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Am @ ee ~~ AA naga SO AAWA Aparna Waa aRAAR A a aaa AA ann in WNNRARRGARARARA it puke iaesdume ies TAA I NAV len on \ rAan AaB BAAN *AAAM AAA Latta i th AANA AN WW. iA . Aas \AAARAA Se Nene coer | ApAABAPOhAA «ac aaa AA BERRA ARAN SARAARARASAGE AAGAA Narn WARM sian ana IIE? A ae AAS RAR AAA ! 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Valalal A, ae " NAAAAAAM A aaAnhAna>.- pa~> Raanen >? RAAAAAR AAR Ma, eae Rp aaalh AANA a AA Weer BAAAAAMAAAAA, Nal ant aan AAAR : AAAS Rn seer en ree nananannnthehasAhanl an: 4: Annet ‘Anh Sua Riiaaaa Banat aaaga A nagaBRASARAR ean aannateten aah ah Re rn’ AR A aagiea: aaa NA anntitiaaneetate ana ; Agar nmanara RAAAA AR SA; ai ’ad AMIAAAAAAN ant ; AN RAAB AAS parr Arahana a nr’ AANA alas Ro Peel * et Bae et ) eee a] ur My x ‘ape PROCEEDINGS OF THE —— ROYAL IRISH ACADEMY, sa Cee ee ot ORS ial aye ore - FOR THE YEAR 1841-2. pay ig A 7 ee : ree a. oe <¢ "i - ait See 3 er: Ages Sh eas Pl PART VI. . 7 DUBLIN: PRINTED BY M. H. GILL, PRINTER TO THE ACADEMY. MDCCCXLIIL PROCEEDINGS OF THE ROYAL IRISH ACADEMY. 1840. No. 25. November 9. SIR Ws. R. HAMILTON, LL.D., President, in the Chair. The President read a letter from the Secretary of State for the Home Department, informing him that her Majesty had been pleased to receive very graciously the address of the President, Council, and Members of the Royal Irish Academy, congratulating her Majesty on the recent provi- dential deliverance of herself and her illustrious Consort. The decease of the Very Rev. the Dean of St. Patrick’s, V.P., having been announced to the Academy, it was re- solved— That we have heard with deep regret of the death of our valued Vice-President, the Dean of St. Patrick’s; and that while we sympathize with all classes of our fellow- citizens, in lamenting the removal of one so universally be- loved and esteemed, we would desire to record our sense of the peculiar loss sustained by the Academy, in being de- prived of the assistance of one who could estimate the value of our Institution, and give to it his most cordial coopera- tion; one who found leisure from the multifarious duties of VOL. Il. B 2 his station, to cultivate successfully the researches connected with the antiquities of Ireland, and had earned for himself a high place among those who labour to illustrate her ancient records, or to save from destruction the perishing relics of her former civilization. Samuel Ferguson, Esq., was elected to the vacant place in the Council; and the Rev. J. H. Todd, D.D., was ap- pointed by the President, under his hand and seal, to suc- ceed the Dean of St. Patrick’s in the office of Vice-Presi- dent. The Rev. T.R. Robinson, D.D., M.R.I.A., gave the Aca- demy an account of a large reflecting telescope, lately con- structed by Lord Oxmantown, and of the processes em- ployed in forming its specula. After explaining the relative importance of magnifying and illuminating power, Dr. R. proceeded to give a brief sketch of the history of the reflecting telescope, which seemed to have been forgotten for many years after its in- vention, till it was revived by Hadley. The labours of Short soon gave it celebrity ; yet even this artist limited himself in almost every instance to sizes which were not more powerful than the achromatics of his day, and his large instruments appear to have been failures.* It was not till a full century after the publication of Newton’s paper, that Sir William Herschel gave this telescope the gigantic development which has crowned him with imperish- able fame; and by the construction of telescopes of nineteen * A Newtonian of six feet focus, and 9-4 inches aperture, is said by Maskelyne to have shewr the first satellite of Jupiter 13” longer than a triple achromatic of 3:6 inches aperture. The telescope of twelve feet focus, and eighteen inches aper- ture, now at Oxford, shewed 1oultiple rings of Saturn. ———: nity inl 7] and forty-eight inches aperture, placed regions almost beyond the scope of measurement within the reach of human intel- lect. But as Short, in a spirit unworthy of his talents, took care that his knowledge should die with himself, and Her- schel published nothing of the means to which his success was owing, the construction of a large reflector is still as much as ever a perilous adventure, in which each individual must grope his way. Accordingly, the London opticians themselves do not like to attempt a mirror even of nine inches diameter, and demand a price for it which shews the uncertainty and difficulty of its execution. In Ireland we are more fortunate, for a member of our Academy, Mr. Grubb, finds no difficulty in making them of admirable quality up to this size, or even fifteen inches; but with all his distinguished mechanical talent, he is believed to be doubtful of the possibility of more than doubling this last magnitude in perfect speculum metal. Under these circumstances, too much praise cannot be given to Lord Oxmantown, who, in the midst of other pur- suits, has found leisure for such researches ; and by a rare combination of optical science, chemical knowlege, and prac- tical mechanics, has given us the power of overcoming the difficulties which arrested our predecessors, and of carrying to an extent which even Herschel himself did not venture to contemplate, the illuminating power of this telescope, along with a sharpness of definition scarcely inferior to that of the achromatic. The chief difficulties which are to be overcome in the construction of reflectors, arise from the excessive brittleness of the composition of which specula are made, and from the necessity of giving them figures which shall be free from aberration. The great mirror in the Newtonian form is (if the eyepiece and plane mirror be correct) the conical paraboloid. B 2 4 It is necessary that speculum metal should possess, in the highest attainable degree, the qualities of whiteness, brilliancy, and resistance to tarnish. Lord Oxmantown has found that these conditions are best satisfied in the definite combinations of four equivalents of copper to one of tin; or by weight, 32 and 14°7 nearly. Metals differing from this by a slight excess of either component, are, when first polished, scarcely less brilliant, but are dimmed so rapidly that the lapse of a few days produces a sensible difference. On the other hand, some large specula of the atomic com- pound have been lying uncovered for years, without ma- terial injury to their polish. But this compound is brittle almost beyond belief; a slight blow, or even the application of partial warmth, will shiver a large mass of it; though harder than steel, its sur- face is broken up with the utmost facility, and it has a most energetic tendency to crystallize. The common pro- cess of the founder fails with it, except for masses of very limited magnitude, as the cast cracks in the mould, and the subsequent difficulties of the annealing are such, that it has been a very general practice to use an alloy lower (contain- ing more copper) than the atomic standard. Even Sir William Herschel was obliged to yield to this necessity. It appears froma letter of Smeaton, (Rees’ Cyclopedia, Art. Tele- scope,) that for his 20 feet mirror of 19 inches aperture, the composition was 52 copper to 12°4 tin; and that for the 40 feet it was even lower. Yet two out of three attempts to cast this huge speculum failed. Lord Oxmantown at first endeavoured to evade the diffi- culty, by constructing a speculum in pieces, soldering plates of fine metal to a back ofa peculiar brass, ascertained to have the same expansion; and has completed one of thirty- six inches aperture and twenty-seven feet focal length, which performs very well on stars below the fifth magnitude, 5 but above that exhibits a cross formed by the diffraction at the joints; and in unsteady states of the air exhibits the six- teen divisions of the great mirror on the star's disk. By dimi- nishing the number and size of the joints it is found, that these inconveniences can be diminished, so as to be scarcely perceptible; and in all probability this is the process by which the remotest limits of telescopic vision will ultimately be attained. It is, however, not necessary for instruments of even greater dimensions than this, since Lord Oxmantown has succeeded, by a contrivance as simple as ingenious, in casting at the first attempt a solid mirror of the same size ; and there is no reason to suppose that it will be less effec- tive on a much larger scale. But however difficult it may be to obtain the rough spe- culum of large dimensions, it is still more so to give it a proper figure, combined with that brilliant polish which is technically called black, because it reflects no light out of the plane of incidence. In such mirrors as can be wrought by hand, they are worked by short cross strokes on the polisher, and at the same time have a slow rotation relative toit. This might be expected to produce merely a spherical figure; but by varying the length of the stroke, by circular movement, elliptic figure of the polisher, or removing por- tions of its pitch covering, a parabolic figure is obtained. For sizes above nine inches diameter, the work must be per- formed by machinery; but in all which Dr. R. has seen, (the most remarkable of which are those of Sir William Herschel* and Mr. Grubb,) the cross stroke is given by a lever moved by hand; and it is supposed that perfect results cannot be obtained but by the feeling of the polisher’s’ action. Sir John Herschel is believed to have made important ES * Dr. R. had the good fortune to see this at Slough, in 1830, while at work on a twenty-feet mirror. 6 additions to his father’s apparatus; and it is t» be hoped he will soon redeem his promise (Mem. R. Ast. Soe. vol. vi.) of publishing his improvements. Lord Oxmantown has in many respects deviated from the usual process. His polisher, of the mirror’s diameter, intersected by transverse and circular grooves, into por- tions not exceeding half an inch of surface, is coated, first, with a thin layer of the common optical pitch, and then with a much harder compound. It is worked on the mirror, and counterpoised so that but little of its weight bears; but the want of pressure is compensated by a long and rapid stroke. The mirror revolves slowly in a cistern of water, maintained at a uniform temperature, to prevent the extrication of heat by friction, The polisher moves slowly in the same direc- tion, while it is also impelled with two rectangular move- ments. The machine is driven by steam, and requires no superintendence, except to supply occasionally a little water to the polisher, and to watch when the polish is complete. By an induction from experiments on mirrors from six to thirty-six inches aperture it was found, that if the magni- tudes of the transverse movements be $ and +3, of the aper- ture, and their times be to its period of rotation as | and 1°8 to 37, the figure will be parabolic: but to combine with this the highest degree of lustre, it is found necessary to apply, towards the close, a solution of soap in liquid ammonia, which seems to exert a specific action. The certainty of the process is such, that the solid mirror of thirty-six inches aperture, after being scratched all all over its surface with coarse putty, was, in Dr. R.’s pre- sence, perfectly polished in about six hours, and was placed in its tube for examination, without any previous trial as to quality. Lord Oxmantown has preferred the Newtonian to the Herschelian form, and, in Dr. R.’s opinion, with good — a _ ‘ reason. In the latter, the inclination of the great mirror to the incident rays must deform the image,* and it is now known, that even with faint objects sharp definition is of high importance. It should, in fact, be a segment of a paraboloid, exterior to the axis; and though a theorem of Sir William Hamilton (Trans. R. Irish Acad., vol, xv. p- 97,) might seem to indicate mechanical means of approxi- mating to the figure, yet Dr. R. fears there would be greater difficulty in applying them than in enlarging the aperture of the Newtonian, so as to make up for the loss of light. Another serious objection is, that in the Herschelian the obseryer’s position at the mouth of the tube, must cause currents of heated air, which will materially interfere with sharpness of definition. As to the loss of light by the second reflexion, Dr. R. thinks it has been much overrated, and expresses a wish that acareful set of experiments were made on reflexion by plane specula at various incidences, on prisms of total reflexion, and the achromatic prism, proposed as a substitute by Sir David Brewster. As to the rest of the instrument, it may suffice to say, that it bears a general resemblance to that of Ramage, but that the tube, gallery, and vertical axis of the stand are counterpoised, so that one man can easily work it, notwith- standing its enormous bulk. The specula, when not in use, are preserved from moisture or acid vapours, by connecting their boxes with chambers containing quicklime, which is occasionally renewed. This arrangement, (which also oc- curred to Dr. R., and has been for several years applied by by ge bed bees 2 ee Ole) 2S * Any one who has a Newtonian telescope can verify this, by inclining a little the great mirror, so however as not to pass the edge of the plave mirror by the pencil. In Lord O.’s iustrument, an inclination of 11’ sensibly injures it ; were it Herschelian, the inclination must be 3° 11’. 8 him to the Armagh reflector,) appears to be very effective in preserving the polish. In trying the performance of the telescope, Dr. R. had the advantage of the assistance of one of the most celebrated of British astronomers, Sir James South; but they were un- fortunate in respect to weather, as the air was unsteady in almost every instance; the moonlight was also powerful on most of the nights when they were using it. After mid- night, too, (when large reflectors act best,) the sky, in general, became overcast. The time was from October 29th to November 8th. Both specula, the divided and the solid, seem exactly parabolic, there being no sensible difference in the focal adjustment of the eyepiece with the whole aperture of thirty-six inches, or one of twelve; in the former case there is more flutter, but apparently no difference in definition, and the eyepiece comes to its place of adjustment very sharply. The solid speculum showed a Lyre round and well de- fined, with powers up to 1000 inclusive, and at moments even with 1600; but the air was not fit for so high a power on any telescope. Rigel, two hours from the meridian, with 600, was round, the field quite dark, the companion separated by more than a diameter of the star from its light, and so brilliant that it would certainly be visible long before sunset. Z Orionis, well defined, with all the powers from 200 to 1000, with the latter a wide black separation between the stars; 32 Orionis and 31 Canis minoris were also well sepa- rated. It is scarcely possible to preserve the necessary sobriety of language, in speaking of the moon’s appearance with this instrument, which discovers a multitude of new objects at every point of its surface. Among these may be named a mountainous tract near Ptolemy, every ridge of which is 9 dotted with extremely minute craters, and two black parallel stripes in the bottom of Aristarchus. The Georgian was the only planet visible; its disc did not show any trace of aring. As to its satellites, it is diffi- cult to pronounce whether the luminous points seen near it are satellites or stars, without micrometer measures. On October 29, three such points were seen within a few seconds of the planet, which were not visible on November 5; but then two others were to be traced, one of which could not have been overlooked in the first instance, had it been in the same position. If these were satellites, as is not im- probable, there would be no great difficulty in taking good measurement both of their distance and position. There could be little doubt of the high illuminating power of such a telescope, yet an example or two may be desirable. Between «<' and & Lyre, there are two faint stars, which Sir J. Herschel (Phil. Trans. 