by any other method, and thai the colours are then only four; red, yellowish green, blue, and violet, in the linear proportions of the numbers IS, 23, 36, 25 ; and that these proportions will be the same whatever refractive substance be em- ployed, provided that the inclination of the prism remain unchanged. In the light of the lower part of a candle, the spectrum is distinguished by dark spaces into five distinct portions. Tlie second paper was On the oblique refraction of Ice- land crystal. It contains a confirmation of the experiments of Huygens on this substance, with ailditional evidence, deduced from the superiority of Dr. WoUaston's mode of examining the powers of refraction. He observes, that Ds. Young has already applied the Huygcnian theory with con- siderable success to the explanation of several other optical phenonaena, and that it appears to be strongly supported by such acoincidcnceof thecalculationideilucedfrom it,wiih the results of these experiments, as could scarcely have happened to a faUc theory. Huygens supposes the undu- lations of light to be propagated in Iceland crystjl in a spheroidal instead of a spherical form ; and infers that the ratio of the sine of incidence to the oblique ordinate of re- fraction mjist be constant in any one section, but different for different planes. Dr. Wollaston observes, that, though we do not fully understand the existence of a double refraction, and are utterly at a loss to account for the phe- nomena occurring upon a second refraction, by another piece of the spar, yet that the ^jlique refraction, when considered alone, is nearly as weH' explained as any other optical phs- nomenon. 680 ACCOUNT OF THE On the first of July, a paper was read, entitled, an ac- count of some cases of the production of colours nothither- to described, by Thomas Youne;, M.D. F.R.S. When a small fibre, such asa human hair, ora silkworm's thread, is held near the eye, while it is directed to a minute or distant luminous object, an ajipearance of parallel fringes of coloured light is produced, the colours succeeding each other in the same order as those of thin plates seen by transmitted light, and being larger and more distant as the diameter of the fibre is smaller. Dr. Young explains this cir- cumstance from the general law of the interference of light (Syllabus, 376.) ; the two portions being here found in the light reflected and inflected from opposite sides of the fibre: and from a single experiment, calculated to determine the angular distance of the fringes, produced by a hair of known magnitude, hedcduces a measure agreeing, within one ninth, with the dimensions of the thin plates as ascertained by Newton, and he considers this experiment both as a con- firmation of Newton's measures, and of the cjiplanation of these coldurs. It appears probable that the colours of all atmospherical hales are produced in a similar manner. The colours of mixed plates constitute another new class of phenomena. When a little moisture, or oil, is scantily interposed between two pieces of glass, proper for exhibiting the common rings of colours seen by transmitted light, we may observe an appearance of other rings much larger than these, which are most conspicuous when they are placed a little out of the line joining the eye and the luminous object. These appear to originate in the interference of two portions of light, passing, the one through the particles of water or oil, the other through the air interposed, and travelling, of course, with ditferent velocities : the explanation is con- firmed by the effect of substances of different refractive den- sities, applied either vrith air intervening, or with each other, *nd the measures agree with the calculation. Dr. Young observes, that he has repeated Dr. WoUaston's experiments on the division of the prismatic spectrum, with success ; and thinks it probable that the separation of the bluish light of a candle, into distinct portions, is a phenome- non of the same kind, as is observable when the light trans- mitted through a thin plate of glass or air is analysed by means of a prism. He also adds, that he has had an oppor- tunity of confirming his former observations upon the very low dispersive power of the human eye in its collective state. A paper on the composition of Emery was communi- cated to the Society by Smithson Tennant, Esq. K.U.S. This substance hits in general been considered as an ore of iron, but it appears to have very little title to that denomi- nation. Mr. Wiegleb conceived that it consisted prlncipsliy of silex, but there appears to have been some mistake with respect to the substance that he examined. Mr. Tennant finds that emery is dissolved with some difficulty in a strong heat by carbonate of soda, and after the subsidence of a little iron , the earth contained in the solution is almost purely argillaceous. This result is exactly similar to Mr. Ktaproth'a analysis of diamond spar or corundum. From lOO parts Mr. Tennant procured 80 of argil, 3 of silex, and 4 of iron, with an undissolved residuum of 3 parts, and a loss of 10; great care having been taken to separate the parts at- tracted by the magnet : some portions however contained almost one third of iron. The hardness of emery and dia- mond spar appears to be equal. The emery used in England is brought principally from the island of Naxos ; it is im- ported in the form of angular blocks, incrusted with iron ore, with pyrites and mica ; substances which usually ac- company the corundum from China. A catalogue of 500 new nebulae, nebulous stars, planet- ary nebulae, and clustersof stars, was laid before the Society, by William Herschel, LL.D. F.R.S. ; and the prelimi- nary remarks on the construction of the heav<;ns were also read. Dr. Herschel takes a very enlarged view of the sidereal bodies composing the universe, as far as we can conjecture their nature : and enumerates a great diversity of parts that enter into the construction of the heavens, reserving a more complete discussion ofeachtoa future time. The first species are insulated stars ; as such the author considers our sun, and all the brightest «tars, which he supposes nearly out of the reach of mutual gravitation ; for, stating the annual parallax of Sirius at 1", he calculates that Sirius and the sun, if left alone, would be 33 millions gf years in falling together ; and that the action of the stars of the milky way, as well as others, would tend to protract this time much more. Dr. Herschel conjectures that insulated stars alone are surrounded by planets. The next are binary side- real systems, or double stars ; from the great number of these which arc visible in different parts of the heavens, and the frequent apparent equality of the two stars. Dr. Herschel calculates the very great improbability, that they should be at distances from each other at all comparable to those of the insulated stars : hence he infers, that they must be subjected to mutual gravitation, and can only pre- serve their relative distances by a periodical revolution round a common centre. In confirmation of this inference, he promises soon to communicate a series of observations made on double stars, showing that many of them have actually changed their situation in a progressive course, the motiun 4 PllOCEEDlNGS OF THE ROYAL SOCIET?. 681 of some bei4ig direct, and of others retrograde. The pro- per motion of our sun does not appear to be of this kind, but to be rather the effect of some perturbations in the neighbouring systeins. Tlie same theory is next applied to triple, quadruple, and multiple systems of stars, and parti- cular hypothetical cases arc explained by diagrams. Some such cases. Dr. Herschel is fully persuaded, have a real existence in nature. The fourth species consists of cluster- ing stars, and of the milky way : the stars thus disposed constitute masses, which appear brighter in the middle, ^ and fainter towards the extremities, being perhaps collected in a spherical form. Groups of stars the author distin- guishes from these by a want of apparent condensation about a centre of attraction : and clusters of stars, by a much more complete compression near such a centre, so as to exhibit a mottled lustre, almost resembling a nucleus. The eighth species consists of nebulae, which probably differ from the three last -species only in being much more remote ; some of them. Dr. Herschel calculates, must be at so great a distance, that the rays of light must have been nearly two millions of years in travsUing from them to our system. The stellar nebulae, or stars with burs, form a distinct species. A milky nebulosity is ne.tt mentioned, which may in some cases resemble other nebulae, but in others appears to be diffused, almost like a fluid : the author is not inclined to consider it as either resembling the zodiacal light of the sun, or of a phosphorescent nature. The tenth species is denominated nebulous stars ; these are stars surrounded with a nebulosity like an atmosphere, of which the magnitude must be amazingly great ; for the apparent diameter of one of them, described in the catalo- gue, was 3'. The planetary nebulae are distinguished by their equable brightness, and circular form, while their light is still too faint to be produced by a single luminary of great dimensions. When they have bright central points. Dr. Herschel considers them as forming a twelfth species, and supposes them to be allied to the nebulous stars, which might approach to their nature, if their luminous atmo- spheres were very much condensed round the nucleus. On the 8th of July, the first part of a paper on the recti- fication of the conic sections was laid before the society by the Rev. John Hellins, B.D. F. R. S. It contained nine theorems for the rectification of the hyperbola, by means of infinite series, one only of which had been before pub- lished, each having its particular advantages, in particular cases of the proportions of the axes and of the ordinatcs, so that they appear to contain a complete practical solution of this important problem, and they are illustrated by a va- riety of examples. The author obseives that Dr. Waring's theorems, for computing the length of the curve, from ordi- VOi« I. nates referred to the asymptote, are in their present form of little use, but might easily be corrected in a manner similar to that which he has pursued. He defers, to a future oppor- tunity, the publication of similar investigations relative to the ellipsis. Observations on Heat, and on the action of bodies which intercept it. By Mr. Prevost, Professor ofNmpasses,1.101, II. 144, 145. Compass for wheelwork, II. 183. Compensation balances, I. PI. 16, II. 195. Compensations in time- keepers, II. 194. Composite column, I. PI. 12. Composition, I. 392. Composition of force, I. PJ. 3, II. 134. Composition of motion, I. 23, PI. 1, II. 28, 131. U Compound agitations, II. 273. Compound bodies, II. 136. Compound capstan, II. 197. Compound confined nio-> tion, II. 139. ,„,f„o.> Compound interest, II. 1 17.- Compound microscopes, II. 78. Compound pendultjms, II. 189. Compound rotations, II. 554. Compound sounds, II, 273.< Compound tides, I. PI. 38. Compound vibrations,I. PI. 2, II. 343. Compressibility, 1.370, II, 378. Compressibility of Hfater, II. 64, 372. Compressibility of water and mercury, I. 276. Compression, I. 135, 136, 220, II. 204, 385. Compression of a columnj I. PI. 9. Compression of the air, II, 220,408. '; Concave lens. If. 72. Concave mirror, I, 416, 471, 11.72, 282,406. Concavoconvex lens, I. 416. Conchoidal epitrochoids, II. 561. Concords I. 391. Condamine. , See Lacon- damine. Contjensation, I, 619, 632, 640, II. 385. Condensation of mixtures, II. 610. Condensation of the air, I. 715, 11. 220,408. Condensed air, II. 265, Sgi INDEX. •Condenser of air, 1. 342. PI. 24, II. 253, 385. Condenser of electricity, I. 681, PI. 40. n. 434. Condenser of force, 11. 182. Condorcet, II. 114. Conducting powers for elec- tricity, I. 666, II. 419, 509. Conducting powers for heat, I. 635, II. 404, 405, 509. Conducting powers formag- netisni, I. 686. Conductor, I. 680. Conductors for liglitning, I. 715, IL 485. Conductors of electrical machines, II. 433. Conductors of electricity, II. 421. Conductorsof heat, II. 404. Conductors of light, 11.983. Conduit, II. 2ir. Conduits, II. 245. Cone, II. ir, 21, 45, 121, 375. Cones at Cherbourg, II. 232. Cones of the stars, II. 326. Confined motion, I. 42. II. 33, 132. Confluence of rivers, II. 824. Confusion of colours, II. 315. Congelation, II. 394. Congelation from electri- city, II. 423. Congelation of quicksilver, II. 520. Conical paradox, II. 133. Conical pendulums, I. Pi. 2. Conical pipes, II. 266. Conical tube, II. 665. Conical vessels, II. 219. Conical wheels, I. 216, II. SOI. Conic sections, 11. 121, 114. Conjugate foci, I. 415, II. 71. Conjunction, I. 527. Conuaissance dcs tcms, II. 373. Connected cylinderSjII. 138. Connected systems, II. 138. Considerations on roads, 11. 203. Consonants, I. 401. Consonni, II. 296. Constellations, I. 753, PI. 36, 37, II. 376. Constrained revolution, II. 188. Construction des grands globes, n. 374. Construction d' un tele- scope, II. 286. Construction of a lunar ob- servation, 11. 357. Construction of equations, II. 121. Constructionofinstruments, n. 145. Construction of the hea- vens, II. 320. Construction of thermome- ters, II. 398. Contact, I. 611, II. 378. Contact exciting electricity, 11. 425. Content of a sphere, II. 21. Contents of the catalogue of references, II. 89. Continents, I. 571, II. 365. Contingencies, II. 117. Continuation, II. 120. Continued sounds, I. 378. Contracting rivers, II. 234. Contraction, I. 640. Contraction of a stream, I. 280. Contraction of moist ropes, IL 380. Contraction of the earth's orbit, II. 334. Contraction of the muscles, II. 427. Contrate wheel, I. 177, PI. 15. Cohverging series, II. 116. Conversion, II. 137. Convex lens, II. 72. Convex mirror, I. 416, II. 72. Conveying boats, IL 235. Conveying coals, II. 202. Conveying heat, II. 411. Cook, L " 565." Cooling, II. 386, 404, 408. Cooling liquors, II. 411. Cooling water, I. 746, II. 395. Cooper, II. 436, 678. Cooper's work, IL 180. Copernican system, I. PI. 38. Copernicus, I. 596, 597, 598, 604, II. 324. Copleian medal, I. 671. Copper, II. 266, 509. Copper plate printmg,!. 1 2 1 . Copper plates, I. 1 18. Coppersmith's work, II. 206. Copying,!. 93, II. 143, 159. Copying letters, I. 121. Copying statues, I. 113. Copying writing, IL 205. Coquebert Montbret, II. 1«2. Coral, II. 519. Corchorus, II. 190. Cordage, IL 186. Cording stuffs, IL 188. Cords, IL 186. Corelli, U. 572, 611. Corinthian column, I. PI. 12. Cork cutting, II, 208. Corn, II, 215. Cornea, I. 447, II. 83, »1I, 530, 587. Corner of a passage, II. Corn fan, I. 345. Corn mills, I. 232, 233, PI. 18, II. 107. Cornwall, II. 484. Coronae, I. PI. 30, IL 317. Coronae round a candle, II. 316. Correction of dispersion, I. PI. 28. Corrections of quadrants, II. 350. Corrections of lunar obser- vations, II. 357. Corrections of observations, IL 354, 355. Corrections of timekeepers, IL 194. Correspondingdistances,II. 348. Corundum, IT. 675, 677, 680. Cosine, IL 15. Cosmotheoros, II. 344. Coster, I. 246. Cotes, I. 249, 253. II. 120, 122, 219, 287, 556,557. B. 1682. D. 1716. Cottages, II. 174. Cotte, IL 39), 146, 452. Cotton, I. 184, II. 184 . . 186, 218. Cotton mill, II. 238. Coudrayc, IL 454. Coulomb, I. 132, 133, 134, 146, 152, 154, 163, 293, 658, 682, 685, 686, 751, PI. 40, IL 166, 241,438. Coulomb on friction, IL 170. Counteraction of gravita- tion, I. 203. Counterpoise for a chain, I. 210. IKDEX. 695 Coantcrpressure of fluids, 1.324, PI. 21,11. 237. Country measure, II. 150. Couraus magnetiques, II. 4.S6. Cours d'architecture rurale, II. 519. Course of rivers, II. 225. Courtivron, II. 205, 230. Cousin, II. 119, 325: Coventry, II. 626. Coventry's scales, I, 112. Covering houses, II, 179. Cowley, II. 117, 123. C. Petr. II. 108. Crabtrie, 11.331. Cracking, I. 643. Craig, II. 120. Crane, I. PI. 17. Cranes,!. 208 . . 210,11.198. Cranks, I. 173, 193, 335, PI. 14, II. 182. Cramer, II. 489. Crampton, II. 678. Crape, I. 186, II. 187. Crape micrometer, II. 289. Crawford, I. 651,750, II. 38), 391, 408, 508. D. 1795. Crayons, I. 95, II, 142. Creation, II. 498. Credibility, II. 117. Crell.II. 110. Cressy, n. 263. Crested fringes, II. 640, 643. Creve, I. 752, II. 427. Crichlon, II. 399. Cricoid cartilage, I. 400. Croesus, I. 238. ■Cromorn pipe, I. PI. 26. Croonian lecture, II. 671. Cropping cloths, II. 188, Crosier, I. 498. iCross attending the moon, II. 304. Cross bows, II, 207. Cross hair, IT. 351. Cross stitch, II. 189. Cross wires, II. 290. Crotalaria, II. 185. Crotch, II. 280. Croune, I. 719, 756. Crow, II. 210. Crown, I. 497. Crown wheel, I. .177, PI. 15. Croy. Due de Croy, II. 566. Cruiksliank, I. 753. Crushing a column, I. 145. Crusius, 11. 126. Crutch scapement, I. 194. Cryptogamous plants, I. 726. • Crystalline gland, II. 599. Crystalline lens, 1. 