+ af i” Palen ve . : “7 f 7e } ; ayes eG 4% yh BU ate, Kk eae } ee BHCALAMAGAZ) ae Oe BEOUMNAL OF SCLENDT. nit) bait Waren, rae f is, i Hace, Bs at am, bh: ae i PA as ee, te a : ae We eek beak RNa, Ral “ ; PANDA Bad in ; hy ove yi ay ; h wie ne sae ger. het ab ety > it es ca Bie a bs Fi oe : we dea. Silt, Pie Dies oo HG: : zs Poe ae A BRA Som ELC Relics *. a " : > Ang Cane, Bhat ee ae me haved figtvcem neg Joledee inthe Bg pennant ron py aye ep Betton a aa P PAGRLANE TEP H AP: ae : Di Maet : ava: ( Ai varlia ae THE LONDON, EDINBURGH, ann DUBLIN PHILOSOPHICAL MAGAZINE AND JOURNAL OF SCIENCE. CONDUCTED BY SIR DAVID BREWSTER, K.H. LL.D. F.R.S.L. & E. &e. SIR ROBERT KANE, M.D., F.R.S., M.R.I.A. WILLIAM FRANCIS, Pu.D. F.LS. F.R.AS. F.C.S. JOHN TYNDALL, F.RS. &e. “Nec aranearum sane textus ideo melior quia ex se fila gignunt, nec noster vilior quia ex alienis libamus ut apes.” Just. Lips. Polit. lib. i. cap. 1. Not. VOL. XVIIIL—FOURTH SERIES. JULY—DECEMBER, 1859. LONDON. TAYLOR AND FRANCIS, RED LION COURT, FLEET STREET, Printers and Publishers to the University of London ; SOLD BY LONGMAN, GREEN, LONGMANS, AND ROBERTS ; SIMPKIN, MARSITALL AND CO.; WHITTAKER AND CO.; AND PIPER AND CO,, LONDON :—— BY ADAM AND CHARLES BLACK, AND THOMAS CLARK, EDINBURGH; SMITH AND SON, GLASGOW ; HODGES AND SMITH, DUBLIN; AND PUTNAM, NEW YORK. “Meditationis est perserutari occulta; contemplationis est admirari perspicua . . . . . Admiratio generat queestionem, questio investigationem, investigatio inventionem.”—Hugo de S. Victore. — Cur spirent venti, cur terra dehiscat, Cur mare turgescat, pelago cur tantus amaror, Cur caput obscura Phoebus ferrugine condat, Quid toties diros cogat flagrare cometas ; Quid pariat nubes, veniant cur fulmina ccelo, Quo micet igne Iris, superos quis conciat orbes Tam vario motu.” J. B. Pinelli ad Mazonium. CONTENTS OF VOL. XVIII (FOURTH SERIES.) SS ES NUMBER CXVII.—JULY 1859. M. Pliicker on the Action of the Magnet upon the Electric Current, from a new point of view ...-++-+eerrsrss ert M. Pliicker on the Spectra in highly rarefied Gases of different kinds during the passage of the Electric Discharge........ Sir C. Lyell’s Remarks on Professor C. Piazzi Smyth’s sup- posed proofs of the Submarine origin of Teneriffe and other Volcanic Cones in the Canaries ....----eese es eecerres Prof. Hennessy on the Thickness and Structure of the Earth’s Chi Re ee i one cacoronitny Deron ocr arr Prof. Volpicelli on Frictional Electricity ....-++++++++-+- +5 Dr. Gladstone and the Rev. T. P. Dale on some Optical Pro- perties of Phosphorus.....--.++-+eerreererreecestesss Mr. A. Cayley on the Theory of Groups as depending on the Symbolic Equation 6*=1.—Part. HI... +--+ +2 see sees Prof. Miller on the employment of the Gnomonic Projection of the Sphere in Crystallography .-+---+-+++e+rseeeercere Mr. J. Cockle on the Theory of Equations of the Fifth Degree. Messrs. W. H. Perkin and B. F. Duppa on Jodacetic Acid... . Prof. Challis on the ‘ Loss of half an undulation ” in Physical Opiies,. eevee > 27 he eee Ad Jet START oeTEIS Notices respecting New Books :— M. Delesse’s Etudes sur la Métamorphisme des Roches . The Rev. G. Salmon’s Lessons Introductory to the Modern Higher Algebra .....-----se--erecersreerrrseces Proceedings of the Royal Society :— Dr. Hofmann on a New Class of Organic Bases ........ Mr. W. J. M. Rankine on the Thermodynamic Theory of Steam-engines with dry saturated Steam.......-...-- Mr. C. V. Walker on Platinized Graphite Batteries .... Proceedings of the Geological Society :— Messrs. J. Lancaster and C, C. Wright on the Sinking for Coal at the Shireoaks Colliery near Worksop, Notts. Mr. A. R. C. Selwyn on the Geology of Southern Australia. On Thermography, or the Action of Heat considered as a means of producing Images on Sensitive Paper, by M. Niépce de aa WAGIOES, peck de ec cere mee ine nee ee pepe nes a Notice of Traces of Eruptive Action in the Moon, by the Rey. De Wie WEED ea ions asr.e'se aoe Page 77 ly CONTENTS OF VOL. XVIII.— FOURTH SERIES, NUMBER CXVIII..«-AUGUST. Page Mr. H. C. Sorby on the Expansion of Water and Saline So- lutions at High Temperatures ...... 05-2 seee esse seeees 81 Prof. Draper on a New Photometric Process for the Determina- tion of the Diurnal Amount of Light by the Precipitation of St) a een preteen 91 Mr. G. Gore on the Rotation of Hollow Spheres of Metal by Hent oo i Seen PS eS Wo as be ei geen 94 Mr. J. Drummond on some points of analogy between the Molecular Structure of Ice and Glass; with special reference to Professor Erman’s observations on the Structural Divisions of Ice-on Take Baikal : 3353.) ccccip oceans scare eee 102 Mr. H. C. Sorby on the Freezing-point of Water in Capillary Tubes) occ coy + = sen on 0 os 7 gee eens oe 105 Prof. Davy on the presence of Arsenic in some Artificial ‘Ma- nures, and its absorption by Plants grown with such Manures. 108 Prof. Langberg on the influence of Capillary Attraction upon the Hydrometrical Measurement of the Specific Gravity of Liquids” 0.00.0. Uo nine ae Be Se oe ee le ae 113 Mr. A. Cayley on an Analytical Theorem relating to the ‘Dis- tribution of Electricity upon Spherical Surfaces——Part I... 119 Mr. C. P. Smyth on Teneriffe Fossils, and Sir Charles Lyell’s Notice in the Philosophical Magazine for July 1859 ...... 127 Dr. Atkinson’s Chemical Notices from Foreign Journals .... 128 Proceedings of the Royal Society :— Dr. Matthiessen on the Action of Nitric Acid and of Bin- oxide of Manganese and Sulphuric Acid on the Organic Bases sso. o atec ce swiss yelerahehetescnemeyalen Pe ier ON nie eeek aan 136 Dr. Smith on the Action of Food upon the Respiration.. 139 Mr. J. J. Bennett on the Discovery of the Composition of Water o6 oasis co cape eee alee eee SO ye 141 Dr. Dobell on the Influence of Light on the Growth and Nuixition of Animals 0 ooectg, 2 22 se amen came te 143 Dr. Alison on the Intensification of Sound through Solid BOdies. «ss -a/s)3) Secinny qetatets oie. revere nee tie eters eens 146 Dr. Hofmann on Diphosphonium-compounds .......... 148 Mr. J. P. Muirhead on the Discovery of the Composition BE Waterss coos. Sap ee eee Sito inkednes othe e» 151 Proceedings of the Geological Society :-— Mr. J. Lamont’s Notes on Spitzbergen ..........-.-. 153 Mr. T.S. Hunt on the Formation ofGypsums and Dolomites. 153 The Rey. S. Hislop on the Tertiary Deposits, associated with ‘Trap-rocks, in the East Indies . sh 1o3 On the Expansion of Crystalline Bodies by Heat, ‘by H. ‘Hahn. . 155 Description of various Processes made use of for finding out the Configuration of Optical Surfaces, by M. Léon Foucault .. 157 On the Organic Substance in the Meteoric Stone of Kaba, by Pidiedsbr W dliler ‘..:.'.' 6's’ es veeeede’s by iva bars pede eet Tamale CONTENTS OF VOL. XVIII.—FOURTH SERIES, NUMBER CXIX.—SEPTEMBER. ° Page Prof. Magnus’s Hydraulic Researches.—Part II. (With Two , Pr laatesa) tere cise atiatte oe < cere cro: sretetereial ccale,aletale, Slanetaabasthe edie os moe. Ae Gages OF Vavianitiels sites: « s)p stale amcuaes e. ph jee. ore. ry,008 M. F. Eisenlohr on the Relation between the direction of the Vibration of Light and the Plane of Polarization, and on its determination by means of Diffraction.................. Mr. A. Cayley on an Analytical Theorem connected with the Distribution of Electricity on Spherical Surfaces.—Part II. . Mr. W. K. Sullivan on the nature of Lactic Fermentation, and on an apparent conversion of Caseine into Albumen which accompanies the production of Lactic Acid in Milk excluded eA S15 pants} a's pigunsegate eb msl afarnioi ney ots ica als eS lille dies «0 2 = 475 Mr. H. Bauerman on the eee of the South-east ce of Vancouver’s Island ........ : . 475 vill CONTENTS OF VOL. XVIII.—FOURTH SERIES. Page Sir R. I. Murchison on the Crystalline Rocks of the North- west Highlands /. ......000s een eere cere cecsenes 476 Suggestions as to the Structure of the Tails of Comets, by the Rey. T. W. Webb . i. bie. ce ete cee cone n a sat ages 479 On the presence of Vanadium in the Clay of Gentilly, by P. Beauvallet ........ cece ee eee e cesses &.+ 5 gant ae vite e 480 NUMBER CXXf1I.—SUPPLEMENT TO VOL. XVIII. Dr. Bolley’s Critical and Experimental Contribution to the Theory of Dyeing. (With a Plate.) ...-..-... see cree . 81 Mr. J. Gockle on the Theory of Equations of the Fifth Degree. 508 Prof. Schénbein on the Polarization of Oxygen ..........:- 510 M. R. Bunsen’s Blowpipe Experiments ........+e..--++ 0s 513 Mr. A. H. Church on Parabenzole, and on the Isomers of Tur- PENUNE 5... ews wees ee Sete e se eW awa Ree eee 522 M. Becquerel on the Luminous Effects produced by the action of Light upon Bodies.. ......s. 500s ee cere ee eee eee eave 524 Proceedings of the Royal Society :— Mr. I’. Elefanti on Arithmetical Progressions .......... 582 Prof. Matteucci on the Electric Properties of Insulating or Non-conducting Bodies... .:.... ccseesceteccsecves 533 Mr. J. A. Wanklyn on the Synthesis of Acetic Acid.... 534 Messrs. W. Fairbairn and T. Tate on the Resistance of Glass Globes and Cylinders to collapse from external pressure, and on the Tensile and Compressive Strength of various kinds‘of'Glass ./.3. 260. SP. es ote tare 535 Prof. Brodie on the Atomic Weight of Graphite ...... 539 Dr. Matthiessen on the Specific Gravity of Alloys ...... 540 Messrs. F. C. Calvert and, R. Johnson on the Conductivity of Mercury and Amalgams- ...... 06... +e eeeecees 541 On a simple Apparatus for observing Atmospheric Electricity, by Prof. 'W.. Thomson .... 00.2.2 .ste cee eec ees s gave, 042 On the supposed Acid Reaction of Muscular Fibre, by E. du Bois-Regmond 6.6... 5. ses a\eme'eaa wee eis sdanine wa ok ana IMGT. os sates ia'e. ‘ PLATES. I. II. Illustrative of Prof. Magnus’s Hydraulic Researches. III. Illustrative of Dr. Bolley’s Paper on the Theory of Dyeing. THE LONDON, EDINBURGH anv DUBLIN PHILOSOPHICAL MAGAZINE AND JOURNAL OF SCIENCE. [FOURTH SERIES.] J UL.Y 859. I. Observations on the Electric Discharge. By M. Pucker. [Continued from vol. xvi. p. 418.] On the Actiun of the Magnet upon the Electric Current, from a new point of view. 76. 7 pase rotary motion of a magnetic pole around the con- ducting wire, and of the conducting wire around a magnetic pole, are phenomena which, on their discovery by Faraday, arrested the attention the more, because they were not connected by analogy with any previously observed phenomena. Laplace and Biot, by considering the action between the pole and a single element of the linear conductor of the current, obtained an elementary force whose magnitude is inversely pro- portional to the distance between the pole and the current- element, and whose direction is perpendicular both to the direc- tion of the stream-element and to that of the straight line con- necting this element with the pole. This force, which is reversed in direction both by an inversion of the magnetic polarity and by an inversion of the direction of the current, would move the stream-element, if it were free to move, parallel to itself, in a circle around the line which passes through the pole and is parallel to the stream-element. If, instead of the imaginary polar point, which must always be a mathematical fiction, we place a magnet of arbitrary form, then in determining the direction of the force, the straight line passing through the pole becomes replaced by that magnetic curve which is perfectly defined in position by passing through the current-element. There is no force present either to change the direction of the current-element, or to force it along the magnetic curve to a point of greater magnetic activity. i pa ai by Dr. F. Guthrie, from Poggendorff’s Annalen, vol. civ. : Phil. Mag. 8. 4. Vol. 18. No, 117. July 1859. B 2 Prof. Pliicker on the Action of the Magnet 77. The above gives, in the form of an integral, the expres- sion for the total action of a magnet upon a current whose con- ductor is a linear one of arbitrary form. It has, however, been assumed here that this form remains continually unchanged. We obtain a new point of view if we regard the conductor as perfectly fle«ible, and then inquire what would be the form of such a conductor as current-bearer under the influence of the magnet. From the simplest mechanical principles the following laws are derived. 78. I. If any magnetic forces act upon a perfectly flexible con- ductor through which an electric current passes, equilibrium can only exist when each element of the conductor is so disposed that the magnetic action upon it disappears, that is, when the conductor assumes the form of a magnetic curve. If this condition cannot be fulfilled, the smallest portions of the conductor, unless held together by cohesion or other forces, must necessarily be rent asunder in consequence of the magnetie action. Nothing is altered in the above consideration, if, in place of the perfectly flexible stream-conductor, we imagine an electric current itself, which is not cweumscribed to a conductor, but which is free to seek its path through a space in which ponderable matter occurs which serves for its conduction. Be- fore the magnet begins to act, such a stream will follow a more or less variable path, but under the magnetic influence it will adopt the course of a magnetic curve. If it is wnable to do this, the current cannot continue: the electricity must be lost with- out the formation of such a stream. 79. Il. In order that the perfectly flexible conductor under the influence of the magnet may be in equilibrium over a given surface, the direction of the furce acting at every point of the conductor must coincide with the normal to the surface at this point. In order that this condition may be fulfilled for every point in the conductor, the element of the magnetic curve passing through this point, as well as the element of the conductor itself, must fall in the given plane; and hence again the in- ference is easily drawn that in the case of equilibrium, the per- fectly flexible conductor is the geometrical locus of those points in which the element of the magnetic curve passing through them falls upon the given surface. This geometrical locus, which changes in form and position by an alteration in the position of the given surface towards the magnet, is therefore the only way which the current can pursue upon the given surface, and it only adopts this path if its terminal points, which we consider fixed in position, both lie upon the geometrical locus just defined. Such curves may be appropriately named “ epipolar-magnetic.” Before and after an inversion, both of the magnetic polarity and upon the Electric Current. 3 of the direction of the current, the stream in the same portion lying betweer. the two given points is, in the one case, depressed towards the surface, in the other drawn away from it. It is only in the first case that a proper current can exist. In the second case, as well as generally, where the terminations of the stream are not points of the curve described, the magnet pre- vents the formation of a current *. 80. In the theoretical consideration of Law I. we encounter three cases, which are also again met with in experiment. (1) The electric discharge takes place between two given fixed points. This is the case of Davy’s are between carbon-points, which at first are in contact, and are then gradually separated from one another and held at a fixed distance apart. If no dis- turbing influence is at work, the path of the electric discharge in air, as in a rarefied atmosphere, i is the straight line connectin; g the two carbon-points, or the metallic points which may replace them. The glowing particles which are carried over and which may be recognized in the spectrum, are to be considered, in part at least, as conductors of the current. In long tubes, in which the gas is in a condition of maximum rarefaction, no such par- ticles are transported when Ruhmkorff’s apparatus is discharged through it: in such case the rarefied gas alone is the bearer of the current; for the spectra obtained characterize each gas * Jn order to illustrate as graphically as possible that electric light, first observed by me, which collects in magnetic curves, I imagined the ex- istence of perfectly flexible, infinitely fine magnetic threads (47 to 49). It is to be noted that such a thread, when rigidly held in one of its points, will remaim in equilibrium under the influence of the magnet when it assumes the form of the magnetic curve passing through that point; just as is the case also with a linear, perfectly flexible, electric conduc- tor. In the first case we immediately recognize the force which gives form and position to the magnetic thread of arbitrary form and posi- tion, when equilibrium is established. In the second case, however, the circumstances are otherwise. If, for instance, we imagine moveable rectilineal conductors proceeding radially in all directions from a given point, and which are subjected to the action of a given magnetic pole, we may suppose all these conductors to be distributed upon conic surfaces whose common axis is the straight line connecting the given point with the given pole. All such conic surfaces rotate uniformly around their common axis. If we take the case of an arbitrary magnetic action and suppose the conductors to be infinitely small, all the conductors rotate in conic surfaces whose common axis 1s the tangent of the corresponding magnetic curve at the given point. That conductor alone which follows the course of this curve, remains at rest without the other conductors being forced into this position. The difficulty of the question consists in our being obliged to consider the current not as already formed, but in the course of formation; and although we have no definite notion as to the formation of a current in general, we know at least so much, that under the magnetic influence it can only shape itself according to the magnetic curve. B2 4 Prof. Pliicker on the Action of the Magnet employed, just as the spectra of Davy’s are show the character of the electrodes. Under the influence of a magnet, Davy’s are of light assumes the form of a magnetic curve, if the end-points of the two electrodes are so situated with respect to the magnet as to constitute two points of the magnetic curve. If the end-points of the two elec- trodes are brought into another position where the above con- dition is no longer fulfilled, the are can no longer exist ; it must be broken, and, according to the density of the surrounding gas, gives rise to the appearance of a springing, hissing, or undulatory hght. The previous experiments in this direction of so many eminent physicists, are amply sufficient for consideration from this point of view. I shall therefore at present only refer to my own observations, which will be found in the next sueceeding paper. With the exception of some older ones, they have been performed with the direct purpose of verifying Law I. 81. (2) One of the two extreme points of the electric discharge is fixed, and the second is subjected only to the condition of lymg on a given surface of arbitrary form. These conditions obtain in the remarkable behaviour of that light which I have called the magnetic light, on the very account of its adopting the path of magnetic curves. This light is formed in exhausted tubes at the negative electrode, and passes in all directions from every point in it, to the walls of the glass tube surrounding this electrode, which become more or less blackened by the trans- ported platinum. What becomes of this electric light after it has touched the walls, is a question which cannot be considered in this place. If the electrode be isolated with the exception of a single point, this point is the only one from which the electrical discharge takes place, and whose different paths, corresponding to elementary currents, are made visible by the single luminous rays. (For our present purpose of consideration it is indifferent whether all the rays proceed from the fixed point, or travel towards it.) Every such elementary current, according to the above Law I., can only be in equilibrium under the influence of the magnet when it is bent in a magnetic curve; and here this curve is the same for all elementary currents, and is perfectly defined by passing through the given fixed point. The whole light, therefore, proceeding from the unisolated point is concen- trated, therefore, in the magnetic curve passing through it; and the curve becomes in consequence brightly lummous. The whole continuous series of light-radiating points of the wnisolated negative electrode, corresponds to a continuous luminous surface formed from magnetic curves. Inasmuch as the magnetic curves remain the same if the upon the Electric Current. 5 magnetic polarity be inverted, it follows that after such an in- version, exactly the same appearance is shown. The beautiful phenomena first observed by me (see Phil. Mag. for August and December 1858), as well as similar ones, after- wards to be described, formed at the positive electrode, are therefore fully explained. 82. (3) The discharge occurs between two given surfaces, or between different portions of the same given surface ; so that the elementary discharge-currents may, within certain limits, seek their terminal points upon these surfaces. In this case also experiment had preceded theory. The first observation of this kind was made upon an evacuated ellipsoid, which formed the central portion of a Geissler tube (63). If it was placed equa- torially upon the approximated armatures, a vaulted arch con- sisting of luminous magnetic curves was formed in its interior, far removed from the two electrodes. After the eye had once had its attention directed to these phenomena, it recognized them also under other and very different circumstances. 83. It now only remains to make some preliminary remarks concerning the application of Law II., which determines the only possible path which the electric discharge, under the influence of the magnet, may follow on the internal surface of the glass tube; that is, which determines the epipolar-magnetic curve. Let us, for example, suppose that the internal surface has the form of a triaxial ellipsoid, and that this lies with its middle point above the middle, between the two horizontal armatures, so that one of its thin axes is vertical : it is clear that the section- ellipse, in that portion of it which belongs to the principal section which falls in the equatorial plane, belongs also evidently to the curve in question ; for every magnetic curve which passes from one of the two armatures to the other, cuts the equatorial plane at right angles, so that the elements of that one of these curves which cuts the ellipse, lie within the surface of the ellipsoid. A regular current is only possible when it enters the ellipsoid in one point of the ellipse and leaves it in another one. This stream describes, then, on the ellipse between the two points, one or the other path according to its direction (compare the experiment of § II.). It is in consequence of a secondary action (which always increases with the magnetic influence, and is of very different intensity according to the different contents of the tube) that the current, when drawn towards the magnet, becomes disintegrated into an undulating light. This phzeno- menon is conditioned by the occurrence of the action corre- sponding to the third case (82) of Law I.; and consequently the unexplained (15) is rendered clear. If the current enters and departs through any two points which are not both points of 6 On the Action of the Magnet upon the Electric Current. the ellipse mentioned, or, what comes to the same thing, which are not both in the equatorial plane, in general no current is formed. Only in the exceptional case that both points belong to the same magnetic curve, and the are of this curve between the two points falls entirely within the ellipsoid, does the first case of Law I. immediately occur. 84. A second simple example is offered in the case of a wide cylindrical tube, which is laid horizontally upon the armatures, and inclined at an angle of 45° to the equatorial plane. Then the middle of the epipolar-magnetic curve consists of two distinct spirals, which, taken separately, are brightly illuminated by streams in opposite directions. 85. The above laws may be also very beautifully illustrated by means of induced currents, although not with the same splendour as in the case of the direct discharge. I took for this purpose (to adduce here only one instance) a simple glass bulb, without electrodes, of about 80 millimetres diameter, which, after exhaustion, contained only traces of a gas. If the outer surface of this sphere be touched in any point with one of the electrodes of Rubmkorff’s induction apparatus, a diffused light, the colour of which is peculiar to the gas, spreads throughout the whole sphere, from a point of the internal glass surface corresponding to the point touched on the outside. If the sphere be laid in the middle upon the approximated armatures of the electro-magnet, this light collects to a single are of light, corre- sponding to that magnetic curve which passes through the fixed point. A second electric current traverses the same path in an opposite direction. If the electrode in contact with the sphere be the negative one, a strong positive stream proceeds from the point of contact ; a weaker current returns by the same path to the same point. If the touching electrode be the positive one, the two currents mutually exchange their intensities ; the positive stream which passes to the point of contact being the stronger. If the sphere be touched simultaneously in any two points with both electrodes, the two arcs of light corresponding to the two electrodes appear simultaneously, independently, and apparently without interfering with one another. It is only when the two electrodes touch the sphere in two points of the same magnetic curve, that the two luminous ares unite to form one. 86. If we lead the terminal point of an electrode along the surface of the sphere, the luminous are undergoes a continual alteration of form and position. The length of the are dimi- nishes on approaching the epipolar-magnetic curve. From a point of this curve no magnetic curve passes into the interior of the sphere. Even on touching such a point with the electrode, the light remains on the internal surface of the sphere, and is On the Electrical Discharge through Rarefied. Gases. 7 concentrated into two currents of unequal intensity, which ex- tend upon the epipolar curve in contrary directions from the point of contact. This curve is, in the present case, the great circle which lies in the equatorial plane, which is cut at right angles by an infinite number of magnetic curves upon the surface of the sphere. In addition to this double epipolar- luminous stream, the free arc of light, corresponding to the two touching electrodes, continues to exist undisturbed in the interior of the sphere. It is only when both electrodes touch the sphere in points of the epipolar-magnetic curve, that the two epipolar double currents unite into a single double current, which pos- sesses the luminous intensity of both the former ares*. Bonn, July 15th, 1858. II. Observations on the Electric Discharge. By M. PitcKkert. On the Spectra in highly rarefied Gases of different kinds during the passage of the electric discharge. 88. I BELIEVE that I was the first to declare positively that the luminous appearance which accompanies electrical discharge through long tubes of rarefied gases, is (without con- sidering the special phenomena in the neighbourhood of the two electrodes) entirely and completely attributable to the traces of gas remaining in the tubes; further, that the beauty and great diversity of such spectra for various gases offer a new cha- racteristic for distinguishing them, and that any chemical altera- tion in the nature of the gas may be thereby at once recognized. This seemed to me to be the most important part of the subject, pointing, as it does, to a method of physico-chemical investiga- tions of a new kind. 89. I find that my opinion, that no particles of metal are transferred from one electrode to the other, has been supported by Mr. Gassiot{. Metal is transported from one electrode alone —the negative one—to the portion of the inner surface of glass immediately surrounding it; and such transportation occurs * The author states how the new point of view developed in the above, threw such a clear light upon some further experiments of his (see the following paper), of which some use has been made in this communication, that a revision of the latter was considered necessary before publication. + From Poggendorff’s Annalen, vol. ev. No. 1, p. 7. + “The minute particles of platinum are deposited in a lateral direction from the negative wire, and consequently in a different manner from what is described as occurring in the voltaic are (De la Rive, ‘ Electricity,’ vol. ii. p- 288), so that the luminous appearance of discharge from the induction machine can in no way arise from the emanation of particles of the metal.” (Proceedings of the Royal Society, March 4, 1858.) 8 Prof. Pliicker on the Spectra in Rarefied Gases whatever be the nature of the metal forming the electrode. The surrounding surface of glass is gradually blackened by the finely divided metal; when the deposit becomes thicker, a beautiful metallic mirror is formed. A thin deposit of platinum appears blue in consequence of its fine state of division, and precisely resembles in colour one of the shades of Faraday’s finely-divided gold*, I have seen a beautiful mirror of zine at one end of a wide glass tube, which extended as far as the zine electrode pe- netrated. This mirror was shaded off grey at the limits of its opake borders. Jn this manner a new series of experiments might be performed in reference to the optical properties of metals in a state of extreme division. 90. In order to lessen the unpleasant blackening of the glass which occurs under ordinary circumstances, instead of the thin wires ordinarily taken, which become hot and sometimes glow brightly when serving as negative electrodes, we may employ thick wires, which do not undergo any sensible warming in the current. In the case of thin wires bemg employed, the great transference of the metal from the negative electrode appears to arise in part from the greater amount of heat. developed, and not to be exclusively owing to the greater concentration of the elec- tric current upon the smaller surface of the thinner electrode. M. Geissler sought in another manner to avoid the blackening of the glass, namely, by surrounding the negative platinum elec- trode by a narrow glass tube which projected a little distance beyond the free end of the wire into the wider glass cylinder. The inside surface only of the smaller tube became black in this case, as far as the electrode reached. 91, The followmg observation supports in a manner, and inde- pendently, the opinion that in tubes of rarefied gases the metal is not the bearer of the electrical discharge, and consequently the cause of the phenomenon of ight. Three different tubes, of a form previously described (63), were respectively filled with pure hydrogen, with arseniuretted and with antimoniuretted hy- drogen, and then exhausted as far as possible. The stream of light in the narrow part of each tube gave the characteristic instantly-recognizable spectrum of hydrogen. The two last- mentioned gases had obviously suffered decomposition by the electric current. The metals arsenic and antimony separated by this decomposition cannot be detected in the current of light. 92. Before proceeding to the analysis of the light of the dif- ferent gas-vacua, we must briefly consider the question whether an absolute vacuum bars‘the passage of the electric current, and, by doing so, extinguishes the light. An absolute vacuum, like a mathematical pendulum, is a fiction ; and the practical question * “ Experimental Relations of Gold to Light,” Phil. Trans. 1857, p. 145. during the passage of the Electric Discharge. 9 is only whether no electric discharge passes through the nearest possible approximation to an absolute vacuum which we can procure. A Torricellian vacuum, especially such a one as exists in the tubes prepared by M. Cassella for Mr. Gassiot, which show the broad clouds of light, is evidently more perfect than the gas-vacua in the different Geissler tubes which were produced by means of a mercury air-pump, and in which a lower tension than 1 millim. is probably unattainable. At my request M. Geissler has also lately made Torricellian vacua in longer and wider tubes with great care. The best of these tubes allow the passage of the direct discharge of Ruhmkorff’s apparatus. This discharge, which is accompanied by a white light, soon, however, becomes intermittent, and after one or two minutes it completely ceases. If, in accordance with the analogy of an experiment before described (73), we are justified in forming an opinion as to what takes place in such a tube, we must assume that the oxygen of the immeasurably small quantity of air which has remained behind goes to the electrode, and that the residual nitrogen no longer suffices to convey the current. I agree with the opinion that ponderable matter is necessary for the formation of an electric current. Such matter is, how- ever, in general a gas, and not as (at least partly) in Davy’s lumi- nous arc, metal or carbon passing over in the extremest state of division *. 93. I introduce here an observation which was made with every tube containing a Torricellian vacuum. Coatings of tin- foil were fastened near to both ends of such vacua, in order to be able to pass induced currents through them. (See subsequent par. 118). After the passage of the direct current had ceased, the induced current might still be passed through for a long time with undiminished brightness. On reconnecting the wire extremities of Ruhmkorff’s apparatus with the ends of the two platinum wires fused into the ends of the tubes, the direct cur- rent was re-established, but soon disappeared again. The same experiment might be repeated at pleasure. 94. Most gases, when the current is passed through them in * The transference of the substance of the electrodes from the one to the other of them has been, since Davy’s time, the subject of numerous investigations. In general it was assumed that this transference took place from the positive to the negative electrode. M. von Breda, however, proved that a simultaneous transference occurred from the negative to the positive. In Geissler’s tube the particles of metal simply leave the nega- tive electrode without reaching the positive one. It would seem as if anomalies existed here similar to those relating to the occurrence of heat at both electrodes (46). Experiments which I have quite recently per- formed upon the occurrence of the luminous arc in bulbs of rarefied gases (under the influence of the magnet), and which will be described in the next communication, will, I believe, throw light upon the subject in question. 10 Prof. Pliicker on the Spectra in Rarefied Gases Geissler’s tubes, suffer changes which are at once visible on account of the simulta- neous alteration in colour. These changes are often sudden, especially when the cur- rent is concentrated by the magnet; fre- quently, however, they take place quite gradually. Such changes are accompanied by a decomposition of the gas, or by the gas or its constituents entering into com- bination with the electrodes. (It must be borne in mind that we have here to do with immeasurably small traces of gas.) I may here relate a curious example of this kind. M. Geissler had observed that tubes which contained traces of sulphurous acid, suffered a remarkable alteration by means of the electric current. I had previously observed how a tube containing a probably less perfect vacuum of the same acid sud- denly changed during the passage of the current under the influence of the magnet (16). In this case the change was slow and continuous. The tube of which I am now speaking was 400 millims. long and 25 wide. It showed at first a beautiful strati- fication in the violet light, accompanied by the customary phenomena. As Ruhm- korff’s apparatus was being discharged for several minutes through the tube, the violet light gradually became decolorized, and the whole appearance was changed. After a long time a constant appearance was esta- blished, the tube then behaving exactly as the most beautiful ones of Mr. Gassiot (118). The sulphurous acid having entirely disappeared, a Torricellian va- cuum, so to speak, had been form- ed. The light about the negative pole was separated by a broad dark space from the broad white ne- bulous clouds of light. These latter extended to the positive electrode, each one having a bright white boundary towards the ne- gative electrode, and gradually shading off with a grey tint towards the positive one. On during the passage of the Electric Discharge. ll touching the dark part of the tube near the negative electrode with a weak horseshoe magnet, the system of white clouds were drawn further into the dark space: a beautiful appearance was thus presented, which I had already seen produced by Mr. Gas- siot, but which I had up to that time not been able to produce in Geissler’s tubes. On touching with two fingers that part of the tube where the first light-cloud bordered on the dark space, the whole of the clouds were driven back towards the positive pole ; that is, there was repulsion where in the former case attraction occurred, and the whole phenomenon became more stable. In this case the tube presented the appearance of fig. 1. 95. The same experiment succeeded with all similar tubes ; but they did not all present quite the same appearance after the change had taken place. In place of the inch-wide white cloud, there frequently occurred a much narrower stratification of the white light, such as always occurs in the Torricellian vacuum. In one instance, indeed, the light was of a reddish colour, correspond. ing to that produced by nitrogen, and of the tint which I ob- served it gradually to become in the hands of Mr, Gassiot when he, by an ingenious contrivance, allowed traces of air to enter very gradually. It hence appears certain that in all the “ sul- phurous-acid vacua,” greater or less traces of air were present, and that this was especially the case in the tube last described. It is probable that sulphurous acid, when quite dry and free from air, furnishes us with the best means for making the best approximation to an absolute vacuum. 96. The following observation seems to me worthy of notice. On heating the extremities of the cylindrical tube into which the platinum electrodes were fused, over a spirit-lamp, the original beautiful stratification in the violet light immediately reappeared. The sulphurous acid was formed again by the recombination of its constituents. The latter (probably both of them) had become combined loosely with the platinum, and were separated from it again by the heat of the lamp. The passage of the current de- termined the re-formation of the white cloudy stratification by gradually decomposing the sulphurous acid. After this stra- tification had again ceased, it might be again restored by a fresh application of heat; and thus the two phenomena might be alternately produced a few times, but each time with dimi- nished beauty. 97. It seems to me to follow from the above, that the light accompanying discharge through tubes which have been filled with any gas, and exhausted so as to contain only traces of the gas, is quite independent of the metal of the electrode, and, further, that no discharge takes place through an absolute 12 Prof. Pliicker on the Spectra in Rarefied Gases vacuum, and accordingly no light is then produced. We are led therefore to the conclusion that the light of the discharge-cur- rent, and the consequent corresponding spectrum of such gas- vacua, entirely depend upon the residual traces of gas, and are consequently characteristic of the gas employed on each occasion. For the determination of the special spectra, I chose, to begin with, hydrogen, oxygen, aud carbonic acid; and I obtained for these three gases perfectly definite, constant, and distinct spectra. It is true that it is impossible in a graphic representation to re- produce even approximately the original colours of such spectra. Such representation is also rendered the more difficult by certain parts of the spectra being characterized by an unusual intensity of light. But such a representation furnishes a true picture of the phenomenon for those who have once seen it, and it suffices completely for subsequent comparison. 98. Graphic representation is also rendered less exact by the fact that the circumstances conditioning the subjective judg- ment of colours are of a very complex kind, and that such judg- ment loses all value when weakly illuminated portions are bounded by tints of a bright colour. ‘The impression made upon the eye by the beautiful spectra of many gases stands in contradiction to the fundamental law of the theory of colours, namely, that the colour of the light depends upon the length of the undulation, according to which, for the same prism, light broken to the same extent must have the same colour under all conditions. I may mention in illustration of this, the (im- pure) spectrum of fluoride of boron already provisionally de- scribed (71), in which a beautiful violet colour follows immedi- ately upon a (certainly somewhat faded) green colour. If the blue were entirely wanting, as is the case with other gases, the violet would be bounded by a black space towards the side of the red. It seems most natural to assume that a faint blue is pre- sent in the spectrum, and that this is converted apparently into a green by a subjective yellow, the complementary colour to the neighbouring and unusually bright violet. Nevertheless it seemed to me desirable for our gas-spectra, to support the above law by a direct experiment. 99. In the formation of such spectra I employed the method already described (69), with some modifications. The luminous electrical discharge-current was concentrated in thermometer- tubes, whose internal diameters were nearly the same for the different gases examined, being about 0°6 millim. (A column of mercury, 155 muillims. long, in such a tube weighed 0-6677 gr., which gives this diameter for the internal circular section of the tube.) Fig. 2 shows the form of the perfect separate gas- tubes, as well as the manner in which they may be connected on during the passage of the Electric Discharge. 13 a piece of board, so that the narrow parts of both (at the parts where they are bent at an angle of rather more than 90 degrees) Fig. 2. ee touch one another, and have exactly the same direction. (The glass cock given in the figure has reference to a subsequent ex- periment.) On discharging a current through such a system of two different tubes, a straight thread of light appears in the narrow part, which is broken only in the middle, and half of which belongs to the one gas, half to the other. However dis- similar the spectra of the two gases might be, any one colour of the one spectrum (in those cases where it was not extinguished) was continued in a straight line in the other one; this was usu- ally accompanied by a change in its brightness. 100. In observing the spectra, I employed a Fraunhofer’s telescope, which was set up at a distance of from 4 to 5 metres from the vertical line of light in the tube. The flint-glass prism, whose refractive angle was 45 degrees, was fastened immediately before the object-glass, whose aperture was 15 Paris lines. The magnifying power of the eye-glass was so chosen that an increase in its power did not show an additional number of narrow lines, but only diminished the intensity of the light. The combination of two glass tubes described in. the prece- ding paragraph is capable of another application. If, namely, the telescope be directed to the part where the narrow tubes meet, the spectra of the two separate gases, being seen at the same time, may be compared with one another, and the respective sizes of the different parts measured. The spectrum of hydrogen seems to me to be the most suitable, of those as yet examined, for a standard of comparison, on account of its peculiar constitution. 101. The tubes which I first examined were originally filled 14 Prof. Pliicker on the Spectra in Rarefied Gases with hydrogen, nitrogen, and carbonic acid, and, after as complete as possible rarefaction, showed characteristic and beautiful spectra entirely distinct in nature from one another. I confine myself here to a mere noting of these and the hitherto observed spectra, reserving a more exact description together with pictorial deli- neation*. 102. In the spectrum of hydrogen, almost the whole of the light is concentrated into three bands,—namely, a dazzling red at the extremity of the spectrum, a beautiful greenish blue, and finally a violet of inferior brightness, whose distance from the greenish blue is about two-thirds of the distance of the latter from the dazzling red. In the narrow tube the electric light- stream appears red. 103. In the spectrum of nitrogen all the colours are fine, none of them being faded, as is the case in the broad spaces lying between the bright bands of the hydrogen spectrum. In the spaces of the red, orange, and yellow, there are about fifteen narrow dark-grey lines at nearly equal distances apart. Six of these belong to the orange and yellow: both of these colours "are beautiful. The red; in the direction away from the orange, is shaded off into brown, but becomes brighter and purer towards the extremity of the spectrum, which stretches beyond the daz- zling red bands of the hydrogen spectrum. A broad green space is separated from the yellow by a narrow black band. The greater part of this space appears shaded with black in the di- rection away from the black band. On more careful examination, however, this shading is seen to consist of very fine black lines, which are at equal distances apart, but nearer together than the previously mentioned bands in the red, orange, and yellow. The rest of the green space is again subdivided. The green is bor- dered by two beautiful bright-blue bands, which are sharply sepa- rated from one another and from the green by narrow black bands. The blue and red-violet ends of the spectrum form nine sharply- bordered violet bands, alternating with dark ones. The former have various degrees of brightness ; the latter appear partly dark violet, partly black. The fourth and fifth bright-bands, sepa- rated by a black band, possess the most light ; the four followmg ones are Jess prominent; the last one, however, which forms a sharp boundary to the whole spectrum, is the most distinct. The light of the discharge-current in the narrow tube is yellowish red. 104. In the spectruin of carbonic acid (see 115), six bright bands sharply separate the bright portion into five spaces, of which the two first are of equal breadth, the third, and especially the two last, somewhat broader. The first of the six bands 1s * T have been assisted in drawing the different spectra by MM. Lick - and Dronke. during the passage of the Electric Discharge. 15 situated on the extreme boundary of the red, the second is reddish orange, the third greenish yellow, the fourth green, the fifth blue, and the last violet. Both of the two first spaces are divided into three equally broad subdivisions by narrow black-grey bands, of which two always border upon the bright band. The first space is brown-red, the seeond dirty-orange and yellow. The third and fourth spaces are of a rather faded green, and much subdivided by different degrees of shadmg. The fifth space, which is very faded, is divided into two equal spaces, which are shaded off from the red side towards the violet. After the last- mentioned violet band, another dark portion of the spectrum occurs about as wide as the red-yellow portion. In this dark portion three spaces are separated by three prominent and well- marked violet bands, whose breadth is of the same value as that of the before-mentioned six bands. The last of these violet bands forms the visible boundary of the spectrum. The first of these three spaces, which is contiguous with the above six bright bands, is somewhat broader than the third. Both are perfectly black. The second and middle space is about as broad as the first and third together, and is of a very dark violet colour. The first band, which at the moment of commencing was of an especially brilliant red, lost almost the whole of its brightness after the stream had passed through the tube for a long time (115). The light of the galvanic current in the narrow tube was greenish-white. 105. After the spectra of the three above-named gases had been accurately determined and copied, the double tube repre- sented in fig. 2 was filled with two different gases, carbonic acid and hydrogen, and then exhausted as far as possible. The gases, which were originally separated from one another, could be put into communication by means of a cock. This was done while the stream passed simultaneously through both tubes, through the one with a greenish-white, through the other with a red light, and while the spectrum of the one gas (the carbonic acid) was observed through the telescope by the prism., Imme- diately on opening the cock, a dazzling red line was at first seen merely flickering now and then at the boundary of the spectrum. It soon took up and maintained a constant position: this.was the red band of the hydrogen gas. The colour of the light in the two narrow tubes was the same; the two spectra had become constant and identical in kind. Universally, if two different gases are mechanically mixed in a tube, and the two spectra of the separate gases are known, it is easy to see how the spectra of the separate gases overlap one another, forming the spectrum of the mixed gas. 106. Next, a single tube was filled with ammonia and ex-. 16 Prof. Pliicker on the Spectra in Rarefied Gases hausted. The spectrum was evidently the result of the superpo- sition of the two spectra for hydrogen and nitrogen ; the ammoniacal gas was immediately decomposed into its constituents, and it had not been possible to obtain the spectrum of the chemically combined ases. Z 107. The determination and delineation of the oxygen spectrum appeared now to be of chief importance. But here I encountered new and unexpected difficulties, so that as yet I have not been able to obtain a complete idea of this spectrum. I shall there- fore confine myself here to the mere mention of two narrow bril- liant bands, of which the one forms the boundary of the spectrum, the other extends even into the orange. The space between the two bands is of a dark brown. The red boundary of the oxygen spectrum extends somewhat beyond that of the hydrogen spec- trum ; and accordingly the dazzling-bright bordermg bands do not coincide. The above-mentioned difficulty in determining definitely the spectrum for oxygen, consists in the gradual disappearance of the free gas, which combines with the platinum of the negative elec- trode. That such combination actually occurs, is not only evinced by the alteration of the spectrum, but is shown at once by the fact that the finely-divided oaide of platinum as it is formed is deposited of a yellow colour upon the neighbouring internal glass surface, showing by reflected light the colours of Newton’s rings in a very beautiful manner. If the tube contains traces of hydrogen or nitrogen, pure metallic platinum is trans- ferred to the glass surface. . 108. The colour of the electric light-current in the narrow tube was at first red; it passed through a flesh-colour to green, and then through blue to reddish violet. It would be of especial interest, by a careful examination of the oxygen spectrum, to determine in what sequence the sepa- rate prismatic colours disappear during the gradual extinguishing of the electric light-current caused by the gradual abstraction of oxygen gas, and the consequent withdrawal of the ponderable matter essential for the conduction of the electricity. The above seale of colours, through which the light passes in the narrow tube, appears to justify the conclusion that at first the least re- frangible rays are removed ; certainly the two bright-red bands of the spectrum are first seen to become paler and perhaps wholly to disappear. In order, however, that the phenomenon may be examined with perfect accuracy, it is necessary for espe- cial precautions to be taken that the oxygen may be absolutely ure. ; 109. For if even the most minute traces of another gas be mixed with the oxygen, the foreign gas will take a continually during the paesage of Electric Discharge. TF increasing effect upon the spectrum of the oxygen in proportion as the latter gas is removed: for this reason two tubes had to be rejected for accurate determinations. In the first one, to which the above remarks have reference, the previously described spectrum of carbonic acid became continually more and more prominent. For this fact, which at first seemed very surprising, a sufficient explanation was soon found. The same exhaustion- apparatus, namely (constructed with mercury), had been employed just before to exhaust carbonic oxide, which here has the same action as carbonic acid (115). In the second tube, traces of ni- trogen were recognizable; this tube had also to be rejected, be- cause it evidently contained air mixed with the oxygen gas. 110. In the extinction of the electric current in oxygen gas, I have already (73) recognized a proof that no current can exist im an absolute vacuo, to which we can only approximate practically to a greater or less extent. I may here add that the electric cur- rent in an empty space (if one can exist there) certainly cannot be luminous; for if this were the case, the spectrum for empty space would necessarily reappear in the different gas-spectra. The latter, however, have nothing in common. 111. I next endeavoured to determine the spectrum of the oxide of nitrogen (NO?). The attempt, however, was unsuccess- ful ; a tube of binoxide of nitrogen gave the spectrum for ni- trogen itself with a modification evidently attributable to pure oxygen, which was proved by the existence of a bright band near the red, and because the brownish red became a bright red at the boundary of the orange. The narrow characteristic lines in the red, orange, and yellow retained their entire sharpness. The extreme ones alone, which the bright band partly covered, had disappeared, so that only six such lines remained between the new bright band and the boundary of the orange. The brilliant red band was gradually extinguished ; and the result was the formation of the pure spectrum of nitrogen gas of a splendour which I had never before observed. Binoxide of nitrogen, present in so small a quantity as to be scarcely recognizable by the most sensitive balance, was thus che- mically analysed. It was instantly decomposed by the passage of the current into its constituents ; nitrogen and oxygen, and the latter disappeared by gradually forming oxide of platinum with the metal of the negative electrode. 112. In consequence of the above-observed behaviour, it was scarcely to be doubted that the higher and less stable stages of oxidation of nitrogen would immediately separate into their simple constituents. For confirmation, a tube was filled with nitrous acid (formed by mixing binoxide of nitrogen and oxygen in the right proportions) and then exhausted. The spectrum was the Phil. Mag. 8, 4. Vol. 18, No. 117. July 1859. C 18 Prof. Pliicker on the Spectra in Rarefied Gasses same as in the case of the binoxide of nitrogen tube, excepting that the red band due to the oxygen was at first of still greater brilliancy. 113. A further experiment showed that nitrous oxide (NO) also immediately splits up into its simple constituents. The band due to the oxygen was less bright. 114, The next gas examined was aqueous vapour. M. Geissler prepared an excellent tube for this purpose with his accustomed skill, in the following manner. Two large bulbs were blown upon a tube, one of them being provided with a cock towards the end of the tube; the tube, having been filled with water, was heated until the last trace of air was driven out and nothing but aqueous vapour remained. The cock was then closed. The tube was then heated over a spirit-lamp, while the bulb with the cock was immersed in a freezing mixture. This bulb, to which the cock was attached, was then fused off. The same operation was repeated by plunging the second bulb in the freezing mixture, and then fusing it off while the tube itself was heated. The electric current in the narrow tube showed the most beautiful deep red. The spectrum was that of pure hydrogen with its three prominent bands, in comparison with the brightness of which, the rest of the luminous divisions were so insignificant, that here the shading off of colour and luminous intensity was scarcely to be recognized. The aqueous vapour had separated into its simple constituents; but unfortunately M. Geissler had already passed the current through. The one constituent, namely oxygen, had already been removed by combining with the negative platinum electrode. 115. After the above-described experiments, it necessarily seemed very doubtful whether the spectrum of carbonic acid previously described really belonged to this acid in its undecom- posed state. It was not possible for the acid to have been de- composed into its simple constituents ; for in that case we must have obtained the spectrum for oxygen gas, while the small quantity of solid carbon must have been deposited (perhaps in inappreciable quantity) on the interior of the glass tube. Hence the only possible remaining alternative was either that the acid had continued undecomposed, or had split up into oxygen and carbonic oxide. The fact of a deposit of oxide of platinum having been formed, was hostile to the first supposition (107). All doubt was removed on determining the spectrum of carbonic ovide. This spectrum was identical with that into which the carbonic acid spectrum was soon transformed by the diminution of the brightness of the extreme red. The spectrum of carbonic oxide, obtained either directly or by the abstraction of free oxygen, is not constant, although its alteration is very gradual. As oxide during the passage of Electric Discharge. 19 of platmum is deposited, the less refrangible light disappears from the spectrum (104) ; asthe oxygen is gradually removed, the in- terior of the tube approaches to a vacuum. 116. The remarkable analogy in the chemical relations of iodine, bromine, and chlorine, reappears also in their spectra*. [ shall not at present describe these spectra, because the manner in which the tubes have hitherto been made did not admit of complete exclusion of the air, and the spectra consequently were not pure, but a superposition of two spectra. Moreover, during the passage of the current, the above bodies combine with the platinum of the negative electrode. The iodine spectrum remained sufficiently long to admit of being copied. It was necessary to employ four bromine tubes in succession, each of which sufficed for the determination of one portion of the spectrum. The entire spectrum was formed by putting the four portions together. The spectrum of chlorine was of short duration, so that one could see it distinctly but could not copy it. That which the three spectra have in common, and by which they are distinguished, as far as present observations extend, from all other gas-spectra, consists in lines of light, which at first are constant, but after- wards only flickering, and whose width is about the same as that of the narrow Fraunhofer’s black lines. In the iodine spectrum, the position in the green of five such lines of light of great brightness has been determined ; two of these lie close together. The bromine spectrum showed a greater number of such lines, extending over many of the central colour divisions, and accom- panied by black lines precisely similar to those of Fraunhofer. In the chlorine spectrum there appear to exist a greater number of such narrow lines, both black and bright ones ; the position of these, however, it has not been as yet possible to determine. 117. The chemical results hitherto obtained may be summa- rized briefly as follows :— I. Certain gases (oxygen, chlorine, bromine, and iodine va- pours) combine more or less slowly with the platinum of the negative electrode, and the resulting compounds are deposited upon the neighbouring glass surface. When the gases are pure, we thereby gradually approach to a perfect vacuum. IJ. Gases which are composed of two simple gases (aqueous vapour, ammonia, nitrous oxide, nitric oxide, nitrous acid), imme- diately split up into their simple constituents, and then remain unchanged if these latter (ammonia) do not combine with the platinum. If one of the constituents is oxygen (in water and * The action of the magnet upon chlorine, bromine, and iodine vapour, is characteristic of these bodies, as I have already noted (16, 17,59). I shall return to this point subsequently. C2 20 Sir C. Lyell on the Submarine Origin of Teneriffe the different stages of oxidation of nitrogen), this gradually dis- appears and the other gas alone remains. saety III. If the gases are composed of oxygen and a solid simple substance, complete decomposition by the current only takes place gradually, while the oxygen goes to the platinum of the negative electrode (sulphurous acid, carbonic oxide, carbonic acid). Carbonic acid is instantly decomposed into the gaseous lower stage of oxidation and into free oxygen, which gradually goes to the platinum (I). The carbonic oxide is gradually decom- posed by the oxygen leaving the carbon and combining with the negative electrode*. Bonn, August 25, 1858. III. Remarks on Professor C. Piazzi Smyth’s supposed proofs of the Submarine origin of Teneriffe and other Volcanic Cones in the Canaries. By Sir C. Lyeut, F.R.S., D.C.L. &e.F Co the publication in the Philosophical Transactions of my paper on the Lavasof Mount Etnat, a Report by Prof. “Smyth, Her Majesty’s Astronomer for Scotland, has been printed by the Admiralty of Great Britain, ‘“‘ On the Teneriffe Astrono- mical Experiment of 1856,” in which a chapter on geology and * volcanic theories” is introduced. This chapter, which did not form part of the original Report as published by the Royal Society in the Philosophical Transac- tions for 1858, contains a discussion of Von Buch’s theory of craters of elevation, together with critical remarks on passages in my writings, and those of Mr. Poulett Scrope. I do not feel myself called upon to reply to any of these comments, as they relate to subjects to which the Astronomer for Scotland cannot be expected to have devoted much time or attention ; but when facts are cited, respecting Teneriffe and other islands of the Canarian Archipelago, supposed to be conclusive on a contro- * T have already described two such spectra, in order to give a prelimi- nary idea of a gas-spectra. The first was shown by a not very narrow hydrogen tube, which was among the first which M. Geissler made. I chose this on account of its simplicity; but it does not belong to pure hy- drogen, as we now see at a glance. The second beautiful spectrum described, which is mentioned as belonging to fluoride of boron, probably also does not belong to the pure gas. If we consider its less refrangible portion with the narrow grey lines, we may assume with tolerable certainty that the gas contained nitrogen (air) (70), (71). + Communicated by the Author. { “ On the Structure of Lavas which have consolidated on steep slopes ; with Remarks on the Mode of Origin of Mount Etna, and on the Theory of ‘Craters of Elevation,” by Sir Charles Lyell, Phil. Trans. part 2, 1858, p. 703 and other Volcanic Cones in the Canaries. 21 verted question of high theoretical interest, and in a work brought out under the sanction of the Admiralty, I think it right to point out the mistakes into which the author has fallen, and the insufficiency of the evidence on which he relies. At p. 553 of the new edition of the Report above alluded to (dated February 1859), the following passage occurs :— “ The question of the submarime origin of Teneriffe no longer depends only on the general structure of its lava-beds, or on analogies from the fossiliferous strata of the adjacent islands of Grand Canary and Palma, but has now the additional and most unanswerable argument of fossil shells having lately been dis- covered about the slopes of the crater.” And again in the same page : — “The proof of fossil shells, so long demanded, has now been supplied ; and with them must be accepted the fact of the slopes on which they rest having been once submarine, though now sub- aérial. The Great Crater, then, having incontestably suffered elevation, was that elevation necessarily connected with its present form and character ?” &c. When I first read these passages, I naturally concluded that some new discovery had been made of marine fossils on the slopes of the great outer cone of Teneriffe, or “crater,” as it is termed in the Report above cited ; but having never seen or heard of such a fact myself when in the island, I wrote to Prof. Smyth to know where and at what height above the sea, and under what geological circumstances, he or his informants had detected these shells. In reply he could give me no information on any one of these three heads, “he had merely given the statement on report, and not from his own observations.” It appears, then, that he had simply learnt that marine fossil shells had been met with somewhere in the island of Teneriffe, a fact well known before his visit in 1856, and before Mr. Hartung and I were there in 1854. These shells, however, did not occur “on the slopes of the crater,” but in the suburbs of Santa Cruz, along the shore to the north-east of the town, a part of the island which is geographically and geologically independent, not only of the Peak, which is more than twenty miles distant, but also of that voleanic chain which extends many miles from the flanks of the great cone, trending in a north-easterly direction. The separa- tion of the Santa Cruz rocks from the chain to which the Peak belongs, will be understood by a glance at the maps of Von Buch and Captain Vidal, and by reference to the view of Santa Cruz which Vidal has given in the margin of his map. The tufaceous breccias and sandstones containing marine shells near Santa Cruz do not conform “to the slope” of any crater or cone. So far as they can be seen, they appear to be nearly horizontal, 22 Prof. Hennessy on the Thickness and and occur only at slight elevations above the level of the sea. We were told that the same remark holds good in reference to certain other deposits containing shells, which we did not ex- amine, in the north-eastern extremity of the island, still further from the Peak. In the first of the passages above cited, Prof. Smyth has alluded to fossiliferous strata in the islands of Grand Canary and Palma. In regard to Palma, I may mention that Mr. Hartung and I, when we were there in 1854, searched in vain for fossils ; no travellers had then found any ; and our correspondents in the Canaries have still no knowledge of any having been obtaimed im that member of the Archipelago. Lastly, as to the Grand Canary, Von Buch was, I believe, the first to call attention to the existence of marine shells in that island, where Mr. Hartung and I collected them in abun- dance in 1854, and ascertained that they are imbedded in nearly horizontal strata continuous over a large area, where they form an elevated platform about 400 feet high, near the town of Las Palmas, a platform terminating abruptly in a range of cliffs near the sea, facmg the north-east. These upraised sedimentary strata, with some intercalated basaltic beds, are far removed from the slopes of the great dome-shaped volcanic mass, which forms the central nucleus of the Grand Canary; and if they have any bearing on the question of “ Craters of Elevation,” they certainly do not corroborate that hypothesis, but, on the contrary, are directly opposed to it; for though they have been upheaved in a district where intermittent voleanic action has never ceased, they do not dip away in all directions from a central axis, nor have they assumed a conical or dome-like form. IV. On the Thickness and Structure of the Earth’s Crust. By Henry Hennessy, F.R.S., Professor of Natural Philosophy in the Catholic Unwersity of Treland. To the Editors of the Philosophical Magazine and Journal. GENTLEMEN, I HAVE read with interest a letter addressed to you by Arch- deacon Pratt, which has appeared in your Number for last May. In a problem so extremely difficult and obscure as the determination of the thickness of the solidified crust of the earth, I am not surprised that some differences of opinion should exist. The views which I have published on this subject have been eri- ticized by Archdeacon Pratt on two grounds :—Ist, on account of the assumption that the shell is sufficiently rigid to resist, without change of form, the pressure upon its inner surface which arises Structure of the Earth’s Crust. 23 from its not continuing a surface of fluid equilibrium ; and 2ndly, because I suppose the nucleus to shrink in cooling more than its solid envelope. The first of the assumptions alluded to is con- tained in Section IV. of my Second Memoir on Terrestrial Phy- sics*, It does not, of course, imply that when the shell was very thin it was not capable of modifying its shape in conformity with that of the fluid matter beneath. But it should be remem- bered that the changes of shape in the surface of the fluid mat- ter which have been discussed by me are such as would neces- sarily be continuous and extremely slow, from their dependence on the slow refrigeration of the whole earth, and gradual deposi- tion of new strata of solidified matter upon the inner surface of its crust. No abrupt changes of shape in the figure of the fluid nucleus could take place from such causes, while the viscous and plastic matter which may happen to be passing into the solid state would be directly influenced by its immediate contact with the nucleus. It is thus I have been led to the con- clusion, that the ellipticity of the strata of equal density in the shell would not follow the law prevailing in those of the nucleus, or of the entire mass when it existed in a state of fluidity, namely, that of an increase im proceeding from the surface towards the centre. I have only recently ascertained that M. Plana+ had arrived at a conclusion very similar to mine, not long after the publication of my researches. My conclusion is, that the least ellipticity which the inner strata and the inner surface of the shell can have, could not be less than that of the outer surface. M. Plana’s is, that all the strata would have the same ellipticity as the outer stratum. The difference between my result and that of the distinguished Sardinian mathematician arises from the circumstance that he does not appear to have considered the change of volume which the fluid matter may undergo in passing to the solid state. This I have attempted to do, because all the experimental knowledge which we possess relative to the solidi- fication of fused rocks, points to a dimimution of volume as an accompaniment of their gradual transition to a state of solidity. It is true that rapidly-solidified and scoriaceous lava is lighter than the same substance in a fluid condition, and it is therefore observed to float upon the latter during the progress of volcanic eruptions; but observers are also well aware that slowly-solidi- fied and compact fragments of the same rock will gradually pe- netrate and sink through the viscous surface of a molten stream. Still more decisive are the results separately obtained by MM. Bischof, Ch. Deville, and M. Delesse, regarding the coefficients of cubical contraction of the crystalline rocks in passing from the * Phil. Trans. 1851, p. 525. + Astronomische Nachrichten, No. 860, vol. xxxvi. p. 315. 