1824) calls “ de- bilissima,” and which seem to have been, at that time, the only set visible in the twenty-feet reflector. These, at the altitude of 18° were visible without an eye-glass, and also when the aperture was contracted to twelve inches. With an aperture of eighteen inches, power 600, they and two other stars (seen in Mr. Cooper’s achromatic of 13°2 aper- ture, and the Armagh reflector of 15) are easily seen. With the whole aperture, a fifth is visible, which Dr. R. had not before noticed. Nov. 5th, strong moonlight. In the nebula of Orion, the fifth star of the trapezium is easily seen with either speculum, even when the aperture is contracted to eighteen inches. The divided speculum will not shew the sixth with the whole aperture, on account of that sort of disintegration of large stars already noticed, but does, in favourable moments, when contracted to eighteen inches. With the solid mirror and whole aperture, it stands out conspicuously under all the powers up to 1000, 10 and even with eighteen inches is not likely to be over- looked. Comparatively little attention was paid to nebule and clusters, from the moonlight, and the superior importance of ascertaining the telescope’s defining power. Of the few examined were 13 Messier, in which the central mass of stars was more distinctly separated, and the stars themselves larger than had been anticipated ; the great nebula of Orion and that of Andromeda shewed no appearance of resolution, but the small nebula near the latter is clearly resolvable. This is also the case with the ring nebula of Lyra; indeed, Dr. R. thought it was resolved at its minor axis; the fainter nebulous matter which fills it is irregularly distributed, having several stripes or wisps in it, and there are four stars near it, besides the one figured by Sir John Herschel, in his catalogue of nebulz. It is also worthy of notice, that this nebula, instead of that regular outline which he has there given it, is fringed with appendages, branching out into the surrounding space, like those of 13 Messier, and in parti- cular, having prolongations brighter than the others in the direction of the major axis, longer than the ring’s breadth. A still greater difference is found in | Messier, described by Sir John Herschel, as ‘‘a barely resolvable cluster,” and drawn, fig. 81, with a fair elliptic boundary. This telescope, however, shews the stars, as in his figure 89, and some more plainly, while the general outline, besides being irregular and fringed with appendages, has a deep bifurcation to the south. From these and some other discrepancies, Dr. R. thinks it of great importance that the globular nebule and clusters should be all carefully reviewed, as it is chiefly from their supposed regularity that the hypothesis of the condensation of nebulous matter into suns and planets has arisen, an hypothesis which he thinks has, in some instances, been car- ried to an unwarrantable extent. ll On the whole, he is of opinion that this is the most powerful telescope that has ever been constructed. So little has been published respecting the performance of Sir W. Herschel’s forty-foot telescope, that it is not easy to institute a comparison with ¢hat, the only one that can fairly be made to compete with it. But there are two facts on record which lead tv the inference that it was deficient in defining power; one, the low power used, which Dr. R. thinks was not above 370; the other, the circumstance that neither the fifth nor sixth stars of the trapezium of the nebula of Orion were shewn by it. As to light, there is no reason to believe that the composition of the forty-foot mirror was as reflective as that of the twenty-foot; and if Dr. R. be correct in the opinion, that the latter* did not shew the fifth star easily, or the sixth at all, and that it only exhibited the “ debilissima” and one star near the ring-ne- bula, then z has decidedly less illuminating power than eighteen, perhaps not more than fourteen inches aperture of Lord Oxmantown’s mirror, notwithstanding the loss of light in that by the reflexion at the second speculum. However, any question about this optical pre-eminence is likely soon to be decided, for Lord Oxmantown is about to construct a telescope of unequalled dimensions. He in- tends it to be six feet aperture, and fifty feet focus, mounted in the meridian, but with a range of about half an hour on each side of it. If he succeeds in giving it the same degree of perfection as that which he has attained in the present instance, which is exceedingly probable, it will be, indeed, a proud achievement; his character is an assurance that it will be devoted, in the most unreserved manner, to the ser- vice of astronomy, while the energy that could accomplish * In its original state, not as improved by the more perfect means latterly employed by Sir John Herschel. 12 such a triumph, and the liberality that has placed his disco- veries in this difficult art within reach of all, may justly be reckoned among the highest distinctions of Ireland. DONATIONS. Eleven Quern Stones of different Kinds. Eight Methers of different Sizes and Patterns. A round wooden Goblet. An ancient Horn Vessel. Presented by Captain Portlock, M.R.LA. An ancient Spur found in the Grave-yard at Ferns. Pre- sented by Stephen Radcliffe, Esq., per Haliday Bruce, Esq., M.R.LA. A Papal Bulla, found near the Foundation of the Cathe- dral of Cloyne, (Clemens PP. IIIT.) Presented by R. J. Graves, M.D. Fisica di Corpi ponderabili. 2 vols. 8vo. By the Che- valier Amadeo Avogadro. Presented by the Author. Third Annual Report of the Proceedings of the Botanical Society of Edinburgh. Presented by the Society. Sixth Report of the Poor Law Commissioners in Ireland. Presented by George Nicholls, Esq. Ancient Laws and Institutes of England. Presented by the Commissioners of the Public Records of the Kingdom. 4 Geological Map of England and Wales. By G. B. Greenough, Esq. Presented by the Geological Society. Transactions of the Geological Society of London. Vol.V. (1840.) Presented by the Society. Quarterly Journal of the Statistical Society of London. July, 1840. Presented by the Society. Address of the General Secretaries of the British Associ- ation. Presented by the Authors. Journal of the Franklin Institute. Vol. XXV. (1840.) Presented by the Institute. 13 Transactions of the Royal Society of Gottingen, from 1828 to 1831. Vol. VII. Presented by the Society. Proceedings of the American Philosophical Society, to July, 1840. (No. 12.) Presented by the Society. Directions for using Philosophical Apparatus. By E. M. Clarke, Esq. Presented by the Author. Manuscript Notices relating to the Cathedral of St. Patrick, Armagh. By John Davidson, Esq., M.R.I.A. Presented by the Author. Ordnance Survey of the King’s County. In 49 Sheets, including Title and Index. Also, Ordnance Survey of Carlow. In 28 Sheets, including Title and Index. Presented by His Excellency the Lord Lieutenant. November 30, (Stated Meeting.) SIR Wma. R. HAMILTON, LL.D., President, in the Chair. Dr. Kane read a Paper “On the Production of Audible Sounds,” of which the following is an abstract. _'The sensation of sound is produced upon the ear by the tympanum being thrown into vibratory motion, isochro- nous with the vibrations transmitted from the sounding body. Any body which vibrates as a single mass gives origin at the same moment to two waves, whose motions are in opposite directions, and of which one is rarefied and the other con- densed. If these two arrive at the tympanum at the same mo- ment and with equal power, perfect neutralization should result, and no sound be heard: hence, where a vibratory body produces upon the ear the sensation of sound, it arises 14 from one wave of the two being either totally intercepted or, at least, diminished in force, and the loudness of the sound is proportional to the difference of the intensity of the two waves when they affect the ear. All instruments for increasing sound, and producing re- sonance, act upon this principle. The following facts will illustrate these principles in de- _ tail. A tuning fork is a centre of four BS waves, two + and two —, but unless it be os - very close to the ear, no sound is heard from + it; because the centre of all the four waves being very close, all act on the ear with equal force, and the difference is 0, (approximatively.) Now, if an open tube, of the same length as a one-phase wave from the fork, be approached to one centre, as A, in the adjoining figure, the air in it commences to vibrate in unison with the fork, from being set in motion by the first B wave which passes into it: a the vibration of the tube is, A ete A (~ however, a phase behind +\ that of the fork, and hence, ° when a — wave passes from the centre a, it meets a + wave from the end of the tube gE; and both are destroyed. The — centre, c, destroys also a + centre, as D, and there remain only the centres of + waves, B from the fork, and F from the tube, and these acting in concert on the tympanum produce the sound that we hear. If the tube be closed, and of only one-half the length, the + wave, which emanates from the centre A, passes in, and being reflected from the bottom, issues again at the moment when the next — wave from a is about to enter; FE and a then destroy each other, and c and p also interfering, there results only the + wave B, which acts unimpeded on —_ 15 gs », theear. The sound of an open he eel tube is, therefore, ceteris paribus, |- Ej) ite f- © much stronger than that of a . ite ‘ closed tube, as there are two waves in place of one. That the office of closed tubes, when resonant, is to de- stroy a portion of the sound of the original vibrating body, and of the open tubes to afford, in addition to that, a new centre of a wave of the same phase as that which remains, may be exhibited in many ways. Thus, Mr. Adams shewed long since, that when two closed tubes are placed at right angles to each other, they interfere when made to speak to a tuning fork, and for this effect no explanation has hitherto been given. But it is evident that the tubes being at right angles to each other, the waves destroyed are in opposite phases, and those which remain are in opposite phases also, so that the effect is the same as if no tubes were present at all. The same effect may be produced by a single tube, bent so that its aper- tures may be at right angles to each other; A B N x x XAn£© the — and + waves, p and c, meeting in D ie the tube, produce neutralization, and the waves A and B, also + and —, which re- main, interfere also, and hence no sound results.. In an open tube bent into a circle, as in the figure, the two waves destroyed (a c) are of the same phase, and also those which : remain, (B D,) and hence, such a tubesounds with nearly double the r ot power of an ordinary open tube. That it is the sound of the waves which do not go into the tube, and not that of the waves in the tube, we hear, may be shewn by applying two closed tubes, as in the next figure. When the two — waves are absorbed + D 16 by the circular open tube, each closed tube absorbes a + wave, and hence, notwithstanding that there is so much vibrating mate- rial, no sound is heard. But if the tubes aand Bwere open, then the vibrating centres should have been simply transferred to their farther extremities, and the tubes would emit sound as the fork had done without them in the preceding figure. If the open tube be double the length of a phase, then the neutralization oc- curs as in the figure, + the residual waves Peas ee Eves ie G being B andF, in op- ce posite phases; but as their centres are separated so far, they interfere only in hyperboloidal planes, which are not detected unless when carefully sought for, but have been noticed to exist by Savart, although he did not suspect their cause. All these principles have received very full verification from an instrument constructed for the purpose, and termed a Chorizophone. It consists of a square glass plate, which is placed above a set of closed tubes of such size, that when the plate vibrates in four pieces, with diagonal nodal lines, the length of each tube is half the length of the phase of the wave produced, and their form is triangular, of the magnitude of one of the four vibrating portions of the plate; when one of these tubes is presented to the plate, and this brought to vibrate by a violin bow applied to the centre of one of the sides, the tube resounds, and more loudly in proportion as the plate is brought nearer to its orifice. Nowhere the entire 17 wave from the plate is caught by the tube, and the more per- fectly its escape into the air is prevented, the louder is the sound produced, the sound must arise therefore from the waves which do not pass into the tube. Any one or more waves may thus be absorbed by the closed tubes, and a range of loudness of sound produced from the same plate with one or more of the four tubes, according as they are disposed as follows : The vibrating plate gives eight waves, four above and four below, 4 being + and 4 minus. With one tube, one wave is absorbed, and 3 + and 3 — destroying each other, a wave remains opposite in phase to that which is absorbed, and produces an audible sound. With two tubes, the waves absorbed may be either of op- posite or of the same phases. If opposite, then, the remain- ing waves are 3 + and 3 —, and no sound is produced ; but if the waves absorbed be of the same phase as +, then there remains 4— and 2+, and hence the ear is doubly affected by 2—. The two tubes may be either both above or both below, or one above and one below the plate. With three tubes, the absorbed waves may be either all ‘of the same phase, or two of one and one of the other. Inthe first instance, 3 + being absorbed, there remains 4 — and 1 —, and the ear receives the impulse of 3—. Inthe other case 2 + and 1 — being absorbed, there remains 2 + and 3— and the impulse on the ear is only 1—. ‘The position of the tubes may yary in this as in the former case. With four tubes, the absorption may be either all of the same phase, or 24+-and 2—. In the former case, the re- maining waves will be either 4 + or 4—, in which case the greatest sound the plate can produce is heard, or else there remain 2 + and 2 —, in which case the plate gives no sound. These results prove fully that it is the residual sound that is heard, and not that which passes into the tube. VOL. Il. c 18 A vibrating