448,451, II. 82, 311, 525, 530, 552, 592, 597, 605. Crystalline zone, II. 605. Crystallization, I. 628, 642, 695,724,11.321,511. Crystals, I. 445, IL 383, 511. Ctesibius, I. 242, 253, 353, 366, 404, 407. II. 293, 385. Fl. 135. B. C. Ctesiphon, I. 233, 253. Cube, II. 17. Cube in perspective,t.Pl. 8. Cubic equations, II. 115. Cubit, II. 152. Cubit of the Nile, II. 148. Cuff, II. 235. Cuffnells, II. 24L Culinary heat, I. 637, II. 282. Cullen, I. 740. Cultivation, II. 519. Cultivator, II. 212, 213. Cumana, IL 501. Cumberland, II. 147. Cumming, I. 196. PI. 16. II. 191, 195. Cunn, II. 117, Cupping, I. 274. Curr, II. 258. Current, I. 587. Current at the .Straights, I. 708. Current of air, II. 193. Currents, II. 458. Currents of air from elec- tricity, I. 665. Curtius, I. 238. Curvature, II. 22, 120. Curvature of an ellipsis, II. 23. Curvature of an image, I. 419,425, 429, PI. 28. II. 76. Curvature of a rod, I. 139. Curvature of a spring, II, 168. Curvature of a surface, II. 650. Curvature of chords, II. 267. Curvature of the earth's surface, II. 359. Curvature of the sky, II. 313. Curvature of the surface of a fluid, I. 621. Cbrve cutting others, II. 120. Curve described by light, II. 300. Curved surfaces, II. 123, 227, 650. Curve line, II. 9. Curve of equable descent, II. 226. Curve of equal pressure, II. 227. Curves, II. 22, 120. Curves of descent, II. 227. Cusanus, II. 558. Cushion, I. 680. Cuthbertson, I. 342, PI. 24, II. 254, 416, 432. Cutlery, II. 207. Cutting, II. 279. Cutting cloth, 11. 188. Cutting combs, II. 210. Cutting glass, II. 210. Cutting instruments, 1. 227, II. 207, 308. Cutting screws, II. 210. Cutting straw, II. 208. Cuttlefish,!. 95. Cuvier, II. 601. Cyanoraeter, 11. 474. Cycloid, I. 44, PI. 1, 10, II. 34, 51, 122 . . 124, 132, 226, 281, 558. Cycloidal curves, II. 555. Cycloidal paths, I. 527. Cycloidal pendulum. 1. 197, PI. 2, II. 34. Cygnus, I. 496. Cylinder, 11. 17, 40, 123, Double cylinder, I. 67. Cylinder of an electrical machine, I. 680. Cylinder rolling upwards, II. 134. Cylinders, I. 228, II. 135. Cylinder with a thread round it, II. 138, 139. Cylinder scapement, I. 195, Cylindrical vaulting, II. 177. Cylmdroids, II. 20, 122, Sec corrections. Cymbal, I. 401. Dakar, II. 324. Dalby,!!. 301, Dalembert, I. 60, 250, 253, 360, 366, 406, 480, 483, II. 130, 219, 273, 322, 541, 454. B. 1717. D. 1783. Dalibard, II. 415. Dallebarre, II. 285. Dalton, I. 370, 613, 639, 706 . . 708, 753, II. 266, 393, 398, 400, 409, 447, 466, 467, 470, 696 INDtXi Damaged ships, 11. 24S. Damascus sword blades, If. 207. Damen.II. 478. Dancing, H. 563. Danske selskab, 11. 108. Dante, 1.746.3.1265. D. 1321. Danzig. Society «t Danzig, n. 108. Darcy, II. 130, 260. Dark disc micrometer, II. 352. Darkness, 11.474. Dark rays, II. 647. Darrac, II. C77. Darwin, II. 324. R. Darwin, I. 481,11. 515,518. Dasymeler, II. 462. Dates, II. 217. Dati, II. 558. Caubenton, II. 750, 756. B. 1716. D. 1790. Daval, II. 6*3. Davies, II. 503. Da Vinci. See Vinci. Davis, II. 114. . Davison, II. 114. Davis's quadrant, II. 350. Davy, I. 639, 653, 678, 681,720,752,753,11.623. Dawes, II. 148. Day, I. 525, II. 344. Dead beat scKpement, I. 195. PI. 16, II. 193. Dead water, I. 304, PI. 21. Deaf, II. 278. Deafness, 11. 271, 430, 67 1. Deal, II. 86. Debility of sight, II. 316. Debrosses, II. 275. Decade, II. 111. Decagramme, II. 162. Decametre, II. 152. Decalitre, II. ,247. DeCaus,II. 247. Decay of lightj 11; 394. Decay of sound, I. 376, II. 266,539. • Deception of sight, II. 314. Dechales, II. 119, 224. Decharges, II. 264. Decigramme, II. 162. Decilitre, 11. 152. Decimal arithmetic, II. 4. 124. Decimal fractions, I. 108. Decimetre, II. 152. Decistere, II. 162. Declination, I. 536, 542, PI. 35. Declination of columns, II. 173. Declination of falling bodies, II. 358. Dccliiiatiou of the com- pass, I. 691, PI. 41. Declination in London, II. 44-3. Declination of the stars, II. 844-, 355. Declivitiesof mountains, II. 498. Decomposition, II. 291. Decomposition of water, I. 672. DecompositiSn with light. I. 435. Decrement of heat, II. 404. Decrements, II. 7. Decremps, II. 127. Decyphering, II. 143. De Dominis. See Dominis. Defects of sight, I. 450. Definition, 1. 18. Deflective forces, 1. 33. Defondeur, I. 246. Degaulte,II. 445. Dcgeer, 1. 750, 756. B.1720. D. 1778. Degnguet, 11. 217. Degrees, I. 104, 569,11.358. Degrees of a spheroid, II. 363. Delairas, II. 12R. Delambre,II. 361. Delarive, II. 267. Delaunay, II. 435. Delaval, 1.481, II. 321. Delft ware, II. 216. Delineator, II. 284. Delisle, II, 324,366,386. Delius, II. 211. Delia Torre, II. 493. Deloys,II. 127. Delta, I. 721. Deltoid muscle, L 128. Deluc,1. 706, 709, 7 10, 750, 751, II. 128, 367, 388, 390, 391, 393, 398, 418, 446, 406, 469 . . 473, 497. Dekre's hygrometer,I.P1.41. Deluge, II. 495, 497, 498. Deluge, n. 4196. Demetrius Phalcreus, I. 592. DemOcriWs, t. 2S8, 253. 744, 745, 756. B. 470. D. 361. B.C. Demoivre, I. 249, 253, II. 113, 117. B.1667.D.1754. Deijiolition, 1. 234, II. 216. Denarius, II. 162. Dendcra, II. 377. Dendrometer, I. 107, II. 156, 351. Denebola, I. 497. Denier, II. 161. Denmark, II. 367. Royal Society of Denmark, I. 108. Densities, II. 503. Densities of the sun and planets, I. « 565." Density, I. 610. Density of air, II. 404, 471. Density of brine, II. S88. Density of the atmosphere, I. PI. 19. Density of the earth, I. 575, II. 364. Density of the moon, II. 336. Density of the planets, II. 333,539,859,372. Density of water, II. 389. Deoxidation, II. 323. Deposition, I. 707, II. 396. Depositions of the sea, II. 497. Depression of liquids I. PI. 39. Depression of mercury, II. 381. Depth of a river, 225, 236. Depth of the sea, I. 6791, 581, II. 255, 343. Depth of vessels, II. 396. Derham, I. 201. 370, II. 107, 125, 191, 325, 457, 541. B.1657.D. 1735. Derivations, II. 119. Derwent lake, II. 458j' " Desaguliers, I. 129, 181, 250, 253, 360, II. 126, 148, 165 . . 167, 171, 246, 414. B. 1603. D. 1742. Design, II. 142. Descartes, I. 29, 248, 253, 474, 475, 483, 747, 74d, 756, II. 112, 272, S06, 323, 523, 527, 557, 558. B. 1596. D. 1650. Descent, II. 181. Descent in air, II. 226. Descent in chords of a circle, I. 43, PI. 2, II. 33. Descent in curves, I. PI. 2. Descent in water, II. 227. Descent of a rod on a cy- linder, II. 138. Descent of ground, II. 49B. Descent of spheroid*, II. 138. INDEX. 697 Descent of water, 11. 222. Descent on a given surface, II. 33. Descent on elastic surfaces, II. 133. Descent to a centre, II. 29. Description dcs couraus magnetiques, II. 436. Description d'un tliermome- trc, II. 386. Description of curves, II. 120. Description of equal areas I. PI. 1, II. 31. Dcsfontaines, I. 727. Dcslandes,II. 370. Despiles, II. 142, 217. Deto, II. 154. DetrusioQ, or distrusion, I. 135. Deutscher Mercur. II. 474. Deviation of ligfo, II. 71. Dew, II. 301, 465, 474. De Witt, II. 204. Diagoiud.I. PI. 1,11. 13. Diagonal diviisions, II. 155. Diagonal scale, I. PI. 7. Dialling, I. 538, PI. 35, II. 348. Dial plate, II. 194. Dials, II. 318, 375. Diameter, II. 9. Diameters of the planets, II. 372. Diamond, L 145, 412, II. 509. Diamonds, ^I. 217, 293. Diapason pipes, 1. 402, PI. 26. Diaplianometer, II. 282, •474. Diaphragms of a vessel, II. ■ -223. Diusporomctcr, II. 232. : Dibbling, II. 218. Dickson, II. 519. DIcqucrowc, II. 645. , VOL. II. Diclionnaire des arts et me- tiers, II. 141. Dictionnaire des origines des inventions, II. 217. Dictionnaire des sciences naturcUes, II. 129. Dictionnaire d'histoire na- turelle, II. 503. Diek, II. 284. Dictcrich,ll. 325. Differential method, II. 119. Differential thermometer,!. 649, Pi. 39, H. 389. Diffraction, I. 437, II. 310, 316, 621,642. Digester, 11.410,412. Digges, I. 474, II. 144. Digging, 11.211. Digging in water, II. 232. Digits, I. 530. Dijon, II. 110. D'Iuarre,lI. 416. Dikes, I. 312, 11. 118, 233. Dilatation of air, II. 408. Dilatations of pipes, 11.299. Diminishing friction, II. 200. Diminution of columns, II. 173. Diminution of degrees, II. .S58. Diminution of the sea, II. 496. Diminution of the sun, II. 339. Dinocrates, I. 239, 253. Fl. 300. B. C. Diogenes I.:iertiiip, II. 216. Dionaca, I. 724. Dionis du Sejour, II. 337, 34 4,416. Diophantus, I. 243, 253, IT. • 115. Fl. 156. Dioptrical fonmdac, 11.287. Dioptric glasses, H. 231. Dioptrics, I. 414;, H.tC^2C0. 4 X Dioscorides, 1. 746, T56.F1. 23. Dip, I. 692, PI. 41 . . 43, II. 299, 301, 302,355, 440, 443. Diplantidian telescopes, II. 351. Dipping needle, I. 689, PI. 41,11. 444. Direction, II. 27. Direction of balloons, II. 256. Direction of motion, I. 20. PI. 1. Direction of sounds, II. 575. Direction of the electric current, I. 669. Direct motions, I. 527. Direct tide, I. 579. Disappearance of heat, II. 408. Discharge of air, II. 531. Discharge of electricity, I. 666, II. 422. Discharge of fluids, I. 279, II. 61,222. Discharge of pipes, I. 293, PI. 20. II. 222, 223, 225. Discharger, I. PI. 40. Discharging electrometer, « II. 434. Discords, I. 394,11. 571. Discourse on local motion, II. 130. Discs of planets, I. 527. Diseases, I. 740. Diseases of plants, I. 730. Disengaging horses, II. 203. Dished wheels, I. PI. 18. Dispersion of light, I. 463. 11.77,282,287,295,320, 637. Dispersion of the eye, II. 312, 313, 5«4, 638. Dispersive pouers, II. 298, J!*9.> 50S^ 679. Drsplacerhent of rtie eqtia> tor, II. 342. Dissimilitude of meridians, II. 841. Distance, II. 9. Distance of objects, I. 45S. Distance of the sun, de- fluced from the theory of gravity, II. 310. Distances of the planets, I. 506, PI. 32. II. 333, 372. Distances of the Satellites, 11.373. Distances of the starsj II. 329. Distemper, I. 95. Distilling, II. 396, 41S. Distinctness of t^eiwopCI, II. 289.1 .1 , .:>iv.a[ Distinguisher of electricity, II. 434. Distorted iris, II.>B03'. • Distribution of electricity, I. «61. r: \- ' Distribution of magnetism, I. 668. Distribution of pressure,!. 44, 134. Di:>tribution of water, II. 235, 245. Distribution of weight; H. 211. Disturbing force of the rofe, I. 520. Ditton, II. 119,219, 381.. I^iurnal variation, II. 442, 443. Divergence of i streatn bf air, II. 534; Divergence of light, t. 420. Divergence of soimJ, 1. 37!i. II. 265, 338. Divergence of unduUcioat, II. 619; 620. Divergence of wavcBy I. JEt. ,20.: Divided eye glass. I. 4SS, PI. 23, II. 290. .698 INDEX, Divided object glass, 1. 432, n. 289. Divided speculum, I. 433. Dividingengine,!. 105,112, II. 145. Dividing stones, II. 209. Dividing thermometers, 11. 398, 399. Diving, II. 243. Diving bell, I. 246, 342, PI. 24,11.255. Diving boat, II. 256. Diving machine, II. 244. Divining rod, II. 480. Divisibility, I. 607. Divisibility of matter, II. 378. Division, II. 2, 3. Division, I. 227, II. S06. Division of a circle, II. 121 . Division of a magnet, I. > . (93. Division of an angle, II. 149. Division of labour, 1. 244. Division of the quadrant, II. IIB, 145. Division of time, II. 349, Division without sharp in- . etruments, II. 209. Divisors, II. 116. Diwisch, II. 482. Dixon, II. 362. Dobson, II. 467. Docks, II. 233. Dodart, II. 550. Dodgson, II. i252. Dodson, I. 749, n. 113, . 117. Dog, n. 516. DoUond, I. 431, 478 . . 480, 483, 602, 604. Doilort sea, II. 495. Dolomieu, II. 492, 494, Dome, I. 164, PL 12, U. . 43, 175, 176. Dominant, I. 393, II. 570. Dominis. De Dominis, I.^ 474, 483, 11. 280, 306. B. 1625, D. 1664. Donati, II. 366, 496. Donndorff, II. 416. Door, I. 148. Doppclmaier, II. 326, 328, 422. Doria, II. 610, 611. Doric column, I. PI. 12. Dornavius, II. 478. Dort, n. 495. Double axis, I. 67. Double balance, II. 194. Double capstan, I. PI. 4, II. 135, 197. Double capstan crane, II. 199. Double concave lens, 1. 416. Double cone, I. PI. 3, II. 133, 134, 138. Double convex lens, 1. 416, Double curvature, II. 650. Double images, I. 441. Double lights, I. 464,'Pl. 3, 11.316,624,633,639. Double magnifier, I. 431. Double microscope, II. 78. Double pen, II. 144. Double pendulum, II. 139. Double pfefraction, I. 445. PI. 29, II. 309. Donbler of electricity, I. 682, PI. 40, II. 434. Double shot, II. 263. Double stars, I. 494, 11. 328. Double sun, II. 301, 681. Double touch, I. 693. Double vision, I. 453, II. 315. Doabling, II. 186. Doubling spar, II. 310. Dough, II. 216. Douglas, II. 497, 516. Dover and Calais, II. 495. Downs, II. 233. Diachm, II. 101. Drachma, II. 162. Drag, II. 203. Dragging hay, II. 202. Dragon, I. 496. Drags, II. 203. Draining, I. 328, II. 213, 249, 250. Drain plough, II. 212, 213. Drains, II. 235. Draught, I. 154, 215, II. 165, 181. Draught of a chimney, I. 345. Draught of carriages, II. 201. Drauglitsman'sassistant,II. 142. Drawbridge, II. 178. Drawing, L 93, 94, II. 142, 158. Drawing in perspective, I. PI. 7,8. Drawing off liquors, 11.251. Drawing piles, II. 216. Drawing ships, II. 213. Drawing weights, II. 200. Drawing wire, II. 205. Dray, I. 212, II. 172, 200. Dray cart, II. 202. Drebel, I. 649, 747, 756. B. 1572, D. 1634. Drebelian thermometer, II. 389. Dresdnisches raagazin, II. 109. Dressing corn, II. 215. Dressing hemp, II. 185. Dressing stuffs, II. 188. Drill, II. 211. Drill plough, II. 212. Driving piles, II. 206, 207. Drop, I. 620, 624, PI. 39, n. 380,655,656,664. Drop between plates, I. £25, II. 655. Drop in a conical tube, II. 665. Drop of water, II. 382, 396. Drosera, I. 724. Drum, I. 101, II. 268, 374. Drum and axle, I. PI. 3. Dryander, II. 105. Dryness, II. 476, 477. Dry rot, II. 180. Dubois, II. 416. Ducaila, II. 375. Ducarln, II. 384. Duck, II. 184. Du Crest, II. 388.. Ductility, 1.141,629,11.378. Dudin, II. 159. Dufay, I. 670, 750, 756, II. 283. B. 1698, D. 1739. Dufrcsnoy, II. 142. Dugdale, II. 233. Duharael, II. 107, 125, 158, 168, 179, 186 . . 189, 205 . . 208, 211, 213, 240, 242, 513. H. L. Duhamel, B. 170O, D. 1782. J. B. Duhamel, B. 1624, D. 1706. Duillier, II. 370. Duke of Bridgwater, 11.197. Dulcimer, I. 398. Duraaitz, II. 240. Dumb, II. 278. Dundas. Lord Dondas, II, 259 Dunkirk, II. 233. Dunn, II. 442. Duodcciraal arithmetic, II. 40, 116. Duplex scapement, I. 196, PI. 16. Duplicate proportion, 11. 125. Duration of the world, II. 332. Dusdjour. See Dionis. Dutch camels, II. 238. Dutch Society, II. 109. INDEX. 699 Dutch weights, 11. 160. Dutens, II. 105, 217. DUtour, 1. 480, 483, II. 417, 653, 654. I Dutrone, II. 519. Duverncy, II. '271. Dying, II. 188. Dynamoraeter,I.127,II.105. Eagle, II. 311. Ear, I. 387, PI. 25, II. 271, 574. Earnshaw, I. 197, 198, PI. 16, II. 191, 195. Earth, I. 161, 507, 720, II. 172, 220, 358, 371, 372. Earth as a planet, II. 333. Earthenware, I. 223, II. 217. Earthquakes, I. 716, 717, 745, II. 490. Earths, II. 677. Earth's axis, II. 364. See corrections. Earth sinking, II. 495. Earth's motion, II. 358, 376. Earth's radius, II. 364. See corrections. East, 1. 500. Easter, II. 349. Easterly wind, I. 702. See corrections. Eastern le.irniiig, I. 236. ' Ebhing well, II. 479. Eberhard, II. 110, 126, 320, 376, 436. Ebert, II. 127. Ebullition, II. 396. Eccentricities of the pla- nets, II. 372. Eccentric wheels,!. 178.PI. 15. Ecclesiastical music, 1. 404. EcJiO, I. 374, II. 542. , Echometer, II. 279. Echos, II. 266. .' Eckhardt, 11. 211, 237. Eckstrand, II. 496. Eclipses, I. 528, PI. 34. 11, 345, 374. Fclipsts of Jupiter's satel- lite?, II. 346. Ecliptic, I. 503, 524, 11. 334. Ecole polytechnique.Elcvcs do I'ccolc polytechnique, II. 280. Economy of heat and cold, II. 410. Economy of motion, II. 182. Ecphantus, II. 377. Eddies, II. 2-22. Eddystone, I. 159, PI. 11, II. 174. Edge tools, II. 207, 208. Edgcworth, I. 306. ' Edifices of particular kinds, II. 180. Edinburgh, II. 399. Society of Edinburgh, II. 108. Edinburgh medical essays, II. 312. Ed. tr. II. 109. Edward, I. 354. Edwards, II. 157. Effect ot a stream, II. 62. Effect of macliines, II. 54. Effects of cold, II. 386. Effects of heat, I. 639, II. 385, 399. Effects of light, II. 320, 321. Effects ofmachincs, II. 141. Effects of sound, I. 378,11. 269. Effervescence, II. 440. Eft;, II. 516. Egelin, II. 415. Egg, I. 734. Eggers, II. 489. Eggs, II. 424. Egypt, I. 236, II. 498. Egypte, II. 111. Egyptian measures, II. 148. Egyptian system, I. PI. 38. Egyptian year, I. 639, II. 349. Eichen, II. 480. Eimcr, II, 155. Eintraechtige frcunde, II. 111. Eisenschmidius, II. 358. Elastic bar, II. 48. Elastic bodies, I. 75, II. 136. Elastic curve, II. 136, 650. Elastic fluids, II. 60, 260, 396. Elastic force, II. 268. Elastic gum, I. 142, 145, II. 246. Elastic instruments, II. 274, Elasticity, I. 28, 137, 628, II. 268, 379. Elasticity of steam, II. 897, 400. Elasticity of the air, I. PI. 19, II. 220. Elastic joints, II. 138. Elastic medium, I. 654, II. 321. Elastic pipes, I. 291. Elastic plates^ I. S85. Elastic rings, I. 385. Elastic rods, I. 384, 11. 67, 83. Elastic rods bent, I. PI. 9. Elastic springs, II. 136. Elastic stones, II. 383. Elastic substances, ll. 46. Elastic surfaces, II. 133. Elden Hole, II. 496. Elective attractions, II. 659. Electrical apparatus, II. 430. Electrical attraction and re- pulsion, I. 678, II. 419. Electrical balance, I. 683, PI. 40, II. 433. £Iectrrcal crystals, II. 435. Electrical fishes, 11. 435. Electrical forces, II. 417. Electrical heat, II. 423. Electrical kite, 11. 482. Electriral lamp, If. 423. Electrical tight, I. 435,670. Electrical machines, I. 680. PI. 40, II. 43J, .133. Electrical mists, 11. 