24. Prof. Hennessy on the Thickness and fused to the solid condition. These results have been pub- lished in some of the most widely circulating scientific collections of Europe. Some of them have been referred to by Alexander von Humboldt* and by Sir Charles Lyell+; and all have been quoted by M. Elie de Beaumont in his Systémes de Montagnes tf, as well as by other well-known investigators. In venturing to base a great portion of my reasonings upon such results, I felt that in the present state of our knowledge no facts could be quoted which could outweigh those deduced from the experi- ments of such careful observers, and that it would therefore be impossible for me to overlook the very definite conclusions to which these gentlemen have been independently led. The foregoing remarks will in some measure answer Arch- deacon Pratt’s objection to my views regarding the superior con- traction of the fluid matter composing the nucleus compared to that of the solid shell. The general laws of contraction of fluids and solids for similar changes of temperature are admitted to be such as to give a greater contraction to the former than to the lat- ter. On this account Humboldt and M. Elie de Beaumont have gone still further, by maintaining the possibility of a tendency to separation between the shell and nucleus, a conclusion from which I have dissented, in accordance with some of the results of Mr. Hopkins combined with some of my own. While I hope that these remarks will satisfy Archdeacon Pratt as to the legi- timacy of the assumptions which he has called in question, I trust that Professor Haughton§ will see that there are some students of nature who not only hold the opinion that the crust of the earth is denser than the fluid from which it was formed, but who have based that opinion upon the results of exact expe- rimental inquiry. The results obtained by M. Plana and myself, show that Mr. Hopkins’s formula, quoted by Archdeacon Pratt, must be per- fectly nugatory for the determination of the thickness of the earth’s crust. The shape in which it is finally presented by its author is PoP €) 1:3. : g—l where P, denotes the precession of a solid homogeneous spheroid of which the ellipticity=e,, and P! the precession of the earth supposed to consist of a solid shell enclosing a fluid heterogene- * Kosmos vol. i. section on Voleanos. + Principles of Geology, 9th ed. p. 173. t p. 1230-31. § See Phil. Mag. for June. Structure of the Earth’s Crust. 25 ous nucleus, ¢ and ¢, being respectively the inner and outer ellip- ticities of the shell. If, with M. Plana, we regard ¢,—e=0, or if, in conformity with my conclusions, we consider it even possi- ble that ¢,—e> 0, this equation cannot assist in determining the fraction 1, which is a function of the radius of the vas Pal nucleus, and from which the thickness of the shell is estimated. Although I am far from regarding the numerical results which I have myself obtained relative to the thickness of the earth’s crust as perfectly accurate, I believe that the mechanical and physical principles to which I have appealed are those from which the complete solution of this problem will arise. If the problem were simply mathematical and mechanical, I should be induced to concur with Professor Haughton* as to its insolubility, not only from studying that gentleman’s researches, but also from the previously published investigations of Professor Stokes+ relative to Clairaut’s theorem. If the surface of the solidified shell were identical or similar to what may be called the astronomical sur- face of the earth, namely that of its oceanic coating, all the sta- tical and dynamical results depending on the internal constitu- tion of the globe might be the same. whether the crust were merely a thin pellicle, or whether the earth were always solid to its centre. But although the surface of the ocean is necessarily perpendi- cular to gravity, we have no reason to conclude that the surface of the shell, stripped of all its fluid and sedimentary coatings, would possess the same property. Whatever knowledge we pos- sess respecting the configuration of the bed of the ocean and of the great islands which rise above its surface so as to form the continents of the eastern and western hemispheres, tends to show that the surface of the solidified shell is not similar to the sur- face of equilibrium assumed by its liquid covering. Here I may be allowed to refer to Archdeacon Pratt’s attempt at confirming Mr. Hopkins’s conclusion relative to the supposed very great thickness of the earth’s crust. He proposes to ascertain the conditions of equilibrium of that portion of the crust occupied by the great peninsula of India stretching from beyond the Hima- layan Mountains to Cape Comorin. The meridional section thus studied comprises an are of about 24°, and the curvature of this segment of the shell is a very important element in the con- sideration of its stability; yet it has been totally neglected. Moreover, the Himalayan Mountains and plateau of Central In- * Trans. Royal Irish Academy, 1852. + Cambridge Mathematical Journal, May 1849. 26 Prof. Volpicelli on Frictional Electricity. dia are assumed to be masses superimposed upon the erust, the under surface of which is supposed to be uniform. This seg- ment of the erust is not only treated as a nearly flat plate band, but great inequalities of thickness are assumed ; and the problem is thus invested with circumstances from which it readily follows that a very thick crust becomes necessary in order to compensate such remarkably weakening conditions. As we know that the first of these conditions is decidedly incorreet, and that the other is at least wholly unsupported by facts, we cannot be expected to admit the conclusion to which they would lead. Dublin, June 8, 1859. Henry Hennessy. V. On Frictional Electricity. By Prof. Votricexur*. rs Watts a year ago Prof. Volpicelli drew attention to certain striking anomalies observed by him on attempting to develope electricity by the friction of certain resinous substances, After repeating his experiments with a great many different bodies, and thus familiarizing himself more perfectly with the anomalies in question, he is at length enabled to state more pre- cisely the conditions of their existence. If a stick of ordinary sealing-wax be held by one extremity and pulled briskly between the finger and thumb of the other hand, no matter whether the latter be naked or covered with a woollen or other glove, negative electricity will zn general be de- veloped, as may be seen on presenting the stick thus rubbed to the knob of a dry-pile electroscope. On varying the energy of the stroke, however, it will be found that the indications of the electroscope are by no means constant. For example, negative electricity having been developed in the manner described, let the stick be exposed a second time to friction and in the same manner, the energy of the stroke alone being diminished ; the negative character of the developed electricity will be also dimi- nished ; in fact, on repeating the stroke last described, and after each stroke testing the nature of the electricity, the stick may be reduced to the neutral state, and subsequently converted into a positively electrified body. A little practice is alone necessary in order to obtain these effects with certainty, and to have the stick of sealimg-wax per- _fectly under control, so that by a single stroke of greater or less energy, a positive, negative, or neutral electric condition may be imparted to the sealing-wax, whatever may have been the previous state of the same. Continuing the friction with * Abstract of a communication made to the Academia de’ Nuovi Lincei of Rome, February 6, 1859. Prof. Volpicelli on Frictional Electricity. 27 properly adjusted energy, either electric state may be rendered permanent, or seizing the stick by the middle and stroking one extremity more vigorously than the other, the first may be made negative, the second positive; and thus different electric polarities may be developed simultaneously in one and the same body by rubbing its extremities with the same substance, but with differ- ent degrees of energy. To the phenomenon above described, Prof. Volpicelli has given the name of alternate polarity, in order to distinguish it from another, successive polarity, where, by changing the energy of friction, the developed electricity may be changed in one or the other way, but not back again. The three resinous bodies with which the phenomenon of alternate polarity may be obtained with certainty, are common sealing-wax (cera di Spagna), gum- lac, and jalap resin (resina scialappa). With ten other resins which were examined, as well as with amber, negative electricity alone could be obtained, no matter to what extent the energy of the friction was varied. A cold dry atmosphere is of course favourable to the success of the experiments with the three resins ; but at all times the effects described may be obtained, and that no matter whether the finger and thumb which impart friction be naked or covered; in the latter case, however, the glove should be well fitted to the hand. Amongst the few kinds of gloves with which the experiments do not succeed are fur and india-rubber ; with the former the electricity developed is always negative, and with the latter almost invariably positive. Another important condition appears to be a compact and polished resi- nous surface. Sulphur, which is not susceptible of such a polish, and whose particles are disintegrated by friction, does not mani- fest the alternate effects. If a stick of one of the three resins, after having remained for some time in a neutral state, be gently pressed between the finger and thumb, without intentional longitudinal fric- tion, positive electricity will be developed ; and subsequently this may be cancelled, and even transformed into negative elec- tricity, by gradually increasing the pressures. It would appear, however, that this negative electricity cannot be reconverted into positive by the reverse process, that is to say, by gradually di- minishing the applied pressures. Under favourable atmospheric conditions, negative electricity may often be changed to positive, without actual friction, by merely passing the fingers covered with an insulating tissue along- side the stick and as close to it as possible without contact. On raising the temperature of the three resins by means of the flame of a spirit-lamp (taking care not to render them flexible or plastic), they lose the property of producing positive elee- 28 Prof. Volpicelli on Frictional Electricity. tricity,—a fact which suggests the probability that, at a lower temperature, the ten resins before alluded to might exhibit the alternate phenomena. On rubbing a stick of sealing-wax, a yard in length, briskly with a linen cloth, it becomes negative throughout its whole length ; whilst in this state, if the same cloth be passed a few times more gently along the surface, the extremities will be found .to possess unlike polarities, and in the middle will be a neutral zone. The condensing electrometer of Volta was occasionally used in the foregoing experiments, but more generally the dry-pile electroscope. The latter was even placed under the exhausted receiver of an air-pump, when the effects were, if anything, still more manifest. The disturbing influence of air-currents, there- fore, was beyond all question eliminated. On first experimenting with glass rods and cylinders 6 or 8 inches in length, the alternate effects obtained with resins did not manifest themselves ; it was only afterwards, when rods a yard in length, and rubbers of fine fur were used, that the experiments succeeded perfectly. Here, again, energetic friction tends to produce negative electricity, and gentler friction positive; and, as before, the passage from either electric condition through the neutral to the opposite may be brought about by changing solely the quantity of friction. The experiments succeed best with a rubber of fine fur, the thicker and finer the better; nevertheless the phenomena may also be obtained with a woollen rubber. Many different kinds of glass were examined, and with none were the experiments unsuccessful ; the ordinary greenish Roman glass, however, ex- hibited the effects with the greatest facility. The most conve- nient form was found to be that of a solid cylinder, 33 centi- metres in diameter, and not less than 3 decimetres in length; with shorter bars the developed electricity is almost invariably positive. As in the case of resins, the production of negative electricity is facilitated by previously raising the temperature of the bar over a spirit-lamp; and under favourable atmospheric conditions negative electricity, once developed, may be changed into positive without contact, by merely passing the rubber alongside of, and close to the bar. Here, too, a single stroke often suffices to develope negative electricity at one end of a bar, and positive at the other. English barometer-tubes in particular often presented this curious phenomenon. Some crystalline bodies also present the phenomena of alter- nate polarity. For instance, if one of the polished faces of a crystal of Iceland spar or of selenite be rubbed more or less briskly against a piece of flannel, fixed at one end and stretched ~ Prof. Volpicelli on Frictional Electricity. 29 by the hand at the other, it will change the nature of its polarity. Here, however, it is important to observe that, contrary to the deportment of resin and glass, energetic friction tends to deve- lope positive, gentle friction negative electricity. Although it would be premature at present to attempt to explain the alternate phenomena above described, one or two hypotheses may be safely advanced. The change of temperature consequent upon more or less energetic friction can at most have but an indirect influence on the effects. To be convinced of this, it will be sufficient to recall the following facts :— First. The contrary electricities may be made to succeed each other as rapidly as may be desired, each by a single stroke dif- fering very little in energy from the preceding one, and hence producing no sensible variation in temperature, especially after the alternations have been continued for some time. Secondly. A rod of glass or resin may be made to manifest both kinds of electricity at one and the same time, its tempera- ture remaining sensibly the same throughout its whole length. Thirdly. Negative electricity may be changed to positive by passing the rubber alongside the rod without contact. Fourthly. At the commencement, positive electricity may be developed on glass or resin by means of very gentle friction, which will be accompanied by a small elevation of temperature ; afterwards more energetic friction may increase the temperature greatly, and still not change the nature of the electricity. These and many other facts would lead us to believe that change of temperature cannot be regarded as a direct cause of the phenomena under consideration ; indirectly, however, by facilitating more or less the vibration of the superficial molecules of the body, temperature is no doubt influential. The cause of the alternate effects must, in fact, be sought in the different kinds of vibration imparted to the molecules of the body; the experiments described appear to indicate that a mere difference in the amplitude of these vibrations may be sufficient to alter the electric state,—a greater amplitude (at least in resin and glass) corresponding to negative, a less to positive electricity, greater and less having reference to a certain mean amplitude which corresponds to a neutral electric state. The electric state of a body depending so essentially upon the quantity of motion impressed upon its superficial molecules, it ean no longer surprise that one and the same body entering into different chemical combinations should act at one time as the electro-positive, and at another as the electro-negative element. The distinction between vitreous and resinous electricity is at once seen to be untenable; and the electrical classification of bodies given in most physical works, and founded upon the 30 Dr. Gladstone and the Rev. T. P. Dale on some results obtained by rubbing one against the other, must neces- sarily be inexact, inasmuch as in many cases the electricity thus developed depends upon the energy of friction. Lastly, it follows at once from the foregoing facts, that in electrical researches, the dry-pile electroscope possesses import- ant advantages over all others wherein the unknown quality of the collected electricity is ascertained by means of comparison with that developed by the friction of resin or glass. Amongst the countless determinations of the nature of a given quantity of electricity which, for centuries now, have been made, who shall say how many have been erroneous ? VI. On some Optical Properties of Phosphorus. By Dr. J. H. Guapstone, F.R.S., and the Rev. T. P. Daz, M.A., F.R.A.S.* O* of the substances examined during our investigation of the influence of temperature on the refraction of lightt, was melted phosphorus; and so remarkable were the phenomena presented by this elementary body, that we have since examined it more fully, and with reference to other optical properties. Phosphorus has the reputation of being extremely refractive ; and the indices 2°125 and 2:224 have been assigned to it—num- bers only exceeded by that of diamond, 2°439, and of realgar and chromate of lead, which are reckoned to transcend even that amount. Unfortunately, however, in the above determinations of phosphorus it is not indicated what part of the spectrum was measured, nor is the temperature specitied—two very essen- tial particulars. Our measurements, made with the instrument of the Rev. Baden Powell, give the following as the refractive indices of solid phosphorus at 25° C. :— | | | Fixed line A, Fixed line D, End of violet. 2-1059 2-1442 2:3097 On account of a peculiar difficulty in distinguishing the fixed lines through phosphorus, to be noted hereafter, it is impossible to say whether the extreme limit of the visible spectrum corre- sponded precisely with H, or not. These numbers indicate not only a very high refractive power, but an unprecedented amount of dispersion. Assuming the end * Communicated by the Authors. + Phil. Trans. 1858, p. 887; also Phil. Mag. No. 113, p. 222. Optical Properties of Phosphorus. 31 of the violet to be H, it gives— Length of spectrum . . .) #a—a=0'2038 Dispersive power MuHa _o.178) Lp—} The spectrum seen through bisulphide of carbon is not half so long as this, wy—pa being at the same temperature only 0:0906. The dispersive power is 0:1460. Oil of cassia is also largely exceeded in this respect by phosphorus, and the only substances which are reputed to be its rivals are realgar and chrolmate of lead; but to them have been assigned the scarcely credibe dispersive powers of 0°255 and 03. Strange to say, the measurements of the spectrum seen through phosphorus, which have been hitherto published, assign to it a length little exceeding that of the bisulphide of carbon spectrum, and con- sequently a dispersive power considerably less. Liquid Phosphorus.—The determination of the refractive and dispersive power of phosphorus in a liquid condition was attended with some difficulty, not merely on account of the inflammability of the melted element, but also because it attacked so readily the cement of the hollow prism and caused it to leak. After several trials, plaster of Paris was found to be an efficient means of retaining it. The following are the indices of refraction at 35° C. :— rf | D. 2-0389 | 2-0746 F. G. 21710 End of violet. 2-1201 2:2267 These numbers indicate a considerable diminution both in the refractive and in the dispersive power. The change from the solid to the liquid state is also attended with a considerable diminu- tion of density ; and the ratio between the density and the mean refraction, p—1, is not far from being the same in the two conditions. Thus, in the paper already referred to, the index of refraction for the orange ray just before the line D, was found to be for solid phosphorus at 35° C., 2°1168 ; and for the same specimen when melted, but at the same temperature, 2°0709. The specific gravity of phosphorus in the two states at about 35° C. has been subsequently determined. The following Table shows the ratio obtained by dividing the specific gravity by the mean refraction, that is, the refractive index minus unity :— ea Substance. Mean Specific Refractive refraction. gravity. power. Solid phosphorus at 35° C. ... 1-1168 1-823 1632 Liquid phosphorus at 35° C... 1:0709 1:763 | 1646 32 Dr. Gladstone and the Rev. T. P. Dale on some From the indices given above for melted phosphorus, the fol- lowing numbers may be calculated :— Length of spectrum . . . =0:1878 Dispersive power . . . . =0°1745 These numbers are considerably less than those obtained for the same element in a solid condition: indeed the decrease in the dispersion would appear to be proportionally greater than that in the refraction. Till, however, H is actually measured, the data for an exact determination of this point are wanting. As with other liquids, the refractive index of melted phos- phorus diminishes as the temperature increases. Our former observations on the orange ray just before the fixed line D, led to the formation of the followmg Table :— Temperature. Refractive index. pei ced per 30 C. 2:0741 35 ,, 2-0709 ee 40 ” 2°0677 0:0037 45 » 2-0640 00037 50,, 2-0603 0-0046 55 ,, 2:0557 00042 60 ,, 2:0515 oa 65 ,, 20473 ete | Kies 2-0422 The sensitiveness evidently increases as the temperature rises ; and it is far greater than that exhibited by any other substance examined by us, with the single exception of bisulphide of car- bon, which is about equally sensitive. The effect of changes of temperature on the dispersion could not be accurately determined. Phosphorus, as is well known, dissolves with extreme readi- ness in bisulphide of carbon. A saturated solution is almost as refractive and dispersive as melted phosphorus itself: indeed from one which was not perfectly saturated, the following ob- servations were made :— Extreme red ray. 1-980 Yellow ray. | End of violet. 2-013 2°205 These numbers are not worthy of much confidence, especially at the more refracted end of the spectrum. From a somewhat weaker, and therefore more manageable solution of phosphorus in bisulphide of carbon, the following indices were obtained :— Optical Properties of Phosphorus. 33 E. A. | a ida F. G. H. 1-9209 | 19314 1-9527 | 19744 | 1-9941 | 2-0361 | 2-0746 | | From these indices may be calculated — Length of spectrum . . . . =0°1537 Dispersive pdwer. . . . . =0°16138 The angular measurements from which these various indices were calculated were made only to minutes, as the fluctuations due to temperature rendered any greater nicety of no value. Another and more serious obstacle arose from a certain indi- stinctness of the spectrum as seen through phosphorus, which caused the recognition of the fixed lines to be very difficult. It is not easy to assign a reason for this: it is not due to the great refraction or dispersion; and though the extreme degree of sensitiveness may be a partial cause, it certainly will not account for the whole phenomenon. It is independent of the more or less crystalline condition of solid phosphorus, and of the presence of unmelted matter in the same substance when liquified ; for it is equally observable in a solution of the element in bisulphide of carbon, which of course may be obtained per- fectly clear. It is curious to observe how, on the addition of successive portions of phosphorus to bisulphide of carbon, the lines of the spectrum, which were originally sharp, become more and more cloudy. We are rather disposed to attribute this in- distinctness to a slight opalescence, caused by the beam of light ‘ converting a little of the phosphorus into that allotropic condi- tion which does not melt at so low a temperature, and which is insoluble in bisulphide of carbon, and therefore assumes the solid form even while the observer is looking at the rays. The phosphorus experimented on was colourless, having been heated under water with bichromate of potash and sulphuric acid. The ordinary yellowish phosphorus, unlike most yellow substances, absorbs the extreme red rays, and transmits the blue, no doubt much weakened in intensity. This appears the more worthy of notice when we remember that another form of the same element reflects the red and absorbs the other rays. Phosphorus flame.—A strong solution of phosphorus in bisul- phide of carbon was burnt in a lamp. The intense white flame which resulted was found to exhibit a spectrum extending from about the fixed line a of the solar spectrum to the extreme violet, but perfectly free from any indication of dark lines or bands. Phil. Mag. 8. 4, Vol. 18. No. 117. July 1859. D [ 34 ] VII. On the Theory of Groups as depending on the Symbolic Equation 6" =1.—Part II.* By A. Caytry, Esq.t ober following is, I believe, a complete enumeration of the groups of 8 :— De igs koi pul he pe ee aL) a TSM ere eb ha, Ba Ca (aeHi, p=, aS ea): ATT 2s x, aX, 0°, 8, Ba, 2a*, pao (el, P=) abe), PVi Ce; a4, 2°; 6)'Ba, Baty ba’ (oF) B= 2", aes )- V. 1,4, 8, Ba, y, ye, yB, yBa (e®=1, P=], y=. aB=Ra, ay=yo, By=y8). That the groups are really distinct is perhaps most readily seen by writing down the indices of the different terms of each group ; these are—- I, ins, 4 8, 28, 4.9 LL. 31 Us ep nd th oe A Ill. 1, 4, 2, 4, 2, 2, 2,2 a ade a ae Sh RS a ae V.. 1,2. 2100. poo 9. It will be presently seen why there is no group where the symbols «, 8 are such that a4=1, 6? =1, «8=Ra*. A group which presents itself for consideration is la, Ca att, B, Ba, Ba’, Bab (at=1, PP=a?, a= Be) ; but the indices of the different terms of this group are 1, 4, 2, 4, 2, 4, 2, 4, and if we write Ba=y, then we find y?=RBaBa=PBac=ai=1, ay=aB8a=Baa=ya; and the group is 1, a, 07, a3, y, yo, yo?, ya? («t= 1, y2=1, ay=ya), which is the group II. The group IV. is a remarkable one; it appears to arise from the circumstance that the factors 2 and 4 of the number 8 are not prime to each other; this can only happen when the num- ber which denotes the order of the group contains a square factor. But the nature of the group in question will be better understood by presenting it under a different form. In fact, if we write Bai=y, «2 =6?=8, then we find «?=3a, Ba? =I, Ba=Ay, and the group will be Ly a, B, Y 3, Sa, SB, Sy, * See Phil. Mag. vol. vii. (1854) pp. 40, 408. + Communicated by the Author. Theory of Groups depending on Symbolic Equation @"=1. 35 where the laws of combination are oy By=a, ya=B, ab=y, yR=aS=3a, ay=BS=38, Ba=yS=Sy. Observe that 3 is a symbol of operation such that $?=1, and that 3 is convertible with each of the other symbols a, B, y. It will be not so much a restrictive assumption in regard to $, as a definition of —1 considered as a symbol of operation if we write $= —1; the group thus becomes d; a, B, Y> —1, =a; —B, Ms =fP=y'=-1, a=PBy=—yP, B=ya=ay, y=aB=Pa. Hence a, 8, y combine according to the laws of the quaternion symbols i,j, k; and it is only the point of view from which the question is here considered which obliges us to consider the symbols as belonging to a group of 8, instead of (asin the theory of quaternions) a group of 4. Suppose in general that the symbols «, 8 are such that a=), Bi=1,)0e8=Be", ap’ = Bra" ; and therefore if v=n, a% =a" or g%"-) =1, whence u(s"— 1)=0(mod.m) ; or since wis arbitrary, s*— 1=0(mod.m), an equation which, if m, n are given, determines the admissible values of s; thus, for example, if n=2, and m isa prime number, then s=1 or s=m—1. The equation «"8"=/"e"" shows that any combination whatever of the symbols «, 8 can be expressed in the form 6%«? (or, if we please, in the form #8"). It is proper to show that the assumed law is consistent with the associative law, viz. that the expression Brae, Bx. Blue ean be transformed in one way only into the form B%«?. We in fact have Bra" Bia =p’. a“Q* ee c— >, B a aa ae = 3+ gst and multiplying this by the remaining factor Bf’, we have pre, asttcBye a’, Dre where then we find 36 Theory of Groups depending on Symbolic Equation 0” =1. which is equal to df i Bord | Bias’ tl tes’. ye, or finally to Borat fqast + cs! +e, And the result would have been precisely the same if, instead of thus combining together the first and second factors and the product with the third factor, we had combined the first factor with the product of the second and third factors, so that the associative law is satisfied. It is now easy to see that if, as before, C= PH: esa pe", conditions which it has been shown imply s”=1 (mod. m), then the symbols @%a” (or, if we please, «”8"), where p has the values 0,1,2...(m—1), and q the values 0,1, 2...n—1, form a group of mn terms. In particular, as already noticed, if n=2 and m is prime, then s=1 or s=m—1 ; the two groups so ob- tained are essentially distinct from each other. If n=2, but m is not prime, then s has in general more than two values: thus for m=12, s?==1 (mod. 12), which is satisfied by s=1, 5, 7, and 11; the group corresponding to s=1 is distinct from that for any other value of s, but I have not ascertaimed whether the values other than unity do, or do not, give groups distinct from each other. For the sake of an observation to which it gives rise, I write down an example of a group corresponding to n=2, s=m—1, say m=5, and therefore s=4, so that we have =i bene BeGat, And the group is i a, a a, oo iss Ba, Ba?, Ba’, Bat, : the indices of the several terms being Lb, oebel bo oo ee The group is here expressed by means of the symbols a, £, having the indices 5 and 2 respectively, but it may be expressed by means of two symbols having each of them the index 2. Thus putting Ba=y, we find 6?=1, y?=1, (By)®=1, which is equivalent to (y@)°=1, and the group may be represented in the form : 1, B, y, By; YB; ByB, y8y, ByBy, yBYB, By8yB=ByBy, the equality of the last two symbols being an obvious consequence of the equation (By)°=1. It is clear that for any even number - 2p whatever, there is always a group which can be expressed in this form. On the Gnomonic Projection of the Sphere in Crystalloyraphy. 37 I take the opportunity of noticing that the theorem in sphe- rical trigonometry, which I gave in the February Number, is not new, but, as pointed out by Prof. Chauvenet in the Mathe- matical Monthly (Cambridge, U-S.), is to be found in Cagnoh’s ‘Trigonometry’ (1808).—A. C. 2 Stone Buildings, W.C., June 9, 1859. VIII. On the. employment of the Gnomonic Projection of the Sphere in Crystallography. By W. H. Miuuer, M.4A., F.R.S., Professor of Mineralogy in the University of Cambridge*. I. HE first great improvement in the methods of crystallo- graphy, after its establishment as a science, was un- -doubtedly made by Mohs and Weiss, independently of each other, in substituting axes for hypothetical integrant molecules, in the enunciation of the geometric laws discovered by Hauy. Next to this in importance was the graphic method invented by Neumann, and described in his Beitrage zur Krystallonome. He indicates the position of any face of a crystal by the outer extremity of a radius of a sphere, drawn perpendicular to the face; and that of a zone, or assemblage of faces intersecting one another in parallel lines, by a great circle the plane of which is perpendicular to the intersection of any two of the faces which constitute the zone. The several faces of a crystal being in this manner indicated by points upon the surface of a sphere, or by their poles, as it will be convenient to call them, and the zones by great circles passing through the poles of the faces of the zone, the points or poles may be projected upon a plane surface by any of the known methods of projection. Of these the stereographic offers many advantages on account of the facility and the accuracy with which the distances between the originals of any two points may be measured; or the points determined in the projection, having given the mutual inclinations of the faces they represent. In the gnomonic projection, the corresponding constructions are less simple. This projection labours also under the disadvantage that the half of a crystal cannot, as in the stereographic projec- tion, be exhibited on a single surface of finite extent. On the other hand, great circles being projected into straight lines, the zones to which a given face belongs can be very readily ascer- tained; and the situation of a face common to two zones can be much more easily determined than in the stereographie projec- tion. There are also constructions of great simplicity for find- ing the symbols of points in the projection, or for laying down * Communicated by the Author. 38 Prof. Miller on the employment of the Gnomonic the points when their symbols are given, depending upon the equality of the anharmonic ratios of points and great circles on the sphere, with those of the points and straight lines into which they are projected gnomonically, which I now proceed to inves- tigate. “Arts. (2), (13), though to be found in every treatise on modern geometry, and art. (3), which occurs in Muleahy’s ‘ Principles of Modern Geometry,’ are given in order to save the trouble of reference. The results of (6), (7), (9), (10) have also appeared before ; the methods, however, of deducing them by spherical trigonometry, now given, are very much more simple and direct than those which I had previously employed. 2. Let four straight lines passing through the point K, meet any other straight line in the points A, B, C, D. AB sin ABK=KaA sin AKB, DBsinDBK=KD sin DKB, AC sin ACK = KA sin AKC, DCsin DCK=KD sin DKC. Whence we easily obtain AB DC _ sin AKB sm DKC DBAC” snDKBsmAKCO ~*~ ~~ ~ (4) If the straight limes KA, KB, KC, KD meet any other straight hne in the points E, F, G, H, it is evident that ABDC _EF HG 8 DAG a EEGOe tibebkle selins a i 3. Let four great circles passing through the point K, meet any other great circle in the points A, B, C, D. sin AB sin ABK = sin KA sin AKB, sin DBsin DBK= sin KD sin DKB, sin AC sin ACK=sin KA si AKC, sin DC sn DCK=sin KDsin DKC. Whence sin AB sin DC i sin AKB sin DKC sin DB sn AC” smDKDsmAKC ¢ * (7) If the great circles KA, KB, KC, KD meet any other great circle in the pomts E, F, G, H, it is evident that sin AB sin DC _ sin EF sin HG 5 eDbeadG; siHicn EG: )s fee Projection of the Sphere in Crystallography. 39 4. Let X, Y, Z be the poles of the sides of the spherical triangle ABC, opposite to A, B, C re- spectively; P any point on the surface of the sphere; a, 0, ¢ any positive constants. Let P be de- noted by the symbol / k /, where a b Cc i cos PX =~ cos PY = - cos PZ. l Diameters of the sphere passing through X, Y, Z will be called axes ; the constants a, b, c parameters; and the quantities h, k, | the indices of the point P. It is easily seen that if h, k, / be supposed all positive when P is within the triangle ABC, / will be positive or negative ac- cording as PX is less or greater than a quadrant, and that h will be zero when Pis in the great circle BC. The signs of k, / are determined by a similar rule. The symbols of the points A, B, C are 100, 010, 001 respectively. It is evident that the point P is equally well denoted by the symbol nh nk nl, where n is any positive quantity. The opposite extremities of the dia- meter of a sphere have the same indices with contrary signs. B. cos PX = sia PC sin PCB= sin PB sin PBC, cos PY + sin PA sin PAC=sin PC sin PCA, cos PZ =sin PB sin PBA=sin PA sin PAB. Hence : HAR : sin PAC, : sin PBC= : sin PBA, Oe ea ROR, ia tie fst sr LO a b sn ABsn BAP smBH sin BC sin CBP _ sin CK sinCAsinCAP sinCH’ smABsin ABP sin AK’ sinCAsin ACP sin AL sin BC sin BCP” sin BL’ Hence k smBH _ /smCH 7 sn CK _ A sin AK b sin AB csinCA’ c smBC” asinAB’ AsmAL & sn BL (t) a snCA 6 snBC' ° 40 Prof. Miller on the employment of the Gnomonic 6. Let the great circle EF y meet the great circles BC, CA, AB in the points D, E, F. Let uvw be the symbol of any point Pin EF. Draw the great circles AP, BP, CP meeting Bo, CA; Aa m U,V; WwW: a By (y), sin BD sin CU sin CD sin BU = Ww A _sinBPD snCPU _ sin VPE sn CPA _ sin VE sinCA ~ sinCPD sn BPU ~ smCPE sin APV™ sinCE sn AV" But sin VEsinCA=sin CE sin AV— sin AE sin CV. Therefore sin BD sin CU sin AE sin CV snCDsnBU smCE sn AV’ The symbol of P is ww, therefore by (), vsn BU wsnCU wsinCV_ usin AV bsinAB~ csinCA’ esinBC” asmAB Hence smAEsinBCu sinBDsinCAv w_ sinCE smABa'smODsnABb c~ Let Akl, pgr be the symbols of any two points in EF, not being opposite extremities of a diameter of the circle. Substi- tute h, k, /, and p, g, r successively for u, v, w in the preceding equation, and two other equations are obtained. The three equations give (kr —1q)u+ (lp—hr)v + (hq—kp)w=0. If u=kr—lq, v=lp—hr, w=hq—kp, . . (n) uvw may be taken for the symbol of the great circle passing through the points hkl, pqr. The equation u+tvw+ww=0 ..... . (6) expresses the condition that the point wow lies in the great circle uvw. 7. Let uvw be the symbol of the point in which the great circles hkl, pqr intersect. Then by (@), since ww is a point in each of the great circles, hu+ kv +lw=0, pu+qv+rw=0. Whence u=kr—lq, v=lp—hr, w=hq—kp. . . (¢) Projection of the Sphere in Crystallography. 41 8. The expressions for u, v, w in terms of h, k,l, p, g, 7, when uvw is the symbol of a great circle passing through the points hkl, pqr, ave the same as the expressions for wu, v, w in terms of h, k, 1, p, q, r, when wow is the symbol of the intersection of the two great circles hkl, pqr. These expressions are easily remem- bered if we observe that, when written in a line, the last letter in each of the six products is obtained by writing p, g, r twice in inverse order. A rule for forming them was also given in the Philosophical Magazine for May 1857. 9. Let efg be the symbol of the % great circle K P meeting BC, CA, AB in D, E, F respectively ; pqr the symbol of the great circle KR; ki, uvw the symbols of any points Q, S. Draw the great circle QS meeting BC in N, and KP, KR in P, R. Draw the great circles DQ, DS meet- ing the great circle BE in T, V. Draw Big cecal circles KQ, KS; and sia 3 suppose the great circles CT, CV ® drawn. The symbols of A, B, C are 100,010, 001 respectively ; therefore (n) the symbols of BC, CA are 100,010. There- fore (c) the symbols of D, E are Og—f, g0—e. The symbol of BE is eOg, the symbol of DQ is —(fk+gl) fh gh, and the symbol of DS is —(fv+gw) fu gu. Hence (c), the symbol of T is fgh g(eh+fk+g/) —eth, and the symbol of V is feu g(eu+fv+egw) —efu. By (6), (y), sin PQ sn NS_ sin ET sinBV _ sin ECT sin BCV sn NQ sn PS” sin BT sin EV sin BCT sin ECV’ By (€), "8! sin BOT = oleh + + 8) sin BCT, - sin ECV = ete dit sw) sin BCV, Hence sin PQ sinNS _ u eh+th+gl sin NQ sin PS ~ h ew+ fu+ew' In like manner sin RQ sin NS u ph+qk+rl sn NQ sin RS ~ h put+qv+rw’ H ; ; ic sin PQ sin RS — eh+fk+ gl put qu+rw sin RQ sin PS — ph+qk+rl eu+fo+ Sapte (x) 42 Prof. Miller on the employment of the Gnomonic where P, Q, R, S are four points in a great circle, efg, pqr are the symbols of any great circles through P, R, neither of which coincides with QS, and Ak/, uvw are the symbols of Q, S. Each of the ares PQ, RQ, RS, PS being supposed less than a semicircle, sin PQ sin RS, sin RQ sin PS have the same signs, except when one only of the points Q, S lies between P and R. 10. By (7), sin PKQ sm RKS _ sin PQ sin RS sin RKQ sin PKS ~ sinRQ sin PS’ Therefore sin PKQ sin RKS _ eh+fk+g/ put+qu+rw (n) sin RKQ sin PKS ph+qk+rleu+fv+gw’ where KP, KQ, KR, KS are four great circles passing through the point K, efg, pqr are the symbols of KP, KR, and Adi, uvw are the symbols of any points in KQ, KS, neither of which coincides with K. Each of the angles PKQ, RKQ, RKS, PKS being supposed less than two right angles, sin PKQ sin RKS, sin RKQ sin PKS have the same signs, except when one only of the points Q, S lies in the lune PKR. 11. When the points upon the surface of a sphere referred to in the preceding pages are the poles of the faces of a crystal, it is found that the ratio sm PKQsin RKS: sin RKQ sin PKS is always that of two whole numbers. Hence, it readily follows that the indices of the poles, and of the great circles passing through any two of them, are whole numbers, either positive or negative, one or two of which may be zero. 12. Let the straight lines, four of which pass through the point K, intersecting the fifth in the points P, Q, R, S be the 6 gnomonic projections of great circles of a sphere, the centre of which is O, Let K, P, Q, R, S be the originals of K, P, Q, R, 8; and let efg, pqr be the symbols of the great circles KP, KR; hkl, uvw the symbols of Q, S. By (e), sinPKQ smnRKS_ PQ RS _ sin POQ sinROS _ sin PQ sin RS sn RKQ sin PKS RQ PS sinROQ sn POS” sin RQ sin PS’ Hence by (a), («), snPKQsinRKS PQ RS __eh+fk+el/ pu+quvt+rw snRKQ sin PKS RQ PS ~ ph+qk4+r/ eut+fv+ew () The anharmonic ratios in which the letters P, Q, R, 8, deno- P Projection of the Sphere in Crystallography. 43 ting either points in a plane, or on the surface of a sphere, enter in the order PQ.RS: RQ.PS are positive, except when one only of the points Q, S lies between P and R. 13. Let four straight lines passing through K, meet any other straight line in A, B, C, D. Through D draw DE parallel to KA, meeting KB in E, and K C in F. Through E draw EL parallel to KD, meeting KA J in L. Draw the straight line DL meeting K Bin M, and KC im N. Let 48 AB DC _ sin AKB sin DKC ~ DB AC ~ sin DKB sin AKC’ By similar triangles, KA) SAB ADF OC DH DB? KA AC: Hence st =), DF, DE being measured in the same direction or in opposite directions, according as 2 is positive or negative. Since M is the intersection of the diagonals of a parallelogram, DM=LM, therefore (8) AB DC _LM DN _DN DBAC DMLN LN’ Hence N= D, L being on opposite sides of N, or on the same side, according as 2 is positive or negative. These properties afford constructions by means of which, having given the straight lines KA, KB, KC, KD, or the points A, B, C, D in a straight line, the value of X may be found ; or, having given ) and three of the straight lines KA, KB, KC, KD, or three of the points A, B, C, D, the fourth may be found. 14, Let the points D, E, F, G, no three of which are in one straight line, be the gnomonic projections of four poles the symbols of which are known. To find the symbol of any pole P given in position. Let www be the symbol of P. Since the symbols of D, E, F,G are given, the symbol of the lines joming them two by two may be found by (7). By equating the value of sin EDF sin GDP: sin GDF sin EDP, obtained by construction, with its value as given by (u) in terms of the indices of DE, DG, F, P, an equation is obtained of the form au+bv+cw=0, where a, b, ¢ are integers. By equating the value of sin DEGsin FEP : sm FEG sin DEP obtained by con- struction, with its value in terms of the indices of DE, FE, Ad Prof. Miller on the employment of the Gnomonic G, P, a second equation is obtained of the same form as the pre- ceding. From these two equations the ratios of u, v, w may be found. When P is in one of the lines through two of the points D, E, F, G, the equation (7), which expresses this condition, may be used in the place of one of the preceding equations invol- ving U, v, w. 15. Let the points D, E, F, G, no three of which are in one straight line, be the gnomonic projections of four poles the symbols of which are known. To findP, having given its symbol uvw. Since w, v, w, the indices of P, are given, as well as the indices of DE, DG, F, X, the numerical value of sm EDF sin GDP: sin GDF sin EDP may be found. Hence DE, DF, DG being given, and the value of A, DP may be constructed. Inthe same manner, with ED, EG, EF, and the numerical value of sm DEG sin FEP : sin FEG sin DEP, EP may be constructed. The intersection of the lines DP, EP is the point P required. When the numerical values of uw, v, w are such as to show by (@) that P is in one of the lines joining every two of the points D, E, F, G, one only of the lines DP, EP suffices to deter- mine P. Or, since this line meets one of the other lines through every two of the pomts D, E, F, G, in a third point the symbol of which can be found, P may be determined by means of these three points, and the numerical value of the anharmonic ratio of these three points and P. 16. Hence, if the gnomonic projections of four poles of a ery- stal, no three of which are in one straight line, and their symbols be given, the symbols of all the other poles can be found ; or, the symbols of the latter being given, the poles themselves can be determined, without any knowledge of the centre of the pro- jection, or of its distance from the centre of the sphere, or of any of the angles of the crystal, or even of the system of ery- stallization to which it belongs. 17. Quenstedt indicates the positions of the faces of a crystal by the lines in which planes drawn parallel to them, through a given point O, intersect a given plane. The lines which repre- sent the faces are therefore the gnomonic projections of great circles of a sphere having their planes parallel to the respective faces of the crystal. The axis of a zone is represented by the gnomonic projection of one extremity of a diameter of the sphere drawn parallel to the axis of the zone. The lines and points G E Projection of the Sphere in Crystallography. 45 may be denoted by the symbols of the faces and zones they respectively represent. 18. Let the straight lines four of / which pass through the point K, in- tersecting the fifth in the points P, Q, R, S, represent faces of a crystal, O being the fixed point. Let efg, pqr be the symbols of the zones the axes of which are represented by the points P, R, Akl, uvw the symbols of the faces represented by the lines KQ, KS. Oo By (2), PQ RS _ sin POQ sinROS RQ PS~ sinROQ sin POS’ But OP, OQ, OR, OS are four zone-axes in one plane. Con- sequently the corresponding zone-circles pass through one point. The sine of the angle between any two zone-axes is equal to the sine of the angle between the two corresponding zone-circles. efg, pqr are the symbols of the zones of which OP, OR are the axes ; hk/, uvw are the symbols of faces in the zones of which OQ, OS are the axes. Hence by (a), (A), sinPKQ sin RKS_ PQ RS eh+fk+ gl put+quv+rw sn RKQ sin PKS RQ PS ~ ph+qk+rl eut+fo+eu' ) 19. Let the symbols of the 5 faces represented by the lines AB, AC, BC, DE be given, and let www be the symbol of the face represented by the line MN. By equating the value of AD .BM : BD. AM, as given by construction, with its value as given by (v) in terms of the indices of the points A, B, and those of the lines DE, MN, an equation is obtained of the form au + bv +cw=0, where a, b, c are integers. The comparison of the value of AE. CN : CE. AN, as obtained by construction, with its value as given by (v) in terms of the indices of A, C, DE, MN, yields a similar equation. By elimination between these two equations the ratios of u, v, w may be found. 20. Let the symbols of the faces represented by the lines AB, AC, BC, DE be given, and let u, v, w, the indices of a face to be represented by a line MN, be given. The numerical value of AD.BM: BD.AM can be found by (v) ; knowing this, and the M 46 Prof. Miller on the employment of the Gnomonic three points A, D, B, the point M may be constructed by (18): In like manner, the point N may be constructed from the nume- rical value of AE.CN: CE. AN, and the points A, E, C. The line MN then represents the face uvw. 21. Let the symbols of three faces in one zone, represented by the lines KP, KQ, KR, be given. Let the line KS re- present any other face ww in the same zone. By equating the value of sin PKQ sin RKS : sin RKQ sin PKS, found by con- struction, with its value as given by (v) in terms of the indices of KP, KQ, KR, KS, an equation is obtained of the form au+bv+cw=0, where a, 6, c are integers. The condition that the face represented by KS is in the zone represented by K, (0) furnishes an equation of similar form. From these two equa- tions the ratios of u, v, w may be found. 22. Let the symbols of three faces in one zone, represented by the lines KP, KQ, KR, be given, and let wu, v, w be the indices of a face to be represented by a lime KS. The numerical value of sin PKQ sin RKS: sin RKQsin PKS can be found by (vy). From this, and the three lines KP, KQ, KR, the line KS can be constructed by the methods of art. 13. 23. Hence, if the lines representing four faces of a crystal no three of which pass through the same point, and their symbols be given, the symbols of the faces represented by all the other lines can be found; or, the symbols of the latter being given, the lines which represent the faces may be constructed. It is not requisite that the place of the fixed point O, or the angles of the crystal, or the system of crystallization to which it belongs, should be known. 24. In the preceding investigation spherical trigonometry has been employed in preference to analytical geometry of three di- mensions, because a knowledge of the former is practically indis- pensable to the mineralogist, while we are not bound to assume that he is acquainted with the latter. Moreover, the methods of spherical trigonometry appear to be more appropriate than those of analytical geometry, in discussing the relations between points and circles on the surface of a sphere, and the points and straight lines by which they are respectively represented in the gnomonic projection of the sphere. The results of arts. (6), (7), (9), (10) may, however, be easily and concisely deduced by the aid of analytical geometry. An expression equivalent to (6) combined with (7) was obtamed by Levy in this manner (Edinb. Phil. Journ. vol. vi. p. 226). Its usefulness was, however, greatly im- paired by the employment of a very defective notation. 25. The plane which has for its equation h—+ke +12 =d, a b c Projection of the Sphere in Crystallography. 47 where a, b, ¢ are constants, and d is any positive quantity, will be denoted by the symbol Aki. Let the plane Ak/ meet the axes OX, OY, OZ in the pots H, K, L respectively. Then a b c Therefore On OK {OL ha Shae Sa . ot diy (eens Por a eat) (é) The three letters h, k, 1 will be called the mdices of the plane HKL. The plane HKL is equally well denoted by the symbol nh nk nl, where x is any positive quantity. 26. The equations to planes parallel to the planes Aki, pqr, passing through the origin, are ner kt 412 =0, a b c Sins Oa COs Poy re =O; and the equations to the line in which they intersect are 7a Bee: ua vb we where ; u=kr—lq, v=p—hr, w=hq—kp... . (0) Any straight line parallel to the straight le having for its equations will be denoted by the symbol uvw. The three letters u, v, w will be called the indices of the line. Any three quantities pro- portional respectively to u, v, w, may be taken for the indices of the line. 27. Let wow be the symbol of a plane parallel to the lines hkl, pqr. Ifa plane be drawn through the origin of coordinates parallel to the plane wow, and if lines be drawn through the origin parallel to the lines hkl, pqr, the lines will be contained in the plane. The equation to a plane through the origin, par- allel to the plane wow, is ue +v44w2=0, a c b and the equations to lines through the origin, parallel to the lines hkl, pqr, are 48 Prof. Miller on the employment of the Gnomonic Therefore, since the plane contains the lines hu+kv+lw=0, pu+quv+rw=0, u=kr—lq, v=lp—hr, w=hq—kp. . . (7) 28. Through O, the origin of coordinates, draw the straight lines OP, OR, parallel to the lines efg, pqr, meeting the plane hkl in H, L, and the plane ww in U, W. Let planes parallel to YOZ, passing through the pomts H, U, L, W, meet OX in H’, U', L', W'. Draw OQ, OS parallel to HL, U W respectively. The equations to the lines OP, OR are Oe ae ea fb ge’ faite ROE pa qb re’ and the equations to the planes hci, uvw are hake ele = a b c a zZ ey eb ee <3 a c b The distances OH’, OU’, OL', OW’ are the values of « at the points in which OP, OR intersect the planes Ak/, uvw. There- fore (eh+fk + gl)OH' =ead, (ew + fv +gw)OU! =eat, (ph+qk+r/)OL! =pad, (pu+ qv+rw)OW'= pat. By similar triangles, OH'_OU' |, OL/_ow OH ~ OU’ * OL OW Hence © OL OU _ eh+fk+gl putqu+rw OHOW ph+gk+rieut+ttv+gw 9 © 7 (p) Projection of the Sphere in Crystallography. 49 But sin POQ sin ROS smOHLsnOWU_ OL OU sinROQ sin POS ~ sinOLH sinOUW~ OH OW’ Therefore sin POQ sn ROS _ eh+fk+ 91 put+qu+rw sin KOQ sin POS ph+qk+rleu+fv+ew’? ~ (2) where OP, OQ, OR, OS are four lines in one plane, efg, pqr the symbols of the lines OP, OR, and Aki, uvw the symbols of planes parallel to the lines OQ, OS. Each of the angles POQ, ROQ, POS, ROS being supposed less than two right angles, sin POQ sin ROS, sin ROQ sin POS will have the same signs except when one only of the lines OQ, OS lies in the angle POR. 29. Let h, 1, u, w be the orthogonal projections of the points H, L, U, W in the preceding figure, on a plane through O, per- pendicular to the intersection of the planes hkl, uvw. In this plane draw lines perpendicular to Ou, hl, Ow, uw, meeting a circle described round the centre O, in the points P, Q, R, S. OQ, OS are respectively perpendicular to the planes Aki, ww. OP, OR are respectively perpendicular to planes containing the lines efg, pqr, parallel to the intersection of the planes Akl, uw. By similar triangles, Oh us; On, J Ol Ow OH Ov’ ** OL OW: Therefore sm PQ sin RS _ sin Ohl sin Owu sin RQ sin PS ~ sin Olh sm Ouw _01 Ou _OL OU ~ Oh Ow” OH OW Hence snPQsn RS _ eh+fk+gl pu+qu+rw sin RQ sin PS” ph+qk+rl eu+fv+gw’ where OP, OQ, OR, OS are perpendiculars to four planes inter- secting one another in parallel lines, efg, pqr the symbols of lines in the planes perpendicular to OP, OR, and Aki, www the symbols of the planes perpendicular to OQ, OS. Each of the arcs PQ, RQ, PS, RS being supposed less than a semicircle, sin PQsin RS, sin RQsin PS will have the same signs except when one only of the points Q, S lies in the are PR. 30. The expressions for the indices of a plane when referred to new axes, are easily deducible from (p). Let efg, hkl, pqr be Phil, Mag. 8. 4. Vol. 18. No. 117. July 1859. KE (7) 50 Mr. J. Cockle on the Theory of Equations the symbols of the straight limes OU, OV, OW meeting the plane Awv in A, M,N, and the plane ww in U,V, W. By substituting A, N for H, L, and A, pu, v for h, k, 2 im (p), and then writing M for N, and h, k, | for p, q, r in the result thus found, the following equations are obtained :— eut+fut+gw OU _hu+kv+lw OV _ pu+quv+rw OW ea+fut+gvOA” ha+ku+lyOM ~ pr+qu+rv ON’ Or, writing a’, L!, c! for the respective denominators of the pre- ceding fractions, (eu + fv + gw) = =(hu+kv+lw) = =(put+qu+rw) ae Hence by (£) the symbol of the plane ww, when referred to the straight lines efg, hkl, pqr as axes, will be w'v'w!, where ul =eu+fv+gu, v =hu+kv+lw, I (v) wl=pu+quv+rw. IX. Observations on the Theory of Equations of the Fifth Degree. By James Cocks, M.A., F.R.A.S., F.C.P.S. &¢.* [Continued t from vol. xvii. p. 357.) 42. UTTING the trinomial under the form v°—5Q2?+ EK=0, the equation in O(a), or 0, is (+ 5°QHO + 57Q*)?=5!9(108Q°E— E") 6. 43. The assumptions po'=a, wO'=0, 52Q2u4=E, conduct us to the still simpler system 2° —5T2?+ F=0, (+ 5H@+5H)?=(108—H)H?0, in which the accents are suppressed after transformation, and P=57P=2 (573; yA 5 PP per, 44. In order to apply the formule of Euler and Bezoutt, I * Communicated by the Author. T Art. 41 is misnumbered “40.” In art. 36, line 5, for “ ./5 ” read 5. ft The notation at p. 200 of Ross’s translation of Hirsch’s Collection is substantially the same as that of Bezout at p. 544 of the Paris Mémoires for 1765, and is more convenient than Euler’s at pp. 91, 92 of vol. ix. of of the Fifth Degree. 51 take 5°3= /—6, 5r9=X, 5rd = X,, and, combining the relations a=rs, b=r5, c=——, d=-, with the subsidiary equations 1 1 u=rd+ = v=7s— =f u= f/v—48, v= Vv?+48, wo'=w, the latter of which afford w? =u? + 43(u?—v?)— 1697, . . . «.. (d) 2Q=ur(u+v)+(u—v)(23—w), . . . . (e) 63?=uv(u? + v?) + (u?—v?—29)w, . . . . (f) —E=wv?+v°—53(u+v)(u2—v?-38—w). . . (g) 45. The symbols r and 7, have been eliminated by means of 2r=utu, 2287r,=v+40, and their reduced reciprocals. 46. Since u+v is a value of x, the operation B(u+0) {(u+)(e) + (f)} +2(8); which reproduces the trinomial, suggests that « and v should be separately determined in terms ‘of $ and « then formed by adding these expressions. 47. Fixing # and varying 3, we find x in terms of different values of 3 which are thus connected with each other. Each particular value of x is, indeed, linked with three particular fac- I find the Petersburg Novi Commentarii. The former may be simplified; for if 2° —5Px®—5Qa?— 5Ra2+h=0, a=ai+b?+c3+di*, and abed=—2, then P=ad+bc, Q=a?c+ab?+hd2+ ed, R=03b+ b'd-+ ac*+ cd?— P? —33?, —E=:3a°—5PQ— 108? , a = =), In the trinomial under consideration, I fy 283,72) - 259 a a4 ] pe co E=30° +105 (Q+=" 7) =Sa’—108 (Q i adchegies 4-). 2 E 2 52 Mr. J. Cockle on the Theory of Equations tors of innumerable expressions of the fifteenth degree which can be found by combining two and two the values of 0. 48. Let O-=2,4 ix, +7794 Brg t 24, 0;= @', , Oya2) = 0',, ®ya3) — 0’, On.) =O, Oey =p Ono = Oe where, the interchange (23) being omitted, the relations are expressed by Oyjap) =O! and the transpositions (4B) have reference to the roots of the trinomial. 49. Let ©", ©", and @iv denote what ©! becomes when 7 is replaced by 7?, 73, and 7* successively ; then ©,+6,+, + Or =52;, ©,0; + ©,0, =0, ©,0,,0;, On =9,, for all values of n. 50. We also have the alternative theorem*; either HET OLLE cg eee a+B—l» or . . OQ, oh oY — ©, 4- ©, an . . . ° . ° (i) where a and b occur in the pairs 1 2 3 Ae ibnlitaad Dap and (h) holds for the first pair, and (i) for the second and third. 51. And, R being a rational function, we have R(@,, 4,,) (ap) a R(Oy, Ay), where #,, 2%, are any two of the four roots 2}, %q, #3, and x4, and a', b! as well as a, b occur in the foregoing pairs. * Hence } : (o',)?+ .. +(0%)?=(0n,)?+ .. +(e), and since e!, + Ov 2254 (i+74)(a) +24) +(F+25)(a.+25), we find that if =,=20!,e,"=(06',+0,i")(e,"+0,'") =5f 47, + (a +24)(%2 +25) t, then # is the root of a cubic whereof the coefficients are rational functions of zs. of the Fifth Degree. 53 52. Hence, if E,=R(A,, 44), £,=R(6,, 9), E,=R(O;, 85), we may form the cubic 4 aé + bE+c=0, the coefficients of which will be rational functions of 2. 53. But, even were the six values of 0 independent, we could, by introducing the suffixes in any three pairs, construct a cor- responding cubic E84 ACE? 4+0E4+¢=0: E ‘= oO; Al 0, 3 then, using a notation analogous to that of art. 30, Fea © b =D*‘,— (@, O40, O e+ 0"; Py) C=D;—D (0, 440, 0'6+8's 0's) = {POP +O) +O. (Pot Oe) +P 30 (03 +05)}- 54, Consequently it is upon the special forms of the functions R that the important question of the solvability of the equation in 6 turns. The cubic function &34+a&*%+ ...is always a divisor of the 15-thic function £+4+5D',)&"+ ... as the cubic function £+aé+...is of the 15-thic function &°+ 5D,é4+ ...; and the coefficients D‘,, D',,... are symmetric functions of 6’, as D,, D,,... are of 9: but D,, Dg, ...are also rational functions of the coefficients of the given trinomial. 55. Let (0; +.")2— (6/7 2— (@ -0*)(0;—-@) = 5?(u? —v? —w, = 570. ex. gr. let 56. Then, expressing ©, as linear functions of ©,, we find 50,0; =30,0, +5’, 50,0, =30;07 —5%. 57. Consequently 570,= — (5997 —3.5?.3,)? and 53y=—35,; or 44=9—Fh, if we replace 53 by ¢. And (g) becomes B40 +2—52(u+v)$,9,=0.......-. (J) 58. But (see arts. 44-46) 7 is a rational function of 4,. Hence 3, is a rational function of $,, and ¢, of ¢). 59. I infer therefore that the trimomial 2” —5aaz?+a°=0 54 Messsrs. Perkin and Duppa on Jodacetic Acid. admits of finite algebraic solution. For one of the roots of its resolvent (t+ 5att?— 5a4)?= (a*#— 108)a%?, or +504? +a? Vat—108 . t—5at=0, is a rational function of another, and, if so, this sextic may be solved by the process of Abel. 4 Pump Cowt, Temple, E.C., June 14, 1859. Note. Arts 55-59 were added by a postscript dated June 25, 1859. X. On Todacetic Acid. By W. H. Perxtn, F.C.S.; and B. F. Dupra, Esq.* ye studying the action of bromine on acetic,acid, it struck us naturally that we might succeed in replacing the hydrogen of acetic acid, not only by bromine, but also by iodine. We first attempted to produce the substitution by acting on acetic acid with iodine at high temperatures ; but, proceed as we would, we were unable to obtain any results, the iodine appa- rently exercising but little action on this acid. A mixture of iodine and acetic acid, on being heated to about 200° C. for a fort- night in a strong sealed tube, gave a mixture of hydriodic acid and charcoal as a result. We mention this to show how far we carried the experiment of direct substitution. We have also tried to produce iodacetic acid by treating acetic acid with chloride of iodine, but without success. Having been unsuccessful in the above experiments, it appeared possible that we might obtain the acid in question by treating chloracetic acid, bromacetic acid, or one of its compounds with an iodide; for this purpose we selected bromacetic ether and iodide of potassium. On mixing equivalent proportions of bromacetate of ethyle (diluted with three times its volume of alcohol) and finely- powdered iodide of potassium, a reaction takes place, the liquid gets slightly warm, and becomes yellow when exposed to direct sunlight. After being digested at about 40° C. for a couple of hours in the dark, it must be filtered from the bromide of potassium which has formed, and which should be repeatedly washed with cold aleohol. The filtrate, after having been sepa- rated from the alcohol by distillation in a water-bath, and washed * Communicated by the Authors. Messrs. Perkin and Duppa on Iodacetic Acid. 55 with water to separate any remaining bromide of potassium, con- stitutes the iodacetate of ethyle. Its formation will be easily understood as under :— C+ HS, C4(H? Br)O*+ KI=C? H®, C*(H? 1)0* + K Br. Bromacetate of ethyle. Todacetate of ethyle. To obtain iodacetic acid from this compound, it is first con- verted into the barium salt, which is afterwards decomposed by sulphuric acid in the following manner. The new ether is agitated with hydrate of barium and water in the cold, which soon decomposes it; the excess of hydrate of barium is separated by means of a filter, and carbonic acid passed through the filtrate throws down any that may be in solution ; it is again filtered, and the resulting liquor carefully evaporated and allowed to crystallize. The iodacetate of barium thus obtained is then dissolved in water, and decomposed by very cautiously adding dilute sulphuric acid until all the barium is precipitated as sulphate ; by this means an acid liquid is obtained, which is then concentrated in vacuo over sulphuric acid until it crystallizes. These crystals consist of crude iodacetie acid, and are rendered pure by being recrystallized two or three times. Thus obtained, iodacetic acid is a colourless substance, cry- stallizing in thin, tough, pliable, rhombohedral plates, which, when pressed together, look like mother-of-pearl. It is not de- liquescent. It has a very acid taste. It fuses at 82° C., and solidifies at 81°5; even at this low temperature it undergoes slight decomposition, becoming pink from free iodine: at a higher temperature it is quite decomposed, iodine being evolved in considerable quantities; a small quantity of the acid appears at the same time to be volatilized, and has a smell similar to bromacetic acid. Hydrate of silver added to the acid, or any of its salts, imme- diately seizes on the iodine and forms glycolic acid. The following combustions and iodine determinations were made, and, as it will be seen, agree very well with theory :— I. -7902 of acid gave °3716 of carbonic acid*. II. -9890 of acid gave -4659 of CO? and °1610 of water. III. -5420 of acid gave *6787 of iodide of silver. Per-centages :— r. 1H III. Carbon °. '.. =. 12°83 12°83 Hydrogen . 158 Jodine. ae ie 67°89 * The hydrogen was lost. 56 Messrs. Perkin and Duppa on Jodacetic Acid. The formula C4(H°1)O* requires— Carbine 22* 2 Ma. a Mydravenr i. 6 es 1:60 Todine Ss "tie. (3 26842 We have been able to produce but few of the iodacetates, or to study the metamorphoses of the acid, as it is so difficult to obtain in quantity. Iodacetate of Ammonium is a very soluble erystalline salt, not deliquescent. Todacetate of Potassium is a soluble crystalline permanent salt. Lodacetate of Barium is a crystalline salt, tolerably soluble in water, and precipitated from its solution by alcohol. Analysis gave the following results, which we place in juxtaposition with the theoretical numbers :— Theory. Experiment. Gian a Carbon (4 equivs.) . . 24 9:46 9°81 Hydrogen (2 equivs.) . 2% ‘78 82 Todine wo salen iii Oe. (Ue 49°63 _ OPIN ok ahhh a) Ue le Ue 26°90 Oxygen (4 equivs.) . . 32 12°65 253°47 100-00 We should have repeated this analysis had we possessed suffi- cient substance; but the numbers agree closely enough when those obtained from the acid are taken into consideration. Todacetate of Lead crystallizes in prisms, is difficult to obtain pure, as it readily splits up into glycolic acid and iodide of lead : this is most readily effected by boiling. When we attempted to decompose the aqueous solution of this salt by sulphuretted hydrogen, we found that the liquid con- tained hydriodic acid and glycolic acid?, the iodacetic acid having been completely decomposed. Todacetate of Ethyle is an oily liquid heavier than water, of a very irritating nature, if anything worse than the corresponding bromacetic compound. We did not make an analysis of this, as it was quite impossible to obtain it sufficiently pure. It soon becomes brown from spontaneously giving off iodme. Todacetate of Amyle is an oily liquid heavier than water. It has the odour of pears, similar to the bromacetate of amyle, and also when heated irritates the eyes and nose. We hope in the course of a very short time to publish our in- vestigations on diiodacetic acid, which we have lately obtained. Lica] XI. On the “ Loss of half an undulation” in Physical Optics. By Proressor CHaruis*. B* experiments on light, certain facts have become known, which are described in the language of theory by the terms “loss of half an undulation;” but the theory of light usually adopted gives no explanation of the facts. It is not, however, to be inferred from this circumstance that the Undu- latory Theory of Light is at fault, since the theory alluded to, which for distinction might be called the Vibratory Theory, does not really involve the consideration of undulations. The only existing theory of light which is strictly undulatory is that which I have proposed in various published memoirs. The two views, as I have before urged, are essentially different. In the one the zxther is regarded as a continuous medium, and the phenomena of light are attributed to its motions en masse in waves or undulations: in the other the same phenomena are attributed to the vibrations of its constituent atoms. The expla- nation of phenomena in the former view necessarily requires the solution of partial differential equations ; in the other, as in every instance of the small vibratory motions of a discrete body, the equations to be solved are common linear differential equa- tions. Now it is possible that the vibratory theory fails to account for apparent instances of the loss of half an undulation, because common differential equations are inappropriate to the explanation of phenomena of light. At least, it may be shown, as I now propose to do, that such instances admit of explanation by means of deductions from partial differential equations. The loss of half an undulation is said to occur when light passes out of a transparent medium into vacuum, the phase of the light reflected at the boundary of the medium being the opposite to that of the incident light. An analogous fact occurs in air, when vibrations excited at one end of an open cylindrical tube are propagated to the other end. A condensed wave is reflected at the mouth of the tube as a rarefied wave, and a rarefied as a condensed wave. The explanation of this fact given by the mathematical theory of aérial undulations is such as fol- lows:—The density of the air which’ has issued, or is on the point of issuing, from the mouth of the tube, can be but very little different from that of the surrounding air, on account of the lateral spreading to which the condensation or rarefaction is subject on being propagated from the tube. If we consider an elementary particle situated at the mouth, and suppose it to be urged from within to without by an accelerative force due to the fluid pressure, then there must be at cach instant contiguous to * Communicated by the Author. 58 Prof. Challis on the “ Loss of half an undulation” that position a decrement of density from within to without, due partly to the original waves, and partly to the lateral spreading. So far as the decrement is due to the original waves, the propa- gation from within to without tends continually to merease the density at the mouth of the tube. But this tendency is imme- diately counteracted by the lateral spreading, the effect of which, consequently, in producing decrement of density from within to without near the tube’s mouth, has at each instant a given ratio to the decrement due to the original waves. Analogous consi- derations apply to the case in which the particle is urged by an accelerative force from without to within. In this case the den- sity increases from within to without, and, so far as the increment is due to the original waves, the tendency of propagation is to diminish the density at the mouth. This diminution is imme- diately counteracted by the external lateral spreading, and the increment of density from within to without, due at any instant to the original waves, is thus augmented, and in the same con- stant ratio asin the former case. Hence, if the accelerative force impressed on the particle by the original waves be /f, the actual accelerative force is gf, q being a certain constant. In order that the density at the mouth of the tube may be always equal to that of the external air, or that the position of what is called a loop in this class of vibrations be at the mouth, it is necessary that the factor g be equal to 2. When this is the case, the motion within the tube, as the mathematical theory proves, con- sists of two equal series of undulations propagated in opposite directions. Consequently, as the motion is excited at one end of the tube, the effect that takes place at the opposite open end is a reflexion of the undulations im a phase contrary to that of incidence. A reflexion of the same kind would be produced by placing a diaphragm transverse to the axis of a tube along which a series of waves is propagated, and giving to it just double the velocity which the fluid im contact with it would receive from the undisturbed effect of the propagated waves. The diaphragm will thus impress on the fluid an accelerative force equal to that due to the waves, and give rise to two additional series of waves, equal in magnitude to the original series ; one of opposite phase and propagated in the opposite direction, and the other of the same phase and propagated in the same direction. By giving to the diaphragm any other motion having a given ratio, q, to the undisturbed motion, these effects may be altered at pleasure. If g=1, no effect is produced, and if g be less than unity, the return waves are of the same phase as the incident. In order to apply these considerations to the reflexion of light at the surfaces of transparent media, I shall suppose, for the sake of simplicity, that the light is incident perpendicularly in Physical Optics. 