plate gives some sound always, even without the tubes, for since there are at least eight waves, some one will always be more favourably disposed for acting on the ear than another, this difference will increase with the number of waves; and hence, the independent sound of a plate in- creases in proportion as the vibrating portions into which it divides, become more numerous. A string vibrating in free space, produces little or no sound; but if it be strung over, or in connexion with, an elastic board or box, a great resonance is produced. ‘This arises from two sources ; first, the string when by itself is the centre of two waves excessively close, and the action of which is therefore interfering. But ifthe string an, vibrate near a plane surface c, the wave —1, which passes towards it is reflected back, and meeting the wave + 2, which follows, it neutralizes it partly, and enables the wave — 2, to reach the ear without diminution. It is probable, however, that the great portion of the sound arises from the board or plate B itself vibrating in parts, or as a whole. If in parts, these parts are variously situated, as regards the ear, and hence produce an effect upon it. Or if, as a whole, the plate c is so broad, or bounded, if a box, that one wave is lost by internal reflexion, and only the wave emanating from the outer surface can arrive at the ear. When a tuning fork is placed on a table, one wave is lost by internal transmission and reflexions, whilst that directed from the outer surface reaches to the ear. In the case of reed instruments, the reed produces two waves, which, if it vibrated freely, should neutralize each other on the ear ; but in practice whilst an open passage is al- lowed to one by the mouth-piece, the other wave is lost within the cavities of the lips and mouth. In mouth-piece instruments, as bugles and trumpets, the cavity of the mouth 19 serves also for the absorption of the one wave, leaving the other free to act. The following note, ‘On the Course of the diurnal Fluc- tuations of the Barometer,” by James P. Espy. A.M., of Phi- ladelphia, was communicated by Dr. Apjohn. * It isa law of inertia, that if a body is forced upwards, it will react and press on its support, more than its natural gravity ; and if itis permitted to descend, it will press on its support less than its natural gravity, and the increase and diminution of pressure will be proportional to its velocity. ** Moreover, if a body is permitted to descend with a cer- tain velocity, and then retarded, it will, when retarded, press more on its support than its natural gravity, and that in pro- portion to the rapidity of its retardation. “This principle will explain the four fluctuations of the barometer which occur every day. ** Just before sunrise, when the atmosphere is neither becoming hotter nor colder, the barometer will indicate the natural weight of the air, which we may call a mean; as the sun rises the air will begin to expand by heat, andthe whole atmosphere will be lifted up by this expansion, and by its reaction will cause the barometer to rise; and this will be the greatest, at the time when the air is receiving the most rapid accessions of heat, which must take place before the hottest time of the day, when the air is becoming neither hotter nor colder. On this principle, then, the maximum day fluctuation will take place between daylight in the morn- ing and the hottest time of the day, and this corresponds with the fact; for this maximum, which amounts to more than the tenth of an inch, takes place about nine or ten o'clock, A. M. *« At the hottest part of the day, when the air is neither expanding nor contracting, it is manifest that the barometer will stand again at a mean. Soon after this, however, the air 20 will begin to contract from diminishing temperature, and at the moment of the most rapid acceleration of contraction, the barometer will stand at its day minimum, which will probably be late in the afternoon; and it is found in fact to be from four to five o’clock. From this time the rapidity of the down- ward motion of the air from contraction begins to diminish, and the barometer of course begins to rise; and at the mo- ment when it is most rapidly retarded in its contraction, the barometer will be at its maximum night fluctuation, and will again be above the mean, but not so much as the day max. “‘ This max. is found to occur about ten or eleven o'clock, p.m. The air will now go on contracting more and more slowly, until about daylight, when it will be at rest, and the ba- rometer will again be at a mean. “* This theory was given by me to the Journal of the Franklin Institute, and published ten or twelve years ago. “ T ventured in that paper to predict, notwithstanding some alleged observations at St. Bernard’s Hospital to the contrary, that it would be found by more careful observations that the morning max. fluctuation would be greater in lofty situations on the sides of mountains, provided they were not very lofty, than on the plain below. ** For it is manifest, that there will be not only a reaction at these lofty situations, (a little less, it is true, than below,) but some ofthe air will be lifted up, by the expansion of the air below, above the upper place of observation ; which would in all probability more than compensate the diminished re- action at moderate elevations. ** This prediction has been entirely verified by Lieute- nant-Colonel Sykes’s observations in India, and this verifica- tion may be considered as a strong proof of the correctness of the theory. It is quite probable, that max. day fluctua- tion occurs later at considerable elevations than on the plain below. “The theory would lead us also to suppose, that at very 21 great elevations, where the reaction is very minute, only two fluctuations would be found in the day: the maximum at about two o'clock, p. M., when most air would be above the barometer; and the minimum at daylight in the morning, when least air would be above it; but I know of no observa- tions to confirm or refute these deductions.” Mr. Ball brought under the notice of the Academy the fact, that the ordinary sturgeon of the Dublin markets is an undescribed species. He stated that Mr. Thompson of Bel- fast, and Professor Agassiz, concurred with him in this opi- nion, and he proposed to call it Accipenser Thompsoni, pur- posing, if permitted, to give figures and full descriptions in a future number of the Proceedings. A notice of an unpublished Irish coin of Edward IV. was read by A. Smith, M.D., M.R.LA. ** Within the last month some workmen were employed in cleaning one of the city drains in the Cross Poddle, and a few coins werefound. Among them was one of no intrinsic value, and apparently of nointerest whatever. It is made of brass, and was originally plated with silver, traces of which still remain. On one side it has a crown within a circle of pellets, outside which, in place of a legend, are crosses and roses alternately ; on the other side it has the common type— a cross, with three pellets in each quarter; the legend is de- faced. It weighs nearly five grains, and is now in the cabinet of Lieutenant-Colonel Weld Hartstonge. ‘This little coin bears no evidence in itself which would enable us to say towhat king’s reign it should be appropriated, or even to what country. But on referring to an Act passed in the second year of Edward IV., at a parliament held in Dublin, we find it enacted, ‘ that a coyne of copper mixed with silver, be made within the Castle of Dublin, having on one side the print of a cross, and on the other part a crown, of which four shall be taken for a penny; and that the said 22 coyne shall have graven within the circumference of the said cross, the name of the place where it was made; and on the other part suns and roses in the circumference of the said crowne.”* “Tt is to be regretted, that this little coin, the only one of the kind which has been found, is not in better preservation ; but such as it is, it corresponds in every particular with the description in the Act; and, therefore, we do not hesitate to assert that it is one of the farthings of mixed metal ordered to be made in 1462. “It may be objected, that this coin has crosses instead of sunsround the crown, and itwould be difficult indeed to give a more accurate symbol of the sun, in so many places, within so limited a space; but we should recollect, that similar crosses occur on some of the silver groats of Edward IV., coined in Dublin, in the beginning of his reign. On these groats, immediately over the crown, on the obverse, are placed three small crosses, which have usually been considered as privy marks.+ “ Now taking for granted, that these crosses on the groats were intended to represent suns, as they evidently were on the farthing, we suspect we can account for them, not only as privy marks, indicating that the coins on which they are found belong to Edward IV., but also assign a probable rea- son why three only should appear. ‘** The sun was first introduced by Edward IV. upon the coins, ‘ in commemoration ofan extraordinary appearance in the heavens, immediately before the battle of Mortimer’s Cross, in Herefordshire, (in 1461,) where three suns were seen which shone for a time, and then were suddenly conjoined in one.’ “Tt matters little whether the extraordinary phenomenon * Simon’s Essay on Irish Coins, Appendix, No. VII. + Simon, pl. 4, fig. 71. + Ruding’s Annals of the Coinage, vol. ii. p. 359, 2nd Edition, 8vo. 23 just alluded to be explained or not ; it is sufficient for our purpose to know, that it gave rise to the introduction of the sun as a privy mark on the coins of Edward; and we may be permitted to hazard the conjecture, that the three crosses on his Irish groats, coined shortly after the battle of Mortimer’s Cross, were intended to represent the three suns. “We could refer to many instances in which dates and other matters were determined with certainty, by studying with attention minute particulars in the type of coins, con- cerning which the records were unsatisfactory, or altogether wanting ; and there are still in existence authentic records of more than one Irish coinage, specimens of which have not yet been discovered ; and within the last few years numerous coins, whose existence had not been suspected, have come to light, for the preservation of many of which we are indebted to the indefatigable zeal and research of a highly esteemed and deeply lamented individual, whose memory will long be regarded with respect and admiration, and the recollection of whose labours in preserving the proud memorials of our country, will, we trust, be perpetuated by depositing within these walls his collection of Irish antiquities, in accordance with his well known intention, and thus constituting a monu- ment worthy of the late Dean of St. Patrick’s.” The Archbishop of Dublin made some observations on a remarkable meteor, lately seen in different parts of Britain: Resolved—That the Committee of Antiquities be re- quested to take immediate steps towards opening a subscrip- tion for the purchase of the collection of Irish antiquities which belonged to the late Dean of St. Patrick’s. DONATIONS. Memoires de l Academie Imperiale des Sciences de St. Petersbourg. Tome I.—XI. 24 Sciences Mathematiques, §c. Tome 1V. 3rd and 4th Livraisons, and Tome IV. Sciences Politiques, Histoire, &c. 4th and 5th Livraisons. Novi Commentarii Academie Scientiarum Imperialis Pe- tropolitane. 'Tom. I.—XX. Nova Acta Academie Scientiarum Imperialis Petropoli- tane. Tom. VI. VII. VIII. and XV. Recueil des Actes del Académie Impériale des Sciences de St. Petersbourg. An. 1838 and 1839. Nos. 13 and 14. Presented bythe Academy. The Polytechnic Journal. Vol, Il. Part 5. Presented by W. Farran, Esq. Quarterly Journal of Statistical Society. Vol. 111. Part 3. Oct. 1840. Presented by the Society. An Inquiry into the Causes of popular Discontents in Ireland. By an Irish Gentleman. 1804. Presented by Joseph Hone, Esq. Descriptive Catalogue of the Museum of the Royal Col- lege of Surgeons in Ireland. Vol. Ul. By John Houston, M.D.,M.R.I.A., &c. Presented by the College of Sur- geons. On the Diminution of Temperature with Height of the Atmosphere. Researches on Heat. Fourth Series. Additional Experiments on terrestrial Magnetism in 1837. By James D. Forbes, Esq. Presented by the Author. Memorie della Reale Academia delle Scienze di Torino. Second Series. Vol. II. Presented by the Academy. Transactions of the American Philosophical Society. New Series. Vol. VII. Part 1. Presented by the Society. PROCEEDINGS OF THE ROYAL IRISH ACADEMY, Sete ee a ee 0 CS 1840. No. 26. December 14, 1840. Rey. J. H. TODD, D.D., Vice-President, in the Chair. Dr. Apjohn read the following notice, by George J. Knox, Esq., of ‘‘ some Improvements in the Voltaic Pile.” “ The chief imperfection in the voltaic pile, its want of a _ constant uniform powerof long duration, by which itis rendered almost useless as an instrument of research, having been overcome by the ability of Professor Daniell, the only thing that remained to render it efficient seemed to be, to increase its power; a desideratum accomplished by Mr.Grove, by sub- stituting for copper and sulphate of copper, platinum and ni- tric acid. To give to Grove’s battery a constancy of action equal to that of Professor Daniell’s, would require an increase in the quantity of acids, (particularly the sulphuric,) into which the metals are immersed ; but inasmuch as in galvanic batteries of the ordinary construction an increase of acid so- lution would require an increased distance of the metals from each other, producing a diminution of intensity, I endea- voured to obviate these disadvantages by the following con- trivance. Porous vessels are fixed half an inch apart in lateral wooden supports, in which grooves are cut, to retain the zinc plates from touching ; the porous vessels are filled with ni- tric acid, from a long glass tube, sealed at one end, and bent VOL Il. D 26 at the otherat right angles. Along the side of the tube also holes are bored at distances corresponding to the distances of the porous vessels from each other; so that, upon pour- ing nitric acid into the tube, the vessels are all filled at the same moment; when filled, the entire apparatus is placed in a vessel containing sulphuric acid. The advantages of this arrangement were, that I had only two solutions to pour in, whatever number of alternations were employed ; a sufficient supply of acid solutions to keep up a constant action for a length of time; and a distance between the plates scarcely exceeding the thickness of the porous vessel employed. “The following experiments were undertaken with the intention of estimating the relative values of the different con- structions of Grove’s battery, recommended by Mr. Knight of Foster Lane, as far as respects the arrangement of the zinc and platina plates, when, to my surprise, I found the same quantity of electricity to be evolved when the zinc is bent so as to expose an opposing surface to each surface of a platinum plate, as when a platinum plate, of the size of the former zinc, is similarly placed with respect to a plate of zinc of the same size as the former platinum, affording an economical method of arranging a Wollaston’s battery, the zincs being bent round the coppers, in place of the coppers round the zincs. *< Experiments with Grove’s Battery. “The acid solutions were those recommended by Mr. Grove, i. e. pure nitric acid, in contact with the platina ; sul- phuric acid + 4-5 water by measure, in contact with the zinc. The surfaces of zincs immersed were 3 by 2°5 inches ; those of the platina, bent round the porous vessel holding the zines, were 6 by 2°5 inches. The glasses containing the acid, &c., were 3°2 inches long, 1°5 broad, 3-5 deep. The length of the porous vessel of pipeclay was 2°5 inches, the 27 breadth 0-3, the depth 3'5. ‘The number of alternations was five. Cubic Inches. Time;’2 minutes, = 4.6 ees ce TIS BO The battery-being at rest for 10 minutes,. . . . 