48?, Electrical polarity, II. 419. Electrical pressure, I. 663. Electrical pump, IT. 431. Electrical tliermometer, II. 423. Electric current, II. 421. Electric effluvia, II. 614. Electric fluid, I. 659. Electricity, I. 17, 685, 75a, II. 414, 437, 465, 479, 431,513,519. Electricity in equilibrium, I. 658. Electricity in motion, I. 668. Electricity of a compass, II. 445. Electricity of the air, II. 481. Electrics, I. 673, II. 419. Electrified spheres, I.PI. 39. Electrometers, I. 682, PI. 40, II. 420, 433. Electromicrometer,II. 434. Electrophorus, I. 680, PI. 40, II. 432. Electroscope, II. 433, 485. Elements, II. 377, 520. Elements and practice of naval architecture, II. 24). Elementsofrigging,II. 239. Elements of the planetary motions, II. 371. Uements of the solar sys- tem, II. 372. Elevation of a projectile, I, 39. 700 INDEX. EUvation ol liquids, I. 6^, PI. 39,11.651. Elevatioas, I. 572, PI. 38. Elkiiigton, II. 935. Ell, II. 150, 153, 154. Ellicott, I. 200, II. 390, 391. Elliot, II. 2ri. Ellipsis,I. 37,47,116,375, PI. 9, II. 23, 122, 562, (S81. Elliptical parallax, H. 357. Elliptic coinpusscs, II. 144. Ellipticity, II. 316. EUipticity of the earth, I. 569, II. 360, 3S3. Ellipticity of the planets, II. 372. Elliptic motion of a pen- dulum, I. 47. Elliptic orbits, I. 504. II. 31. Elliptic spliLToids, II. 339. Elliptic vibrations, I, PI. 2. Ellis, II. 537. Elm, II. 509. Elongation, I. 527. Elongation of Vacuus, I. PI. 34. E. M. II. 110. E. M. A. II. 1 10. Emanations of odorous bo- dies, II. 397. Enibaiikmeots, I. 312, PI. 21, II. 233. Embossing cloth, II. 188. Kmbioidery, II. 189. Emerson, II. 113, 11,9, 125, 130, 169, 174, 2,19, 370, 557. B. 1701, "D. 1782. Eraery, I. 195. II. G80. Emission of ligjit, I. 436, E. M. M. II. 110, 184, Empedoclcs, I. 472, 483, ?44, 745, 756. B. 473, D. 413. B. C. E. M. PI. II. 110. Encaustic pauitings, I. 97. II. 142, 180. Enc. Br. II. 111. Encroachraants of tlie sea, I. 721. Encyclopaedia Britannica,I. 60, II. Ill, 607. Encyclopedic, I. 250. Encyclopedic raethodique, II. 110. Endless chain, II. 219. Energy, I. 78, 225. U. 51, 52, 140. Enfield, II. 128. Engelman, II. 478. Engines, II. 140. England, II. 367, 447. England once a peninsula, U. 495. Englefield, I. 639. II. 269, 308, 341, 352, 373, 594, 674. English foot, I. 111. English philosophers, I. 7. English standards, II. 147. EngUsIi weights, II. 100. Engramelle, 11. 275. Engraving, I. 93, 118, 216, II. 29, 153. Engraving plate, II. 208. Engravings, II. 157. Engyiueler, 1. 107, II. 156, £51. Entertainment, II. 181. Entoiiiology, II. 516. Eolipiie, n. 257. Epact, 1. 54i, n. ai^, Ephcmerides acarlejjiiac Cacsareac, II. 107. Ephemerides astronomicac, 11.373. Ephemerides soc^otatia Pa- latinae, IL -1-17. Ej^cureuns, I. JC, 598- Epicurus, I. 240, 253, 604, 745, 756. B. 342, D. 270. B.C. Epicycles, I. 594. Epicycloid, U. 122, 247, 309, 558. Epicycloidal surface, II. 55 • Epicycloidal teeth, I. PI. 15. Epicycloids, II. 344. Epiglottis, I. 400. Epigonus, II. 567. Epistolae ad Velserum, II. 331. Epitrochoid, II. 553. Epoch, II. 349. Epochs of planetary mo- tions, II. 371 . Eprouvette, I. 134. Equal areas, I. PI. 1. Equalisation of force, I. 193. Equalising discharge, II. 245. Equal quantities, II. 1, 2. Equal temperament, II. 554- Equal times, II. 27. Equated clocks, I. 538, II. 194, 347. Equation of time, I. 537, PI. 35, II. 347. Equations, II. 114, 121, 146. Equations of cycloidal curves, II. 560. Fxiuator, II. 373. Equatorial instruments, II. 353. Eqiutorial micrometer, II. 290. Equilateral triangle, II. 10. Eqniljhr^uiji, I. 59. PI. 3, 0, II. 37. lijdrostatic equilibrium,, II. 57. Pneu- matic equilibrium, II. 60. Stability of cquilibi;iuni, 1. 261. i Equilibrium of.i^alniuls, L 61. Equilibrium of a revolving fluid, II. 339. EquiUbrium of compound bodies, II. 134. Equilibrium of elastic bo- dies, II, 136. Equilibrium of elastic sub- stances, II. 46. Equilibrium of electricity, I. PI. 39. Equilibrium of floating bo- dies, 11. 220. Equilibrium of fluids, I. PI. 19. Equilibriuraof gasesji. 270. Equilibrium of gravitating bodies, II. 339. Equilibrium of heavy sys- tems, 11. 135. Equilibrium of liquids, 11. 219. Equilibrium of radiant heat, I. 637. Equilibrium of systems, II. 134. Equilibrium of the sca, II. 342. Equinoctial tides,, I. 577, II. 370. Equinox, I. PI. 54. Equisetum palustre, II.23.>. Equitangcntial curve, II. 556. Eratosthenes, I. 501, 593' 604. Erect vision, II. 313. Erfurt, II. 109. Eridanus, I. 498. Eruption of a moss, II. 496. Eruption of mud, 11.498. Eruption of wutcr«, II. 479. Eruptions of volcanos, II. 49-''. . .- Erxlebeu, II. IM), 128. Escapements, II 193. Eskinard, I. 4i70, II. 280, 323. INPEJf. 701 Essai de batir sous I'eau, If. ^3U. Essay on signals, II. 113. Essay on tune, II. 273. Essay on windmills, 11.239. Essays on Gothic aicliilec- ture, II. 172. Essential properties of mat- ter, I. 605. Esteve, II. 272. Etching,!. 119,11.158,218. Ether, II. 338, 377, 400 . . 402,614. Ether, II. 653. Ethereal mediuiu,I.615,630 Ethereal vibratioiis,II. 541. Etherial vapour, II. 397. Etna, II. 493. Etres organises, IT. 497. Euclid, I. 239, 253, 473, 483, II. 556, 557. Fl. 300. B. C. Euclides,II. 117. Eudiometry, II. 462. Eudoxus, I. 239, 253, 604. Euler,I. 249, 250, 253, 361, 366, 384, 406, 407, 459, 479, 480, 483, 522, 531, 602, 604, 749, 756, II. 112, 114, 119, 123, 126, 129, 165, 166, 239, 260, 265, 269, 272, 275, 288, 895,340, 341,373, 638, 541 . . 543, 547 . . 549, 550, 614, 623, 651, L. Euler, B. 1707, D. 1783. J. A. Euler, II. 236, 417, 624, 671. Eumenes, I. 98. Euphon, II. 275. Evanescent quantities,!!. 16 Evaporation, I. 641, 706, II. 396, 408, 432, 424, 427, 458,464,467. Evaporation ofice, II. 396. Evaporation of mercury, II. 322. VOL. II. Evaporation of snovr, II, 395, 396. Evaporator, II. 411. Evelyn, II. 158. Evolute, II. 22. Evolutes, II. 120. Exauien de la pouiire, II. 260. Examen des ouyragos faites pour determiner la figure de la terre, II. 359. Excitation, II. 421. Excitation of electricity, I. 425. Excitement of heat, I. 632. Excise, II. 510. Excretions of !)lants,II.614. Exercise, II. 181. Exhalations, II. 499. Exhaustion, II. 385. Eipanduig fluids, II. 257. Exj)anse of the universe, I. 489. Expansible fluids, II. 379. Expansion, I. 640. II. 385, 509. Expansion of cold water, II. 389. Expansion of pendulums, I. 199. Expansion of spirits, 11. 393 Expansion of the air, I. PI. 24. Expansion of water, II. 392 Expansions, I. 646. Expansions of gases, II. 393 Expansions of liquids, II. 391. Expansions of solids, II. 391 Expectations, II. 117. Expense of gunpowder, II. 261. Experiment on elasticity, I. 28. Experiments and observa- tions on light and co- lours, II. 321. Experiments of the society for the advancement of naval architecture,!I.a28 Experiments on magnetism, II. 439. Explosion, II. 673. Explosion in the air, II. 499. Explosion of a furnace, II. 494. Explosion of a steam en- gine, II. 259. Explosion of grindstones, II. 383. Explosions, I. 717. Explosions of electricity, n. 422. Explosive letters, II. 276, 277. Exponential quantities, II. 8, lie. Expressing a number of facts, II. 347. Extension,!. 135, 136, 138, 222,607,11. 205. Extension by percussion, II. 205. Extension of a column, I. PI. 9. Extension of light, II. 320. Extension of threads, II. 168. Extinction of fires, II. 410, 413. Extinction of heat, II. 484. Extinction of light, I. 464, II. 639, 642. Extraction of roots, II. 115. Extraction of the crystal- . line, 11.592. Eyck. Van Eyck, 1. 96, 246, 253. B. 1371,D. 1441. Eye, I. 447, PI. 80, II. 82, 311, 530, 578, 638, 680. Eyeglasses, II. 288. Eyepiece, I. 430, PI. 28, II. 80, 289. 4 r Eyes of animals, II. 311. Eyes of birds, II. 601. Eyes of insects, II. 601,678. Eytelwein, I. 365. II. 130, 148, 154, 230. Fabre, II. 225, 250. Fabri, II. 380. Fabricius, I. 736, II. 331, 516. Fabricius abAquapendente, 11.310. Fabroni, I. 752. Faculae, 11. 331. Faenza, 11. 217. Fahrenheit, I. 632, 648, IT, 386. Fair, II. 148, 160. Fairy rings, II. 483. Falck, II. 257. Falconer, I. 746, II. 239. Fall, II. 131. Fallacy of sight, II. 313. Fallen mttctjrs, II. 501. Fall in a Ouid, I. 268. Fall in air, II. 226. FaHing bodies, II. 228, 339. Falling stars, II. 365, 50O. Falling stone, II. 358. Fall of a heavy body, I. 30, 111. Fall of a feather, I. 57. Fall of bodies, II. 342. Fall of earth, II. 498.- Fall of leaves, I. 730. Fall of rain, II. 477. Fallows, II. 213. • Falsetto, II. 550. Fan for corn, I. 345, II. 215. Fannius, I. 353, II. 160. Fans, II. 252. Farina, II. 512. Farm buildings, II. 174, Farmer's calendar, II. 519. Fascination, II. 518, 519. Fass, II. 155. Fasting, II. 516. 702 INDEX. Fata Morgana, I, 441, II. 301, 314. Faujas deSt. Fond, II. 494. Faurc, II. 431. Fecundation of plants, II. 514. Felbiger, II. 446, 485, 489. Felice, II. 380. Felling timber, II. 168. Felt, 1. 186. Felting, I. 189. Felts, II. 189. Fens, II. 495. Fenwick, II. 141. Ferber, II. 494, 497. Fer de la Noverre, II. 234. Ferguson,II. 112, 127, 130, 325, 416. Fermat, I. 475, 598, II. 377. Fern, 11. 512. Fernel, II. 360. Fernelius, II. 363. See cor- rections. Fcrrein, II. 550. Ferro, II. 494. r«rroni, II. 116.119. Ferry boat, II. 242. Fibres, II. 184, 680. Fidler, I. PI. 8. Field glass, I. 430, PI, 28. Field of a micrometer, II. 289. Field of view, II, 80. Field of vision, II. 575. Fiery meteors, II. 500. Figure of fluids, II. 380. Figure of gravitating bo- dies, 11.339. Figure of secants, II. 374, Figure of sines, II. 25, 122, 545, 558. Figure of snow, II. 478. Figure of tangents, II. 122. Figure of the eartli, I. 568, ri. 34, II. 358. Figures, II. 124. Figures of the planets, II. 332. Files, II. 207 . . 209. Filing, II. 210. Filtering wells, II. 246. Filters, II. 246. Filter with sand, II. 246. Finger board, II. 274. Fir, II. 509. Fire, I. 037, II. 175, 383. Fire arms, II. 202, 260. Fire balls, II. 411, 499, 501. Fired gunpowder, 11. 260. Fire engines, I. 334, 353, PI. 23, II. 247, 263. Fire escapes, II. 181. Fire in the Apennines, II. 499. Fire ladder, II. 175. Fire places, II. 410, 412. Fires, II. 490. Fires. Extinction of fires, 11.410,413. Fire ship, II. 242. Fire wheel, II. 257. Firmness, II. 383. First movers, 11. 164. Fir wood, II. 47. Fischer, II. 217. Fish, II. 229, 291. Fishery, II. 519. Fishes, I. 304, 497, 735, II. 271,311,312. Fish hooks, 11. 208. Fishing nets, II. 189. Fissure in the moon, II. 346. Fits of light, II. 616. Fixed air, II. 513. Fixed ecliptic, I. 503,P1.32. Fixed fire, II. 405. Fixed instruments, II. 352, Fixedness, 11,396. Fixed plane, If. 141. Fixed stars, I. 187, PI. 36, 37,11. 325. Fixing instruments, II. 354. Flageolet, I. 402. Flails, II. 215. Flakes of snow, 1. 444. Flame, I. 16, II. 291, 383, 419. Flamsteed,I. 601, 604, II. 324. B. 1646, D. 1719. Flat, II. 570. Flat arches, II. 176. Flaws, II. 316. Flax, I. 183, II. 185. I'lax of New Zealand, II. 185. Fleecy hosiery, II. 187. Flemish weavers, I. 244. Fletcher, II. 144, l6l. Fleurieu, II. 192. Flexibility, II. 383. Flexible bodies, 11. 138,267. Flexible fibres, I. 180, II. 184. Flexible knives, II. 208. Flexible roads, II. 181. Flexible threads, II. 136, 138. Flexible vessfels, I. 269. Flexure, 1. 135, 138, 145, 147, 627, 629. Flexure in cooling, II. 404. Flexure of a bar, II. 48. Flexure of a column, II. 46 . . 48. Flexure of columns, II. 173. Flexure of columns and bars, I. Pi. 9. Flexure of compound bars, II. 389. Flight of birds, II. 256. Flint glass, II. 381. Flints, II. 263, 498. Floatboards, II. 23C. Flo.iting balls, II. 382. Floating boats, II. 243. Floating bodies, I. 266,624, PI. 19, 11. 59, 220, 656. Floating bridge, II, 242. Float regulator, II, 245. Floodgates, 1. 313, PI, 21. Floor, I. 143. Floor paper, II. 190. Floors, II. 178. Flour, II. 215. Flower, I. 726, II. 512. Flue, II. 410. Fluents, II. 120. Fluid, I. 259. Fluidity, II. 381, 383, 396. Fluidity of sand, II. 220, 232. Fluidity of sand and earth, 11. 173. Fluids, I. 257, II. 227,405. Motions of fluids, II. 57. Fluoric acid, I. 120. Fluor spar, I. 486. Flute, I. 402, U. 267, 567. Flute pipe, 1. PI. 26. Flute player, II. 184. Flutes, II. 275. Fluxion of an arc, II. 16. Fluxion of an area, II. 22. Fluxion of a solid, II. 20. Fluxions, 1. 249, II. 7, 119, 124. Fly, 1. 131. Fly wheels, I. 179, II. 165, 182. Flying, 11. 164. Focal distance, II. 315. Foci, II. 281. Focus, I. 414, 111 71, 283. Focus of a lens, I. 417,11. 281. Focus of an ellipsis, II. 23. Focus of a sphere of vari- able density, II. 82. Focus of telescopes, II, 287. Focus of the eye, I. 450! Fog, II. 474, 476. Folding, II. 188. Folkes, II. 152. Fpmalhant, I. 497, Fondeur, 1. 190. INDEX, 703 Fontaine, II. 557. Fontana, II. 112, S12, 463, 512. Fontenelle, I. 249, 532, II, 217,344. Food of plants, II. 515. Foot, 1. 111,11. 150. Foramen of the retina, II. 311. Force, 1. 36, 33, 79, 11. 28; 129, 131, 139, 164. Acce- lerating force,I. 27. Cen- trifugal force, I. 35. Defi- nition offeree, I. 27. De- flective force, I. 33. Re- gulation of force, I 91. Force of electricity, I. 134. Force of freezing water, II. 379. Force of gunpowder, XL 260. Force of horses, II. 167. Force of light, II. 294,618. Force of machines, II, 141. Force of magnetism, 1. 134. Force of mules, II. 167. Force of steam, II. 133. Force of water, II. 236. Force of wind, II. 457. Forcer for a pump, II. 251. Forces, II. 377. Reciprocal forces, II. 37. Regula- tion of hydraulic forces, I. 316. Forcing pump, I. 332, 353, PI. 23, II. 250. Fordyce, 11.513,518. Forest, II. 498. Forfait,!!. 234. Forge, II. 205. Forge hammer, I. PI. 18. Forges, I. 224, II. 252. Forging, I. 142. Forkel, II. 264. Form of tlie earth, II. 374. Form of the sky, I. 454. Forms of columns, II. 173. Forms of the planets, I. 518. Formula fur the elasticity of steam, II. 398. Forrest, II. 455. Forster, II. 366. Forsyth, I. 730, II. 519. Fortification, II. 260. Fossil bones, II. 497. Fossils, I. 720, II. 496. Fossombroni, II. 146. Fougeroux, II. 179, 180, 207. Founderies, II. 252. Foundcry, II. 157. Fountain of Hero, II. 337. Fountains, II. 245, 247. Foureroy, I. 753, It, 179, 675, 678. Fournier, If. 158. Fowl, II. 279. Fowler, II. 427. Fraction, II. 1. Fractions, II. 114. Fracture, I. 135, 143, 146, II. 169. Fracture from beat, I. 643. Fracture of a pillar, II. 174. Fragment ueber die geogo- nie, II. 497. Frame for rectilinear mo- tion, I. PI. 14, II. 183. Frame saw, I. PI. 4. Frame work, II. 182. Franc, I. 124, II. 102. France, II. 365. Francoeur, II. 130. Franf ois de Neufchatcau, 11.213. Franklin, I. 658, 715, 750, 754, 756, II. 112, 280, 410. B. 1706, D. 1791. Franklin's experiment on oscillations, 11. 223. Frederic, I. 189, 596. Freestone, II. 509. F reezing, 1. 642, 699, 11. 379, 394. Freezing mixtures, II. 410. Freezing of acids, II. 395. Freezing of water in pipes, II. 246. Freeiing water, II. 386. French calendar, II. 349. French measures, I. Ill, II. 151. French weiglits, I. 124, II. 160, 161. Fresco, 1. 96. Fr^zier, I. 176. Friction, I, 93, 152, 632, 667, II. 134, 137, 138, 169, 176, 200, 293, 383, 385, 414, 679. Avoiding friction, I. 203, 212. Friction of a pallet, II. 560. Friction of fluids, I. 292, PI. 20, 21, II. 61, 226. Friction of ice, I. 653. Friction of scaperaents, I. 195. See corrections. Friction of sluices, I. 314. Friction of water, II. 227. Friction of wheelwork, II. 55, 184. Friction quadrant, 11. 200. Friction wheels, I. 213, PI. 14, 18, II. 200. Frigid zone, I. 570. Frigorific experiments, II. 385. Fringes, II. 189, 641. Fringes of colours, I. 466, 11. 316, 639. Fringes of Griinaldi, 11.640- Frisi, I. 250, II. 130, 234, 325, 338, 359. Fritsch, 11. 303, 446. rrug,II. 312. Iroidour, II. 234. Fromantil, II. 216. FroQtinus, II. 224. Front view of a tekscope, II. 287. Frosts, II. 451, 45?. Fructification, II. 514. Fry. II. 144. Fuel, 11. 385, 410. Fulling, I. 186,11. 188. Fulminating mercury, IT. 262. Fulton, II. 234. Funccius, II. 264. Functions of the eye, II. 312. Funk, 11.127,264,366. Funke, II. 326. Funnel, II. 222. Fur, II. 190. Furiong, II. 150. Furnaces, I. 346, II. 410 . . 412. Fnrze, 11. 233. Fusee of a watch, 1. 192, PI 15, 16, II. 193. Fusorius, I. 246, 253. Fl. 1450. Fuss, II. 287. Fust, I. -246, 253. Fustians, II. 218. Gabler, II. 127, 437. Gaertner,II. 511. Gage for wheels, 11. 181. G.^ges for air pumps, I. 341, PI. 22. G.iilenreuth, II. 497. Gi» II. 249. Herschel, I. 428, 429, 482, 456, 481, 490, 491 . . 494, 499, 501, 507, 509, 510, 511, 516, 603, 637, 638, 698, 754, PI. 31, 33, 39, II. 79, 282, 289, 291, 319, 326, 329,. 406, 585, 609, 624, 631, 648, 673, 676, 677, 680, 681. Ilertel, II. 286. Herz,II. 128. Hesiod, II, 214. Hessian academy, II. 109. Hessian bellows, I. 345. Hessian pump, II. 217. Hevelius, I. 598, 604, II. 324, 335, 347. Ilewson, II. 646. Hides, II. 208. Iliero, I. 240, 241, 352. Iliggins, II. 175,321,410, 411. High water, I. 576. High wheels, II. 201. Hillary, 11. 