59 on the surfaces. As we have here to consider the action of transparent media on waves of light, it is necessary to make suppositions respecting the constitution of such media, and the dynamic relations subsisting between them and the luminiferous ether. On these points I have already advanced, with reference to a theory of physical forces, very definite hypotheses, from which, in the present theory, I shall not have occasion to depart. The following explanation, consequently, so far as it is success- ful, may be regarded as a corroboration of the truth of the hypotheses. I have supposed that visible media generally con- sist of a collection of hard and inert spherical atoms, which act upon each other dynamically only through the intervention of undulations of the ether. Accordingly the ether is of the same density within the media as without, and any effect which the media produce on the undulations propagated within them is due solely to the obstacles they present to the free motion of the zther, and the reflexions which take place at the surfaces of their atoms. In my communication to the ‘ Philosophical Magazine, for last March, I have given reasons for concluding that the part of the reflexions which is unaccompanied by con- densation produces a mutual repulsion between neighbouring atoms. But, if this be the case, it is evident that the same re- flexions must also act on the fluid itself. The effect of such action on waves propagated in transparent media, appears to admit of the following investigation. In the first place, it is to be re- marked, that the breadth X of a luminous undulation has a very large ratio to the mean interval between the atoms. This fact, as 18 known, has been established in the instance of glass, by microscopic observation of finely-drawn parallel lines on its sur- face, which are still seen distinctly separate, when the mean interval between them is less than X. By considering, in con- Junction with this fact, that the radius of an atom must be ex- ceedingly small compared to the interval from atom to atom, some idea may be formed of the extreme minuteness of the di- mensions which must be attributed to the ultimate particles of matter. Now I have elsewhere shown that if V be the velocity incident on a spherical atom of radius r, supposed at rest, the velocity reflected in a direction making an angle @ with the di- rection of incidence is, at the distance of R from its centre, very 2 nearly equal to V7 es 6. This expression applies to the re- flexion of velocity from an atom situated apart from all others. But in the case of an aggregation of atoms, the velocity reflected from a given atom in its turn suffers reflexion from all the atoms within a certain distance from it, and thus the decrement of velocity with increase of distance takes place more rapidly than 60 On the “ Loss of half an undulation” in Physical Optics. according to the law of the inverse square. Taking account of this circumstance, and the extremely small value of 7, it may be presumed that any effect of the reflected velocity on the fluid at a position P, is sensibly due only to reflexions from atoms situ- ated within a very small distance from P. That is, if a be the distance of P from a fixed plane, the effect at P of the reflected velocities may be supposed to be due only to atoms situated at distances from the plane between a—a and a+a, & being very small. Hence, if V be the velocity of the fluid at any distance z, and it be assumed that through the small interval 2, the ee : value of =a is very nearly constant at each instant, the re- sultant (v) of the reflected velocities is at the distance z in a given ratio to V, and the actual velocity at that distance is com- pounded of the velocities V+v and —v. Thus, by the retarda- tion due to the atoms, the effective accelerative force of the fluid is diminished in a constant ratio. Hence the fluid situated at the plane boundary of the medium is subject to precisely the same disturbance as that communicated by the diaphragm in the case above supposed, of aérial waves in a cylindrical tube ; that is, on the fluid in this position an accelerative force is impressed, which has a given ratio to that which would be due to the condensation of the incident waves if there were no disturbance. At the instant of intromittence into the medium, the disturbance acts as asudden retardation, and corresponds to a value of q less than unity. The reflected wave is, therefore, in the same phase as the incident. There is no reflexion after intromittence, because the retarding force then acts continuously, and has only the effect of altering permanently the relation of the condensation to the velocity, and the rate of propagation. On the passage of the waves out of the medium into vacuum, the retarding force sud- denly ceases, the rate of propagation and the relation of the con- densation to the velocity return to what they were before intro- mittence, and the effect on the fluid situated at the plane boundary of the medium, is the same as if an accelerative force were there impressed, having a given ratio q, greater than unity, to the accelerative force due to the original waves in vacuum. Consequently, the waves reflected back into the medium have the contrary phase to that of the incident waves. In this manner, as J conceive, the facts of observation are shown to be consistent with the undulatory theory of light, and the apparent loss of half an undulation is accounted for. Another instance of the supposed loss of half an undulation is mentioned in Art. 966 of Sir John Herschel’s ‘Treatise on Light.’ When a plane-polarized ray is bifurcated by transmis- sion through a thin plate of a uniaxal crystal, and the two por- Notices respecting New Books. 61 tions are incident in the same phase on a glass-refiector at the angle of complete polarization, no reflexion takes place if the plane of reflexion be perpendicular to that of the polarization of the original ray. As the reflexion is considered to bring the two rays to the same plane of polarization, it is imagined that the non-reflexion is caused by interference, and, as the lengths of the respective paths do not accord with this supposition, it is further supposed that one of the rays has suffered the loss of half an undulation. The necessity for these gratuitous suppositions arises out of the inadequacy of the vibratory theory of light to explain the phe- nomena. According to the hydrodynamical theory of polariza- tion, which I have given in vol. vii. part 3 of the ‘ Cambridge Philosophical Transactions,’ the two parts of a plane-polarized ray, bifurcated in the manner above stated, constitute, on meeting in the same phase, a plane-polarized ray equivalent to the origi- nal one, and having the same plane of polarization. It is for this reason, solely, that the compound ray is not reflected when in- cident on the glass-reflector in a plane perpendicular to that of original polarization. This simple explanation essentially de- pends on an investigation of the properties of polarized rays by means of partial differential equations, as will be seen by con- sulting the paper above cited. These are the only instances of the supposed loss of half an undulation in physical optics which require to be brought under discussion. Cambridge Observatory, June 20, 1859. XII. Notices respecting New Books. Etudes sur la Métamorphisme des Roches. Par M. Dr.zssz, Ingénieur des Mines, Professeur de Géologie dl Ecole Normale. 8yo. Dal- mond et Dunod, Paris. Bs this work M. Delesse has brought together part of his re- searches into the interesting subject of the metamorphism of rocks, the publication of which had hitherto been scattered through the Annales des Mines. He first of all considers metamorphism under two heads, namely, normal or general metamorphism, which proceeds from causes which are not obvious, and is produced on a large scale, and abnormal or special metamorphism, or what is called contact metamorphism. It is with the latter that he alone concerns himself in this work, in which he gives a great number of details on the metamorphic action pro- duced by eruptive (intrusive) rocks. This action is twofold, since not only does the intrusive rock exert a metamorphic action on the rock which it penetrates, but it is itself often more or less changed by the rock with which it comes in contact. 62 Notices respecting New Books. Secondary actions, moreover, are often set in motion in conse-~ quence of the infiltration of heated water, or of vapours; and these actions may extend to some distance from the actual intrusive mass, He divides the intrusive* rocks into lavas, trappean rocks and granitic rocks; and he examines the action of each upon the various rocks which include or surround them, as the ores, the combustible rocks, the felspathic rocks, and calcareous, siliceous, and argil- laceous rocks. The first conclusion which M. Delesse states as the result of his investigations, is that the metamorphic effect of mere heat has been greatly exaggerated; and he then gives an account of the action of heat on some substances, as observed in the laboratory and in sub- terranean fires in mines. We must say that the conclusions to be drawn from these experi- ments, as well as those derivable from the observation of the action of lava-streams on rocks, do not appear to us to be necessarily applicable to the action of deeply-seated rocks, without much caution and reserve. The conditions of pressure, and its action on the volatile constituents of certain rocks; the possible more or less complete exclusion of atmospheric air at great depths, and the difficulty of excluding it from rocks heated in laboratories or mines, and the possibly indefinite differences in the rates of cooling in the two cases, require, we think, to be taken into account to a much larger extent than they usually are. We examine a granitic or trappean dyke and the rock it traverses at the present surface of the ground, or in some mining gallery near the surface, and we often forget that at the time that dyke was injected ‘there was perhaps 5000 or perhaps 10,000 feet of rock or more above what is now the surface. From Mr. Sorby’s recent admirable researches, indeed, it appears probable that in the case of many granite veins, instead of 5 or 10, we ought more probably to suppose 50 or 60 thousands of feet to have been incumbent on the rocks at the time of the injection of the granite. M. Delesse gives several careful descriptions, however, of locali- ties where trap-dykes were injected into rocks that were, at all events, not so deeply buried at the time of injection. Several of these places are in the County Antrim, where a vast mass of inter- stratified basalt and ‘‘ tuff” rests upon the chalk. He describes, at one place near the Giant’s Causeway, a bed of lignite as covered by a bed of trap, and so little altered that it is impossible, according to him, that the trap could have been a molten mass when it flowed over the lignite. He also gives a detailed description of the dyke * M. Delesse, as is usual on the Continent, uses the term “ eruptive” instead of intrusive ; as, however, the word eruptive seems to involve the idea of the rock reaching the surface, and as there can be little doubt that all the granitic rocks appear at the surface only in consequence of vast subsequent denudation, and were originally cooled and consolidated at great depths, it appears to us better to use the term “intrusive” for all the igneous rocks. Notices respecting New Books. 63 at Woodburn, which cuts through greensaud and chalk, both becoming crystalline near the dyke, and says that the existence of the Glauconite (a hydrosilicate of iron and potash) in a limestone which has become crystalline from the contact of trap, ‘‘ entirely excludes the hypothesis of that crystallization being the result of an action exclusively igneous.” His remarks on the metamorphic action which the trap or whin- stone of the neighbourhood of Edinburgh have produced on the grits of the Carboniferous formation there, are very interesting. The specimen of whinstone examined by M. Delesse contained— Residue insoluble in acid Sara OR a Oe!) DU AGEI Eee eS cin aos. fio, crete cree MEET hears, fale? TOS CAENONIC BCIG) 36, cits aids: cos ee ote ae ee 6°86 It made a considerable effervescence when plunged into acid, con- taining carbonates of lime, of iron, and of magnesia. The great quantity of carbonic acid in the trap, he thinks, might have been the result of infiltrations of carbonate of lime, proceeding from the calcareous grit into which the trap was injected. This calcareous grit was, indeed, rather a sandy limestone than a grit, as M. Delesse observes ; for it contained 66°19 per cent. of carbonate of lime. He particularly points to the apparent presence of a mixture of zeolite in the grit when near to the trap ; and finishes his remarks on the metamorphism of the siliceous rocks, by calling attention to the fact of the frequent development of hydrated minerals, proving, as he believes, that in this metamorphism the “ premier rdle’”’ does not belong to igneous but to aqueous action. _,,His account of the action of the trap at Portrush in the North of Ireland, is given in the following abstract :— «« At Portrush, in the north-east of Ireland, we find a rock which at first sight appears to be trappean, and which nevertheless con- tains well-preserved fossils. “The partisans of Werner, Kirwan, Dr. Richardson, and Du- bourdieu liken this rock to a basalt ; they conclude, therefore, from the presence of fossils, that basalt has an aqueous origin, and was formed at the bottom of the sea. “The partisans of Hutton, Sir James Hall, Playfair, Dolomieu, contend, on the contrary, that the rock of Portrush was deposited in the bosom of the waters, and has since been modified by an igneous action. _ ‘Ata more recent epoch, the deposit of Portrush has been studied with much care by Messrs. Conybeare, Buckland, Bryce, Oldham, but above all by Mr. (now Sir Richard) Griffith and Colonel (now General) Portlock. 1 visited it myself in 1852; and I proceed to give a summary description of it, and will afterwards inquire what were the alterations undergone by the metamorphic rock of Portrush.” He then states that the base of the promontory is formed of a greenstone, which reappears in the Skerries, and that on this reposes a stratified rock which has been called ‘ chert, flint-slate, siliceous 64 Notices respecting New Books. basalt, pseudo-basalt, porcellanite, thermantide, lydianstone, horn- stone, petrosilex, and jasper.” He prefers to call it jasper. This jasper, he says, belongs to the Lias, as is proved by the many fossils it contains, and is covered conformably by the chalk. The thickness of the Lias here is only from 1 metre to 2°7 metres (say from 3 feet 4 inches to 8 feet), but it has under it a still more altered portion, which has been examined by Sir R. Kane, and found to contain augite and bronzite. It is traversed by veins, which become more numerous as we approach the greenstone, and are themselves filled either with green- stone or zeolites, while the stratification becomes more confused as we approach the greenstone, till the two rocks seem almost blended together. The greenstone is a dolerite very different in appearance from the basalt which covers the country around. It is formed of greenish Labradorite in macled crystals of several centimetres (1 centimetre= 0°39, or nearly ;4,ths of an inch), and of blackish-green augite in fine crystals. We can also distinguish protoxide of iron, and some- times bronzed mica in plates of 1 centimetre. It is traversed by many zeolites, such as chabasite, natrolite, mesotype, mesole, Harringtonite, Heulandite, stilbite, apophyllite, Laumonite, aluminite, Scoulerite (Thomsonite), &c. It has also veins of carbonate of lime, white, yellowish, and spathose,—of iron pyrites, of stellite, and even of felspar, as also of augite, in very large crystals. The specimen examined by M. Delesse was taken from the large quarry, and contained 4°22 of water, leaving in hydrochloric acid a residue of 75 per cent. It contained no carbonate, as most trap- rocks do. The normal lias near Portrush is blue, argillaceous, calcareous, and consists, according to an analysis by Dr. Apjohn, of— Argillaceous and siliceous residue .......... 56°90 Alumina 2;,2:chtt.t3 26) ccihidient . @ Geetha ese a Oxide: of ir6nist.a.:. eek Saleh en ek ees Water and loss) 02.5 > .onicteras olteh cee ee 10°95 Carbonateéiof diniesia a4 sist. ae ast ees 19-02 Carbonate of magnesia, .\. «4. 66st sem « 3°94 100-00 The lias metamorphosed into jasper splits into angular fragments, and contains veins of zeolite like those before mentioned in the dolerite. It may be divided into five varieties, varying in density from 2°836 to 2°610, and in quantity of water contained, from 1°33 to 3°88. It melts easily but unequally at a red heat. It leaves a residue of 76°75 in hydrochloric acid. A specimen of a blackish- grey variety gave the following analysis :— Notices respecting New Books. 65 SUL ra gage ge A tilleb aee Geeta reste eats a'e .. o7°45 SMUD «5 wats = 8 apm wen 3 Be erate eek t2. alpen fc)! Protoxide of iron ......2.%, Pate reaens: 8°55 GE ETC cine ciate caine pai nse 40 *,0 traces uh 1 separ ap eles 2 PCS Eg te a: I 2 Magnesia (diff.)..... RR RES wees ashe sem Od PSE co saaine dels 5 2 ace a RE eae Ae ee Wo: EE eee era hes ie Ap dae SM wee OES 3°69 Water and loss by ignition ............ ae p00 100:00 It contains no carbonates; so that they have been destroyed by the metamorphism—but slowly, since the calcareous body of a Belemnite had been changed into a paste of petrosilex which preserved the structure. The lime had not been entirely removed, a part at least remaining as a hydrosilicate. If Dr. Apjohn’s analysis be a good representation of the normal lias, we see, since it contains no alkalies, that the altered lias had gained 6 per cent. of them. The occurrence of potash is remarkable, and is probably connected with that of the apophyllite, which is a zeolite having the composition KO, 2Si0*+8 (CaO, SiO*) +16HO. The proportion of silica is small for its name of “ flint-slate,” but is greater than that possessed by basalt. It is but little for a jasper, but is more than that usual in clay. Lastly, M. Delesse, admitting that the presence of black volcanic augite indicates a great heat, maintains that the occurrence of zeolite in such large quantity demonstrates the presence of water or aqueous vapour, and proves that the metamorphism of the lias was due to an action at once igneous and aqueous. Our space will not permit us to mention more of the numerous examples of this part of the subject which the book contains. M. Delesse gives a number of details respecting the alteration of the intrusive rock ; but in looking over these we have been struck by the difficulties of the investigation. It must generally be con- ducted by examining one specimen from the heart of the intru- sive rock, and another from the margin where it is near the in- cluding rock, and comparing the difference of the two. But it must necessarily follow that near the junction of the two rocks each is more likely to be “ weathered” or acted upon by the infiltration of water, &c., than at a distance from that junction. ‘he very line of division between the two gives access to the atmospheric influences. It becomes, then, exceedingly difficult to distinguish between the alteration produced by mere ‘ weathering” or infiltration, and that received by the intrusive rock from the reaction of the adjacent rock at the period of intrusion. It is only where the whole mass of one part of an intrusive rock differs from the whole mass of another part, the two parts being surrounded by rocks of a different charac- ter, that we can be sure that the difference arises from that source. The observat.ons of Prof. Haughton on the granite of the Mourne Mountains and ‘the neighbourhood, form the best, if not the only good Phil. Mag. 8. 4, Vol. 18, No. 117. July 1859. F 66 Notices respecting New Books. examples of this kind of investigation that we are acquainted with, though we know many cases where a similar research would be equally well rewarded. : We add M. Delesse’s final theoretical conclusions. ** When we study the phenomena of metamorphism produced by the different eruptive rocks, we find that there exists a great analogy between them. «« Thus the metamorphism of limestone is nearly the same at its contact with lava, with trap, and with granite. “ We must nevertheless recognize the fact that lava alone bears, in itself and in its metamorphism, the stamp of a clearly evident igneous origin. *‘ Trap and the rocks which have a felspar of the sixth system for a base may present at the same time traces of an igneous and an aqueous action ; but, if we except basalt, the principal part is played generally by an aqueous action. In fact, these rocks have often produced no alteration on rocks with which they come in contact, and which are nevertheless very easily decomposed by heat; as, on the other hand, they have been very fluid, not only at great depths, but at the surface of the earth, on which they have been spread out in immense beds, we must admit that they could become entirely plastic without being actually reduced to a state of igneous fusion. I am induced to believe that they are susceptible of forming with water, aided by pressure and even by a moderate heat, a perfectly fluid muddy paste, which might be compared to a mortar; it is only in becoming crystalline and in losing a part of its water that this can assume its hardness and its great cohesion. “ On the other hand, we have seen that granite, when even it has been erupted in a fluid state, has not always caused an alteration in the rocks over which it has been poured out, nor in those which it traverses in the form of veins. The metamorphism at its contact is in every case very different from that of lavas. Consequently we must necessarily admit that granite can, like trap, become plas- tic without passing through igneous fusion such as we know occurs in lavas. ‘«* These theoretical conclusions are, it is true, far removed from the ideas which are generally adopted as to the origin of the erup- tive rocks; they appear to me, nevertheless, to be immediately de- ducible from the studies which we have now made on metamor- phism.” Fully agreeing with M. Delesse on the very remarkable fact of the slight metamorphic action sometimes exercised by even large masses of igneous rocks on such matters as limestone or coal with which they come in contact, and not denying the probability of the pre- sence of water or vapour in many if not in all cases of subterranean igneous action, we yet cannot let the above remarks pass without a word of caution. The continental geologists in general seem to neglect, to a dangerous extent, the important subject of denudation, by which so many once deeply-seated rocks have been brought to the surface. We hold it impossible for any one to show a case of Notices respecting New Books. 67 nite or any similar igneous rock having been erupted at the sur- face in the manner apparently taken for granted by M. Delesse, and that rocks so erupted are always lava (whether doleritic or trachytic) or basaltic rocks, such as those which he says have alone the marks of decided igneous action. We think it most likely, then, that the difference in the effects of the lavas and the granitic rocks is due, not to the former having been more purely igneous than the latter, but to the different conditions under which they have acted. Lessons Introductory to the Modern Higher Algebra. By the Rev. GrorcE Satmon, A.M., Fellow and Tutor, Trinity College, Dublin. Dublin: Hodges, Smith & Co., 1859. Within the last eighteen years the old and well-trodden field of Algebra has been invaded by a host of new and strange intruders, with the odd-sounding names of ‘ Determinants,’ ‘ Hyperdetermi- nants,’ ‘ Discriminants, ‘ Emanants,’ ‘ Invariants,’ ‘ Evectants,’ * Bezoutiants,’ ‘ Hessians’ (having no connexion, however, with either ‘ Boots’ or ‘Crucibles’), ‘Canonizants’ (of no religion), ‘ Dialytics,’ and ‘Quantics.’ Many a reader of the Cambridge Mathematical Journal, the Philosophical Magazine, Philosophical Transactions, &c., has wondered what it all meant—wondered sometimes, indeed, whether there was any meaning at all in these new expressions and their symbols. Very few even of the best mathematicians of the day have paid much attention to the subject as yet; but they are beginning to do so, finding that there is really something like a new branch growing out of their old tree—nay, more, that this young off-shoot is already bearing fruit. This ‘ Alge- bra of Linear Transformations’ ‘‘ may be said to date from a paper published by Prof. Boole in the Cambridge Mathematical Journal for Nov. 1841, which was mainly occupied with applications of the fol- lowing theorem :—Let an ordinary algebraic equation be made homo- geneous by writing 2: y for «; let these variables then be linearly transformed by writing \v+ py, 'v7+p'y for vw and y; and let V=0 be the condition that the transformed equation shall have equal roots ; then the function V will be equal to the similar function for the original equation multiplied by a function of A, , d’, pw’, and not involving the coefficients of the original equation. . i eee ated Mr. Boole having in the paper just cited made important use of the principle here enunciated, Mr. Cayley subsequently proposed to himself the problem to determine @ priori what functions of the coefficients of a given equation possess this property of invariance ; viz. that when the equation is linearly transformed, the same func- tion of the new coefficients shall be equal to the given function multiplied by a quantity independent of these coefficients. The result of Mr. Cayley’s investigations was to discover that the pro- perty of invariance was not peculiar to the functions which had been discussed by Mr. Boole, and to bring to light other important functions possessing the same property. Subsequently it was found that functions could be formed involving the variables as well as the coefficients, and possessing the same permanent relation to the 68 Royal Society :— original equation; that it was thus possible to form two functions connected by a certain relation between their coefficients, and such that, when both functions were linearly transformed, the same rela- tion should continue to exist between their coefficients. Functions so related have been called co-variants. The geometrical importance of this theory is now manifest. When we are given the equation of any curve or surface, the theory of linear transformations at once presents us with equations representing other curves and surfaces, and possessing permanent relations to the given one, which will be unaffected by any change of the axes of coordinates: and in like manner the same theory presents us with certain functions of the coefficients of the given equation, the vanishing of which must express.a property of the given curve or surface wholly independent of the choice of axes. Besides these geometrical applications, the theory has other important uses, which I shall not stop to enume- rate. That so valuable a theory is not yet as well known in this country as it deserves to be, must arise from the difficulty of becom- ing acquainted with it. I am sure that there are many mathema- ticians who find with regret that the more recent memoirs on this subject are unintelligible to them in consequence of their having overlooked the earlier memoirs, of the importance of which they were not aware at the time that they were published. And I feel that such persons will be ready to welcome an elementary guide to this branch of Algebra.” —Preface, p. vi—viii. From this book of Mr. Salmon, taken in conjunction with Mr. Spottiswoode’s on ‘ Determinants,’ and the work of Brioschi (trans- lated from the Italian into French by Combescure), any one may learn enough of the subject to qualify him for reading the original memoirs of Messrs. Cayley, Sylvester, &c. XIII. Proceedings of Learned Societies. ROYAL SOCIETY. [Continued from vol. xvii. p. 442.] Jan. 27, 1859,—Sir Benjamin C. Brodie, Bart., Pres., in the Chair. TLE following communications were read :— “Researches on a New Class of Organic Bases, conducted by Charles 8. Wood, Esq.” By A. W. Hofmann, LL.D., F.R.S. In his remarkable memoir* on the action of reducing agents on nitro-compounds, in which Zinin first pointed out the formation of organic bases by the substitution of hydrogen for oxygen, some expe- riments are recorded on the deportment of dinitronaphtaline (nitro- naphtalese) with sulphuretted hydrogen. Zinin states that this pro- cess gives rise to the formation of a basic compound crystallizing in delicate copper-red needles, and yielding with acids white scaly salts. In a subsequent paper+ Zinin returns to the action of sulphuretted * Bulletin Scientifique de St. Pétersburg, x. 18. fT Journ. fiir Prakt. Chem. Bd, xxxiii. 29, Dr. Hofmann on a New Class of Organic Bases. 69 hydrogen on dinitronaphtaline, and gives a fuller account of the pro- ducts obtained in this process, The basic substance arising from dinitronaphtaline crystallizes in colourless needles of great brilliancy, which contain C,, H,N, or C,, H,, N,. It is a well-defined basic body, which Zinin describes under the name of seminaphlalidam. From this later communication it would appear that the copper-red coloration originally observed was due to the presence of a foreign colouring matter, which can be separated by crystallizing the base alternately from alcohol and water. Subsequently the copper-red body appears to have been observed by Laurent*, who states that the action of sulphuretted hydrogen upon dinitronaphtaline gives rise to the formation of a carmine-red alkali. He did not, however, analyse this substance, and the dis- covery of nitranilinet having established the existence of basic nitro- substitutes, the compound in question was hitherto believed to be nitro-naphtylamine. The red crystals have of late been minntely investigated in my laboratory by Mr. Charles Wood, whose experiments have led to an unexpected result, which I beg to lay before the Society. A current of sulphuretted hydrogen transmitted through a boiling solution of dinitronaphtaline in weak alcoholic ammonia slowly reduces the nitro-compound. The process is continued for two or three hours, during which time the greater part of the spirit distils off ; the residue is acidified with dilute sulphuric acid, and the liquid heated to ebul- lition. The filtered liquid deposits on cooling a yellowish brown sulphate, which may be purified by several crystallizations from boiling water. The addition of ammonia to the solid sulphate immediately changes the colour to a fine dark carmine-red ; the base thus libe- rated is washed with cold water, and finally purified by crystallization from water or very dilute alcohol. Thus prepared, the substance, for which Mr. Wood proposes the name ninaphtylamine, is a light flocculent mass, composed of little acicular crystals, which are partially decomposed by exposure to a temperature of 100°C. — It is difficultly soluble in boiling water, but extremely soluble in alcohol and ether. In the analysis of the base dried iz vacuo over sulphuric acid, Mr. Wood has obtained results which lead to the formula C,, H, N; O,. This expression was confirmed by the examination of several of the salts of the new base. Sulphate of ninaphtylamine is obtained either by recrystallizing the crude salt formed in the preparation of the body, or by dis- solving the pure base in dilute sulphuric acid. It forms white scales, which are apt to be decomposed by recrystallization from pure water. The salt dried in vacuo over sulphuric acid contains 2(C,, Hi, N, 0.), i, 8, O,. * Compt. Rend. xxxi. 538. + Muspratt and Hofmann, Memoirs of the Chemical Society, vol. iii. 111. 70 Royal Society :— Hydrochlorate of ninaphtylamine forms acicular crystals; they are obtained like the sulphate, which they resemble in their general deportment. Composition : C., H, N, O,, H Cl. The platinum-salt of ninaphtylamine forms rather soluble yel- lowish-brown crystals, which are obtained by adding a concentrated solution of dichloride of platinum to an alcoholic or ethereal solution of the base. It has the usual constitution, containing C,, H, N, O,, HCl, Pt Cl,. If it be permitted, in the absence of further experimental evidence, to speculate upon the molecular constitution of the body which forms the subject of this note, the simplest interpretation of its composition and formation would be to view it as a substitution-product of naph- tylamine, but differing from the ordinary nitro-substitutes, by con- taining the elements of binoxide, instead of tetroxide of nitrogen. C., H, Naphthylamine ..C,,H,N = H iN, H : C,, (H, NO.) Ninaphthylamine. . C,, H, N,O,= H ;N ; H Its formation would then be represented by the equation C,, [H, (NO,).]+4 H,8,=3 H,0,+88+C,,[H, NO,] N SSS ee ee Dinitronaphtaline. Ninaphthylamine. Bodies in which binoxide of nitrogen figures as a material of sub- stitution are as yet extremely rare, whilst nitro-substitutes containing the elements of hyponitric acid are of the most general occurrence. Some chemists have considered nitrous ether as a binoxide of nitrogen derivative of alcohol. Aleehol 72 See Se CFO: Nitrous ether ..s6500¥5 0s C, (xo )o.- The most interesting illustrations of this kind of substitution, how- ever, have been furnished by Messrs. Church and Perkin* in the colouring matters produced by the action of nascent hydrogen on dinitro-substitutes, or of nitrous acid upon certain monamines. Phenylamine ............ C,, H,N. Nitrosophenyline ........ C,, (wo): Naphthylamine.......... C,,H,N, Nitrosonaphtyline........ Cx No.) Expressed by these formulz, the substances in question appear to be closely allied to Mr. Wood’s base ; in fact, nitrosonaphtyline has * Journal of Chemica! Society, vol. ix. 1. Rankine on the Thermodynamic Theory of the Steam-engine. 71 the same composition as ninaphthylamine. But a superficial com- parison of the properties of the two bodies excludes any idea of their being identical. The formule of nitrosophenyline and nitrosonaph- tyline have not as yet been finally established by the analysis of their compounds, these substances, like colouring matters in general, being of an indifferent character. It is probable that they are formed by the association of several molecules, a supposition which receives considerable support from the discovery of ninaphthylamine. The formation of ninaphthylamine promises to add considerably to the number of nitro-derivatives of the aromatic monamines. To each of these substances probably corresponds a nitrous and a nitric substitution-base, but as yet we are unacquainted with a single one in which both derivatives are known, as shown by a glance at the groups best examined. Phenyle Group. Naphtyle Group. CO, of Phenylamine. . .. “ik SN, Naphthylamine ie H H C,, (H, NO,) C,, (H, NO,) Unknown .. pan N, elt pe | N H eoeee sei Nitrophenyl-" a i N, Unknown ie ee: N amine. . . - H “ tr “Qn the Thermodynamic Theory of Steam-engines with dry saturated Steam, and its application to practice.” By W. J. Mac- quorn Rankine, C.E., LL.D., F.R.S.S.L. & E. In 1849 it wasdemonstrated, contemporancously and independ- ently, by Professor Clausius and the author of this paper, from the laws of thermodynamics, that when steam or other saturated vapour in expanding performs work, and receives no heat from without, a ortion of it must be liquefied. That theoretical conclusion has since been confirmed by practical experience. The principal effect of the “ steam-jacket”’ invented by Watt is to prevent that liquefaction. The presence of liquid water in any considerable quantity in the cylinder of a steam-engine acts injuriously, by taking heat from the steam while it is being admitted, and giving out that heat to the steam which is about to be discharged. Most of the heat so trans- ferred is wasted. The only exact thermodynamic formule for the work of steam hitherto published (by the author in the Phil. Trans. 1854, and by Professor Clausius in the Philosophical Magazine for 1856), are adapted to steam which receives no heat in expanding. The present paper, after recapitulating the general equation of thermodynamics, and the special formule for the pressure, volume, and latent heat of steam, proceeds to the investigation of the exact 72 Royal Society :— formule for the work of steam which is supplied during its expan- sion with just enough of heat to prevent any appreciable portion of it from condensing, for the expenditure of heat in producing and using that steam, and for its efficiency in producing motive power. There is explained a convenient approximation to the exact for- mul, founded on the facts, that for initial pressures of steam of from 30 to 120lbs. on the square inch (including atmospheric pressure), and for ratios of expansion up to sixteen, the pressure of saturated steam varies nearly as the seventeenth power of the six- teenth root of its density, and that the expenditure of heat in an engine in which dry saturated steam is used, expressed in units of energy, is nearly equal to fifteen-and-a-half times the product of the initial pressure and volume of the steam expended. Lastly, there are given examples of the application of the formule to the engines of three steam-vessels lately experimented on by the author. The displacements of those ships are from 700 to 1100 tons; the indicated horse-power of their engines from 226 to 1180; the initial absolute pressures of steam in their cylinders range from 32 to 1084 1b. on the square inch, and the ratios of expansion from 4 to 16. In each case the difference between the results of calcula- tion and experiment is within the limits of error of observation, and ranges from =), to +4, of the actual work of the steam. The author has computed Tables of the results of the formule, exact and approximate, which are now in the course of being printed. SumMARY oF ForMuLz.—WNotation and Constants. t, absolute temperature in degrees of Fahrenheit, = temperature measured from the ordinary zero + 4612. Pp; pressure in pounds on the square foot. v, volume of one pound of steam in cubic feet. t,, Py V,, refer to the admission of steam into the cylinder. t., PD. V., to the end of the expansion. 7=V,~+0,, ratio of expansion. ps,= pressure of exhaustion. t,, absolute temperature of feed-water. J, ‘‘Joule’s equivalent,” or specific heat of one pound of liquid water, =772 foot-pounds per degree of Fahrenheit. W, work of one pound of steam. %, expenditure of heat per pound of steam in foot- pounds. a=1109550 foot-pounds. 6=540'4 foot-pounds per degree Fahrenheit. Efficiency of steam, W +2. Exact Formule. t W=a hyp. log re — bE, —t,) +v,(p,—Pps)- t 2 =a(1 +hyp. log a) —bt,+ J(é,—t,). Mr. C. V. Walker on Platinized Graphite Batteries. 78 Approximate Formule. W +2,=p,(1 ae 1617 i6) —Pp,- 1 ®H +v,= = In applying the exact formule, the relations between p, v, and ¢ may be found by means of known formule or Tables. February 3.—Sir Benjamin C. Brodie, Bart., President, in the Chair. The following communication was read :— “On Platinized Graphite Batteries.’ By C. V. Walker, Esq., F.RB.S., F.R.A.S., &e. In a short note communicated to the Royal Society on March 9th, 1857, and which was read on March 19th, reference was made to the voltaic combination that I had adopted for certain telegraphic purposes ; namely, zinc-graphite. Graphite in its crude state had for some years been of great service to me, especially for batteries whose resting time is great in proportion to their working time. Since the date of that notice, I have considerably increased the value of graphite for electrical purposes by platinizing it according to the process first described by Mr. Smee, whose platinized silver battery has been long known and much used. The material to which I refer by the term “ Graphite,”’ is the crust or corrosion that is col- lected from the interior of iron gas retorts that have been long in use. My first crude graphite battery of twelve pairs of plates was set up on April 5th, 1849, for working the telegraph from my residence at Tonbridge to the Telegraph Office about a mile distant. It was charged with sand saturated with diluted acid; and had not been dis- mounted in March 1851, when I changed my abode. During the interval, the sand was from time to time moistened with acid water or water only. The plates in this case had been roughly chipped out and rubbed on stone into something like shape. In the mean time I had some sets of plates cut at the Locomotive Works, Ashford, and was thus enabled to obtain further results. I forwarded a graphite battery to the Great Exhibition in 1851, for which a prize medal was awarded, The introduction of graphite into anything like general use was for a long period no easy matter, on account of the difficulty of finding any one who would undertake to cut it into plates, its hardness destroying the tools; and the then limited de- mand did not encourage any one to construct special machinery for the purpose. My wants at length reached the ear of Mr. J. Robin- son of Everton, Liverpool, who took the matter thoroughly in hand, and has succeeded perfectly in cutting plates into any form and to comparatively any size, at a very moderate cost, for which I am much indebted to him. I have before me plates 12 inches X 10 inches, of smooth texture and uniform thickness, and have seen some of double that size. The plates in common use for bell signals are 73 inches x 3 inches 74 Royal Society :— and 2 inch thick, of which about 2000 are in daily use on the South Eastern Railway, and the greater portion of these are now platinized. The plates are delivered to me in their crude state, that is to say, they are merely cut into form. Immediately on arrival they are placed in a stone pan, and covered with a mixture of 1 sulphuric acid + 4 water, in which they are allowed to remain for three or four days or more. They are taken out as required, and are washed under a tap of running water ; this operation dissolves out any foreign matter that might be pernicious in a voltaic combination wherein sulphuric acid was employed ; they are then partially dried. A hole for a rivet is next drilled in the middle, near the top of each plate— a belt of varnish one inch wide is applied to the top on both sides of each plate—a blank one inch square, having the rivet hole for its centre, being left unvarnished on each side—electrotype copper is then deposited on the blank square in the usual way. The deposited metal is then tinned, no part of the copper being left bare; a con- necting slip of copper, 6 inches x 1 inch is prepared and also entirely tinned ; this is riveted to the graphite plate with a copper rivet, also tinned. The soldering iron is now applied, and a little solder run in between the two surfaces. By thus protecting all the exposed copper with tin, the formation of sulphate of copper and its attendant inconveniencies are prevented. The plate is now platinized. A mixture of 1 sulphuric acid + 10 water is placed in a vertical glass cell, to this are added a few crystals of chloride of platinum till the solution presents a faint straw colour. The battery power em- ployed for platinizing is three cells of platinized. graphite and zine. The positive electrode is platinum or graphite itself, and is presented to both sides of the plate that is to be platinized. The action is allowed to go on for about twenty minutes. ach finished plate is tested as to its power of liberating the hydrogen of electrolysis, by placing it in acid water in contact with an amalgamated zine plate. I have drawn out the above description in the presence of our assistant, who attends to this department of the telegraph establish- ment, in order to be correct in the small details. The battery-cells for the plates above described are quart jars of stone-ware that resists acid. The exciting solution is 1 sulphuric acid + 8 to 12 water. Zinc plates are riveted to the other end of the copper connecting slip, also with tin rivets. The zinc is strongly amalgamated. It is dipped in a vessel containing 1 sulphuric acid + 4 water, and after a few seconds, more or less, is withdrawn and thrust in its then condition into a trough of mercury, and set aside to drain. On the following day it is treated in a similar manner. When the batteries are being put together, and before the zincs are placed in the jars, the foot of each is placed in a trough or slipper of gutta percha, 3 inches by } inch, containing about a couple of ounces of mercury. A battery thus carefully prepared will stand for an indefinitely long period with little perceptible waste, and be ready for use at all times. Under ordinary circumstances it is not neces- sary to dismount the batteries employed for telegraph ‘signaling more than once a year. Mercury is added during the interval, and Mr. C. V. Walker on Platinized Graphite Batteries. 75 the jars are filled up as occasion requires. The greater portion of the mercury is recovered: when old plates come home, a considerable quantity of rich amalgam is scraped from the plates; this is placed in jars of acid water, and a few pieces of graphite are thrown in; the electro-chemical action makes the amalgam poorer of zine, and mer- cury is easily expressed. By continuing the operation, more mer- cury, to the amount in all of nearly three-fourths, is recovered. As an illustration of the economic importance of this material in applied science, I am informed that the silver plates of the batteries constructed for the Atlantic Telegraph cost £2520 or more. On my having directed the attention of the Company to graphite as a sub- stitute for silver, a set of plates were ordered, equal in number and size, which were supplied (furnished with electrotype copper and connecting wires) for £216. The following Table illustrates the effective working powers of platinized graphite, as compared, under like circumstances, with pla- tinized silver, given in lifting powers in pounds. A third column is added, giving the results when table salt is dissolved in the water employed with the graphites. Table I. Electro-magnet; 10 yards No. 16 wire. 12 cells in series. 12 cells in double series of 2 sixes. 5 o 2 Bibho seks 2 g | st8 = 2 aq a 3 = we ‘gd — i=") [=a] 4 i") i] D ted F] 3 2 TA 3 SI Bal 7 So) 6 |e lee? cl eae pa | oS yds. || lbs. | lbs. | Ibs. || yds. Ibs. | lbs. | Ibs. 10 co) Y 14'75| 14 15 I 22°5 | 20°§ | 20 184 | 10 12°5| 9 147 14 10 9 247 || 7 9 | 8 284 825] 7 7 421 6 7 |-6 421 5 5 4 558 || 5 5 | 4 558 3°25| 3 2°5 695 || 4°5 ad Re 695 2 2°25) 1°5 832 || 3 2°5| 2°5 || 832 2 I's 1'25 6 cells in double series of 2 threes. 695 I I fe) 12'25| 10 10 14 14 14 147 9 625) 7 147 4 4 5 284. 5 4 4 284. 2°5 2°25) 2°5 421 3°5 4 25 || 421 2 75 2 558 2°25 2 558 1'5 Ak x 2 = I I I 76 Royal Society. Table II. Electro-magnet ; 274 yards No. 16 wire. 12 cells in series. Resistance. || Silver, Graphite. Graphite. yds, lbs. lbs. Ibs. 137 X2 14 18 22°5 137 X3 12°75 15°75 14 137 X4 10 13 II 137X5 9 12°5 II 137 X6 9 10°75 II 137X7 | eS) 955 137X8 | 8°75 95 8°75 6 cells in series. 137 X2 | 9°75 12°75 11 137X3 8 10°75 10 137X4 || 7°25 10 9°5 1375 | 7°75 9 9 137 X6 7 8 9 137X7 6°75 9 3°75 137 X8 7 8°75 8 6 cells in double series of 2 threes. 137X2 | 8°75 10 II 137 X3 7°25 9 9 137 XA 6 9 9 137X5 picks) 8 th 137 X6 | 4°25 6 5 137X7 . | 4 1.6 4°75 137X8 || 4°25 5 6 In all the above experiments the cells were charged with 1 sul- phuric acid + 13 water (salt water in the third column) ; and 13:5 square inches of surface were immersed. The silver-zine pairs were 1 inch apart, the graphite-zinc, 2 inches. The lifting powers were not read off more closely than to quarter-pounds. The electro-mag- net used in Table I. was a small horse-shoe containing about 10 yards of No. 16 wire; that used in Table II. was one of the electro- magnets used in the construction of the signal bells before described (vide Proc. Roy. Soe., vol. viii. p. 419), and containing 274 yards of No. 16 copper wire. The resistance added in each successive experiment was one bobbin of a similar electro-magnet or 137 yards of wire. ‘The resistances in the Table include the resistance of the electro-magnet. The total resistances in Table II. are all multiples of the contents of a single bobbin or 137 yards. A glance from left to right on the same horizontal line shows the comparative value of each combination in the several experiments. One or two small irregularities in Table II. in the six-cell results, are doubtless due to the poles of the magnet not having been ground true. With respect to durability, the graphite plates in use since 1850 are in as good condition as the new ones now in course of manu- Geological Society. 77 facture. Silver plates employed by us under like circumstances, commenced perishing after twelve months or more of use; they crumble away in great measure, they cut apart at the surface level, and they get eaten into holes throughout. GEOLOGICAL SOCIETY. [Continued from vol. xvii. p. 447.] June 1, 1859.—Major-Gen. Portlock, Vice-President, in the Chair. The following communications were read :— 1. “On the Sinking for Coal at the Shireoaks Colliery near Worksop, Notts.” By J. Lancaster, Esq., and C. C. Wright, Esq., F.G.S. In two shafts sunk for the Duke of Newcastle on the north-west side of his estate of Worksop Manor, it was found that the New Red Sandstone and marl have a thickness of 54 ft., and the Permian beds 112 ft. ; the latter consisting of hard yellow limestone (54 ft.), blue limestone and shale (20 ft.), blue shale (33 ft.), and soft gritstone, probably equivalent to the “Quicksand” of the north (5 ft.). Below the gritstone the coal-measures commence with 5 feet of blue shale, in which there are four bands of ironstone; another band 15 inches thick, lies immediately below. This iron-ore is chiefly in the state of peroxide, gives an average of 42 per cent. of metallic iron, and promises to be of great economical value. ‘The first seam of coal (2 feet thick and of inferior quality) was cut at a depth of 88 yards. Four yards below this is a compact sandstone 66 feet thick. ‘The sinking through this rock occupied 20 months; each pit made 500 gallons of water a minute, which was stopped in detail by cast-iron tubing. The pressure from the gas at the bottom of this thick rock was at times as high as 210 lbs. per square inch, but is now about 196 lbs. per square inch. Shales, with coal-seams and bands of ironstone, all thin or of inferior quality, were met with in the next 170 yards. At 346 yards the first thick coal was cut, and found to be 4 ft. 6 in. thick, and of good quality. This is con- sidered to be the ‘“‘ Wathwood Coal.” The ‘ Top Hard Coal” was cut at a depth of 510 yards, and found to be 3 ft. 10 in. thick: the strata intervening between this and the ‘‘ Wathwood Coal” were found to have much the same characters and thickness as they are known to have elsewhere. The sinkings were commenced in March 1854, and perseveringly continued until their completion on February Ist, 1859. Altogether 37 feet of coal were passed through; but only four seams are of workable thickness. ‘The authors of this communication remark that the district appears to be remarkably free from faults, that the dip decreases considerably towards the east, and that the “‘ Top Hard Coal” appears to thin out eastwardly. 2. ‘Notes on the Geology of Southern Australia.” By A. R.C. Selwyn, Esq., Director of the Geological Survey of Victoria. Ina Letter to Sir R. I. Murchison, F:G.S. Mr. Selwyn remarked that, as to the impoverishment of auriferous veins in depth, the only evidence of such being the case in Victoria is the great richness of the older drifts; for, judging from the large 78 Intelligence and Miscellaneous Articles. size of the nuggets sometimes found in the gravels, compared with that of the nuggets met with in the gold-bearing quartz-veins (usually from about 3 dwt. to }0z., though occasionally as much as 12 ozs. or even 13 |bs.), the upper portions of the veins, now ground down into gravel, were probably richer in gold (us formerly sug- gested) than the lower parts, now remaining. As far as actual mining experience shows, some of the ‘ quartz-reefs” in Victoria prove as rich in gold at a depth of 200, 230, and 400 feet as at the surface ; the yield, however, fluctuates at any depth yet reached. According to the author’s latest observations, the gold-drifts, and their accompanying basaltic lavas, are of Pliocene and Post-pliocene age. Miocene beds occur at Corio Bay, Cape Otway coast, Murray basin, and Brighton; and Eocene beds on the east shore of Port Phillip, Muddy Creek, and Hamilton. Two silicified fossils (Echi- noderm and Coral), thought by Prof. M‘Coy to be of Cretaceous origin, have been found in the gravel near Melbourne. This letter also contains some remarks on the probability of some of the coal of Eastern Victoria being of ‘‘ Carboniferous”’ age,—on the occurrence of Silurian fossils in the rocks of all the gold-districts, —on the newly-discovered bone-cave at Gisborne, about twenty-five miles north of Melbourne,—and on the progress of the Geological Survey of the Colony. XIV. Intelligence and Miscellaneous Articles. ON THERMOGRAPHY, OR THE ACTION OF HEAT CONSIDERED AS A MEANS OF PRODUCING IMAGES ON SENSITIVE PAPER. BY M. NIEPCE DE SAINT-VICTOR. os experiments I am about to describe are an extension of those of Messrs. Moser, Knorr, and Draper. I believe I have succeeded in adding to the facts already established a considerable number of new and interesting observations, of a kind calculated to throw some light on this class of phenomena. If, upon a metallic plate, heated by contact with boiling water, you place an engraving, or page of writing printed in unctuous ink, and lay upon that a sheet of paper rendered sensitive, first with nitrate of silver, and then with chloride of gold, you will obtain a violet-blue image of the dark parts of the engraving or letters. If, however, the paper be prepared with nitrate of silver only, the lights of the engraving are reproduced of a dark (distre) colour. With paper prepared with the salts both of gold and silver, large printed letters will produce an image even at a distance of several millimetres; but if a continuous, though thin, plate of mica, or metal, or even a sheet of vegetable paper be interposed, no image will be produced. Drawings in aqueous ink, in black-lead, or in charcoal, produce no image when on ordinary paper ; but they do when on vegetable paper. Plates and flat surfaces of varnished porcelain, with black letters or coloured drawings, which have been subjected to the action of fire, but have not been enamelled, have afforded me impressions ; but letters or drawings on enamelled porcelain produce no image. Intelligence and Miscellaneous Articles. 79 Coins and cameos are reproduced very distinctly, even at the di- stance of a millimetre, and notwithstanding the interposition of a thin continuous sheet of mica, silver, or copper, provided only the relief be strong and the temperature sufficiently elevated. If a paper on which a drawing had been traced in lamp-black, or even wood-charcoal, be raised to a temperature sufficient to scorch the paper, the portions of the reverse corresponding to the lines of the drawing will be observed to have become more highly carbonized than the rest. A similar effect may be observed with respect to the lights and shades of variegated feathers or coloured woollen fabrics ; that is to say, the action of the heat is greater on the shades than on the lights. If, while a coloured fabric is being heated, it be kept in contact with paper impregnated with cyanide of potassium, the shades produce a stronger impression than the lights. Tissues of different materials, shaded with black and white, or with colours of various kinds, produce impressions on paper rendered sensitive with the salts of gold and silver; but the image is very uncertain: in general the dark tints are most decidedly marked; but in certain cases the light tints produce the strongest impres- sions,—these differences depending, no doubt, on the nature of the colours used and of the mordants employed to fix them. Indeed, colours produced by the same substance (as madder, for instance), but fixed with different mordants, produce very unequal and very various impressions. When cotton cloth is dyed with indigo, the pattern being left in white, the blue background alone produced an impression ; whereas, if the cotton be similarly dyed with prussian blue, it is the white pattern which is reproduced. If either cotton cloth or porcelain be covered with alternate stripes of indigo and prussian blue, the indigo stripes produce an image, the prussian blue do not. I have endeavoured to obtain images in the focus of a lens, which, of course, ought to give a representation of the heated body, but hitherto in vain. I do not know whether the images in the focus of a concave mirror would prove more effective. The action which gives rise to the thermographic image is, without doubt, very complex. The calorific radiation probably plays a con- siderable part in producing the result; but the material vapours emanating from the heated body may also have some effect. In the case of metallic bodies and dry wood, the action of the heat is cer- tainly prepcnderant; and it seems to me to be clearly demonstrated that, under certain circumstances, a sufficiently high temperature produces effects analogous to those which we see every day resulting fromthe action of light—the reduction, namely, of the salts of gold and silver, the alteration of tissues, &c. In conclusion, I may be permitted to state that the experiments described in this notice date from the month of J anuary last, since which time I have occasionally shown thermograph pictures to several members of the Academy; and on the 29th of January I performed, in the presence of Mr. Wheatstone, those experiments of which the ‘Cosmos’ makes mention in its number for February the 1lth,—Comptes Rendus, May 28, 1859. 80 Intelligence and Miscellaneous Articles. NOTICE OF TRACES OF ERUPTIVE ACTION IN THE MOON, BY THE REV. T. W. WEBB. } The inquiry as to the continuance of volcanic or explosive action on the surface of the moon must be admitted to be a very interesting one. Astronomers are generally agreed as to its entire cessation on any conspicuous scale; but this would not necessarily infer the im- possibility, or even improbability, of minor eruptions, which might still continue to result from a diminished but not wholly extinguished force. ‘Till the publication of the labours of Beer and Midler, the necessary data for the determination of the question were very im- perfect ; and since that time the general impression would seem to be adverse to the idea of any physical change. Before, however, it is entirely acquiesced in, it may be well to see whether any evidence of an opposite nature exists. Want of leisure has hitherto prevented me from entering upon the subject in any other than the most inci- dental manner; but I would request permission to direct attention to one or two regions where an accurate investigation might be desirable. One of these is the spot named Cichus, near the south extremity of the Mare Nubium. Here, many years ago, in comparing Schroter’s drawings with the moon, I was struck with the apparent enlargement of the small crater which has defaced one side of the ring. On pro- curing the map of Beer and Midler, I found that they had also seen it enlarged. Could we in this instance depend upon the older draw- ings, we might reasonably infer the probability of a change since the year 1792. Schréter was, undoubtedly, a coarse draftsman ; but still he was faithful and careful, nor does there seem any appearance, but the reverse, that his designs were copied from one another to save trouble; if not, the agreement of three separate figures seems fair evidence that this little crater was not then of its present magnitude. The second case seems more satisfactory. It is that of the spot Messier, in the Mare Foecunditatis, where two small craters lie side by side at the end of two parallel white streaks, resembling the di- vided tail of acomet. In consequence of an observation of Schroter, Beer and Miidler directed their attention especially to this region, and examined it more than 300 times between the years 1829 and 1837, with the result that the two craters were perfectly and sin- gularly alike in size, shape, height of ring, depth of cavity, and even the position of some peaks upon the rings. I cannot say that I have ever been able to obtain a perfectly distinct view of this spot, from atmospheric causes; but every sight i have had of it has strength- ened my impression that this remarkable similarity no longer exists. I first noticed a difference in the aspect of the two craters in 1855, Noy. 14. Since that time, in the occasional use of four instruments of very different size and power (one an object-glass of 53 inches by Alvan Clark, now in my possession), I have invariably felt con- vinced that neither in size, form, nor depth are those two craters any longer precisely similar, but that, on the contrary, under suitable angles of illumination, such as must have repeatedly occurred during the 300 examinations by Beer and Miidler, the difference between them is obviously so great as to indicate some permanent alteration in the surface during the space of twenty years.—Proceedings of the Royal Astronomical Society, vol. xix. p. 284. THE LONDON, EDINBURGH anv DUBLIN PHILOSOPHICAL MAGAZINE AND JOURNAL OF SCIENCK. [FOURTH SERIES.} AUGUST 1859. XV. On the Expansion of Water and Saline Solutions at High Temperatures. By 1. C. Sorsy, F.R.S. &c.* i studying the fluid-cavities in various mimerals, I found it requisite to ascertain the relation between the temperature and the volume of water and of saline solutions, up to as high a temperature as could be employed with advantage. My chief object was to make out whether there is any such simple rela- tion between the volume and the temperature, that the tem- perature could be readily caleulated from the observed volume ; which is a most important point in the study of the fluid-cavities in many minerals. In his memoir on the dilatation of liquids+, M. Isidore Pierre showed that the expansion of many may be represented very accurately by expressions of the form V=1+At+B+C8#, where V is the volume, ¢ the temperature in degrees Centigrade, and A, B, and C are constants ; the volume at 0° C. being taken for unity. He, however, says that the expansion of water cannot be represented by such a formula; in which remark I think he must especially refer to the expansion below 25° C., for, as I shall endeavour to show, if we only take into consideration tempera- tures above that, the expansion may be represented with consider- able accuracy by a very simple expression. Similar formule are made use of by Kopp in his investigations on the expansion of some liquidst ; but in discussing the expansion of water, he em- ploys four different formule to enable him to ascertain the volume at any given temperature differing from those actually * Communicated by the Author. + Annales de Chimie et de Physique, S. 3. vol. xv. p. 325. t aes ’s Annalen der Physik und Chemie, vol. 1xxii. 1847, pp. | an . Phil. Mag. 8. 4. Vol. 18. No, 118, Aug. 1859. G 82 Mr. H. C. Sorby on the Expansion of Water and observed. In the same volume of the work just cited, Franken- heim shows that the expansion of many liquids may be expressed with sufficient accuracy by means of equations of the form V=A+Bt+C#, but says that here and there the regular progress of the differ- ences between the results calculated from the formule and the observations shows that another term, involving @, might be employed with advantage. My own experiments lead me to agree to a great extent with this last remark. They show that probably the expansion really follows a law expressed by a series involving ascending powers of ¢, but the coefficients of higher powers than the second have such small values, that, for a very considerable range of temperature, they have scarcely any more influence than the unavoidable errors of observation. In discussing the relative volumes at various temperatures, the method of successive differences can be made use of with very great advantage, if the volume be known at equal intervals of temperature. So far, however, as I have been able to learn, previous observers have not employed it, either from not having thought of it, or from having considered it preferable to ascer- tain the volume of the liquid at various accidental temperatures, without endeavouring to raise the heat to particular given. tem- peratures. If the law of the expansion of a hquid be really of the form V=A+Bt+C+ D864 &e., and if the volume at a number of equidistant temperatures be known, it is easy to see what terms of the series should be taken into consideration, by determining the successive differences of the volumes. From the well-known properties of such a series, if each volume subtracted from that next above it give these first differences of the same value throughout, there can be no term involving a higher power of ¢ than the first. If, however, these first differences increase in magnitude from a low to a higher temperature, but, when we subtract each of them from that next above it, if we find that these second differences are of a constant value, we may be equally sure that there is a term involving ¢?, but no higher powers. The same law holds good for @, #4, &c.; and therefore, as will be seen, this method is so extremely suitable for the inquiry now before us, that in my ex- periments I ascertained the volume of the liquids at given equi- distant temperatures, in order to be able to make use of it. Before commencing my own experiments, I discussed by this method of successive differences the relative volumes of water at various equidistant temperatures, deduced by Kopp from the Saline Solutions at High Temperatures. 83 four formule which he considered requisite, and obtained the following results :— | Volume accord- | First Second Third rature. | ing to Kopp. | difference. | difference. difference. 100 1042986 Es 007589» |} .¢ggesae | | 30. | Logeesy | 096816 | “oooaga | -st:000292 | ff aescive 006335 = ae 60 | 1-016599 | ‘005656 00832 | 008153 50 1011766 | ‘004824 000589 | +7000248 40 1-007531 004235 00768 | — 200179 30 1-004064 Spaniel 000970 | ~~ 000202 30 | 1001567 | “O)2a! 001054 | — 000086 10 1-000124 000124 001319 0 1-000000 2 It will thus be seen that between the limits of 30° and 100° the third difference is sometimes positive and sometimes nega- tive, having a mean value of only ‘000001, as if the varying third difference were almost or altogether due to errors of obser- vation; and therefore apparently for temperatures higher than 30° the empirical formula should not involve any terms having higher powers of ¢ than the second. It is evident that for tempera- tures below 30° an entirely different formula would be requisite; but since this paper has special reference to high temperatures, I need not further dwell on those when the same cause which gives rise to the expansion of water somewhat above the freezing- point, has evidently begun to make itself apparent. Calculating from the above data, I deduce the following general formula, giving the volume at ¢° C. :— V='997696 + :0001101¢ + :000003432?. The volumes at various temperatures, calculated by means of this formula, are compared with those given by Kopp in the following Table :— | f , Tempe- | Theory. Eopp's Difference. | 100 | 1043006 | 1042986 = -000020 | 90 | 1:035388 1035397 — 000009 80 1:028456 1028581 — 000125 70 1:022210 1022246 — 0000386 60 1-016650 1016590 +-000060 | 50 1:011776 1011766 | +-000010 | 40 1007588 1007531 = 4+-000057 | 30 1004986 | 1:004064 | +-000022 20 1001270 1-001567 — 000297 10 “999140 1-000124 — "000984 0 997696 1:000000 — 002304 | re ASS) jor 84. Mr. H. C. Sorby on the Expansion of Water and It will thus be perceived that from 30° to 100° the agreement is on the whole sufficiently close ; for the differences obey no de- finite law, as if due to errors of observation. Below 30°, how- ever, there is a most decided gradual increase in the difference, evidently owing to a relative expansion taking place as the tem- perature decreases. Since, then, for temperatures between 30° and 100° the volume can be expressed with very considerable accuracy by means of one simple formula, I was very anxious to ascertain whether the law would hold good up to a much higher temperature; for, in that case, it would not only be much more simple than any formula involving higher powers of ¢, but could be applied to the object I had especially in view, since it would enable us to deduce the temperature from the observed volume by solving the formula as a quadratic equation, which of course could not be done if it were essentially requisite to take higher powers into con- sideration. I was not able to carry on the experiments at a higher temperature than 200° C., because the water then begins to act very powerfully on the glass tubes, and entirely decomposes them in the course of time. At that heat the elastic force of the vapour of water is very considerable, according to the experi- ments of Dulong and Arago* being equal to 16 or 17 atmo- spheres, or to about 240 lbs. to the square inch. It was there- fore necessary to make use of glass tubes strong enough to remove all fear of fracture and explosion; and since it was also far more desirable to determine the volume with moderate accu- racy up to a very high temperature, than with great accuracy to only a low temperature, I employed tubes of equal diameter for their whole length, made from the tubing manufactured for spirit thermometers, having an internal diameter of about 55th of an inch, and a thickness of glass equal to about jth of an inch. Having drawn out both ends of a portion about 24 inches long, so as to pass quickly into a capillary tube capable of being sealed up with the blowpipe, it could be filled very easily, and the liquid sealed up so as to leave a bubble of air about 5rd of an inch long. I had thus a column of liquid of uniform width, about 2 inches long, and a bubble of air, which could be made to move to any part of the tube by violent swings of the arm; and by thus causing it to move to each end of the tube where drawn out and of less width than the rest, and by making suit- able measurements both then and when it was in that part where the diameter was uniform, I was able to ascertain what would have been the true length of the column of liquid, if the tube had been of the same diameter for its whole length. In order to measure with great accuracy the length of the * Quarterly Journal of Science, January to June 1830, p, 191. Saline Solutions at High Temperatures. 