80 po Poster tee ek te ee ais Sh. gp ee a] 4 Ee sales. ED BE f 19 hours, . . - .none “ The porous vessel was found filled with sulphate of zinc, which stopped the action of the battery. ‘* Second Experiment. “ The zinc plates being of the same.size as the former pla- tina, and the platina of the same size as the former zincs, the zincs bent round the platina, all other things being as before. Cubic Inches. nee eaten I cad Hct Se oe 8 SEE Hea te 2. Se et ae ” 25 rT) . . . . . . . . . . . . 8: “ Third Experiment. * Another battery, the diameter of the cells of which was 21 inches, gave a diminution of only one-half of the quantity of gas after the lapse of forty-eight hours, shewing the advan- tage of having a large supply of sulphuric acid.* _ “ Experiments with Smee’s Battery of Platinized Silver. “The acid solution was of the same strength as before, and the sizes of the zines and platinized silver the same as aoe * « The porous vessels were of pipeclay. The same expertments repeated with unglazed porcelain gave 10 cubic inehes in two minutes ; with very porous pipe- clay, they gave as much as 15 cubic inches in two minutes, shewing the import- ance of attending to the nature of the porous vessel employed.” p2 28 of the zincs and platina formerly employed. The zines were bent round the platina.* Cubic Inches. Tiop, 2 minutes, . sis. + «cs =\,eone eS After 5 minutes, .x}:+ iii: (o} 10 ia eid Qeegtogtss lero “ Second Experiment. “ The zincs being raised out of the acid, cut in two, and re-immersed. Cubic Inches. Tinie, 2 minutégeetulaecsscsbussle- +8 3 eee eee After S-minutes, Anaad inane. . ig “ Third Experiment. “ The zincs and platinized silver being removed, the acid remaining untouched ; the platinized silver plates were bent round the. zincs. Cubic Inches. Qe 2 austen, es eats et) on pe ee IV igen er MUNIUES) nfo |e Geter e ai icc. s acdsee “ Fourth Experiment. * The platinized silver cut in two. Cubic Inches, Amero WMULES; se ne c) octane a le ee PRICE OUMMULES, St gs an. esa we ee “‘ Supposing from these experiments the same quan- tity of electricity to be developed, whichever of the opposed surfaces of the two metals be the greater, I placed in sepa- rate glasses five zinc cylinders, one-inch diameter, immerged *, “ The most advantageous. method of arranging a Smee’s battery is, packing the zines and platinized. silvers in the manner, recommended by Dr. Faraday in his 10th series, (also by Mr. Young, Phil. Mag. vol. x, p. 241,) placing the package on supports so as to allow the sulphate of zinc to fall to the bottom of the vessel, while the fresh acid rises to the surface.” 29 eight-tenths of an inch in the acid ; platina foil, connected by binding screws with the zincs, was rolled into cylinders two- tenths of an inch in diameter, and then immersed in pip eclay tubes one inch deep. Cubic Inches. aune,.2 minutes, © Awsiwiaora ciel.) ee LO Merit MaInntons 30, 2.7 ao ee hae te ke» oie O ** Second Experiment. ‘ Platina foil of the same size as the zines, and zine rods of the same diameter as the platina cylinders being employed, the effects were precisely the same. Cubic Inches. MT OMIMMAEH IS Ay. oes akc t ied we 8 kU PE LO TIIHUNEH 2 Fe a ian, soe eS ae, ot * Third Experiment. “ The zinc cylinders being made twice the diameter of the former; the quantity of gas generated in two minutes was the same as before; the increased number of lines of elec- trical force compensating the increased resistance offered by the acid solution. “ Fourth Experiment. ** With cylinders twice the diameter of these, a very fee- ble current passed, the obstacle being too great to be over- come ; by increasing the diameter of the porous vessels, and thereby of the nitric acid solution, which is a good con- ductor, the impediment is diminished, as shewn in experi- ment fifth. Thus Mr. Binks (Phil. Mag. vol. xi. p. 68) finds, that in dilute sulphuric acid, the size of the copper compared to a given surface of zinc, to produce a maximum effect, should be 16, that of the zinc to a given surface of copper being 7; while in a galvanic arrangement, in which the zinc is immersed in dilute sulphuric acid, inclosed in a mem- 30 branous bag, and the copper in a surrounding solution of sul- phate of copper, the proportion of zinc to copper was as one to eight, the impediment to the passage of the current being double in the latter case what it was in the former. “ Fifth Experiment. “ Five cylinders of zinc, 10 inches high, 3 diameter, were placed in glass vessels, containing sulphuric acid, as before. Into these were placed cylindrical earthenware vessels, 1} inches diameter, containing pure nitric acid; slips of platina foil were rolled into cylinders as before. Cubic Inches. (eee ei oe ee a After 10 me Sess SUT) nie we oi ee 5 00 = UTES SA” Fone iS Eo, nn “From these data may be calculated the heights of the zinc pipes, and the weight of platina foil required to obtain any given decomposition, to be employed, as shewn by Jacobi, either as a motive power, or applied to light-houses, to the polariscope, or to the fusion of refractory substances. For the latter purposes, I had fixed to a strong, shallow woolf bottle, two tubes with glass cocks, and to them tubes containing chloride of calcium, applied to a Daniell’s jet, playing upon a cylinder of lime, rotated by clock work. A third tube was inserted in the bottle, intended as a regu- lation of the pressure, or a safety valve, in case of explosion.” Dr. Apjohn then made a brief verbal communication on the subject of the Composition of Pyrope. This mineral, long * “The dilute acid in the voltameter began to boil ; the cause of the increase of decomposition, compared to what took place in the small cylinder, was the small Stratum of sulphuric acid between the porous vessel and the zinc. For a continu- ous action the zinc pipes, sealed at one end and amalgamated, should be connected by pipes at top and bottom, with an earthenware vessel, containing the sulphuric acid.” 31 confounded with garnet, is known to be distinguished from it by containing chrome, and by exhibiting, not the dodeca- hedral, but the hexahedral form. The best analyses of it, however, which are by Kobel and Wachtmiester, are ob- viously imperfect, of which no better proof can be given than that Gustavus Rose, in his Crystallography, does not attempt to give the formula of the mineral, but contents himself with enumerating the different oxides of which it is composed. Under these circumstances, Dr. Apjohn conceived that a re-examination of the constitution of pyrope would not be without interest. He, therefore, undertook its analysis ; and the result has been that he has detected in it yttria, one of the rarest of the earths; one, in fact, which had previously been known to exist only in a few minerals of exceeding scarcity. The yttria was insulated in the following manner. The mineral being fused with carbonate of potash, and the silex separated in the usual way, the peroxide of iron, alumina, and yttria were precipitated together by a mixed solution of ammonia and sal-ammoniac. The alumina was taken up by caustic potash; and to the iron and yttria, dis- solved in a minimum of muriatic acid, such a quantity of tartaric acid was added, that upon subsequently pouring in ammonia in excess there was no precipitate produced. The iron was now removed by sulphuretted hydrogen; and the solution evaporated to dryness, and ignited in a large pla- tinum crucible, so as to volatilize the ammoniacal salts, and burn away the carbon of the tartaric acid, left the yttria slightly coloured by oxide of chrome. From this latter sub- stance it is separated, but not perfectly, by the action ofa dilute acid, and by the addition of ammonia, or caustic potash, to the solution the yttria is again recovered. That the sub- stance thus obtained is yttria seems proved by the following considerations. It is separated, though not completely, from acids by 32 ammonia largely diluted with sal-ammoniac, and hence cannot be one of the alkaline earths. It is insoluble in potash, and is, therefore, not alumina or glucina. After ignition it dissolves readily in dilute acids, and is hence not zirconia or thorina. From zirconia it is further distinguished by its saline solutions, being eer by ferrocyanide of potassium. It is not oxide of cerium, for it does not redden in the exterior flame of the blow-pipe, and because its salts are not precipitated by the sulphate of potash. The quantity of the yttria amounts to at least 3 per cent. Dr. A. is still engaged in investigating the composition of pyrope; and expressed his intention of bringing his re- sults on a future occasion in a more detailed form under the notice of the Academy, when he hoped also to be able to assign the true formula of the mineral. Mr. J. Huband Smith exhibited to the Academy an an- cient monastic seal, from an impression of which the annexed wood engraving is taken. This seal has been for some time supposed to have been that of the Dean and Chapter of Lismore, and it was recently found among the effects of the late Rey. Sir George Bisshopp, formerly Dean of Lismore; but the legend around the seal shews this supposition to be totally groundless. Itreads thus: “SIGILLVM : CAPITYLI: PRIORIS : ET: CONVEN- TVS: DE: BVLLYNGIONA.” It surrounds the figures of the Vir- gin and Child. She appears seated, and wearing a highly ornamented crown; her robe, which falls in gracefully ar- ranged folds, displays no inconsiderable degree of skill and tastefulness of design. In her right hand is a star of five rays, intended possibly to represent the star of Bethlehem, to which the infant Saviour points. It is observable that his head displays the ecclesiastical tonsure. The seal is of 53 a pointed oval form, and measures two inches and seven- eighths in length, and one inch and three-quarters in its greatest breadth. It has been surmised, with considerable appearance of probability, that this seal (which, if an inference were drawn solely from the style of the characters, might be pretty con- fidently referred to the close of the fourteenth, or the beginning of the fifteenth century) belonged to a monastic establishment dedicated to the Virgin, as Archdall states, [Monast. Hibern. 626,] at Ballindown, on Lough Garagh, in the county of Sligo, of which but inconsiderable remains now exist. It is said to have been founded by M‘Donogh, lord of Corran and Tirreril, A.D. 1427, for nuns of the order of Saint Dominick, about the very period to which the cha- racters of the legend may be attributed, Like other names of places in Ireland, that of Ballindown is variously written. In a tract entitled, ‘‘ Valor beneficiorum ecclesiasticorum in Hibernia,” we find “V.de Ballendowne 34 in the *‘ Dicecesis Tuamensis,” of which the ‘‘ Extenta et taxatio facta fuit, 28mo. Eliz.” So that it seems highly pro- bable that ‘“ Bullyngiona” may have been but an arbitrary Latinization of the same name by the artificer by whom the seal was made, possibly a monk of the religious house to which it belonged. Mr. Clibborn made the following communication on the subject of the Leyden Jar. “In Brand’s Manual of Chemistry, vol. i., 3rd Edition, p- 76, I find it stated, that, ‘if one Leyden jar be insu- lated, with its internal surface connected with the positive conductor, another jar may be charged from its exterior coating ; and if this second jar be insulated, a third may be charged from its exterior coating, and so on for any number of jars, provided always that the exterior coating of the last jar be connected with the ground.’ ‘As my electrifying machine was but small,it occurred to me that I might economise both time and labour by con- structing a battery of jars so arranged that I should be able to take advantage of this principle, and make one jar charge another, instead of my being obliged to charge the whole series; for, though they are all connected together, and charged by the same operation in the common electric bat- tery, yet the time and labour consumed in charging the battery is exactly the same as if each jar were charged sepa- rately and then added to the series. A great saving of labour and time would have been effected had the arrangement of jars answered, for it was exactly the same as that described by Brand, so far as the charging part of the apparatus was concerned; but when the jars were loaded, or rather should have been loaded, they were made to turn through a qua- drant, and form a new arrangement, by which all their out- side coatings were connected together by a common con- ductor. A similar arrangement connected all their inside 35 coatings, which made all the conditions necessary to the perfection of the common battery; and I found it capable of being charged by the electrifying machine in this form, but it could not be charged to any extent in the other. It ap- peared, that but few sparks would pass from the conductor to the first jar. If the last one was removed, and its chain fastened to the next, the first jar would take a few more sparks, and so on; for it was found that whenever the last jar in the series at any time was removed, the same results followed; and this was the case when the last but one was removed, clearly proving, that the capacity or aptitude of the first jar to take a charge was influenced and diminished by the second, more so by the third, fourth, &c. Its apti- tude was greatest when it was by itself, and not connected, as described, with the others. ‘‘ This result disappointed my expectations, so far as my intended improvement on the electric battery was concerned; and it also appeared to point out the existence of a principle influencing the charge of the electric jar, which was not recognized in the popular treatises on electricity. I procured a number of glass plates with fixed and moveable coatings. These plates were insulated and arranged with and without coatings in every way that Brand’s rule required, but the general result was the same as that given above. «From numerous experiments made with these plates, I came to the following general conclusions : “1, That the actual quantity of the positive and negative electricities which we can accumulate in the opposite sur- faces of an electric or non-conductor, as a plate of glass or dry ice, depends upon the distance of these surfaces. «9, Every case of charge of one jar or plate may be assimi- lated to that of any number of jars or plates in a series, such as Brand’s, by supposing the one jar or plate to be divided into the greater number, its thickness being the sum of the thicknesses of all the segments or plates. The inside of the 36 first jar or