383. Hill raised, II. 498. Hills, II. 476. llindenburg, II. Ill, 114, 254, 388. Hindlpy,II. 145. Hindoos, II. 349, 376. Hinge, II. 179. Uipparchus, I. 496, 506, 519, 589, 593, 594, 604, II. 349. Histoire de I'Academie Royale, II. 107. Histoire de Vfeuve, II. 493. History of acustics, II. 279. History of astronomy, I. 589. History of astroBomy and geography, II. 376. History of hydraulics and pneumatics, I. 352, II. 263. History of mathematics, II. 124. History of mechanics, I. 236, II. 216. History of music, I. 403. History of optics, I. 472, II. 323. History of terrestrial phy- sics, I. 742. Hoar frost, I. 711. Hobert, II. 128. Hodometers, II. 156. Hoe, II. 211. Hoell, I. PI. 23. Iloell's machine, I. 336. Hoesen, II. 283. Iloeseu's mirrors, 11. -406. Hoffmann, I. 637. Hoffmann, 11.283, 031. Ilofmann, II. 125. Hogshead, I. 124, II. 150, 151. Ilolden, II. 273. HoWer,II. 27^. Iloldsworth, II. 143. Holes, II. 213. IloUandse maatschappy te Haerlem, II. 109. HoUmann, II. 111. Hollow bars, II. 175. Hollow beain-s, I. 140, II. 60. Hollow Kricks, II. t75» Hollow cylinders, II. 168. Hollow masts, I. 149. Holm, II. 474. Holstein, II. 498. Home, II. 519, 573, 586, 692, 600, 601, 671, 672, 678v Homer, II. 506. Homogeneous medium, I. 408. Hooey dew, II. 475. Hooke, I. 7, 100, 137, 160, 188, 190, 198, 248, 253, 268, 271, 335, 355, 356, 366, 385, 475 . . 477, 482, 483, 5Q4, 599, 604, 748, 749, 756, PI. 6, II. 107, 112, 124,218,264, 285, 317, 359, 376, 396, 014, 627, 629. B. 1635, D. 1703. Hooke's counterpoise, I. 311, PI. 19. Hooke's joint, I. 173, PI. 14, II. 182. Hooke's lamps, II. 245. Hooke's law, II. 221. Hoop, I. 34, II. 180. Hooper, II. 128,514. Hope, I. 728. Ilopson, II. 384. Hop stalks, II. 218. Horizon, I. PI. 35, 11. 354. Horizontal moon, I. 454, PI. 30, II. 313. Horizontal range, I. 39, PI. 2. Horizontal refraction, I. 441, II. 300, 301. Horizontal scapement, I. PI. 16. Horizontal surface, 1. 200. Horizontal watch, I. 195. Horn, I. 402, II. 187. Horn plate work, II. 200. Horrebow, II. 447. Horrox, I. 544. Horse, I. 132, II. 164, 167, 279. Positions of a horse's legs, I. 48. Horse hoe, II. 212. Horse mill, IL 167. Horse pump, II. 249. Horses, I. 218, PI. 18, II. 165, 181. Horses falling, II. 218. Ilorsley, II. 127. Horticultural instruments,. H. 20. Horticulture, II. 519. Hosack, II. 591. Hosiery, II. 187, 218. Hospital. See L'Hospital. Hothouses, II. 412. Hot springs, II. 494. Hour glasses, I. 188, IL 196. Houses, II. 17A 708 INDEX. Howard, I. 535, 722, II. 155,498, 502,674. Hoyle, II. 673. Hube, II. 128, 465, 539. Hubius, II. 360. Hurldart, I. 182, 183, 481, II. 187. Huebner, II. 492. Huepsch, II. 480. Hugenius, II. 112. Huilier,II. 119. Hulk, II. 243. Human strength, II. 165. Human voice, I. 400, II. 266, 275. Humboldt, 1. 498, II. 514. Humidity, I. 709. Humming top, I. 402. Hundred weight, H. 161. Hunter, II. 311, 517, 573, 597. Hunter's screw, I 72, 208. Hurdy gurdy, I. 399. Huret, II. 157. Hurricane, 11. 457. Hurricanes, II. 458. Hutchinson, II. 239. Huth, II. 172. Hutton, I. 364, II. 110, 112, 113, 115, 118, 121, 128, 152, 177, 229, 322. 407. Huygenian theory, II. 679. Iluygens, I. 190, 192, 248, 253, 277, 357, 358, 366, 443, 445, 458 . . 460, 462, 477, 479, 480, 482, 483, 492, 517, 567, 598, 604, II. 112, 136, S06, r 320, 509, 541, 556, 614, 619, 622, 623, 630. B. 1629, D. 1695. Hydra, I. 724. Hydracontistcrium, 11.247. Hydraulic air vessels, I. 336. PI. 23, Hydraulic architecture, I. 308,312,11.232. Hydraulic bellows, I. PI. 24,11: 253,254. Hydraulic forces, 1.316, If. 235. Hydraulic instruments, H. 245. Hydraulic machines, 1.327, II. 245, 247, 264. Hydraulic mean depth, II. 61. Hydraulic measures, I. 318. Hydraulicostatics,I. 300. Hydraulic pendulum, II. 247. Hydraulic pressure, I. 59, 300,357,11.62,226. Hydraulic ram, 1. 337, PI. 23, II. 249. Hydraulics, I. 258, 277, 352, II. 60, 221, 263. Hydraulic siphon, II. 249, 251. Hydraulic wheels, II. 237. Hydraulum, IL 275. Hydrodynamic measures, II. 235. Hydrodynamics, I. 255, II. 57, 219. Hydrogen gas, II. 256, 265, 279, 509, 541. Ilydrographical charts, II. 374. Hydrology, II. 342, 368, 479. Hydrometer, 1.309. PI. 21, 11.231.419. Hydrometrical fly, I. 318, PI. 22. Hydrostatic balaiice, 1. 308, PI. 21,11. 159. Hydrostatic equilibrium,!!. 57. Hydrostatic instruments, I. 308, II. 231. Hydrostatic lamp II. 245. Hydrostatic machine, II. 237. Hydrostatic paradox, I. 263. Hydrostatic press, I. 322. Hydrsstatic pressure, I. 663. Hydrostatics, I. 257 . . 259, PI. 19,11.219. Hyctometcr, II. 476. Hygrology, II. 464. Hygrometer, 1. 709, 753, PI. 4), 11.465,468,474. Hygrometry, 1. 751, II. 465, 469. Hygroscopes, II. 468. Hypatia, I. 352. Hyperbola, I. 623, II. 121, 122, 123,381,681. Hyperbolical logarithms, II. 8. Hyperbolical pipes, II. 266. Hyperbolic cylindroid, II. 122, 123. Hyperbolic fringes, I. P1.30, II. 643. Hyperbolic glasses, II. 283, 384. Hyperbolic rainbow, !I. 309. Hyperbolic sectors, n. 119. Ilyperoxygeniied muriatic acid, II. 673. Ilypocycloid, II. 122, 558, 562. Hypotenuse, H. 13. Hypotheses, II. 613. Hypotheses of electricity, I. 658. Hypotrochoid, H. 558. Ibn Junis,I. 191,595,604. Ice, I. 444, 577, 699, 746, II. 86, 216, 221, 293, 385, 394, 395, 410, 411, 479, 480, 509, 511. Ice boat, II. 342. Iceland, II. 498. Iceland crystal, 1. 445, 477, PI. 29, II. 309, 435, 511, 629, 679. Ice melted, I. 634. Iconantidiptic telcscope,II. 286, 351. Idioelectrics. See Electrics. Igneous meteors,!. 722, II. 499. Ignis fatuus, I. 435, II. 499. Ignited charcoal, II. 25^^. Illumination, I. 423, II. 77, 291, 312. Illumination of the planets, I. PI. 34. Illustrations of astronomy and geography, II. 374. Image, I. 418, 423, PI. 27, 28, II. 71, 73, 281. Image on the retina, I. 448, PI. 30, II. 82. Imaginary quantities, II. 114'. Images, II. 283. Imisou, II. 129. Immersion of thermometers, II. 388. Impact, II. 136. Impelling boats, II. 243. Impelling ships, II. 242. Impenetrability, I. 609. Impenetrability of matter, I. 28. Imperfections of sight, H. 315. Impossible quantities, U. 114. Impossible roots, II. 1 15. Impregnation, II. 518. Impregnation of seeds, U. 514. Impulse, II. 51. Impulseof abullet, II. 136. Impulse of a fluid, I. 59. Impulse of a jet, I. 301. Impulse of a vein, 11. 227. INDEX. 709 Impulse of fluids TI. 220. Impulse transmitted by an elastic mediunv, 11. 68. Impulsion, IT. 136. Inanimate force, I. 90, II. 167. Inarre, II. 410. Ince, II. 179. Inch, II. 151. Inclination of strata, 11.354. Inclinations, II. 118. Inclinations of the plane- tary orbits, I. 504. II. 340. Inclined float boards,II.236. Inclined plane, I. 42, 70, PI. 4, 5, 17, II. 33, 42, 54. Inclined planes, II. 138, 197, Inclined surface, II. 138. Inclosures, II. 180. Incombustible houses, II. 17.5. Increase of the globe, II. 495. Increase of the sea, II. 496. Increments, II. 7, 119. Index, I. 99, II. Correc- tions. Incomnnensnrable quanti- ties, n. 14. Index of refraction, I. 412. Index ofrefractive density, n. 70. Indian cycle, 11. 370. Indian ink, I. 95, II. 143. Indian measures, U. 148. Indians, I. 591. Indian weights, II. 160. Indian zodiac, II< 376. Indiction, II. 349. Indigo, II. 214. Indistinct vision, II. 310. Indivisibles, I. 36. Induced electricity, I. 664. II. 418. VOL. ir- Induction, I. 15, II. 124. Induction, II. 664. Inelastic bodies, I. 78. Inertia, I. 33, 51, 614, II. 130, 379. Incvaporablc fluids, II. 397. Infants, II. 518. Inferior tides, I. 583. Infinite, II. 557. Infinite quantity, II. 119. Infinites, I. 36, II. 119. Infinite series, II. 116. Infinity of the stars, II. 330. Iiifliiramable air, II. 263. Inflammable bodies, I. 412. Inflannnabtc vapours, II. 259. Inflammation, II. 290. Inflecting atmosphere, II. 632. Inflection, II. 310,317, 543, 629, 661. Influence of light, II. 321. Ingcnhousz, II. 112, 128, 424, 432, 513. Ingenhousz's electrical ma- chine, II. 432. Indian ink, I. 95. Ink, I. 66. See correc- tions. II. 143, 144. Inkstand, II. 143. Inlaid work, II. 179. Inlaying, II. 143. Inquiry into the effects of heat, II. 383. Inscription of figures, II. 118. Insects, II. 311, 312, 382, 458, 510, 518, 519, 620, 678. Insensibility of electricity, II. 424. liistinct, I. 449. Institutions de physique, II. 126. Inbtitut uatioual, II, 111. Instruments. Musical in- struments, I. 397. Op- tical instruments, I. 420. Instruments for observa- tion, II. 349. Instruments of penetration, II. 207. Instruments subservient to music, II. 279. Instruments subservient to seamanship, II. 244. Insulated stars, I. 494. Insulation, 11. 419. Integral calculus, 11. 119. Intensity of electricity, I. 683. Intensity of light, I. 420,11. 77. Intensity of sound, II. 265. Interception of light, 1. 409, II. 294. Interception of sound, I. 376. Interest, II. 117. Interference of light, 1. 46 1, II. 633,639,071. Intermediate spring, I. 193. Intermitting springs, I. 286. Internal reflection, II. 296, 030. Interpolations, II. 110,340. Ii.tcstines, II. 184. Introsusception, II. 510. Inundation, II. 370, 480. Inundations of large rivers, I. 713. InvaUds, II. 181. Inversable chair, II. 201. Inversable coach, II. 201. Inverted images, II. 301. Inverted pump, I. 336. Inverted rainbow, II. 309. Inverted tide, I. 579. Invisible girl, .1. 376, II. 271. Invisible heat, I. 654, 406. Invisible rays, IL 296, 407. 5 A Involute, II. 22. Involute of a circle, II. 55, 122, 562. Involutes of circles, I, PU 15. Ionian school, I. 237. Ionic column, I. PI. 12. Ireland, II. 451. Iris, I. 447, 451, II. 311, 530. Iris for telescopes, II. 288. Irish academy, II. HI. Irish car, II. 202. Iron, I. 152, 228, 244, 685, II. 48, 169, 266, 438, 501, 509, 510. Iron blocks, II. 177, Iron bridges, II. 177. Iron filings, I. 688, 693, PI. 41. Ironmongery, II. 179, 207, Iron roads, II. 204. Iron wheelways, I. 218. Irradiation, II. 310. Irregular refraction, II. 301. Irrigation, II. 235, 251, 264. Irritability, II. 518. Irritability of plants, II. 513. Irritation of the nerves, II. 427. Ir. tr. II. 111. Irvine, I. 650,051,750. Island. New island, II. 495, 498. Isochronous curves, II. 133. Isoperimotrical problems, II. 123. Italian school, I. 237. Italy, II. 450, 496. Ivory, II. 179, 209, 509. Izarn, 11. 501. Jack, I. PI. 17,11.182, 198. Kitchen jack, I. 179, .II. 181. Jackal, II. 516. Jack for pump rods, II. 199. 710 INDEX. Jacket, If. 21 1. Jacks for telescopes, II. 286. Jackson, II. 158. Jacob, n. 201. Jacobson, II. 127. Jacotot, II. 129. Jacquet, II. 41C. Jacqiiiii, II. ICl. Jallabert, II. 415. Jamaica, I. 700. Jainard, 11. 273. Jansen, I. 474, 483. Jars, I. 068. Jars for electricity, II. 433. Jeaurat, I. 480, 483. B. 1704, D. 1803. Jeffries, II. 210. Jesuit, I). 167. Jet, I. 286, P!. 20,11. 60, 61, 247. Jcttees, II. 233. Jet witli a ball, I. 247. Jewellery, II. 206. Jewelling, I. 193, II. 191. Jew's harp, I. 402. Jib for a crane, II. 199. Joggles, I. 168, PI. 13. Joiner's work, II. 178. Jointed cart, II. 202. Jointed work, II. 182. Joint focus, I. 418. Joint for steam tubes, II. 246. Joints, I. 166. Joints for beams, I. PI. 13. Joints of stones, I. PI. 11. Jones, IIo 113, 126, 273, 447, 597. Jordan, IT. 317, 622, 635. Journal dcpliysitjue, I. 251, II. 109, 110. Journal des savans, II. 107. Journal polytechnique, II. 111. Journals, I. 250, 251. Journals of rain, II. 476. Journals of the weather, II. 448. Juan, I. 363, 364, 366, II. 239. B. 1713, D. 1773. Judgment of distance, I. 453. Juergen, I. 244, II. 218. Juices of vegetables, II. 514. Julian, II. 567. Julian period, I. 541. Julian reckoning, 11. 349. Jung, II. 124, 141.^ Juno, I. 508, 534, IF. 334, 372. Jupiter, I. 508, 531, 534, 702. See corrections. PI. 33, II. 335,340,372,-376. Jupiter's satellites, I. 530, II. 346. Jurin, I. 478, 483, 754, 756, II. 140, 524, 584, 593. B. 1680 .' D. 1750. Jussieu, I. 732, 750, 756. B. 1699, D. 1777. Jiisli, II. 141, 496. Justus Byrgius, II. 217. Kaestner, I. 360, II. 112, 124, 126, 134, 290, 325, 338, 361. Kaiserliche academie, II. 107. Kamtchatka, II. 306. Kanne, H. 155. Kant, 11.324,378. Karstens, II. 113, 127, 249. Keel, I. 325. Keil, II. 125, 324, 495. Keir's lamp, I. 311. Kellner,II. 107. Kelly, II. 119, 371. Kempe, I. 244. Kempelcn, I. 401. Kent, II. 172. Kepler, I. 36, 253, 474, 481, 483, 495, 504, 505, 597, 598, 599, 004, 11. 280, 824, 332, 373, 523. B. 1571, D. 1030. Kcplerian laws, I. 504, 517, PL 1. Kepler's problem, II. 340. Kett, II. 129. Kettle, II. 411. Key note, I. 392. Khell, II. 126. Kies, ]I. 424. Killarncy, II. 480. Kiln, II. 175, 411. Kilogramme. See Chilio- gramme. Kin, II. 162. King, I. 238. Sec correc- tions. I. 637, II. 128, 291, 501, 631. Kingdoms of nature, I. 723. Kingpost, I. 169, PI. 12. King's College Chapel, I. 245, PI. 12. Kiobenhavnske seUkab, II. 108. Kirb roof, I. PI. 13. II. 42. Kirby, II. 157, 602. Kircher, I. 405, 407, 280, II. 272, 436. B. 1601, D. 1680. Kirnbergcr, II. 273, 551, 554, 564. B. 1721, D. J1783. Kirwan, I. 698, 700, 750, II. 392, 408,409,451, 452, 498, 508, 511, 677, 678. Corrections. Kitchen range, II. 411. Kite, I. 324, PI. 22. Kites, II. 227. Klaproth, II. 675, 680. Kleist, II. 750, 756. Klingenstierna, I. 479, 483, II. 281, 415, 444. Klostermann, II. 361, 363. See corrections. Kl^egcl, 1.480, II.1]3,]28, 130, 249, 281,288,375, 484. Kluver, II. 495. Kneading, I. 234, II. 216. Knecht, 11. 551. Knees, II. 168. Knife, II. 143. Knight, I. 729, II. 377, 444, 515. Knitting, II. 188. Knives, I. 227, II. 207. Knoll, II. 49-]. Knowles, II. 229, 456. Knots, II. 189. Knox, II. 678. Koenig, II. 587, 595. Koeiiig's law, II. 140. Koestlin, II. 424. Koinarzewski, II. U5. Krafft, II. 307, 450, 464, 681. Kraft, II. 126, 130. Kramp, I. 249, II. 256, 301. Kraschennicoff, II. 366. Kratzenstein, I. 461, PI. 26. II. 128, 276, 379, 417, 449, 464. Krayenboff, II. 424. Krueger, II. 126, 496. Kruenitz, II. 128,215,414, 416, 480. Kunze, I. PI. 39, II. 128, 410, 430. Kurdwanowski, II. 294. Lahelye, II 176. Labillardiere, II. 185. Laborde, II. 274. Labour, I. 79, 90,331, II. 165. Labour of a man, I. 131. Lac, II. 421. Lacaille, II. 130, 280, 324, 363. See corrections. II. 373, 393. Lacam, IL 437. INDEX. 7]1 Lace, II. 188, 218. Lacepede, I. 750, II. 416. Lacondamine, II. 151, 358, 362, 303, 457. Liicroix, II. 114, 118, 119, 120. Ladder, II. 175. Laf;rtius, II. 216. Lafaille, I. 247. Lafond. See Sigaud. Lagrange, I. 7, 250, 287, 406, 604, 522, II. 110, 130, 224, 537, 539, 544, 546, 547, 548, 618. Laliire, I. 129, 249, 253, II. 307, 373, 524, 557, 558, 561. B. 1610, D. 1718. Laliirc's pump, I. 332, 348, n. 23. Lake, I 579. Xake of Geneva, II. 480. Lakes, II. 451, 479, 498. Lakes of America, II. 307. Lalandc, I. 501, 540, 598, PI. 33, II. 143, 150, 190, 214, 234, 325, 346, 371, 377, 381. Lallaraaiid^I. 750. Lamarck, II. 481. Lambert, I. 375, 406, 407, 480, 483, 491, 493, 526, 631, 637, 751, 756, II. 145, 280, 291, 295, 300, 314, 325, 387, 393, 404, 408, 473, 538, 681. B. 1728, D. 1777. Lambton, U. 362. Laiii<-therie, II. 110, 497. Laminating, II. 188. Laminating machine,I. 222, II. 205. Limp, I. PI. 21, IL 290,412. Lampadius, 11.384,417,483. Lampblack, II. 485. Lamp furnace, II. 411. Lamp micrometer, II. 290, 352. Lamp of Amiens, II. 245. Lamps, LSI 1,11. 245. Lampyris, II. 292. Lamy, II. 219. Land, L 571. Landaulet, II. 202. Land breezes, I. 704. Landen, I. 250, 353, IL 113,116,350.8. 1719, D. 1790. Landriani, II. 250,448,486. Lane, I. 683, PI. 40. Langenbuecher, II. 431. Limfjez, II. 170. Langlais, II. 263. Langsdoi f, I. 365, II. 11 1, 219, 225. Languedoc, II. 231, 496. Langwitli, II. 319,013,644. Lantern, II. 184, 196. La Peyrouse, II. 185. Laplace, I. 7, 60, 108, 110, 249, 250, 370, 407, 441, 460, 482, 505, 521, 522, 541, "565", 580,589,684, 652, 750, 754, 755, II. 130, 325, 363, 364, 873, 391, 393, 409, 466, 501, COO . . 666, 669, 670. Laplatricre, II. 187, 188, 211. Larcher, II. 333. Larive. See Delarive. Larynx, I. PI. 26, II, 550. La Sevre, IL 384. Last, II. 151. Lasts, II. 189. Latent beat, 1. 652, II. 409. Lateral adhesion, I. 140, 627. Lateral cohesion, II. 174. Lateral friction, IL 251. Lateral friction of fluids, I. 297, II. 222, 223. Lateral vibrations of rods, II. 263. Lathe, I. 228, II. 122, 209. Latitude, I. 536, 54S, II. 364, 365. Latitudes of stars, II. 334. Latorre, II. 285. Launching ships,ll. 172,240. Laurie, I. PI. 24. Laurie's bellows, II. 253. Lausanne, II. 111. Lavoisier, I. 634, 652, 750, II. 390, 408, 503, 508. B. 1743, D. 1794. Law of aberration, II. 294. Law of equilibrium, 11.45. Law of interference, II. 633. Laws of gravitation, I. 515. Laws of gravity, IL 338. Laws of heat, II. 404. Laws of mechanics, II. 140. Laws of refraction, I. 413. Lazowsky, II. 448. Leach, II. 211, 234. Lead, II. 383, 403, 509. Leaden pipes, I. 317, IL 205, 245. ieague, II. 151. Leaky, II. 369. Least action, II.' 140. Leather, II. 184, 189. Leaves, I. 729, II. 513. Lecat, II. 516. Leccbi, II. 219, 224. Lee, I. 244. Leeuwenhock, IL 1)2,527, 596, 599. Leeuwenhoek's micro- scopes, II 285. Lee way, I. 325, II. 240. Legeudre, II. 149, 360. Legentil, II. 292. Legs, I. PI. 9. Lehmann, II. 306, 492,496. Lehrgebaeude dcr optik,Il. 280. Leibnitz, I. 79, 249, 368, 475, II. 112, 377. B. 1040, D. 1716. Leidenfrost, IT. 396. Leipzigermagazin, II. 110. Leiste, IL 254. Lelyveld, II. 118. Lemaire, II. 362. I^moine, II. 217. Lempe, II. 141. Lemoniiier, II. 336, 370, 437, 520. Length of a pipe, II. 569. Length of curves, II. 121. Length of the pendulum, II. 146, 363. Lenoir. IL 149, 150. Lens, 1.416, IL 72. Crys- talline lens, II. 311. Lens of least aberration, II. 281. Lenses, I. 423, 472, PI. 27. II. 210, 281. Grinding lenses, I. 231. Lenses not spherical, II. 283, 284. Leo, I. 504. Leone, II. 492. Leroy, II. 263, 365. Lescailler, II. 239._ Le Sags, II. 377, 510, Lescmelier, II. 384. Leslie, I. 372, 030, 649, 710, 754, II. 49, 223, 231, 384, 475, 520, 662. Leslie's discoveries, II. 407. Leslie's hygrometer, 11. 