85 bubble at various temperatures, I fixed a lens, having a focal length of 5 inches, as an object-glass to a microscope, and pulled out the tube of the microscope until the distance of the eye-piece was such that each division of the micrometer in the eye-piece corresponded to z35th of an inch. In this manner the length of the bubble in the tube could be easily measured to within toooth of an inch. Of course when the liquid in the tube ex- panded the length of the bubble diminished to the same extent, and thus a knowledge of the length of the bubble at various temperatures was sufficient to enable me to ascertain the amount of the expansion of the liquid to within about z,),5th of its volume. This may indeed be thought not at all an accurate determination ; but in making the experiments at a high tem- perature, there are several sources of error which have such a great influence, that to attempt an apparently greater accuracy would not really give a better result. In order to heat the tube to various high temperatures, I fixed it in a glass beaker containing melted paraffine, which, on ac- count of remaining so liquid and transparent, is a substance ex- tremely suitable for such experiments. I so arranged the whole apparatus that the bubble in the tube was in the focus of the microscope, which was placed horizontally, so that the length of the bubble could be accurately measured whilst the liquid in the tube was at the temperature shown by a thermometer passing into the paraffine through a hole in a piece of card-board cover- ing the beaker. In making the experiments at high tempera- tures, I found it very difficult to maintain the paraffine at nearly the same heat for so long a time that there was no doubt that the liquid in the tube would have the temperature shown by the thermometer. By carefully managing the gas-lamp, this could be accomplished moderately well; but it was so difficult that I found it best to cause the heat to increase very slowly, and, when at the correct temperature, to quickly measure the length of the bubble. I then caused the heat to diminish gradually, and again measured the length when at the correct temperature ; and, if all this was carefully performed, the length of the bubble was nearly the same, whether the temperature was increasing or de- creasing, and therefore the mean of the two could not be far from the truth. Still, with every care, the various measure- ments differed very notably, perhaps on account of its being im- possible to make the whole of the bath of paraftine of precisely the same temperature, and therefore I made a considerable num- ber of measurements, and adopted the mean of all for the true determination. Having then ascertained the length of the column of liquid in the tube at a given temperature, and likewise measured the 86 Mr. H. C. Sorby on the Expansion of Water length of the bubble, I heated the tube in a bath of water or paraffine to 0°, 25°, 50°, 75°, 100°, 125°, 150°, 175°, and 200°C., and carefully measured the length of the bubble at all those temperatures; and I took care to repeat the measurements in descending order, and to adopt the mean of both, so as to com- pensate for the slight but very notable action of the water on the glass at the highest temperatures. I have employed the Centigrade scale, because it makes the formule so much more simple, and has been used by all the previous experimenters already referred to. The various data described above give only the apparent ex- pansion, and require some correction before we arrive at the real expansion. To the apparent expansion of the liquid must be added the expansion of the glass, which would be about ‘0026 for each 100° C.; and moreover it is requisite to make allow- ance for the diameter of the bubble in the tube being not quite so great as that of the column of water, because the sides of the tube were wet and covered by a film of water, which, according to my experiments, was about zg5th of an inch in thickness. Having applied all these corrections, I found that the volume of water was as follows :— eae! by - P Firs S d Third ration et aiiercne: diff raid. aiterenes: 200 1:1566 : - 0362 175 11204 0307 0055 +0002 Per ES) 1:0897 Os “0053 | s é 0254 r +0012 - 25 1:0643 ae 0041 Ae 0213 +0002 100 1:0430 ; 0039 = 0174 —‘00038 7a 1:0256 ere ‘0042 a z Poy 0132 x +:0006 50 10124 -0096 0036 0082 25 1:0028 -0028 ‘0068 re 0 1:0000 It will thus be seen that the second difference is not constant for temperatures above 25°; but no doubt this is in great measure due to errors in the observations, for the third difference is very irregular. Still the second difference is greater at high than at lower temperatures, but not so much so as to make it quite cer- tain that a term involving ¢° ought to be taken into considera- tion. Possibly that, and even still higher powers, might more accurately express the true law of the expansion, and their in- fluence may be masked by the increasing rate of the expansion of the mercury of the thermometer, or of the glass of the tube ; but, since the water begins to act on the tube at these high tem- peratures, it is almost impossible to determine the volume so accurately as to remove all doubt. Taking into account the temperature included between 25° and 175°, I deduce the follow- 87 ing formula, which gives the results shown below, and corre- sponds sufficiently well with that deduced from Kopp’s experi- ments, to prove that the expansion follows much the same law, both above and below 100° C. :— V='9977 + :000123¢ + -0000033072. and Saline Solutions at High Temperatures. Temperature.| Calculation. Experiment, Difference. 200 11543 11566 — "0023 175 1-1202 1:1204 —0002 150 1:0904 1:0897 +0007 125 1-0646 10643 +0003 100 1:0430 1:0430 “0000 75 1:0255 1:0256 —0001 50 10121 10124 — 00038 25 1:0028 1:0028 ‘0000 0 9977 10000 — 0023 Not taking into consideration the volume at 0°, these calculated numbers agree with the experiments as well as could be expected, except at 200°, which is a determination far more open to doubt than any of the others; and I therefore think that we may con- clude provisionally, that the formula would enable us to deter- mine with approximate accuracy the volume of water at still higher temperatures, whilst at the same time we must always consider it probable that this calculated volume would be less than the truth. Thus, for instance, it indicates that at 300° C. water would occupy at least $ of its bulk at the ordinary tem- perature of the atmosphere. Having found it requisite to ascertain what influence the pre- sence of various salts exercises on the expansion of water, I made a number of experiments, which lead to some curious results. In the case of chloride of potassium dissolved in three times its weight of water, I found the volumes to be as under :— 1:0000 Tempe- First Second Third rature, Me difference. difference. difference. 200 1-1228 5 175 11000 728 0030 0198 +0011 150 10802 0019 a . O17 ey —0001 125 1-0623 eee: TORO : 0159 | : +0003 100 10464 ees sulliousnole J ~ $ 0142 | +0001 7 10322 ‘ 0016 , 0126 — 0001 50 1-0196 an 0017 aie 25 10087 Disy 0022 Though the amount of the expansion varies very considerably, the general facts are much the same as in the case of water. The 88 Mr. H. C. Sorby on the Expansion of Water second difference is nearly uniform from 0° to 175°, but is de- cidedly greater at 200°. Calculating, however, the formula as before, from 25° to 175°, we obtain very different values for the coefficients of ¢ and #2, to those in the case of water; for I obtain the formula given below, which yields results compared with ex- periment in the following Table :— V= 9997 + :000326¢ + 000001412. Temperature.| Calculation. Experiment. Difference. 200 1-1213 1:1228 —-0015 175 10999 1:1000 —°000] 150 10803 1-0802 +:0001 125 10624 1:0623 +0001 100 10464 10464 “0000 75 1-:0321 1-0322 —'0001 50 10195 10196 —'0001 25 10087 1:0087 0000 0 9997 1:0000 — ‘0003 In this case the agreement is very close from 0° to 175°, and it is only at 200° that the difference is more than the probable limits of error in observation. On comparing the formula with that deduced for water, it will be seen that the coefficient of ¢ is much greater, whilst that of ¢* is much less than when no salt is in solution,—thus proving that the expansion of the saline solu- tion is much more uniform than that of water. In the case of water, the expansion from 0° to 100° is to that from 100° to 200° as 1 to 2°64, whilst in the case of this saline solution it is as 1 to 1:64. It will also be seen that, whilst the expansion of the saline solution is greater than that of water from 0° to 100°, it is much less from 100° to 200°. This is still more strongly marked in the case of a solution of chloride of sodium in three times its weight of water, as will be seen from the following Table :— Up to 100°. Up to 200°. Solution of NaCl . 1:0529 1:1328 Waters) ¢.: iene 0 eal O450 1:1566 +0099 —*0238 I have obtained similar results with various other saline solu- tions; but I need not describe them in detail, for the general facts will be shown sufficiently well by the following Table, in which all the formule are compared together. They differ from those given in my paper on the microscopical structure of crystals*, because in it the apparent, and not the real expansion was required. * Quart. Journ. Geol. Soc., vol. xiv. p. 462. and Saline Solutions at High Temperatures. 89 Water according to Kopp’s pee = -997696-+-0001101¢-+4-000003432. ments ...... pteteseeeeeseneenenees Sevens .. Water according to my own aoe EN = 9977 +-000123¢ +-000003302. PTTPTTET ITT ments Water with 10 per cent. of chloride of } V = -9991 +4-000215¢ +-000002512 POtASSIUM ....eeseeeeeeec senses tee eee ees j Water with 25 per cent. of chloride of V = -9997 +-000326¢ +-000001412 POtASSIUM .... 2... eee eeeece este een eees 4 Water with 123 per cent. of ditto, and tie : : 4 124 per cent. of chloride of sodium 0 ie la he esse ce Water with 25 per cent. of chloride of ine é f > sodium ...... HS de ceetdasaccosas \v =1-0000; +--0008975: --R000012722, ee ea ee These various saline solutions, therefore, indicate much the same facts. The presence of the salt in all cases tends to make the expansion of the liquid more uniform, increasing the value of the coefficient of ¢, but diminishing that of ¢?; the extent of this influence varying with the amount and nature of the salt. The discussion of this fact appears to lead to some curious results. According to the experiments of myself and others, the mean specific gravity of chloride of potassium is about 1°94. Hence the relative volume of one part by weight to three of water would be 1466 to -8534; and, if there were no change of dimensions when the two mixed together, on solution the united volume would be 1:0000, and the specific gravity should be 1:138. I however found, by experiment, that the specific gravity is really 1:1745 ; thus indicating that the united volume is only ‘969, and that there is a contraction of one or other of the consti- tuents equal to 31 per cent. of the whole bulk. Hence 1-000 part of the solution would contain about *880 part of water and ‘152 part of KCl, making a total volume of 1:032, but contract- ing on being mixed to 1000. Now, if we calculate what would be the volume of this *88 part of water at various temperatures, as ascertained by actual experiment, supposing it to exist ina free state, we obtain as shown in the following Table ; and deduct- ing these various volumes from the actual volumes of the saline solution as found by experiment, we ascertain what is the differ- ence in the total bulk made up by the chloride of potassium. | Tempe- Volume of Volume of Volume of | rature, the solution. the water. the KCl. } 200 1:1228 10178 “1050 175 1:1000 9859 1141 150 1:0802 -9589 +1213 125 1:0623 9366 257 | 100 10464 ‘9178 1286 75 1-0322 ‘9025 “1297 50 10196 | 8909 | :1287— | 25 10087 | ‘8824 | ‘1263 | 0 10000 | “8800 1200 90 On the Expansion of Water at High Temperatures. At first sight we are therefore led to conclude that the dis- solved salt gradually expands up to about 75°, and then gra- dually contracts, so that its bulk at 200° is only about #ths of what it is at 75°. We cannot, however, suppose that this result is in reality due to the contraction of the salt, but it appears far more probable that it is to be explained in the following manner. Before being mixed, the respective volumes of the chloride of potassium and the water in 1:0000 part of the solution would be, as shown above, ‘1466 and °8534. According to the experi- ments of Playfair and Joule*, the expansion of chloride of potas- sium from 0° to 100° is ‘01094, and therefore, providing that this expansion be uniform, the volume of the *1466 part, at the tem- peratures given in column I. of the following Table, would be as shown in column II. According to my own experiments, the volumes of the *8534: part of water would be as in column III. ; and these, added to the corresponding numbers in II., would be the total volumes given in IV., which the salt and the water would occupy before being mixed together. When, however, the salt is dissolved, the experiments described above prove that the actual volumes are as given in V.; and subtracting these from those in IV., we obtain the values shown in VI., which represent the reduction in volume that takes place when the salt is dissolved. Subtracting these values from the corresponding numbers in II., and calculating the difference on the supposition that in each case the numbers in II. are taken for unity, we ob- tain column VII., representing the relative volume with which the salt enters into solution, if no part of the diminished volume be ascribed to a contraction of the water. The results for 300° are deduced by means of the formule already given; but the rest are all determined from the experiments. I. Il. III. IV. Vv. Vi. VII. 300 | 1514 | 1°1364 | 1:2878 | 1:1815 | -1068 | -298 | 200 | 1498 | -9851 | 1:1349 | 1°0835 | -0514 | -603 175 | 1494 | 9560 | 1:1054 | 1:0615 | -0439 | -706 1490 | -9305 | 10795 | 1:0424 | -0371 | -751 125 | :1486 | -9085 | 1:0571 | 1:0251 | -0320 | -785 100 | -1482 | -8901 | 1:0353 | 1:0098 | 0285 | -801 75 | 1478 | °8751 | 1:0229 ‘9961 | 0265 | -819 50 | :1474 | :8640 | 1:0114 ‘9839 | 0275 | -814 25 | :1470 | +8558 | 1-0028 ‘9734 | 0294 | -800 0 | 1466 | -8534 | 1-0000 ‘9650 | 0350 | -761 _ or i) It therefore appears, from the facts shown by column VII., that, according to the above supposition, the volume with which the salt enters into solution is not the same at all temperatures. Not taking into account the very lowest temperatures, as being * Chemical Society’s Memoirs, vol. i. p. 121. Prof. J. C. Draper on a new Photometric Process. 91 connected with the expansion of water near the freezing-point, it will be perceived that the volume differs so little up to 100°, that the fact of there being any difference would have been doubtful, if the experiments had been limited to that tempera- ture. At higher temperatures, however, the volume diminishes very rapidly, so much so, that if the formule already given for the expansion of water and the saline solution hold true up to 300°, the chloride of potassium would enter into solution with only about {ths of the volume it would occupy when not dis- solved. It may, indeed, be doubted whether the above be really the true explanation of the small amount of the expansion of saline solutions as compared with that of water. If it be not owing to this cause, it must be that the presence of the salt exerts such an influence on the expansion of the water, that the saline solution has a rate of expansion of its own, independent of that of its constituents, since it is quite certain that the ex- pansion of the mixture differs in a remarkable manner from the united expansion of the separate constituents. XVI. On a New Photometric Process for the Determination of the Diurnal Amount of Light by the Precipitation of Gold. By Joun C. Draper, M.D., Professor of Analytical Chemistry in the University of New York *. ne influence of light on a solution of the peroxalate of iron, and the use of such a solution as a photometric agent, has been noticed by my father, Prof. J. W. Draper, in the Philoso- phical Magazine for 1857. The adaptation of the peroxalate to this purpose may be greatly improved by the addition of perchloride of iron; and I have used such a mixture for the determination of the diurnal amount of light, being thus enabled to compare the diffuse light of one day with that of another, or of one portion of a day with that of another portion. In these experiments the exposure of the sensitive solution was to the north, or rather to the region about the pole. The amount used on each occasion was 10 cubic centimetres, placed in a thin glass tube 74ths of an inch in diameter, and graduated to cubic centimetres. In order to protect the exposure-tube and its contents from stray light, it was placed in a box darkened in the interior, so that only rays which entered by an opening 1°5 inch square, and 1:3 inch distant from the tube, could reach its contents. The sensitive solution was prepared as follows :—In the expo- sure-tube, mentioned above, 3 cubic centimetres of a solution of * Communicated by the Author. 92 Prof. Draper on the Determination of the Diurnal perchloride of iron (sp. gr. 1020 at 60° Fahr.) were measured. In a test-tube 3 cubic centimetres of a solution of oxalic acid (sp. gr. 1022 at 60° Fahr.) were placed, and boiled for a few minutes with an excess of fresh moist peroxide of iron ; the re- sulting peroxalate of iron was then filtered, the filtrate being collected in the exposure-tube containing the perchloride, and the contents of the filter washed with hot water until the liquid in the exposure-tube amounted to 10 cubic centimetres. This solution, when carefully prepared in the dark, and all light ex- cluded for a few days, gives no precipitate with perchloride of gold; but when it has been acted on by light up to the first appearance of turbidity, on the addition of perchloride of gold it precipitates metallic gold freely ; and exposed as indicated above, answers to measure the diffuse light of half a hot summer’s day, a second solution in a similar tube being substituted at mid-day. The following experiments, taken from a series extending from August 15, 1858 to November 11, 1858, serve to give some idea of the value of this method. No. I.—September 23, 1858. Time. | Thermo- |Dew-point.|Barometer. meter. 7am.| 49F. | 43 F. | 29°86 | Perfectly clear all day. 12 Mm. 56; ARs 29°86 | 41 milligrammes of gold. 6p.m.| 55 ,, AD a 29-82 | No. II1.—September 28, 1858. Time. | Thermo- |pew-point.|Barometer. meter. 7am.| 50F. | 478. | 30-02 | Perfectly clear all day. 12 m. 60 ,, 49 ,, 29:90 | 40 milligrammes of gold. Gem.| 58,, | 50,, | 29-85 Nos. I. and II. represent days nearly alike as regards tem- perature and condition of the sky; and we find accordingly that the amount of chemical action indicated by the weight of gold precipitated is nearly the same in each case, No. I1].—October 7, 1858. | Thermo- Dew-point.|/Barometer. Time. meter. —— — 7am.| 60F. 54 F. 29:50 | Cloudy and rainy. 12 m. 65 ,, 64 ,, 29°30 | 19 milligrammes of gold. Gem.| 68, | 63,, | 29:10 -Amount of Light by the Precipitation of Gold. 93 No. 1V.—October 13, 1858. Time. | Thermo- | pew-point.|Barometer. meter. 7am.| 58F. | 54F. | 29-80 |Cloudy and rainy. 12 m. 59 ,, 58 ,, 29°70 |22 milligrammes of gold. 6pm.| 59, | 58, | 29°63 Nos. III. and IV. represent days nearly alike in temperature and cloudy condition, and they also show a similar amount of chemical power in the light of each; but when compared with I. and II., we find the effect of the cloudy condition of the sky in the decreased amount of gold precipitated. No. V.—September 7, 1858. Time. | Thermo- |New-point.|Barometer. meter. —— 7am.| 72 F. 65 F. 29:70 |Perfectly clear all day. 12 m. 80 ,, 66 ,, 29°69 (56 milligrammes of gold. Gem.| 76, | 68,, | 29°64 No. VI.—November 4, 1858. Time, | Thermo- |pew-point.|Barometer. meter. | Zam.| 46 F. 45 F. 29°70 |Very dark and raining. 12 m. 48 ,, Aq. 29-60 |7 milligrammes of gold. 6pm.| 46,, 45 ,, 29°55 Nos. V. and VI. represent extremes, the first being a clear warm day, while the latter was cold, very cloudy, and dark; accordingly we find the diffuse light of the clear warm day had eight times as much chemical power as that of the colder and darker day. These experiments serve to demonstrate the capabilities of this process, and may perhaps recommend a trial of its merits to such as are interested in photometric pursuits; and by the use of the same quantities of a similar solution, exposed in a like manner in various countries, valuable tables might be con- structed. [ 94 ] XVII. On the Rotation of Hollow Spheres of Metal by Heat. By G. Gorn, Esq.* a the Supplementary Number of the Philosophical Magazine, June 1858 (see also the Number for February 1859), I described an apparatus for producing rotation of tubes and hol- low spheres of metal by means of heat of electric conduction- resistance, the moving body being placed upon a_ horizontal metallic railway, and the heat being produced by passing a pow- erful electric current from one rail through the ball or tube to the other by means of their points of mutual contact. Since that period I have further considered the conditions of the phenomenon referred to, and have constructed the following apparatus for producing similar motion by means of ordinary heat. A and A’, fig. 1, is a massive circular ring or railway, com- Fig. 1. (Scale th.) posed of metallic copper}, and cast in one piece (seen in section, fig. 2) ; the outer rail, A, is 10 inches in diameter, and the inner one, A’, is 6 inches; the height of the outer rail is 12 inch, and that of the inner one is ;5th of an inch less; the distance * Communicated by the Author. + The ring contained a little brass in its composition, to enable it to be more readily melted and cast. On the Rotation of Hollow Spheres of Metal by Heat. 95 between their edges is 13 inch, and they each taper from a sharp edge at the top to about {ths of an inch thick at the bottom. The edges of the rails are turned perfectly true and smooth*, and in some instances have been coated thickly with silver by electro- deposition in order to protect the copper at those parts from oxidation when subjected to a high temperature, but with unsa- tisfactory results; the greater expansibility of the silver caused it to separate from the ring in the form of corrugations and large blisters. BBB is a horizontal brass triangle with three brass pins (two only, C, C, being shown in the cut) projecting from its upper surface to support the rmg. The triangle is sup- ported by three long brass screws, D, D, D, provided with bone feet to obstruct the transmission of heat to the table, and with set-screws, , E, to hold them steady when adjusted. FF, fig. 2, Fig. 2. (Scale 4th.) is a flat circular groove, half an inch wide and ;j,th of an inch deep, turned in the base of the outer rail to receive the ends of the pins C, C. There are three longer pins fixed in the triangle (of which only two, G, G, are shown), to assist as guides in placing the red-hot ring upon the triangle; both these pims and the pins C, C must be so fixed as to allow for the expansion of the copper ring, the amount of which is nearly $ths of an inch in its diameter at a full red heat. H is aspherical shell of German silver, 4 inches in diameter, as thin, as perfect in form, and as uniform in thickness as it can possibly be made. As the phenomenon of rotation in this case is much more delicate than in the other by electricity, already referred to, and the success of the experiment depends greatly upon having suit- able balls, and these are difficult to obtain, I give the following particulars respecting the mode of forming them. A stout plate of brass is turned into a ring whose inner diameter is the same as that of the required ball; it is then divided into two equal parts, and one of these is retained to serve as a pattern or tem- plate by which to form the hemispheres composing the ball. A * The ring should be previously heated to bright redness and slowly cooled, otherwise the heat to which it is subjected in the experiments will alter its form. 96 Mr. G. Gore on the Rotation of hemispherical chuck of either hard wood or iron is tiirned in the lathe to fit the pattern, and several sheets of the best quality of German silver are formed into cups upon it in the lathe with the greatest possible degree of exactness by the mechanical process termed “spinning.” The thickness of the metal sheet employed will not affect the future operations; but that best suited for the spinning process is termed “No. 10.” In this mode of forming the hemispheres there is some difficulty in continuing the proper curvature completely up to the edge of the cup, in consequence of the persistent elasti- Fig. 3. city of the metal; but this may be overcome by spinning the sheet of metal to some distance beyond the edge of the chuck in the form of a cylindrical prolongation and cutting this superfluous elastic portion off, or by increasing the curvature of the chuck near its edge, as in fig. 3*. Having obtained a number of hemispherical cups, carefully ex- amine their forms and dimensions by means of a template, a rule, and a pair of callipers, and see that their height when placed upon their edges is exactly equal to half their diameters; if they are more, they must be reduced in a lathe. It will be found that in the process of spinning, the metal, being weaker in cohesion across its fibres than along them, will have stretched slightly more in that direction than in the other, and the hemispheres will in con- sequence be slightly oval across their axes, probably about 34nd of an inch in a 32-inch ball; a mark should therefore be made upon the outside of the cup to indicate the direction of the fibres, so that when two hemispheres are joined together their ovals may be placed at right angles to each other, and thus cor- rect the ellipticity. The cups should now be selected in suitable pairs, and the edge of each one drawn slightly inwards by gentle blows of a very small wooden mallet uniformly all round the edge, the edge of the cup being held upon a suitably-shaped piece of bright steel or iron held firmly in a vice. To ascertain that the two cups forming a pair are of exactly the same cireum- ference, they should be coated with a film of solder composed of 5 parts of tim and 1 part of zine all round the edges, and to 3/5th of an inch down on the inner side, and slightly soldered at inter- vals of about 1 inch all round with the aid of a strong solution of hydrochlorate of ammonia. If the cups are found to be unequal in circumference, they should be separated, and corrected by means of a mallet in the manner described. The object of using the above particular solder is to prevent the junction of the ball * Suitable hemispheres may be obtained of Messrs. Griffiths and Co., Bradford Street, or Mr. Revill, Constitution Hill, Birmingham. Hollow Spheres of Metal by Heat. 97 being loosened by heat in the experiments: ordinary soft solder would frequently melt ; and hard brass solder would not admit of the hemispheres being readily separated for alterations. The two hemispheres are now to be reduced to equal weights by filling one of them with nitric acid; then a very small hole formed in the pole of each in a lathe, and stopped by melted sealing-wax: the object of these holes is to prevent heated air bursting the ball during experiments, and to prevent the ball collapsing by cold after an experiment. The two cups are now to be soldered perfectly water-tight all round, and the ball turned a number of times in a lathe, shifting its position in the chuck frequently, until by means of a callipers and template it is found to be sufficiently round, and finally turned and polished until, upon being placed upon the surface of water, it remains steady in every position. A number of scratches should now be made upon the outside of the ball across the soldered junction at intervals of 1 or 13 inch apart all round the ball, the hemispheres separated by means of a penknife and weighed: they will probably be now unequal in weight, and will certainly be far too heavy for successful ex- periments; a pair composing a 4-inch ball will weigh from 2000 to 2500 grains, and will require to be reduced to about 500 or 600 grains. To reduce them to equal weights and to the requi- site degree of thinness, they are placed upon small glass beakers in alight place (for advantage in watching their surfaces), and filled to within a quarter of an inch (or less) of their edges with mode- rately strong nitric acid, to dissolve their inner surfaces gradually. They must be frequently emptied, weighed, and examined for thin places during this process ; and when they are becoming very thin, they must be continually watched to prevent holes being formed in them. The production of a hole is generally preceded by an inden- tation in the outer surface. If byaccident a small hole should occur or a very thin place be formed, it must be covered on the inte- rior with a thin film of the solder already mentioned, then heated and rubbed with sealing-wax, and the process of dissolving con- tinued until the two cups are of equal weights, and until, by passing one’s finger with gentle pressure over the outer surface of the cups, slight indentations visible in the interior are pro- duced, or, by passing the end of a blunt tool over the inner surface, its progress may be observed on the outside. They are now to be soldered accurately and water-tight together by aid of the marks made upon them, the soldered junction filed and trimmed with emery-cloth, and the ball cleaned by placing it securely in a cage of stiff brass wire, dipping it into nitric acid and then into water. Indentations accidentally produced in the ball may, if the ball be sufficiently thin, be removed by suction Phil, Mag. 8. 4, Vol, 18, No, 118. Aug. 1859. H 98 ~ Mr. G. Gore on the Rotation of: on the outer surface of the metal. When the balls are exceed- ingly thin, slight indentations occur upon the outer surface, as if that. surface was relieved from a state of mechanical tension. ~ In using the apparatus, the triangular support is placed in a firm and steady position upon a board containing three shallow holes to receive the feet; the ring is placed upon the triangle and set to a perfect level, either by means of a spirit-level or one of the balls. The ring is then placed in a red-hot closed muffle and heated to bright redness (the hotter the better, so that it is not fused) ; it is then taken out and placed carefully upon its support by the aid of the guide-pins G G, and the ball at once placed steadily upon it. As soon as the ball conmimences to revolve the time is noted, and the number of revolutions also noted during 80 seconds, and, if desired; during half a minute longer. If other experiments are to be tried, the ring is at once replaced in the muffle. In the various experiments I have made, the ring has occupied 8 minutes in first acquiring its heat, and 5 minutes each time of renewing it. The following is a list and description of the balls which have been experimented with ; they were all formed of the best qua- lity of German silver (except A, which was composed of one hemisphere of German silver and one of iron; and gilded). List of Balls. A. 22 inches diameter; 756 grains weight. B. 3 5) » 3 £03 ry) ” be by 3 5 er) oe ees «3 with a bar of Ger- man silver weighing 228} grains fixed in it from pole to pole* ; total weight 835 grains. 33 inches diameter; 1000 grains weight, and of defective shape. E. D reduced to 774 grains weight. F, E reduced to 6872 ,, » anda bar of German silver weighing 268 grains fixed axially within it ; total weight 9503 grains. G. 33 inches diameter; 1029 grains weight. 5 Sle 5 = eas RIWLE Pra » With a bar of Ger- man silver weighing 224 grains fixed from pole to pole ; ; total weight 1000 grains. I. 33 inches diameter; 1026 grains weight, with an axial bar of German silver weighing 392 grains; total weight 1418 grains. * The object of usimg axial bars was to ascertain whether a certain degree of pressure upon the rails was favourable to the success of the experiment. Hollow Spheres of Metal by Heat. 99 J; A inches diameter; 2425 grains weight. K. G reduced to 493 grains weight. i. J ey BOL ” M. B 99 3 843 ”? » N. C reduced to 342 grains weight, and a bar of German silver weighing 2281 grains replaced. within it; total weight 570+ grains. QO. I reduced to 3721 grains weight. PL » 35 961 ” ” Experiments. No. 1. The copper ring silvered all over, and rather thickly upon its edges ; raised to a moderate red heat : the ball A placed upon it did not vibrate or show any signs of motion. The ball D immediately placed upon it, began at once to vibrate through a space of one-sixth the circumference of the ring, and continued to do so for 25 minutes, until the ring was quite cool. No. 2. The ring as in experiment No. 1, but rather less hot; the ball A showed no motion; and the ball E vibrated less than D*in experiment No. 1. _ No. 3. The ring thickly coated with 1} ounce of silver upon its edges by electro-deposition, and raised to a full red heat, the silver became very much blistered, but was partly remedied by rubbing with a burnisher. Ball B exhibited a feeble tendency to vibrate. Ball C vibrated backwards and forwards about one- fifth the circumference of the ring. Ball F vibrated complete revolutions within about one-eighth of ai inch during several minutes. Ball G vibrated through one-sixth the circumference of the ring. Ball H vibrated about one-fourth of a complete revolution. Ball J exhibited no signs of motion. N.B. The ring was only once heated for this experiment. No. 4. The coating of silver was removed from the edge of the outer rail, and the ring was heated to a full red heat. Ball F vibrated through one-fourth of a revolution. Ball I exhibited decided motion, but less than ball F. Ball K made 7 complete revolutions in 1 minute in a right-handed direction, 7. e. in the same direction as the hands of a watch. Ball L vibrated through one-fourth of a revolution. N.B. The ring was only once heated for this experiment: No. 5. The ring as in No. 4; heated to bright redness. Ball M made about 6 revolutions in half a minute, in a left-handed direction. Ball N made about 4 revolutions in half a minute in a similar direction. Ball K made about 3 revolutions in half a minute in the same direction. N.B. The ring was only heated once for this experiment. ’ No. 6. The ring as in No. 5, and heated uniformly to bright H 2 100 Mr. G. Gore on the Rotation of redness before placing each ball upon it. Ball M started at once all round in a left-handed direction, and made 5? revolutions in half a minute; it then burst by expanded air, but continued its motion and made 4% revolutions in the second half minute. Ball N started with decidedly less vigour than ball M, and made 4 revolutions in a left-handed direction in half a minute. Ball O started with much greater energy than ball N, went at once completely round, and made 6% revolutions in a left-handed direction in half a minute. | Ball P started with greater force than ball O, and made 8} revolutions in a left-handed direction in half a minute; owing to some defect either in its form or distribution of weight, it made one long vibration before starting on its journey. N.B. The ring was reheated for each ball. No impetus was given by the hand to either of the balls, they were simply placed upon the rails. The apparatus was also protected from currents of air. As these experiments were only made with a view of obtaining complete revolving motion, they were not, except in “No. 6,” conducted under such conditions of equal temperature, freedom from currents of air, &c., as to be strictly comparative. “ The following appears to me to be an explanation of this phenomenon of motion :—Immediately the cold ball is placed upon the heated rails, two small protuberances (produced by the heat) emerge from its surface at the points of contact, whilst two corresponding hollows are produced in the rails at the same points by contact of the cold ball, but in consequence of the inferior heat-conductivity of German silver, and the thinness of the spherical shell, the heat is prevented from quickly spread- ing, and the maximum of local expansion is produced in the ball, whilst at the same time, from the superior heat-conduc- tivity of copper and the massiveness and form of the ring, the minimum of local contraction is produced in the rails, and thus the protuberances in the ball are greater in amount than the hollows in the rails, and the ball is at once placed im a state of unstable mechanical equilibrium, somewhat like an egg placed upon its end in a watch-glass, and is caused to move either in one direction or the other by the slightest disturbing influence, such as a breath of air, a minute inequality in the original form or distribution of weight of the ball, &e. To account for the continuance of the motion, I suppose that a minute period of time is occupied by the heat in producing the expansion, and that during this period the ball has by its momentum moved forwards a minute distance; and thus the ever-recurring points of maximum expansion are always kept a little behind the line of the centre of gravity of the ball, and act as a propelling power, pushing it forwards by gentle leverage. Hollow Spheres of Metal by Heat. 101 The direction of motion appears to me to be simply dependent upon the direction of the first impulse. Another mode of ex- planation is thus :—Let A signify a pomt or locality upon the advancing side of the moving ball, which will, by the motion of the latter, be brought into contact with one of the heated rails. The sources of A’s gaining heat are by radiation from the heated copper, and by conduction from the hotter parts of the ball; and its means of losing heat are by radiation into the atmosphere, and by conduction to colder parts of the ball ; in addition to these influences, its temperature is slightly affected by upward currents of heated air from the ring. As this point or locality A is moving downwards towards the rail, its temperature is gradually augmented, and goes on increasing not only until it touches the rail and is precisely under the centre of the ball, but probably also until it has passed that position a minute distance, because its rapidity of loss of heat by con- duction is less upon the receding than upon the advancing side of the ball, the advancing side having been more completely cooled by radiation. If the temperature of the locality A is at its maximum at some small distance behind the point of contact of the ball with the rail, the maximum of expansion must also be a little behind that point, and thus constitute a propeiling power, as in the previous explanation. As nearly as I have been able to ascertain, the following appear to be the most favourable conditions to a successful result :—1. The rails perfectly equidistant and horizontal. 2. The ball as spherical as possible, and of uniform thickness, or at least with its centre of gravity in the centre. 38. The maximum of tem- perature in the rails and the minimum in the ball. 4, The maximum of heat-conductivity in the rails and the minimum in the sphere. 5. The maximum of expansibility in the metal of the ball and the minimum in that of the rails. 6. A sufficient degree of thinness in the metallic shell to ensure quickness of local expansion. 7. A sphere of large diameter; and 8. The surfaces of the rails and ball as smooth as possible. The same conditions, with modifications of 3, 4, and 5, would probably be also the most favourable ones in the experiments of rotation by electric heat, already referred to. The apparatus has been presented to the Royal Institution, and may be seen there by those who are interested in the matter. In conclusion, I have to thank Messrs. Griffiths and Co., of Birmingham, for kindly granting me the unrestricted use of their enamelling furnace for the experiments. Birmingham, June 14, 1859. [ 102 ] XVIII. On some points of analogy between the Molecular Structure of Ice and Glass ; with special reference to Professor Erman’s observations on the Structural Divisions of Ice on Lake Baikal. By James Drummonn, Esg.* . [upon the lake] was perfectly transparent, but traversed by per- pendicular cracks..... These cracks were all extremely narrow, and filled with air. Many of them reached from the surface onl to a certain depth, which was the same for all, and seemed to be a third of the entire thickness of the ice. The other cracks then began at this depth, and reached down to the water... . . Quite different in look and origin from the cracks here described were the much wider fissures which are formed by the cooling and contraction of the ice subsequent to its perfect congelation. I found one of these at the place where we were stopping...... It had throughout a uniform width of 4 inches, and reached from the upper surface to the water. It was filled with new ice, which gave it the look of a vein or dyke in rock. What added to this resemblance was, that the ice fillmg the crack was always much whiter than the surrounding. It was traversed by fine cracks or flaws in a very regular and remarkable manner. One of these cracks formed a continuous and somewhat waving line, which occupied almost exactly the middle of the vein, and from that proceeded, at an acute angle, an immense number of smaller flaws to each side, just like the lateral ribs of a leaf issumg from the central rib.” + Such, then, are the phenomena; but before proceeding to their consideration, I shall briefly notice those bearing upon the molecular structure of glass, to which I have referred. If we cut a thin slip from a piece of sheet or crown glass, and hold it, while slightly bent, in a polarizing apparatus, coloured fringes will be observed, one set being separated from the other by a dark neutral line running through the centre of the glass. The * Communicated by the Author. + Phil. Mag. for June 1859, p. 406. Mr. J. Drummond on the Molecular Structure of Ice. 103 fringes will be positive or negative, according as the slip is bent o the one side or the other—the negative appearing always upon the convex side, and the positive upon the concave,—show- ing that the molecular structure, whatever may be its nature, is the same on each side of the dark neutral line. If we now turn to the change produced upon glass during the process of devitri- fication, some light will, I think, be thrown upon the nature of this structure. Réaumur was the first to observe and describe this phenomenon, which he had produced by exposing a vessel of common bottle or green glass, filled and enyeloped on all sides by a mixture of sulphate of lime and sand, to the heat of a pot- tery furnace during the whole course of a firmg. When after- wards examined, the glass appeared to have exactly in its centre a dark line, from Sh on each side and parallel to each other, an infinite number of small needle-shaped crystals proceeded to the exterior surfaces. Now in this phenomenon it will be ob- served that we have the same dark central line found in homo- geneous glass by polarized light, on each side of which the cry- stals are arranged at right ‘angles. That this is the mode of arrangement which the molecules assume in their homogeneous state previous to the crystalline metamorphosis, we have no direct reason to conclude; neither have we any to reject the idea. It seems to me, however, the most probable hypothesis ; and I shall therefore assume it. Again, when glass has been cooled rapidly, _ as in the case of what are termed Prince Rupert drops and the Bologna or philosophical phial, we have another class of phzeno- mena closely connected with molecular structure. In these cases a peculiar tendency is induced to subvert the force of cohesion by which the molecules are held together, in consequence of which the slightest force is sufficient instantly to cause each portion to fly in pieces, or be converted into powder. The cause of this has been investigated by Dumas; but his conclusions it Were unnecessary to repeat. Keeping, however, all these phe- nomena in yiew, we shall he enabled, I think, to elucidate those observed by Prof. Erman. And first of all, reverting to his description, I would point out the opposite character of the fractures in the two classes of ice examined by him. In the case of that which formed the coyer- ing of the lake, the cracks proceeded from the outer, or rather the upper and lower surfaces of the sheet, towards its centre ; while in the ice with which the great fracture was filled, the principal crack ran through its centre, the others proceeding laterally from it towards the sides. From these phenomena the following conclusions may, I think, be drawn :— Ist. That the molecular séructure in both cases was the same. 2nd. That the molecular s/a¢e in each was entirely different. 104 Mr. J. Drummond on the Molecular Structure of Ice. 3rd. That the structure in both cases was closely related to, if not identical with that of ordinary sheet glass. And 4th. That the ice formed in the fracture possessed a disrup- tive structure, analogous in some respects to that of glass when cooled rapidly. It is only, of course, from the direction of the cracks that we can trace by the eye the nature of the structure. But conclu- sions drawn from these would be of little value, could we not at the same time trace them to the action of molecular forces. Thus considered, however, the value of the cracks as evidence of structure will be at once apparent. In the ice with which the great fracture was filled, the principal crack passed through the centre, others proceeding from it laterally. Now the line of this erack is exactly that of the molecular axis of sheet glass, the principal characteristic of its structure to which I have drawn attention. Again, in the case of the great Lake sheet, Prof. Erman states that at a depth of about a third of the entire thick- ness, the cracks proceeding from the upper and lower surfaces met, and that this depth was the same for all. Now if this point be taken as that of the position of the central molecular axis, we have here also the same structural characteristic. ‘True, we have not here any direct evidence of its existence; but the considerations to follow will render it more conclusive. The cracks I suppose to be the result of molecular forces act- ing in each case in an entirely opposite manner. We have still, therefore, to trace the causes which produced this opposite mole- cular action ; and these, I think, are to be found in the opposite conditions under which the two descriptions of ice were formed. First of all we may take it for granted that the great Lake sheet was solidified under ordinary circumstances, that is to say, when the temperature could not be much lower than the freezing- point. Subsequently, when the temperature was considerably reduced, the great fracture was formed. Further, when this rent was newly made, the water must have rushed up, filled it, and become instantly solid. But when solidification was thus going on at a temperature within the mass of 32°, the walls of the fracture to which it was immediately exposed were at a tempera- ture lower by many degrees than the freezing-point. The sheet therefore was solidified under circumstances analogous to the process of rapid cooling in the case of glass, and by which a dis- ruptive structure is produced. In this condition, therefore, we have, it seems to me, the cause of the difference between the molecular states of the two classes of ice,—a difference in ac- cordance with which they appear to have strictly acted. For when the temperature subsequently became further reduced, those of the Lake sheet shrank towards its molecular axis, thereby On the Freezing-point of Water in Capillary Tubes. 105 causing the fractures to proceed from its outer surfaces towards it, while the sheet enclosed within the great fracture, from the opposite cause, or an after increase of temperature, was burst completely asunder, its molecules being apparently repelled from its axis, thereby causing the principal rent to proceed along that axis, and many others from it laterally towards the outer sur- faces. Indeed, it is not at all an improbable hypothesis that-the much whiter colour of this ice, as noticed by Prof. Erman, may have been due to its complete disruption, to innumerable frac- tures traversing its entire mass, and too minute for detection by the eye. If this were so, then the phenomenon would be more directly analogous to that of the disruption of the molecules of glass in the case of the Prince Rupert drops, and resulting from the same cause, viz. instantaneous congelation under a reduced temperature. The analogy which I have thus briefly attempted to establish between the molecular structure of glass and ice seems to me to be, if successful, a not unimportant step in this inquiry, more especially as regards the principle of a disruptive structure. How far, for example, this principle might elucidate the phenomena of the veined structure of glacier ice, the white colour of its alter- nate bands, and their more porous character, are questions which will at once occur. Meantime, however, if by leading to further investigation I thereby lead to more luminous results, my object will be attained. Greenock, June 14, 1859. ’ XIX. On the Freezing-point of Water in Capillary Tubes. By H. C. Sorsy, F.R.S. §c.* aes of two years ago, when making some experi- ments in order to ascertain the true nature of the liquid contained in the fluid-cavities in quartz, I thought that its freezing-point was well worthy of being determined. Sir Hum- phry Davy had long before shown (Philosophical Transactions, 1822, p. 867) that in many cases this fluid was water; and I had myself proved to my own satisfaction that water is given off from the cavities when the crystal containing them is heated so that the expansion of the fluid bursts them; but I was anxious to confirm this conclusion by some independent experiment, and to prove that it was water whilst still in the cavities. I therefore kept for a sufficiently long time a portion of rock-crystal, contain- ing very excellent and distinct fluid-cavities about ;4,th of an . . . . . 1 00 inch in diameter, in a mixture of snow and salt at a tempera- * Communicated by the Author. 6 Mr. H. C. Sorby on the Freezing-point ture far below the freezing-point of water; and then quickly placing it in a saturated solution of common salt previously re- duced to a very low temperature, I was much surprised to find that the liquid in the fluid-cayities had not been frozen, but the enclosed bubbles still moved about like those in spirit-levels, when the fragment was turned round, just as they did at first. I again repeated this experiment along with Dr. Tyndall; and we both came to the conclusion that the fluid would not freeze at a temperature nearly 20° C. below the freezing-poit of water, or even lower than that of strong saline solutions, and therefore there was some doubt as to whether it really could be water or some saline solution. I, however, had such confidence in the value of other independent proofs, that I still adhered to the idea of its being water, and that the phenomenon must be owing to some peculiarity in the freezing of water in minute cavities. I afterwards learnt that Dr. Perey had made some experiments with water in capillary tubes, and had arrived at a similar con- clusion. He has not, I believe, published an account of these, but kindly told me all the particulars. In his experiments the water apparently did not freeze at all: but when in such minute tubes, it is difficult to ascertain for certain whether the water is frozen or not, if it be merely examined with an ordinary magni- fying glass; and therefore, thinking there might still be some doubt about this, I resolved to carefully investigate the whole subject. Of course we all know very well that the temperature at which water will freeze is not necessarily that at which it thaws. It has long been known that the temperature may be reduced very considerably below 0° C. if no ice be present and the water be kept tranquil, freezing, however, when agitated. If the water be in a glass tube about one-fourth of an inch in diameter, the temperature can easily be lowered to —5° C. (23° F.), even when the tube is shaken; andif kept quiet, the temperature may be reduced somewhat more. At —6°, however, it freezes at once, eyen when kept perfectly quiet. The same takes place in tubes 2th of an inch in diameter ; but when much less than that, the result is very different. To ascertain beyond all doubt whether the water in very minute tubes was liquid or in the state of ice, I had recourse to the aid of the microscope and polarized light. In using this, some‘care is required. Theanalyser should be so arranged as to haye a per- fectly dark field; and the plane of the polarization of the light should be either in the line of the length of the tube or at right angles to it ; for, if not, the light is depolarized by the curving sides of the tube. When all is properly arranged, and the focus adjusted to the centre of the tube, if it contain liquid water the - of Water in Capillary Tubes. 107 whole field-appears dark, and no white line is to be seen down the centre of the tube ; whereas, if the water be frozen, the double refraction of the ice depolarizes the light, and the tube appears as if it contained a white substance, which vanishes as the ice thaws. In order to delay the thawing, the small tube should be examined when inside a larger vessel containing a strong solu- tion of common salt. The capillary tubes used in my experiments were prepared by drawing out, when melted, the tubes used for alcohol thermo- meters; and their interna] diameters were ascertained by mea- suring them at the broken ends by means of the microscope- micrometer, because the bore appeared about 3 of the actual diameter when seen at the side through the curved glass. I made experiments with those whose diameters yaried down to nearly ;j5yth of an inch; but when so small as that, the depo- larizing action of the ice is so weak, that it is impossible to be quite sure whether they contain water or ice. Those, however, from 345th to }5th of an inch in internal diameter are in eyery respect most satisfactory; for there is no difficulty whatever in deciding this point with polarized light in the manner just de- scribed. When water is contained in such tubes, we can readily reduce the temperature to below —15° C. without using any care to keep them quiet; and even when we shake them very violently, it will not freeze. The temperature may even be re- duced to —16° C. (3° F.) without taking any precaution to keep it still; but at —17° C. the water freezes at once, even when kept perfectly quiet. It will thus be perceived that there is a difference of about 11° C. (20° F.) between the temperature at which water freezes in tubes of about 1th of an inch in diameter and in those less than z3,th, which is so great a difference that there is no chance of its being an error of observation. So far as I was able to ascertain, there was no very decided difference in the temperature in the case of tubes varying from zaoth to 745th of an mch in diameter, nor in the case of tubes from ith to z5th; but in a tube of about ,1,th the water froze at about —13° C., but not at —11°, which is clearly a tempera- ture intermediate between that required for those of jth and sath. It must not, however, be supposed that water will not reeze in minute tubes at a temperature very little lower than 0° C., if the water be in contact with ice. When a tube of con- siderable diameter in one part is ever so fine in another, the contact of ice causes the water to freeze right down into the ca- pany part of the tube at a temperature yery little lower than ° C.; and ice thaws as usual at O° C. when in tubes in which meter wil not freeze until the temperature has been reduced to —16° C. 108 Prof. Davy on the presence of Arsenic It therefore appears to be completely proved that water will not freeze in tubes of very small internal diameter, even when they are shaken, at a temperature very considerably lower than that at which it freezes at once in larger tubes, even when kept perfectly still, as though the actual size exerted a most decided influence in preventing the crystallization of water, which freezing essentially is. In this respect water does not stand alone; for the same retarding action is exerted on the crystallization of salts from solution. This is well seen in the case of bichromate of potash ; for in some cases, when in a very minute state of divi- sion inside the fluid-cavities in other salts, a strong hot solution will not deposit any crystals on cooling, even after having been kept for upwards of a year, but remains as a deep yellow liquid, containing relatively far more of the bichromate in solution than can be retained when the liquid is in larger quantity. Small portions of lava have also often remained as an uncrystalline glass inside the minute cavities in the minerals of voleanic rocks, though it has entirely passed into a crystalline stone when in larger masses. XX. On the presence of Arsenic in some Artificial Manures, and its absorption by Plants grown with such Manures. By Epmunp Witiiam Davy, A.B., M.B., M.R.IA., Professor of Agriculture and Agricultural Chemistry to the Royal Dublin Society*. c is well known to chemists that sulphuric acid or oil of vitriol, as it is met with in commerce, almost always contains variable proportions of arsenic; but it appears to me that this fact has been overlooked by the public, and that they are not aware to what extent this highly poisonous substance occurs in general in commercial sulphuric acid, and thus becomes the means by which arsenic enters the different substances in whose preparation that acid is employed. My attention was first called to this subject by the difficulty I experienced in procuring any commercial sulphuric acid which did not contain a comparatively large proportion of arsenic, ren- dering it quite unfit and dangerous to be used for many purposes of experimental illustration. This arises from the fact, that the vitriol manufacturer has found that it is far more economical for him to make sulphuric acid from iron pyrites (a compound of sulphur and iron), which he can obtain for about twenty-five shillings a ton, than from native sulphur, for which he is obliged * Communicated by the Author, having been read before the Royal Dublin Society, April 29, 1859. in some Artificial Manures. 109 to pay about seven pounds for the same quantity. This ore of iron contains almost invariably more or less arsenic, which passes into the sulphuric acid manufactured from pyrites; whereas the native sulphur containing little or no arsenic, the sulphuric acid made from it is not so liable to be contaminated with that poison- ous substance. Pyritic sulphuric acid, on account of its being much cheaper, seems in a great measure (at least in Dublin) to have taken the place of that manufactured from native sulphur ; and hence the occurrence latterly of so much arsenical sulphuric acid in commerce, and the presence of arsenic in so many sub- stances in the preparation of which that acid is directly or indi- rectly employed. The vitriol and manure manufacturers have been in the habit of making an inferior kind of pyritic sulphuric acid, which, owing to its dark colour, is termed brown sulphuric acid: this contains a comparatively large proportion of arsenic, and is chiefly used in making superphosphate and other artificial manures ; and the manufacturer appears to think that the acid which is too impure to be used in the arts, is good enough for making manures and for other agricultural purposes. This, however, from the experiments I shall presently refer to, appears to be a great mistake. Knowing that sulphuric acid containing arsenic was so largely employed in making superphosphate and other artificial manures, and that they therefore must contain variable quantities of that substance, I have for some time thought that it was not impro- bable that plants grown with such manures might imbibe or take up from the soil where those substances had been employed, a certain quantity of arsenic, and in this way be rendered more or less unwholesome as articles of food. As a preliminary experiment to ascertain if plants had the power of taking up arsenic when it was presented to their roots in the soil, I transplanted into a flower-pot, in June 1857, three small plants of peas, and when they had recovered the trans- planting, I commenced watering them every second or third day with a saturated aqueous solution of arsenious acid; and this treatment was continued for more than a week without its ap- pearing to exercise any immediate injurious effects on the plants. At this time, however, I was obliged to leave home for some months, so that I was unable to continue longer the watering with the arsenical solution, or to observe further its effects on those plants. On my return I found that they had grown to about their full size, had flowered, and produced seed, showing that arsenic, though so yery destructive a substance to animal life, had not apparently exercised any decided injurious effects on those plants. 110 Prof. Davy on the presence of Arsenic Having collected the stalks, leaves, and pods of the peas, I care- fully kept them for examination, to ascertain if those plants tider the treatment they had been subjected to had taken up any arsenieé: Professional business, however, of one kind or another preventéd at the time my pursuing the subject any further; and I did not resume the inquiry till recently, when, being engaged in the de- tection of arsenic in a case of suspected poisoning, my attention was again called to this subject. In the case I allude to, the quantity of arsenic present in the stomach and its contents was very minute, and I had recourse to several methods for the detection of that metal before I could affirm positively as to the existence of arsenic; and I found that by employing conjointly Reinsch’s and Marsh’s methods, by far the most satisfactory results were obtained. These methods are well known. The first consists ii boiling the suspected substance along with diluted hydrochloric acid, together with some pieces of metallic copper, when, if arsenic is present, it will be deposited in the metallic state on the surface of the copper, giving it a peculiar steel-grey appearance ; and on heating the copper after being washed and dried, the arsenic cati be volatilized as arsenious acid, and identified by its appropriaté tests. The second method consists in bringing the suspected substance, in a state of solution, in contact with a mixture of zine and diluted sulphuric acid contained in asuitable apparatus; when the arsenic, if present, will combine with the hydrogen being generated, and will form arseniuretted hydrogen, a gaseous compound which is characterized by its producing a stain of metallic arsenic when any cool surface is held over a stnall jet of the gas whilst burning. On trying by these methods the stalks and Jeaves of the pea-plants which [ had watered with arsenious acid, I found that arsenic could be readily detected in them, and was present even in the seeds; showing clearly that arsenic had been freely taken up by those plants, and that every portion of them appeared to have imbibed the poison. This experiment having shown me that arsenic might be taken. up in considerable quantity by plants without its destroying their vitality, or appearing even to interfere with their proper fune- tions, | proceeded to ascertain if the arsenic, as it existed in dif- ferent artificial manures (such as the superphosphate), would in like manner be taken up by plants growing where those manures had been applied. To determine this, I transplanted, last April, a small cabbage-plant into a flower-pot in which I had previously put a mixture of one part of superphosphate to four parts of garden mould. The cabbage after a short time appeared to recover the transplanting ; and when it had been growing in the mixture for three weeks, I cut off the top of the plant, which in some Artificial Manures. ® Sit looked perfectly green and healthy. On examining it for arsenic, I obtained the most distinct indications of the presence of that substance, though only a very small amount of cabbage, viz. 113 grains, were used in the experiment. This result was therefore perfectly conclusive as to the power possessed by some plants, at least, of taking up arsenic from manures containing that sub- stance. As in this experiment I was aware that I had placed the plant in a most favourable condition for absorbing the poison, and that a larger proportion of superphosphate had been em- ployed than was used in practice, my last experiments were to ascertain if the presence of arsenic could be detected in our crops grown with superphosphate in the ordinary way. : I procured for this purpose some Swedish turnips which had been grown with superphosphate, and having most carefully washed each turnip to remove every particle of adhering clay, I eut up in small pieces 2 lbs. weight of one of the turnips, and boiled them in a large glass flask for about three hours with 86 fluid ounces of distilled water, to which I had added 3 ounces of hydrochloric acid (spec. grav. 1:14), placmg in the mixture a hundred grains of perfectly clean and bright turnings of metallic copper. After removing the copper turnings and washing them well with water to separate the vegetable matter, and then boil- ing them for a few moments in a mixture of spirit and ether to remove any fatty matter which might have been deposited on the metallic copper; and finally, after the spirit and ether had been poured off, washing well with distilled water, the copper was found to have acquired the characteristic steel-grey appearance produced by the presence of arsenic under such circumstances. The copper turnings were then carefully dried, and afterwards heated strongly in a glass tube closed at one end, when a very perceptible white sublimate was produced, which, on being dis- solved in hot distilled water, and this solution added to a Marsh’s apparatus in operation (the hydrogen flame, which before the addition of the solution did not give the slightest indication of a metallic stain on a cool piece of white porcelain being placed over it), produced immediately the characteristic stains of me- tallie arsenic in a most striking manner, proving beyond all doubt that the matter deposited on the copper was metallic arsenic, and the sublimate arsenious acid, formed during the heating of the metal. This experiment was repeated with the same results, using 24 lbs. weight of turnip taken from another of the turnips, it being previously peeled. I may observe that in these, as well as in the foregoing experiments, I was most careful that no source of fallacy might arise from the arsenic being derived from the reagents employed, which were previously ascertained to be. free 112 On the presence of Arsenic in some Artificial Manures. from arsenic ; and to avoid all possibility of error, comparative experiments with the reagents alone were made in almost every step of the different investigations. The turnips I experimented on were grown by Mr. John Rath- bone, Dunsinea, Co. Dublin; and I was informed that six hun- dredweight of superphosphate had been used to the Irish acre,— the superphosphate being previously mixed with peat and clay, in the proportion of one part of superphosphate to three parts of the mixture of peat and clay. These experiments appear to me to be perfectly conclusive as to the power possessed, by some plants at least, of taking up arsenic when it is introduced into the soil by artificial manures which contain it, even when they are employed in the usual way and proportions by agriculturists, and how objectionable it is to use any materials in the preparation of those manures which will introduce so destructive and dangerous a substance as arsenic into the soil. I thought it would be desirable to ascertain the proportion of arsenic present in the brown sulphuric acid used by one of our Dublin manufacturers for the purpose of making superphosphate and other manures. In 12 fluid ounces of the acid, by the usual methods of determining the quantity of arsenic in such cases, I obtained an amount of metallic arsenic equivalent to about 12 grains of arsenious acid, or 1 grain to each fluid ounce; and the ounce of acid weighing about 800 grains, the arsenious acid would be z1,,th part of the weight of the acid, which would be equivalent to about 2°8 lbs., or nearly 3 lbs. weight in the ton of sulphuric acid. But it is probable that the generality of brown sulphuric acid employed contains much more arsenic than this sample I examined, its specific gravity being only about 1-780, whereas the usual strength of the acid is 1°845. Dr. Owen Rees found 13°5 grains of arsenious acid in 12 fluid ounces of commercial sulphuric acid ; and Mr. Watson, in the London Medical Gazette, states that the smallest quantity of arsenious acid which he detected in the same amount of commercial acid was 21°3 grains. There is therefore every reason to suppose that the acid usually employed for agricultural purposes contains a far greater quantity of arsenic than the sample I examined ; and as the proportion of sulphuric acid used in making these artificial manures is very large (thus, for example, in the manu- facture of superphosphates, the most valuable manure of this class, about one ton of acid is used for every two tons of bones employed), the quantity of arsenic present in such manures must be considerable. These facts appear to me to have some important bearings ; for though the quantity of arsenic which ocewrs in such manures On the Measurement of the Specific Gravity of Liquids. 118 is not large when compared with their other constituents, and the proportion of that substance which is thus added to the soil must be small, still plants may during their growth, as in the ease of the alkaline and earthy salts, take up a considerable quantity of this substance, though its proportion in the soil may be but very small. Further, as arsenic is well known to be an accumulative poison, by the continued use of vegetables contain- ing even a minute proportion of arsenic, that substance may col- lect in the system till its amount may exercise an injurious effect on the health of man and animals. As connected with this subject, I may observe that I was in- formed of a curious fact,—that sheep did not appear to like Mr, Rathbone’s turnips which were grown with superphosphate, so well as those where the ordinary farm-yard manure had been employed, and that they could not be made to eat enough of the former turnips to fatten them properly. If this was really the case, it would appear to favour in some degree my views as to the probable unwholesomeness of vegetables grown with manures containing even in smal] quantities so deadly a poison as arsenic, which my experiments have shown that plants are capable of taking up from such manures. Finally, these investigations appear to have a medico-legal bearing ; for in cases of suspected poisoning by arsenic, where the evidence may chiefly depend on the detection of a small quantity of that substance in the liver and other viscera, as is sometimes the case, my experiments would tend to throw much doubt and uncertainty on such cases, because the presence of a minute quantity of arsenic in the viscera may not be owing to its direct administration, but to its having found its way mto the system through the vegetable and, indirectly, animal food taken by the individual. These and other important considerations connected with this subject can only be determined by aseries of carefully conducted experiments, which 1 purpose commencing, and I hope at some future time to have the pleasure of communicating their results to this Society. “ XXI. On the influence of Capillary Attraction upon the Hydro- metrical Measurement of the Specific Gravity of Liquids. By Cu. Lanesure, late Professor of Natural Philosophy at Christiania*, [* order to test the accuracy of an hydrometer, you may either immerse it in various test-spirits of known alcoholic strength, or you may adopt Brisson’s method, which, as is known, * From Poggendorff’s Annalen, vol. evi. p. 299, Phil, Mag, 8, 4, Vol. 18, No, 118, Aug. 1859, I 114 Prof. Langberg on the influence of Capillary Attraction upon consists in loading the instrument with the weight that sinks it (or rather that ought to sink it) in water to the division mark of the scale, at which the unloaded instrument floats in a liquid the specific gravity of which is indicated by that particular mark. As I was trying several hydrometers in both these ways, 1 was struck by the fact that they never gave altogether consistent results. If, for instance, the instrument tested according to the first method appeared to be accurate, according to Brisson’s method it always showed an excess of alcohol in a given mixture. Hydrometers, for example, made at Berlin (even those adjusted at the Royal Prussian Gauge Office) showed from half to one per cent. too little aleohol in comparison with the actual density of the liquid, while the same instruments tested according to Bris- son’s method were found almost correct. After due consideration, I think the following explanation may be given of the circumstance in question. . If a cylinder be floated upright in a liquid that wets it com- pletely, the latter, as is well known, rises all round the cylinder against its sides and forms a conical surface, which below spreads out asymptotically to the horizontal surface of the liquid, and above joins the surface of the cylinder with a sharp turn, so that the tangent of the generating curve at the highest point is ver- tical. Now this elevated fluid ring must exert a downward force equal to its weight or hydrostatic pressure, and, if the cylinder float upright, must sink it as much deeper as would be the case if no portion of the liquid were elevated by capillary attraction, but the weight of the cylinder itself were increased by an amount equal to the weight of the liquid raised. If a cylindrical disc, a4, be brought into contact with the surface of a liquid that wets it, and be then slightly raised, the liquid follows it and rises also in the form cabd. Now this elevated liquid column exerts on the dise a downward force, which may be considered as consisting of two parts; one due to the weight of the cylindrical portion a op, the other to that of the conical ring aoc, bpd. The first of these is known the Measurement of the Specific Gravity of Liquids. 