surface of first plate, in contact with conductor, and outside of last jar or plate in contact with the ground, being considered as the proper opposite surfaces of the pro- per plate, and those on which the electricities evolved by the friction of the cylinder and rubber of the electrifying machine are accumulated or heaped. “Ifwe make a pile of the plates coated or not, and charge the outside surfaces by coating them, and connecting one with the cylinder and the other with the rubber of the ma- chine, we find all the conditions of the experiment complied with. There is nonecessity for any connexion with the ground, which in Brand’s can act merely as the conductor to convey the negative charge of the rubber to the extreme surface. “* Let us now unpack the pile, and we find that the charge of the intermediate plates diminishes, as we approximate towards the centre of the pile, being greatest near the ex- tremes. At equal distances the charges are equal ; for the charges of the first plate but one, and the last but one, will as perfectly neutralize each other as the charges of the sur- faces of the first and last. The same is found to be the case with the surfaces of the third plates from each extreme, and so on of the others; but it is not the case with a second and a third, a first and a fourth plate, and so on, no two unequals as to place exactly neutralizing each other. Hence we may conclude, that the charge of the intermediate jars in a series, such as described by Brand, though it really de- pends on inductive agency, is altogether different from that kind he alludes to, which may be inferred from his erroneous representation of the actual fact; and the charge of the extreme surfaces is immediately the result of that action only, which several electricians have called conduction, arising from the connexion of these surfaces with the sources of the free electric forces. The fact here described appears capable of throwing much light on the corpuscular arrangement of the atoms of 37 bodies, which retain an electric charge on their surfaces, or which, by a change of form from mechanical pressure or dif- ference of temperature, exhibit differences of electric state. In speaking of a charged electric, we may consider it a pile of an infinite number of plates, each of which, except the extreme surfaces, is composed of a surface of atoms, which are acted on by. two sets of induced electric forces, whose differences, arising from their distances from the extremes, we discover when we split the plate, or if itbe.a pile, when we separate the plates from each other.” January 11, 1841. His Grace the ARCHBISHOP OF DUBLIN, V.P., in the Chair. Rev. Henry Barry Knox, Rev. John West, Thomas Fortescue, Esq., M. P., Chichester Bolton, Esq., and Henry Coulson Beauchamp, M. D., were elected Members of the Academy. The Rev. Thomas H. Porter, D.D., read a paper “ On the Deposits of Gravel in the Neighbourhood of Dublin.” After detailing the facts commonly known as to the stra- tified beds and ridges of limestone gravel, lying over the great central limestone region of Ireland, and the continu- ance of deposits containing a large proportion of rounded pebbles and stones of the same material, over the granite’ and other primitive rocks to the eastward of the limestone country ; it was argued that there were clear indications of a great diluvial action from west to east, by which the sur- face of the limestone was reduced to its present level, and the remains of its upper portions spread over the limestone 38 region itself, and carried eastward to the sea. The occur- rence of similar calcareous deposits in the seaward glens and valleys of the Dublin and Wicklow mountains for some miles south, and on their sides to a considerable height, was ascribed to the current of the same deluge, sweeping the transported substances over the lower parts of the moun- tain range, and then turning southwards along the sea coast, after passing the north flank of the mountains. Similar facts, but in an inverted order, from south to north, have been observed towards the southern flank, in the County Wexford. It was urged, that the subsiding waters of this inunda- tion, rushing down the valleys, and meeting below with the main current on the plains, would throw up those ridges along the sides of the hills, and on the flats beneath; of which a remarkable example is presented in the glen of Ballynascorney, (through which the Dodder descends from the Dublin mountains,) and in the gravel hills in front of that, from Tallaght to Crumlin. The direction assumed in this paper for the diluvial cur- rent agrees remarkably with that assigned by Professor Phillips, as the cause of the distribution of the Shapfell boulders over the north-east of England. A conjecture was proposed as to the possible occasion of such a move- ment of water over the country. The limestone tract was evidently formed under the sea. Its elevation may have been connected with the last great convulsion, which deter- mined nearly the present form of the surface. Great disturbances are seen at Killiney, the Scalp, &c., to have attended the appearance of the granite, and even to have followed that period, affecting the granite itself. Many parts of the Irish coasts present such abrupt terminations towards the sea, as to indicate either a violent raising of the island from a continuous tract at the bottom, or a sudden sinking of an extent of dry land around the present surface. 39 Either of these events would create immense commotions in the waters, Reference was made, in the course of this argument, to the theory of Professor Agassiz, respecting the supposed evidence, that glaciers once existed in the mountains of this island, and produced, as moraines, some of the accumula- tions of mountain debris commonly attributed to the agency of water. This theory having been pushed so far by some eminent British geologists as to have almost every ridge of gravel and stones unhesitatingly called a moraine, it was urged, that their principle could not be applied here at least, since the limestone abounding in the deposits of the glens could never have been brought down by ice from mountains in which no limestone rocks exist. It is but justice to Pro- fessor Agassiz to state, that he did not ascribe the limestone gravel ridges at Ballynascorney to a glacier; but professed to find the traces of one higher up the course of the stream. Against the glacier theory, in general, it was maintained, that evidences of a glacier having existed in any locality must be derived from the existing form of the ground; and that, therefore, no considerable change of the surface could be admitted, since the time when the moraines were imagined to have been thrown up. More especially, no deluge could have taken place since their formation; for in that case, the moraines must have been swept away. Hence they must be supposed to have existed between Noah’s flood and the commencement of the historical periods. ‘This inter- val, it was contended, would not allow time for their forma- tion and disappearance. A gradual change of the temperature of the whole nor- thern hemisphere would be at variance with the fact esta- blished by geologists, that the heat of the earth’s surface had been formerly much greater than now. Had the degree of cold necessary for the formation of glaciers, been owing to a greaterelevation of this entire coun- 40 try, its sinking to its present level must have been attended with convulsions and floods, which could scarcely have failed to obliterate all vestiges of moraines. An objection, brought from the known change of tempera- ture in Greenland within modern times, was met by observy- ing, that Greenland in its best days was always a land of glaciers ; in the extent of which it is easy to suppose an oc- casional increase or diminution, Mr. J. Huband Smith gave an account of the discovery, in the month of November last, of a human skeleton, accom- panied with weapons, ornaments, &c., interred on the sea shore, in the vicinity of Larne, in the county of Antrim. He suggested, that a timely effort to preserve a record of such interesting discoveries, can hardly fail to rescue from destruction some valuable ‘‘ scattered leaves belonging to the lost books of history.” The locality in which these remains were found is one of considerable historical interest ; it was within less than a mile of Olderflete Castle, where it will be remembered that Ed- ward Bruce landed with a considerable force for the invasion of this country, in the beginning of the fourteenth century. A very cursory inspection, however, suffices to shew that these weapons and ornaments could not have belonged to one of his followers, but must be referred to a period considerably more remote. They consist of a sword of very characteristic form, double edged, and rounded at the point; measuring two feet eight inches and nearly a quarter in its extreme length; a small portion, said to have been about six inches in length, was broken off and lost at the time of its discovery ; the blade varies from two inches to two inches and a quarter in breadth ;—the head of a lance (both this and the sword are of iron or steel, much corroded) ;—a small and very elegantly formed bronze pin, which measures five inches and a half in 41 length, thickly encrusted with verd antique, and of the shape usually supposed to have been used in fastening the cloak or mantle ;—and lastly, four fragments of bone ; three of them be- ing portions of a comb, the back of which (attached to the serrated part by rivets) is slightly but not untaste- fully carved-on both sides ; and the fourth is so minute and indistinct, as to render its original use and form uncertain. The manner in which the skeleton was discovered was thus : some lime quar- ries having been lately open- ed along the shore, at a dis- tance from the jetty, or wooden pier, at which small coasting vessels, trading be- tween Larne and the op- posite ports of Scotland, usually take in their car- goes, it became necessary, for the greater convenience of transporting limestone from the newly opened quarries, to construct a rail or tramway. In level- ing the line marked out for the purposes of such construction, in the afternoon of the 7th of last November, the workmen discovered these re- mains ata spot three quarters ofa mile distant from the town VOL, I. E 42 of Larne, about seventy yards from the sea shore, and about five feet above the level of high water mark. The skeleton, when uncovered, lay obliquely, the head pointing towards the N. W. The soil about it, consisting of sand, without almost any admixture of clay, may have, in the lapse of time, shifted its depth; but there scarcely appeared to have been more than from eighteen inches to two feet of sand or soil above these remains. There was no appearance of stone kist, or hollow space formed by flags set edgeways, which appear to belong ex- clusively to the more ancient interments preceded by crema- tion; fragments of the skeleton alone being found in such, with indications of the action of fire, and usually accompanied by one or more cinerary urns. Yet although there was in the present instance no trace of coffin, either of stone or wood, there appeared no reason to doubt that the inter ment was effected inaregular and orderly manner. Across the breast was found the sword, its handle disposed towards the right hand. On the same side, but beneath the sword, was the lance head. ‘The position of the remaining articles was not noticed at the time by the workmen, and therefore cannot now be ascertained. Mr. Smith placed beside these weapons a sword and lance from his collection, selected from some found in the remark- able heap of bones in the townland of Lagore, near Dun- shaughlin, in the County of Meath; a paper descriptive of which was read before the Academy by Doctor Wilde, on the 27th of April last. The straight shape and uniform breadth of the blade of this last mentioned sword, and the form of the lance head, appeared remarkably similar, though on a reduced scale, to those of the weapons found near Larne. The comb _ and bronze pin are nearly identical with several of those dis- covered at Dunshaughlin, where, it is observable, no brazen weapon of any description occurred. ————— 43 From a consideration of all these circumstances, Mr. Smith ventured to express an opinion thatthe remains found at Larne, as wellas those at Dunshaughlin, are to be referred to that re- mote period when the use of brass or bronze was superseded by iron and steel inthe manufacture of offensive weapons, while it was yet retained in the lighter works of ornament.. From the invariable shortness of the Dunshaughlin swords, he was disposed to infer, that the remains there discovered were of a period not far removed from the age of the bronze swords of similar length, still not unfrequently found in Ireland ; while he suggested, that the articles to which the present paper re- ferred might be considered as furnishing a closely following, though later link in the chain. ' The sword bears no slight resemblance. to one which has been engraved in Walker’s Essay on the Costume and Arms of the Ancient Irish, and which, attributing it to the Knights Templars, he states to have been found about forty years before, near the site of the old priory of Kilmainham. It was accordingly objected, that the weapons found at Larne belonged to some one of that Order, and were therefore of a much later date than that assigned to them as above men- tioned. In reply to this, Mr. Smith urged the remarkable circumstance of the bronze pin, of unquestionable antiquity, having been found in connexion with the sword, a fact of which he was able to give the most decisive assurance, upon the testimony of the overseer of the works, a person of strict- est integrity, and who, not having any antiquarian predilec- tions, could not be aware of the force or nature of the evi- dence he was furnishing. It was also to be recollected, that long antecedent to the establishment of the priory of Knights Templars by Richard Earl Strongbow, in 1174, a monastic institution had been founded there by St. Magnen, from whom Kilmainham (which in many ancient documents is writ- ten Kilmaynan) took its name so early as the sixth or se- venth century of our era; and that the adjoining burial 44 ground was used by the Irish, we learn from the Munster book of battles, attributed to Mac Liag, a poet who died in the year 1015, where it is recorded, that several of the chiefs who fell at the battle of Clontarf were interred at Kilmain- ham. In the hall of the Commander of the Forces is suspended a sword of the same shape and character found in the old burial ground, vulgarly known by the name of “ Bully’s Acre,” about forty years ago. In some adjacent fields, between the immediate grounds of the Royal Hospital and the brink of the river Liffey, about four years ago, some labourers, em- ployed in raising gravel, discovered a skeleton, around which were disposed a variety of weapons and ornaments; they are now in the possession of the Commander of the Forces, and Mr. Smith had the advantage of inspecting them. They con- sist of a sword, lance head, and brass or bronze pin, all of pre- cisely the same form and character as that now exhibited to the Academy. The total length