469. Leslie's thermometer, I. PI. 34. ■ Lesparat, II. 148. • Letherland, 1. 195. Lettere fisicomttcorologi- che, IL 500. Letterpress, I. 122. Letters, II. 276. LeucippuB, IL 744. Leupold, I. 250, 253, II. 118, 125, 25'3, 282. D. 1727. Lcutmann, II. 413. 712 INDEX. Lerel.. Spiritlevel, I. 310. Levelling, 1. 105. Levelling land, IL 213, 216. Levels, I. 572, IL 353. Lev6que, IL 3rO. Lever, I. 65, PI. 3, 4, IL 40, 134, 135, I3r. Levers, I. 173, 203, II. 54, 181, 196, 219. Hy- draulic levers, II. 236. Lever with a wheel, IL 184. Levigating, I. 234. Levigation,n. 213, 214. Levity, I. 16. " . Lewis, I. 210, PI. ir. LexcU, I. 513, II. 335. Leyden phial, I. 666, II. 418, L'hospitaljIL 121. L'huilier,II. 119, 123, 378. Li, II. 153. Libella,II. 311. Libes, II. 129. Libra, I. 497, 504. Libration of the moon, I. 528,11.345. Lichtcnberg, II. 391, 426, 486. Lichtenberg's drum machine for electricity, II. 432. Lichtenberg's figures, II. 419. Lieberkuehn, II. 285. Liebknecht, II. 366. Liesgauig, II. 362. Life, I. 725. life annuities, II. 107. Life boat, II. 242. Life of plants, I. 730. Litters, II. 214. Lifting pump, I. 333, PI. 23, II. 249. Lifting stock, II. 196. Light, 1. 408, 457, 489, 654, 655, 745, PI. 39,11.70, 200, 319,385, 397,403, 406, 511, 513, 514, 531, 514, 607, 613, 645,66], 671, 673,679. Intensity of light, IL 77. Light compared with sound, 11.541. Light from combustion, II. 290. Light from electricity, I. 670. Light from friction, I. 435, II. 293. Light house, I. PI. 11. Lighthouses, II. 174. Light in a storm, II. 482. Lightning, I. 713, 743, 750, n. 445, 481. Lightning in the moon, II. 336, 345. Lightning without thunder, II. 483. Light of a candle, I. 438, II. 638, 646. Light of diamonds, II. 422. Light of electricity, II. 42'2. Light of fires, 11.322. Light of fish, II. 291. Light of stones, II. 435, 436. Light of the heavenly bodies, L 531, n. 314. Light of spirits, I. 438. Light of the moon, II. 337. Light of the new moon, II. 345. Light of the sea, II. 291, 292. Light of the stars, I. 490. Light round the sun, II. 345. like causes, II. 27. Lime, II. 175,408. Lime kilu,lL 209,411,422. Lime mixed witli gunpow- der, II. 262. Limestone, II. 498. Lime tree bark, II. 185. Limits of equations, II. 115. Limperch, II. 213. Lincoln Cathedral, I. 245. Lind, II. 457. Line, II. 8, 151. Linen, IL 187, 189, 217. Line of congelation, 11.154. Line of draught, II. 55. Lines, I. 100. Lines of the third and fourth order, II. 122. Lines or hatches, I. PI. 0. Link, IL 112, 150. Linnaeus, II. 502. Linne, I. 730, 731, 733, 736, 750, 756, II. 511. n. 1707, D. 1778. Linnean Society, II. 503. Linncau system, I. 700, 750. Lintearia, I. PI. 19. Lion, 1. 497. Lippie, II. 151. Liquefaction, I.643,n.395. Liquid, I. 259. Liquid adhering to a solid, I. 623. Liquidity, I. 619. Liquids, I. 535, 613, PI. 39, IL 380. Litre, II. 152. Litron, U. 152. Living force, II. 140. Living under water, II. 255. Load, II. 151. Loaded chain, I. PI. 11. Loaded cylnder, I. PI. 3. Loaded pendulum, II. 139. Loaded thread, II; 267. Loaded waggon, I. PI. 3. Loading ships, II. 199, 213. 2 Loadstones, II. 444. Lobe, II. 597. Local heat, II. 451. Local motion, II. ISO. Loci solidi, II. 122. Lock, II. 179. Lock filled from a reser- voir, I. 282. Locker, II. 456. Lockic, IL 113. Locks, II. 235. Locus of right lines, II. 123. Loevcns, II. 435. Log, L 112, PI. 22, IL 192, 244. Hydraulic log,I.318. Logarithmic circle, I. PI. 7,11. 146. Logarithmic curve, I. Pl. 10, II. 3. Logarithmic tangents, IL 374. Logarithms, I. 106, 272. Sec corrtctiiins.I.598,II. 6,9,116,117. Logistic circle, II. 146. Log glass, II. 196. Log line, II. 218. Lohineier, I. 365, II. 256. Lomonosow, 11. 290. London, 1.454,700,11.365. Loudon bridge, II. 234. Long, II. 325. Longevity, II. 516, 517. Longitude, I. 251, 536, 543, 601, II. 357, 376. Longitudes, II. 364, 365. Longitudinal sounds, I. 380. Longitudinal vibrations of rods, II. 269. Ix)ngtube, 11.286. Looking glasscs,II.210,283, 323. Looming, I. 441. Looms, II. 187. Lorgna, II. 116, 146, 225, 347, 481. INDEX. 713 Lorimer, II. 437. Lotteries, II. 117, 180. Louis XV, I. 601. Lovett,n. 126,415,437. Lowering boats, II. 200. Lowering weigtits, II. 196, 200. Lowitz, I. PI. 29, II. 221, 254, 374. Low water, I. 576, 11.368. Loxodromic circle, II. 374. Lubinietz, II. 337. Lucernal inicroscope, I. 425. Lucid disc micrometer, I. 432, II. 352. Luc. See Dcliic. Luckoinbe, II. 158, 217. Lucretius, I. 16, 57, 240, 253, 490, 598, II. 54, 124. Ludlam, II. 145, 347, 350. Lullin, II. 4 le. LuUin's card, II. 422. Lulofs, II. 366. Lunoiiious arches, II. 489. Luminous bodies, I. 409. II. 291. Luminous cros?, II. 587. Luminous insects, II. 292. Luminous meteors, II. 499. Lunar atmosphere, II. 345, 346. J.unar c«rona, II. 317. Lunar equations, II. 341. Lunar globe, 1. 534. Lunar heat, II. 451. Liinar influence, II. 450. Lunar motions, I. 519, PI. 34, II. 340. Lunar mountains, II. 336, 846, 358, 368. Lunar observations, I. 344, II. 357, 365. Lunar orbit, II. 340. Lunar parallax, 11. 341, 367, 361. Lunar periods, II. 346, 490. Lunar rainbow, I. 443, II. 309. Lunar itones, IT. 501. Lunar volcanos, I. 722. Lunar year, II. 376. Lunes, n. 118,123. Lungs, II. 253. Lute, I. 399. Luz, II. 388, 393. Ljxopodiurij, I. 624. Ljcosthenes, II. 303, 446. Lyonnct, I. 608. Lyons,II. 119, 416. Lyra, I. 496. Lyre, I. 397, 403, II. 274, 566. Maberly, II. 593. Macclesfield, II. 300. Macli. A. II. 107. Machin, I. 249. Machine for equations, II. 115. Machine for measuring strength, I. 151. Machinery, I. 172, PI. 14, IL 181. Machinery for eutartain- ment, II. 184. Machinery of fluids, I. 316. Machines, I. 89, II. 141, 166. Compound ma- chines, II. 135. Machines approuv<^es, II. 107. Machin's law, TI. 132. Machy, II. 175. Mack.iy, II. 365, 371. Mackenzie, 11.156. Maclaurin, L 65, 82, 250, 253, 323, 359, 360, 366, II. 113, 119, 120, 126, 140, 539, '556, 557, 558, 561. B. 1698, D. 1746. Macrobius, I. 5T6, II. 567. Madder, II. 213. Madeira, I. 700. MafFei, n. 481. Magazin cncyclop^dique, IL 111. Mag.izine pistol, II. 263. Magdeburg hemispheres, I. 274, 630. Magellan, II. 347, 350, 384, 460. Magic lantern, I. 473,11. 284, 323. Magnet, L 690,743,751. Magnetical apparatus, II. 443. Magnetical attractions and repulsions, I. 687. Magnetical curves, I. PI. 41. Magnetical effects, I. PI. 41. Magnetical eflJuvia, 11.1614. Magnetical globe, II. 443. Magnetical measares, II. 446. Magnetical paste, I. 693. Magnetical substances, I. 686, II. 438. Magnet in a globe, I. 689. Magnetism, I. 685, II. 436. Magnetism by induction, I. C90. Magnetism of animals, IL 439. Magnifier. Double magni- fier, I. 431. Magnifying powers, I. 422, II. 78, 80, 287. Magnifying powers of tele- scopes, I. 427, 430. Magnitude of the earth, II. 358. Magnitude of the planets, I. PI. 34. Magi'.itude of the stars, I. 490, II. 329. Magnitudes of the stars, II. 282,352. Magrath, II. 158. Mahon,II. 416. See Stan- hope. Maillard, II. 257. Maillet, II. 496. Maintaining power, II. 192. Mair,I. 747. Mairan, I. 502, II. 450, 488. Maire, I. 428. Mako, II. 482. Malcolm, IL 272. Malebranche, I. 479, IL 614. Maler,II. 127. Mallet, II. 114, 121,360, 363. Malouin, II. 214. Maltii, I. 587. Malt kiln, IL 412. Malt mill, II. 214. Malton, II. 157. Mammalia, I, 734, II. 516. Management of colours, 'II. 314. Management of rivers, II. 234. Management of timekeep- ers, II. 195. Manchester, I. 245. Manchester memoirs, II. 111. Mandoline, I. 599. Margin, II. 384. Mangles, L 221. IL 205. Blanilias, I. 604, IL 324. Mann, IL 451. VOL. II. S B 7U INDEX. Mannichfaltigkeiten, II. 109. Manoeuvres of ships,II.?39. Manometers, II. 461. Manometry, II. 4C2. Mansard roof.I.Pl. 13,11.42. Manufactures, I. 243, II. 141, 184. Manures, II. 519. Maple, II, 513. Map of the world, I, PI. 42, 43. Maps, II. 3r4. Marat, II. 296, 384, 416. Marble, I. 230, 231,11.175. Marbles, II. 210. Marc, 11. 161. Marcellus, I. 58, 210, 242. Marcliand, II. 2 IT. Marchetti, II. 168. Marc of Charlemagne, II. 161. Marie, II. 130. Marigni, I. 399. Marine barometer, 11. 461. Marine fossils, II. 490. Marine observations, II. 349. Marine octant, I. PI. 35. Marine puiup, II. 251. Marine quadrants, II. 245. Marine spencer, II. 244. Marine surveyor, II. 244. Marine worms, II. 518. Marjotte, I. 355, 356, 366, 443, 444, 477. See cor- rections. I. 483, II. 112, 308. D. 1684. Mariotte's theory of halos, 11.3:6. Maritime observations, II. 239. Maritime snrveying,tII.156. Marias, II. 337. Marivetz, II. 127. Marly, U. 249, 250. Marne, II. 384. Marpurg, 273, 551, 554. Marquois's scales, I. 102, PI. 6. Mars, I. 507, 534, PI. 32, 33, II. 834, 372. Marsden, II. 367. Jlarsh, II. 233. Marshes, II. 199. Marsigli, II. 292, 365. Martial flowers of sal am- moniac, II. 323. Marsupium nigrum, II. 600, 601. Martenson, II. 414. Martin, II. 126, 157, 249, 256,288,292,415. Marline, U. 126, 386. Martini, II. 567. Martinierc, II. 366. Martinique, II. 166. Marum. See Van Marum. Mascheroni, II. 118, 177. Maseres, II, 116. Maskelyne, I. 493, 575, PI. 28,11. 148, 150,360, 363, 370, 473, 672, 674. Mason, II. 362. Masonry, II. 174. Masses, I. 50. Masses in motion, II. 134. Masses of the planets, II. 372. Mass of iron, 11. 501, Masts, I. 149, II. 178, 241. Material bodies, II. 618. Materials for building, 11. 174. Materials for manufac- tures, II. 184. Mathematical machines, II. 146. Mathematical mechanics, 11. 142. Mathematical society of Bohemia, II. 110. Mathematical symbols, II. 555. Mathematici veteres, I.?40, 242, II. 113. Mathematics, II. 1, 112, 124, 130. Matrass, II. 189. Matrix, I. 122, II. 158. Mattaire, II. 217. Matter, 1. 605, 11. 131, 377. Impenetrabilityof matter, 1.28. Matter of fire, II. 383. Matthesius, I. 356, II. 263. Matting, II. 188. Maty, II. 106. Maunoir, II. 279. Maupertuis, I. 21, 495, 11. 112, 140,339,362. Maurolycus, I. 474, 483. Mawe, II. 511. Maxima, II. 338. Maxima and minima,II.172. Maxima of curves, II. 123, 133. Maximum, II. 8. De qui- busdammaximis, II. 123. Maximum of eflfect, II. 54, 140. Maximum of heat, II. 387, 388, 389. Maximum of labour,II.1 66. Maxwell, II. 611. Mayer, I. 602, 749, 751, 756, II. 112, 332, 336, 341, 373, 375, 384, 393, 427, 438, 473. T. Mayer, B. 1723, D. 1762. Mazdas, 1. 480, II. 625. M. B. Library of the British Museum. M'Culloch, I. PI. 41. Mean depth, II. 61. Mean image, II. 76. Mean of observations, II. 116,346,347. Mean tones, II. 554. Measure. Common mea- sure, II. 13. Measure»e4»t of angles, II. 143. Measurement of light, II. 288. Measurement of refractive powers, II. 282. Measurement of the earth, I. 593, II. 358. Measurement of transpar- ency, II. 282. Measurements of degrees,!. 570. Measure of force, I. 79, II. 139. Measure of speech, II. 270. Measures, II. 146, 180. Hydrodynamic measures, II. 235. Measures of atmospheri- cal electricity, II. 485. Measures of heat, 1. 646, II. 383. Measures of the undula- tions of light, II. 640. Measures of lime, II. 196. Measures of various coun- tries, II. 152. Measures of wind, II. 244, 455. Measuring, I. 93. Measuring a ship's way, II. 244. Measuring distances, 11. 156. Measuring earthquakes, II. ,492. Measuring heat, II. 408. Measuring heights, II. 396. Measuring instruments, I. 111,11. 155. M^chain, II. 149, 674. Mechanical arts, II. 124. Mechanical ccntres,II.136. Mechanical curves, II. 122. Mechanical force, I. 79. Mechanical paradox, II. 184. INDEX. 715 Mechanical power, T. 331, II. 137, 140. Mechanical powers,II. 135. Mechanics, II. 27, 129, 137, 216. History of me- chanics, I. 336. Mechanism of the eye, II. .313. Medical electricity, 11. 424. Medical galvanism, II. 429. Mediterranean, 1. 587, 708, II. 234, 367. Medium of soand, II. 265. Medusae, II. 292. Medusa's head, I. 496. Mcgameter, II. 351. Meibomius, I. 405, 11.240. Meindert Sorrcy, II. 441. Melanderhjehn, II. 325, 362. Melanges de Turin, 11.109, Melody, I. 392, II. 563. Melody of speech, II. 276. Melted glass, II. 396. Melting, II. 394, 427. Melting of ice, II. 408. Melting point, II. 509. Membraua pupillaris, II. 311. Membranatympani, 11.271. Membranes. Vibrations of membranes, I. 381. M3inoires de Dijon, II. 110. M6 iioires de Turin, 11.109. M^moirespresent^s, 11.107. Md;noires sur I'E^ypte, II. 111. Memory, II. 124. Men, II. 164. Mendoiia, II. 357. Mendoza y llios, II. 371. Meniscoid, It. 603. Meniscus, 11. 662. Meniscus lens, 1. 416, II. 79. Menkar, I. 49r. Menstrual parallax, !. 334 Mensuration, II. 118, 156. Menzies, 11. 518, Menzoli, II. 272. Mercator, II. 375. Mercurial air pump, II, 254. Mercurial column, I. 270. Mercurial level, II. 353. Mercurial phosphorus, II. 422. Mercurial pump, II. 166, 247. Mercurial thermometer, I. 647. Mercurial vapours, II. 252. Mercury, the metal, I. 276, PI.39.II.381,382,403,461, 509,653,654,659. Pres- sure of mercury, I. 265. Mercury, the planet, I. 506, 532, 622, 623, II. 889, 353, 372, 659. Meridian, I. 109, 536, PI. 35, II. 147, 341, 354. Meridians of Greenwich and Paris, II. 360. Jleridional line, II. 374. Meridional parts, II. 374. Mersenne, I. 253, 405, 407, II. 124, 264, 272, 546, 558. B. 1588, D. 1648. Mersennus, II. 610. Mery, II. 601. Messenger, I. 205, II, 197, Messier, I. PI. 31. Melacentre, I. 266, II. 59, Metacentric curve, II. 241. Metallic surface, I. 709. Metalline thermometer, II. 386, 389. Metals, I. 411, 678, II. 3 16, 654,659. Meteoric stones, 11. 501. Meteorographic instru- ments, II. 448. Meteorological apparatus, II. 448. Meteorological thermome- ters, II. 454. Meteorologische briefe, II. 482. Meteorology, I. 696, 753, II. 446. Meteors, I. 721, 722, II. 499, 675. Meto, I. 540, 592, 604. Metre, I. 106, II. 148, 152. Metrologie constitutionelle, U. 148. Metrometer, II. 279. Metternicb, II. 170, Metz, II. 155. Mexicans, I. 97, II, 377. Mezzotinto, I. 119. Michael III, I. 595. Micheli, II. 388. Michell, I. 492, 493, 575, II. 399, 630. Michelotti, II. 222, 823. Microelectrometers, 11.434, Micrometer, I, 432, PI. 28, II. 145. Micrometer for wires, II. 275. Micrometers, II. 289, 351. Micrometrical scale ,I.P1.7. Microscopes, I. PI. 28, II. 78 . . 80, 285, Double microscopes, I. 427. Simple microscopes, I. 422. Solar microscopes, I. 425. Slicroscopic observations, II. 646. MicroteleBcope,II,285,287, Middle ages, I. 243. Mile, II. 150, 153, 155. Military engines, II. 207. Military mining, II. 211, 216. jVIilitary telescope, II. 990. Milk, It. 180. Milky way, I. 493, 496, PI. 31, II. 338, Mill, 218. Miller, II. 511. Milli, II. 206. Milligramme, II. 162. Millilitrc, II. 152. Millimetre, II. 152. Mills, I. 232, PI. 18, II. 167, 213, 446. Millstones, II. 209, 214,21*. Milner, II. 416. Mina, II. 162. Minasi, II. 30. Mine, IT. 152, 364. Mineral electricity, II. 435. Mineral materials, II. 185* Mineralogy, I. 725, 510. Minerals, I. 723. Mines, II. 249, 257, 481, Miniatures, I. 95. Minimum, II. 8. Minimum of action, IF. 140, 377. Minimum of vision, 11. 31?. Mining, I. 229, II. 211. Minor scale, I. 394. Minot, II. 152. M. Inst. II. 111. Mirage, 11. 301. Mirbel, I. 728, II. 513. Mirror, I. 416, PI. 27, II, 286, 406. Mirrors, I. 433, PI. 28. II. 283, 287. Miscell.inea Berolinensia, II. 107. Miscellanea curiosa, II. 107. Miscellanea TaurinensiSj II. 109, Mississippi, II. 501. Misterton Carr, II. 368. Mists, I. 711,11. 474. Mitchcl, II, 444, Mitterpaclittr, If. 867. Mixed gases, f. 61", II. 221,465. Mixed goods, II. 218. Mixed metals, II. 510. 716" IVDEX. Mixed oscillations, II. 139. Mixed pktes, I. 470, PI. 30, II. 635, 680. Mixed pump, I. 332. Mixed semivowels, 11. 276, S77. Mixing malt, II. 316. Mixture, 1.310, II. 510. Mixture of colours, I. 440. Mixtures, II. 408, 503. Mock sun, II. 803. Mock suns, II. 301. Modelling, I. 113, II. 157. Models, II. 1?6. Modes of the ancients, II. S79. Modification of hydraulic forces, II. 235. Modification of motion, II. 181. Modulus of elasticity, I. 137, 368, II. 46 . . 49, 84, 86, 169, 509. Modulus of superficial co- hesion, II. 381. Modulus of tension, 11. 66. Mocris, I. 236. Moist air, II. 471. Moist ropes, II. 380. Moisture, I. 707, II. 468. Moisture contained in air, II. 4«6. Moivre. See Demoivre. Moleciiarattraction^I.380, Mole plough, II. 213. Moliferes, II. 126. Molina, II. 367. Momentum, I. 53, 59, 220, PI. 2, II. 36, 134. Momentum of light, II. 322. Momentum of water, II. 249. Monde naissant, II. 495. Mon^sier, II. 478. Monge, I. 754, II. 157, 303, 649, 652, 656. Monitum ad observatores mcteorologicos, II. 447. Mouochord, II. 272. Monocotyledonous plants, II. 513. Monoculus, II. 312. Monsoons, I. 703, PI. 42, 43. Mont Blanc, II. 447. Montbret, I. 121, II. 161. Montgoifier, I. 338, 365, PI. 23, II. 256, 264. Monthly magazine, II. 111. Monthly review, II. 105. Montpelier, I. 700. Mont Perdu, II. 447. Montucla,II. 124,217,378, 558. Moon, I. 454, 510, 528, 533, PI. S3, II. 294, 303, 335, 345, 449. Moon as causing tides, II. 577. Moonlight, II. 290. Moons, I. 509. Moon's age, I. 541. Moon's appearance, II. 358. Moon's atmosphere, II. 336. Moon's distance, II. 337. Moon's light, II. 280. Moon's mass, II. 337. Moon's motions, II. 373. Moon's phases, I. PI. 34. Moon's rotation, II. 342. Moon's surface, I. PI. 34. Moore, II. 371. Moors, II. 377. Morgan, II. 417. Morhof, II. 105, 270. Morne Garou, II. 494. Moro, II. 495. Morse, II. 366. Mortar, I. 160. Mortar for water, II. 232. Mortar mill, I. 232, II. 214. Mortars, II. 17i. Mortise, I. 168, II. 174. Moneau, II. Ill, 126, 654, 656, 659. Mosaic work, I. 97, II. 143. Moscati, 11. 