115 when the distances ab, ao and the specific gravity of the liquid are given; the other part might be calculated if the equation of the curved surface acbd were known. If y denote the height eg of any point in the curved surface above the level of the liquid, p and p! the radii of greatest and least curvature of the surface at that point, and m a constant, then generally bes I y=n(5+ 7) eC irs tee (1) an equation first evolved by Young*, and afterwards confirmed by the researches of Laplace+, Poisson{, and Gauss§. Young proceeded on the hypothesis that there existed in the surface of a liquid a sort of tension, which was the same at every point,—an hypothesis which agrees entirely with the later researches above as al to, though the latter partly rest on other suppositions as well, If, now, T denote the tension in a strip of the surface whose breadth is unity,and é the weight of a unit of volume of the liquid, the constant in the above expression is, according to Hagen ||, a Mase ee ee ee ee @) At the highest point of the curve bed (whose ordinate bp we will indicate by H), p! is equal to the radius of the cylinder itself, and p to the radius of greatest curvature of the curve bed, which by revolution round the axis of the cylinder, describes the capil- lary surface of double curvature. And it is easy to see that these two radii lie in the same straight line, and that the one is positive and the other negative. In this case, therefore, equa- tion (1) takes the form y=n(2-3). ile Pade ean Although it is not difficult from expression (2), given above, to find the differential equation of the curved surface, the inte- gration of that equation is involved in great and probably insu- perable difficulty. I have therefore adopted the same method as Hagen 4], whereby, although the equation of the surface is not found, m receives a * “ An Essay on the Cohesion of Fluids,” Phil. Trans. 1805. + “On Capillary Attraction,” and “Supplement to the Theory of Ca- pillarity,”’ Mécanique Céleste, vol. iv. (1805). { New Theory of Capillary Attraction (1831). § “Principia generalia theorize figure fluidorum in statu aquilibrii,” Comm..Soe. Scient. Gétting. vol. vii. (1829), || Poggendorff’s Annalen, vol. Ixvii. p. 1. §| Ibid, vol, Ixvii. pp. 27 and 28, I2 116 Prof. Langberg on the influence of Capillary Attraction upon value by means of which T can be calculated, when H is known from observation. If we admit that which is in itself very probable, namely that the generating curves of the capillary surfaces raised by all wetted cylinders of whatever radii are similar, or even (what in this case is alone essential) that the radius of curvature of the generating curve at its highest point bears a constant proportion to the ordinate of that point, then we have pope a: or yl OP, Fale where p denotes the radius of curvature answering to the height H, p"' that answering to the height H". If, now, 7(=p'), the radius of the cylinder, be infinite, that is to say, when a plane surface is placed upright in a liquid, equation (3) can be integrated without difficulty, and we find* p'=iH" and p=i3H; so that from (3) we have eal m H H=m(5—->)=F(2- 5)» H?2 m= Ao oe Paes, r or If, then, x and H are determined by measurement, m( = = can be easily calculated. In order to test how far the above hypotheses are correct, Hagen measured the height H for discs of different radii, and thereby discovered that the difference between the observed and calculated heights fell within the limits of error of observation. Having made several experiments with floating cylinders, I have arrived at the same conclusion. Equation (4) may therefore, it seems, be applied with confi- dence. If in this manner m, and thereby T, be determined, the downward force exerted by the body of water elevated by the dise may easily be calculated. The weight of the fluid cylinder abop = Unr?k, and the force exerted by the above-mentioned ten- sion =2zrT; wherefore, the whole downward force being denoted by G, we have G=Horrk+2erT. 2 we wend) * “On Fluid Surfaces,” Poggendorff’s Annalen, vols. Ixvi, and lxxvii. the Measurement of the Specific Gravity of Liquids. 117 For a floating hydrometer properly wetted, we have, then, G=2rrT=2armk ; and the effect of this force must obviously be the same as if the weight of the instrument had been increased by G. Let, then, h denote the increased distance to which the hydrometer sinks in the liquid when loaded with the weight G; then, ifm and T are determined by observation, # may be calculated as follows :— Let V be the volume of the part of the hydrometer immersed in the liquid in consequence of its own weight P, dv the increased volume immersed by the additional weight G; then ii: V Geer: and since 1 vi ke? PG G aha anes but dv=tr*.h, por Seta SIT TI: and if the value for G above determined, namely 2amrk, be sub- stituted, we get _ 2m =—. h PEE SS (6) If the constant m has different values for different liquids, it follows from this that an hydrometer, the scale of which is cor- rect for a given liquid, will be incorrect for others. Should the scale of an hydrometer be divided according to Brisson’s method, it will sink either too deep, or not deep enough in the liquid for which it is designed, according as for that liquid m is greater or less than for water. Let, then, /! express in the case of the liquid in question the same as / does for water, then the error in the position of the division of the scale caused by capillary attraction will be expressed by h—W’. In order to determine how far the observed differences in the readings of hydrometers mentioned at the beginning of this paper could be explained on the above grounds, I made a large number of measurements which appear to confirm completely the correctness of my hypothesis. For the purposes of compa- rison I made use of the following instruments :—I1st, an hydro- meter, No. 53, by Ch. F’. Geissler of Berlin ; 2nd, an hydrometer of J. G. Greiner of Berlin; 8rd, another instrument by the same 118 On the Measurement of the Specific Gravity of Liquids. maker (all fitted with Tralles’s scales); and 4th, one of Gay- Lussac’s hydrometers made by Nissen of Copenhagen. The error in the division scale, or h—/’', was determined in the following manner :—A glass cylinder, of radius 17°821 mil- lims., was placed upright in the spirit to be examined; a fine steel needle, also upright, was fitted to the cylinder in such man- ner that it could be elevated and depressed by means of a micro- meter-screw, so that its point could be brought into contact with the surface of the liquid. By means of a very exact catheto- meter, the distance between the upper end of the needle and the raised edge of the surface of the capillary ring of liquid was measured, and thus the length of the needle bemg known, the height H was determined. As the specific gravity of the spirit under examination was known, m, T, and h—/’ could then be calculated. For several samples of spirit the following values of H, m, and T were found (1 millimetre being taken as the unit of length) :— She of sleohal ‘a Temperature Pe T in milli- 60° Fabr. Cent. grammes. 84:63 2:2125 178 2:7970 2:3770 69°81 23295 16:8 31213 2°6526 56°20 23727 15:6 3°2472 2-9900 49:19 23930 18-2 33073: 3:0922 40°42 2°4539 18°8 3°4916 33101 29°52 2°6546 178 3°7813 3°6494 14:23 | 2°7462 _ 138°0 4°4570 4:3748 If the per-centage of alcohol be taken as the abscissa and T as the ordinate, the curve representing the tension will be seen to be convex towards the axis of z. From 0 to 40 per cent, it falls rapidly, but afterwards it presents only a slight curvature. This is still more obvious if the weight per cent. of aleohol be substituted for the volume per cent. The curve, then, between 30 and 80 per cent. is very nearly a straight line, and the tension T can, between these limits, be calculated with sufficient prac- tical accuracy from the formula T=a—dp, where a=3°96798, b=0-0204867, and p is the weight per cent. of alcohol. In this manner, for instance, we find Volume per cent. | Weight per cent, T calculated from| Diff. from T as the last formula, observed. 84-63 79-06 23483 +.0-0287 69°81 62°31 2°6914 —0:0388 56:20 47:57 2°9984 —0:0034 49:19 41°77 31123 —0-:0201 40°42 33°76 3°2763 +0:0338 On the Distribution of Electricity upon Spherical Surfaces. 119 The average error for T being 0:036 millim., the probable error 0:024 millim., which, in the determination of h—V', is quite inappreciable. In order, finally, to compare the calculated errors (h—h') in the scalar division with those observed, numerous experiments were made with the four instruments above mentioned, the results of which are put together shortly in the following Table :— Alcohol per h—-h', No. of obser- cent. by : No. of tone! matt = vant: volume. mtrament: Calculated. | Observed. | Error. 1 045 | 0-43 +0-02 per cent. i | 8463 | 2 049 | 0:59 —010 ,, 3 063° | 0°63 0:00 ~—C*=,, 1 0:52 | 0:44 +008 5 , 2 0:57 0:60 —0:03 a tae 3 075 | O76 | 0-01 eg 4 0-40 0:44 —0:04 5 | 1 0-69 0:57 +012 =~, 2 0-70 | 0-78 | —0-08 Meet aig 3 0-88 | 0:88 0-00 4 0:49 | 040 |4009 —,, / 1 0-79 | O91 |-—Ol12 ,, 4, | 40°42 2 0380 | 0:90 O10 55 3 103 | 1:07 =O0:04, 4°, It appears from this Table that the difference between the observed and calculated values of h—h! only twice reached °12, which on the scale answered to about *2 millim., a degree of accuracy which must be pronounced to be perfectly satisfactory. XXII. On an Analytical Theorem relating to the Distribution of Electricity upon Spherical Surfaces. By A, Cayury, Esq.* HERE is contained in Plana’s Mémoire sur la distribution de Vélectricité & la surface de deux spheres conductrices com- pletement isolées (Mém. de Turin, vol. vii. 1845), an identical relation which is remarkable, as well in itself as because by means of it the author corrects an error into which Poisson had fallen in his researches on the same subject. The development of a certain definite integral is obtained in the form (equation 165) MA .,1,, 3.4.5Mh 25 peat t ry oi Poisson had in effect shown that M,=0; and he thence inferred y=—2.3 sin 6+ &e. * Communicated by the Author. 120 Myr. A. Cayley on an Analytical Theorem relating to that, 6 being small, the function in question a sint 50, or what is the same thing, «(1—cos@)*?. In the former part of the memoir, Plana shows that this is not the true form of the deve- lopment ; the foregoing development must therefore be illusory ; and Plana in fact shows, by a laborious induction carried as far as M., that all the coefficients M vanish identically. The iden- tical equation M;=0, where 7 is any positive integer whatever, constitutes the analytical theorem above referred to. Plana’s expression for the function M; is as follows:— B,, B;, B;, &e. denote Bernoulli’s numbers as given by the equation t i i i seq ey Tipe 1 Ne en (B exe B aa B ai B a &e. I have, in conformity eG. er OU ke AS ae aia Te ; with the usual practice, written the equations so as to make these numbers all positive; with Plana they are alternately po- sitive and negative). And in the equation 162, writing for & its value isp we have, X being any positive integer, mara ORS ee Phe ae NA] OB) Onset a abe acs cae eae _AA=1.A=2.2=3p (140)! ean eo Ke S38 NAKL.AHZ-AWB-A—4 AHR (140) 1 19S 5 26 ban + &e., where the series is continued for so long as the factor in the de- nominator is positive. It should be observed that this factor really divides out, and that the rule just mentioned amounts to this, viz. that when 2 is odd, the finite series on the right-hand side is to be continued to its last term; but when 2 is even, the series is to be continued only to the last term but one. And G) being thus defined, the expression for M,; (see equation 164, : syd in which I have written for & its value ia is é' : 1 : j 2 Mp= (140) 4 Get (+2) TF Gas +648) 5A") ins a T.2 : }.2—1 /1+53 ++ (=) Gis + &e. es the Distribution of Electricity upon Spherical Surfaces. 121 where on the right-hand side the finite series is continued up to its last term, the value of which is obviously i+] i+1 (142141) at?) euubaiice cs rene But the form of this equation may be somewhat simplified. We in fact have —lui- 7421 es wen aude i41ii—1 y ein 1s+2 50+) +B +0 —B Te 40 5 74+-3.21 1] 7+2 12.4 ag 2 — SEE eee 4 Te a at tO +B +UP—Be Te (1+0)'4 &e, b, which is at once changed into il. a+oMea st {1504543 tea oy Bea +0)'+ &e, 11 1i+2 i+2.i41 : Toma 7 Oto +B ATS 4) 2+2.i+1.2i—1 ee haa et we. b . 1 care +7 9p{l- 5148 (1 40)4B, 1+38. ey LEBER yy xe, | + &e. Or multiplying by ¢+1, and then putting i—1 in the place of z, we have ee! i—1 1 a(1+)M;-,=0;+ a e O14 oe Oj42+ &c, =0, aH @,=1-}! iis 1i-2.i-3 2 4 )?—B, 1.234 (1+0)4+&e, In this last sie ce the finite series on the right-hand side is, when 7 is even, to be continued up to its last ter m, but when i is odd, then only up to the last term but one. And the equa- tion to be proved is —ll 0= @,+ = I Be Sinise . 9 i Oj+2 + &e., 122 Mr. A. Cayley on an Analytical Theorem relating to where on the right-hand side the finite series is to be continued up to its last term. And the equation holds for any integer value of i whichis 2. This is the simplest form of Plana’s theorem. We have 0;=7(14 d)'G;_,; or writing this equation under the form ©;=7(1 +) ay and comparing with Plana’s developed expressions for ai (which are continued by him as far as Gj7), we find ©, =—6, B,= Tet ny ae Bee 8, = b?, — lpa2ye — 29-1 e, = 5? +5 30 rad ‘ ee Lio 933 — Lys 0,= 54 20 52 ; omy | e435. Ah 51 136 0, =—-go- 4 go + gli + D+ ED, ae 2 50 3423p, 54 2 76 e, = 3? + 4b +a bit 40+ 50, _» 8, , 12s | 84,5. 24, 28, 82, 125 35, Oo= — 3°12 — 8705403701207 — 3 as, &e., which are of course the results obtained by developing the fore- going expression for ©;, in powers of b, and collecting the terms. The formule put in evidence a remarkable symmetry which does not exist in the original expression in powers of (1+). It would be now easy to verify, for moderately small values of the suffix, the equations 2 1 @,+ 5 @,+ pe O1=9% 3 3 1 @;+ 5 Oat Fz Ost Fs Oe=0, 28 &e. This is, in fact, Plana’s process, which, however, as the suffixes the Distribution of Electricity upon Spherical Surfaces. 123 increase, becomes a very laborious one, and the law of the terms which destroy each other is not in anywise exhibited thereby. I have succeeded in obtaining a complete demonstration, founded on Herschel’s theorem for the development of a function of e', and the expression thereby given for Bernoulli’s numbers. The theorem in question is, that for any function of e* which admits of development in positive integer powers of ¢, f(e)=fl+ Ajet, where the right-hand side denotes the series the general term whereof is i” ¥ Lo 6g and f(1+A) is of course to be developed in powers of A, and the different terms A, A*%, A’, &c. applied to the symbol 0” (viz. AO”=1"—0", A?0"=2"—2.1"+0", &e.). This gives _# _log (+4) 2. | e—l A And comparing the development of the right-hand side with the development i pa he lig ie IO pare oe eke te he we find 7 log (1+A) po _ Az ol log (1+4) m1 A ome log (1+A)_,, . A 0° =(—) + Bega log (1+A oe tO) 9-10 (a> 1). It is now easy to obtain the equation log (1+ A) i i ==, —{G+00+4)) —(—0(1+2))'}. In fact, the first two terms of the development of the expression on the right-hand side agree with those of the foregoing expres- sion for ©,. For any even power 2w (except, when ? is even, the power 27=7) the term is [i] a, log (1+) 4, feu ae HO) rer ns os 124 Mr. A, Cayley on an Analytical Theorem relating to which agrees ; and when 7 is even, then for the power 2x=i there are twojequal and opposite terms which destroy each other, and the whole term in @; is, as it ought to be, zero. For any odd power 2x—1 (> 1) (including, when ¢ is odd, the power 2a—1=7), the term vanishes as containing an evanescent factor. And the expression for @; is thus shown to be true. I write for shortness, log (14A).., <, 6 or, where X=1+40(1+0), Y= —0(1+0). Forming the expression for 7(1+ ae -—1l > 9 b? +5 Oi42+ &e., =@0;+ ds Oi41 ia this is rl soem P®08{ (x(443))-(x(0+ DY and we have =(1+0)(1+)—2, and .. + 1+) b 1+ =(1+0)——, (x(14+ F)) =(FE) +9104 0040)—a}, Y=—0(1+d), uA 1+). 1 1+ ,— a a a mae p (0(1 +2) —3}, (v(1+5)) =74*) @oa+H-0): We see that the expression for (xQ + *))is deduced from that of (¥(1+4 5 )) by writing therein 1+0 in the place of 0; we have therefore (x(1+8))'a040i(x(0+4))) * - the Distribution of Electricity upon Spherical Surfaces. 125 and consequently (x(1+4)) - (x(1+7 y. =A(¥(1+5)) _( —-) a(0(0(1 +2) —2})* Whence also i(1+))Mi= (2+?) og (1+A)(O{0(1+4)—4})4 We have by the general theorem, t= log e‘= log (1+ A)e‘:°; and consequently whenever z <{< 2, log (1+ A)0"=0. But 7 <|< 2, and the function (0{0(1+4)—4})! contains only O' and the superior~powers ; it is therefore reduced to zero by the operation log (1+ A), and we have z.7—-1 1 a ae and the theorem in question is thus proved. The foregoing ex- pressions for @,, ©, &c. show that these functions all divide by 6, and moreover that when 7 is even and greater than 2, then that @,; divides by 8? The equation @,= EEF) 4001 +0))'—(—001-+8))'} u(1 +4)Mi1=O;+ 7 +; O;+1 + —————_ Oi+e+ &e.=0; gives generally for the term in ©; involving 4*, the expression (a* ,«bes as [#]" And it is to be shown, first, that the coefficient vanishes for a=0 ; and next, that when 7 is even and > 2, the coefficient also va- nishes fora=1. Putting «=O, the coefficient is log (1+ A) A {(1+0)'-20*—(—0)'}. {(1+0)'—(—0)'}, which is equal to eT 1 A—(—J1}0, 126 On the Distribution of Electricity upon Spherical Surfaces. or to ‘ : ._, log (1+A) , Jog (1-+A)0'+ (1—(—)'1} “ES Aoy, where, since i << 2, the former term vanishes, as above remarked ; and the latter term, when 7 is even, vanishes on account of the factor 1—(—)'1; and when 7 is odd, on account of the other factor. Hence the coefficient vanishes for e=0. Next, if i is even, and a=1, the coefficient becomes log (1+A ae : Set ta 10) one), which, writing (1+0)—1 for 0, becomes log (1+A ° ; se Eoke at +0)'—(1+0)"~’ —0}, which, since (14+ 0)'—0'=A0', (14+.0)?=(14+A)0°", is equal to log (1+ A)O'— (1+ A) 1g (1+A) om}, or since the first term vanishes, to __ (1+A) log (1+A) A om But this function is to a numerical factor prés the coefficient <= J auadae we write —? in the place of ¢, we find t u of 75m ee , or what is the same thing, in in the expression for ay t 4 jt Ss st+Bi yy ae SEO | + &e. Hence 7 being even and greater than 2, the function in question vanishes. Hence in the case the coefficient vanishes for a=. Writing 6 for z i—a, OF assuming «+ 8=i, the symmetry of the foregoing expressions for O4, Os &c. shows that we ought to have log (1+A eeu {(l EO O = (— =0)**F} , where the upper or under sign is to be taken according as a+8 Mr. C, P. Smyth on Teneriffe Fossils. 127 is even or odd. Or separating the two cases, we find log (1+A 28 CF) (1 +0)'0°—(1+0/°0"}=0, 2 +8 even, and log (1+ A ae i £(14.0)°0° + (14-0)°0"+2.0°*}=0, «+ Bod. I have not attempted to verify & posteriori these elegant formule. 2 Stone Buildings, W.C., June 18, 1859. XXIII. Teneriffe Fossils, and Sir Charles Lyell’s Notice in the Philosophical Magazine for July 1859. By C. Prazz1 SMytH. To the Editors of the Philosophical Magazine and Journal. GENTLEMEN, Edinburgh, July 16, 1859. ITH some surprise I see, on page 21 of the Philosophical Magazine for this month, that Sir Charles Lyell has dragged into print a portion of a private letter. While glad in any way to learn the scientific opinions of so highly and deservedly esteemed an authority as the celebrated author of the ‘ Principles of Geology,’ I regret that I cannot in this case agree with him, or allow that he has materially invali- dated any essential part of my ‘ Teneriffe Report for 1856.’ He allows, for instance, that the important information there given, of fossil shells having actually been discovered in Teneriffe, is perfectly true; but objects, first, to the discovery being spoken of as “late,” rather than “old;” and secondly, to the locality being alluded to as “on the slopes of the great crater.” Yet with regard to the first objection, he does not give any earlier printed authority than my own pages; and with reference to the second, absolutely refuses all discussion of what it must depend on,—under plea, too, of certain @ priori opinions, which could not have been shared in by the Royal Society Committee of June 1856, when they recommended to the Admiralty that “ there are also various points of interest relating to the geology and geo- graphy of this region (Teneriffe) which Prof. Smyth may possibly find time to attend to.” (See page 476 of part 2 of Phil. Trans. for 1858.) Sir Charles Lyell moreover alleges, at the very opening of his communication, that my ‘ Report’ has been printed by the Admiralty since the publication of a paper of his in the Phil. Trans. for 1858, part 2. But as the last one, of the few pages that were printed by the Admiralty, was worked off on the 4¢h of 128 Fritzsche on Isonitrophenie Acid. February, 1859; and as the part of the Phil. Trans. cited was not published until three months afterwards—or, more exactly, on Monday, May 16, 1859,—it is plain that the facts of the case have been inverted in the pages of the Philosophical Magazine. This point is of the more importance, as Sir Charles Lyell immediately proceeds to say, at the end of his first, and begin- ning of his second paragraph, that in the ‘Report’ so printed by the Admiralty, 7. e., according to him, subsequently to May 16, 1859, a “chapter on geology and ‘volcanic theories’ is introduced,” “ which did not form part of the original Report as published by the Royal Society in the Philosophical Transac- tions for 1858.” In answer to which it may be enough to state that the “original Report” was presented by the Admiralty, through the Astronomer Royal, to the Royal Society nearly zwo years earlier than_the date indicated, or on June 2, 1857, and contained a chapter on “ Geology ;” also, that all the chapters were revised on going through the press. I have the honour to be, Gentlemen, Your obedient Servant, C. Prazzi Smytn. XXIV. Chemical Notices from Foreign Journals, By Hi. ArK1n- son, Ph.D., F.C.S., Teacher of Physical Science in Cheltenham College. [Continued from vol. xvii. p. 430.] peda * hasinvestigated nitrophenicacid, C!*H*(NO*)O? (nitrophenole). It is obtained by distilling a mixture of 2 parts of pure hydrate of phenyle, 100 parts of water, and 3 parts of strong nitric acid. The nitrophenic acid passes over in the form of oily drops, which crystallize on cooling; subsequently an aqueous solution distils over, which, when cooled to 0°, also de- posits crystals. The ‘acid, when purified by redistillation and crystallization from alcohol, is of a pale yellow colour with an aromatic odour. It melts at 45° and boils at 214°, It is readily soluble in alcohol, ether, and benzole. The nitrophenates, C!? H* (NO*) M 0%, are of a scarlet-red or orange colour, according to the quantity of water of crystalliza- tion which they contain. The residue remaining in the retort from the preparation of nitrophenic acid contains a new acid isomeric with nitrophenic acid, and to which Fritzsche gives the name isonitrophenic acid. This is easily obtained by slightly modifying the above propor- * Bulletin de St. Pétersburg, vol. xvi. p. 11. Liebig’s Annalen, May 1859, M. Griess on Phenylic Alcohol. 129 tions, and proceeding as in the preparation of nitrophenic acid. When about half the liquid is distilled off, the residue in the retort is filtered while hot; on cooling, drops of the new acid are deposited. A resinous mass remaining on the sides of the retort is exhausted with boiling water, the filtered aqueous solu- tion mixed with excess of caustic soda, by which a yellow cry- stalline precipitate of isonitrophenate of soda is obtained. The acid is obtained by dissolving the purified soda salt in warm water and adding hydrochloric acid. On cooling, the liquid becomes turbid, and then filled with a mass of fine needles. These needles are quite colourless: they are very soluble in ether, and are obtained on evaporation from an etherial solution in large crystals with a fatty aspect and a reddish-yellow colour. These appear to constitute a dimorphous modification of the colourless needles. On evaporating the aqueous solution of the coloured crystals, the colourless needles are again obtained. The needles again become coloured by the action of light. Isonitrophenic acid fuses at 110°, under water it fuses at 40° or 50°. It volatilizes partially below its fusing-point. It forms acid and neutral salts, but must be regarded as a monobasic acid, for it only forms one kind of ether. Isonitrophenic ether crystallizes in colourless prisms very soluble in ether, Some further derivatives of phenylic alcohol have been de- scribed by Griess*. Dinitrochlorophenylic acid, C'* H? (NO*)? ClO?.—Chlorine is passed for some time into phenylic alcohol; the resultant chlori- nated product is mixed gradually with three times its bulk of strong nitric acid: the action begins in the cold, and is accom- panied by disengagement of red fumes, and of an odowr resem- bling chloropicrine. When the action is over, the oil is washed to remove oxalic acid, and then treated with aqueous ammonia, by which it solidifies to a mass of crystals consisting of dinitro- phenylate of ammonia. The free acid is obtained by treating a boiling solution of this salt, purified by frequent recrystallization, with nitric acid, by which the acid is set free in beautiful golden- yellow laminz. It is more soluble in alcohol and ether than in water. It dissolves in strong sulphuric, hydrochloric, and nitric acids, and is separated by the addition of water. _ The dinitrochlorophenylates are distinguished by the great beauty of their crystals: they all dissolve with difficulty in water, and are deposited from a hot aqueous solution, on cooling, in reddish or yellowish crystals. Duinitrochlorophenylate of silver, AgO, C!? H? Cl] (NO*)?0, when erystallized from water, is ob- * Liebig’s Annalen, March 1859. Phil, Mag. 8. 4. Vol. 18. No. 118. Aug. 1859. K 130 M. Duclos on Cresylic Alcohol. tained in beautiful carmine-red laminz with a green lustre, and which appear under the microscope in acute rhombic columns. Amidonitrochlorophenylic Acid, C'* H* C] NH? (NO*) O?, — When dinitrochlorophenylic acid is digested with sulphide of ammonium, the solution assumes a blood-red colour, and sulphur is deposited. On evaporating the filtrate and adding acetic acid, this acid is obtained. It is not very soluble even in hot water, and crystallizes out on cooling in yellow silky needles. By passing a current of nitrous acid through a solution of this acid, it is transformed into a new acid, which the author names diazonitrochlorophenylic acid, C!? H8 Cl (NH?)(NO*) 0? + NO?=C!* H?CIN?(NO*)0?+3 HO. Spada ree FORNEY Ye Dipcontjrorlorpphensa acid. acid. The author views this acid as being derived from nitrochloro- phenylic acid, C!* H* Cl (NO*) O?, by the substitution of two atoms of hydrogen by two atoms of nitrogen. In an investigation of the creosote from coal-tar oil, Fairlie established the existence of a new alcohol, C'4 H® 0, hydrated oxide of cresyle, homologous with hydrated oxide of phenyle, Duclos* has confirmed the existence of this alcohol in coal-tar creosote, and has further found that it is contained in wood-tar creosote. The crude wood-tar was rectified, and the distillate between 150° and 220° C. collected. By treating this with solu- tion of soda the neutral oils were removed, and the soda solution was decomposed with sulphuric acid. This treatment was re- peated until the product was quite soluble insoda. It was then washed with water, dried over chloride of calcium, and fraction- ally distilled, by which a fraction boiling at 187° consisting of phenylic alcohol, and one boiling at 203° consisting of cresylic alcohol, were obtained. In his description of the properties of cresylic alcohol, Duclos confirms the statements of Fairliet, but observes, contrary to what had been stated by Gerhardt, that cresylic alcohol is about as soluble in ammonia as phenylic alcohol. Potassium liberates hydrogen from eresylic alcohol, and forms a deliquescent crystalline mass consisting of fine needles. Cre- sylic alcohol dissolves in sulphuric acid with a reddish-brown colour and formation of sulphocresylic acid, the lead and baryta salts of which do not crystallize. Mononitrocresylic Acid, CH’ (NO*) O?, is obtained by the cautious addition of very dilute nitric acid to an aqueous solu- tion of cresylic alcohol. It is a yellowish-brown liquid of a * Liebig’s Annalen, February 1859. T Ibid. M. Hlasiwetz on Isopurpuric Acid. 131 syrupy consistence, is inodorous, and colours the skin yellow. It appears to combine with ammonia and potash. Dinitrocresylic Acid, C'4 H® (NO*)? 0%, is best obtained by warming an aqueous solution of sulphocresylic acid with a little nitric acid and then allowing the mixture to cool. A resinous body separates, which is filtered off, and the filtrate then heated to boiling, and dilute nitric acid added. An oil separates which has the above composition, and in its properties resembles the mononitrated compound. Trinitrocresylic Acid, C\* H® (NO*)3 O?.—This is obtained by heating a solution of sulphocresylic acid with nitric acid. The resinous body which at first separates is filtered off, and the filtrate evaporated with excess of nitric acid to dryness: the binitro-compound at first formed is changed into trinitrocresylic - acid, which along with oxalic acid is contained in the residual mass. Trinitrocresylic acid crystallizes from alcohol in fine orange- yellow needles. It dissolves in 450 parts of water at 20°: picric acid dissolves in 80 parts at the same temperature. Heated to above 100° it melts to an oil, which solidifies, on cooling, to a crystalline mass. Treated with hypochlorite of lime, the odour of chloropicrine is obtained. Trinitrocresylate of potash consists of fine yellow needles, very soluble in water, and which detonate strongly when heated. The study of the reduction of organic nitro-compounds has hitherto been limited to that of the action of sulphide of ammonium, of sulphite of ammonia, of acetate of iron, and of nascent hydrogen. Hlasiwetz* has examined the reducing action of cyanogen on picrate of potash; andthe curious results he has obtained promise for this agent a more extended use. When hot concentrated solutions of cyanide of potassium and of picric acid are mixed, the solution immediately assumes a blood-red colour, becomes filled with fine dark crystals, and, on cooling, solidifies toa mass of crystals. The mass smells strongly of ammonia and of hydrocyanic acid: it is expressed between bibulous paper, subsequently washed with a small quantity of cold water, again pressed, and then dissolved in hot water and filtered. The purple-coloured filtrate soon deposits brownish- red laminar crystals with a green lustre. These form the potash salt of a new acid, which the author names isopurpuric acid. The potash salt is but little soluble in cold, but readily so in hot water. The solution has a most intense purple colour. Heated on platinum, the salt detonates. Its solution precipitates the * Liebig’s Annalen, June 1859. K2 132 M. Hlasiwetz on Isopurpuric Acid. salts of silver, lead, mercury, and baryta, but not those of lime, strontia, zinc, and copper. The composition of the potash salt is C!’H*K N°O!; and from two nitrogen determinations made by means of soda-lime, it appeared that 2 equivs. of nitrogen were contained in a form other than that of NO*, Cyanogen could not be detected. The soda salt is obtained by treating picric acid with cyanide of sodium. It is more soluble than the potash salt, and is of a dark green colour with metallic lustre. The ammonia salt, C!® H4 (NH*) N° O!, forms beautiful wedge-shaped crystals of a brownish-red colour and green lustre. The baryta salt, formed by adding the potash salt to a solution of chloride of barium, is a vermilion-red precipitate, which when dried possesses a splendid light-green metallic lustre, and when rubbed becomes red again. The lime salt, C!®H*CaN°O!? +3 HO, formed by adding solution of chloride of calcium to a solution of the ammonia salt, forms very beautiful green needles, often half an inch long, and with a metallic lustre. The lead salt, when ery- stallized from hot water, in which it is somewhat soluble, appears under the microscope in the form of very fine reddish-brown needles, possessing a green lustre. It was not possible to obtain the free acid. When the potash salt was decomposed by means of a stronger acid, further decom- position was set up. For this reason it is not possible to dye with solutions of the salts, beautiful as they are; for without mordants, the colours on cloth are neither beautiful nor perma- nent, and on mordanted cloths decomposition is soon induced. - The salts of this acid are isomeric with those of purpuric acid (which is also unknown in the free state) obtained from uric acid; on this account it has been named isopurpuric acid. Like purpuric acid, isopurpuric acid appears to be bibasic. The salts of the two acids present great similarity, both as respects colour of the solutions, solubility, and deportment when heated. The optical relations of the isopurpurates were examined by Grailich. Isopurpurate of ammonia and murexide (which are isomeric) are perfectly similar in their optical and crystallogra- phical deportment. They appear to belong to the rhombic system. The formation of isopurpuric acid may be expressed by the following equation :— C!? H3 (NO*)80? 4+ 3C?NH +2 HO=C'* H°N°O!?+C?044 NHS, Picric acid. Hydrocyanic Isopurpuric acid. acid. Free picric acid is not altered either in the cold or in the warm by hydrocyanic acid; but the reaction is immediately set up in the presence of a base. In reference to the rational constitution of isopurpuric acid, it M, Nachbaur on a New Base. 133 may be observed that it differs from picramic acid (which is also produced by the action of reducing agents on picric acid) by the elements of cyanic acid, C!2 H5 N3 0104 C4 N202=Cl6 NS FS OL. Picramic acid Tsopurpuric acid. But picramic acid could not be detected among the products of the decomposition of isopurpuric acid. Geisse* has found that chloropicrine, C? Cl’ NO4, when sub- mitted to the reducing action of acetate of iron, or of protosul- phate of iron, is converted into methylamine. The action is in accordance with the equation He CCP NO'+12H=NJ © ye +3HCl+ 4HO. Chloropicrine. Methylamine. By distilling acetate of lime with prussian blue or with cya- nide of mercury, Bonnet obtained a product consisting of water, and a colourless, neutral, uninflammable liquid, with an odour resembling both prussic acid and tobacco smoke. This substance he stated to be cyanoform, C? H Cy, analogous with chloroform, iodoform, &c. Nachbaur} has investigated this reaction, and has found that Bonnet’s statements are erroneous. The crude product obtained by the distillation is a complicated mixture, containing acetoni- trile, acetone, and hydrocyanic aeid, and besides this a new and peculiar volatile base. To obtain the latter, the crude product is rectified in the water-bath—about one-half passes over between 77° and 80°; the receiver is now changed, and the distillate tested from time to time with sulphuric acid; and as soon as this produces a crystalline precipitate, the receiver is again changed. The distillate now contains the volatile base. It is an alkaline and colourless liquid which becomes gradually yellow. Its odour is unpleasant, and resembles propylamine, Heated for some time with water it is decomposed, with forma- tion of hydrocyanic acid. It gives a precipitate with chloride of platinum. The base could not be obtained pure. Its composi- tion was deduced from that of its salts, which are with diffi- culty obtained pure from their ready decomposability. The oxalate consists of brilliant white crystalline needles. The sulphate is also crystalline. The base forms with iodide of mer- cury a beautiful compound, crystallizing in lustrous lamine. The composition of the base, as deduced from its salts, is * Liebig’s Annalen, March 1859. T Ibid. June 1859, ‘184 M. Strecker on Sarcine. C'© H® N4, and it doubtless contains C* and N* in the form of cyanogen. Nachbaur views it as being analogous in composition with Hofmann’s cyaniline, which is also distinguished by its instability. A new mode of the formation of chloride of benzoyle has been observed by Beketoff*, who, however, does not state whether it is advantageous in a practical point of view. When a mixture of chloride of sodium and anhydrous acid sulphate of soda acts upon benzoate of soda at about 200° C., hydrochloric acid and chloride of benzoyle are set free. The latter remains diffused in the mass, but may be extracted by means of ether. The action is as follows :— ay) aa F Q +8034 Na? C?2=€? HO, Cl+Na?S04+ HCl. The sulphate of soda combined with the anhydrous acid serves to prevent the action of sulphuric acid on the benzoic acid, and formation of benzoesulphuric acid. In the preparation of creatine by Liebig’s process, there is obtained a syrupy mother-liquor which contains several sub- stances, among which are creatinine, imosinic acid, and lactic acid. Strecker+ has further discovered in it a substance pos- sessing feeble basic properties, which he names sarcine. It is obtained by adding to this mother-liquor a solution of acetate of copper, with which it forms a compound; this is then decom- posed by means of sulphuretted hydrogen. Sarcine is a erystal- line powder which can be heated to 150° without decomposition. It is somewhat soluble in boiling water, but dissolves with diffi- culty in cold water and in boiling alcohol. Its composition is C!° H* N40?; it has feeble basic properties ; it forms a crystalline compound with hydrochloric acid, which has the formula C!°H* N40?, HCl+2aq. This compound forms a double salt with bichloride of platinum. The nitrate and sul- phate of sarcine are crystalline bodies, but are decomposed by being crystallized from water. Sarcine also combines with bases and with salts. A compound with baryta has the formula C!° H* N40?+2Ba0+2aq. It also forms a compound with nitrate of silver, C'!° H*N*+0?, Ag NO®, and with oxide of silver, C!° H® Ag? N4 02+ aq. In its chemical relations sarcine has great similarity with gua- nine, a nitrogenous substance discovered in considerable quanti- ties in guano by Unger, the principal difference being in the action of nitric acid on the two substances. * Bulletin de la Société Chimique de Paris, January 11, 1859. + Liebig’s Annalen, May 1857, October 1858. M. Strecker on the Artifeial Formation of Xanthine. 185 Xanthine or xanthic oxide, a nitrogenous basic substance which was discovered by Marcet as a rare constituent in urinary caleuli, has considerable similarity with sarcine and with guanine. It contains the elements of uric acid and of sarcine, 2010 H4 N404=GC! H4 N4 064 C0 H4 N42. Xanthine. Uric acid. Sarcine. But it was impossible to effect its formation by acting on urate of potash with hydrochlorate of sarcine. Sarcine has been declared by Scherer* to be identical with hypoxanthine, a substance which he discovered some time ago in the animal organism. The same chemist has found that xan- thine is a normal constituent of the human and animal organism. Between guanine and sarcine there exist similar relations to those which exist between glycocol and acetic acid, as is seen by the equations, C!0 H5 N5 02=C! H4 N402+4NH. Guanine. Sarcine. nen = Cont UO - Na Glycocol. Acetic acid. Strecker}, im the expectation of being able to transform gua- nine into sarcine, tried some experiments on a nitrogenous deri- vative of guanine. This substance was first obtained by Neu- bauer and Kernert, by dissolving guanine in nitric acid and adding small fragments of nitrite of potash, which dissolves with a lively disengagement of gas, but without formation of binoxide of nitrogen. When red vapours appear, the liquor is added to a large quantity of water, by which orange-yellow flakes are pre- cipitated. These are washed, and then crystallized from boiling water. The substance did not give very accordant results to rig ee ; and it was impossible to decide whether its formula was Gd Noe bNS 0 or orf No: tN OF. Strecker dissolved this nitro-compound in potash, and then added ferrous sulphate and boiled the liquor. A black precipi- tate of ferroso-ferric oxide was formed, which was filtered off; and the colourless filtrate, treated with acetic acid, gave a floc- culent precipitate, which was collected and washed with cold water. It was neither guanine nor sarcine, but was found to be identical in its properties and composition with Marcet’s xanthic oxide. It is a white or yellowish powder, soluble in 723 parts of boiling, and in 1950 of cold water. Its potash solution, ex- posed for some time to the air, deposited crystalline plates, which * Liebig’s Annalen, March 1858. + Ibid, November 1858. { Ibid, vol. ci. p. 318. 136 Royal Society :-— eave on analysis the composition C!° H4 N4 04, which is that of xanthic oxide. Neglecting the intermediate nitrogenous products, the trans- formation of guanine into xanthine may be thus represented :— C!° H® N° 024 08 =C" H4 N4 01+ HO+N. Guanine. Xanthine. Xanthine does not lose weight when heated even to 100° or 150°. Its solution gives precipitates with corrosive sublimate, with acetate of copper, and with nitrate of silver. Its ammoniacal solution gives precipitates with an ammoniacal solution of chlo- ride of zinc or of chloride of cadmium. Its basic properties are even less strongly pronounced than those of guanine or of sarcine. Strecker further found that xanthine is contained in small quantities as a normal constituent of urine. It may be separated by taking advantage of its pro- perty of forming a precipitate with acetate of copper or nitrate of silver. XXV. Proceedings of Learned Societies. ROYAL SOCIETY. (Continued from p. 77.] February 3, 1859.—Sir Benjamin C. Brodie, Bart., President, in the Chair. fe following communications were read :— «On the Aquiferous and Oviductal Systems in the Lamelli- branchiate Mollusks.”? By George Rolleston, M.D., Lee’s Reader in Anatomy, and Charles Robertson, Esq., Curator of the Museum, Christ Church, Oxford. ‘Qn the Action of Nitric Acid and of Binoxide of Manganese and Sulphuric Acid on the Organic Bases.” By A. Matthiessen, Ph.D. In the Proceedings of the Royal Society (vol. ix. p. 118), I stated that by the action of nitrous acid on aniline I had obtained ammonia and nitrophenasic acid ; since then I have acted on several other of the organic bases with the same reagent, as well as with nitric acid, and with binoxide of manganese and sulphuric acid ; and I will now shortly enumerate the experiments. 1. Action of Nitrous Acid on Amylaniline. The dilute solution of the nitrate of amylaniline was acted on by nitrous acid at 100° C. for 12 hours. Amylaniline and ammonia were obtained, but in quantities too small to be quantitatively determined. 2. Action of Nitrie Acid on Amylaniline. Amylaniline was boiled with dilute nitric acid (1 part acid to 2 of On the Action of Nitric Acid on the Organic Bases. 187 water) until the reaction began, which was immediately stopped by adding cold water to the solution. This was filtered when cold from the nitrophenasic acid, and after potash had been added, it was again filtered to separate any undecomposed amylaniline. ‘The filtrate was distilled, the distillate redistilled per ascensum into hydrochloric acid, and the acid solution evaporated to dryness. The residue was then extracted with absolute alcohol, and the fil- trate evaporated to dryness. This operation was repeated four or five times. A platinum-salt* made with the chloride, which was soluble in absolute alcohol, gave 33°55 per cent. platinum. The chloroplatinate of amylamine requires 33°66 per cent. The plati- num-salt of that chloride which was insoluble in absolute alcohol gaye 43°9 per cent. platinum. The chloroplatinate of ammonia requires 442 per cent. The above reaction may be explained as follows :— Cs a, C,, iz? C,,H,,>N+H,0,+NO,HO0= H ;/N+C,,0,0,+NO, HO H i and OA i. H H $N+H,0,4+NO, HO=H }N+C,,H,,0,+NO, HO. H H The free nitric acid present converts the phenylic alcohol into nitrophenasic acid, and the amylic alcohol into nitrite of amyle. 3. Action of Nitric Acid on Ethylaniline. Ethylaniline was treated in the same manner as amylaniline. The platinum-salt of the chloride which was soluble in absolute alcohol gave in two experiments 39°6 and 39°5 per cent. platinum, The percentage of platinum in chloroplatinate of ethylamine is 39-3, The platinum-salt of the chloride which was insoluble in abso- lute aleohol gave 44 per cent. platinum, which agrees with the number required for the chloroplatinate of ammonia. 4. Action of Nitric Acid on Diethylaniline. Diethylaniline was treated with dilute nitric acid (1 part of acid to 4 of water), and heated till the temperature reached 54° C., when, on being left to itself, it soon became turbid, and the temperature rose about 10°C. After a while the solution cleared itself again, but remained very dark. When quite cold, it was filtered from the nitrophenasic acid, and the’ filtrate was treated in the same manner as described in Experiment 2. The solution of the chlorides (5-6 grms. were obtained from about 50 of diethylaniline), which were soluble in absolute alcohol, was partially precipitated with bichloride of platinum (precipitate No. 1); then another portion was precipi- tated, which was not used; after this, more bichloride was added (precipitate No. 2); and lastly, an excess of bichloride was added * All the platinum-salts determined were recrystallized in water. 138 Royal Society :— (precipitate No. 3). The platinum found in the three precipitates was No. 1. No. 2. No. 3. 39°2 per cent. 35°5 per cent. 35°4 per cent. The chloroplatinate of ethylamine contains 39°3 per cent., and of diethylamine 35-3 per cent. platinum. A platinum-salt made with chloride insoluble in absolute alcohol, gave 44°2 per cent. platinum, which is exactly the amount contained in the chloroplatinate of ammonia. The reaction was as follows :— C,H, C, H, C, H: N+H,0,+NO, HO=C, H,}N+C,,H,0,+NO, HO; C, H; H ©. a: C, H, C, H, LN +,0,4NO, HO= H [xe H, O,+NO0, HO; H and C, H, H H | N+H,0,4+ NO, HO=H | N+C, H, 0,4 NO, HO. H H As in the case of amylaniline, the phenylic aleohol and the alcohol are converted into nitrophenasic acid and nitrite of ethyle; the am- monia being in both cases partially oxidized. 5. Action of Binoxide of Manganese and Sulphurie Acid on Aniline. Aniline was dissolved in an excess of dilute sulphuric acid (1 part of acid to 6 of water) and heated to boiling, when a small quantity of binoxide of manganese was added. The reaction was allowed to continue for 3 or 4 minutes, and it was stopped by cooling the flask in water. Potash was then added, and the solution filtered. The filtrate was distilled as described in experiment 2, and the distillate evaporated to dryness with hydrochloric acid, and extracted with ab- solute alcohol, to dissolve any chloride of aniline present. A plati- num-salt made from the chloride, insoluble in absolute aleohol, gave 44:0 per cent. platinum, which corresponds to the platinum in the chloroplatinate of ammonia. 6. Action of Binoxide of Manganese and Sulphuric Acid on Diethylaniline. Diethylaniline was treated in the same manner as aniline, but only for about one minute. Potash was added, &c., as in the foregoing experiment. The platinum-salt partially precipitated, as in Ex- periment 4, from the chloride soluble in absolute aleohol, gave :— Precipitate No. 1. Precipitate No. 2. 37°6 per cent. 35°4 per cent. platinum. No. 1 appears to be only a mixture of the chloroplatinates of ethylamine and diethylamine ; the quantity of salt first precipitated being too small to be properly recrystallized (on account of former experiments showing that the quantity of ethylamine present was yery small), No. 2 corresponds with diethylamine, and of this sali Dr. Smith on the Action of Food upon the Respiration. 189 there was a large quantity, so that it was recrystallized twice. A platinum-salt made from the chloride insoluble in absolute alcohol (of which there was only a very small quantity), gave 44:3 per cent. platinum, which is almost the same as the amount in chloro- platinate of ammonia. No phenylic alcohol was found nor any of its compounds ; and according to an experiment of Long (not yet published), on the oxidation of phenylic alcohol, that chemist always, excepting when he used spongy platinum, obtained a resinous mass. From the above experiments, it appears that by the action of nitrous acid, nitric acid, binoxide of manganese and sulphuric acid, permanganate of potash*, potash+, and in some cases by the pre- sence of acids alone (as sulphuric or hydrochloric) {, on the organic bases in the presence of water, water only is decomposed in the first stage of the reaction; and the fact that the radicals contained in the bases are replaced by hydrogen by degrees, makes it plausible that by these means we may be able to determine the constitution of the natural organic bases. I am now experimenting with narcotine, and to all appearance, I shall succeed in determining its constitution. In conclusion, I may here be allowed to thank Dr. Holzmann for his assistance in carrying out the above experiments. February 10.—Sir Benjamin C. Brodie, Bart., President, in the Chair. The following communication was read :— “Experiments on the Action of Food upon the Respiration.” By Edward Smith, M.D., LL.B., L.R.C.P. The author had proved in his former Paper that the maximum influence of food is observed within two and a half hours after its exhibition ; also that the action of food is in two degrees; viz. that which sustains the respiratory changes to the minimum line (or that which occurs with complete abstinence), and that which is observed as the maximum point to which the respiratory function is increased after ordinary meals. His aim in this communication was to show the variations in the influence of food between these two lines. His method of inquiry was to take a moderate quan- tity of a single article of food alone, before breakfast, whilst the body was at rest and in the sitting posture, and to determine the ‘influence every ten or fifteen minutes during a period of about two hours. He noted the amount of carbonic acid exhaled and of air inhaled, with the rate of respiration and pulsation, and also the temperature and the barometric pressure of the atmosphere. The apparatus employed was that described in his former Paper, and the gentlemen who submitted themselves to the investigation were chiefly the author and Mr. Moul, with Professor Frankland, Mr. Hofmann, and Mr. Reid, who engaged in a few experiments. The following foods were subjected to inquiry :— 1. The starch series, viz. arrowroot, arrowroot and butter, arrow- * By its actionon aniline, ammonia is obtained. +t In its action on the amides, t In the case of asparagine, benzamide, &c. 140 Royal Society :— root and sugar, commercial starch, wheat starch, gluten, bread, oat- meal, rice, rice and butter, potato. 2. The fat series, viz. butter, olive oil, cod-liver oil. 3. Sugars, viz. cane-sugar, cane-sugar and butter, cane-sugar with acids and alkalies, grape-sugar, sugar of milk. 4. The milk series (cows’ milk), viz. new milk, skimmed milk, caseine, caseine and lactic acid, lactic acid, sugar of milk and lactic acid, cream. 5. Alcohols, viz. alcohol, brandy, whisky, gin, rum, sherry wine, port wine, stout, and ale. 6. The tea series, viz. tea, green and black, hot and cold, in various quantities, and with acids and alkalies ; coffee, coffee-leaves, chichory, and cocoa. 7. Some other nitrogenous substances, viz. gelatine, albumen, fibrine, almond-emulsion. The author found that pure starch scarcely increased the amount of carbonic acid evolved, but the combination of starch with gluten and sugar in the cereals caused an increase of about 2 grains per minute. Wheat flour, oatmeal, and rice had similar effects, but potato had a less enduring influence. Fats lessened the amount of carbonic acid evolved, and when taken with starch, the cereals, or sugar, somewhat lessened their power to produce carbonic acid. Fats increased pulsation. Sugars increased the carbonic acid evolved to the maximum extent of from 14 to 23 grains per minute in about half an hour. Cane- sugar was more powerful than milk-sugar, and still more so than grape-sugar. Acids increased the maximum influence of sugar. Milk increased both the pulsation and the carbonic acid, and the latter to a maximum of nearly 2 grains per minute. All the com- ponent elements except lactic acid had a similar influence, but new milk was much more powerful than any of its elements separately, or than any artificial combination of its elements. The effect of milk differed in degree, and of caseine in direction, upon the author and Mr. Moul. Tea and coffee increased the production of carbonic acid to the extent of from 14 to 3 grains per minute. Tea was more powerful than coffee, and coffee than chichory. Cocoa was as powerful as coffee. Coffee-leaves lessened the amount of carbonic acid. Acids added to tea rendered it more stimulating, and alkalies made it more soothing. Alcohols differed in their effect, according both to different kinds and samples of the same kind. Spirits of wine always increased the quantity of carbonic acid evolved to a maximum of less than J grain per minute. Rum commonly increased it, and sometimes to 13 grain per minute. Ale and stout increased it to upwards of 1 grain per minute. Sherry wine (3 oz.) commonly slightly increased it. Brandy and gin, and particularly the latter, always decreased it. Whisky varied in its effects. The inhalation of the volatile elements of wine and spirits, and particularly of fine old port wine, lessened the quan- tity of carbonic acid, and increased the amount of vapour exhaled. On the Discovery of the Composition of Water. ‘141 Gluten, caseine, gelatine, albumen, and fibrine increased the amount of carbonic acid exhaled, the two former to about 1 grain per minute, and the last to about 3 grain per minute. Almond-emulsion did not increase it. From these facts the author infers that there is a class of foods which might be called “ excito-respiratory ;”’ a class which embraces nearly all nitrogenous foods, and is almost entirely composed of these substances. The xon-excitants are starch, fat, some alcohols, and coffee-leaves. The respiratory excitants are sugar, milk, the cereals, potato, tea, coffee, chichory, cocoa, alcohol, rum, ales, some wines, gluten, caseine, gelatin, fibrin, and albumen. Of the hydrocarbons, sugar acted very differently from starch and fat. All the “respiratory excitants”’ increased the depth, but not the rate of respiration. Some of them acted with great rapidity ; as, for example, sugar and tea, which sometimes caused an increase of | grain of carbonic acid per minute in from five to eight minutes. Others, as gluten and caseine, acted with less rapidity. In many, as tea and gluten, there was not a proportionate increase in the carbonic acid with in- crease in the quantity of the “excitant.’’ Some of them, as tea, produced much greater effect when a small dose was frequently repeated, than when the whole quantity was given at once, and caused a much greater evolution of carbon than they supplied. The duration of the increase was very different with different foods, but that with sugar was the least, and then that with tea, while that with the cereals and rum and milk was the greatest. The amount of carbonic acid progressively increased at each examination until the maximum was attained; after which it remained nearly sta- tionary for some time, as with the cereals, or subsided rapidly to the basis quantity, as with sugar. February 17.—Sir Benjamin C. Brodie, Bart., President, in the Chair. The following communications were read :-— “ Statement of Facts relating to the Discovery of the Composition of Water by the Hon. H. Cavendish.” In a Letter from J. J. Ben- nett, Esq., F.R.S., to Sir B. C. Brodie, Bart., P.R.S., dated February 12, 1859. Since the death of our late excellent and lamented friend Mr. Robert Brown, several appeals have been made to his executors to publish certain evidence presumed to have been in his possession relating to the much-agitated question of the priority of Cavendish or Watt in the discovery of the composition of water. As the execu- tor to whom Mr. Brown entrusted his papers, and having been for many years honoured with his entire confidence, I feel called upon to respond to these appeals, and I therefore request that you will kindly lay before a Meeting of the Royal Society the following brief statement on the subject. The date and nature of Cavendish’s communication to Priestley 142 Royal Society :— have always been considered as essential elements in the determina- tion of the question; and it was the evidence which Mr. Brown possessed in regard to these particulars, which, in his estimation, «placed Cavendish’s claims as the discoverer of the composition of water beyond dispute.” That evidence, however, was not derived from any unpublished document, but formed part of a section of Deluc’s “Idées sur ia Météorologie,’’ which although especially entitled,—* Anecdotes relatives a la découverte de ( Kau sous la forme d@ Air,’ —appears entirely to have escaped the notice of those who have advocated Cavendish’s claims. It is the more conclusive as coming from Deluc, the “ami zélé,” as he justly terms himself, of Watt, and who, in relation to this question, believed himself “4 portée d’en connoitre toutes les circonstances.” The testimony of Deluc is as follows :— Vers la fin de l'année 1782 j’allai A Birmingham, ov le Dr. Priest~ ley s’étoit établi depuis quelques années. I] me communiqua alors, que M. Cavendish, d’aprés une remarque de M. Warltire ; qui avoit toujours trouvé de /eau dans les vases ot il avoit bralé un mélange @ air inflammable et d’ air atmosphérique ; s étoit appliqué 4 décou- vrir la source de cette eau, et qu'il avoit trouvé, ‘“ qu’un mélange @ air inflammable et d’ air déphlogistiqué en proportion convenable, étant allumé par l’étincelle électrique, se convertissoit tout entier en eau.” Je fus frappé au plus haut degré de cette découverte*. The italics and inverted commas are Deluc’s own. In this communication made by Cavendish to Priestley the theory of the composition of water is clearly indicated. The two gases (known to have been hydrogen and oxygen) were mixed together in due proportion, and by means of,the electric spark were entirely converted into water. Referring to one of Cavendish’s experiments, as recorded in his journal, Lord Jeffrey, the most candid and judicious of Watt’s advocates, has said: “ if he [Cavendish] had even stated in the detail of it, that the airs were converted, or changed, or turned into water, it would probably have been enough to have secured to him the credit of this discovery, as well as to have given the scientific world the benefit of it, m the event of his death, before he could prevail on his modesty to claim it in public +.” The evidence which this distinguished critic and judge regarded as sufficient to establish Cavendish’s claim is now afforded, not by a note in his private journal, but by the testimony of the zealous friend of Watt, who states that it was communicated to Priestley towards the end of the year 1782, that is to say, several months before Watt drew his own conclusions from Priestley’s bungling repetition of Cavendish’s experiments. It was, moreover, published to the world, and suffered to remain uncontradicted, while all the parties were alive and in frequent intercourse with the author and with each other. I have only further, in Mr. Brown’s name also, to do an act of justice to the memory of Lavoisier, by relieving it from the obloquy * Tdées sur la Météorologie, tome ii. 1787, pp. 206-7. + Edinburgh Review, vol. Ixxxvii. p. 125. Influence of Light on the Growth and Nutrition of Animals. 1438 which has rested upon it from his supposed persistence in unjustly claiming priority for himself. The following extract from a Report to the Academy of Sciences on M. Seguin’s experiments, dated 28th August 1790, and signed Lavoisier, Brisson, Meusnier, and Laplace, the last named being the reporter, will prove that Lavoisier was not unmindful of the appeal which had been addressed to him by Blagden some years previously, and that he distinctly resigned the priority of discovery to Cavendish :-— «°M. Macquer a observé dans son Dictionnaire de Chimie que la combustion des gaz hydrogéne et oxygtne produit une quantité d’eau sensible; mais il n’a pas connu toute importance de cette observation, qu’il se contenta de présenter, sans en tirer aucune con- séquence. M. Cavendish paroit avoir remarqué le premier que l’eau produite dans cette combustion est le résultat de la combinaison des deux gaz, et qu'elle est d’un poids égal au leur. Plusieurs ex- périences faites en grand et d’une manitre trés-précise, par MM, Lavoisier, La Place, Monge, Meusnier, et par M. Lefevre de Gineau, ont confirmé cette découverte importante, sur laquelle il ne doit maintenant rester aucun doute.””—Annales de Chimie, tome 7, pp. 258-9. Joun J. BENNETT. “On the Influence of White Light, of the different Coloured Rays and of Darkness, on the Development, Growth, and Nutrition of Animals.’ By Horace Dobell, M.D. In this communication the author laid before the Society the par- ticulars of a series of experiments, having for their object to discover what influence is exerted by ordinary light, by the different coloured rays, and by darkness on the development, growth, and nutrition of animals, After referring to the experiments of Edwards, Higginbottom, E. Forbes, Morren, Wohler, Hannon, Moleschott, and Béclard, the results of which were shown to be somewhat contradictory, the author described the precautions taken by himself to avoid sources of fallacy. The original experiments detailed in this Paper were conducted in the years 1855, 1856, 1857, 1858. The subjects selected were the Ova and Larve of the Silkworm (Boméyzx mori) and of the Frog (Rana temporaria). A comparative experiment in the vegetable kingdom was also made on the Sweet Pea (Lathyrus odoratus). An appa- ratus contrived for the experiments on Tadpoles was described and figured ; it secured the following desiderata :— 1. That each of six compartments or cells should be supplied with water from the same source, at the same time, subject to the same changes, and capable of being refreshed without interfering with the cells. 2. That each of the cells should be placed in the same condition with respect to the supply of air and of food. 3. That during exposure for examination of the animals, the whole series should be opened the same length of time and to the same extent. 144 Royal Society :— 4, That each cell should receive no light but that transmitted by its proper cover. One of these six cells was open to the air and to light ; one was covered with ordinary white glass; one was made completely dark by a covering of blackened opaque glass; one was covered with blue, one with greenish yellow, and one with red glass. The transmit- ting and absorbing powers of these glasses were detailed from expe- riments made upon them by Mr. Cornelius Hanbury, jun., and by the author. The apparatus used for the Silkworms was, in all essential par- ticulars, the same as that for the Tadpoles, only without water. A tabulated analysis of the daily journal kept during the experi- ments was given, and its separate items compared and discussed ; after which the author concluded his Paperwith the following résumé. If we may venture to reason on so small a number of observa- tions, so far as the results of these experiments are concerned, the following propositions may be advanced. All other conditions being the same, (1.) The Ova of Insects are not directly influenced in their development by white light, by the different coloured rays, or by darkness. (2.) The Larve of Insects are not directly influenced in their development, growth, nutrition, or metamorphoses by white light, by the different coloured rays, or by darkness. (3.) The Larve of Batrachian Reptiles are not directly influenced in their development, growth, nutrition, or metamorphoses by white light, by the different coloured rays, or by darkness. (4.) The Materials necessary to the Colour of Insects and Rep- tiles are prepared equally under the influence of white light, of the different coloured rays, and of darkness. ' These results are so opposed to preconceived ideas upon the sub- ject to which they relate, that they cannot fail to excite some surprise and incredulity ; when, however, they are carefully considered, they assume a theoretical probability, which assists us in believing that the practical results are without fallacy. (a.) With regard to the development of the ovum, when we con- sider the unity of plan which appears to preside over the germs of the simplest and of the most complicated forms, and the infinite variety of external conditions in which these germs are placed throughout the animal kingdom, we are led to the conclusion that their development must be so arranged as to be independent of the direct influence of light. (b.) That after emerging from the ovum the animal is not di- rectly influenced by light, is more difficult, at first, to believe, be- cause experience seems to have taught us that “to live without light is to live without health ;’? but this familiar fact may be at once disposed of in the argument and explained by its coincident, that, under ordinary circumstances, the admission of light is in- separably connected with, 1, The regulation of external temperature. 2. The free circulation of a respiratory medium. Influence of Light on the Growth and Nutrition of Animals. 145 3. Those processes of vegetable life and of inorganic change upon which the proper condition of the respiratory medium depends. Speaking generally then, it must be admitted that light is essential to the development, growth, and nutrition of animals, but only in- directly. In the foregoing experiments, the usual coincidents of light, a proper supply of food, a due aération of the respiratory medium, a properly regulated external temperature, &c. having been provided in each cell, the direct influence of light only being changed, no corresponding change occurred in the animal life. In the vegetable kingdom the case is quite different, and the ex- periments on Lathyrus odoratus recorded in this paper demonstrate again, what has been shown by numerous other experimenters, that light as a direct agent is essential to the nutritive processes of plants. An interesting exception occurs, however, in the vegetable kingdom, which serves to strengthen the probability that the con- clusions arrived at concerning animals are correct, viz. that fungi— which derive their nutriment, like animals, from organic compounds already prepared for them—perform their vital functions without dependence on the influence of light. Under the head of colour, it would seem that the familiar phe- nomenon of etiolation witnessed in plants which have been deprived of light, has led to erroneous anticipations as to the effect which alterations of light would produce upon the development of the colouring materials in animals. In the experiments here recorded, it is seen that neither white light, nor the different coloured rays, nor darkness altered the de- velopment of those materials necessary to the exhibition of colour, when the animal was seen in ordinary light. The experiments of Dr. Gladstone, on plants, also show that the development of colouring matter in the petals of flowers is independent of the influence of light ; that flowers raised under the different coloured rays and in darkness have the same colour in their petals as when raised in or- dinary light. Thus, even in vegetables, e¢iolation is confined to those parts of the plant which depend for their colour upon the condition of the chlorophyl, to the green appearance of which some portion of the solar beam is evidently essential. Although, therefore, at first sight, the results of my experiments under the head of colour may appear questionable, I think we must rather throw the question upon the correctness of our preconceived notions on the subject; and the facts elicited by Prof. Edward Forbes (referred to in the Paper), while retaining all their value and interest as assistants in determining the depths of primeval seas, cannot, I think, be taken as evidence against the correctness of my observations. On the other hand, the results of my experiments may be found to put a new construction upon the facts observed by Prof. Forbes. He discovered that increased depth of sea corre- sponds with diminished light, and that both of these conditions again correspond with peculiar changes in colour, and ultimately with loss of colour in the shells inhabiting these depths; but there Phil. Mag. 8. 4. Vol. 18, No. 118. Aug. 1859, L 146 ; Royal Society :— is no evidence to show that these colourless shells have deyeloped any materials capable of manifesting colour after exposure to the influence of light; whereas my own and other experiments show that the etiolated stalks and leaves of plants speedily manifest the characteristic colour of the chlorophy] if placed in the sun’s rays. So far, therefore, as our present knowledge on the subject justi- fies any conclusion, the varieties of colour and the absence of colour in the mollusks are physiologically separated from the phenomena of etiolation in plants, and may be placed in the same category as the varieties of colour and the absence of colour in the corollas of flowers, which depend upon the development of materials having certain optical properties. The beautiful facts observed by Prof. Forbes, instead of being regarded as the consequence of imperfect exposure to light, must, I think, take rank with the phenomena of coloration observed through- out the animal kingdom, such as the peculiar markings of reptiles, birds, and wild animals, according to their different habitats and modes of life ; the colours of the upper and lower surfaces of fish, and the like; which cannot be shown to depend upon the exposure or non-exposure to light with which they frequently, but not always, coincide. These facts appear only to form a part of the vast and perfect plan of creation, in which everything that exists is suited in eyery particular to the conditions of its existence; thus, those mol- lusks which are designed to inhabit depths scarcely permeable to light, can have no need, and hence haye no provision, for elements, to the manifestation of which light is an essential condition. ‘*On the Intensification of Sound through Solid Bodies by the in- terposition of Water between them and the distal extremities of Hear- ing-Tubes.” By 8. Scott Alison, M.D., Assistant-Physician to the Hospital for Consumption. In this Paper the author gives an account of various experiments which he has recently made on sounds proceeding through solid bodies. He has found that sounds which are faint, when heard by a hearing-tube applied directly to solid sounding bodies, become augmented when water is interposed between these bodies and the distal extremity of the hearing-tube. He has been able, by the em- ployment of water, to hear the sound of a solid body, such as a table, which, without this medium, has been inaudible. Experi- ments haye been made upon water in various amounts and in different conditions, Thus a very thin layer, a mere ring round the edge of the hearing-tube, masses of water in larger or smaller vessels, and a bag of water, have been employed. The results haye been the same as regards augmentation. The degree of augmentation was greatest when the hearing-tube was immersed freely in water. In experi- menting upon water in vessels, it was found necessary to close the extremity of the tube to be immersed, by tying over it a piece of bladder or thin india-rubber ; for the entrance of water into the in- terior interfered greatly with the augmentation. The effect of water in augmenting sound is materially reduced if Dr. Alison on the Intensification of Sound. 