of the sword is 3 feet 2 inches, the blade being 2 feet 8, and the handle 6 inches in length; the pin measures about 6 inches. There was also found along with these a hatchet head, and some frag- ments of iron, so much shattered and corroded as to occa- sion some difficulty in coming to the conclusion, which how- ever may be just, that they once formed an iron skull cap. Common rumour asserts, that the labourer, by whom these re- mains were discovered, had also the good fortune to find with them some ornaments of gold of considerable value; which fact, for prudential reasons, he kept profoundly secret; but its effects became speedily apparent, in a well-stocked shop, which he soon afterwards opened in a village not ten miles distant from Dublin. In the Memoirs of the French National Institute,* a me- moir is given, furnished by M. Mongez, concerning a Gaulish sword, as he denominates one found in the bed of the river * Literature et Beaux Arts, tom. V. 45 Somme, near Abbeville. A comparison of his description, as well as of the engraving appended, shews this sword to have been nearly identical in form and size with those found in Ireland. This description, which applies in a remarkable manner to the sword exhibited to the Academy, is as follows : “Sa lame et sa poignée ne font qu’un tout solidement af- fermi; elle a deux tranchans, et, loin d’étre terminée en pointe, elle est obtuse et arrondie a son extremité..... Il n’y manque que l’osier tressé, ou la corde, ou le bois, ouenfin la substance qui entouroit la soie pour former une poignée solide... . . La lame prolongée forme la soie sur laquelle est fixée la traverse de la poignée par le moyen de deux clous rivés; et la masse imparfaitement arrondie qui la ter mine est travers¢e et maintenue par cette méme sole... . - Longueur totale, 33 pouces 10 lignes; lame seule, 28 pouces 10 lignes ; poignée, 5 pouces ; largeur de la lame a la poig- née, 2 pouces 3 lignes.” If it be kept in recollection, that the French inch is some- what greater than the English, these measurements will be seen to correspond surprisingly with those ofthe sword found at Larne. M. Mongez’s paper exhibits great research and learning. He quotes passages at length, from Polybius, Plu- tarch’s Life of Camillus, Dion Cassius, and Strabo, which describe with considerable minuteness the swords which the Gauls used in their engagements with the Romans; and he rests his argument not only on the identity he alleges of these descriptions with that of the sword found near Abbeville, but also on the fact of bronze and brazen ornaments having been found with skeletons having similar iron or steel weapons about them, discovered in 1788 at Velu, near Bapaume, in Artois. He adds, “ Je puis done assurer que l’épée qui est sous les yeux de la classe est l’épée gauloise décrite par les auteurs anciens. J’ajouterai que c’est la seule 4 ma con- naissance qui soit conservée. On jugera d’apres cela com- bien elle est précieuse pour l’etude des costumes anciens.” 46 Mr. Smith, in conclusion, drew the attention of the Aca- demy to the circumstance that those and many other venera- ble and most interesting remains of remote antiquity, which are but rarely, and at distant intervals of time, discovered in Great Britain, and on the Continent, literally abound in Ire- land; and hence inferred, the incalculable advantage which will be attained, in the study,of the ancient history not only of this country but of the world, by the formation of a great National Museum of Irish Antiquities, such as is at present projected to be formed under the auspices of the Academy. ‘* Without claiming any undue importance for the pursuit of antiquarian research, it nevertheless has its office, and that by no means an ignoble one, as the handmaid of history— ‘ Principatum non habet; ancillari debet.’ It furnishes the critical student not only with curious information and the most valuable commentary on minute points, but summons up for him a host of most important witnesses, whom, though silent, he can subject to the most scrutinizing examination again and again; on whose testimony, carefully weighed as to its true value, history ever rests as on its securest basis.” The reading of a paper by the Rev. T. R. Robinson, D. D., “ On the Constant of Refraction, determined by Ob- servations with the Mural Circle of the Armagh Observa- tory,” was commenced. A paper by Dr. Andrews of Belfast, “ on the Heat deve- loped during the Combination of Acids and Bases,” was read. The general conclusions at which the author arrives are contained in the two following Laws. Law 1. “ The heat developed during the union of acids and bases is determined by the base, and not by the acid; the same base producing, when combined with an equivalent of different acids, nearly the same quantity of heat, but dif- ferent bases a different quantity.” 47 Law 2. “ When a neutral is converted into an acid salt, no change of temperature occurs.” In the commencement of the paper a preliminary experi- ment is described, the object of which is, to determine the ex- act quantity of heat evolved during the combination of nitric acid and potash. The solutions, both acid and alkaline, were taken so weak in this and all the other experiments detailed in the communication, that subsequent dilution with water did not produce any change of temperature. On neutralizing the solution of caustic potash, containing 0'353 grammes of pure alcali, with nitric acid, the temperature of the resulting solu- tion of nitrate of potash, whose weight amounted to 30 gr., was found (after all corrections had been made) to rise 6°75°,F. To illustrate law first, the author adduces tables which shew, ata glance, the heat produced when an eqnivalent of each base is neutralized by different acids. Thus, when the same proportion of pure potash is combined under similar circumstances with the arsenic, phosphoric, nitric, boracic, hydrochloric, hydriodic, and oxalic acids, the elevations of temperature, indicated by the thermometer, vary only from 6°8° to 6°6°. Sulphuric acid produces rather a higher temperature than any other acid (7°3°), and the acetic, formic, tartaric, citric, and succinic acids, give ra- ther less heat than those before mentioned (from 6:4° to 61°) In like manner, ammonia produces an increase of tempera- ture varying from 5:7° to 5°5°, when neutralized by the nitric, hydrochloric, hydriodic, arsenic, oxalic, and acetic acids ; the greatest divergence from these numbers occurring, on the one hand, with the sulphuric acid (6°3°), and on the other, with the citric, tartaric, and succinic acids (5°1°). Analogous results are described as having been obtained with other bases, such as soda, barytes, magnesia, lime, and the oxides of zinc and lead. On the contrary, the heat developed by each base is peculiar to itself; and, consequently, the same acid gives different elevations of temperature, with equiva- 48 lents of different bases. To take, as an example, the nitric acid, which also produces very nearly the mean quantity of heat given by all the acids, the following numbers ex- press the increments of temperature obtained on combining the same quantity of it with each base: magnesia, 8°1° ; lime, 7'2°; barytes, 6°9°; potash, 6°8°; soda, 6°5° ; ammonia, 5°6° ; oxide of zinc, 4°8°; oxide of lead, 4°2° ; oxide of silver, 3°2°. The numbers for barytes, potash, soda, and ammonia, are strictly comparable with one another (except a slight correc- tion for differences in the specific heats of the solutions ;) but in the case of the other bases, an absorption of heat, unknown in amount, takes place in consequence of their conversion from the solid to the fluid state. Hence the numbers for these bases are all below the truth. Two singular anomalies are described as occurring in the combinations of the peroxide of mercury with the hydracids, and in those of the hydrocyanic acid with the bases. In confirmation of the second law the author adduces a series of experiments, which prove, that during the conver- sion of a neutral into a supersalt no heat is produced. “Thus while the normal development of heat occurs when a solution of caustic potash is neutralized by oxalic acid, the subsequent additions, first of one, and afterwards of two more atoms of the same acid, so as to convert the neutral oxalate into the binoxalate, and the latter again into the quadroxalate of potash, is not accompanied by any change of temperature in the solutions. In testing the accuracy of this law, it is neces- sary to select examples where all the compounds are soluble in water, otherwise the heat arising from the formation of precipitates would interfere with and complicate the result. The second law does not extend to the case of the conver- sion of neutral into basic compounds,—a part of the subject which the author has carefully investigated. PROCEEDINGS OF THE ROYAL IRISH ACADEMY, 1841. * No. 27. January 25, 1841. SIR Wm. R. HAMILTON, LL.D., President, in the Chair. The Rev. Dr, Todd, V.P., made some remarks on two large. medallion busts, with Greek inscriptions, which are preserved in the Manuscript Room of the Library of Trinity College. These busts have been in the possession of the College for upwards of a century, but there is no record in the archives of the University stating how or from whom they were obtained. In. the Appendix to the Preface of -Gudius’s Inscriptiones Antique,* the editors of that work have given a list of inscriptions, which they state to have been furnished by Herman Van der Hoorst, Chaplain, to the Dutch in Smyrna; and, in this list, the very busts now in Dublin are thus described, (No. XIII): _ “No. XII. Smyrne in domo cujusdam Greeci Zacharie * The full title of this work is as follows :—“ Antique Inscriptiones olim a Marquardo Gudio collecte, nuper a Foanne Koolio digest, hortatu consilioque Joannis Georgii Greevii; nunc a Francisco Hesselio edite, cum annotationibus eorum.”, ;Leovard,. 1731,.. Fol. VOL. II. F 50 nomine, duz muliebres imagines sculptz adfabre, et incor- rupte ; altera cum hac inscriptione, KAS. AYSIMAXHN THN ®IAANAPON O OPEVAS OHAYMITPHS altera cum hac inscriptione THN NEAN MYHSION IIOAIN TIAD ATTIKOS.” Dr. Todd stated that he had met with a letter in the Bodleian Library, in which these busts are mentioned, and the interpretation of the inscriptions discussed. It is preserved in the valuable correspondence of Dr. Thomas Smith, who | was Fellow of Magdalen College at the Revolution, and whose lot it was to have been twice deprived of his Fellow- ship by the opposite parties of that period ; first, by King James II., when the attempt was made by that monarch to alter the constitution of the College; and secondly, by King William III., when Dr. Smith resigned his preferment rather than take the oath to the new dynasty. The letteris addressed by Dr. Smith to Dr. Narcissus Marsh, then Lord Primate of Ireland, who had been Principal of St. Alban Hall, Oxford, and subsequently Provost of Trinity College, Dublin. The portion of the letter which relates to the busts is as follows :— ‘“‘ The two busts sent to Dublin from Legorne, I suppose came from Smyrna, or the country thereabout, where old monuments are continually discovered. ‘“‘ The first erected to the honour (for so I will favourably interpretit) of Clodia Lysimache(whoisstyled there giAavdpoc, i. e. vird sive mariti amans ; tho’ oftentimes ¢iavdpog yuri is taken in an ill sense for a lascivious and incontinent woman) by one who bred her up and maintained her, viz., Thelymi- tres, if that be his proper name, which is not unlikely, tho’ the appellative OnAdpirpoc is used of an effeminate man abandoned to the excessive love of the other sex, and there- 51 fore explained by Suidas by the word répvoc. But bee that as it will, hee was desirous to preserve the memory of his Operr) or Alumna by this representation, as some of the Opemriipec or of Opilavrec used to do frequently enough, as is evident from undoubted inscriptions, “Tis pity, that the other inscription is imperfect and erased. Stephanus Byzantinus, in his booke epi wéAcwv, mentions: Ming a city of Ionia, its 20vKcov or Gentilitium nomen Mutjooc, wis the name in the inscription; but whether Myes bee here meant by véa wédrc then newly erected into a city, or some other city built by the inhabi- tants of the former, forced to remove to a more convenient and healthier place, the defect in the beginning, owing to the injury of time after so many ages, will not suffer us to know now who it was that did honour to this new city by setting up this monument, who I suppose was a Greeke of Attica, and the word preceding it may be the name of the tribe or Siuoc to which hee belonged. If it be the same with Myius, Mvove, as is very likely, then it is certaine that it was a mari- time city of Ionia, not farre from the river Meander, w™ I passed over in my travells to take a view of the once famous churches of Asia, on a rotten wooden bridge going thence, leaving Caria on the other side into Ionia, of w° wee have several accounts given by Strabo, Pausanias, and Pliny, not to mention other authors both Greek and Latine. Pliny now lying upon my table I think fit to transcribe his words, Nat. Histor. lib. v. cap. 29—Myitis, quod primo condidisse Tones narrantur, Athenis profecti. But I do not pretend to writea commentary on these marbles, but leave that to be done by those learned men, who are in possession of them.” In a P.S. he adds : ** Reviewing those hasty notes upon the two Greek in- scriptions, I began soone to doubt of my conjecture about Atticus, as ifit had beene a patronymic, and the name of the tribe or djuoc of Attica prefixed : but now I am prone to be- F2 52 lieve that this Atticus reckoned among the most famous orators of Greece, who flourished in the times of Hadrian and Antoninus Pius, and who had been sent upon several em- bassyes wpecBeiac to Smyrna, and other free cityes of the lesser Asia, where hee presided with great honour, as appears from Philostratus in the life of Scopelianus, and was the father of Herodes Atticus, as hee is commonly called by the Roman writers, as if it were the name of the familye : whereas it should bee more properly Herodes Aittici, viz., filius, as in the inscription on his monument at Athens preserved by Philostratus in his life. 9 ~ ¢ Arrixov ‘Hpwenc, Mapabdrioc, ov rade wavra Keira rade rapy, Tavrobev evodKimoc. This Herodes succeeded his father in the same honours at home, and in the like governments abroad, and was magnifi- cent in his buildings and public works, in Greece and Italy, having been preceptor to Marcus Aurelius in the studyes of oratory (of which he was universally esteemed a most cele- brated Master) as Julius Capitolinus has observed in the life of that Emperour, and Consul A.U.C. 896. A. Ch. 143. But I thinke to the father, rather than the son, the Atticus in the inscription is to bee ascribed, and if so, how hee comes to bee called Hippitias or Hippotias if that bee his pre- nomen, and the right reading, or whether Hippatias, or whatever it should bee, bee the proper name of the person, who put up the monument, and Atticus of his country, I have not time nor leisure to enquire; and in the whole am no way fond of my conjecture, w™ I look upon as altogether uncertaine.” ** 4 Nov. 1707."* t * Collect. Smith, vol. 58, p. 257. 