460. Moses, I. 97. Moss, 11. 496. Mother of pearl microme- ter, II. 290. Motion, I. 18, PI. 1. 11.27, 129,137,138,377. Com- position of motion, I. 23. Confined motion, I. 42. Measure of motion, 1.79. Perpetual motion, I. 91, II. 142. Quantity of mo- tion, I. 52. Resolution of motion, I. 25. Motion of a rod, II. 138. Motion of light, I. 408. Motion of lighted wicks, II. 389.' Motion of sound, II. 265. Motions from heat, II. 404. Motions of a point, 11- 130. Motions of connected sys- tems, II. 138. Motions of plants, II. 512. Motions of systems, 11. 136. Motions of the electric fluid, II. 421. Motions of the stars, I. 516. Mould board, II. 212. Moulds, II. 404. Moulin, II. 525. Mountaine, I. 749, PI. 41. Mountainous countries, I. ri2. Mountains, I. 573, PI. 38, II. 366, 474, 497, 498. Mountains of Venus, II. 333. Mourgue, II. 449. Mouth, II. 353. Mouths of rivers, I. 731,11. 324, 480. Moveable body, II. 35. Movers, II. 104. Moving boats, II. 242. Moving flour, II. 200. Moving force, II. 140. Moving forces, II. 131. Moving globe, II. 376. Moving ground, II. 200. Moving media, II. 226. Moving statues, II. 20J. Moving trees, II. 200, 209. Mowing, II. 218. Moxon, II. 141. Mozart, II. 572. M. Taur. II. 109. M. Tur. II. 109. '»! Mud, II. 494, 498. Mudge, I. 196, PI. 16, II. 352. Mudge's measurement of an arc, II. 362. Mudge's scapements, II. 194. Mueller, II. 415, 435. Muid, II. 152. Mulberry bark, II. 190. Mule, II. 279. Mules, II. 167. Multiple arcs, II. 122. Multiple fraction, II. 2. Multiplication, II. 2, 3. Multiplication of images, II. 282. Multiplier of electricity, I. 682, PI. 40. II. 434. Multiplying glass, I. 416. PI. 27. Mural quadrant, I. PI. 35. II. 350. Murbert, II. 496. Murdoch, II. 370. Murhard, II. 105. Muriate of lime, II. 400 . . 402. Muriatic apid, II. 673. INDEX. Murray, 11, 840. Muscles,!. 198,739,11. 164. Muscles of the eye, II. 311, 591. Muscularity of the crystal- line lens, IT. 525. Muscular motion, II. 518. Mus£e, II. 111., Music, II. 279, 563. His- tory of music, I. 403. Musicae scriptores Mei- botnii, II. 272. Musical characters, I. 121. Musical chord, I. PI. 25. Musical instruments, 1. 397, II. 274. Musical notes, II. 07. Musical pen, I. PI. 6. Musical sounds, I. 379. Musical strings, II. 268. Musical typos, II. 159. Mushet ball.II. 227. Muskets, II. 262, 2C4. Muslin, IT. 187, 218. Musschenbroek, 1. 152,250, 253, 666, 750, 754, 756, II. 107, 125, 126, 168, - 170, 313, 378, 390, 391, 520, 524, 527, 528, 652, 653, 659. B. 1692, D. 1761. Mustel, II. 513. Mutchkin, II. 151. Mute letters, II. 276, 277, Mutilations, II. 518. Muys, II. 195. Mylius, IT. 336. Myopia, II. 315. Myopic sight, I. 452. Myriogramme, 11. 162. Myriolitre, II. 152. Myriometre, II. 152. Myrmecophaga, II. 678. Nail,I.;i65, IT. 150. Nail drawer, 11.216. Nails, U. 180, 206. Nairne, I. ri5,P1.40,II.431, 443. Nairne's machine, 1. 683. Nap, II. 188. N. A.Petr. II. 108. Napier, I. 247, 253, 598, 604. B. 1555, D. 1622. Napier's logarithms, II. 8, 124. Naples, II. 493. . Nasal semivowels, II. 276, 277. Nasal vowels, IT. 276. Native iron, IT. 501. Nativity of Christ, I. 539. Naturae curiosi, II. 107. Natural history, I. 723, 745, 750, II. 502. Natural hygrometer, 1. 7 10. Natural orders of plants, I. 739. Natural philosoph)', II. 105, 124. Natural zero, I. 651, II. 38P, 409. Naturder dinge, II. 127. Nature of colours, II. 320. Nature of light, I. 457, IT. 319- Naturforschende frcunde, II. 110. Naturforscher, IT. 107, 468. Nauchc, II. 429, Nautical Almanac, I. 602, IT. 370. Nautical angle, II. 375. Nautical astronomy, IT. 370. Naval architecture, II. 228, 239, 240. Naves of wlieels, IT. 203. Navigation, II. 234, 370. N. C. Gott, II. 108. N, C. Petr. IT. 108, Neap tide, I. 577. Ncbel, 11. 444. Von der cntstchung des nebels, II. 474. Nebula, I. 492, 494, II. 328, 680. Nebula in Orion, I. PI. 31. Nebulosity, I. 494. Needle, I. 746, II. 444. Needle floating, II. 382. Needles, IT. 189, 208, 218. Negative electricity, I. 661. Negative quantities, IT. 1,3. Negativoaflirmative arith- metic, II. 115. Neptunian theory, I. 720. Neret's amalgam. If. 432. Nerves, I. 739, 740, IT. 164. Nerves of the crystalline lens, IT. 526. Nerves of the eye, II, 597, 605. Nettis, I. PI. 29. Neue physikalische belus- tigungen,II. 109. Neufchateau, II, 213. Neutonianismo per !e don- ne, II. 280. Newcastle. Duchess of Newcastle, 11. 124, Ncwcomcn, I. 347, 357, PI, 24. New island, IT. 498, New river, II, 264, New stars, IT. 3f.'l, Newton, I, 6, 7, 26, 28, 36, 37, 44, 55, 65, 83, 248, 253, 287, 357, 366, 405, . . 407, 412, 437, 439, 457, 458, 463, 466, 469, 471, 476 , , 478, 480, 482, 483, 489, 506, 522, 542, 569, 575, 586, 591, 598, 599, 001, 602, 604, 607 . . 609, 611, 614, 638, 654, 7^9, 756, II 112, 121, 125, 217, 295J 296, 306, 317, 363, 376, 404, 413, 537, 538, 541, 556 . . 558, 009, 613 . .618, 620 , , 623, 025 , , 631, 633,634,637,636, 640, 641, 643, 645, 659, ()57, 661, 604, 666,671, 679. B. 1642, D, 1727. Newton, II. 141. Newtonian reflector, I. 429, Newtonian rules of philo- sophy,!, 16, Newtonian telescope, I. PI, 28, II, 79. Niagara, II, 480, Nicetas, I. 592, 596, 604, Nlch. II. HI. Nich.II. 8, 111, Nicholson, I, 111, 196, 201, 227, 682, 753, PI, 16, 33, 40, II. 128, 132, 196, 371, 607, 630, P, Ni- cholson, II. 172, 173, 178, Nicholson'scircle, I, 107. Nicholson's journal, II. Ill, Nickel, I. 686,11. 438. Nicolai, II. 114, 128. Nicole, IT. 558. Nieuhoff, II. 436. Nicuwentyt, II, 125. Nieuwe Vcrhandelingen van hct Batafsch (je- nootschap, II, 258, Night, I, 595, IT. 344. Night lamp, IT. 290. Night watch, II. 19^. Nile, 1.713, Nilonieter, I. 593, Nitocris, I. See Correc- tions. Nitrate of lime, IT. 292. VOX. II. 0 c 718 INDEX. Nitre, I. 634. Nitrogen gas, II. 509. Nocetus, II. 489. Noctuary, II. 192. Nodes, I. 504, PI. .34, II. 340, 372. Nodes of chords, II. 268. Nodes of the planets, I. PI. 32. Nollet,I.750,r56,II. 126, 189, 414, 520. B. 1700' D. 1770. Nonconductors, I. 666. Nooth, II. 432. Norfolk, II. 495. Noria, I. 327, PI. 22. Norinibergeiise comnier- ciuin, n. 108. Norraan, II. 486. Norske selskab, II. 109. North, I. 500. Northern crown, I, 497. Northern hemisphere warmer, I. 702. Northern lights, II. 488. Northern passage, II. 366. North pole, I. 687. Norway, II. 498. Society of Norway, 109. Norwood, I. 600, 11.362, 370, 376. Notation of music, II. 273. Notes of music, I. 396, II. 280". Nourishment of plants, II. 513. Nouvelliste, II. 435. Noya Caraffa. Duo de Ui Noya Caraffa, II. 435. Nucleus of a coinet, I. 512. Numa, I. 743. Number, II. 1, 113. Numbering vibrations, II. 272. Number of the stars, I. 490, II. 326. Numerical equations, II. 8. Numerorum quadratorum tabula, II. 115. Nunnez, II. 370. Nuova raccolta, II. 222. Nut, I. 72, PI. 5. Nutation, I. 506. Nutation of the earth's axis, I. 509,11. 334. Nutation of the moon's orbit, II. 341. Nutrition ^of animals, I. 738. Nutrition of insects, II. 518. Oak, II. 168, 169, 509. Oaks, II. 240. Oars, II. 236, 242. Oats, n. 151. Obbiezzioni alia teoria di Newton, II. 296. Obelise, II. 348. Object glasses, II. 80, 284, 286, 288. Oblique collision, II. 136. Oblique cylinder, II. 123. Oblique float boards, I. 322. Oblique forces, I. PI. 3. Obliqae impulse, II. 226. Oblique vjnpulse of fluids, 303 Oblique reflection, I. 437, II. 294. Oblique refraction, II. 605. Oblique threads, II. 41. Obliquity of the crystalline, II. 315. Obliquity of the ecliptic, I. 518, 593, II. 334. Obolus, II. 1C2. Obscure heat, II. 40e. Obscure light, II. 322, 407. Observations, II. 346, 371. Observations dans les Py- lAces, II. 367. Observations for finding the situations of places, n. 364. Observations made in Cook's voyage, II. 371. Observations .of tempera- ture, II. 452. Obserrations of the earth's motion, II. 358. Observations of the places of the planets, II. 357. Observations of the second- ary planets, II. 357. Observations of the stars, II. 355. Observations of the sun, II. 355. Observations of tides, II. 368. Observations of time, II. 348. Observations sur les ombres colorees,II.314. Observations sur la phy- sique, II. 110. Observatories, II. 347. Observatory, I. 148. Observatory for meteorolo- gy, II. 448. Observatory of Green- wich, I. 601. Observing distances, II. 156. Occultations, II. 3J0, 345. Octave, I. S93. Octant, I. PI. 35. Octants, II. 350. Ocular music, II. 320. Ocular spectra, I. 455, PI. 30, II. 314. Odorous bodies, II. 397. Odorous emanations, II. 397. Odours, II. 423. Oencmeter, II. 231. Oil, II. 291, 458. ££fect of oil on waves, II. 328. Oil candle, II. 245. Oil colours, II. 143. Oil mill, I. 222. Oil mills, II. 214. Oil paint, 11. 180. Oil paintings, I. 96. Oil press, II. 204. Oils, II. 322. Oil spreading on water, I. 625, II. 659. Oil swimming on water, II. 220, 223, 381, 382. Oily substances, I. 213. 01bers,I. 508, 603,11. 312. 334, 586, 591, 597, 673, 675, 676. Corrections. Old manuscripts, II. 159. Olive oil, II. 509. Oliver, II. 337. Oncia, II. 154. Opera glass, II. 78. ' Ophion,II. 333. Opposition, I. 527. Opposition offerees, I.Pl. 5. Optical centre, I. 418. Optical compass, II. 350. Optical fallacy, II. 646. Optical instruments, 1. 420, 11.76, 281. Optical pencil, II. 287. Optical scenery, II. 284. Optic nerve, 1. 448, 450, II. 82. Optics, I. 259, 408, II. 280, 323. Optometer, I. 452, II. 575, 604, 605, 671. Opuscoli scelti, II. 110. Oran outang, II. 279. Orbit of the sun, J. 500. Orbits of chords, II. 554, Orbits of come t», I. 521, II, 341. Orbits of the planets, II. 332, 372. Orbits of the primary planets, II. 339. INDEX. 719 Orbits of the secondary planets, II. 340. Orders of arcliitecture, I. 165. Orders of plants, I. 732. Ordinate of an ellipsis, II. 24. Ordnance, II. 263. Ore, II. 213. Organ, I. 402, 404, II. 275, 554, 610. Organic geometr\', II. 120. Organ pipe, II. 569. Organ pipes, I. 385, 401, 402, PI. 26. n. 266, 275, 537, 539. Organs of the voice, II. 275. Oriani, II. 300. Orifices, II. 61. Origine des fontaines, II. 479. Origines des inventions, II. 217. Orion, I. 497, II. 672. Ornithorhynchus, II. 672. Ornithorliynchus hystrix, II. 678. Orreries, I. 507, II. 374. Ortliographical projection, I. 116, PI. 8, II. 21. Oscillation, II. 53, 137. Oscillations, II. 194. Oscillations of a system, II. 139. Oscillations of a thread, II. 139. Oscillations of floating bo- dies, II. 220, 223. Oscillations of fluids, I. 287,11. 223. Oscillations of the sea, II. 343. Oscillations on pulleys, II. 138. Osiris, I. 403, II. 566. Ostrich, II. 311. Otto, II. 367,496,4)8. Oulton, II. 249. Ounce, II. 161. Oval, II. 557. Oval dome, II. 176. Ovallathe,II. 122, 209. Ovarium, II. 517. Oven, II. 403. Ovens, 11.410,411. Overflowing lamp, I. PI. 21. Overflowing well, II. 246. Overflow of the sea, II. 490. Overshot wheel, 1.320, PI. 22, II. 236. Ovid, I. 237. Owl, II. 312. Oxen, II. 181. Oxidation, II. 424, 498. Oxidofiron, 11. 211. Oxygen, I. 434, II. 514. Oxygen gas, I. 634, II. 292, 509. Oyster shells, II. 293. Packing press, II. 204. Padlock, II, 180. Pain, II. 178. Painters, II. 217; Painting, I. 454, II. 142, 217, 323. Painting wood, II. 180.- Palatine academy, II, 109. Palatine society, II. 447. Palladio, I. 253, PI. 11, II. 172. B. 1508, D. 1580. Palladium, II. 323. Palladius, II. 245. Pallas, I. 508, 531, II. 334, 372, 497, 674, 676. Pallet, II. 560. See Cor- rections. Palm, II. 153. Palmo, II. 154. Palpable characters, II.3 16. Pan, II. 154. Pane of glass, II. 294. PanciroUus, II. 217. Pangrapli, II. 144. Panorama, I. 455, 11. 314. Pantheon, I. PI. 12, II. 459. Pantograph, I. 103, PI. 6, II. 144. Pantomcter, II. 144. Pantometrum Pauccianum, II. 156. Paper, I. 98, 187, 244, II. 143, 217, 218. Paper hangings, II. 190. Paper making, II. 190. Paper mills, II. 190,213. Papers on naval architec- ture, II. 239. Papier mach^, II. 157. Papin, I. 345, II. 141, 24S, 347, 253. Papin's digester, II. 410. Pappus, 1. 243, 253, II. 113. Fl. 388. Papyrus, I. 98. Parabola, I. 39, 375, PI. 2, II. 24. Parabolas, I. PI. 10. Parabolic glasses, II. 283. Parabolic jet, I. 286. Parabolic orbit, I. 522. Parabolic path, II. 33. Parachutes, I. 306, II. 256, 263. Paradox. Hydrostatic pa- radox, I. 263. Parafeu, II. 200. Paragallo, II. 493. Parallax, 1. 54 2, II. 329,555. Parallax of a micrometer, II. 289. Parallax of a spheroid, II. 357. Parallax of the sun, I. 544. Parallel circle, II. 350. Parallelepiped, II. 18. Parallelepipeds, II. 19. Parallel lines, II. 9, 12, 13, 118, 158. Parallel motion, I. PI. 14. Parallelogram, I. 2,5, II. 13, IS. Parallel planes, II. 17. Parallel rulers, I. 102. PI. 14, II. 144. Paralysis, II. 314. Parajjet, II. 174. Paraselenes, II. 303. Paravolcan, II. 494. Parchment, II. 143. Pardies, I. 357, 366, 479, II. 118, 129. B. 1636, D. 1673. Parent, I. 219,324,11. 129. B. 1666, D. 1716. Parent's mill, I. 331. Parhelia, I. 443, PI. 29, II. 303. Paris, I. 454, II. 360, 365. Parisian academy, I. 249. Park, II. 442. Parker, I. 171, II. 175, ISO. Parker's lens, II. 407. Parkinson, II. 130, 498. Parrot, If. 466. Partial differences, II. 119. Partial electricity, I. 661. Partial reflection, I. 461, II. 584. Particles of light, II. 320. Particular geography, II. 365. Partridge, II. 605. Pascal, I. 748, 756, II. 112, 472, 558. B. 1623, D. 1662. Pasigraphy, II. 143. Pasquich, II. 130. Passage, II. 562. Passage of heat, II. 405. Passive strength, I. 93, PI. 11, II. 168, 169. Patent pipes, II. 205. Paternoster work, I. 335. Path of light, II. 299, 321. Path of the centre of gra- vity, I. PI. 3. Path ofthesun, I. 595. 720 INDEX. Paths of the planets, I. PI. 34. Piittens, II. 189. Patterns, II. 187. Paucton, II. 147. Paul, II. 279. Paulet, II. 186, 187. Paut, 11. 190. Pavements, II. 174. Pavhig roads, II. 203. Pear gage, I. 341, PI. 24, II. 254. Pearl barley. If. 215. Pearls, II. 519. Pearson, I. 567. Peart, 11. 417,437, 518. Peat borer, II. 211. Peat mosses, II. 498, 514. Pedestrian, I. 129. Pedometer, II. 156. Pegasus, I. 497, 753. Pemberton, I. 250, 253, 599, II. 125, 319, 524, 596, 643. Pen, I. 94. Pencil, I. 94, 95. Pencil of light, I. PI. 26, II. 70. Pencils, II. 149. Pendulous bodies, II. 139. Pendulum, I. 44, 107, 191, 595, PI. 2, 5, II. 34, 146 . . 148, 216, 343, 363. Circular pendulum, I. 197. Pendulum of two threads, II. 139. Pendulums, I. 526, 578, II. 132, 133, 136, 194, 218, 227, 339, 358, 359, 572. Penetrating into space, II. 330. Penetration, I. 144, 156, 224, II. 140, 206. Penetration of glats by wa- ter, II. 379. Penknives, II. 807. Pennant, I. 750, 756. B. 1726, D. 1798. Pennington, II. 403. Pennsylvania, 11. 367. Pcimyweight, II. 161. Penpark hole, 11. 495, 498. Penrose, II. 436. Pens, 1.99,11. 144, 217. Pens for lines, I. 100. Pentrough, 11. 237. Penumbra, I. 528. II. 313. Perambulator, II. 156. Perception of external ob- jects, I. 449, II. 313. Perception of Yegelables, 11.513. Perche, II. 151. Percussion, I. 223, II. 53, 136, 137, 140, 205. Perez, II. 145. Perforation in the moon, II. 335, 336. Perforation of ajar, I. 669. Performance of men, 11.166. Periodical springs, II. 480. Periodical stars, II. 331. Periodical winds, I. 701. Periods of sounds, II. 544. Periods of the planets, I. 506, P1.-32. Periods of the satellites, II. 373. Peripheric focus, II. 73. Peripheric image, II. 76. Periscopic spectacles, I. 495, II. 315. Perkinism, II. 428. Perks, II. 556. Permanence of sensations, II. 455. Permanent effects of heat and cold, II. 403. Permeability of matter, I. 610. Perpendicular, II. 9, 11. Perpendicular to a plane, n. jr, 18. Perpendicular to the meri- dian, II. 358. Perpetual motion, I. 91, PI. 6, II. 142, 238. Perrault, I. 204, 249. B. 1613, D. 1688. Perrault's ropes, I. 214. Perret, II. 207, 208. Perronet, 11. 176. Perseus, I. 496. Persians, I. 540, 595. Person, n. 141. Perspective, I. 93, 114, PI. 7, 8, II. 21, 157. Perspective instruments, II. 257. Perspcctire practique, II. 157. Perspiration of plants, II. 514. Perturbations, I. 518, II. 339. Perturbations of the ct)- mets, II. 341. Perturbations of the pla- nets, II. 340. Pestle, II. 214. Petersburg, II. 246, 452. Academy of Petersburg, II. 108. Petharlin, II. 496. Petit, II. 383, 579, 596, 599,601. Petrefaction, II. 497. Pewter ware, II. 206. Pezenas, II. 370. Pfaff, 1.753,11. 427. Pfannenschroid, II. 314. Phantasmagoria, I. 426, PI. 28, II. 285. Phases of planets, I. 527. Phases of the moon, I. 528, 345. Phenicians, I. 96. Pherecydes, I. 237, 253. B. 600, D. 515. B. C. Philadelphia, II. 109. Philibert, TI. 324, Philip, III. I. 601. Phillips, II. 234, 2G3. Philo, I. '24:0, 243, 253, 353, Philolaus, I. 592, 604. Philosophical transactions, 11. 