147 even a small. amount of solid material be interposed between the water employed and the mouth of the hearing-tube. A_ piece of wood, not much thicker than a paper-cutter, materially interferes with the augmenting power of water. The augmentation of sound thus obtained by water seems to be due to the complete fitting of the liquid on the solid body and also round the mouth of the hearing-tube, whereby the column of air is thoroughly enclosed ; also to the less impediment to the vibrations of the instrument when held in contact with water, than when held in contact with a solid body, the water yielding in a greater degree than a solid. The mode of judging of the augmentation was twofold: Ist, one sensation was compared with another perceived by the same ear, the one sensation following immediately upon the other; 2nd, the dif- ferential stethophone was employed, by which two impressions are simultaneously made upon the two ears; in which case, if one impression be materially greater than the other, sound is per- ceived in that ear only on which the greater impression is made. To obtain the advantage of the differential stethophone,—or “ Pho- noscope,” as it might here perhaps be more correctly designated— when sounds at some distance from the ear were being examined, its length was increased by the addition of long tubes of india-rubber. Experiments were made upon other liquids besides water, such as mercury and ether. Other materials besides liquids were found to afford a similar in- tensification of sound from solid bodies, such as laminz of gutta- percha, or of india-rubber, and sheets of writing paper, but the amount of augmentation was less. . The hearing-tubes employed were various. Many of the experi- ments were performed with the author’s ordinary differential stetho- phone, an instrument described in the Philosophical Magazine for November 1858. India-rubber tubes fitted with ivory ear-knobs, and with wooden or glass cups (the size of the cup or object-extremity of ordinary tpuderenesy, and haying an ear-extremity to pass into the meatus, and brass tubes, were also in turn employed. Tubes closed at their distal extremity with solid material, such as glass, did not answer so well as those closed with membrane. The water-bag increases the impression conveyed to the ear by the wooden stethoscope, if it be placed between the flat ear-piece and the external ear. It may be employed alone to reinforce sound. The name of Hydrophone has been given to it. A postscript is added, in which the author records an experiment made on the bank of the Serpentine river. A sound produced upon the land was heard at a point in the water when it could not be heard at an equal distance on the ground, if the two limbs of the differential stethophone were employed simultaneously. The sensation upon the ear, connected, by means of a hollow tube, with water in sonorous undulations, was found to be much greater than that upon the ear connected with the same water by means of a solid rod. When both tube and solid rod were employed simul- taneously, sound was heard in that ear only supplied with the tube L2 148 Royal Society :— February 24.--Sir Benjamin C. Brodie, Bart., Pres., in the Chair. The following communications were read :— “Researches on the Phosphorus-Bases.’”’—No. V. Diphospho- nium-Compounds. By A. W. Hofmann, LL.D., F.R.S. &e. In a note* on the deportment of dibromide of ethylene with tri- ethylphosphine, I have stated that the reaction between these two substances gives rise to the production of Bromide of triethylbromethylene- eee mene} (C,H), (C,H,Br)P] Br, whilst two other bromides, viz. sae of triethylphosphonium —__[(C,H,), HP]Br and romide of triethylvinyl-phos- pitied Oe KO, Hi) (Cee are generated in consequence of secondary processes. But I did not fail to remark in the same note, that in addition there is formed in this reaction a fourth bromide, the nature of which, at that time, I had been unable to fix by experiment. I have continued the study of this substance, which has led to the following results. All attempts to eliminate the bromide in question by frequently recrystallizing the direct product of the action of dibromide of ethyl- ene on triethylphosphine have entirely failed. Considerable sacri- fice of precious material and often repeated analyses of the different crops of crystallization taught me nothing, except that the body which I endeavoured to grasp is most abundantly produced when the triethylphosphine is rather in excess. Indeed, it would appear, that under those conditions, the bromide in question constitutes the principal product of the reaction. Not more successful was an attempt to increase the chances of separation by reducing the number of the bromides. As I have previously stated, treatment with oxide of silver de- stroys the triethylated bromethylene-phosphonium, converting it into a basic compound, which contains no longer any bromine, whilst the same agent transforms the bromide of triethylphosphonium into the oxide of argento-triethylphosphonium, and the dioxide of tri- ethylphosphine. On saturating again by hydrobromic acid the liquid thus produced, the solution now contained only the new bromide, the bromide of the debrominated body, and the dibromide of triethyl- phosphine, the extreme solubility of which rendered its presence al- most harmless. The task was thus virtually reduced to the separation of two bromides. Unfortunately, the two substances resemble each other to such an extent, that this hope also had to be abandoned. A modification, however, of this process led to the solution of the difficulty. On saturating the alkaline solution, produced by the action of oxide of silver upon the crude bromides, with hydriodic instead of hydrobromie acid, a mixture of the corresponding iodides was ob- _tained, the separation of which could be easily accomplished. On moderately concentrating this solution, a beautiful iodide of * Phil, Mag. vol. xvii. p. 134. Dr. Hofmann on Diphosphonium-compounds. 149 limited solubility was deposited. This substance readily dissolved in boiling water, from which it crystallized on cooling in long white needles. It was less soluble in alcohol, insoluble in ether. The analysis of this compound, carefully purified by repeated crystallizations, led to the following atomic expression :— C,,H,,PI. This formula received ample confirmation by the examination of a platinum- and gold-compound. Converted into chloride and pre- cipitated by dichloride of platinum, the new body furnished a crystal- line, difficultly-soluble platinum-salt, differing from the platinum-salts of all the other compounds of this group. This salt dissolves in boiling concentrated hydrochloric acid without decomposition, and crystallizes on cooling in beautiful yellow needles containing C,,H,,PCl, PtCl,. The gold-salt is a bright yellow crystalline precipitate, difficultly soluble in boiling water, and not recrystallizable without some altera- tion. The gold-determination agreed with the formula C,,H,,PCl, AuCl,. The preceding formule are simple translations of the analytical results, but they convey no idea regarding the nature of the new body. Legitimate interpretation of these expressions, and a due apprecia- tion of the conditions in which the new compounds are formed, un- avoidably lead us to the conclusion that the formule: must be doubled. The molecule of the new iodide thus becomes Se all gol corresponding to an original bromide, be H,, us Br,, which is simply formed by the association of 2 equivalents of triethyl- phosphine and 1 equivalent of dibromide of ethylene, 2C,,H,,P+ C,H, Br,=C,, H,, P, Br,. The formule of the platinum-salt and of the gold-salt of course have likewise to be doubled: Platinum-salt C,,H,,P,Cl,, 2PtCl,, Gold-salt C,, H,,P,Cl,, 2AuCl, ; the number of platinum- and gold-equivalents which respectively exist in these compounds being apparently determined by the number of triethylphosphine-equivalents associated in the new salt. I have vainly endeavoured to produce compounds containing only one equi- valent of platinum and gold, but have succeeded in procuring a well- defined silver-compound : C,H Por, Aghr, which is formed by treating the new bromide with a quantity of oxide of silver insufficient for complete decomposition. This compound is a double salt of equal equivalents of the proximate constituents. The deportment of triethylphosphine with dibromide of ethylene, and more particularly the formation of the new bromide, is not with- 150 Royal Society :— out theoretical interest. The molecule of dibromide of ethylene, equivalent to 2 molecules of hydrobromic acid, fixes in this reaction 2 molecules of triethylphosphine, equivalent to 2 molecules of am- monia; the result being a compound saline molecule, equivalent to 2 molecules of sal-ammoniac. 3: ict ep Tt: BO 5) (Oy ie H, (C, Hy)” ay é j 2 molecules of Molecule of the diatomic sal-ammoniac. bromide: It is not quite easy to frame a name for this complex body, in which, under the influence of the diatomic ethylene, 2 molecules of triethylphosphine are, if I may say so, dovetailed together. We have in this case to deal with a compound molecularly representing 2 equi- valents of chloride of ammonium, with phosphorus in the place of nitrogen, bromiue in the place of chlorine, 6 equivalents of ethyle and 1 equivalent of diatomic ethylene being substituted for the 8 equiva- lents of hydrogen ; in fact, the compound is a dibromide of hexethyl- ethylene-diphosphonium, sit venia verbo. Be Those who have accorded some attention to the direction of these researches, cannot have failed to observe that the conception of the compound which forms the subject of this note was the point from which I started in examining the deportment of triethylphosphine with dibromide of ethylene. In a note on polyammonias, presented to the Royal Society about a year ago*, I first pointed out the exist- ence of similar compounds in the nitrogen-series, adducing in favour of this view such experimental evidence as I was enabled to collect from the materials at hand. I have since endeavoured to expand this evidence by the realization of a variety of bodies of analogous constitution. For this purpose I have examined the action of am- monia on dibromide of ethylene ; a process, which, owing to the num- ber of bodies simultaneously produced, presents considerable difficul- ties. With the view of simplifying the reaction, I have passed step by step to the primary, secondary, and tertiary monamines, in which the advancing state of substitution promised a reduction of the number of compounds capable of being generated under the influence of dibromide of ethylene. These experiments, some of which have been laid already before the Royal Society, whilst others are still in- complete, have furnished many additional illustrations of the group of polyammonias ; but most of these reactions are complicated, and the compounds produced are far from always presenting the salient characters which I could have desired. In fact, it was not until I pursued the inquiry into the phosphorus-series, and relying on the promptness and precision with which these substances act, examined the deportment of dibromide of ethylene with triethyl- phosphine, that the experiments were attended with the desired SUCCESS. “ * Phil. Mag. vol. xvi. p. 309. Dr. Hofmann on Diphosphonium-compounds. 151 The new diphosphonium-compounds which form the subject of this note are remarkable for their well-defined characters, and for their stability. They may be heated to 250° C. without undergoing the slightest change. Even the dioxide, which is readily liberated by the action of oxide of silver upon either the bromide or the iodide, is a very stable compound. The solution of this substance, which obviously corresponds to 2 molecules of water, Hi, oO, L(C, H,), (C, Hy)" Ps)" oO Hef ~* Hi f >? : — ; 2 molecules Molecule of the diphosphonium- of water. . compound. is a powerfully alkaline liquid, attracting with great avidity the car- bonie acid of the atmosphere, and precipitating the metallic oxides like potassa. The solution may be evaporated without change to a syrup-like liquid, and it is only at a very high temperature that decomposition actually takes place. At one time I had hoped to see this body splitting under the influence of heat into the ethylene- alcohol (glycol) and triethylphosphine, but the transformation ensues in another form; only traces of phosphorus-base being liberated; while the principal product is the dioxide of triethylphosphine, which, in the latter stages of the distillation, coats the neck of the retort with a network of beautiful needles ; a small quantity of gas (hydride of ethyle?) being simultaneously evolved. The reaction is probably 4 n ! : [(C, Hs), (C, Hi)" Ba!" \ 0,=C, H,+2[(C, H,), PO,] ; this equation, however; is not experimentally established: The molecule of the diphosphonium-bromide contains the elements of 1 molecule of bromide of triethylphosphonium and 1 molecule of triethyl-vinyl-phosphouium, [(C,H,),(C,H,)’ P,]" Br,=[(C, H,), HP] Br+ (0, H,),(C, H,) P]Br { have eiideavotred to split the latter in accordance with the above equation, but without success. Triethylphosphine acts with eletgy upon the homologues of dibro- tide of ethylene ; I have not yet examined, however, any of the pro- ducts thus obtained. Mr. W. Valentin, to whoni I am indebted for much valuable assistance during my experiments; has found, more- over, that triethylarsine unites with dibromide of ethylene. He has iiot yet completed the investigation of the crystalline body which is generated in this reaction. “Qn the Different Types in the Microscopic Structure of the Ske- leton of Osseous Fishes.” By A. Kolliker, Professor of Anatomy and Physiology in the University of Wiirzburg. March 10.—Sir Benjamin C. Brodie, Bart., President, in the Chair. The following communication was read :— “Letter from James P. Muirhead, Esq., to Sir Benjamin C. Brodie, Bart, Pres: R.S., dated March 8, 1859, relating to the Dis- covery of the Composition of Water. I have how, with your permission, to reouest you to lav before the 152 Royal Society. Royal Society the fullowing brief remarks on the quotation from De Luc’s “Idées sur la Météorologie,’’ which has been referred to as fresh evidence in the controversy as to the discovery of the Compo- sition of Water. It is only at first sight, and when taken in an isolated form apart from the rest of De Luc’s narrative, that the passage in question could bear the interpretation now sought to be put upon it; for Dr. Priestley’s communication of Cavendish’s experiment is said by De Luc to have been made “vers la fin de ’année 1782.” But in the same section of the same volume he distinctly and positively says, that when in September [1783] he returned to Birmingham, «Nous ignorions, M. Watt et moi, que M. Cavendish eit eu des idées fort semblables aux siennes sur la Cause de ce Phénoméne *.” Now, we may well ask, how could this possibly have been the case with De Luc in 1783, if Priestley’s communication to him in 1782 had extended to the conclusions, as well as to the experiments, of Cavendish ? De Luc adds, on the next page of his work, that “Au mois de Juin” (an evident mistake for Janvier), “1784, M. Cavendish remit 4 la Société Royale un Mémoire, dans lequel il joignit, au récit de ses expériences de 1781, sa théorie sur la formation de l’ Hawt.” Here, for the first time in De Luc’s narrative (with the exception of an allusion to Blagden’s statement at Paris in June 1783), occurs a clear and distinct notice of Cavendish’s theory or conclusions, as distinguished from his experiments. What M. De Luc’s opinion of the memoir was, in which those conclusions were announced, when he perused it in March 1784, and sent an analysis of it to Mr. Watt, is well known from his letters already published {. We are thus enabled to set against the interpretation attempted to be put on the quotation from the ‘ Météorologie,” the most con- clusive of all testimony; that, namely, of De Luc himself: for if he had intended to say that in the end of 1782 the conclusions of Cavendish had along with his experiment been communicated by Priestley, he could not possibly have gone on to say, as he has done a few pages later in the same volume, that in September 1783 he was ignorant of Cavendish having entertained any such ideas; nor would he have felt the astonishment, and entertained the suspicions which he so strongly expresses, on his perusal of Cavendish’s memoir in March 1784. De Luc’s account in the “ Météorologie,”’ it must also be observed, is not a contemporaneous one, published at the time of Priestley’s communication in 1782, and before the conclusions of Watt were made known; but is given from memory, at an interval of several years, when such a mistake as that of June for January shows how little it can be relied on. Tae der ’ 3 Jas. P. MurrHEAD. « “Tdées sur la Météorologie,” tome ii. p. 224. f Ibid. p. 225. ¢ M. De Luc to Mr. Watt, Ist and 4th of March, 1784. Geological Society. 153 GEOLOGICAL SOCIETY. [Continued from p. 78.] June 15, 1859.—Prof. J. Phillips, President, in the Chair. The following communications were read :— 1. * Notes on Spitzbergen.”” By J. Lamont, Esq. Mr. Lamont cruised about Spitzbergen in his yacht in the summer of 1858, and went up the Stour Fiord, which, he remarks, is a Sound dividing the Island, not a gulf. The first thirty miles of coast along which he sailed on this Fiord consisted almost entirely of the faces of two or three enormous glaciers: the water is shallow, seldom as much as sixteen fathoms, and such appears to be the case all around Spitzbergen; and hence icebergs of very large size are not formed. The shores are mostly formed of a muddy flat, from half a mile to three miles broad, with ice or hard ground at from 12 to 18 inches under the surface ; this is intersected with muddy rivulets, and bears saxi- frages, mosses, and lichens, on which the reindeer fattens. Pro- truding trap-rocks appear at many spots on these flats. A steep slope of mud, snow, and debris succeeds the flats, and reaches up to perpendicular crags of schistose rock, above which extend the great glaciers. Above these, peaks, probably of granite, appear when free of mist. ~ The upper part of the Sound has much drift-wood, chiefly small pine-trees, weather-worn and water-logged, and some wreck-wood. Bones and skeletons of whales are numerous. Drift-wood and bones of whales were observed several miles inland and high above high-water mark—at least 30 feet. Whales’ skeletons were also seen high up on the Thousand Islands. These circumstances, con- nected with the fact that seal-fishers and whalers state their belief in the shallowing of these seas, lead the author to think that Spitz- bergen and the adjacent islands are emerging from the sea at a rate even more rapid than that at which some parts of Norway have been shown to be rising. 2. “On the Formation of Gypsums and Dolomites.” By T.S. Hunt, Esq., of the Geol. Surv. Canada. The points to which the author calls attention are, first, the for- mation of sulphate of lime and bicarbonate of magnesia by the action of bicarbonate of lime upon a solution of sulphate of magnesia, and their successive deposition in the forms of gypsum and hydrous carbonate of magnesia, during the process of evaporation; and, secondly, the direct union, under certain conditions, of this carbonate of magnesia with carbonate of lime to form a double carbonate, which is dolomite. 3. ‘On the Tertiary Deposits, associated with Trap-rocks, in the East Indies.” By the Rev. S. Hislop. With Descriptions of the Shells by the Rev. 8. Hislop; and of the Insects by A. Murray, Esq. (Communicated by the President.) In the first place, the author referred to his views, already given in the Society’s Journal, of the great outpouring of basalt in India having taken place under no great aqueous pressure, and of the 154 Geological Society. flatness of the tops of trap-hills being the effect of well known laws, to which lava, like every other liquid body, is subject. While the deposit now covered up by trap was being formed in a lake or lakes in Western and Central India, there was, he remarked, a contem- poraneous formation, similarly overlain, going on in an estuary or sea towards the south-east, about the mouths of the Godavery. The amygdaloid; which is generally found underlying the sedimentary rock, he believes to have been liquid at a period subsequetit not only to the deposition of that rock, but also to the consolidation of the upper trap, both of these having apparently been broken up by it: still he thinks it probable that the lava in both positions belonged to the same eruption, the upper portion of it havirig cooled first. - The author formerly held that the arenaceous strata which have been described by some as the “diamond-sandstoiie” were of tiearly the same age as the fern-beds of Silewdda, &c., the carbonaceous Shales of Umret and Damiutda, and the argillaceous sandstone, witli Brachyops, of Méngali; but he how considers that they must. be classed with the intertrappean deposit mentioned above, which they underlie. They contdin abundance of wood, chiefly silitified, and a few Paludine. This tertiary sandstone is metamorphosed itito gneiss by the intrusion, apparently, of some deep-seated plutonic rock; evi- denced by veins of pegmatite. Some minerals from the trap, gneiss, &c. were then entimerated, especially the ‘‘ Hunterite” and “ Hislopite” lately discovered by Prof, Haughton. The Fossi/s were next alluded to: namely, Fish-remains—some like the Sphyrenodus of the London Clay ; also Reptilian remains, and bones of Pachyderms. The Shells, both freshwater (from the neighbourhood of Nagpur) and marine (from Rajamandri, near the mouth of the Godavery), were described by the author in detail. Cyprides are numerous ; two species have been named by Mr. Sower- by; and some new forms will be described by Mr. Jones. Plant- remains are abundant, but have not been yet described: Many reiiains of Insects occur; and, as far as Mr. Andrew Murray can form an opinion on them, they differ from recent species. The author, after comparing the fossil shells of Nagpur with those of the Nummulitic fauna described by Viscount D’Archiac, and with the recent fauna of India, offered the conclusion that they are pro- bably of Lower Eocene date. The nearest European analogue is found in the Physa-bed (Physa gigantea) at Rilly, in France. These Tertiary deposits, with their pachydermatous remains, are decidedly (in the author’s opinion) older than those of the Sewalik Hills, so well known from Cautley and Falconer’s researches. There are yet newer deposits with huge fossil bones (probably of Upper Pliocene age) on the banks of the Nerbudda and elsewhere. Lastly, the author inferred that the upper or diamond-sandstone must be of Lower Eocene age, like the intertrappean deposit with which it is associated, and consequently that plutonic and meta- morphic action must have taken place since that era. Shells from the freshwater strata of Nagpur and lg hah parts of Central India (all, but three, new species);— Intelligence and Miscellaneous Articles. 155 Melania quadrilineata, J. Sby.; M. Hunteri; Paludina normalis; P. Decca- nensis, J. Soy.; P. Wapsharei; P. acicularis; P. pyramis; P. subcylindracea ; P. Sankeyi; P. Takliensis; P. soluta; P. conoidea; P. Rawesi; P.. Virapai ; Valvata minima ; V. unicarinifera ; V. multicarinata ; V. decollata ; Succinea Nag- purensis ; Limnza_ oviformis ; L. subfusiformis ; L. attenuata; L. peracuminata ; L. Spina ; Physa Prinsepii, J. Sby., var. elongata, var. inflata; Ph. Bradleyi; oe Malcolmsoni; U. Hunteri; U: cardioides; U. mamuiillatus ; U. imbricatus ; . Carteri. Shells from the estuary strata near RAjdmandri (all new spe- cies) :-— Pseudoliva elegans ; Natica Stoddardi; Cerithium multiforme ; C. subcylin- draceum ; C. Leithi; C. Stoddardi; Vicarya fusiformis ; Turritella prelonga; Hydrobia Ellioti; Hemitoma? multiradiata; Ostrea Pangadiensis ; Anomia Kate- ruensis; A. modiola; Perna meleagrinoides; Modiola, sp. 3 Corbis elliptica ; Cor- bicula ingens ; Cardita yariabilis; Cytherea orbicularis; C. Wilsoni; C. Wap- sharei; C. Rawesi; C. Jerdoni; C. elliptica; C. Hunteri; Tellina Woodwardi; Psammobia Jonesi; Corbula Oldhami; C. sulcifera. Fossil Insects from the Tertiary strata near Nagpur :— Lomatus Hislopi, sp. nov. ; and three other Buprestide (indefinable). Meristos Hunteri, noy. ; and seven other Curculionide (indefinable). XXVI. Intelligence and: Miscellaneous Articles. ON THE EXPANSION OF CRYSTALLINE BODIES BY HEAT. BY H. HAHN, JT is a law long since discovered by Mitscherlich, that crystalline bodies expand equally in the direction of their similar axes, but un- equally in the direction of their dissimilar axes. According to this law, only those bodies that belong to the regular system expand equally in all directions, while those that belong to the quadratic and hexagonal systems present ¢wo axes, and those belonging to the other systems three axes of unequal expansion. The greatest expan- sion is not, however, as might have been expected, in the direction of the principal axis (calc-spar, bitter-spar), but sometimes in the direction of the other axes (quartz). The author gives a calculation of the expansion of certain crystals in the direction of their different axes. Calc-spar (hexagonal system).—According to Mitscherlich, the terminal dihedral angle of the primary rhomboid becomes 8! 34”-5 more acute, on its temperature being raised to 100°C. At the mean temperature 14° R. (= 17°5 C.) it measured 105° 5!; at 100° C: it is therefore 104° 56’ 25”°5. Calculated from the first of these angles, the proportion of the axes is as follows :— a@:c=1°1706;1=1 : 0°8543; from the second, a: ce=1'1650: 1=1: 0°8584. The expansion of axis a up to 100° being taken as unity, axis ¢ then increases 100479 times as much as a, or for one degree ‘0121792 times as much. ‘The cubical expansion is three times the linear ; if, then, v be the expansion in the direction of the axis of a, that in the direction of the axis ¢ will be # x 1:00479, and the cubical expan- sion will be « x 3°00479, Kopp found that the cubical expansion 156 Intelligence and Miscellaneous Articles. of calc-spar for 1°, from 0 to 100° (between which limits it expands uniformly), to be 0°000018. From 17°-5 to 100° it expands there- fore 82°5 x 0:000018=0-001485, whence we have x x 3:00479=0°001485 and <=0°0004942. Axis a shee as by 0:0004942, te 0:00049657. For 1° a expands by 0:00000599, » € ” 0:00000602. We arrive at these last values also if we indicate the expansion of axis a for 1° by x; we then have zx X 3'0121792=0:000018, &c. Bitter-spar (muricalcite) (hexagonal system).—The terminal di- hedral angle of the principal rhomboid at the temperature 17°'5 is 106° 15'; at 100° it becomes 4! 6” more acute, and measures there- fore 106° 10' 54”. In the first case the ratio of the axes is as follows :— a: c=1:2016: 1=1: 0°8322; in the second, a: c=1'1993 : 1=1: 0°8338. Axis c therefore expands 1:00192 asmuchasa; or for 1°, 0'012144 times as much. If the cubical expansion of bitter-spar be known, the absolute expansions of a and ¢ can be calculated as in the former case. Arragonite (rhombic system).—At 17°°5 the. acute angle of the prism o P (axis 6) =63° 48! 14”; the polar dihedral angle of the prism P »©=108° 27'. At 100° the first of these angles becomes 63° 44! 32” ; the second, 108° 21' 31”. Axes 6 and c¢ have therefore expanded more in proportion than axis a. The two temperatures in question give the following proportions between the axes :— a7e "Se 100°. a:b6:c=1: 1°'60643:1°:15754 | a:b:c=1: 160836: 1°16088 =0°62249 : 1 : 0°72056 =0°62175: 1:0°72177 =0°86389 ; 1:38780: 1 =0°86142 : 1°38547 : 1 Axis 6 therefore expands 1°001201 as much as a; axis c 1°19027 as much; and the latter 1:00167 asmuchas 6. For 1°, 6 0:0121357 times, and c 0°0144275 times as much as a, ¢ expanding 0°0121414 times as much as b. Kopp found the cubical expansion of Arra- gonite for 1° to be 0'000065. ‘The expansion in the direction of a for 1° being called z, we have x X 3°0265632=0:000065, 0:000065 =e 0) OO00DT4 7. 3'0265632 Ora at The crystal expands therefore in the direction of— a for 1°, 0:00002147 6 o 0:00002173 Css 0°00002199 —— Intelligence and Miscellaneous Articles. 157 For 82°5 (that is, on the temperature being raised from 17°5 to 100°)— The expansion in the direction of the axis of a is ‘001771 + ry 6 is ‘001794 ”» ” ” c 1s 001814 Therefore cubical expansion for 82°5 is. . ~. °005379 —Archiv d. Pharm. vol. cxlviii. p. 19. DESCRIPTION OF VARIOUS PROCESSES MADE USE OF FOR FINDING OUT THE CONFIGURATION OF OPTICAL SURFACES. BY M. LEON FOUCAULT. One of the principal advantages of the reflecting telescope con- sists in having, instead of an object-glass, a mirror which acts by means of a single surface; which surface being concave, lends itself with remarkable facility to the application of the processes of exami- nation which permit the appreciation of its figure even to the least details. I conjointly make use of three different processes. The first con- sists in placing very near to the centre of curvature a very small object, such as the point of a pin, in order to obtain an image of the same size as, and very near to the object itself; this image can then be observed by means of a microscope and compared directly with the object. We are thus enabled to judge with certainty, by means of the amount of definition, of the effect which the mirror mounted as a telescope will give. If the image is imperfect, it is better then, with the view of ascer- taining the faults of figure, to take a luminous point and observe the appearance of the pencil of light within and without the focus. It will be seen to decompose itself in partial images, the discussion of which gives at once some information respecting the configuration of the surface of the mirror. But the two processes I am about to point out are still preferable, and give this information with greater precision. An object having parallel sides, such as the edge of a thin piece of steel, 1 millimetre (0°03937 inch) in thickness, is placed in the neighbourhood of the centre of curvature; and in order that the object may project itself in outline, it is enlightened from the side opposite to the mirror, and the image which is formed by it, being on a luminous ground, becomes very apparent, and presents in its aspect some peculiarities which depend upon the figure of the mirror. ‘This image, being observed with the naked eye at the di- stance of distinct vision, is seen in each of its parts, but by means of rays passing through the pupil after having been reflected from a very small part of the surface of the mirror; so that in these circum- stances the mirror only acts but partially, that is, by more or less restricted portions of its surface, which contribute severally to the formation of different parts of the image. Thus if the curvature be not uniform, the different parts of the image will not form them- selves in the same plane, and the angles subtended at the eye by the different parts will not be proportional to the corresponding part of 158 Intelligence and Miscellaneous Articles. the object ; in short, the image will be deformed, contractions and dilatations will be seen, showing a decrease or an increase of the radius of curvature of the corresponding element of the mirror, The method becomes more correct and more conclusive if, instead of allowing the edge to have an indeterminate position in space, we fix on the eyepiece of a small telescope, magnifying but little, and pro- vided with a narrow diaphragm comparable with the pupil. It is very rare that an image observed in such way will show itself free from any distortion, and such as a perfectly spherical mirror would give it; the edges, instead of remaining rectilinear, are bent most frequently in the shape of an hyperbola, and turn their con- cavity towards the interior of the field of the telescope; in presenting themselves under that shape they indicate that in every meridional section of the mirror the curvature goes on gradually diminishing from the centre towards the edge, which tends to correct to a cer- tain degree the spherical aberration. Lastly, it remains now to describe a process which allows of the examination of concave surfaces, so as to recognize directly, by an effect of relievo, the elevated and depressed parts which affect the figure. A thin piece of metal, pierced with a small hole of ;4th of a millimetre (0°00328 inch, or about =4=th of an inch), and enlight- ened by an artificial light, is placed within the centre of curvature; through that little hole the diverging pencil of rays falls on the sur- face which is being examined, and comes back converging to form an image which is situated a little beyond the centre. By placing the eye in the cone of rays which diverge anew, and bringing it towards the image, we at last receive the whole of the pencil of rays, which passes freely through the pupil; and at the same time the surface of the mirror will be seen entirely illuminated. Now if an opake and rectilinear edge be brought near the image of the hole and made to infringe on it by degrees, the mirror will also lose by degrees its brilliancy; and when all the light is about to disappear, the whole of the irregularities of the surface of the mirror will be plainly seen. In fact, supposing the surface to be correctly spherical, the image is perfectly well defined, and when allowed to emerge a little from the opake screen which is brought forward to intercept it, the rays which are not stopped off come from the whole surface of the mirror, which presents to the last a uniform brilliancy ; if, on the contrary, this surface shows here and there some parts which are situated above or below the spherical level, the elements which do not present themselves under the proper incidence cause certain rays to deyiate, instead of converging with their fellow rays (congénéres), towards . the different parts of the image, and to be dispersed in all directions. It results from this, that every point of the image, and in particular each of those which emerge from the opake screen, receives rays which do not belong to it, and does not receive those which do be- long to it. The missing rays will leave in their corresponding places on the surface of the mirror a deficiency of light, the accumulated rays will a a Intelligence and Miscellaneous Articles. 159 produce an increase of intensity in others; and from the contrast. of these different degrees of brilliancy, and on account of an effect of clair-obscur, an enormously exaggerated manifestation of the inequal- ities which really exist on the surface submitted to this sort of test will result. As the observation can only be made by means of a single eye, it happens that, under a mental influence independent of the will of the observer, the valleys and hills seem to overlie each other ; but with a little attention, what is a mere illusion will soon be distinguished from reality by considering that the true rising parts are neces- sarily contained between two opposite declivities, one of which being turned towards the screen, which hides the image, appears dark, whilst the other presents an increase of brilliancy. In other words, the true figure of the mirror is analogous to that which would corre- spond to the apparent relievo interpreted on that hypothesis, in which an oblique light would ccme from the side opposite to the screen. This process offers particularly the advantage of being at the same time expeditious and direct ; that is to say, a surface can be judged of in a few seconds, and when it is defective, the faults of it are known immediately with great precision. Generally, all that has any influence on the direction of the rays, or anything which prevents them from converging simultaneously towards a point of common convergency, becomes visible and is de- tected. By means of this kind of observations, among several causes which affect the result, that one which exercises a predominant influ- ence is easily distinguished from the rest. Thus the permanent irregularities of a surface will not be mistaken for the varying altera- tion due to the flexure of the mass of glass; and we can perceive the inequalities in the density of the ambient air, which passes whirling before the mirror, or which shows itself like stratified layers in the interior of the tube of the telescope. By taking the necessary precautions, all causes capable of producing an accidental disturb- ance are successively avoided, and the intrinsic faults or defects of the surface are the only ones which subsist. But, guided by the observation itself which causes them to be discovered, we suceeed, as I have demonstrated before, in correct- ing locally these defects; and, lastly, they can be reduced to such proportions as to exercise no sensible influence on the quality of the images. The mechanical processes by which the working of glass surfaces is usually effected seem to lose something of their efficacy as soon as they are applied to pieces of unusual dimensions; the results which they then furnish are but an approximation, a sort of trial which is far from being satisfactory ; but where mechanism becomes powerless, the hand of man can do something more: assisted by the resources placed at his disposal by optical science, and guided by a system of observations the efficacy of which increases with that of the instrument which is to be constructed, the human hand is enabled to proceed with the work, and to carry it out to the greatest degree of precision. If it be required to verify by optical means any one of the ellip- 160 Intelligence and Miscellaneous Articles. soidal surfaces which lead from the sphere to the paraboloid, the same identical process can be applied, provided that the object which is used as a mark be placed at one of the foci, and the image examined at the other. The information which is thereby obtained, and the corrections which must be deduced therefrom, are based on the same appearances; only they have reference especially to the sort of surface given by the position of the foci, and the inequalities which are discovered show deviations which are reckoned in the same way as for the spherical figure, viz. from the level of the correct sur- face which it is desired to obtain.—Proceedings of the Royal Astro- nomical Society, June 10, 1859. ON THE ORGANIC SUBSTANCE IN THE METEORIC STONE OF KABA. BY PROFESSOR WOHLER. The following note on the organic matter contained in the meteoric stone of Kaba was communicated by Haidinger to the Academy of Sciences at Vienna. Experiments made with about 10 grms. of powder and small frag- ments of the meteoric stone of Kaba, have shown that this meteorite, beside its free carbon, contains a carburetted substance which appears to have some similarity with certain fossil carburets of hydrogen, such as the so-called mineral tallows, Ozokerite, Sche- rerite, &c., and is undoubtedly of organic origin. Perhaps it is only a small residue of a larger quantity which the meteorite pre- viously contained, and which was destroyed, at the moment of the fiery phenomenon, with deposition of carbon. The fragments were reduced to powder, exhausted with perfectly pure alcohol, which was then filtered and evaporated. There re- mained a colourless, white, apparently crystalline mass, which pos- sessed a weak, peculiar aromatie odour. It was soluble in alcohol ; and this solution was rendered milky by the addition of water. In sether it was broken up into small oily drops, as if it had been decom- posed into an insoluble fluid, and a soluble solid portion. On the evaporation of the ether, the latter remained in a distinetly ery- stalline form. When heated in the air, the substance was volatilized in white fumes of a slightly aromatic odour. When, on the con- trary, it was heated in a narrow tube, it fused very readily, and was decomposed by a stronger heat, with deposition of a black coal and evolution of a fatty odour. The substance remained unaltered in caustic soda. The pulverized stone which had been treated with alcohol, when ignited in oxygen gas, gave but little vapour, and only a trace of sublimate, but a large drop of water, although it had been carefully dried beforehand. The powder, which had acquired a cinnamon- brown colour, became heated when water was poured over it; for it contained a large quantity of sulphate of magnesia, extractable by water, and some sulphate of nickel, formed by the sulphur of the sulpburet of iron contained in the stone—Sttzungsber. der Akad der Wiss. zu Wien, xxxiv. p. 7. THE LONDON, EDINBURGH ann DUBLIN PHILOSOPHICAL MAGAZINE AND JOURNAL OF SCIENCE. [FOURTH SERIES.] SEPTEMBER 1859. XXVII. Hydraulic Researches—Part Il. By G. Maenus, Pro- fessor of Natural Philosophy in the University of Berlin*. [With Two Plates.] On the swellings formed in jets issuing from circular orifices. 116. i the former part of my hydraulic investigations +t I con- sidered the shape of the water-jets. The remarkable forms assumed by streams issuing from angular orifices were there, I think, satisfactorily explained by showing that they depended upon the phenomena which occur when two jets meet one another at various inclinations. I also described the very much more regular shapes assumed by streams issuing from circular orifices. The singular swellings or “ ventral segments ” produced in circular jets by the sounding of a musical note, and which occupied the attention of F. Savart t, were there only considered in a general manner. Since then, by examining them with the aid of different appliances, I have succeeded in determining more decisively their nature and their cause. My observations are contained in the following communication. Those swellings were especially examined which are formed on vertically-descending streams; for these, being obtainable with greater regularity and uniformity than others, afford greater security for correct observation. 117. Inallowing the water to flow out, a vessel was employed of 04 metre in height and 0°8 metre in diameter, which was placed upon a firm stand of strong wood, 1°75 metre in height. This vessel is more fully described in Part I. § 40. As there Translated by Dr. F. Guthrie, from Poggendorff’s Annalen, vol. evi. p- 1. tT Phil Mag. ser. 4. vol. xi. pp. 89, 178. } Ann. de Chim, et de Phys, 2nd series, vol. liii. p. 337. Phil, Mag. 8. 4. Vol, 18, No. 119. Sept. 1859. M 162 Prof. Magnus’s Hydraulic Researches. described, plates could be introduced into the middle of the bottom of this vessel, containing orifices of various diameters. The streams issuing from these holes fell into a vessel placed upon a soft support and quite separate from the above-mentioned stand, in order that the motions in the receiving vessel might be as little as possible communicated to the floor and thence to the first vessel. Again, in order to reduce these motions to a mini- mum, and to avoid the noise occasioned by the falling water, a board was so placed in the receiving vessel as to make a small angle with the vertical, as is described in § 42. The jet of water on falling upon this, slid down it so as to occasion a scarcely audible noise. In order to make the stream as regular as possible, the “ tran- quillizer ” (Beruhiger) described in § 38 was placed in the first vessel. The circular motions in the water, and the consequent twistings in the jet itself, were thereby avoided. Jets without swellings. 118. In the first place, I must mention that repeated experi- ments have convinced me of the correctness of the assertion made in § 85, namely, that no swellings whatever are produced in a jet which flows out quite calmly, provided that the rotation of the liquid in the interior of the vessel is prevented by the “ tran- quillizer,” and that the jet is not subjected to the vibrations produced by a note or otherwise. Such a stream forms a con- tinuous, perfectly smooth mass, the diameter of which diminishes with the distance from the efflux-orifice to the point where disin- tegration commences. In its descent from this point the stream assumes a turbid appearance; at the same time it acquires a greater diameter, presenting an appearance like that shown in Plate I. fig. 1. There is no trace of alternate contractions and expansions either in the smooth and continuous, or in the turbid and discontinuous part. Now and then very small drops spirt out laterally from the point of commencing turbidity, and often also below it. This lateral projection of drops seldom occurs in jets issuing from orifices of 5 millimetres and more in dia- meter; but when the streams are narrower, the orifice being about 1 millimetre in diameter, the whole water-current is disin-. tegrated into fine drops, thereby assuming the form of fig. 2. 119, Savart* also mentions that the jet shows no swell- ings when all vibrations in its neighbourhood are avoided. His description agrees perfectly with that given in the previous para- graph, with the exception that he does not mention the small drops. In jets, however, of the diameter of those employed * Ann. de Chim. et de Phys. 2nd series, vol. liii. pp. 864, 365. a — oe Prof. Magnus’s Hydraulie Researches. 163. by Savart, these are seldom present in_such quantity as to be especially striking. 120. Even with a perfectly regular flow, it is difficult to esta- blish a quite steady stream; for if the water flows out under a pressure of about 20 centimetres, it is impossible to ensure the perfect constancy of the jet, even when the “tranquillizer” is used. With a smaller pressure, the jet, it is true, appears perfectly smooth ; but the smallest motion—that, for instance, occasioned by the passage of a carriage in a distant street—is sufficient to displace the image of an object seen by the reflexion from the jet. The formation of the swellings. 121. No swellings, however, are occasioned hy such shakings. In order that these may be formed, the vessel from which the water flows must receive regularly and quickly recurring motions. The fittest means for this purpose is furnished by the sounding of a note. Indeed for the production of regular swellings, scarcely any other means is applicable. For, as already remarked, for this effect to be produced, regular and quickly succeeding motions are necessary ; and such always produce the impression ofa tone. The effect of such regular vibrations is to cause swellings of about the form shown in fig. 3. The first swelling always lies much nearer to the orifice than does the point where the jet without swellings commences to become turbid. 122. As is well known, the jet itself occasions a tone, partly because its single separate masses of water set the air, through which they fall, in motion, but especially by the impact of these masses upon some solid or liquid. Hence swellings are often produced without the intentional production of a tone. It is only on the prevention of the percussion upon a solid body or upon water which has already flowed out, by allowing the stream to fall upon a board very ‘slightly inclined from the ver- tical, that the note of the jet is too weak to occasion any swellings, 123. Savart* asserts that if the note which the jet pro- duces by falling through the air, be sounded upon a musical in- strument, swellings are immediately produced, and that these are also formed by the sounding of certain other notes which stand in a simple relation to the first. He asserts, moreover, that, on the contrary, no such swellings are produced by the sounding of notes which have no such simple relation to the note of the jet itself. My experiments have confirmed this aesertion ; but only for the case where the stream flows out under a pressure of at least 10 centimetres. If the pressure be * Loe. cit. p. 357. M 2 164 Prof. Magnus’s Hydraulic Researches. smaller, say 2 or 3 centimetres, swellings are produced by every note sounded in the neighbourhood of the jet. Under such cir- cumstances even the human voice is sufficient to produce them. Very high notes alone seemed incapable of causing swellings ; at least by very high notes I was unable to form them in a jet of 5 millimetres diameter. 124. If the pressure under which the water flowed out was so great that swellings were not produced by any but the original note of the stream, or tones standing in simple relation to it, such swellings were nevertheless caused by bringing the sound- ing body into immediate contact with the vessel from which the water flowed, or with the stand on which the vessel rested. 125. For producing the notes, I have made much use of a small electro-magnet, the keeper of which was fastened to a spring whose motion alternately broke and completed the circuit. This arrangement, known as “ Neef’s hammer,” or the magnetic hammer, may be so adjusted that the motions of the spring and keeper correspond to certain tones which, at least within certain limits, may be varied at pleasure. 126. Sometimes, instead of this apparatus, I employed differ- ent tuning-forks, especially one very large one which sounded C below the line. 127. The magnetic hammer, however, has the advantage of producing one and the same note for a long time with undimi- nished strength, thus allowing precise observation. Moreover, in employing it, no mechanical force is necessary, as is the case with stringed instruments, organ-pipes, &c., which force, when the sounding body is in contact with the vessel from which the water flows, or with its stand, imparts a swinging motion to the latter, and consequently to the entire jet. 128. When the magnetic hammer produced a different note from the original one of the jet, or one not simply related to it, no swellings were observed as long as the hammer was held in the hand, however nearly it might be held, during vibration, to the stream. But on laying the hammer upon the stand upon which the vessel stood from which the water flowed, the swellings were immediately produced. They appeared with especial sharp- ness and distinctness when the hammer was firmly screwed down upon this stands For, when this was the case, the vibrations became more régular, and the note less grating and harsh, than when the hammer was simply pressed upon the stand with the hand. Similar phenomena were produced by the use of the tuning- fork (§ 126). If the fork were struck and held in the hand, no change was produced in the jet, unless the note of the fork accidentally coincided with the original tone of the stream. No Prof. Magnus’s Hydraulic Researches. 165 swellmgs were formed even when the fork was held quite close to the stream. If, on the contrary, after being struck, the fork was held upon the stand, swellings immediately appeared, what- ever might be the relation between the note belonging to the jet and that of the fork. With small tuning-forks which did not possess either the ori- ginal note of the stream or notes simply related to it, I was unable to produce swellings even when the forks were placed upon the stand. I was equally unsuccessful with an organ-pipe 0°63 metre long, which was screwed upon the stand and sounded by means of a distant bellows through a tube. It is of course understood that this behaviour only relates to the apparatus mentioned in § 117, and which I usually employed. In another instrument less strongly made, swellings were pro- duced by placing on the stand even smaller forks, whose tones were neither the same as, nor simply related to, that of the jet; and this occurred even when a greater water pressure was employed. The swellings are produced by the vibrations of the orifice through which the water flows, and not by the direct action of the undu- lations of the air upon the jet. 129. It follows from these experiments, that the swellings are chiefly caused by the oscillations imparted to the vessel from which the water flows; and that, on the contrary, the direct communication through the air of the undulatory motion of the sonorous body acts upon the jet only to a very slight extent, or not at all. 130. The fact that swellings are occasioned by sounding bodies which give either the same note as, or a harmonic of the note of the jet, and which, being held in the hand, cannot commu- nicate their motion otherwise than through the air, does not prove that the changes are effected directly through the air. For we must not forget that when the peculiar note of the jet is heard, the vessel from which the water flows invariably gives forth a note as well. Hence the peculiar note of the jet is de- pendent upon that which the vessel itself would give; and the former must stand in some simple relation to the latter. When therefore a note is sounded which is simply related to that of the jet, it must be also simply related to that of the vessel. Consequently the vibrations of the sounding body, although only propagated through the air, augment the vibrations of the vessel, and, as will be shown more clearly in the sequel, the form of the jet is thereby changed. 131. If the note produced by a body held in the hand be suf- ficiently strong, its vibrations are communicated to the vessel 166 Prof. Magnus’s Hydraulic Researches. even when the note sounded is not the same as, nor a harmonic of, the note belonging to the vessel. If the tuning-fork (§ 126) be fastened to a large sounding-box, and, after beg struck, be approached to the stream, swellings are produced even by a much greater water-pressure than when the fork is used without the box. 132. If the pressure under which the water flows out be so chosen that the tuning-fork without the sounding-box produces no swellings when held at some distance below the orifice whence the water flows, when the fork is then approached quite close to the opening, without of course touching it, swellings immediately appear. PP his is an additional proof that the vibrations of the sonorous body are not communicated to the stream directly through the air; for if such were the case, the swellings must occur indiffer- ently, whether the sounding body be approached to the upper or lower portion of the jet. 133. In order to prove the effect of the vessel, and especially of its bottom, the following experiment was made:—Into the bottom of the vessel a plate was introduced provided with a casing projecting downwards of 3 centimetres diameter, having an orifice of the same width. A second casing furnished with a plate, cd (fig. 4), in which the exit-orifice for the water was situated, was fastened to the first case by means of a caoutchouc tube, a, of the same diameter and 8 centimetres long. In this manner the hole for the flow of water was only connected with the reservoir by the caoutchouc tube. On allowing the water to flow out of the apparatus so arranged, the caoutchouc tube became elongated, and the plate with the efflux-orifice began to vibrate in such a manner as to render an examination of the jet impossible. To avoid this, the plate ¢d was made 15 cen- timetres in diameter, and was supported upon two cushions, # 2, of soft woollen cloth. The cushions themselves rested on a firm support, that is, upon a board, fg, provided with a hole 6 cen- timetres in diameter, through which the jet fell. This board, J 9 was also separated from the stand PPQQ by means of woollen cushions, < z. 134. After the vessel had been so arranged, if Neef’s hammer was screwed upon the foot P Q of the stand PP QQ and set in vibration, no swellings were formed. But on connecting the plate ¢d by means of any solid body with the bottom AB of the vessel, as by slipping a piece of wood between AB and ed, swellings were formed of full size and distinctness. The action of the wood or of the solid substance introduced, consists in its communicating to cd the same vibrations as occur in the bottom of the vessel. In the absence of this solid substance, Prof. Magnus’s Hydraulic Researches. 167 the vibrations can only be communicated to the plate through the water, and then no swellings are produced. At first 1 em- ployed a tube of vulcanized caoutchouc. But in this case swell- ings were formed even when no solid body existed between the plate and the bottom; and these swellings were not much in- creased in strength when a piece of wood was introduced. The commercial vulcanized tubes of 3 centimetres in diameter are, however, rather stoutly made, and hence it happened that the vibrations of the bottom were communicated through the caout- chouc to the plate cd. On employing a tube of very thin non- vulcanized caoutchouc, no such communication took place. 135, Hence there appears to exist no doubt that the swellings are produced by vibrations in the bottom plate. Inasmuch, however, as this plate cannot vibrate without setting the mass of water in the yessel in similar vibrations, and as, inversely, the vibrations of the water set the bottom plate or the edge of the egress-orifice in vibration, it follows that both exercise their influence upon the formation of swellings. But it follows from the experiments described in the preceding paragraph, that the vibrations of the bottom plate, or of the edge of the egress-orifice, are the immediate cause of the swellings. 136. If, while the stream is flowing out, a soft body be held below against the bottom plate AB, the swellings undergo an appreciable but inconsiderable alteration. We must not, how- eyer, conclude from this that the bottom does not vibrate. For if a body which is not too soft, such as a plate of cork, be pressed by the hand against the bottom, the vibration is felt through this plate as soon as the sounding tuning-fork is placed upon the stand, or as soon as the battery is connected with the Neef’s hammer, which is screwed upon the stand. The swellings change with the strength of the note. 137, The distance from the efflux-orifice at which the swellings begin, changes with the strength of the note which causes them, although the pitch of the latter remain the same. This distance is smaller the stronger the note. If the tuning-fork be struck and placed upon the stand at P, very strong swellings are immediately produced, the first of which often lies quite close to the efflux-orifice. In proportion, however, as the vibrations of the fork become weaker, the com- mencement of the swellings is depressed, so that the swellings often begin far down the jet. A similar effect is produced on sounding a note on a violoncello. 138. It is not only when the jet flows out of a hole in the thin wall of the vessel that swellings are produced on placing the tuning-fork on the stand; the same are formed when it flows 168 Prof. Magnus’s Hydraulic Researches. through a tube which is narrowed towards the bottom. But in such a case they are less distinct and sharply defined than when the flow takes place through the thin wall. The same is true on employing the magnetic hammer or the violoncello. Nature of the swellings. 139. It is known that the swellings consist of separate isolated masses of water. However regular their form may be, still the separate masses may be recognized in them. If, for instance, a piece of wire, or foil, or other light body be so held in the hand that one of its ends penetrates a little way into the jet, a uni- form pressure is felt when the substance is struck by the smooth part of the stream. But if it be struck by a swelling, a strong vibratory motion is felt. 140. ‘A flame which is brought into the neighbourhood of the jet, burns calmly as long as it is held near the smooth part; it is disturbed on being held near a swelling. The separate masses of water which constitute the swelling, clearly communi- cate their motion to the air, and this agitates the flame; while the smooth part of the stream, being continuous, scarcely moves the air at all. 141. In the investigations on the motions of liquids (Phil. Mag. ser. 4. vol. i. p. 1), I have already mentioned (§ 3) that a flame is not agitated on being brought near the continuous por- tion of the stream. I have found this confirmed. But if, stead of the flame of a candle, that of a Bunsen’s gas-lamp be used, the tap of which is only slightly opened, so that the gas escapes only under a very feeble pressure, then the flame is drawn a little down with the current when the latter passes through the burning gas. It follows from this that even the continuous por- tion of the stream draws the air somewhat with it; but with so small a force that, as soon as the gas leaves the burner under an increased pressure, the flame is not carried along with the current. Observations by means of a rotating mirror. 142. The nature of the jet can be examined with greater accuracy if it be illuminated from a single point, and a mirror be used for observing it in, of a few centimetres in breadth and height, which revolves about a vertical axis. For the illumina- tion, a simple lamp in a dark room is sufficient; it is better, however, to employ a lamp in a lantern from which the light is directed by means of lenses upon the portion of the jet to be examined. In order to effect the rotation of the mirror, I generally employed a piece of clockwork, which was set up at a distance of about a metre from the stream. If the mirror remains in the same situation, only a small portion of the stream can be Prof. Magnus’s Hydraulic Researches. 169 seen init. In order therefore to observe the different portions of the jet, it was necessary to fasten the mirror with the clock- work upon a stand which could be raised or lowered at will. In the same manner the lamp was obliged to be fastened upon another stand in order to illuminate the different portions of the jet. : 143. When no note is sounded and all is in perfect tran- quillity, if the strongly-illuminated smooth part of the stream be viewed, a broad luminous surface is seen in the rotating mirror. If, however, swellings are produced by means of the magnetic hammer mentioned in § 125, and the mirror is adjusted to one of them, isolated separate luminous lines are seen in the mirror in the manner shown in fig. 5. 144. These lines can only arise from the observed part of the jet either consisting of separate rounded masses, or having an- nular swellings—that is, alternating greater and smaller dia- meters. For if we imagine a small round mass of water—a drop—to remain in a fixed position, and the mirror in which the drop is seen reflected also to remain still, we can only see a luminous point, because the rounded mass of water only reflects the light fallmg upon one point of its surface in such a manner that it can pass from the mirror into the eye of the observer. If the mirror remains stationary without revolving while the drop is moving downwards, instead of a point, a luminous vertical line is seen. But if the mirror turns round while the drop is falling, the vertical line is changed into one inclined to the horizon, and under certain circumstances into a bent one, whose inclination is greater according as the mirror rotates more quickly. But at the place at which the drop was first seen, a second, then a third, &c. appears, each one forming a similar inclined or bent line of light. As, however, the mirror has already changed its position when the second drop comes into the place of the preceding one, the different drops are reflected simultaneously from different parts of the mirror, and hence the lines appear to run together side by side. The di- stance between these lines depends upon the angular velocity of the mirror. I have seen them most distinctly when the mirror turns once in a second upon its axis. 145. These lines may also be seen if the mirror be not set in rotation by clockwork, but if it be moved backwards and forwards by hand. In this case, however, the lines cross one another and form a net-like figure, similar to fig. 6. 146. If the continuous portion of the stream above the swell- ings be viewed by the mirror when swellings are produced by Neef’s hammer, and remain very constant, lines similar to those produced by the swellings are seen; these, however, are much 170 Prof. Magnus’s Hydraulic Researches. broader, having nearly the form of fig. 7, Frequently no inter- vals at all occur between them. They then form a luminous Hite which appears notched above, but irregularly bounded elow. 147. It follows from the above, that when swellings are pre- sent in the stream, even that portion of it which otherwise ap- pears smooth to the eye has alternating greater and smaller diameters. But, as stated, this is only the case when swellings occur in the lower portion of the stream. When these are absent, the upper continuous part of the jet next the efflux-opening is perfectly smooth ; that is, its diameters continually decrease to the point where it begins to be turbid. Savart’s method of observing the jet. 148, In order to investigate the different parts of the jet, Savart, as is well known, made use of the endless strap described by him*, provided with alternate bright and dark bands. In place of this strap we may employ, as Savart himself proposedt, and as has since been done by many other experimenters, a wheel provided with spokes, which is placed between the strongly- illuminated jet and the observer, or between the source of light and the stream, so that in the latter case the stream is between the wheel and the observer. If, then, the wheel be put into such quick rotation that the separate spokes can no longer be distinguished, the part of the jet above the swellings ap- pears quite smooth and continuous, presenting thus the same appearance as it does to the naked eye, only somewhat more faintly illuminated. But if the wheel with the spokes be placed opposite a swelling, isolated masses separated from one another in a yertical direction are recognized, if the proper velocity of rota- tion be given to the wheel. The form of these masses, however, cannot be recognized by means of the spoked wheel, even although the stream be illuminated in a darkened room by the system of lenses mentioned in § 142, 149. A simple consideration is sufficient to inform us why the form cannot be recognized. If, namely, two motions occur in opposite directions, as is here the case in respect to the stream of water and the spoked wheel, the outlines of the sepa- rate moying masses cannot appear as they are in reality. We need only remember that two wheels, having spokes as broad as the spaces between them, and turning with equal velocity on a common axis in opposite directions, give the appearance (if the number of the spokes of the wheels is the same) of one wheel with the double number of spokes. Each spoke appears then half as broad as it is in reality. * Loc. cit. p. 349. t Loc. cit. p, 348. Prof. Magnus’s Hydraulic Researches. 171 If only one spoked wheel be employed, in conjunction with a dise placed behind it and provided with circular holes, when the dise and the wheel revolve in opposite directions, the holes no longer appear round, but oblong; and by using different dises, it is easy to convince oneself that the outlines always appear of a different form to what they are in reality. 150. The anorthoscope described by M. Plateau, as well as the other very ingenious contrivances which this physicist has given for similar metamorphoses, depend, as is well known, upon this alteration in the outline. 151. In order to make such alterations in outline visible, I have had an apparatus constructed by means of which two dises of the most different kind may easily be made to revolve in the same or opposite directions with the most variable velocities. The discs are made of thin pasteboard; so that any number of them, very various in respect to the shape and number of their orifices, may be easily procured. If such dises be covered with a solution of shell-lac, they do not absorb moisture from the air, and are very durable. Lach disc has its own axis; but both lie in the same horizontal line. Each axis receives its motion by means of a cord passing oyer a roller. The two rollers are parallel, but are placed vertically against a large brass plate, against which they are pressed by springs. On turning the brass plate, the rollers which are pressed against it turn also through friction. One of the two rollers may be moved along its axis. If the system is so arranged that the two rollers touch the brass plate on opposite sides of its centre, they revolve in opposite directions. If they both lie on the same side, they turn in the same direction. The nearer the moveable roller is to the middle of the plate, the smaller is its velocity. This principle of motion has already been employed by Mr. Faraday*, in a somewhat different form, for a similar purpose. * Poggendorff’s Annalen, vol. xxii. p. 601. + The apparatus which I have had made is shown in Pl. I. fig.8. ab and ed are the two axes with their dises AB and CD. The axis ad is set in motion by means of the strap fy: the latter passes over the roller p, which is furnished with a projecting rim. Its axis is fastened in the frame z z, by which it is pressed by the spring & against the brass plate MN. The axis ed is set in motion in the same manner by means of the strap hh passing over the roller g. The axis mn of the latter fits into the frame az. The roller itself has no projecting rim; instead of this, there is upon the same axis mn the small metallic disc r, which is somewhat greater than the roller g. The dise r may be moved along its axis mn, so that it can be brought between m, the centre of the plate MN and n, or between m and q. The frame xz is fastened at 11 between points, and is so pressed by the springs // against the plate MN, that when the latter moves on its axis m, the dise r is moved by Fietion, and sets its axis mn, as wellas the roller q, in motion. In order to give the plate MN the necessary velocity, a pinion is fasts 172 Prof. Magnus’s Hydraulic Researches. Observation by means of the electric spark. 