53 The following are exact representations of the inscrip- tions reduced to one-fifth of the original size: S Fay 505 QJ LJ — == = eas \AN M ¥HSINNITCAIN TIAZ 79 the absence of those phenomena, by showing that a pro- tective provision has always existed to prevent them. Mr. Ferrall went on to state, that the most beautiful por- tion of this mechanism remained to be described. It was one of those exquisite manifestations of design which abound in the animal frame. In the anterior portion of this tunic were to be found six different well defined openings, through which the ten- dons of the muscles pass to their insertion in the sclerotic coat ofthe eye, and over which they play as over pulleys in their progress. ° The annexed engravings, executed from original draw- ings made in April, 1840, for Mr. Ferrall’s clinical lectures in St. Vincent’s Hospital, display this conformation faith- fully. Fig.1, shows the tendon of the internal rectus, emerging from behind the tunic, and passing through its pulley to be inserted in the eyeball. Fig. 2, represents the eyeball drawn downwards, in order to expose the exit of the tendons of the superior 80 rectus and superior oblique muscles; the superior rectus plays over its pulley, and the superior oblique passes beneath the former to reach its insertion in the sclerotic coat. The presence of some such contrivance as is here ex- hibited might have been inferred from its necessity, and yet it has never been suspected to exist. The four recti muscles running from the bottom or apex of the orbit, forward to grasp the eye, must, without it, have had the power of retracting the ball of the eye, and yet no such retraction has ever been ob- served in the human eye. Retraction is certainly performed in some of the lower classes of animals; but they are provided with a strong retractor muscle, independent of the four recti muscles. Again, the rotatory movements of the human eye, which enlarge the sphere of vision, and contribute to ex- pression, are not easily accounted for by the received ana- tomy of the orbit, because the course of the muscles from the bottom of the orbit forwards, manifestly gives them a power of retracting rather than of rotating the eye upon its centre. Thus, then, there appeared to be no provision for 81 the rotatory movements of the ball of the eye, which are of constant occurrence, and nothing to prevent retraction, which we knew did not take place... A knowledge of the existence of this new and beautiful mechanism reconciles and explains these anatomical and physiological contradictions. Mr. Ferrall said, he had found these structures in several of the lower animals, in whom they appear to enable the recti to antagonize the proper retractor muscles. Several phenomena in diseases. of those parts, formerly obscure, are now easily understood; but Mr. Ferrall re- frained, on this occasion, from discussing questions of a - practical nature. The Auditors appointed by Council to examine the Trea- surer’s Account, for the year ending December 31, 1840, re- ported as follows : «© We have examined the above account,* with the vouchers pro- duced, and have found it to be correct; and we find that there is a balance in Bank of £100 7s. and in the Treasurer’s hands, of £110 9s. 4d. making.a total balance of 210 16s. 4d. «« (Signed,) “ FRaNnc SADLEIR. “ SamvuEt Litton. « March, 13th 1841.” “ The Treasurer reports that there is £1390 17s. 4d. in three per cent. consols, and £1526 6s. 1d.in three and a-half per cent. Govern- ment Stock, to the credit of the Academy, in the Bank of Ireland ; the latter being the Cunningham Fund. « (Signed,) « Tuomas HERBERT ORPEN. “ March 18th, 1841.” The ballot for the annual election having closed, the scrutineers reported that the following gentlemen were duly elected Officers and Council for the ensuing year : ee ES ae ee ee * Entered in the Treasurer’s book. H 82 President. Sir Wm. Rowan Hamilton, LL.D. Committee of Science. Rev. Franc Sadleir, D.D., Provost; Rev. Humphrey Lloyd, D.D. ; James Apjohn, M.D.; James Mac Cullagh, Esq., LL.D. ; Rev. William D. Sadleir, A.M.; Robert Ball, Esq.; Robert Kane, M.D. Committee of Polite Literature. His Grace the Archbishop of Dublin; Rev. Joseph H. Singer, D.D.; Samuel Litton, M.D.; Rev. William H. Drummond, D.D.; Rev. Charles R. Elrington, D.D.; Rey. Charles W. Wall, D.D.; Rev. Thomas H. Porter, D.D. Committee of Antiquities. Thomas H. Orpen, M.D. ; George Petrie, Esq., R.H.A.; Rev. Caesar Otway ; Rev. James H. Todd, D.D.; Henry J. Monk Mason, Esq., LL.D.; Aquilla Smith, M.D.; Samuel Ferguson, Esq. Officers. Treasurer. —Thomas H. Orpen, M.D. Secretary to the Academy.—Rev. Joseph H. Singer, jo Bw Secretary to the Council.—J. Mac Cullagh, Esq., LL.D. Secretary of Foreign Correspondence.—Rev. Humphrey Lloyd, D.D. Librarian.—Rev. William H. Drummond, D.D. Clerk and Assistant Librarian.—Edward Clibborn. The President appointed under his hand and seal the following Vice-Presidents : His Grace the Archbishop of Dublin; the Provost of 83 Trinity College; the Rev. Humphrey Lloyd, D.D.; the Rey. J. H. Todd, D. D. DONATIONS. Résumé des Observations Météorologiques faites en 1839, al Observatoire Royal de Bruxelles, par A. Quetelet. Second Mémoire sur le Magnétisme Terrestre en Italie, par A. Quetelet. Deuxiéme Mémoire sur les Variations Annuelles de la Température de la Terre a différentes profondeurs, par Be, Quetelet. Extraits du Tom. VII. No. 2, des Bulletins de lA. R. de Bruxelles. No.2. Température dela Terre. No. 3. Mag- netisme Terrestre. No. 4. Magnetisme Terrestre. Par A. Quetelet. Presented by the Author. Bulletin de V Academie Royale de Bruxelles. Nos. 1—8 An. 1840. Presented by the Academy. American Almanack for 1841. Presented by the American Philosophical Society. Nautical Observations on the Port of Cardiff. By Cap- tain W. H. Smith, R. N., &c. Presented by the Author. Ninth Report of the British Association. Presented by the Association. A Catalogue of the Miscellaneous ia aaieis in the Li- brary of the Royal Society. By J. O. Halliwell, Esq., F.R.S., &e. Presented by the Royal Society. A Collection of Letters illustrative of the Progress of Science in England. Edited by J. O. Halliwell, Esq., E.R.S., &c. Presented by the Editor. Proceedings of the Royal Society of Lordon, 1839—40. Nos. 41—44. List of Members of the Royal Society of London, (30th November, 1840). Philosophical Transactions of the Royal Society of London for 1840. Parts I. and II. Catalogue of the Miscellaneous 84 Manuscripts in the Possession of the Royal Society. Pre- sented by the Society. Remarks on the Classification of Human Knowledge. An Elementary Treatise on the Tides. On the Theory of the Moon. On Currency. By J. W. Lubbock, Esq. Presented by the Author. An Examination of the ancient Orthography of the Jews. Vol. Ill. By Rev. C. W. Wall, D.D. Presented by the Author. The Negroland of the Arabs. By W. Desborough Cooley, Esq. Presented by the Author. Constitution and By-Laws of the National Institution for the Promotion of Science at Washington. Discourse on the Objects and Importance of the National Institution for the Promotion of Science. By Joel R. Poin- sett, Esq. &c. Presented by order of the Directors. Memoires de la Société Géologique de France. Tome 4me. lre partie. Pesented by the Society. PROCEEDINGS OF THE ROYAL IRISH ACADEMY, 1841. No. 29. April 12. SIR Wm. R. HAMILTON, LL.D., President, in the Chair. The following gentlemen were elected Members of the Academy : William Monsell, Esq., Robert Tighe, Esq., W. E. Hud- son, Esq., G. Fitzgibbon, Esq., William Phibbs, Esq., Rev. James Reid, William Lee, Esq-, F.T.C.D., Robert Jones, Esq., Thomas Wilson, Esq., Beriah Botfield, Esq., M.P., W. T. Mulvany, Esq. Mr, Ferguson made a communication on the Classification of ancient Military Weapons found in Ireland. DONATIONS. Transactions of the Cambridge Philosophical Society. Vol. II. Part 2; Vol. III. Parts1, 2,3; Vol. 1V. Part.1; Vol. V. Part 3. Presented by the Society. On the Geological Structure of the Northern and Central Regions of Russia in Europe. By R.J. Murchison, F.R.S., &c. Presented by the Author. Proceedings of the Geological Society of London. Nos. 74 and 75. Presented by the Society. Journal of the Franklin Institute. Vol. XX VI. (1840). Presented by the Institute. The Numismatic Chronicle. No. 12. Presented by the _ Numismatic Society of London. VOL, II. 1 ssaansva4y ‘NTAUO LUIHUDH SVNOHL “‘pauays eT GG Set ene wea ek 8 ee eo. BRON FP OOURIEET vat GL “8 8 8 to see ss spuey sdounsvely, UT Q50 (OFF So cease oe U8 SP OR RUIN JRUee OF “AONVIVA AHL JO ALVIS 6 OL MIF!) «8 OR, ts le © gr0jog/ee oBrvYyO OU, @ 9 PILLS 0 @t PLP yD verses *— D 0c ° <> @ st991) ° = Geet FO yt 69 ss ss ss 8s Kulaproy ay} jo ANoary ut oouvleg OL WL SSO SS ne” Se! PS Me 8) BAO TWIOT, any: — VIsos. “xX Ber ot tt tt ee 8h pgrpmesurtiog | 9 ors 6.2 066 ' tate ff 8 8 8 8 8 soap SasBAQ [eIUBAIAG “saTrEIUS 9 PLS rae $6 We * st 8 tf tt 8 KauonBg pur ‘Sunuug ‘sxoog |] 9 ZI OFF OAT Be et ee peop es ve ‘aouvinsuy pue *saxey Suoy e Jor ° ° $8 99 5 5 * Ff fs ss soap aang esnozy Jo si1eday 0 0 00g * ° 1 or ZY Cm « RE e. hy Guo 6) 0 Ss eMien weer ne "Op ‘saypur ‘sje09 6 & ¥L MS chase #43 ‘ os F ps F pes 3 lps F ‘ADUVHOSICG AHL ‘TP81 ‘1€ HOUVW ONIGNA UVAA AHL YOM * * * + 98aeyd (230) ayy, ‘dOUVHO AHL oe ee eee one 8 son IENUULY, ai ea“ PROCEEDINGS OF THE ROYAL IRISH ACADEMY. 1841. No. 30. - ‘a June 14. “SIR Ww. R, , HAMILTON, LL.D., President, in the Chair. : 4 James Patten, M.D., was elected a member of the Aca- Eee Dr. Aquilla Smith read a paper ‘* On the Irish Coins of Henry VII.” ~ In the preliminary remarks, the author entered at some lengthinto the history ofthe Irish coinage during the reignsof. Henry V. and Henry VI., with the view of facilitating his ~ inquiries i in the subsequent part of his essay. And from the, ‘it “evidence . of several Acts of Parliament, which were not known to previous writers on the coinage of Ireland, he in-. ferred that no legal money was coined in this country ‘by Henry V., and that very few coins are known which: can be. appropriated to his immediate successor. " The coins of Henry VII., which are very numerous, were divided into three sections, each distinguished by the form of thecrosson the reverse; and in the last section the au- thor supported Mr. Lindsay’s appropriation to Henry VII. of the untressured groats which Simon had given to Henry V. Rev. H. Lloyd, V. P. read a ‘‘ Note on the Mode of ob- serving the vibrating Magnet, so as to eliminate the Effect of the Vibration.” VOL. 11, “0 116 The following modification of one of the methods pro- posed by Gauss, for the attainment of this end, appears to combine the greatest number of advantages ; namely, to take three readings, at the times fi bs Os Hs Ts t being the epoch for which the position of the magnet is de- sired, and 7 its time of vibration.* In order to show that this method is adequate, it is necessary to deduce the equation of motion of a vibrating magnet ih a retarding medium. Let x denote the horizontal part of the earth’s magnetic force; g the quantity of free magnetism in the unit of vo- lume of the suspended magnet, at the distance 7 from the centre of rotation; and @ the deviation of the magnet from its mean position. The moment of the force exerted by the earth on the element of the mass, dm, is xgrdm sin 6; and the sum of the moments of the forces exerted upon the entire magnet is . xu sin 6; where « denotes the value of the integral { grdm, taken between the limits 7 = + 7, 22 being the length of the magnet. Again, the velocity being small, the resistance may be assumed to be proportional to the velocity. Accordingly, if w denote the angular velocity, the retarding force due to resistance, upon any element of the surface, ds, at the dis- tance 7 from the centre of motion, is — Kds rw; and the entire moment of this force upon the whole mag- net is * In practice, it is sufficient to take the nearest whole number of seconds, for the yalue of rT. 117 — kw §r'ds = — kw — dm : % : where H = re The ratio, Hu, is constant for all bodies of prismatic form; and for these, therefore, the moment of resistance is Sate HO H M denoting the moment of inertia §7°dm. The differential equation of motion is, therefore, But w = — Ms and, @ being small, we may substitute 0 for sin@. The equation thus becomes Kd0 Xu etnate OM Ban ‘ K x F , Making, for abridgment, == 2a, = = B’, the integral is = (c cos / B? — a®. t +e’ sin y/ B — a. t) em". But, a being small, we have approximately e“ =1—at; and, if r denote the time of vibration, JB—A?. T= 7. Hence the preceding equation may be put under the form t den tea 6 = (1 —at?) (ccos m= + c sin) Now, let 8, and 6’ denote the values of 6, when ¢ becomes L2 118 ¢—tTandi+r. It will be seen at once, on substitution, that 64+20+ 7=0. Hence by combining the three readings according to the preceding formula, the deviation of the magnet from its mean position, arising from the vibratory movement, is com- pletely eliminated ; and it will readily appear that the same result may be attained by any greater number of readings, taken and combined according to the same law. Now, let the value of @ contain an additional term, + pt, proportional to the time: or, in other words, let us suppose that there is a progressive change of the declination, which may be regarded as uniform during the whole interval of observation. It is then manifest that 0, + 20 + 0’ = 4pt; and accordingly that the quantity 4(0,+20+6) © will give the mean place of the magnet corresponding to the epoch ¢. The supposition of a uniform change can, however, be regarded as an approximation to the truth, only when the interval of time between the first and Jast reading is very small, in comparison with the interval between the successive maxima and minima, in the fluctuations of the irregular movement. Hence, we may conclude, that it is important, in the first place, to employ three readingsin preference to any greater number ; and, secondly, that it is desirable that the time of vibration of the magnet itself should be as small as possible, consistently with the accuracy of its indications in other respects. Professor Lloyd read the following extract of a letter from the Rev. George S. Smith, containing some facts rela- tive to the storm ‘of May 26th and 27th. ee 119 * It appears that the thunder storm commenced on Wed- nesday night in Tipperary, Clare, Limerick, and Waterford, reaching its greatest violence on Thursday morning at about six. It was on Thursday evening that it was most severe in Carlow and Queen’s County, from nine till twelve p.m., having, however, been felt in the morning of the same day. On Thursday evening it began in Dublin; but the thunder was loudest at half-past three a.m. on Friday morning. On Friday morning, at ten o’clock, a.m., it raged in the county Mayo. ~ ~ “Tn Windsor forest and the neighbouring country it was amore furious tempest, and took place on the evening of Thursday the 27th, as in the county Carlow. “It was reported to me, that there were some remark- able phenomena of the tide in Dublin Bay during the storm ; and I accordingly inquired from a variety of persons on the quays and elsewhere, and they concurred in stating, that about half-past three the tide, which was then flowing and approaching to high water, suddenly retired in half ai hour to low water mark, and that it rapidly returned and rose two feet higher than high water mark, and so quickly that boats were knocked violently against each other. The coal- porters, and dockyard keepers, and various sailors both in the river and Kingstown, agreed in this statement. | ** Further, in the River Foyle, in the North of Ireland, there is an embankment in the course of being formed by Thomas Hutton, Esq., and he states that the tide on Thurs- day night, or Friday morning, retired so suddenly, that con- siderable damage was done to his embankment. ** The concurrence of these phenomena with the storm is a point of some interest; and I write these few lines to in- vite inquiry, and to ascertain, if possible, whether this extra- ordinary tide-wave was generally observed, and on what day and hour, and whether it coincided or not with the storm. 