105. Philosophical transactions abridged, II. 106, 107. Philosophizing, I. 16. Philosophy, II. 124. Phloscope, II. 291. Ph. M. 11. 111. Phormium, II. 185. Phosphorescence of vitrio- lated tartar, II. 293. Phosphoric animals, II. 29i Phosphoric cloud, II. 482. Phosphorus, I. 634. Phosphorus of Bologna, I. 435. Photometers, I. 421, 699, PI. 27, II. 282, 351. Photometry, II. 314. Pholophorus, II. 283, 291. Ph. tr. II. 105. Physical astronomy, I. 488, II. 339. Physical geography, II. 496. Physical optics, I. 434, 11. 80, after art. 460, 290, 317, 318, 639. Physical properties, II. 509. Physics, I. 485, II. 324, 519. Physikalische arbeiten,. II. 111. Physikalische belustigun- gen,II. 108, 109. Physiological effects of elec- tricity, II. 424. Physiological effects of heat, II. 403. INDEX. 721 Physiology, I. 738, II. 516. Physiolo(;yofplants,TI.512. Pianoforte, I. 398, 11. 274. Piaz7.i, I. 508, 603, II. 326, 334,347,377,672,673,676. Picard, I. 569, 600, 11. 152. D. 1682. Pickel, II. 432. Pictet, I. 370, 634, 635, 637, 638, 706, 751, II. Ill, 148 . . 150, 283, 384,467, 631,681, 682. Picture, II. 21. Picliircs, II. 142. Picture* on a wall, II. 284. Pidcrit, II. 415. Pifeces sur Taiman, II. 436. Piers, I. 163, 315. Pietra mala, II. 494. Pigment, II. 218. Pigott, II. 270. Pile, II. 206. Pile engine, I. 225, PI. 18. II. 207. Pile of Volla, I. 676, 752. Piles, II. 216. Piles. See Dcspiles. Pjlgram, II. 447. Pilots, II. 244. Pin, I. 155. Pinacograpbic instrument, II. Corrections. Pincers, II. 204. Pingr^, ir. 337, 365. PJni, II. 172, 275, 497. Pinion, I. 177, PI. 15. Pinions, II. 183. Pink dye, 11. 647. Pinkerton, II. 367. Pins, II. 189, 218. Pint, II. 148, 150, 151. Pipe, II. 151. Effect of a short pipe, I. 280. Vertical pipe, I. 285. Pipemaking, II. 206. Piper, II. 184. Pipes, I. 293, 354, II. 205, VOL. II. 221, 222, 245, 246, 539. Musical pipes, I. 379. Pipes of lead, I. 317. Pipes of pumps, I. 335. Pipes of wood, II. 211. Pir!», 11. 492. Pisce.s, I. 504. Pise, I. 169, II. 175. Pistols, II. 262. Piston, I. PI. 23, II. 237. Pistons, I. 332, II. 246, 248. Pitchers, II. 175. Pitot, I. 318,11. 239. Pittacus, I. 237, 253. B. 652, D. 570. B. C. Pivots, II. 184. rizzati, II. 121. Places of the planets, II. 310, 357, 372. Places of the stars, II. 330, 355. Plagoscopc, II. 456. Plain astronomy, I. 488. Plane, 11. 9. Pliine, IL 208. Plane mirror, I. 415. Plane mirrors, II. 282. Pianos, Xl. 17. Planetarium, I. 567, II. 375. Planetary aberration, II. 294. Planetary atmospheresj II. 332. Planetary orbit, II. 339. Planetary worlds, I. 531, II. 346. Planets, I.503,P1.32. 11.332. Planing, II. 209. Planispliercs, 1. 566, 11.371 . Planks, I. PI. 10. Planoconcave lens, I. 416. Planoconvex lens, I. 416, II. 288. Plant, I. 726, II. 367. Plaster, II. 175, 213, 218. Plaster for trees, II. 515. 5 Plaster of Paris, 1. 113. Plat, II. 189. Plate, II. 206, 208, 209. Plate glass, II. 287. Plate machine, I. 680, PI. 40, II. 431. Plates bandesj II. 176. Platina, I. 610, II. 388, 509, 510. Platina for mirrors, II. 283. Plating mill, II. 205. Plato, I. 239, 744, 756, II. 666,567. B. 429, D. 348. B.C. Platrifcre. See Laplatrifcre. Plaw, II. 174. Playfair, II. 498. Pleiades, I. 497. Plempius, I. 638. Pleurs, II. 495. Pleyel, II. 572. Pliers, II. 204. Pliny, I. 530, 576, 746, 756, II. 567. B. 24,D. 79. Plot, II. 266. Plotting table, II. 116. Plough, I. PI. 18, II. 167. Ploughing, II. 212. Pluchc, II. 129. Plucknctt, II. 197. Plumbery, II. 206. Plumb line, II. 354, 359. Plumier, II. 209. Plunger pump, II. 249. Plungers, I. 331, PI. 23, II. 235. Plurality of worlds, I. 532, II. 346. Plusb, II. 187. Plutarch, I. 239, 240, 598, 745. Pneumatic and bydrauliC' machines, II. 254. Pneumatic apparatus, II. 254. Pneumatic equilibrium, I. 270, PI. 19, II. 60, 220. D Pneumatic experiments, II. 254. Pneumatic filter, II. 246. Pneumatic macliines,1. 339, II. 252. Pneumatics, I. 352,11. 263, 378. Pneumatostatics, I. 258, PI.. 19, II. 220. Po, II. 224. Poda, II. 249. Poetry, I. 532, II. 563. Point, II. 8, 151. Moving point, II. 130. Pointed instruments,II.207. Points, II. 118,485. Points in electricity, 11.422. Point velique, II. 240. Polar circles, I. 570. Polarity, I. 688, II. 439, 440. Electric polarity, II. 419. Polarity of a balance, II. 159. Polarity of light, II. 310. Pole, II. 150, 203. Poleni, I. 357, 366. B. 1683, n. 1761. Poles, I. 570. Pole star, I. 496, II. 354, 365. Poli, IF. 482, 484. Polished surface, I. 412. Polishing, I. 231, II. 210* Polishing lenses, II. 284. Pollen, II. 514. PoUey, II. 141. Pollux, II. 567. Polycratcs, I. 237. ^ PolydorusVergilins, 11.216. Polygon, I. 26. Polygonometry, II. lia. Polygons, II. 118, 209. Polygraph, I. 100, II. 143. Polynoin als, II. 120. Polynomial Uieorcra, II. 144. 733 INDEX. Polypus, II. 516. Pompeii, II. 493. Poncclet, II. 489. Pondicherry, II. 301. Ponds, II. 480. Pont Notre Dame, II. 249. Poppe, II. 217. Population of England, II. 36T. Porcelain, II. 1,57, 206. Porcelain thermometer, IT. 388. Pores, I. 609,11.379. Porisms, II. 118. Porosity, 1. 459. Porta, II. 124. Portable observatory, II. 353. Portclumiire, II. 283. Porter cask, II. 233. Porterfield, I. 452, 478, 433, II. 311, 523 . . 525, 573, 575, 592, 603. Porters,1. 132,210, PI. 17, II. 166. Portfolios, II. 143. Port of London, 11. 233. Port of Toulon, II. 199. Positive electricity, I. 661. Post chaises. It. 203. Postulates, II. 9, 10, 557. Potash, II. 403, 509. Potatoe, II. 292. Potatoe bread, II. 519. Potatoe cutter, II. 208. Potatoe mill, II. 214. Pottery,!. 223,11.206,214, 918. Pouchet, II. 447. Pound, I. 124, II. 161. Pounding, II. 214. Poupart, II. 601. Powder, II. 259. Powder horn, II. 262. Powder magazine, II. 485. Powdermill, 1. 232, 11.813. Powder proof, I. 134, II. 259, 265. Powder thrown on glass, II. 419. Power, II. 124. Mecha- nical power, I. 321. Powers, II. 4. Powers and products, II. lis. Pownall, II. 459. Practical astronomy, 1. 536. 11. 346. Practical mechanics, II. 141. Prange, II. 142, 314. Preceptor, II. 110. Precession of the equinoxes, I. 505,519,11.341,349, 373, 374. Preliminary mechanics, II. 142. Premiums of the Society of Arts, 11. 218, 204. Preparation of food, II. 411. PreparHtion of raw mate- rials, II. 185. Preparations of vegetables, II. 5J2. Preponderance, I. PI. 5, 6, n. 54. Presbyopic sight, I. 452. Presensations of animals, II. 448. Preservation from light- ning, II. 485. Preservation of ships and their crews, II. 243. Preservation of wood, II. 180. Preserving fresh water, II. 481. President of the ft. S. II. 672. Press. Bramah's press, I. 263, PI. 23. Presses, I. 220, 22?, II. 304. Pressure, I. 59, II. 37, 134. Hydraulic pressure, II. 62. Pressure engine, II. 251. Pressure of a fluid, I. 261. Pressure of earth, I. 161, II. 173, 232. Pressure of fluids, I. PI. 19, II. 58, 222. Pressure of running water, II. 223. Pressure of the atmosphere, I. 273. Pressure of the air, EI. 220. Pressure of threads, II. 41. Pressure of water, II. 255. Pressure on a pivot, II. 133, 139. Provost, I. 638, 686, 698 . . 700, 754, II. 406, 438, 681, 682. B. Pre- vost, I. 709. Price, II. 117. Priestley, I. 480, 751, II. 127, 157, 217, 280, 416, 429. B. 1733, D. 1804. Primary mountains, I. 574. Prime number, II. 349. Primes, II. 116. Principle of motion, II. 140. Principles of mechanics, II. 137, 140. Pringle, II. 112, 500. Printer's grammar, II. 158. Printing, I. 93, 118, -121, 246, II. 158, 217. Printing from stones, I. 221. Printing press, 1.22 1,11.204. Printing stuffs, II. 188. Prints, II. 142. Prism, I. 414, 416,438, PI. 56, 27, II. 17. Prismatic micrometer, II. «89, 290. Prismatic spectrum, I. PI, 29, II. 679. Prisms, II. 19, 20. Prize for heat and light, II. 520. Prize respecting heat, II. 384. Proclus, I. 213, 253, II. 485. Procyon, I. 497. Product, II. a. Production of cold, II. 411. Progressions, II. 4. Progressive motion, I. 129. Progressive motion of light, II. 294. Projectiles, I. 33, 37, 286, PI. 2, II. 32, 132. Projectiles from the moon, II. 341. Projectiles with resistance, II. 226. Projection of a knife from a lump of snow, II. 394. Projection of a picture, II. 21. Projection of a Sphere, I. 117, PI. 8. Projection of eclipses, II. 346. Projection of light, I. 459. Projections, II. 374. Projections of areas, II. 118. Projections of the sphere, II. 374. Projections of the stars, II. 328. Prony, I. 36.'?, II. 114, 149, 219,236,360,398. Proofs, I. 644. Propagation of heat in fluids. II. 405. INDEX. 723 Propagation of heat in so- lids, 11. 405. Propagation of impulses, II. 618. Propagation of liglit, II. 320. Propagation of motion, II. 139. Propagation of sound, II. 68, 264. Propeller, II. 243. Proper motions of the stars, I. 493, II. 330. Properties of curres, II. 22, 120. Properties of matter, I. 605, 660, II. ST7, 60r. Prop or store, I. 71, PI. 5, II. 1.15, 212. Proportion, II. 114. Proportional compasses, I. 103, PI. 6, II. 144, 2ir, 218. Proportional quantities, II. 3. Proportional scale, II. 142. Proportions of wheels, II. 183. Props of reservoirs, I. 313. Prosperin, I. 513, II. 337. Protagorides, I. 746. Pi-otractors, II. 115. Proust, II. 674, 675. Provence, 11.502. Provinzialblaetter, TI. 474. Pruning trees, II. 208. Prussian measures, II. 148. Pt ilemaeus, II. 324. Ptolemaic system, I. PI. 31. Ptolemy, I. 473, 483, 495, 504, 530, ,590, 591, 594, 595, 604, II. 349. Fl. 160. Ptolemy Philadelphus, I. 592. Ptolemy Soter, I. 592. Pugh, II. 451, 463. Pullies, I. 68, PI. 4, 11. 40, 54, 138, 170, 172, 197, 200. Pulling up trees, II. 199. Pulsation of heat, II. 40j. Pulsation of the air, II. 407. Pulse, I. 291. Pulverisation, II. 213. Pump, I. 331, II. 166. ■• Pump capstan, II. 251. Pump for fires, II, 413. Pumping, I. 132, II. 165. Pump rods, II. 183, 1f)9. Pumps, I. Pi. 23, II. 177, 236, 247. Pupil, I. 451, II. 530. Purflcet, 11. 485. Purifying air, II. 252. Puschkin, II. 435. Putrescent wood, II. 293. Pyramid, 11. 17, 45. Pyramidical prows, II. 226. Pyramidoidal solids, ' II. 20. Pyramids, I. 593. Pyrenees, II. 366, 367, 447. Pyrites, II. 438. Pyrometer for a bridge, II. 176. Pyrometers, I. 646, II. 385. Pythagoras, I. 236, 237, 253, 403,404, 407,592, 598, 604, 744, 756, 11. 507. B. 568, D. 497. B.C. Pytliagorcans, II. 551. Pythagorean system, I. PI. 38. Quadrangular system of wires, IT. 352. Quadrant, I. 105, II. 76, 302, 350. Quadrant electromttcr, I. 683. Quadrant of altitude, II. 375, Quadrant pump, II. 248. Quadrants, I. 541, PI. 35. II. 349. Quadratic equations, II. 6. Quadratrix of the hyper- bola, 11.123. Quadrature of curves, 11. 120. Quadrature of the circle, II. 124. Quantity, 11. 1, 112,140. Quanz, II. 571, 572. Quarries under Paris, II. 211. Quarry, II. 213. Quart, II. 150, 151. Quarter, I. 124, II. 150, 151. Quays, I. 315. Queen post, I. 199, PI. 12. Querns, II. 2l!5. QuicksilvcT, II. 380, 408. Quiescent space, I. 20, II. 9, 27. Q.uins, II. 217. Quin, II. 231. Quinary arithrhetic, II. 116. Raccolta di autori chi trattano del nioto dcll' acque, II. 222. Nuova raccolta, II. 222. Rucks, II. 181, 183. Rackstrow, II. 324. Radial focus, II. 73. Radial image, It. 7B. Radiant heat, II. 322, 406. Radiation of heat, I. 636, II, 681. Radiations of light, II. 527. Radical quantities, 11. 115. Radius, II. 9. Radius of curvature, II. 22, 120. Rafn, II. 514. Rafter, I. 147, II. 179. Rafters in equilibrium, I, PI. 11. Rag pump, II. 249. Rags, II. 190. Raia torpedo, II. 435. Railing, II. 180. Rail roads, II. 204. Rain, I. 712, 713,11, 174, 216,465,475,483. Rainbows, I. 442, 470, PI. 29, 30, It. 81, 303, 308, 316, 643. Rain gages, II. 476. Ruin of ashes, II. 495. Rain water, II. 475. Rainy winds, II. 476. Raisin, II. 184. Raising a nap, II. 180. Raising ballast, II. 199. Raising boats, II. 200. Raising earth, II. 199. Raising flour, IT. 199. Raising ore, 11. 200. Raising ships, II. 199, 243. Raising stones, II. 199. Raising water, II. 247. Raising weights, I. 203,11. 196. Rameau, II. 272. Ramelli, I. 247, 334, PI. 23, II. 124. Rammelsberg, I. 235. Ramond, II, 447. Rams, n. 205. Ramsden, I. i05, 112, 125, 431, 433, 480, 602, 604, PI. 7, 8, 28, II. 145, 155, 231, 285,350,573, 584, 585, 587, 597. B. 1730, D. 1800. Ramsden's application of a planoconvex lens, II. 288. , 724 ITS'DEX. Ramsgate, II. 233. Ranby, U. 601. Range of a cannon ball, II. 260. Range of a projectile, I. 39, «86, II. 33. Raper, II. 152. Rarefaction, I. 632. Rarefaction of air, II. 220, 253. Rarefied air, II. 265. Rarity of the atmosphere, II. 60. Ras, II: 155. Raspe, II. 494, 496. Rasping mill, II. 215. Rats, II. 241. Rattlesnake, II. 518. Raven, II. 311. Ravenna, I. 587. Ray, I. 748, 756, II. 436, 495. B. 1628, D. 1705. Ray of light, I. 408, PI. 26, II. 70. Razors, II. 208, 209. Razor's edge, II. 389. Razor straps, II. 210. Reaction, I. 55, II. 379. Reaction of water, II. 223. Read, I. 714, II. 482. Reaping, II. 218. Reaping wheelbarrovir, II. 209. Reaumur, I. 632, 648, 748, 756,11.207,386,558,561. B. 1683, D. 1757. Reciprocal action, 1. 51, 55, 56, II. 35. , Reciprocal force, I. 613, Pl.'2, II. 37. Reciprocals of numbers, II, 4,5. Reciprocals of primes, II. 110. Reciprocating springs, II. 480. Reckoning board, II. 143. Reckoning machines, II. 146. Reckoning rods, II. 146. Recoil, II. 260. Recoiling scaperaents, II. 194. Recorde, I. 473, II. 323. Recovery of sight, II. 313. Rectangle, II. 13. Rectification of a curve, II. 124. Rectification of motion, I. 174, PI. 14, II. 182. Rectilinear motion, I. Pli 1. Recueil de tables astrono- miques, 11.373. Recueil de traitea sur I'electricit^, II. 415. Recurrence of sensations, II. 563. Redern, I. 480, II. 366. Red heat, II. 322. Red hot ball, 11. 262. Red light, I. 465. Red rays, II. 407. Red sea, I. 587, II. 234, 367. Reduction of angles, II. 146. Reduction of observations, II. 116, 147. Reeds, II. 185, 1S8. Reel, II. 186. Reeling, 11. 186. Rees, II. 127, 129. References, I. 25. Reflecting instrument, 11. 282. Reflecting instruments for angles, II. 350. Reflecting lamps, II. 282, 290. Reflecting level, II. 353. Reflecting microscope, 11. 79. Reflecting surface, I. 415. \ Reflecting telescope, II. 383. Reflecting telescopes, I. 429, 431,476. Reflection, I. 81, 437, 460, 472,P1.5,26,n. 70, 136, 543, 584, 622. Reflection at equal angles, II. 323. Reflection of a stone, I. 307. Reflection of cold, I. 638. Reflection of heat, II. 406, 631. Reflection of invisible heat, II. 283. Reflection of light, I. 410, 11.291,321. Reflection of sound, I. 374, PI. 25. Reflection of waves, I. 288, 3(5. Refracting mediums in mo- tion, II. 294. Refracting telescopes, II. 286. Refraction, I. 410, 411, 460, 472, 542, 566, PI. 26, 29, II. 70,287,320, 323, 354, 465, 509, 543, 623, 660. Double refrac- tion. II. 309. Refraction of balls, II. 226. Refraction of crystals, I. 445. Refraction of the atmo- sphere, I. 441, II. 81. Refractions, II. 472. Refractio solis inoccidui,II. 302. Refractive densities, I. 412, 421, 473, PI. 27, II. 70, 509, 679. Refractive force, II. 509. Refractive powers, II. 282, 294, 296. Refractive powers of tjje eye, II. 578, 604. Refrangibility, II. 282, 320. Refrangibility of heat, 1. 638. Refrangibility of light, J[l. 286. RetVigeralion, I. 698. Regal organ pipe, I. 401, PI. 26. Regemottc, II. 170. Regenerated paper, II. . 190. Register,' II. 192. Registered cordage, II . 187. Register for a mine,, 11.200. Registers of rain, II. 476. Regnault, II. 217. Regnicr, II. 167. Regression of heat, II. 405. Regulation of descent, II, 181. Regulation of discharge, II. 245. Regulation of force, I. 96. Regulation of hydraulic forces, I. 310. Regulator, I. PI. 2, II. 182. Regulator for a were, II. 234. Regulators of electricity, II. 434. Regulus, I. 497. Reil, II. 59f . Reimarus, II. 482, 486, 498. Relative centre of refrac- tion, II. 74. Relative motion, I. PI. 1. Relief, II. 157. Remarks on lialos, II 306. Remote tide, I. 579. Removing earth, I. 219. Removing ships, II. 243. Removing weights, I. 203, 210, II. 200. IXDEX. 725 Rfiiaud, I. 3S7, 366, II. 239. B. 1652, D. 1719. Reiieaux, II. 256. Ilcjieating watch, II. 192. Kcpertory of arts, II. 111. Reports on the port of London, 11. 233. Reports to the Board of Agriculture, II. 519. Representations of the stars, II. 328. Reproduction, I. 695, 724, If. 517. Reptiles, 11.271, 516. Republican calendar, I. 540. Repulsion, I. 76, 611, 65f, 65.5, PI. 30,rr. 377,378. Repulsions of floating bo- dies, I. 624, II. 655. Repulsions of the electric- fluid, I. 659. Repulsive firce, IT. 661. Repulsive strength, II. 49, 169. Reservoirs, I. 312, II. 233. Resilience, I. 143, 147, 629, II. 50. Resingue, II. 206. Resinous ele :tricity, I. 670. Resinous substances in lenses, II. 288. Resius, 11. 143. Resistance, 11. 134, 138. Resistance of fluids, I. 293, 303, PI. 21, II. 62, 226, 229. Resistance of machines, II. 141. Resistance of solids, 11. 168. Resistance of the air, I. 38, 201,305, 341, PI. 24, ir. 194, 195. Resistance to a globe, II. 320. vol. II. Resistance to a ship, II. 240. Resistance to curved sur- faces, II. 227. Resistance to the tides, I. 580. Resolution of force, II. 131. Resolution of motion, I. 25. Respiration, I. 7t39, IF. 517. Respiration of planrs, 11. 514. Rest, II. 9, 129:. Result of two motions, II. 28. Retardation, I. 29. Retardation of the tides, II. 343. Retarded pcndultiin, II. 35. Retarding force, 11. 