152. In order to observe the form of an object which moves with great velocity, it is sufficient to illuminate it for a single moment. Hence the electric spark has been proposed for in- vestigating the jet. By its means, however, I have not been able to recognize more than that the swellings consist of separate masses. The form of these masses could not be determined, either by those who were engaged with me or by myself. I imagine that the cause of this is the following :—The rounded masses of which the swellings consist reflect the light emanating from a point in such a manner that the eye sees only the single point of each which is principally illuminated. Hence, when the stream is illuminated by the electric spark, the swellings appear like a string of pearls; but their form cannot be recog- nized, because the intensity of the light reflected from the remaining portions of the masses is too small to allow this, on account of the velocity with which the impression is lost. Observations by means of a very narrow rotating shit. 158. Inasmuch as the means mentioned were not sufficient to recognize the form of the separated portions of the stream, I have had to scek for other ones. ‘The object has been com- pletely attained by the employment of a dise having a single slit in the direction of a radius, and not quite a millimetre in breadth. This disc must revolve before the eye with such velocity that we imagine the stream to remain continually visible, although its light can only reach the eye after the completion of a revolution. If the jet be viewed through the slit when it is moving from below upwards, that is, in the opposite direction to the stream, ened upon its axis m (which pinion is not shown in the figure), in which the toothed wheel RS works. The wheel RS is turned by a winch. A trifling arrangement is perhays deserving of mention, by means of which it is possible quickly to replace the pasteboard dises AB and CD by other ones. In order to set up a new paper disc, it is generally neces- sary to loosen completely the screw A by which the dise CD is fastened. In order to avoid this, the paper discs have in the middle a hole of the form ¢«, fig. 10. Upon the axis ed there is a small brass screw which has a projecting rim. In fig. 9, y represents this screw with its rim #. The circular part of the hole ¢¢ in the pasteboard dise fits exactly upon the rim wz, which is a very little conical. There is also a piece of brass, 8, upon the axis cd. The anterior form of this piece of brass has the form 77, which is shown in dotted linesin fig. 10. The piece of brass may be turned round the axis cd, and may be pressed against y by adjusting the screw A. Ifa pasteboard dise has to be set up, its hole, €«€, is passed over A and 8; the piece 8, which also serves the purpose of a washer, is turned and pressed by the screw A against the pasteboard dise. In order that, in taking off the disc, the piece 8 may be easily disengaged, it is advisable to introduce a couple of turns of a spiral spring, », in the rim @. Prof. Magnus’s Hydraulic Researches. 173 the form of the masses appears somewhat shortened, but incon- siderably so, because the slit is very narrow. Inthe same man- ner the form appears somewhat, but inconsiderably, lengthened, if the eye be so placed behind the disc that the observation takes place while the slit is moving in the same direction as the stream. Moreover the observation may be performed at the moment when the slit is parallel to the stream; and then the breadth of the latter appears almost the same as it is in reality, and it is also seen unchanged in the direction in which the water moves. All three kinds of observation may be employed in order to supple- ment one another. But the last-mentioned method of observing the jet is the surest, and it has also the advantage of allowing a much greater portion of the stream to be seen at once. 154. The discs which I used had a diameter of 250 millims. As the breadth of the slit was at most 1 millim., it was about 7eoth of the surface of the disc. The light which reached the eye from the jet on turning the disc, bore, consequently, the proportion of 1: 780 to that which was transmitted when no disc was there. It was necessary therefore to illuminate the stream very strongly if it had to be observed by means of the disc. In order to see the stream uninterruptedly, it was neces- sary to give 20 to 25 revolutions per second to the disc. Be- tween each two of these feeble impressions of light an interval of from ,}, to z;th of a second elapsed; and each impression endured for +55 to ;g;pth of a second. 155. If, instead of one fine slit, four be introduced into such a disc, the observation cannot be properly performed. For if the velocity of the dise remains unchanged, it is true that the time of each separate impression of light remains also unchanged; but the impressions follow one another at intervals of from 4 to ~i,th of a second; and this interval of time is too short for observation. If, on the other hand, the disc be turned more slowly, so that the times between the observations become longer, the slits pass more slowly before the eye, the outlines of the separate masses undergo a more considerable alteration, and the distinctness is thereby spoilt. Appearance of a jet without swellings when seen by means of the narrow slit. 156. But if the apparatus as it is described in § 154 be em- ployed, the jet appears, everything being tranquil and no swell- ings present, as is represented in Pl. II. tig.11. This represen- tation is taken from a jet which issued from a hole 3 millims. in diameter, under a pressure of 5 centims. But all jets which issue from somewhat smaller, as well as from much larger cir- 174 Prof. Magnus’s Hydraulie Researches. cular openings, show a similar behaviour, as far as I have been able to observe them. The higher portion of the stream is smooth; and its diameter diminishes only very gradually to a. From & to 8, where it commences to become turbid, separate contractions appear. The parts of the jet between these assume more and more a sphe- rical form, Finally, the rounded masses separate and form di- stinct drops of various size and form, which follow one another irregularly. : 157. The separation of the jet into distinct masses occurs, therefore, in precisely the same manner as is described by M. Plateau in the second series of his excellent investigations, ‘Sur les figures d’équilibre d’une masse liquide sans pesanteur*. 158. The regularity with which the individual masses form and separate is, however, not very great. I imagine the cause of this to be, that at the considerable distance from the efflux- orifice at which the contractions begin, the velocity of all parts which lie in the same section (at right angles to the axis of the stream) is no longer the same. Hence also occur sometimes the very small drops which move laterally. The smaller the efflux- orifice, the greater is the number of these drops which are formed. Appearance of a jet with swellings when observed by means of the fine slit. 159. The appearance of the jet is quite otherwise when swell- ings occur in it. It is true that the upper contmuous por- tion appears smooth to the naked eye, and even by help of the rotating disc, swellings can scarcely be recognized in it; but on employing the rotating mirror, we may convince ourselves, as has been already mentioned in § 146, that it has alternating greater and smaller diameters. It is very surprising, on employing the mirror, to see how the broad, luminous, smooth band shown by the stream as long as it has no swellings, immediately appears notched as soon as a struck tuning-fork is placed on the stand, or as soon as the magnetic hammer is set in action, Inasmuch as the swellings or differences in diameter of this part of the stream, especially at a small distance from the orifice, are so inconsiderable as not to be recognizable by means of the rotating slit, it is not possible to represent them in the drawing. Viewed, however, through the rotating slit, the swellings appear as they are represented in fig. 12. Above the first swelling at 8, very small excrescences appear, which gradually inerease in size Their forms are very regular throughout. Shortly before separating as distinct masses from the stream, they are only connected by very narrow masses of water, which appear like * Taylor’s Scientific Memoirs, vol. v. p, 585. Prof. Magnus’s Hydraulic Researches. 175 thin rods. From these thin masses of water, as they separate, small drops appear with great regularity between each two of the greater ones. These small drops are not to be confounded with the much smaller ones which move laterally, and which have been mentioned in the previous paragraph and in § 118. Such laterally-moving drops, it is true, are sometimes produced when the stream has swellings, but only when the note which causes them is impure, or when two inharmonious notes are sounded at the same time. These small drops, which regularly occur between two of the larger drops, and which fall vertically, give the appearance of a hollow cylinder placed in the middle of the swelling, as Savart has already mentioned. They are so small that a change in their form cannot be recognized even by means of the rotating slit. On the other hand, as Savart has also mentioned, the larger drops appear in some places broader than they are long, in others longer than they are broad. At the middle, where a swelling occurs, a spheroid is formed whose yer- tical axis is smaller than its horizontal one. On the contrary, at the point midway between two swellings they appear elongated, so that their vertical axis is greater than their horizontal one. 160. It follows from Savart’s observations*, that by means of the band he employed with alternating light and dark stripes, he only observed the swellings to consist of isolated separate masses. The shape which he gives to the curve in drawing is rather a deduced than an actually observed one. The greater the credit due to him! The actual observation by means of the rotating slit is now very simple. 161. If swellings are to be formed in a stream, the regularity in the separation of the drops must not only take place in such a manner that all the drops are equally great, but the time which elapses between the formation of two of them must remain con- stant, and the place also at which the drops separate from the stream must remain always the same. For it is only under these conditions that all drops on arriving at the same part of the stream, for instance at the middle of a swelling, are drawn out to the greatest extent in a horizontal direction, and that in the middle between two swellings they are vertically most elongated. It is just on account of their assuming the different diameters always at the same place, that they produce the impression of swellings. 162. It would be erroneous to suppose that in a jet which does not show any swellings, the separated masses of water do not also change their form in such a manner as to appear at one time elongated, and at another flattened and broad. But these masses are not all of the same size, nor do they separate * Ann, de Chim, et de Phys, 2nd series, vol. liii, p. 349. 176 Prof. Magnus’s Hydraulic Researches. exactly at the same part of the continuous portion of the stream. Hence they do not all appear vertically elongated at the same part, nor all of their maximum breadth at another single point in the stream; but at one and the same part are found masses quickly following one another, some vertically elongated, others extended laterally ; consequently they do not produce the im- pression of regular swellings. But that the separated masses are always broadened, appears not only from observation with the rotating disc, but from the fact that the turbid part of the jet is always broader than the smooth continuous portion. 163. The regular separation of the masses of water is con- ditioned by the vibration of the bottom plate, or, more exactly, by that of the rim of the efflux-hole (as appears from the experi- ment § 134). As this edge moves uniformly up and down, the velocity of the stream which flows out is alternately accelerated and retarded; and through these regularly alternating accelera- tions and retardings the alternating contractions and expansions are produced which, lower down the stream, effect its separa- tion into distinct drops. If these alternate accelerations and retardings are not present, the swellings are wanting, and the separation occurs at a greater distance from the efflux-orifice and with much less regularity. Probably, when swellings are present, the smaller distance at which the distinct masses separate contributes, to no small extent, to the increase of regu- larity ; for all motions in the stream are more regular at a small distance from the efflux-orifice than when more remote from it. 164, The stronger the vibrations of the effiux-orifice, or what comes to the same thing, the greater the intensity of the note which causes these vibrations, the greater also is the difference between the alternating accelerations and retardings, and the less therefore the distance from the efflux-opening at which the sepa- ration takes place and at which swellings are produced. This has been shown by the observations given in § 137. The jet flowing out of a very narrow opening. 165. The following observation furnishes an interesting con- tribution to the effects of the vibrations of the efflux-orifice. If water be allowed to flow from a narrow orifice whose dia- meter is less than a millimetre, the small drops into which the stream separates move quite irregularly, somewhat as represented in fig. 138. But on sounding a note, the particles arrange them- selves with great regularity : a certain number always follow one another immediately ; a somewhat greater interval intervenes ; then the former number of drops occur again, as is shown in PI.I. fig. 14. The greater intervals correspond to the elevations of the orifice. of ~ Prof. Magnus’s Hydraulic Researches. 177 Formation of drops. 166. If water be suffered to flow through a tap so that its velocity may be altered at pleasure, and if the tap be so adjusted that the drops are formed separately and at rather long intervals of time, the drops are seen at first to assume the form of fig. 15 if the efflux-opening has a diameter of 8 millims.: this agrees with Savart’s representation. They then contract, as is shown in fig. 16, and immediately afterwards they fall. If this pro- ceeding be watched by means of the rotating slit, it is seen how, at the moment of dropping, a thin narrow thread of water (ad, fig. 17) is formed out of the contracted portion which connects the drop with the residual water. From this thread are gene- rally produced two or more smaller drops. 167. More than one of these small drops are produced if the greater drops are formed in somewhat quicker succession. The residual liquid (a, fig. 17) is seen then after each separation to move backwards and forwards; and if during these undulations the new drop is separated, smaller drops are produced in greater number ; nor do they then all fall vertically. It is not difficult to understand how such undulatory motions give rise to irregularities in the separation. Similar irregular motions doubtless give rise, even in a stream without swellings, to small laterally-moving drops (§§ 118 and 158) at the extreme end of the continuous portion. 168. If the formation of the drops be accelerated by adjusting the tap so as to gradually increase the flow of water, the drops are suddenly transformed into a continuous stream. Drops are also formed from this, but only at its extreme end. Moreover, in comparison with those which were formed quite close to the efflux-opening, they are very small, because the diameter of the stream rapidly decreases. It is sometimes possible so to adjust the tap, that the drops are formed at the efflux-orifice itself, but following one another with a velocity almost equal to that with which they are transformed into a continuous stream. In this condition only a slight percussion is required to effect this trans- formation and to cause the sudden junction of the drops. It is then very remarkable to observe how very different is the size of the drops which are formed in the two cases. These phenomena, which have doubtless been frequently ob- served, explain, as I imagine, the formation of the smooth con- tinuous part of the stream, as well as that of the small laterally- moving drops in the stream without swellings. The form of swellings which are disturbed by solid bodies, 169. I cannot avoid mentioning some singular forms assumed Phil. Mag. 8. 4. Vol. 18. No. 119, Sept. 1859. N 178 Prof. Magnus’s Hydraulic Researches. by the stream, which show with what regularity the drops move in the swellings. If into the first, second, or any regularly-formed swelling when it is at its maximum breadth, a cylindrical body, for instance a glass tube (c, fig. 18) of 1 centim. in diameter, be introduced horizontally almost as far as the internal cylinder zz formed by the small drops, but with the precaution of not touching it, the swelling assumes the strange shape shown in fig. 18. The small drops pursue their way undisturbed, so that the internal narrow cylinder zz is seen unaffected. The greater drops, on the con- trary, are drawn by capillarity against the glass tube. In con- sequence, however, of the velocity which the water has attained in falling, smaller and greater portions of it pass continually over the glass tube by a, and are thrown out as drops of various mag- nitudes. At the same time a thin surface of water (za, fig. 18) is seen, which below d collects again to an irregular mass, and in which separate peculiarly-formed lines are seen by certain de- grees of illumination. 170. If this portion of the jet be examined by means of the rotating slit ($ 154), it appears as is represented in fig. 19. The great drops are seen to be attracted by capillarity upon the glass tube, and thereby assume a long pointed form. As soon as they are separated from the glass they can no longer retain this form, they are decomposed imto several separate drops, which move, however, with the same velocity, so that they remain in concentric circles whose centre lies in the glass tube c. As long as these drops move uniformly, they appear to the unas- sisted eye like the thin surface of water zab. But at some di- stance down, more and more of them are thrown off laterally, whereby the expansion of the surface is diminished. Examination by means of the rotating slit furnishes no expla- nation of the peculiar lines which, by certain kinds of illumina- tion, are seen in this surface, z ab, fig. 18. Probably they depend upon the reflexion of the light from different drops of equal size. 171. If, mstead of the glass tube, a fine wire be introduced into a perfectly-formed swelling, with the precaution that the narrow internal cylinder zz is not touched by it, the stream is divided as is represented in fig. 20. Here P denotes the fine wire, and zz the narrow cylinder. If the jet having this form be examined by the rotating slit ($ 154), it is seen that the drops in the two limbs, P X, P Y, into which the stream becomes divided, remain at equal distances from the wire P, and that the small drops which form the vertically-descending narrow cylinder Pz move at about the middle point of the distance between each two drops in PX and PY, just as they would have moved between the great drops if these had not been separated by the wire P. In Prof. Magnus’s Hydraulic Researches. 179 fig. 21 this appearance is represented. The drop a, which is divided by the wire P, is very plainly seen, but it is generally situated somewhat below P, as is shown in the figure. It is clear that the drop can only be seen on the wire P if the revolv- ing slit passes before the eye at the exact moment when the drop is upon P. Inasmuch, however, as the distance between two of the great drops is very much greater than their diameter, the slit passes before the eye very much oftener when the wire P is situated in the interval between the drops than in the interval when a drop is passing by. Hence the divided drop is seldom seen on the wire, but generally when it is already beneath it. Deviation of the jet on the approach of an electric body. 172. If an electric body, such as a rubbed rod of glass or rosin, be approached to a jet which has no swellings at the part where it is still quite continuous, the jet is deflected somewhat as is shown in fig. 22, in which E E represents the electric rod, A B the vertical, and BC D the deflected part of the jet. 173. If, in a similar manner, the electric rod be approached to the middle of a regular swelling when the electric action is of a certain strength, it is only the internal narrow cylindrical part 2 z of the stream which is deflected ; so that this portion separates entirely from the swelling, somewhat as is shown in fig. 23. 174, That is, the small drops which form the internal cylin- drical part, are much more easily attracted by the electric body by induction than are the greater drops which give the outer form to the swelling ; so that the lesser ones are deflected from their path, but not the greaterones. This deflection occurs with every small drop in the same mauner and at the same place; consequently they all pursue the same direction, and produce thereby the impression of a narrow curved stream, just as, with- out deflexion, they produce that of a narrow vertical cylinder. So great, however, is the regularity of the motions of the stream, that the lower swellings appear still quite unaltered after the de- flection of the small drops. 175. On the approach of an electric body, besides the regu- larly-deflected internal cylinder, sometimes distinct streams of water proceed out of the swellings, which are as fine as threads of glass, and, like these, follow the electric body. ‘They are formed out of the fine drops which, as mentioned in § 159, sometimes spirt out laterally from the swellings when the note producing the swellings is not pure, or, which is the same, when two inharmonious notes are sounded simultaneously. N2 180 Prof. Magnus’s Hydraulic Researches. Jets moving vertically upwards, or inclined at any angle to the horizon. 176. Hitherto only those jets have been considered which flow from above downwards. All others, whether moving verti- cally from below upwards, or at any inclination to the horizon, behave quite similarly. All jets which issue from a perfectly circular opening are smooth and continuous close to the open- ing; at a greater distance they become turbid, and then have a greater diameter, separating at the same time into distinct drops. On examining the turbid portion by means of the rotating slit, the formation of the drops is seen to take place in a manner quite similar to that described in § 156, of streams flowing from above downwards, which are represented in fig. 11. The dimen- sions alone are somewhat different ; that is, the distances of the rounded masses from one another are smaller. 177. Ifthe efflux-orifice, or the stand on which the vessel or tube is fastened bearing this orifice, is set in vibration by means of a sounding body, swellings are formed in these streams also in exactly a similar manner as in streams flowing vertically down- wards. But the swellings so formed are never so regular as in the former case, because the efflux takes place under a greater pres- sure, and is therefore less uniform. On examination by means of the rotating slit, these swellings behave, it is true, so far similarly to those formed in streams flowing vertically downwards as they consist of separate greater drops which change their form; but the smaller drops occurring between each two of the larger ones, described in § 159, are often entirely absent, or they are often so irregularly disposed as not to move either in the middle be- tween two of the greater ones, or in the same curve with them. Separation of the jet into two or three parts. 178. At a certain inclination of the stream to the horizon, which may be different for the different pressures at which the water flows out, the larger drops often do not all pursue their paths in the same curve. They are then spread through a larger space, and give rise to the appearance which Savart* has called the “ Garbe.” 179. This phenomenon is doubtless due to the very small motions communicated to the efflux-orifice perpendicularly to the direction of the stream by the vibrations of the sounding body, and which may be called transversal motions. Although these motions cannot be detected by the eye, they may be recognized by the hand. The efflux-orifice used in my * Loc. cit. p. 380. — Prof. Magnus’s Hydraulic Researches. 181 experiments for these jets was cut in a plate at the end of a tube which could receive different inclinations. Savart appears to have employed a similar arrangement for these streams, as is seen in the drawings which he gives of them*. If the hand be placed on the tube while the sounding body is on the stand on which the tube is fastened, the transversal movements may be plainly felt. These movements give rise to similar ones in the continuous portion of the stream, which, although excessively weak, are sufficient to give different directions to the drops at the moment of their separation; so that they do not all follow the same curve, but are spread out over a greater space. 180. Sometimes the “ garbe” is transformed into two or three streams which separate from the same point of the original stream, so that the latter is divided into two or three branches which often still show regular swellings. 181. If such a divided stream be examined by means of the rotating slit, two or three different rows of drops, all emanating from the same place, are seen, which correspond to the number of branches into which the chief stream has been divided. But at the same time it is seen that the drops of the different rows do not all leave the point of separation at the same time. For if, for instance, two streams are present, it is seen how the two jets are formed of alternating drops; so that if the drops be re- presented by numbers in the order in which they separate from the continuous part of the stream, the one row contains the drops 1, 3,5, 7, &c., and the other the drops 2, 4, 6, 8, &c. Simi- larly when three rows are present. Inasmuch as the drops of the separate rows always follow the same direction in such a manner as to describe the same curves, it follows that the drops of one kind, for instance the even ones, must leave the continuous part of the stream when it is in a definite place, and the odd ones when it has reached another place. Consequently a defi- nite relation must exist between the intervals of time m which the separations follow, and the times of the transverse motions ; so that the intervals between two drops belonging to one and the same branch must be equal to one transverse backwards and forwards movement of the stream. Since both the separation of the drops and the transverse motions of the stream are produced by vibrations of the efflux-orifice, in consequence of the latter being set in motion by the sounding body, not only in the direc- tion of the stream, but also at right angles to it, a simple relation must exist between these motions; and hence a division of the stream into two branches may easily take place : it is not so often possible to divide the stream into three branches. * Annales de Chimie et de Physique, 2nd serics, vol. lvi. plate 3. 182 Mr. A. Gages on Vivianite. This splitting of the jet also shows how great the influence of the vibrations of the efflux-orifice are upon the jet. LEiffect of a note upon jets issuing from angular openings. 182. If we examine, by means of the rotating slit, a stream which flows out of an angular opening from above downwards during the existence of a note, we see that the higher portion, which shows with great regularity the singular forms described in the previous part of these investigations ($$ 44, 45, 61, 64), con- sists of a continuous mass of water, and that where the regularity is less, rounded masses are formed in the stream. At the com- mencement of their formation these masses appear to be com- posed of several spheres or drops, formed at the edges 77, 7,7, of the surfaces described in § 45, where these surfaces, even to the naked eye, no longer appear smooth and continuous. These spheres gradually unite to a single drop, which still at first shows traces of its derivation, but continually assumes more and more the spherical form. In fig. 24 the attempt is made to represent this appearance as it is presented by a jet flowing out of a long four-sided opening (§ 14), and seen through the revolving slit. 183. If a sounding body or the magnetic hammer (§ 125) be applied to the vessel from which the stream flows, or to the stand upon which the vessel is placed, no swellings, it is true, are formed, as is the case with the circular orifice, but the forma- tion of drops begins (in consequence of the vibrations) at a less distance from the efflux-orifice, and at more uniform intervals of time, than when no note is sounded. In streams of greater diameter this action of the note is less noticeable, but in thinner ones it is very distinct. The influence which the vibrations of the efflux-orifice exercise upon jets which issue from angular orifices, is therefore precisely similar to the effect when the orifices are circular, although in the former case no swellings are formed. XXVIII. On Vivianite. By Atruonse Gacus, M.R.I.A.* fa “eas important functions which phosphates perform in organic nature, give peculiar interest to everything con- nected with the history of their occurrence as minerals. They are found in all formations, not excepting igneous rocks; but the crystallized phosphates are more usually found in the older, while the nodules or masses of phosphate of lime chiefly occur in the more modern formations. Vivianite is, however, a striking * Communicated by the Author. Mr. A. Gages on Vivianite. | 183 exception to what has just been stated, as it has been found in the horns of the Irish elk, and even in human bones. Stalagmitic-like concretions and nodular masses of phosphates appear to be immediately derived from organic bodies, and may have been formed by the double decomposition of phosphate of lime, held in solution in water, by carbonic acid and salts of metallic oxides, or by the reverse action of soluble salts of me- tallic oxides upon earthy phosphates. One of the most interesting mineral phosphates is the blue protophosphate of iron, which, when crystallized, is called Vivian- ite, —the earthy varieties being known as blue iron earth, Angla- rite, &e. This phosphate is found either crystallized or amor- phous in all formations, from the oldest to the most recent ; and there is no doubt that it can be formed in a very brief space of time, as the observations of Schlossberger show that the blue matter sometimes found in the pus of ulcers has the composition of Vivianite, the iron being derived from the disorganized blood- corpuscles. Considerable doubt exists as to the true constitution of Vi- vianite. Rammelsberg assigned to a specimen analysed by him the formula 4(3FeO, POS) + 2(3FeO, PO®) + 3Fe? 08, 2P0°+16HO, or 6(3FeO, PO® + 8HO) +3Fe? 03, 2P0*+8HO. The observations of Barreswil upon Abich’s salt, 3(FeO, SO?) 2(Fe? O?, 380°) +4HO, which he obtained of an indigo-blue colour, appears to lend sup- port to the view that Vivianite contains sesquioxide of iron. On treating the blue sulphate with phosphate of soda, he obtained a blue salt which was not decomposed by water. Rammelsberg assigned to this artificial phosphate the formula 2(3FeO, PO*) +3 Fe? 03, 2P0°+ 16HO. The ordinary basic phosphate of protoxide of iron, obtaimed by adding a solution of basic phosphate of soda, 3NaO, PO, drop by drop, to a solution of a protoxide salt, and which has the composition 3FeO, PO®, is white when first thrown down, but gradually becomes blue on the filter. If the blue colour be owing to oxidation, it must take place very rapidly, and only a very small portion of sesquioxide must be necessary to produce the blue colour; for this is found to have penetrated the whole mass on the filter, even before it is wholly washed. This is further shown by dissolving a portion of the blue earthy phosphate in weak hydrochloric acid, and adding sesqui- 184 Mr. A. Gages on Vivianite. carbonate of ammonia, when a milky-white precipitate, appa- rently of phosphate of the protoxide of iron, is thrown down. This white precipitate, kept from contact with air, sometimes assumes a bluish tint on exposure tothe light. If, instead of using weak cold hydrochloric acid ih the preceding experiments, boiling acid be employed, the solution assumes a reddish tint, and the preei- pitate thrown down by the sesquicarbonate of ammonia is of a reddish colour ; the absorption of oxygen by the precipitate also takes place more rapidly in this case. If we employ caustic ammonia in the first instance instead of sesquicarbonate, the precipitate, instead of being milky white, has a reddish tint. The colour of the crystallized Vivianite also deepens, as well as the streaks, which, being bluish white, soon change to an indigo colour on exposure to the air; and even colourless crystals, as those from the greensand of Delaware, only become blue on exposure. The clay upon which the blue iron earth is found is generally whitish, showing that the iron present is protoxide; and it has been observed that the blue bloom is often formed only after exposure to the air. Berzelius considers that the white compound which becomes blue has the composition of 3 FeO, PO®, or rather a hydrate of it. It is no doubt the same compound which is first formed in the elegant process by which Becquerel has succeeded in producing erystal- lized Vivianite. He forms two cells, separated by a diaphragm of moist clay; in one he puts a solution of sulphate of copper, and in the other one of phosphate of soda; he then dips a copper rod into the solution of the copper salt, and an iron rod into the solution of the phosphate, and brings the two rods into connexion. After a time white crystalline nodules are deposited on the iron, which quickly become blue on exposure to the air. It is not, however, by oxidation alone that Vivianite can be produced; the circumstances under which many specimens are found, show that its formation is due perhaps oftener to deoxida- tion than to oxidation: thus im Cornwall it always occurs asso- ciated with pyrites, or magnetic iron pyrites. In the first, its production may easily be accounted for by supposing the forma- tion of the sulphate of iron and a double decomposition between the sulphate so formed and apatite. Perhaps the Vivianite often found filling the cavities of amygdaloidal trap may have been likewise formed in a similar manner. I have on one occa- sion observed it coating, like blue paint, zeolitic minerals found in such cavities, clearly proving that its formation was posterior to that mineral. The most favourable circumstances, however, under which Vivianite appears to be formed by deoxidation, is during the decay of the organic matter of the bones. During the process Mr. A. Gages on Vivianite. 185 of decay, which in moist earth is necessarily very slow, carbonic acid, marsh-gas, hydrogen, and sulphide of hydrogen are evolved. In the presence of such gases, any sesquioxide of iron present would be reduced to the state of protoxide; in this state the carbonic acid evolved by the decomposing bone or surrounding organic matter is sufficient to dissolve it, as well as phosphate of lime, which under such circumstances would be rapidly taken up, as the experiments of Moride and Bobierre have fully established. Double decomposition would of course ensue between two such solutions, with a formation of phosphate of protoxide of iron. As plants contain a certain amount of phosphoric acid, and as during their decay the same favourable conditions for the reduc- tion of the sesquioxide of iron exist as in the decay of bones, Vivianite may be formed wherever vegetable matter decays in the presence of compounds of iron. For example, the ashes of peat often contain as much as 3 per cent. of phosphate (part being sometimes phosphate of iron); and consequently peaty soils or turf moors may be expected to present the conditions essential to the formation of blue iron earth. It has accordingly been found in many bogs in almost every county of Ireland. The specimen of iron earth which I desire at present to con- sider, presents an excellent example of this kind of reducing action. This specimen was obtained from the margin of the bog of Allen; the blue phosphate is disseminated through a mass of clay and sand mixed with peat, or rather what appears to be carbonized peat. The clay itself exhibits traces of combustion, and it appears to be slightly baked here and there; it very probably formed part of a peaty soil burned for the purpose of reclaiming the land. The remains of the plants usually found in peat are observable, such as species of Sphagnum, hazel-nuts, Erica; a stem of the last-named plant in a perfectly carbonized state, and also some hazel-nuts, are covered over with the blue iron earth. The question naturally suggests itself, whether the action of fire would have had anything to do with the production of the blue phosphate? There can be no doubt that blue phosphatic compounds may be formed at a high heat. If phosphate of magnesia, or lime containing traces of iron and intimately mixed with organic matter, be submitted to a strong heat, it frequently acquires a sky-blue colour, evidently due to the formation of a phosphate of iron. This blue colour may often be seen when phosphate of ammonia and magnesia is burned in a filter containing traces of iron: a slight trace of carbonic acid is evolved on moistening the phosphate with an acid, indicating that some of it has been decomposed. Kyen if we admit that Vivianite contains sesquioxide of iron, 186 M. F. Eisenlohr on the Relation between the direction of we cannot thereby solve the problem of the blue colour. Beu- dant suggests that it may be owing to the hydration of the phos- phates, instancing the example of the white anhydrous sulphate of copper becoming blue on taking up its water of crystallization. This might account very well for the production of colour m compounds which pass from the anhydrous to the hydrated con- dition, but cannot apply to the phosphate, inasmuch as the white phosphate precipitated from protosalts of iron is hydrated while in the white condition; and it has never been shown that there is any change im the quantity of water in passing from the blue moditication. Then there is the formation of a blue phosphate in the crucible, under conditions which preclude the possibility of water of hydration. The change may be allotropic, or per- haps like the change of colours which light produces in some kinds of glass, which gradually assume a decided pinkish tint, although at first free from colour. This tint is due to manga- nese ; but how are we to account for the gradual development of the colour ? XXIX. On the Relation between the direction of the Vibration of Light and the Plane of Polarization, and on its determination by means of Diffraction. By Frinpricu Etsentour of Hei- delberg*. ae question whether the particles of «ther in a ray of polar- ized light vibrate perpendicularly to the plane of polarization, or in that plane, has been lately revived and earnestly discussed. Two distinguished observers, Stokes and Holtzmann, have endea- voured to decide the point by help of the phenomenon of diffrac- tion ; but though the availability of this method cannot be denied, yet the two experimenters in question have in fact arrived at different conclusions. As Stokes has not communicated his own experiments, and as he does not appear to doubt the accuracy of those of Holtzmann, we shall direct our attention principally to the latter. Holtzmann found that a ray of polarized hght which passed through a glass plate, and was diffracted at its lower surface through a grating of lampblack, was diffracted in greater quan- tity when the plane of polarization before diffraction was parallel to the bars of the grating, than when perpendicular; or, gene- rally, that the plane of polarization of the incident ray was in the diffracted ray turned towards the direction of the slits of the diffraction grating. According to the theoretical considerations that had led both him and Stokes to these experiments, this * Translated from Poggendorff’s Annalen, vol. civ. p. 337. ——————— the Vibration of Light and the Plane of Polarization. 187 result seemed to favour the conclusion that the ether vibrated in the plane of polarization. But though it is true that the ex- periments of Holtzmann thus indicated a twisting of the plane of polarization in the opposite direction to that which Stokes, according to his hypothesis, had anticipated, yet on the other hand it must be observed that this twisting was, on the average, actually twice as great as it ought to have been according to the observer’s own calculations ; so that it was at all events very bold to regard those experiments as supporting a theory with which they agreed so ill. I, at least, concluded that neither of the two theories could account for the actual results observed, and that it was necessary to subject the phenomenon of diffraction out of one medium into another to a more accurate examination than it had hitherto undergone; and accordingly, by assuming with Stokes that the «ther vibrations are perpendicular to the plane of polarization, 1 found that we are led to formule which agree very well with the experiments of Holtzmann. The great work of Stokes on diffraction has unfortunately not been accessible to me; but what both he and Holtzmann have to impart concerning the theory in question in communicating their experiments, may be briefly summed up as follows :—The zther-vibrations in a ray of light which falls perpendicularly on a diffraction grating, proceed parallel to the plane of the grating ; if therefore the light be diffracted, the vibrations may be divided into such as are perpendicular to the diffracted ray, and such as are parallel to it,—the former alone giving rise to the diffracted light, the latter being wholly without influence on the diffrac- tion; from which it follows that the plane of vibration of the diffracted ray is always parallel to the vibrations of the incident ray, and, further, that if the vibrations of the incident ray make the angle y with the plane of diffraction (i. e. the plane that contains both the incident and the diffracted ray), while those of the diffracted ray make the angle y', 8 being the angle of dif- fraction, then Whether, however, the longitudinal vibrations are really with- out any effect, deserves more particular investigation. We shall see directly that they produce an effect even in the case of dif- fraction in a single medium, but that when diffraction takes place im the passage from one medium to another, as in the above-mentioned experiments of Holtzmann, their influence admits of no doubt. I would here advert to the formule which Cauchy has adduced for the intensity of reflected and refracted light. Assuming the two hypotheses, that when an ether wave 188 M. F. Eisenlohr on the Relation between the direction of arrives at the bounding surface of two mediums, the motion of the zther at this surface must be the same, and also must be conti- nuous in both mediums, but taking into account therewith the longitudinal vibrations, he found that the formule previously enunciated by Fresnel, which had not regarded these vibrations, must be modified. These modifications were confirmed in the most remarkable manner by the researches of Jamin. The accuracy, indeed, with which the observed elliptic polarization, and the intensity of reflected light, fulfil the hypotheses of Cauchy is so great, that it hardly leaves a doubt of the sound- ness of the theoretical basis of the latter; and particularly the hypothesis advanced by Cauchy, that the vibrations of the par- ticles of ether in polarized light are perpendicular to the plane of polarization, must be regarded as established. I have accord- ingly felt no hesitation in applying to the theory of diffraction the above-mentioned conditions, viz. that the motion of the par- ticles of ether at the bounding surface of two mediums is the same, and is continuous in both. In this way I have found that the longitudinal vibrations, in this case at all events, exert a con- siderable influence; much greater, indeed, than in the experi- ments of Jamin, since in these experiments a magnitude had to be considered which depended on the very small difference of the length of the waves, or, more correctly speaking, of the co- efficients of absorption of the longitudinal vibrations in the two mediums, whereas the intensity of diffracted light depends on the product of these coefficients. For the present I shall con- tent myself with announcing the results I have obtained, and indicating generally the methods by which they were arrived at, deferring the more detailed calculations to another occasion. We might expect to be not far out in determining the relative intensity of rays of light that vibrate perpendicularly to the plane of diffraction and those that vibrate in that plane, if we regarded the ray diffracted out of glass into airas generated by the refrac- tion of a ray whose direction is connected with that of the dif- fracted ray by the law of Snellius, but whose vibrations are parallel to the surface of the glass. In this way, with the assist- ance of the above-mentioned conditions, we get a formula which agrees tolerably well with the experiments of Holtzmann. But the perpendicularly incident light is replaced in its effect on the diffracted ray by an oblique pencil on the surface of the glass itself, though not in the stratum lying infinitely close to that surface, which it is necessary to consider according to the prin- ciple of continuity. If this be so, we get the more accurate equation now to be communicated. Let y and y’ have the same meanings as before, let x be the index of diffraction for glass, X the length of a wave in glass, the Vibration of Light and the Plane of Polarization. 189 ae the coefficients of absorption in glass and air, that is Xr Bi (og to say, the logarithms of the proportions in which the longitu- Xr 2a’ 2' being the angle of diffraction ; then if n sin a= sin a’, we have dinal vibrations diminish when propagated in the path tan y cos (2—a!) 14+2sin($) ein f iss The following Table exhibits a comparison of the results of this formula with the experiments of Holtzmann.- In it I have 1! = as 9°5. tan 9/ = assigned n its ordinary value 1°53, and have taken according to | Y according to a, y- y' as observed. oe eas G). the calculations of Holtzmann, 10 36 45 36 44 27 44 34 45 9 20 17 44 5 40 32 40 32 42 15 20 35 45 36 40 52 41 57 43 43 31 5 45 0 38 6 37 29 40 35 32 17 45 36 38 4 38 9 40 49 How well the observed values of y' agree with those calculated from formula (1), will be seen at once from this Table. The most considerable disagreement, that namely of 1° 5! in the third observation, may be accounted for on the grounds of an error of experiment, since this observation, for a diffraction renter by only 18! than the second, givesa totally different value of EBay If, however, no experimental error has really affected this se then I should imagine that the two observations must belong to two different diffraction-spectra; and I can see therein some evi- dence bet for colours that hie far apart in the spectrum, the mag- nitude —, must have somewhat different values, a conclusion i iF which on other accounts also is not without probability ; but perhaps it is not safe to rest an hypothesis on so small a number of experiments. It might be thought that, at all events, diffraction in a single medium would be governed according to Stokes’s laws. In order to observe the phznomenon, two glass plates, on one of which a diffraction grating had been scratched, must be so pressed together that, if possible, Newton’s rings may wholly disappear. But by means of formula (1) it may be anticipated that, in this 190 M. F. Eisenlohr on the Relation between the direction of case also, the effect of the longitudinal vibrations will be even still more evident. The formula becomes banshee ee Tee, 5 See 2, sin? = From what precedes, it will be seen how peculiar an interest the experiments referred to possess, even though they do not afford so direct a solution as had been anticipated of the problem immediately proposed. They ave, in fact, the best means of testing the existence of longitudinal vibrations in light ; and it is impossible to exaggerate the importance to science of a thorough and varied experimental investigation of these phenomena, since, besides the means they afford of coming to a conclusion on the soundness of the hypotheses here advanced, they throw light on this question of the existence of longitudinal vibrations. To return, however, to the point which gave rise to these experi- ments. I may observe that the view which the above formula involves, viz. that the ether vibrations in polarized hght are per- pendicular to the plane of polarization, receives so much support, not only from the agreement above pointed out between the result calculated from that formula and the experiments, but also from other considerations, that we may, I think, consider it as proved. I have already mentioned, with reference to this subject, that the remarkable confirmation which the calculations of Cauchy received from the experiments of Jamin, is a striking evidence in favour of the view concerning the direction of the ether vibra- tions which the former propounded as the foundation of his cal- culations, and which is the very one above stated. Another evidence is to be found in an old theoretical work of Fresnel, which unfortunately is too little known. From the phenomenon of aberration, we have reason to believe that the ether which surrounds the earth docs not partake of its motion. As, therefore, the light of a star which les im the direction of this motion undergoes some alteration on this account in the rapidity of its propagation relatively to the earth, as well in empty space as in the substance of bodies themselves, and this, too, generally in different degrees, we might expect an alteration in the refractive powers of transparent bodies for such light, so that the image of a star refracted through a prism would be more or less displaced. This displacement must, it would c seem, depend on the first power of a where ¢ represents the ra- v pidity of the carth’s motion, and w the rate of propagation of light ; it must therefore, like aberration, be measurable, and be of a ae Oh 5%" the Vibration of Light and the Plane of Polarization. 191 opposite kind as ¢ changes sign, that is, according as the earth approaches the star or recedes from it. Nevertheless Arago, with the most accurate instruments, was unable to detect any such displacement. Fresnel, in a letter to Arago*, explained this negative result on the hypothesis that the elasticity of cther is the same in all bodies, but that its density is proportional to the square of the index of refyaction ; and it is not easy to see how the fact can be accounted for in any other way. This, at least, as is well known, was the hypothesis which was adopted by that physicist to explain the different velocity of light in different media, and which stands in necessary connexion with the doc- trine that ether vibrates perpendicularly to the plane of polari- zation. The confirmation, therefore, which the above hypothesis receives in Fresnel’s essay extends also to the doctrine in question. I may perhaps hope to assist in disseminating an acquaintance with the interesting demonstration given by Fresnel, by substi- tuting a simple geometrical proof for the algebraical one which he makes use of. Let LL! be a pencil of light A B incident perpendicularly on the & first surface A C of a glass prism, andsuppose it to issuefrom a star from which the earth is moving directly away. It will then pro- eced without deviation as far as PM. For the sake of simplicity, instead of the earth moving and the ether remaining at rest, sup- pose the earth to be at rest and the surrounding. «ther to move with the velocity C in the opposite direction. The density of the ether within the prism being, then, to that without, as A , sides ; : Fee to 1, its rate of motion in the prism will be Ai since the par- ticles of ether, which are at the surface AC at any epoch, must travel a unit of length from it in the same time that it takes those to the depth + in the prism to issue from it, so as to occupy in vacuo a stratum of space a linear unit deep. If, then, w denote the velocity of light, n the index of refraction, the wave of light PM, which begins to leave the prism at M, will move from P to N with the velocity ~ f. and if the time it takes A * Ann. de Chim. et de Phys. 1818, vol. ix. p- 56. 192 M. F. Eisenlohr on the Vibration of Light. be ¢, we have PN=—S. Meanwhile a circular wave will have spread from the point M, and in the time ¢ will have acquired a radius tw; but at the same time it will have been’ carried back a distance ct, so that its centre, instead of being at M, will be at M’, a distance ctf within the prism (it being of course understood that the wave which has issued from the prism remains outside). The position of the emerging ray is therefore obtained by drawing from N a perpendicular upon the line M/R=tw. In order to observe this ray, however, the telescope must be brought into the position MR;; because if MR be its length, the zther moves from M to M’ in the same time that it takes a ray moving in ether at rest to pass over the di- stance M’R, so that the ray takes the resultant direction MR. Now the experiments of Arago have shown that this direction is identical with that which the refracted ray would have in still ether; at least so far as the accuracy of the experiments went, which took account of the ratio =; but not of its square. This fact may be used to determine A ; for if, from N, the perpendicular NS be let fall on MR, then, from what precedes, we must have MS=nPN=tw—cet x Drawing, then, MU perpendicular to BO, and UV perpendicular to MR, on account of the similarity of triangles RNS and URV, and of triangles NMS and MUV, we have NS. UV=RS.RV=MV.MS; and from the last equation it follows, as may easily be seen, that MS=RV=tw—et5, whence n __tw—RV_MR—RV Lice) fttanctege eM ME On account of the smallness of the angle M’RM, UR=VR nearly, and therefore MR—RV=M'U; and if TM’ be drawn parallel to UM, TM may be substituted for UM’, from which it differs inappreciably, and we get n MT snMM'T A MM'~ smMTM” in which only those magnitudes are neglected which depend on c , ; the square of —, and which therefore elude observation. w On the Distribution of Electricity on Spherical Surfaces. 198 But MM’T = NMP, and MTM’=180°—MNS, and also sn NMP_ 1 sin MNS — N° Whence viz sinMM'T _ sin NMP me 1 QA” snMTM'~ sn MNS _ 7’ or oi, which was to be proved. I have said above, that the law of density here assumed con- ditions also the hypothesis that the vibrations of light are per- pendicular to the plane of polarization. If, however, instead of the above supposition that the earth is at rest, we had considered that, as is actually the case, the surrounding zther is unmoved while the earth has the velocity c, the result is obviously the same ; the absolute velocity, however, with which the zther moves in the prism is now equal to the velocity of the prism itself, less the velocity it would have had in the prism at rest on the opposite Pra 72 | ; that is to say, the ether is carried along with the prism, though not at the same rate. This result was confirmed latterly by Foucault by direct experi- n2—1. 1 72 18 nearly 3. act c supposition, or c— A =e( ment with water, where XXX. On an Analytical Theorem connected with the Distribution of Electricity on Spherical Surfaces.—Part II. By A. Cay- LEY, Esq. (Continued from p. 127.] © ie theorem is certainly true ; but its existence gives rise to a difficulty to which I shall advert in the sequel. I pro- pose, in the first instance, to give a demonstration which starts from the expression for fz given by Plana’s equation (115), instead of the deduced equation which was the basis of my former proof. It will be proper to explain the origin and meaning of the formule. We have two conducting spherical surfaces, radii 1 and 4, in contact with each other (so that the distance between the centres is 14+). And then, if z is the distance from the centre of the sphere radius 1 of an exterior point, and «(= cos 0) the cosine of the inclination of this distance to the line from the centre to the centre of the other sphere, the potential $(u, ) of the sphere radius 1 at the point whose coordinates are (a, ) is deduced from the potential fx of a point in the axis ; that is, if fe=Aot Ayat+ Aga? + &e., Phil. Mag. 8. 4, Vol. 18. No. 119. Sept. 1859. O 194 Mr. A. Cayley on an Analytical Theorem connected with then b(, 2) =AgPy+ A,Pyw + AgPq2* + &e., where P,, P,, P., &e. are Legendre’s functions, viz. the functions of » which are the coefficients of the successive powers of # in the development of (1—2u#+2*)~* in ascending powers of 2. And the electrical thickness y at any point of the surface of the sphere radius 1 is given by the formula d x yao es) +2(u, 2), where, after the differentiation, z= 1. The problem consequently depends on the determination of the potential fx for a point on the axis; and this is determined by the functional equation b 1+b—2z ) its bh ibe 1+26-(1 ont ras she TR (Plana’s equation (G), in which I have written for 8, y, H their values, and substituted also for g its value =f). The solution of this equation is (equation (H), writing therein g=/) F ~ 1 ilar J—z ais ae +6)—n(1+d)z : i "oat 1(1+d)—C+n(l +8) a” where P is an arbitrary constant guoad the functional equation, viz. any function whatever which has the property of remaining ; : : 1+6—z ‘ unaltered when # is changed into 14 2%—( 45° Poisson, and —bh> Plana after him, arrive at the conclusion that in the physical problem P=O. It appears to me that there is ground for hold- for e=1 P. (ap (which, if P were retained, would be a term occurring in the ex- pression for the thickness at the point of contact) is not of neces- sity zero. But the term, if it exists, can be replaced at the con- clusion ; and I write therefore x 1 wn 1 fo= in Fen +8) —n( + Be ate aA +b)—(1+n(1 +4)) According to the process by which the solution of the func- tional equation was obtained, this is the true form of the solution ; for although the series are non-convergent, and the two sums are in fact each of them infinite, there is nothing to show a rela- tion between the number of terms which must be taken in each ing that this is only true sub modo, and that the Distribution of Eleetricity on Spherical Surfaces. 195 series. However, nothing immediately turns upon this, as the expression is only used for obtaining an expression for fz in the form of a definite integral, viz., equation (36), dt P—(1—?'-*) fe=bh 9 Lt Faa=a) j or, equation (39), 1 i oa 1 Eee (1+4)(1—2) pes bh dt (t-i+—1)t (1+4)1—2)), 1-¢ the latter of which gives (equation (115), in which I have written for a its value way jas tft wehi=a)~ W(s353=5) } where Z'(p) is Legendre’s function ales Tp, which is develop- able in the form 1 'p Sp mp where B,, B,, &c. are Bernoulli’s numbers. This is the starting-point of the present investigation ; and attending to the equations log (+A) __ 1 A vra rt ae log (1+-A) _.._ A '=0(4> 1), log (1+ A) 0» A 1s erty we see that the development of Z'p becomes log (1+A)/0_ 0? “ A p UW eto — ke.) = log p+ +» Ree tie (r+), which, observing that log (1+A) _ (a 24) Z'p= log p+ logp=0, ean be expressed under the more simple form Zp = PEO A)iog (p +0). 02 196 Mr. A. Cayley on an Analytical Theorem connected with We deduce hence ’ ae hb log (1+ A) 1+b—2 f-qeyady° AS {loe( qa +5) b ie Cessires) oe 0) } =: or what is the same thing, —log (6+ (1—2)(1+ b)0) } ; which may be converted into = Ab log(i+A)(? dt 145 A » o+t(l—z) ab log fists Sge) { toe af Pads Sebo Sl GE oi Co eal as A »l—a+b+(1—a) +50 J, b4+(1—a)(1 +00 f? or what is the same thing, ae hb log(1+A)(' dt ee Ss peme = 9 O+i—tz eo, : dt 1 dt A ~ Ud, A +8)(1 +10)—2(1 +(1 +6)t0) { b+ (1+5)00—2(1+d)t the object of the transformation being to express fx so that # 1 log (1+ A) ae The factor A which multiplies the first of the three definite integrals, might be reduced to unity, but it is more convenient not to make this change. 1 Now if a fraction aS be operated upon by expanding in +0) may only enter under the form ascending powers of z, and multiplying the successive terms of the development by Po, P,, Pa, &c., it is converted into 1 (A2—2A Bua + Bx?)*” Hence from the foregoing expression for fz we pass at once to the expression for f(y, 2); that is, we have _ Ab log(1+A)( dt oUS 2) 146 A J, (A2—2A Bua + B2z?)? -Ueert ot - dt (" dt A oa Al?—9Q A'Blua =e B2x2)* BY Al2_9 A" B" wax rs B!'2z%)* ; the Distribution of Electricity on Spherical Surfaces. 197 | where for shortness, A=6+t, A’=(1+8)(14+20), A”=54(1+0)00, B= f¢, B=1+(1+6)0, Bl= (1+4+08)00 And it may be remarked that 3 A'=1464+B", BI=1+B", A"=5+B". We thence obtain d 2B?) + 24(u, 2) _ fb log crs’ (A? — B72”) dt 146 A Jy (A2?—2AByur + B2x?)? — a Pia + & ea (A’?— —B?a?)\dt dt (Al? — Bl2z 2) dt i} (A? — 2A'Blux + Bi222)3 :-{" (Are 2A" Bl" wx + Bl222)2 and writing =1, a. hb log ama (A?—B?)dt 1+b A o (A2— 2ABy, + B2)2 log (1 Fo f (es (A’?? —B’?\dt 1 (A'?—B" )dt }. A (A? —2A'Bly + B2)2 = (AM2— 2A" Bly + Bl'2)2 The integrals in the foregoing expression are of the form { (G+ Héjdt o (L+2Mt+ Ne#)? The value of the indefinite integral is 1 (NG—MH)t+ MG—LH LN—M?—(L4+2Mt+Ne2)2 from which the value of the definite integral can be at once found. It is easy, by means of the values to be presently given, to verify that, in each of the three definite integrals, NG --MH=0; and the expression for the definite integral is therefore MG—LH 1 ert LN—M? paesroet Li In the first integral we have G=—F, ise 5, H=2s, M=d(1—p), N=2(1—p), whence LN —M?=27(1—,)(1+ p), MG—LH=—23(1+,), L+2M+N=0?+2(1—y)(1+4), L=2?; 198 Mr. A. Cayley on an Analytical Theorem connected with and the integral is —b { 1 of ; I—n LVe420—p)(1t+d) OS" For the second integral we have G=b? + 2b, L=6?4+2(1—,)(14+4), H=20(1+0)0, M=(1—y)(24+4)(1+2)0, N=2(1—,)(1+4)?0?; and thence LN —M?=(1— y)(1+ )b°(1 + 4)?0?, MG—LH=—(1+,)s9(1 +4)0, L+2M+N=2?+2(1 me aaa ace =? +2(1—p)(14+4); and the oe of the integral is 1 aya —)O { ssi. (1+4)((1+0)?4+6(0+0%) 1 ~ V8 4+2(1—p)(1 +5) For the third integral, G=)?, ier H=20(1+6)0, M=(1—,)d(1+3)0, N=2(1—p)(1+6)20%, and thence LN—M?=(1—p)(1 +)67(1 + 0)0?, MG—LH=—(i + )d9(1+4)0, L+2M+N=0?+2(1—p)(1+5)(0°+6(0+02)), i lee — 6; and the value of the integral is : 1 t (1+4)(1—»)0 { Vb? +42(1—p)(1 +4)(0*+(0+0") ) if Hence the expression for y is —hb? — log (1+A) 1 1 Y“(=w+s) OB Ve+214+u)(1+6) 2 hb? log (1 +4) ~ (L=p)(1 +4) o ns alae ei ah eh dl) yn De f Vb? +2(1—p)(1+4)((1+0)?+000+0%)) 2?+ 201 —p)( ah : the Distribution of Electricity on Spherical Surfaces. 199 hb? ~— log (1+.A) Fa=ya4) AT a ee Vb? 42(1 —)(1+5)(0°+4(0+02) ) b ; the top line is destroyed by the second terms of the other two lines, and we have _ =Ab?_—itog. (14+. A) 1 “(l—p)(i+4) A SPORE eT cy 1 : V¥0242(1—p)(1 +H(O+H0408) f° This expression admits of expansion in positive integer powers of 1—m; and when so expanded the result ought, according to Plana’s theorem, to be identically equal to zero. AndI proceed to show that this isin fact the case. The coefficient of (1— pe)! is to a factor prés of the form Hee C9) (1 +08-+0(0+0%))"—(0°+5(0408))"}, which is the sum of a series of terms each of the form lo 1+A) m—27 m—2n B\n BETA) 4 oy"? 10 40%)"; this is equal to log (1+A 08 eb £(1+0)"-"0"—0"™="(1 4.0)" }, which is of the form BC+) £4 soy (1+0)0"}; where « + 8=2m is even, or what is the same thing, a—£ is even ; and, as remarked im the first part of the present paper, such expression is in fact equal to zero. The demonstration, which is very simple, will be given in a note; but assuming for the moment the truth of the proposition, the coefficient of (1—y)"~" is the sum of a finite number of evanescent terms, and it is therefore identically equal to zero. I consider this demonstration as identical in principle with that given by Plana; the same function is, by two processes, different indeed from each other, but which cannot but lead to the same result, developed in an infinite series of positive integer powers of (1—,) ; and it is shown that the coefficient of each power of (1—,) is equal to zero. But the difficulty I find is 200 Mr. A. Cayley on an Analytical Theorem connected with that the investigation proves too much, viz. it appears to prove that y is actually equal to zero. There are undoubtedly functions such 1 as the function e” # (noticed by Cauchy and Sir W. R. Hamilton), which in a sense have the property in question, viz. that if we attempt to develope them in positive integer powers of a, the coefficients are found to be all of them zero ; and it would appear that y is, in regard to 1—y, a function of this nature. But it 1 cannot be asserted simpliciter that e- 2 and its differential coefti- cients do in fact vanish for z=0; they only vanish for z=0 considered as the limit of an indefinitely small real positive or negative quantity. (This is quite consistent with a remarkable 1 theorem of Cauchy’s, by which it appears @ priori that e-# can- not be expanded in positive integer powers of 2, because it is discontinuous for the modulus zero.) And if, instead of a direct 1 application of Maclaurin’s theorem, we first expand e 2, say in positive powers of 1—z, and then develope the several terms in powers of 2, we obtain for the coefficient of 2°, or any other power of z, an infinite series, which I apprehend is not conver- gent, and which can only be equal to zero in the same conven- 1 tional sense in which e # is equal to zero for <=0. This ap- pears to be something very different from finding for the coefti- cient of 2°, or of any other power of z, an expression composed of a finite number of finite terms the sum whereof is identically equal to zero. Plana has given for the calculation of y when p is nearly equal to 1, anexpression (equation (127)) which is deduced from the same development of Z'p which is here made use of; but it appears to me that this expression is, for the following reason, open to objection. The expression referred to contains explicit] positive and integer powers of jw, and also powers of the radical Vi?+2(1—p)(1+4): it would be, for anything that appears to the contrary, allowable to develope as well the positive and integer powers of yas also the powers of the radical in question, in a series of positive and integer powers of (l—); but if this were done, we should obtain as a mere transformation of Plana’s expression (127), an expression for y developed in a series of positive integer powers of (l—); and for consistency with the before-mentioned result, the coefficients of the different powers of 1—p must be each equal to zero. But if this be so, it does not appear how the original expression (127) can be anything else than zero. ‘The difficulty is, I think, a real one; and I do not see how it is to be got over: it seems to render necessary a more careful study of the effect of the multiplication of the suc- the Distribution of Electricity on Spherical Surfaces. 201 cessive terms of the development of a function fe by Legendre’s functions Po, P,, P., &c., so as to pass from fx to the function of two variables $(u, x), as well generally as when this transfor- mation is performed upon the as yet imperfectly studied trans- cendental function Z’. I remark that the original expression for fz is of the form fr=IEn sa —hbS, ewe pea op — yx’ and this gives (Plana’s Ye es (131)) 2__ 9 12__ 12 Y= WE, cee eee Ee 2153, P q a) ° (p?—2pqu+ q?)* °(p?— 2plq'm +9")? the values of p, q, p’, g' being p=b+nl+s), p'=(n+1)(1+9), q= n(1+4), g=1+n(1+d); so that p—q=b=p'—q, and p'+q=2+464%M(1+b)=p+q+2. Hence, putting w=1, we find panse(Otd ve) Bsmy g which is inconsistent with the expression y=0, deduced from the definite integral. If, however, it is assumed that fz contains the term 2 then the corresponding term of y will be 1 P(1—2?) (1—2Qya + x2)? which, when »=1, becomes pee ; and if P be put equal to zero, then it is conceivable that, for z=1, —— > may be equal to P(1+2) ‘ 1— zero, but Te what will be the same thing, See (ap 5 may be finite or even infinite. This is perhaps the explanation of the apparent contradiction. Note on the demonstration of the Theorem log (1+A pete! {0*(1+0)’—0°(1+0)"} =0, a—£ even. ae the function ot) _ 64, 2), 202 On the Distribution of Electricity on Spherical Surfaces. which, it is clear, admits of expansion in positive integer powers of ¢ and z. Changing the signs of ¢, z, we have e—"(—t—z oat) (4, <2), or what is the same thing, e(ti+e2 eet =¢(—t, —z2), and thence CAMEF A) — $(4, 2) —4(— —2) so that the development in positive integer powers of ¢, 2, of the function on the right-hand side does not contain any term ¢%2° for which a—8 is even. Writing the function under the form e(t+z) e*(¢+2) ete.) etry’ and considering the two parts separately, then by Herschel’s theorem extended to two variables, the coefficient of ¢*z* in the first term is (1+A,) log {(1 +A,)(1 +A) } op G+Ajq+A)—-1 0% which is equal to log {(1+A,)(1+A,)} (1+A,)0+4,)—1 or what is the same thing, log Zs +A) (I + 0,)*05, (1+0)%0°. And forming in Fe manner the expression for the coefficient of tz® in the second term, this is log . +4) (+ A) on 4.0)"; the difference of the two expressions therefore vanishes when «— is even, which is the above-mentioned theorem. It would be easy to obtain a variety of similar theorems. 2 Stone Buildings, W.C., June 29, 1859. [ 203 ] XXXI. On the nature of Lactic Fermentation, and on an apparent conversion of Caseine into Albumen which accompanied the pro- duction of Lactic Acid in Milk eacluded from the Air. By Witiram K. Suriivan*. em ROvE four years ago I procured two samples of cow’s milk for the purposes of an investigation which I proposed to make upon the influence which age, temperature, food, and other variable conditions exert upon the relative proportion of the dif- ferent fats composing butter. The milk just drawn from the cow was introduced into clean well-stoppered glass bottles, and stoppered in such a way as to leave no air between the stoppers and the milk. Other occupations having prevented me from proceeding at the time with the inquiry, the bottles of milk were put aside in a cool place, not subject to very great extremes of temperature, and only examined during the last month. As I believe that the results of this examination may possess some in- terest in connexion with the composition of caseine and its rela- tion with albumen, and also with some of the interesting expe- riments recently made by M. Pasteur upon fermentation, I have thought them worth publishing. For some time after the bottles had been laid aside, no coagula- tion of the caseine took place. Ultimately it separated in the usual way, leaving a perfectly clear, bluish-green liquor. After some time the coagulum gradually disappeared, leaving only the butter floating through the liquid, which in time became almost colour- less. Granulations also appeared in the butter, some of which rested on the bottom of the bottles, and others attached them- selves to the glass. No further change was noticed in the ap- _ pearance of the contents of the bottles, which remained, however, unopened for about two years after the formation of the first granules. The contents of one of the bottles was poured upon a filter ; a perfectly clear liquid passed through, having a feeble yellowish tint and a strong acid reaction. The substance on the filter con- sisted almost wholly of the butter, mingled however with a small quantity of a nitrogenous body like coagulated caseine, and affording many of the reactions of that substance. It would, however, be impossible to say that it was unaltered, as the reac- tions which the coagulated forms of all the albuminous bodies afford are so similar that it is always difficult, if not indeed im- possible in the present state of chemistry, to determine which of these bodies we may he dealing with. Part of the glycerides composing the butter had been decom- posed and their acids set free. The granules which had been * Communicated by the Author. 