29. Retina, 1.448, II. 82^311, 526, 530-, 582. Retrograde motions, I. 527. Returning stroke^ I. 713, II. 483. Return of light, I. 412. Reuss, II. 105. Reversionary payments, If. 167. Reversion of a compass, 11. 445. Reversion of series, If. 116. Revolutions from electri- city, II. 425. Revolutions of chords, I. 383, II. 268. Revolutions of the planets, II. 372. Revolving doablcr, I. PI. 40. Revolving fluid, II. 57. Rcvjlving globe, IL 220. Revolving oars, IT. 242. Revolving pendulums, I. 47, Pi. 2, 11.36, 136. Revolving stars, II. 329. Reynolds, II. 142, 528. B. 1723, D. 1792. Rhabdological abacus, 11. 146. Rheita, I. 428, 474, 483, PI". 28, n. 78. lUiemnius Fiinuius, n. 160. Rhinland foot, I. 111. Rhode, II. 473. Rhodi, II. 280. Rhomboid reticle, II. 351. Rhombus, II. S52. Rhythm, I. 39'-', II. 563. R. I. Library of the Royal Institution. Ribbon loom, IL 188. Ribbon machine far elec- tricity, II. 432. Ribbous, II. 187.' Ricciiti, I. 384, II. 86, 549. Ricciolii II. S24, 365. Richard, II. 446^ Richer, II. 357. Riehmann, I. 356, 743, 749, 756, 11. 391, 404, 483, 681, 682. D. 1753. Richter, II. 127. Ricketts, II. 488. Riding, II. 200. Rifle barrels, I. 40, 350, IL 262. Rig by, IL 517. Rigid bodies, II. 267. Right angle, II. 9. Right ascension, I. 536, 542. Right ascension of the stars, IL 344. Right ascensions, IL 349. Right line, IL 9. Ring, II. 189. Ringing, I. 131, IL 165. 5. E Ringing a magnet, I. 694. Ringing a bell, 11^270.- Ring of Saturn, I. 511. Rings from electricity, II. 423. Rings of light, II. 647. Rings of the planets, IT. 333, 346. Rinman, IL 141, 436. Rittonhouse, II. 390. Hitter, I. 437, 481, 639j 753, IL 323, 647. Rise and fall of the tides, I. 583. Rising and setting, I. 566. Risner, II. 280. River, II. 62. River of Amaions, II. 224, 370, 480. Rivers, 1. 292, 312, 572, 721, II. 224, 234, 366, 479. Tides of rivers, L 582. Rivi^re, 11.444, Rizzctti, II. 201, 320, 543. Road. Circular road, I. 48. Road harrow, II. 203. Road plough, IL 203. , Roads, 11.203, 218.. Robert, II. 256. Robertson, I. 427, II. 121; 144, 146, 256, 870, 455. Roberval, I. 598, IL 557^ 558. Robins, L 40, 360, S64, 366, II. 112, 261, 393. B. 1707, D, 1?5L Robison,I. 28,41, 131,132, U6, 250, 253,293,331, 363, 365, 372, 611, 658, 69-1, 751, II. 1218,159, 166, 169, 223, 225,227, 229, 247, 253, 259, 275, 206, 343, S19, 363) 3TT,, 726 INDEX. 397, 400, 409, 438, 443, 444, 459, 473, 607, 609, 610, 631. B. 1739, D. 1804. Rochfort, II. 250. Rochon, I. 121, 11. 295, 456, 4Sr. Rock crystal, II. 290, 309, 310. Rockets, II. 146, 263. Rod, II. 150. Rods, I. Ill, PI. 9, 14, II. 155, 181. Sounds of ro ters, I. 697. Sembrador, II. 212. Semifluids, II. 220, 338, 383. Semimateria) existeoces, I. 610. Semiramis, I, Correo 72B INDTCX. SeinicoDe, I. S9J, 11. 612. Jeraivowels, I. 400, II. 476, 27r. Seuiple, II. S-Sa. St'iicbier, II. 112, 127,321, 514. Seneca, I. 238, 253, 472, 576, II. I'i4, 337. B. 8, D. 65. Senegal, II. -353. Senguerd, II. 125, 953. Scnnert, 11. 124. Sensation, I. 725. Sensation of colours, I. 439. Sensation of li|j;lit, I. 409. Sensation of sight, II. 812. Senses, I. 738. Sensibility of the retina, I. 450. Sensible eftec^s of electri- city, I. 672. Sensible effects of the celes- tial motions, I. 523. Sensitive plant, 11. 512. Sentinel register, II. 192. Sepia, II. 313. S ptier, II. 159. Serain, II. 497. Serao, II. ^3. Serein, I. 711. Serenus,!!. 121. Serge, II. 385. Series of eclipses, I. 529. Series of rods, I. PI. 14. Serpent, I, 402. Serpentarius, 1. 495, 497. Serpentine, II. 4S8. Serpents, I. 735. Serrati, II. 128. Serson's top, II. 137. Serum, II. 180. Scrvetus, I.'748. Serviire, I. PI. 23, II. 125. Settingwbeat, II. 212. Severn, II. 370. Sewing, II. 189. Sex of bets, II. 517. Sex of flowers, II. 513. Sextant, II. 351. Scyffer, II. 309. S'Grave.'iande, I. 250, ?53, II. 185, 219. B. 1688, D. 1742. Shadow, I. 467, PI. SO, II. 348, 641. Shadow of a spheroid, 11. S4C. Shadows, II. 313. Shake, II. 550. . Shag, II. 187, 188. Shark, II. 519. Sharp, II. 570. Sharp instruments, II. 209. Shaw, I. 724,11. 499, 503, 678. Shearing clotlis, II. 188. Shears, II. 199, 208. Slieathlng, II. 2-K), 241. ShcfTield, 1. 24 5. Shehallion, I. 575, II. C64. Sheldrake, II. 450. Shcrwin, II. 117. Shining, II. 414. Ship, 1. 148, 325, PI. 22, II. 182, 241. Ship bolt drawer, II. 216. Ship building, II. 239. Shipley clmrch, II. 266. Ships, I. 304. II. 172, 242, 263. Ship's pumps, II. 236, 251. Ship's sails, I. 359. Ship's stove, II. 411. Ship's way, I. PI. 22, II. 156. Shock of electricity, II. 424, 520. Shoes, II. 189. Shooting a rope, II. 243. Shooting stars, I. 721, II. 499. Shore, I. PI. 5. Shores or props, II. 135. Short, I. 602. II. 624. Shortest descent, II. 133. Shortest roads, II. 203. Short hand, II. 143. .Shot, I. 351,11.262. Shower bellows, I. 344, PI. 24, II. 255. Siiower of ashes, II. 494. Shower of dust, II. 493. Shower of insects, II. 458. Shower of mud, II. 494. Showers of stones, I._719. 11.501. Shrinkage, II. 390. Shroud, I. 182. Shuckburgh, II. 148, 149, 152, 161, 267, 391, 393, S98, 471,473. Shut pipes, II. 266. Shuttles, II. 188. Shwanpan, II. 146. Sicard, II. 278. Sickiiigen, II. 168. Sidereal day, I. 537. Sidereal revolutions, II. 372. Sienna, II. 501, 674. Sieve of Eratosthenes, II. 11.5. Sieves, II. 188, 215. Sigaud de la Fond, II. 127, 416, 437. Sight, II. 312. Sights, II. 286, 823. Signals, II. 143. Signal trumpet, II. 275. Signs of the ecliptic, I. 504. Signs of the zodiac, I. 589. Silberschlag, II. 127, 141, 225, 496, 499. Silk, I. 184,11. 184,217. Silk plant, II. 185. Silk strings, 11. 275. Silkworm's, II. J8-t.' .Silkworm's thread, I. 134, 11.378. Silurus electricus, II. 436. Silver, II. 266, 509. Silver leafj II. 205. Silver plate, II. 209. Silver thread, II. 205. Similar solids, II. 17. Similar triangles, II. 14, 15. Simontdes, I. 403, 407, II. 567. B. 579, D. 469. B.C. Simple fraction, II. 1. Simple machines, II. 1-41. Simple sounds, I. 378. Simpson, 1. 250, 253, 478, 483, 700, II. 113, 117,. 118. B. 1711, D. 17«1. Sinison, II. 113, 117, 121. Sine, 11. 15, 672. Sine of an angle, I. 106. Sines, II. 122. Sums of sines, II. 16. Singing birds, II. 279; Single authors, II. Itl. Single vision, I. 453,. II. S13. Sinking of earth, II. 495. Sinkiug of ground, II. 498.. Siphon, I. 282, II. 196, 221, 238, 245, 251, 380. Siphon of Hero, 1. 188.. Siphons, 1.316. Sirius, I. 492,493,497,11. 330, 680. Sisson, I. 602, II. 148. Sistema participato. If; 554. Situations of places, II. 364. Six, I. 701, II. 447. Six's thermometer, I. C96, PI. 41,11.388. Sixth in music, U. 571. Size, I. 96, 187, II. 187. Size for cotton, II. 185 INDEX. ?29 Sky, I. 454, PI. 30,11.313. Slate, II. 175, 209. Slating, II. 179. Sleep, II. 518. Slicing tallow, 11.209. Slicing turnips, II. 208, 209. Slider pump, I. 334, PI. 23. Sliding rule, I. PI. 7. Sling, I. 33, 226. Slitting mill, I. 227, PI. 18. II. 208, 209, 218. Sloughing, I. 730. Sluice, I. PI. 21. Sluice board, II. 199. Sluice gates, II. 180. Sluices, I. 313,11. 233. Slusius, II. 114. Small, II. 377. Smeaton, I. 69, 79, 84, 158, 160, 168, 207, 250, . 253, 315, 323, 340, 361, 366, PI. 11,11. 128, 167, 233, 390, 391, 457. B. 1724, D. 1792. Smeaton's blocks, I. PI. 4. Smelling of insects, II. 5 18. Smith, I. 429, 478, 483, II. 79, 272, 273, 280, 511, 524, 541, 544, 551, 554, 609 . .611.D. 1768. Smith, II, 367. Pierce Smith, II. 601. Smith's microscope, I. PI. 28. Smith's work, II. 178. Smoke, I. 453, II. 258, 41 1, 534, 553. Smoke jack, 1. 324,11. 410, 411. Smoky chimnies, I. 346, II. 410. Snails, II. 312, 517. Snellius, I. 474, 483, II. 323, 363. B. 1591, D. 1626. Snow, I. 444, PI. 29, II. VOL. II. 30S, 306, 394, 420, 476, 478, 479, 482. Snow line, II. 452. Snow plough, II. 212. Snuff boxes, II. 180, 209. .Snuff mills, II. 213. Snuff press, II. 204. Societa Italiana, II. 110. Societas Palatina, II. 447. Soridte d'agriculture du dcpartement de la Seine, II. 251. Societe dc Lausanne, II. 111. Societfi philomatique, II. 111. Society for the encourage- ment of arts, I. 250, II. 110,218,520. Socin, II. 416. Soda, II. 403. Soft iron, II. 403. Softness, I. 629. Soil, II. 515. Solar altitudes,ll. 349,3.56. Solar and culinary heat, I. 637. Solar and lunar years, II. 340. Solar atmosphere, I. PI. 31. Solar clocks, II. 347, .374. Solar cycle, II. 349. Solar day, I. 537. Solar light, II. 291, 322. Solar microscope, I. 425, PI. 28, II. 284 . . 286, 317. Solar phosphori, I. 435, II. 292, 323, 630. Solar spots, II. 376. Solar system, I. 499, PI. 32, II. 372. Solar tides, I. 584. Solar time, II. 347. Soldering glass, II. 283. Soldner, II. 398. Solid, II. 8. Solid angle, II. 17. Solidity, I. 627, II. 383. Solid of greatest attraction, II. 339. Solid of least resistance, II. 226 . . 228. Solid of revolution, II. 17. Solids, I. 613, II. 123, 156, 658. Solomon, II. 480. Solstice, II. 539,P1. 34, II. 356. •Solution of iron filings, I. 69^1. Solutions, IT. 403, 510. Solway moss, II. 496. Somnambulism, II. 518. Son, II. 185. Sonde, II. 151. Somometer, II. 279. Sonorous cavities, II. 537. Sosigenes, I. 594, 604. Sothic period, I. 590. Sound, I. S67, 655, II. 65, 222, 264, 409, 531, 607. Sound from hydrogen gas, II. 267. Sounding, II. 244. Sound in gases, II. 265. Sounding board, I. 656. Sounding line, II. 156. Sound in water, II. 271. Sound in wood, II. 265. Sound of lead, II. 383. Sounds of chords, II. 549. Sounds of cylinders, II. 268. Sounds of gases, II. 267. Sounds of rods, I. 406. Sources of heat, I. 631. Sources of heat and cold, II. 385. Sources of light, I. 434, II. 290. Sources of motion, I. 90, 131, 164. Sources of sound, I. 378, II. 266. Sous, II. 162. South, I. 500. South America, I. 57 1, II. 447, 498. Southern, II. 256, 672. Southey, II. 501. South pole, I. 687. South Seas, II. 275. Sowden, II. 456. Sowing, II. 212. Space, I. 20,489,11.8,117. Spade, II. 166. Spallanzani, 1. 750, 756, II. 439, 497. B. 1729, D. 1799. Spark, I. 169, PI. 40, II. 420. Sparks from rubbing the . eye, II. 528. Sparks of electricity, II. 423. Spasmodic action, II. 314. Speaking trumpet, I. 375, PI. 25, II. 279. Spear points, II. 481. Specific gravities, 1. 3 10, II. 59, 231, 382, 388, 503. Table of specific gravi- ties, II. 503 . . 507. Specific gravities ofgases.I. 372. .Specific gravity, II. 403, 509, 510. Specific gravity of air, 11^ 221,471. Specific gravity of men, II.' 244. Specific heat, II. 406, 508.. Specimens of sounds, II; 277, 278. -*. Spectacles, II. 315, 323. Spectre, II. 314. Spectrum, I. 438, PI. 29,^ II. 296, 321, 604, 637>: 679. 73or INDEX. Speculum, II. 282. Speculum metal, II. 283. Speculum musicutn, II.S72. Speech, II. 275. Speed, II. 480. Speer, II. 232. Speer's hydrometer, II. 890. ' Spencer, II. 244. Sphere, I. 117, 11. 17,21^ 123, 229, 339, 876. At- traction ofasphere,n.45. Sphere charged with elec- tricity, I. 6G2. Sphere covered by a fluid, II. 220. Sphere of paper, 11. 376. Spheres, I. 515, II. 209. Spheres connected, I. 662. Spherical motion, II. 138. Spherical segments, II. 28fcl,313. Spherical surfaces, II. 71, 120. Spherical triangles, II. 135. Spherical trigonometry, II. 119. Spherical vortex, II. 226. Sphericity, II. 342. Spheroid, I. 577. Spheroidal navigation, II. 371. Spheroidal trigonometry, II. 119, 359. . Spheroids, II. 138, 359,359. Spherometer, II. 284. Spica Virginis, I. 497. Spiders, II. 184. Spider's thread, I. 134. Spider's web, I. 141, II. 352, 378. Spiija, II. 323. Spinet, I. 398. Spinners, II. 218. Spinning, 1. 181,11.185,186. Spinning {uachine, II. 186. Spinning wheel, I. 244, II. 186, 218. Spiral, II. 122. Spiral compasses, II. 144. Spiral mill, II. 236. Spiral of Archimedes, II. 562. Spiral orbit, II. 32. Spiral pipe, II. 238. Spiral pipes, I. 328. Spiral pump, I. 329, PI. 22, II. 248. Spiral spring, II. 139. Spiral vibrations of rods, II. 269. Spirit, I. 716. Spirit level, I. 310, PI. 21. Spirit levels, II. S53. Spirit of wine, I. 372, II. 382. Spirit thermometer, I. 647, II. 390. Spiritual substances, I. ,610. Spirituous liquors, II. 510. Splitting hides, II. 208. Sponge, I. 625. Spontaneous combustions, II. 385. Spontaneous electricity, II. 435. Spontaneous light, II. 291. Spoon for earth, II. 216. Spoon wheels, II. 236. Spots of the sun, I. 501, PI. 31, 11. 331. Spoules, II. 186. Spout, II. 487. Spouting fluids, II. 222, 223. Sprat, II. 107. Spring, I. PI. 2,10,11. 139, 217, 377. Spring of a coach, I. 148. Spring of the air, II. 220, 353. Springs, I. 179, S17, II. 131, 168, 182, 19.1, 203, 245, 383. Springs of water, I. 286, PI. 20, II. 451, 452, 479. Spring steelyard, 1. 127, PI. 9, II. 160. Spring temper, II. 403. Spring tides, I. 577, 585. Spur wheel, I. 177, PI. 15. Square, II. 13. Square of the velocity, II. 140. Squares, I. 102. Squinting, 11.315. Stability of a balance, I. PI. 8. Stability of a wedge, I. 155. Stabihty of equilibrium, I. 62,261, PI. 3,11. 40. Stability of floating bodies, I. 267, PI. 19, II. 59. Stability of fluids, I. PI. 19. Stability of ships, I. 326, II. 240. Stables, II. 174. Stacada, I. 401. Stadium, I. 593, II. 152. Stahl,I. 751,756. B. 1660, D. 1734. Staiolo, n. 154. Staircase, II. 174. Stairs, II. 165. Stalkart,II. 240. Stampers, II. 184, 190, 205. Stamping, I. 224. Standard measures, L 107, II. 146. Standard pendulum, II. 147. Standard weights, I. 124, II. 160. Stanhope, I. 67, 329,658, 664. SeeMahon. Staple, II. 179. Star Lyra, I. PI. 31. Stars, I. 487, PI. 36, 37, II. 325, 342, 355, 680. Eflect of the stars on light, II. 303. Stars visible in London, 11. 327. Statical baroscopes, I. PI. 19, IL 220,461. Statical engine, II.' 237. Statical lamp, II. 245. Statics, I. 93, 123, II. 159. Statics of fluids, I. 308. Statics of semifluids, 11. 220. Stationary planets, I. PI. 34. Station pointer,JI. 145. Statique, II. 129. Stattler, II. 127. Statuary's compass, I. PI. 7. Stay, II. 181. Steam, I. 271,619, IL 200, 386, 394, 397, 404, 464, 509, 519. Warming by steam, II. 410. Steam air pump, II, 259. Steam boat, I. PI. 29, II. 243, 259. Steam engine, I. 48, 133, .346, 361, 362, PI. 24, IL 133, 165, 167, 257, 263. Steam regulator, II. 258. Steam thermoraeter,II.389. Steam tubes, II. 246. Steatite, IL 157. Steel, I, 227, 685, II. 86, 169, 207, 403, 438, 509. Steele, II. 273. Steelyards, I. 126, PI. 8, 9, II. 160. Steelyard with a crane, I. 210, INDEX. 731 'Stemmata, 11. 602. .Stenciling, I. 94. Steno, II. 495. Stephensen, II. 492. Stere, II. 152. Stereographical projection, I. lir, PI. 8, II. 22,375. Stereotomy, II. 123. Stereotype printing, I. 122, II. 158. Stevin, I. 366, II. 134. Stevinus, I. 247, 253. D. 1633. Stewart, II. 113, 118, 340. Stick broken by a blow, I. 86. Stiffness, I. 139, 629, II, 49", 383. Stiffness of a cylinder, II. 83. Stile, I. 98. Stipa, II. 185. Stirling, 11. 119. Stirrup, I. 387, 11. 203. Stockholm. Academy at Stockholm, II. 108. Stocking loom, II. 188. Stockings, I. 244,11.218. Stodart, I. 227. Stone, I. 151, U. 48, 161. Stone bullets, II. 218. Stone cutting, I. 229, 230, II. 208. Stone gatherer, II. 200. Stone quarries, II. 209. Stones, II. 168. Stones fallen, I. 722, II. 501, 674 Stones joined, L PI. 11. Stopcocks, I. 317, PI. 21. II. 246. Stopping holes, II. 243. Stopping horses, II. 203. Storms, II. 45T. Storms of rain, II. 478. Stoves, 11. 253, 410, 412. Strabo, I. 576. Strada, II. 247. Straight line, II. 9. Straights, II. 458, 459. Straights of Dover, II. 495. Strain, I. 169. Strain on a bar, II. 44. Strain on a pl«to, II. 84. Strains of carpentry, II. 176. Stralsundisches magazin, II. 109. Strand, I. 182. Strange, 11. 497. Strap, I. J68. Strap on a wheel, II. 183. Straps for beams, I. PI. 13. Straps for wheels, I. PI. 15. Strata, II. 354. Straw, II. 185, 208. Straw paper, II. 190. Straw plat, II. 189. Straw work, 11. 188. Stream, I. 321, II. 9, 63. Stream bellows, II. 255. Stream of a fluid, I. PI. 20. Stream of air, I. Pi. 21, II. 532, 553. Stream of electricity, I. 670. . Stream of wind, II, 4S8. Streams of air from electri- city, I. 655, II. 424. Streams crossing, II. 222. Strength, I. 143, 144, 629, 11.49,164,168,169,380, 509. Strength in resisting the pressure of a fluid, U. 84. Strength of a column, I. PI. 10, II. 85, 86. Strength of a tube, II. 84. Strength of different sub- stances, I. 151. Strength of elastic sub- ■stances, II. 46. Strength of flood gates, I. 312, II. 84. Strength of gems, 11. 675. Strength of ice, II. 396. Strength of joints, I. PI. 13. Strength of materials, I. PI. 11. Strength of muscles, I. 128. Strength of ropes, I. 183. Strength of wires, II. 169. Striated surfaces, II. 625. Striking a magnet, I. 694. Striking part, I. 202. Stringed instruments, II. 274. String of baskets, I. 219. Stripes of colours, I. 465, PI. SO. Stroemer, 11. 441. Strohraeyer, 11. 387. Stroke, II. 137. Stroke of a bullet, II. 206. Stroke of lightning, II. 484. Strongest column, II. 51. Strongest forms, I. 149, 150, Pi. 10, II. 173. Structure of the eye, II. 311. Structure of wheels, II. 183. Structures of particular kinds, II. 174. Stuart, II. 172. Stuccos, II. 175. Stukely, II. 491. Sturm, II. 113, 125. Sturmius, II. 309. Subaqueous buildings, II. 232. j^ Subaqueous ice, II. 480. Subcontrary section,