204 Mr. W. K. Sullivan on the nature of Lactic Fermentation. observed to form upon the sides of the bottle, consisted of the solid acids of the series C" H" O4 in a crystallized state. This fact is interesting in connexion with the chemical changes which the substance known as bog butter must have undergone in time, as I shall show in a future paper. A portion of the filtered acid solution was distilled in a retort ; a faintly acid liquor came over, smelling strongly of butter. When neutralized with baryta, and the solution evaporated and set aside over sulphuric acid, crystals were obtained which had the characters of baryta salts formed with the volatile acids of butter. When a portion of the filtered acid liquor was treated with moist freshly prepared oxide of zinc, so as to neutralize a consi- derable portion of the free lactic acid, and then heated, it coagu- lated exactly hike a solution of albumen. A portion of the acid liquor, without the addition of oxide of zinc, on being evaporated, did not appear to produce in a very distinct manner the pellicle so characteristic of a solution of caseine. Bichromate of potash, iodate of potash, and ferrocyanide of potassium gave the usual precipitates in the acid solution, which may be obtained either with albumen or caseine. A portion of the acid solution, on being mixed with a solution of chloride of ammonium, coagulated on being heated. A similar result was obtained with common salt, chloride of potassium, sulphate of soda, sulphate of potash, and nitrate of potash. The larger the quantity and the stronger the solution of the alkaline salt, the lower was the temperature at which the coagulation took place. The precipitates formed at very low temperatures were soluble in pure water; but the solutions were not coagu- lated by heat, though precipitable by ferrocyanide of potassium. When recently thrown down and rapidly filtered, they dissolved in acetic acid. Strong alcohol also gave a precipitate in the ori- ginal solution. The distinctive tests for albumen are coagulation by heat, and when a free acid is present, coagulation on the addition of a salt with an alkaline base, the temperature of coagulation being less as the proportion of salt imcreases. So far, therefore, as these tests can be relied upon, it would appear that the caseme of the milk was converted into albumen in the presence of the lactic acid formed from milk sugar, in the absence of air. If this was a simple metamorphosis, it would support the view that caseine was merely an albuminate of soda,—so strongly held, among others, by M. Gerhardt. It is, however, very probable that the change is not so simple as this would make it: for how, in this case, was the lactic acid formed? A portion of the caseine must have first been modified into a lactic ferment, and the re- mainder converted into albumen, according as the lactic acid was Mr. W. K. Sullivan on the nature of Lactic Fermentation. 205 formed. A very small portion of the caseine would be sufficient to perform the function of ferment, so that the great mass might have been changed into albumen. With a view to ascertain whether the relative quantity of albu- men was in accordance with this view of the case, and also whether there remained any dissolved caseine not converted into albumen, I added, as Lehmann recommends, a strong solution of chloride of ammonium to the acid solution, and boiled it for some minutes, so as to wholly coagulate the albumen ; the boiled liquor was filtered, and a solution of sulphate of magnesia added, and again boiled: no precipitate was formed. It is usually considered that if, in such a case, caseine be present, it would be precipi- tated. But, although no substance having the properties usually attributed to caseine was present, the whole of the azotic matter was not precipitated by the addition of the alkaline salts. A considerable quantity of some other substance or substances remained in solution. Whatever this substance was, it putrefied very rapidly on exposure to the air, the liquor becoming in two or three days full of fungi and infusoria. This easily putrescent substance may, however, have been formed after the metamorphosis of the caseie into albumen. But, on the other hand, it is stated that in the putrefaction of fibrine there is produced, among other things, a substance which, according to Strecker, has the composition and all the characters of albumen* ; and, again, some chemists have been led to believe that caseine, as it is extracted from milk, is really a mixture of two different bodies. Schlossbergert+ digested well-washed easeine with dilute hydrochloric acid, and obtained a solution which, on neutralization with carbonate of ammonia, gave a white slimy body, which filtered with difficulty, while another body remained dissolved and was precipitated by hydrochloric acid in excess. Schlossberger found that the first body con- tained sulphur, and the second not. But, even after the sepa- ration of the second body, another substance appeared to have been left behind. Gerhardt did not think the experiments of Schlossberger and others conclusive: undoubtedly it may with truth be objected, that the different substances just described were products of the decomposition of the true caseine resulting from the action of the hydrochloric acid. This objection does not, perhaps, apply with the same force to the following experi- ment of Muldert. Having freed milk as much as possible from blood-globules, by the addition of common salt, he coagulated the milk with dilute hydrochloric acid; on separating the coa- * Gerhardt, Chimie Organique, vol. iv. p. 462. + Ann. der Chem. und Pharm. vol. lviii. p. 92. { Berzelius’s Jahresbericht, vol. xxvi. 206 Mr, W. K. Sullivan on the nature of Lactie Fermentation. gulum, he found that a similar body remained in solution, and could only be thrown down by boiling the hydrochloric acid solution. At present there is no satisfactory mode of accounting for the formation of caseine in the mammary glands. According to the observations of Lassaigne, made a considerable time ago*, the milk is alkaline, and highly charged with albumen forty days before calving, and only ten days before that period does the sugar of milk appear. Some writers also state that albumen sometimes exists in milk during inflammation of the mammary glands. Among others, Moleschott found it in cow’s milk, It may, however, be observed that Scherer prepared from normal milk a caseine coagulable by heat, and that where coagulation alone is depended upon, erroneous results may be obtained. Lehmann has drawn attention to this source of doubt; but, on the other hand, may it not be equally well asserted that the coagulable caseine of Scherer was no longer true caseine, but albumen? A phenomenon the reverse of this has, indeed, been observed in the case of the albumen of serum by Hofmann. When serum is digested at the temperature of 31° to 44° with a piece of rennet, the liquor becomes troubled in the course of about twenty-four hours, and little by little it becomes filled with a flocculent precipitate. The filtered liquor is perfectly neutral, and does not coagulate by boiling, but forms.a pellicle on evapo- ration exactly like caseine. An explanation of the phenomena of the change of albumen into caseine in the animal body, and the reabsorption of the caseine into the blood, would be of great interest; much light may be thrown upon these questions by a complete series of ob- servations carried out from the same point of view as those of Lassaigne, above alluded to. In describing the changes which the caseine of the milk un- derwent as a conversion into albumen, I have naturally assumed that the distinctive reactions between both those bodies, usually relied upon by chemists and physiologists, are such as fulfil the conditions which science demands. It is right, however, to state that, as distinctive tests, they do not, in my opinion, pos- sess the value assigned to them. I believe, and I am sure all who have worked upon the albuminous bodies will agree with me, that no known reaction can be relied upon as a satisfactory distinctive test between two such closely-allied substances as albumen and caseine. But even if we admit that the reactions which I have described do not prove absolutely the conversion of caseine into albumen, assumed to have taken place, the change * « Examen physique et chimique du lait de Vache avant et apres le part,” Ann. de Chim. et de Phys, 1832, vol. xlix. p. 31. Mr. W. K, Sullivan on the nature of Lactic Fermentation. 207 which the milk underwent in the course of three or four years is not the less interesting in several points of view, and especially as throwing considerable light upon the function of digestion. The production of lactic acid from lactine, during this pecu- liar metamorphosis of caseine in the absence of air, is perhaps a still more important phenomenon than that metamorphosis itself, inasmuch as it derives peculiar interest from the recent revival of the much-debated question of the nature of fermentation. Of the many hypotheses which have been proposed since the time of Stahl, two have especially divided the suffrages of che- mists, According to one, first proposed by Berzelius, vinous fermentation is produced by the kind of action which he de- scribed as catalytic, and which he supposed to be the result of a peculiar force exerted by simple as well as compound bodies, whether in the solid or liquid condition, upon other substances with which they come in contact. The consequence of this action is, that a new arrangement of the molecules of the body acted upon takes place without the elements of the intervening body necessarily taking any part in the formation of the new substances. According to Faraday, catalytic action does not con- sist in the development of molecular force by mere contact, but rather in an electro-chemical action between the bodies included in the sphere of action. Liebig, while adopting the fundamental idea that molecular motion may be transmitted to a quiescent body, so modified the previous view, that in his hands it became a large generalization, but differing in many respects from the hypothesis of Berzelius. According to Liebig, vinous fermentation may be looked upon as a species of putrefaction of a hydrate of carbon, or rather a meta- morphosis, in which the elements of such a compound molecule arrange themselves under the action of their special affinities into new groups. This putrefaction is induced by contact with com- plex azotic bodies in which putrefaction commences spontaneously in the presence of water—non-azotized bodies not being capable of themselves to initiate the change. The azotized bodies which are best adapted to enter into this spontaneous motion of their constituent molecules, are vegetable albumen, gluten, and other similar bodies: putrefying animal matter of all kinds is capable of inducing the same kind of change, but much less pertectly than those named. According to this view, Liebig considers yeast to be a sub- stance whose elements exist in a condition of change, the ferment behaving in every respect as an azotic body in a state of putre- faction or decay. Yeast produces fermentation as a result of a progressive decomposition, which it suffers by contact with water and the oxygen of the air, 208 Mr. W. K. Sullivan on the nature of Lactic Fermentation. According to the second view, fermentation is a vegetative process, consisting in the growth of a plant at the expense of the fermenting bodies. This view, which appears to have been first suggested by Erxleben, was adopted by Cagniard de la Tour, Schwann, Kiitzing, Quevenne, Dumas, Mitscherlich, and Mulder. There is this much in favour of the vegetative theory, that yeast is undoubtedly the mycelium of a fungus or mould (a Peni- cillium) in an abnormal condition. It consists of globules or free floating cells, without a trace of rootlets, which are capable of almost endless propagation, and which, from their submerged position, are forced into a peculiar habit of development without ever producing perfect fruit. Several observers, among others Hofmann and Berkeley, have followed up the development of individual yeast-globules in fluid surrounded in a closed cell with a ring of air, and have obtained the true fruit proper to a Penicillium, and to one too which has been more than once observed to grow on fermenting matter. It is also known that other species of mucor promote vinous fermentation as well as the true yeast plant: a case is recorded of the kind where a peculiar myceloid state of Mucor clavatus was developed in raisin wine, the latter being, nevertheless, of pecu- liar excellence*. But while there can now be no doubt that yeast is the myce- lium of a fungus, there is still much room for difference of opi- nion as to whether the plant be the primum movens of the decomposition of the sugar, or only ancillary to it. Pasteur has recently instituted a series of ingenious experi- ments, which have led him not only to adopt the plant theory, but to extend it to all other kinds of fermentation. He says, “That in the same manner as there exists in an alcoholic ferment, beer yeast, which is found wherever there is sugar, which breaks up into alcohol and carbonic acid, so there is a special ferment, a lactic ferment, always present when sugar becomes lactic acid ; and that if every plastic azotized matter may transform sugar into that acid, it is because it is a suitable aliment for the deve- lopment of that ferment.” And further, “ that there exist a great number of distinct ferments, all having their speciality of actiont.” He describes the lactic yeast to be formed of globules, or rather threads somewhat swollen at the extremity, and about ~3,th of a millimetre in diameter, and to be organized like beer yeast. It has long been known that carbonate of ammonia very much favours fermentation ; but Pasteur has explained the reason, by * Mag. of Zool. and Bot. vol. ii. p. 340, quoted in Berkeley’s ‘ Introduc- tion to Cryptogamic Botany,’ p. 295. ti+ Comptes Rendus del’ Académie des Sciences, vol. xlviii. No. 7 (February 1859), p. 337. Mr. W. K. Sullivan on the nature of Lactic Fermentation. 209 showing that yeast can be rapidly formed in a solution of pure sugar if a salt of ammonia and phosphates be added. On trying the same experiment with lactic yeast, he produced a perfectly healthy lactic fermentation with a deposition of yeast-globules. In my paper “ On the presence of Ammonia and Nitric Acid in theSap of Plants*,”’ I dwelt upon the probability that plants derive the whole of their nitrogen from ammonia. There is nothing more natural, therefore, than that the yeast plant should be able to develope itself when provided with its proper food. But if the single cell constituting the yeast plant be capable of assimi- Jating ammonia and building up out of it albuminous bodies, is it likely that it would also possess the power of assimilating all the wide range of substances in all stages of alteration, which go by the name of albuminous bodies? The cell-wall of all the ferment plants is cellulose ; and yet one species produces vinegar, another alcohol and carbonic acid, and another lactic acid,—a difference of function which we can scarcely find between single cells even in the higher families of plants, where every cell may be said to enjoy a different chemical and physiological function. It seems more probable to suppose that azotic matter, in an active state, gives off ammonia (Schmidt showed that ammonia existed in fermenting liquorst),and that as the spores of fungi abound every- where, they at once grow and multiply, wherever the ammonia is thus given off, because there their proper supply of food exists. We know that even the diffusion of a solution of a salt into pure water is enough to produce a certain amount of decomposition : how much more so must this be the case during the exosmosis and endosmosis of complex and therefore unstable substances already in a state of activity, through the cellulose membrane of the yeast-cells. The primum movens may therefore be, as Liebig supposes, an azotic body in a state of change, the yeast-cells growing upon the products of decomposition, and therefore re- moving them from the field, while the flow of liquids through the cell presents greater facilities for decomposition by molecular action. According to this view, vegetation is not the primum movens, but the consequence of fermentation. Pasteur states that the origin of the lactic fermentation, in the experiments which he made, was solely due to atmospheric air. In the case of the milk examined by me, air could not have assisted, as it was wholly excluded. It may no doubt be ob- jected that the milk contained some air when it was introduced into the bottle. I grant it; but why did the lactic fermentation not set in at the usual time, and not after a considerable period, * Atlantis, vol. i. p. 413; and Annales de V'Histoire Naturelle for February 1859. t+ Annal. der Chem. und Pharm. vol. \xi. p. 168. Phil, Mag. 8. 4. Vol. 18. No. 119. Sept. 1859. P 210 Mr. W. K. Sullivan on the nature of Lactic Fermentation, during which the whole of the oxygen must have been slowly used in oxidizing the casemme? Then, again, no trace of yeast-globules could be found in the milk when the bottle was opened; but after a few days mould and abundance of infusoria were developed in the liquid,-partially neutralized by zine. The growth of moulds, as for example the beautiful Penicillium glaucum, from milk-globules has been long noticed. Indeed Dutrochet states that he observed milk-globules changed into the spores of mould, or at any rate developed into moulds. But in all instances the growth of the fungi appears to have been subsequent to the production of lactic acid. Turpin*, it is true, supposed that the growth of P. glaucum might be the cause of the knotted condition of an engorged breast, the germination of the spores taking place in the undischarged milk in the lacteal ducts. But there is no proof whatever that any such growth ever took place in unaltered milk within the body. It is very probable that Pasteur’s lactic yeast was nothing more than the mycelium of Penicillium glaucum. If we recollect that the spores of some fungi are not more than ;,/;,/ in diameter, we may easily understand how germi- nation may take place as the result of an incipient decay wholly unrecognizable by chemical reactions. The quantity of ammonia required to feed such minute plants could not be detected by any means which we possess; and hence we might under certain circumstances be led to suppose that the germination may have preceded the change of the substance upon which the plants ew. The question raised by Pasteur is one of very great import- ance, because if we admit the existence of distinct ferments having each a speciality of action, we must of necessity also admit that the original cause of many diseases, both in plants and animals, is the germination of fungi,—and perhaps also the possibility of spontaneous generation. The latter M. Pasteur appears to accept. Experience, however, shows that although the spores of fungi abound everywhere, they do not succeed in germinating and growing except where certain favourable con- ditions exist. In all cases where fungi have been observed in the animal body during life, it has been on free surfaces, such as the external skin, the mucous membranes, &c.: J. Vogel, a very competent authority, states that he knew of no undoubted case of fungi having been found in the middle of the parenchyma of human organs. I believe that no case has ever been observed of the growth of fungi in the blood, bile, or other secretions during life; and yet there cannot be the slightest doubt that their spores continually find their way into the body. As an * Mémoires du Mus. d’ Hist. Nat, 1840. Mr, W. K. Sullivan on the nature of Lactic Fermentation. 211 instance of this may be mentioned the fact that the yeast plant is continually taken into the stomach, and yet fermentation does not ensue, except where the stomach is diseased, and then the yeast plant grows rapidly, as has been discovered by an examina- tion of the matter rejected from the stomach. The yeast plant has even been found under those circumstances where the patient has not partaken of fermented drmks. The fungus found in urine during acid fermentation, and which so closely resembles the yeast plant, has always been observed after the urme has been some time voided. There is no proof whatever that it ever germinated within the bladder during life. On the other hand, parasitic fungi are often found on putrid ulcers, but only on the uninjured skin or mucous membrane when it has become previously covered with a layer of exudated matter which has begun to pass into a state of decomposition. The growth of fungi, once established, may no doubt spread to healthy parts, as in certain skin diseases, and in bread mould, but it could never commence upon a perfectly healthy clean spot. I have lately had occasion to observe how completely the germination of the spores of fungi depend upon the existence of certain conditions. I laid aside some small beaker glasses covered tightly with filtering paper, and containing very strong solutions of salts, consisting of sulphates of potash and of chrome. The solution in one of the glasses had been treated with excess of ammonia, and boiled for some time, and then filtered to separate the small portion of the sesquioxide of chrome which had been precipitated. After a few weeks, the solution to which the ammonia had been added became filled with an extremely beautiful rose-pink-coloured mycelium of a Penicillium. Nothing grew in the others; but on adding some ammonia, the same mycelium was developed after some time. The supposition that the primum movens of fermentation is the growth of specific ferments, appears to me to be so far premature, that while there may be no doubt that the vegetable form developed during alcoholic fermentation could not produce the lactic, and vice versd, it has not yet been established that they are specifically distinct. May not the same plant be forced into different habits of development in its myceloid state? If the mycelium produced in each kind of fermentation or putre- factive change belonged to a peculiar species, it would be, to a certain extent, an argument in favour of the view that fermenta- tion is due to a vegetative process. But if, on the other hand, the same species may be forced into two different myceloid states, the establishment of the fact would go far to prove that the chemical change is the cause and not the result of the vegetative process, P2 212 Mr. W. K. Sullivan on the nature of Lactic Fermentation. The mycelia of most fungi are so exceedingly alike in the early stages of their development, that the free cells, beaded threads, and ramuli composing ferments, crusts in skin diseases (Porrigo, Favus, &c.), putrid matter, &c. may all be specifically distinct. Botanists have not, however, yet determined this point ; nor is it a problem of easy solution. Kiitzing, who has devoted great attention to this department of botany, in speaking, in his ‘ Phycologia generalis,’ of the lower forms of plants which occur in fermenting fluids, and of the extreme difficulty of distinguishing them into genera and species, says that he once attempted to make the distinction, at a time when he had only investigated and observed a few of those forms, but that the extraordinary variety of the forms which a closer examination had made him acquainted with, had frightened him from the task. This subject suggests two trains of investigation which I would propose for the consideration of botanists and chemists. One would be to cause the spores of well-determined species of fungi to germinate in different kinds of solutions, both of imorganic and organic bodies, and observe the character of the mycelia formed, and the nature of the changes which take place in the fluids. The second would be to follow out, as has been done in the case of the yeast plant, the whole course of growth to full fructification, of all the cellular plant-like substances observed in the more definite characteristic kinds of fermentation and putrefaction. Such investigations would throw light not only upon the nature of fermentation and decay, but would open a new field of inquiry regarding the chemical changes which take place during the growth of plants; for in these experiments we should be able to operate as it were upon individual cells, every one of which probably possesses the same initial physiological value. Perhaps one of the results of the second investigation would be that the myceloid substance of many fermenting and putrifying bodies is formed of the mycelia of several species. But whatever theory of fermentation may ultimately be found to be correct, I do not think the formation of lactic acid in the experiment above described can be satisfactorily explained by the hypothesis of M. Pasteur. I have recorded the result in the hope of inducing him and others to investigate the subject fully, and especially from the point of view just suggested. Very im- portant results may be expected from the labours of such an observer as M. Pasteur, in a field which appears to be one for which he has a special predilection. EI, [ 213 ] XXXII. On the Composition of the Cape Meteorite. By Professor WOuLER*. HE remarkable meteoric stones which fell on the 13th of October, 1838, at 9 a.m., in the Bokkeveld, about seventy miles from Capetown, accompanied by the most fearful and widely-heard thunder-clap, present in their peculiar external condition the greatest resemblance to the stone that fell at Kaba in Hungary, on April 15th, 1857, the analysis of which the author has lately communicated. They are, like the latter, almost black, and consist of a soft incoherent mass in which only a few bright points can be discerned, and none of the little no- dules which the Kaba stone contained in such abundance. The Cape stone was analysed by Faraday as early as 1839; but no explanation was then given of its peculiar colour. It seemed to the author, therefore, that a new analysis of this stone would be of the greater interest, inasmuch as it afforded some prospect of discovering carbon to be the cause of the colour in question, in connexion perhaps with the same bituminous substance for which tlie Kaba stone is so remarkable. This conjecture was com- pletely verified by the following investigations, undertaken by Mr. Harris at the author’s request, and for which Director Hérnes, with the greatest readiness, afforded a small quantity of this rare substance. On heating a small portion of the stone in a tube, the pre- sence of bituminous matter was immediately recognized, a very distinct odour of bitumen being evolved. The whole of the small piece of stone available for the purpose was then powdered and boiled in carefully purified alcohol. On the latter being filtered, it was seen to have acquired a pale yellow colour; and on careful evaporation it left behind a soft, yellow, resinous or waxy substance, precisely similar to that from the Kaba stone. This substance was completely soluble again in alcohol, and, like aresin, formed a milky precipitate on the addition of water. On being heated in a tube, it easily melted, and then decomposed with separation of a black coal and evolution of a strong bitu- minous odour. On account of the small quantity of the material, it was impossible to examine it more accurately ; but there is no doubt that this meteoric mass, falling, as it did, to the earth from’planetary space, contains a carbonaceous substance which can have no other than an organic origin. That the almost black colour of the stone was due to inti- mately admixed amorphous carbon was easily shown. Heated to redness in the air, it became of a light clear brown. On being treated with acids the black colour did not disappear. Heated * From the Bericht d. kais. Akad, d. Wissensch. zu Wiem, vol. xxxv. p. 1. 214 Prof. Wohler on the Composition of the Cape Meteorite. in oxygen it burnt at once to a light brown, with evolution of carbonic acid gas, the quantity of which was measured, and by that means the per-centage of carbon determined. The pre- caution was taken of separating the sulphurous acid, which was formed at the same time, from the carbonic acid by passing the gaseous product through a long tube filled with peroxide of lead, and thence through baryta water and solid moist hydrate of pot- ash, both weighed. As soon as the oxygen, which was absolutely pure, came into contact with the pulverized stone at a low red heat, the formation of carbonic acid evinced itself by causing a dense precipitate in the baryta water. In this manner it ap- peared that the stone contained 1°67 per cent. of carbon, without reckoning that in the above-mentioned hydrocarbon which had been previously dissolved out by means of alcohol. During this combustion it was remarkable how much water made its appearance, and this though the pulverized stone had previously been dried for some time at a temperature of 100°C. At the same time a slight crystalline sublimate was formed, which gave the reactions of sulphuric acid, and not less distimetly those of ammonia. It must for the present remain undetermined whether this water and ammonia were original constituents of the stone, or were formed from its elements, or whether, finally, the stone, by means of the carbon it contained, and of its loose earthy condition similar to clay, merely took them from the atmo- sphere. Faraday also found 6°5 per cent. of water in the stone, but he has not stated at what temperature he dried it. Hydrochloric acid dissolves from the stone much magnesia and protoxide of iron. Onlya very slight evolution of hydrogen accompanies the action of this reagent, showing that very little metallic iron can be present,—a result confirmed by the feeble action of the stone on the magnetic needle. Not the slightest trace of sulphuretted hydrogen is evolved during the process, showing that the sulphur, which analysis proves to be present, is not in the form of sulphide of iron or of magnetic pyrites. On the other hand, no iron pyrites can be present, since a por- tion of stone heated to a bright-red heat in a glass tube, does not give out the least trace of sulphur. If, however, it be heated in the air, a strong smell of sulphurous acid is immediately ob- served. This behaviour seems to show that the sulphur present must be in combination with nickel; but the total quantity of sulphur, 3°38 per cent., is much too great to form either the proto- or bisulphide with the observed quantity of nickel, 1:30 per cent. ; so we must infer that the stone contains some com- bination analogous to sulphide of nickel and iron or magnetic pyrites, the sulphide of iron of the latter being represented by sulphide of nickel. Ifa combination of NiS + Fe? S° be assumed, Prof. Wéhler on the Composition of the Cape Meteorite. 215 we get 1°3 per cent. nickel, 3°14 sulphur, and 2°50 iron, for 6°94 of the compound, the small difference between the amount of sulphur thus calculated and that actually found being explicable on the ground of the presence of a small quantity of a sulphate of some kind. Hot water, indeed, actually extracts some sul- phate of magnesia; and the solution obtained by means of mu- riatic acid gave indications of the presence of sulphuric acid. Mr, Harris made three analyses of the stone—the first with carbonate of soda and potash, the second with hydrofluoric, and third with nitromuriatic acid—from which it appeared that the stone contained 5:46 of silicate insoluble in the latter acid. These analyses gave the following bodies as component parts of the stone. (The composition of the Kaba stone is subjomed, in order to show the great similarity between the two.) Cape stone. Kaba stone. Boma. SS. PS RGR 0:58 Bituminous matter . . . O25 not determined iron ger. | re. tomer. DIBFOO 2°88 mace tS A ee ee 1:37 eupiues . J)... We OOO 1:42 Suri aca. ©... .... BORO 34°24 Protoxide of iron. . . . 29°94 27°41 mirmemigy. 2220 22°19 ee ee SY ee eG 0:66 Braman OPP Eee BOB 5°38 Oxide of chrome . . . . O'76 0°61 Potash and soda . . . . 1:28 0:30 Protoxide of manganese. . 0°97 0:05 Spear ets tL hs Swear ? OOS 0:01 Cobalt . ‘a i Phosphorus fv et races races The amount of metallic iron present could not be directly ascertained, but was calculated on the foregoing hypothesis. The total quantity of oxide of iron which analysis detected answered to 33°15 per cent. protoxide, from which 3:21 per cent. was deducted, and in its place metallic iron calculated to the extent of 2°5 per cent. By means of the nitromuriatic acid, chiefly iron and mag- nesia were dissolved out of the stone, with only a small quantity of lime, alumina, and protoxide of manganese. After subtrac- tion of the iron, which was considered as belonging to the sul- phide of nickel and iron, it appeared that the oxygen of the silicic acid (amounting to 28°22 per cent.) which had been com~- bined with the protoxide of iron and magnesia, was nearly equal to the oxygen of these bases; and that therefore, in this case 216 Prof. Wohler on the Composition of the Cape Meteorite. also, the mineral decomposed by the acid was a silicate of mag- nesia and oxide of iron of the composition of olivine, 3(FeO . MgO) Si0®. Of the silicate not decomposed by the nitromuriatic acid, which only amounted to 5:46 per cent., an analysis was mdeed made; but the quantity available for the purpose was too small to give areliable result. It is very probable, moreover, that the silicate itself had been partly decomposed by the action of the acid. It can only, therefore, be stated that this silicate contains as bases, alumina, magnesia, lime,”protoxide of manganese, prot- oxide of iron, potash, and soda. Its silicic acid amounted to about 44: per cent. From what precedes, it may be taken as probable that the Cape meteorite consists of the following compounds :— Magnesian iron olivine . . . . 84°32 Insoluble sihcate. .. 2 0.0.) 2) dG Sulphide of iron and nickel . . . 6°94 Chromeate of intial ay .2 2, ee OAEDONA Tete elas vesirs oe cetera Bituminous matter. . . . . . °25 Phosphorus, cobalt, copper . . . traces 99°75 [To this communication Haidinger subjoins the following par- ticular account of the fall of meteoric stones above mentioned. | The Cape itself, with its localities and characteristics, has been in a manner brought nearer home to us by means of the Novara expedition. To the north of the district of Worcester, visited by Scherzer, Hochstetter, and Selleny, the Warm Bokkeveld, and next to that the Cold Bokkeveld, immediately adjoins. In the last, fifteen miles from Tulbagh and seventy from Capetown, on the 13th of October, 1838, at 9 a.m., the meteoric fall occurred, of which an eye-witness, Mr. George Thompson of Capetown, on the 28th of November sent a circumstantial account to Mr. Charles- worth, the editor of the Magazine of Natural History (vol. ii. p- 145). (See Lond. and Edinb. Phil. Mag. vol. xiv. p. 891.) Pre- vious to that date, on the 25th of November, Thomas Maclear, the highly talented astronomer of the Cape observatory, wrote to Admiral (then Captain) W. H. Smyth, R.N. (memorable in con- nexion with the Novara expedition, for the letters of troduction he gave our travellers to the former gentleman, who received them with so much attention), in the following words :—“I have for- warded to Sir J. Herschel a splendid specimen of a meteor that exploded about 100 miles from Capetown. The whole mass could not be less than four cubic feet. A pretty sort of solidification if a ee Prof. Wéhler on the Composition of the Cape Meteorite. 217 it took place in our atmosphere! such an origin is scarcely con- eeivable.” (Phil. Mag. S. 3. vol. xiv. p. 231.) According to Mr. Thompson, the noise of the fall was fearful, louder and more pow- erful than the heaviest artillery ; the air was shaken for more than eighty miles in every direction. Several persons at Worcester felt a sensation at the knees as though of an electric shock ; and even there, at the distance of forty miles, the noise was compared to the rolling of rocks down a mountain. From the place of obser- vation on the borders of the Great Karroo, where Mr. Thompson happened to be in company with Mr. Justice Menzies, something similar to a Congreve rocket was seen to approach from the west, and, when almost over the heads of the observers, to burst into drops of fire, or, as it seemed, of transparent glass, At the time of the phenomenon, and still more on the previous night, all the mountains about Worcester and the Bokkeveld were continually illuminated with lightning; and throughout the whole district where the phenomenon was visible, a high state of electric ten- sion was noticed. A farmer saw the falling matter strike the ground before him. Many stones fell, in three spots, within a square of forty or fifty yards. Some fell upon hard ground, being thereby shattered into numerous small fragments; others upon soft ground, in which they buried themselves. According to the account given by Maclear in his letter to Sir J. Herschel, read at the sitting of the Royal Society, March 21, 1839, the fall took place while the air was still and sultry. The fragments were at first very soft, and only became harder afterwards. According to the account of E. J. Jerram of Capetown, the fall extended over a distance of not less than 150 miles in a straight line; so that stones were found with interruptions at distances of 10, 15, 20, 50, &c. miles. Those which fell near Tulbagh were by themselves estimated at several hundredweight, It would perhaps not have been difficult, immediately after the occurrence of the meteoric shower, for anyone possessed of the zeal and perseverance displayed by Freiherr von Reichenbach on the occasion of a similar event at Blankso, on November 25th ; 18338, to have put together a learned account of this great cos- mical phenomenon, in which every contemporaneous circum- stance not strictly belonging to the history of the event itself might have been kept in its proper place; nor would it per- haps have been then difficult to have brought considerable quan- tities of this highly curious and enigmatical substance to Europe for examination. As it was, this only happened gradually. Three entire stones (among the rest, that sent by Mr. Thompson to Mr. Charlesworth)and several fragments were sent to the British Museum. Sir John Herschel received a stone of the weight of 7 Ibs. from M, Truter in Capetown. The late M. Partsch, in 1843, 218 Mr. J. W. Mallet on Brewsterite. in addition to the former piece, could only procure from Von Struve about 43 oz. weight, consisting of a large fragment and three small chips; and it was only in 1845 that he succeeded in purchasing, of Dr. Ferdinand Krauss of Stuttgart, a larger, nearly complete stone, with external crust and weighing about 12,4 oz., which the latter gentleman had brought from the Cape; and it was Sir J. Herschel himself who in the year 1847 made the Royal Mineralogical Cabinet the valuable present of a fragment of the stone with fresh surfaces and external crust, weighing 64 oz., as well as two smaller pieces which together weighed 4 of an ounce. One of the first pieces received from Von Struve, Director Hérnes gave M. Wohler for analysis. So few pieces of the Cape meteorite have, in truth, come within reach of a chemical examination like the latest of Wohler’s (prompted by the fact of the discovery in meteorites of a bitumi- nous substance formed according to the laws of organic matter), that, after the facts here communicated, we need not despair of obtaining somewhat larger quantities of the material in question, so as to make the new substance itself the subject of further in- vestigation. XXXIII. On Brewsterite. By J. W. Mauizt*. i Wess analyses of the mineral species Brewsterite are on record, those of Connellt and Thomson{, both made many years ago. ‘The results were,— Connell. Thomson. Silica! oot Leth :666 53°045 Alumina) i/o pepe Ly A492 167540 Barytas 6 ey gore 6749 6'050 Strontia: . 2) tie. 8 B25 9:005 ainiey's Pui st See ee BAN OAG “800 Witte farys 0 Free Pe 84 14°735 Peroxide of iron. . 292 100°4.54 100°175 It is strange that in Thomson’s ‘Outlines of Mineralogy, Geo- logy,’ &c., the analysis of Connell is given with altogether differ- ent figures, thus :— * From Silliman’s American Journal for July 1859, + Edinb. New Phil. Journ. No. 19. p. 35. { Outlines of Mineral. Geol. and Min. Anal. vol. i. p. 348. ‘ Mr. J. W. Mallet on Brewsterite 219 LE aaa Siaalak dal Seiad 5 1 5 i Minn see ee ROOTS BIRO Potts tee aes oe, Sanit: se RE We eT te ah ee Pee ee ee ce ee Ne ee 208 Peroxide of iron. . . 12°584 95°653 Dr. Thomson remarking at the bottom of the page that the spe- cimen analysed by himself consisted of fine crystals carefully selected, while that examined by Mr. Connell was a mixture of amorphous and crystallized mineral. The method for the separation of baryta, strontia, and lime, employed by Connell—probably by both analysts—namely, the solution of nitrate of lime, and afterwards of chloride of stron- tium, in aleohol—has given place to more reliable processes ; and on this account a repetition of the analysis might be desirable ; but it becomes still more so when the close analogy of Brew- sterite to Heulandite is considered. The two species should in all probability have the same general formula, and this has in fact been assigned to them in Dana’s ‘ Mineralogy ;’ but with the formula for Heulandite these older analyses of Brewsterite do not very well agree. I have recently analysed some fine specimens from the original locality (Strontian in Argyleshire, Scotland) ; and the results appear fully to establish the chemical as well as crystallographic relationship with Heulandite. The mineral formed crusts of minute crystals upon the surface of gneiss: sometimes these crusts could be detached from the rock by careful blows, but in general they adhered very firmly. Some of the crystals were 4th of an inch in length ; most of them were much smaller. The following measurements were obtained, using the lettering of Dana :— O : $-1=175° 49'—175° 53! —175° 55! ft: Z-2=171° 43'—171° 401. 22 i—146b..10), O : 1-2(?) =157° 23!—157° 17!— 157° 20'!— 157° 22!. L2424=112° 18! —112° 17'—112° 12", The specific gravity was found =2°453. For analysis, the crystals were carefuly broken off and picked clean from any dust of the accompanying rock. In one ease the mineral was fluxed with carbonate of soda, so as to ensure per- 220 Mr. J. W. Mallet on Brewsterite. fect decomposition, and consequent purity of the silicic acid weighed ; the other specimens were treated directly with hydro- chloric acid, which seems of itself to be capable of effecting com- plete decomposition. The baryta was precipitated by hydro- tluosilicic acid* ; and the relative amounts of lime and strontia were determined indirectly, by weighing the mixed earths first as sulphates and then as carbonates. The following are the results obtained :— I. ne Ill. IV. Vv. Mean. Atoms, Silica ..nceccscens 54:49 53°66 54°31 54°84 ... 54:42 1-209 4-08 Alumina.......+. 15-42 15:29 15°05... sent, L025) S296) 1 Peroxide of iron trace ‘08 trace Baryta’! mv; this value of 2 therefore corresponds to a maximum of P. When the lower signs are taken, P is negative and less than mv; so that this value of x corresponds to a maxi- mum negative value of P. The curve, obtained by regarding P as ordinate and # as ab- scissa, is of the third order; in the present example its equa- tion is =m K24 Ke 2K? + (@— Ky? whence it is seen that the curve cuts the axis of x (P becomes zero) at the point = —K When z=K, P=mv; when v= +0, P=+0, and the axis of x is an asymptote to the curve on both sides of the origin. Changing the origin to the point ¢= —K, we have, on making 2+K=y, P=mv a] Ky P=mv ya 4Ky 46K? and the values of y which correspond to the two maxima of P are y= KV 6. The first distance y=K G6 corresponds to a percussion P greater than mv, and consequently greater than if the support f had been struck directly with the same force mv. The second value y=—K 6 corresponds to a negative percussion P less than mv; it is of course assumed that the support f resists in both directions. Thus in order, with the same hammer-stroke mv= Mz, to produce the greatest possible percussion against the * Chap. I. art. 23. M. Poinsot on the Percussion of Bodies. 249 support f by means of an interposed free body M placed on the same, with its centre of gravity G at the distance K from the point of contact f, we must strike, not at the point f itself, but at a distance K /6—2K beyond the same. If, in the general expression K?+he K?+ h?+n(a@—h)” we suppose m infinitely small and »v infinitely great, whilst mv remains equal to a finite quantity Q, we have, since n=0, K2+he P=Qaa ae’ P=mv which agrees perfectly with a previous result in art. 5, Cuapter LV. On the method of reducing to the theory of the motion of free bodies that of bodies supposed to be impeded by fixed obstacles. 1. Hitherto we have considered perfectly free bodies alone ; but in mechanics it is often necessary to consider bodies which are only free to turn around a fixed point or axis, to slide over an immoveable plane, and so forth. Instead of new principles being required for the solution of problems of this kind, it will be seen that the preceding ones suffice, and that our theory may be applied in the most direct and natural manner to the singular cases where some fixed obstacle is supposed to impede the move- ments of the body. 2. In fact there is no fixed body in nature. A so-called fixed point is in reality merely a point invariably attached to some body whose mass, being very great, is regarded as infinite in comparison with that of the moving body under consideration. In place of a so-called fixed point, then, we may always conceive a free point endued with an infinitely great mass; in other words, a point in which an infinite quantity of matter is supposed to be concentrated. In this manner, instead of a body of any figure and finite mass M moveable around a point I supposed to be fixed, we have merely to consider a free system composed of the same body M, and of a material point of infinite mass p attached to M at the point I. 3. It is evident that the centre of gravity g of such a body or system will fall infinitely near the pomt I; and that this centre, being charged with an infinite mass 4+ M, can only receive an infinitely small motion in virtue of the action of any finite forces supposed to be applied to it. This centre of gravity g, therefore, 250 M. Poinsot on the Percussion of Bodies. remains immoveable under the action of such forces, and consti- tutes in reality what we call a fixed point. 4. But if the force of inertia or mass of the system M+vyp is - infinite, the moment of mertia around an axis passing through the centre g has a finite value which, as will be seen, is exactly the same as the moment of inertia, with respect to the same axis, of the simple body M, Hence, although the centre of gravity g, in consequence of the infinite mass M+y with which it is charged, remains immoveable under the direct action of all the forces of the system removed, parallel to themselves, to the point g, the body will not remain immoveable under the action of the couples which such a removal originates, but will receive a finite rotation @ around the centre g, in consequence of the finite value of its moment of inertia with respect to an axis through this point g. Hence to solve dynamical questions with respect to a body compelled to turn around a fixed point, it will suffice to apply the solutions already found for a free body, provided that in so doing we regard the fixed point as the centre of gravity of the body, suppose the mass of this body to be infinite, and give to its moment of inertia the true finite value, which we shall now proceed to determine. 5. For greater clearness let us suppose, in the first place, that this material pot which we attach at I to the proposed body M, has only a certain finite mass yz, and let us seek the moment of inertia of the system with respect to its centre of gravity g; we shall then sce what the expression («+ M)K? of this moment becomes when p is supposed to be infinite. 6. Let G be the centre of gravity of the simple body M and d the length of the line GI. The centre of gravity g cuts this line IG into two segments, 7 and d—1, inversely proportional to the masses M and yp, so that 7 (5 Oey I a tlgsd owe d i= Gg we Now the moment of inertia of the material point ~ with respect to the centre g is evidently uz*; and that of the body M with respect to the same point is composed, jirsé, of its moment of inertia around its own centre of gravity G, which may be repre- sented by MD?; and secondly, of the product M(d—z)? of the mass of the body into the square of the distance (d—?) of its own centre G from the point g. Adding these values, we have for the moment of inertia (u+M)K? of the system the value (w+M)K?=pi?+M(d—1)?+MD?; M. Poinsot on the Percussion of Bodies. 251 whence, putting for 7 and d—7 the preceding values, we deduce (u-+M)K*=M i 3) LS de bu If herein we suppose the mass yw to increase from zero to infinity, the moment of inertia will clearly increase from its least value MD? to its greatest M(D?+d?); sothat making ~=oo in order to pass to the mathematical hypothesis of a fixed point in the body M, we have (u + M)K?=M(D? +d’), which is precisely the value of the moment of inertia of the simple body M with respect to the fixed point I. 7. The moment of inertia of the system having, therefore, a finite yalue, it is evident that if we represent the same in the ordinary manner by the product («+ M)K®, the line K or arm of inertia ought to be regarded as zero, the mass (4+ M) being infinite. Nevertheless it is well to notice that this infinitesimal line K is infinitely great when compared with the distance i from the point I to the centre of gravity g of the system, just as the sine of an infinitesimal angle is infinite with respect to its versed sine. In fact, if we compare the expression for K®, which is k= yM| d2+D2(1+ =) +My with that for i?, which is M? ge ee, et (w+ My? we find M 24 Dts ee $ +D (14 =) ee M d? 3 ; ! pri >> which, on making w=, gives BH, and shows that K is infinite times greater than 7. 2 On the other hand, it will be seen that the quantity ai which in geometry represents a line, corresponds here to a finite line J, and not to an infinite one, For on multiplying both sides of the preceding equation by i, and in the second member replacing ¢ 1 7) we find by its value d = M 252 M. Poinsot on the Percussion of Bodies. M Kes, e+D(1 Gin =) : a(1 + J be whence is deduced, on making w=, K2 d?+D? D?2 es ae ee eee This is precisely the expression for the distance IC between the point I and the centre C of oscillation of the body M around I. 8. Herefrom we learn that the same point C, which; in the simple body M, is reciprocal to the point I, is also reciprocal to I in the system composed of the same body M and of the material point of infinite mass w placed at I. If, then, we suppose the system to be struck at an infinitely small distance 2, to the right or left of the centre g, the spontaneous centre of rotation C will be on 2 the other side of g at a finite distance J=d+ =e But however small the distance 7 between the point of impact and the centre g may be, we may always conceive another point O to be situ- ated between the two at a distance # from g imfinitely small with 2 respect to 2, so that the expression = shall: be infinitely great 2 : ; i€ in comparison to — ; hence since the latter corresponds to a ae: | oped idee aes finite line /, the former — will represent an infinite line; and wv the spontaneous centre C! of rotation which corresponds to the centre of percussion O, will be at an infinite distance from the centre of gravity g. Whenever, then, in our formule we en- oe Aw ; : counter the expression — wherein we have to make the inde- Q pendent variable x equal to zero, we must take “= 2 , although ar of MARE ae Fe the similar expression ap corresponds to a finite line 7 when the variable 7, which in this case depends upon K, becomes also equal to zero. 9. In dynamics, therefore, we must guard against confound- ing this infinitely small line K, which represents the arm of inertia of the system, with the infinitely small line 7 which de- termines the distance from the centre of gravity g of the material point yw attached at I, although both these lines become zero under our hypothesis of w=oo. At the same time we must carefully distinguish between the true values of the expressions M. Poinsot on the Percussion of Bodies. 253 K? K? ee } 4 Cl) + C4 H3Cl+ 2P0? Cl? + HCL. Acetal. Pentachloride Chloride Chloride of Oxychloride of phosphorus. of ethyle. ethylidene. of phosphorus. But the action appears to take place in a somewhat different _ * Phil Mag. vol. xvii. p. 276. _ + Bulletin de la Société Chimique de Paris, p. 18. { Ibid. p. 46. Phil. Mag. 8. 4. Vol. 18. No. 120. Oct. 1859. 290 Royal Society :— manner. Beilstein was able to recognize the presence of chlo- ride of ethyle, and of oxychloride of phosphorus, but no trace of chloride of ethylidene. On mixing the product of the action with water, a dense oily liquid separated, which, when purified and analysed, gave numbers agreeing best with the formula 7. H° Cl. If this be its real formula, the reaction is probably thus :— C“?H“Ot + 2PCh = C* H9C8+C*H®Cl+2P0? CE. Acetal. Pentachloride New body. Chloride Oxychloride of phosphorus. of ethyle. of phosphorus. By taking 1 equiv. of pentachloride to 1 equiv. of acetal, the action is very violent, and requires to be greatly moderated. The crude product, cooled down, is carefully decomposed by the addition of ice; a small quantity of a liquid is obtained which appears to be the intermediate chloride of Wurtz and Frapolli, C8 H9 0? Cl, in which case the action would be in accordance with the equation C!? H!4 0?+4+ PC} =C? H® Cl + C8 H9 0? Cl + PO? CIS. Acetal. Intermediate chloride. The chloride C8 H9Cl® formed in the previous experiment would then owe its origin to the action of the second atom of pentachloride on the chloride, C8 H9 0? Cl; thus— C® H9 O? Cl + PCI =C8 H® Cl8 + PO? Cl. If these reactions be correct, the constitution of acetal might be thus written :— 8 902 Czy o£ fs i 02; in which view it would be an alcohol in which 1 equiv. of hy- drogen is replaced by the radical C? H9O?. This radical forms a chloride, C® H9 O? Cl, and a terchloride, C® H9 Cl*; but its sta- bility is not great, and it readily decomposes into ethyle and aldehyde. XLVII. Proceedings of Learned Societies. ROYAL SOCIETY. [Continued from p. 227.] May 26, 1859.—Sir Benjamin C. Brodie, Bart., Pres., in the Chair. i ‘ees following communications were read :— ‘On the Occurrence of Flint-implements, associated with the Remains of Extinct Mammalia, in Undisturbed Beds of a late Geo- logical Period.’”’ By Joseph Prestwich, Esq., F.R.S., F.G.S. &e. The author commences by noticing how comparatively rare are the cases even of the alleged discovery of the remains of man or of his works in the various superficial drifts, notwithstanding the ex- 49," Prete: : ~ \ee — Occurrence of Flint-implements in Gravel-beds. 291 tent to which these deposits are worked; and of these few cases so many have been disproved, that man’s non-existence on the earth until after the latest geological changes, and the extinction of the Mammoth, Tichorhine Rhinoceros, and other great mammals, had come to be considered almost in the light of an established fact. Instances, however, have from time to time occurred to throw some doubt on this view, as the well-known cases of the human bones found by Dr. Schmerling in a cavern near Liege,—the remains of man, instanced by M. Marcel de Serres and others in several caverns in France,—the flint-implements in Kent’s Cave,—and many more. Some uncertainty, however, has always attached to cave-evidence, from the circumstance that man has often inhabited such places at a comparatively late period, and may have disturbed the original cave-deposit ; or, after the period of his residence, the stalagmitic floor may have been broken up by natural causes, and the remains above and below it may have thus become mixed together, and afterwards sealed up by a second floor of stalagmite. Such instances of an imbedded broken stalagmitic floor are in fact known to occur ; at the same time the author does not pretend to say that this will explain all cases of intermixture in caves, but that it lessens the value of the evidence from such sources. The subject has, however, been latterly revived, and the evidence more carefully sifted by-Dr. Falconer; and his preliminary reports on the Brixham Cave*, presented last year to the Royal Society, announcing the carefully determined occurrence of worked flints mixed indiscriminately with the bones of the extinct Cave Bear and the Rhinoceros, attracted great and general attention amongst geo- logists. This remarkable discovery, and a letter written to him b Dr. Falconer on the occasion of his subsequent visit to Abbeville last autumn, instigated the author to turn his attention to other ground, which, from the interest of its later geological phenomena alone, as described by M. Buteux in his “ Esquisse Géologique du Departement de la Somme,” he had long wished and intended to visit. In 1849 M. Boucher de Perthes, President of the ‘Société d@ Emulation” of Abbeville, published the first volume of a work entitled “ Antiquités Celtiques et Antédiluviennes,” in which he an- nounced the important discovery of worked flints in beds of undis- turbed sand and gravel containing the remains of extinct mammalia. Although treated from an antiquarian point of view, still the state- ment of the geological facts by this gentleman, with good sections by M. Ravin, is perfectly clear and consistent. Nevertheless, both in France and in England, his conclusions were generally considered erroneous ; nor has he since obtained such verification of the pheno- mena as to cause so unexpected a fact to be accepted by men of science. ‘There have, however, been some few exceptions to the general incredulity. The late Dr. Rigollot, of Amiens, urged by * On the 4th of May, this year, Dr. Falconer further communicated to the Geo- logical Society some similar facts, though singularly varied, recently discovered by him in the Maccagnone Cave near Palermo.—See Proc. Geol. Soe. 292 Royal Society :— M. Boucher de Perthes, not only satisfied himself of the truth of the fact, but corroborated it, in 1855, by his ‘“ Mémoire sur des Instruments en Silex trouvés 4 St. Acheul.”’ Some few geologists suggested further inquiry ; whilst Dr. Falconer, himself convinced by M. de Perthes’ explanations and specimens, warmly engaged Mr. Prestwich to examine the sections. The author, who confesses that he undertook the inquiry full of doubt, went last Easter, first to Amiens, where he found, as de- scribed by Dr. Rigollot, the gravel-beds of St. Acheul capping a low chalk-hill a mile S.E. of the city, about 100 feet above the level of the Somme, and not commanded by any higher ground. The following is the succession of the beds in descending order :— Average thickness. 1. Brown brick-earth (many old tombs and some coins), with an irregular bed of flint-gravel. No organic remains. 10 to 15 ft. Divisional plane between | and 2a very uneven and indented. 2a. Whitish marl and sand with small chalk debris. Land and freshwater shells (Lymnea, Succinea, Helix, Bithynia, Planorbis, Pupa, Pisidium, and Ancylus, all of recent species) are common, and mammalian bones and teeth are Occasionally found .........ce+.sesereseeesee Ores or rec 2 to 8 ft. 20. Coarse subangular flint-gravel,—white with irregular ochreous and ferruginous seams,—with tertiary flint peb- bles and small sandstone blocks. Remains of shells as above, in patches of sand. Teeth and bones of the ele- phant, and of a species of horse, ox, and deer,—generally near base. This bed is further remarkable for containing worked flints (“ Haches ” of M. de Perthes, and “ Langues de Chat” of the workmen) ..... ppcpuetepddee Wepetiaphad cae ae 6 to 12 ft. Uneven surface of chalk. The flint-implements are found in considerable numbers in 26. On his first visit, the author obtained several specimens from the workmen, but he was not successful in finding any himself. On his arrival, however, at Abbeville, he received a message from M. Pinsard of Amiens, to whose cooperation he expresses himself much indebted, to inform him that one had been discovered the following day, and was left in situ for his inspection. On returning to the spot, this time with his friend Mr. Evans, he satisfied himself that it was truly iz situ, 17 feet from the surface, in undisturbed ground, and he had a photographic sketch of the section taken*. Dr. Rigollot also mentions the occurrence in the gravel of round pieces of hard chalk, pierced through with a hole, which he considers were used as beads. The author found several, and recognized in them a small fossil sponge, the Coscinopora globularis, D’Orb., from the chalk, but does not feel quite satisfied about their artificial dressing. Some specimens do certainly appear as though the hole had been enlarged and completed. * The only mammalian remains the author here obtained, were * On revisiting the pit, since the reading of this paper, in company with several geological friends, the author was fortunate to witness the discovery and extraction by one of them, Mr. J. W. Flower, of a very perfect and fine specimen of flint-implement, in a seam of ochreous gravel, 20 feet beneath the surface. They besides obtained thirty-six specimens from the workmen.—June, 1859. Occurrence of Flint-implements in Gravel-beds. 293 some specimens of the teeth of a horse—but whether recent or ex- tinct the specimens were too imperfect to determine ; and part of the tooth of an elephant (lephas primigenius’). In the gravel-pit of St. Roch, 14 mile distant, and on a lower level, mammalian remains are far more abundant, and include Elephas primige- nius, Rhinoceros tichorhinus, Cervus somonensis, Bos priscus, and Equus* ; but the workmen said that no worked flints were found there, although they are mentioned by Dr. Rigollot. At Abbeville the author was much struck with the extent and beauty of M. Boucher de Perthes’ collection. There were many forms of flints, in which he, however, failed to see traces of design or work, and which he should only consider as accidental ; but with regard to those flint-instruments termed “ axes” (‘haches”’) by M. de Perthes, he entertains not the slightest doubt of their artificial make. They are of two forms, generally from 4 to 10 inches long: the outlines of two specimens are represented in the following dia- gram. They are very rudely made, without any ground surface, and were the work of a people probably unacquainted with the use of metals. These implements are much rarer at Abbeville than at Amiens, fig. 1 being the common form at the former, and fig. 2 at Fig. 2. Ca ra ol Fig. 1. Front section. Side section Side section. Front section. One-third the natural size. the latter place. The author was not fortunate enough to find any specimens himself; but from the experience of M. de Perthes, and the evidence of the workmen, as well as from the condition of the specimens themselves, he is fully satisfied of the correctness of that * To this list the author has to add the Hippopotamus, of which creature four fine tusks were obtained on this last visit. 294. Royal Society :— gentleman’s opinion, that they there also occur in beds of undisturbed sand and gravel. At Moulin Quignon, and at St. Gilles, to the S.E. of Abbeville, the deposit occurs, as at St. Acheul, on the top of a low hill, and consists of a subangular, ochreous and ferruginous flint-gravel, with a few irregular seams of sand, 12 to 15 feet thick, reposing upon an uneven surface of chalk. It contains no shells, and very few bones. M. de Perthes states that he has found fragments of the teeth of the elephant here. The worked flints and the bones oceur generally in the lower part of the gravel. In the bed of gravel also on which Abbeville stands, a number of flint-implements have been found, together with several teeth of the Elephas primigenius, and, at places, fragments of freshwater shells. The section, however, of greatest interest is that at Menchecourt, a suburb to the N.W. of Abbeville. The deposit there is very distinct in its character ; it occurs patched on the side of a chalk hill, which commands it to the northward ; and it slopes down under the peat-beds of the valley of the Somme to the southward. The deposit consists, in descending order, of— Average thickness. 1. A mass of brown sandy clay, with angular fragments of flints and chalk rubble. No organic remains. Base very irregular and indented into bed No. 2.........sescceseceeeees 2 to 12 ft. 2. A light-coloured sandy clay (“ sable gras’”’ of the work- men), analogous to the loess, containing land shells, Pupa, Helix, Clausilia of recent species. Flint-axes and mammalian remains are said to occur occasionally in GLUSTUEM aoe. cnes «chetvamddecanantecscarstcssectcrs Ges osatedeeuancene 8 to 25 ft. 3. White sand (“sable aigre”), with 1 to 2 feet of subangular flint-gravel at base. This bed abounds in land and fresh- water shells of recent species of the genera Helix, Succinea, Cyclas, Pisidium, Valvata, Bithynia, and Planorbis, to- gether with the marine Buccinum undatum, Cardium edule, Tellina solidula, and Purpura lapillus. The author has also found the Cyrena consobrina and Littorina rudis. With them are associated numerous mammalian remains, and, it is said, flint-implements................sseecseeseseecees 2 to 6 ft. 4. Light-coloured sandy marl, in places very hard, with Helix, Zonites, Succinea, and Pupa. Not traversed .....- 3+ The Mammalian remains enumerated by M. Buteux from this pit are LElephas primigenius, Rhinoceros tichorhinus, Cervus somo- nensis?, Cervus tarandus priscus, Ursus speleus, Hyena spelea, Bos primigenius, Equus adamaticus, and a Felis. It would be essential to determine how these fossils are distributed—which occur in bed No. 2, and which in bed No. 3. This has not hitherto been done. The few marine shells occur mixed indiscriminately with the freshwater species, chiefly amongst the flints at the base of No. 3. They are very friable and somewhat scarce. It is on the top of this bed of flints that the greater number of bones are found, and also, it is said, the greater number of flint-implements. The author, however, only saw some long flint flakes (considered by M. de Perthes as flint knives) turned out of this bed in his presence ; but the workmanship was not very clear or apparent; still it was as much so as in some of the so-called flint knives from the peat-beds — : & ‘ , e ‘ { Occurrence of Flint-implements in Gravel-beds. 295 and barrows. There are specimens, however, of true implements (“haches”) in M. de Perthes’ collection from Menchecourt ; one noticed by the author was from a depth of 5, and another of 7 metres. This would take them out from bed No. 1, but would leave it uncertain whether they came from No. 2 or No. 3. From their general appearance, and traces of the matrix, the author would be disposed to place them in bed No. 2, but M. de Perthes believes them to be from No. 3; if so, it must have been in some of the sub- ordinate clay seams occasionally intercalated in the white sand. Besides the concurrent testimony of all the workmen at the dif- ferent pits, which the author after careful examination saw no reason to doubt, the flint-implements (“haches”’) bear upon them- selves internal evidence of the truth of M. de Perthes’ opinion. It is a peculiarity of fractured chalk flints to become deeply and_per- manently stained and coloured, or to be left unchanged, according to the nature of the matrix in which they are imbedded. In most clay beds they become outside of a bright opaque white or porcelainic ; in white calcareous or siliceous sand their fractured black surfaces remain almost unchanged ; whilst in beds of ochreous and ferru- ginous sands, the flints are stained of the light yellow and deep brown colours so well exhibited in the common ochreous gravel of the neighbourhood of London. This change is the work of very long time, and of moisture before the opening out of the beds. Now in looking over the large series of flint-implements in M. de Perthes’ col- lection, it cannot fail to strike the most casual observer that those from Menchecourt are almost always white and bright, whilst those from Moulin Quignon have a dull yellow and brown surface ; and it may be noticed that whenever (as is often the case) any of the matrix adheres to the flint, it is invariably of the same nature, texture, and colour as that of the respective beds themselves. In the same way at St. Acheul, where there are beds of white and others of ochreous gravel, the flint-implements exhibit corresponding variations in colour and adhering matrix ; added to which, as the white gravel contains chalk debris, there are portions of the gravel in which the flints are more or less coated with a film of deposited carbonate of lime ; and so it is with the flint-implements which occur in those portions of the gravel. Further, the surface of many specimens is covered with fine dendritic markings. Some few implements also show, like the fractured flints, traces of wear, their sharp edges being blunted. In fact, the flint-implements form just as much a constituent part of the gravel itself—exhibiting the action of the same later influences and in the same force and degree—as the rough mass of flint frag- ments with which they are associated. With regard to the geological age of these beds, the author refers them to those usually designated as post-pliocene, and notices their agreement with many beds of that age in England. The Menche- court deposit much resembles that of Fisherton near Salisbury ; the avel of St. Acheul is like some on the Sussex coast; and that of Moulin Quignon resembles the gravel at East Croydon, Wandsworth Common, and many places near London. The author even sees 296 Royal Society :— reason, from the general physical phenomena, to question whether the beds of St. Acheul and Moulin Quignon may not possibly be of an age one stage older than those of Menchecourt and St. Roch; but before that point can be determined, a more extended knowledge of all the organic remains of the several deposits is indispensable. The author next proceeds to inquire into the causes which led to the rejection of this and the cases before mentioned, and shows that in the case of M. de Perthes’ discovery, it was in a great degree the small size and indifferent execution of the figures and the introduction of many forms about which there might reasonably be a difference of opinion ;—in the case of the arrow-heads in Kent’s Cave a hidden error was merely suspected ;—and in the case of the Liege cavern he considers that the question was discussed on a false issue. He therefore is of opinion that these and many similar cases require reconsideration ; and that not only may some of these prove true, but that many others, kept back by doubt or supposed error, will be forthcoming. One very remarkable instance has already been brought under the author’s notice by Mr. Evans since their return from France. In the 13th volume of the ‘Archzologia,’ published in 1800, is a paper by Mr. John Frere, F.R.S. and F.S.A., entitled “An Account of Flint-Weapons discovered at Hoxne in Suffolk,” wherein that gentle- man gives a section of a brick-pit in which numerous flint-imple- ments had been found, at a depth of 11 feet, in a bed of gravel con- taining bones of some unknown animal; and concludes from the ground being undisturbed and above the valley, that the specimens must be of very great antiquity, and anterior to the last changes of the surface of the country,—a very remarkable announcement, hitherto overlooked. The author at once proceeded in search of this interesting locality, and found a section now exposed to consist of — feet. 1.) Harthiand+a Wey, Mints et vex ject se sta. ad carob vsavesteserstes des tieckewen ee 2 2. Brown brick-earth, a carbonaceous seam in middle and one o: gravel at base; no organic remains. The workmen stated that two flint-implements (one of which they shortly picked up in the author’s presence) had been found about 10 feet from the surface during the last Winter