120 ‘¢ The newspapers report the occurrence of the storm, as mentioned above; but say nothing of the tide. “The course of the storm seems to have been from south to north; but I think a north-east wind was blow- ing.” A communication by Francis Crawford, Esq., A.B., “ On the Utility of the Irish Language in Classical Studies,” was read. The object of the writer was to show, that, notwith- standing the contempt and ridicule into which the subject had fallen in consequence of the rash and unphilosophic views of injudicious advocates, still there existed reasonable grounds for believing that a careful and sober analysis of Heathen mythological names would resolve them into Celtic elements through the medium of Jrish ; accordingly he pro- ceeded to give numerous instances of such analysis, at the same time declaring, that unless supported by such analogies, or other external evidence, as he offered, investigations of this sort were by no means to be relied upon. After interpreting, in this manner, the names of some of the Syrian deities mentioned by Selden, in his learned work ‘‘ De Dis Syris,” the writer went on to set the whole subject in a more interesting point of view, by attempting to show, that even the Bible might receive illustration and confirmation from such inquiries; to effect this, he under- took to identify the Melchizedek of Scripture with the famous Tyrian Hercules; he shewed at some length, that they were contemporaries in history, that they agreed in cha- racter, that tithes were paid to both, and finally that the name of Malcarth, by which the Tyrian Hercules was best known, when resolved into its Celtic components Mal-ceanz, literally signified ‘‘ Righteous King,” or “ King of Righ- teousness.” The writer, after some further proofs of their identity, — ee ' 121 concluded by giving a description of the rites and ceremo- nies used in the worship of Hercules at Gades, intimating that they denoted a purer mode of religious culture than generally obtained in the heathen world. DONATIONS. Notes on the United States of North America im 1838, 1839, 1840. 3 Vols. By George Combe, Esq-,Hon. M.R.LA., &c. Presented by the Author. . The Silurian System. By William H. Fitton, Esq. Presented by the Author. - Dublin Metropolitan Police Returns of Persons taken into Custody in 1840. Presented by the Commissioners. Ordnance Survey of the County of Galway, in 139 sheets, Presented by his Excellency the Lord Lieutenant. Verhandelingen van het Bataafsch Genootschap der Proe- fondervindelyke Wysbegeerte te Rotterdam, Vols. jie 4 and New Series, Vols. I.—VIII. Part I. A Collection of Temperance Medals. Engraved by J. C- Parkes. Presented by the Artist. J ie 28. SIR Wu. R. HAMILTON, LL.D., President, in the Chair. Mr. Mallet read a paper “ On a new Method of raising Ships of War out of Water for the Purpose of Repair.” Although the author conceived that the objects of the Royal Irish Academy were rather to investigate principles than to apply them in detail, still as any application of these, which proposes to add to our naval power, is of importance, and as on a like subject the Royal Society conferred on Sir R. Seppings their highest reward for his application of diagonal framing to ships, he did not deem it altogether out of place to bring hismethod of raising ships out of water be- 122 fore the Academy, with models and drawings to illustrate it. The inventor first gave a rapid description of the several methods of taking ships ont of water for repair, which have been in use from the earliest times to the present day, viz., by— 1. Stranding on bilge ways. 2. Careening. 3. The machine called the Camel, invented about 1680. 4. The graving dock. 5. Morton’s patent slip. "The acted pom Sobod aie ey ae sari 7. Thehydraulic dock. rae Ler CEPT 8. The floating dock of the River Tyne, used at New- castle. He then pointed out the several disadvantages to which each of these is severally liable. These are briefly, in the first case, costliness, tedious- ness, straining of the ship, and imperfect access to the hull. In the second, great danger and imperfect access to the hull. The Royal George was sunk by careening her. In the third case, want of access to the ship—impossibility of ex- posing the whole hull—straining of the framing, and danger. In the fourth or graving dock, great original outlay ; great labour and loss of time in pumping out water where rise of tide is small; loss of two or three hours of daylight every day by the sunken position of the ship, and awkwardness in handling long spars or timber ; difficulty of inspection, and unhealthiness of situation to workmen; and, lastly, rotting of timbers, from the constant damp atmosphere of a sunk or graving dock. Morton’s slip overcomes most of these evils, but has some peculiar to itself. Ships can only come on and go off the slip at high and low water ; hence, in large ves- sels, the loss of one tide is often the loss of a fortnight ; 123 it cannot be used in foul weather, or with the tail of the slip in a tideway ; the average length of the inclined plane being about five hundred feet, and the rate of elevation of a ship from three to five feet per minute, the time of taking a ship out of water, including the removal of the cradle, oc- cupies from four to six hours ; and hence, thoughnominally cheap, this is by loss of time really adear mode of repair to the ship-owner—the ship lies on an inclined plane, which is inconvenient in hoisting or lowering heavy parts, particularly in steam-ships. The hull is always strained, and new cop- pering is often found wrinkled, by the ship running off the slip, and receiving unequal support from the water meeting her at an angle to her plane of stable floatation. The vibra- tion of the numerous rollers is also injurious in the same way. The American screw and hydraulic docks have the ad- vantage, in point of speed, when in use ; but are unsafe for large ships, and awkward in the posture of the ship’s hull. The Newcastle-on-Tyne floating dock possesses all the disadvantages (except original costliness) of the graving dock, and is without the safety of the latter. The author then explained the nature of his own method, and exhibited it in action by means of a large working model; without plates it is difficult to describe this com- bination. The vessel to be raised, floats in over a timber platform of a suitable size laying at the bottom, and by means of two very powerful cabstern cranes, actuated by a small steam engine, and acting on two large flat linked chains, the platform is raised above the surface of the water, bringing up the vessel along with it, and placing her upon a suitable level for the convenience of workmen to get under andround the hull, for which the platform isspecially adapted. The two chains spoken of lay horizontally at either side of the platform, and above it, and are armed with rollers at 124 equal intervals, resting on a hollow iron railway; and from these points of the chains anumber of suspending rods pro- ceed to the platform; at each side below the latter, are an equal number of jointed struts or supports; and the nature of the motion is such, that, when the platform is at the bottom, these struts are nearly horizontal, and the suspend- ing rods vertical, and vice versa when the platform is at its greatest elevation ; hence, the latter is at all times fully and firmly supported. The combination is such, that power is to the utmost economized, the ratio of the power to the weight increasing as the hull of the vessel leaves the water, and advantage being taken of her own floatage power as long as possible. The inventor stated, that a fifty gun frigate, with her standing rigging up, could be taken out of water, and laid dry and ready for workmen, insixteen minutes from the time she came over the platform, by his arrangement, which is equally applicable where there is no tide, (as at Malta, &c.,) as where the rise and fall are considerable. The objects also held in view, and he conceives attained, by his method, are equal strain, and wear and tear (by principle) on all the parts—and hence freedom from risk of accident—durability and facility of repair in the machine itself. A paper by the Rev. Dr. Hincks, “On the Egyptian Stéle, or Tablet,” was read. Among the Egyptian monuments in museums, there is none more likely to afford information than the stéles, or fu- neral tablets, which resemble in form the head-stones in our grave-yards, and which appear to have been set up in similar positions. The object of this paper is to describe the parts of which the inscriptions that these tablets contain usually consist, with such observations as may enable a person, who should meet with one of them, to form a judgment as to its age, and as to the importance of its contents. It commences with some details respecting two tablets 125 each of which records the dates of the birth and death of the deceased person, and also the length of his life. A dili- gent search should be made for similar tablets, which would evidently be of the greatest value in settling the chronology of the Egyptian sovereigns. One of these, which is at Flo- rence, records that a person named Psammetich was born in the third year of Necho, the tenth month and first day ; that he died in the thirty-fifth year of Amasis, the second month and sixth day; and that he lived seventy-one years, four months, and six days. From this it appears, that the inter- val between the first year of Necho and the first of Amasis was forty years ; and it follows that the reigns of these kings must have commenced in 611 and 571 before our era. The other tablet, which belongs to Mr. Harris of Alexandria, is that of a priest named Psherinphthah, who died, aged forty- nine years, in the eleventh year of Cleopatra, the eleventh month and twentieth day. The chronology of this period being well known from other sources, the dates of the tablet would be of no value, did not that of the birth contain a royal cartouche, which does not occur elsewhere, and an unknown numeral character. ‘The cartouche is shown to be that of ~ Ptolemy Alexander, though it does not contain his usual sur- name; and the unknown character, a bird’s head, is proved to stand for ¢éeventy. The tablet of Te-imothph, the wife of this priest, who was also his half-sister, is in the British Museum; and several circumstances in their family history, taken from the two tablets, are collected together. ‘The birth of their son Imothph, in the sixth year of Cleopatra, and when the father was turned of forty-three, is recorded on both of them, The most usual form of the inscription on a stéle is tran- lated as follows:—‘* An act of homage to A; he has (or as the case may be) given B unto C; who says D.”| The blank at A is filled up with the names and titles of deities ; that at B with an enumeration of gifts ; that at C with the name and description of the deceased person ; and at D is the speech 126 attributed to him, in which he sometimes records the leading events of his life. Sometimes the tablet is without a speech, the inscription closing at the end of C; and sometimes it begins with C, containing only the name and description of the deceased person and his speech. In a few tablets the prefatory matter is somewhat different from the above; but the form given above is much the most usual. No record of facts is to be expected in a tablet till we come to C; the preceding part of the inscription is only va- luable, as it may aid usin the study of the language, and as it may lead us to know the age of the tablet, supposing it to be without a regular date. For this last purpose, a number of criteria of antiquity are proposed, the result of a careful examination ofa great many tablets of known ages. The most remarkable of these is, that in the most ancient tablets the sculptured figures are exclusively those of the deceased person and his relatives ; never these of deities, as in the ta- blets of the eighteenth dynasty and subsequent ages. At the close of the paper some remarks are made on the chronology of the early Egyptian kings, who are mentioned in the course of it. It is demonstrated that the predecessor of Amenemhe II., the first king in the series of Abydos, was Osortasen I. ; the latter being the successor of Amenemhe I., and not his predecessor, as he has been stated to be by Major Felix and others, on the supposed authority of an inscription at Beni-Hassan. This completely overturns the hypothesis of Mr. Cullimore, respecting the connexion of a pretended royal series at Karnac with the series of Abydos. The phonetic hieroglyphics are represented in this paper by Hebrew characters, in preference to Roman. This has been done on account of the author’s peculiar views respect- ing the extended arm, the crux ansata, and some other cha- racters, which he considers to be equivalent to the Hebrew Ayin, and by no means “vague vowels,” as Champollion supposed. He regards these characters as essentially dis- 127 tinct from the feather, the eagle, and others, with which they have been hitherto confounded, and which he represents by the Hebrew Aleph. The Rey. Charles Graves, F.T.C.D., read a paper “Ou the Application of Analysis to spherical Geometry.” The object of this paper is to investigate and apply to the geometry of the sphere, a method strictly analogous to that of rectilinear coordinates employed in plane geometry. Through a point 0 on the surface of the sphere, which is called the origin, let two fixed quadrantal ares of great circles ox, oy, be drawn; then if arcs be drawn from Y and x through any point P on the sphere, and respectively meeting ox and oy in m and Q, the trigonometric tangents of the ares OM, ON, are to be considered as the coordinates of the point p, and denoted by w and y. ‘The fixed ares may be called arcs of reference. An equation of the first degree between # and y represents a great circle ; an equation of the second degree, a spherical conic; and, in general, an equation of the n‘ degree, between the spherical coordinates x and y, represents a curve formed by the intersection of the sphere with a cone of the n degree, having its vertex at the centre of the sphere. Though it is not easy to establish the general formule for the transformation of spherical coordinates, they are found to be simple. Let a and y be the coordinates of a point referred to two given arcs, and let 2’, y/’, be the coordinates of the same point referred to two new arcs, whose equations as referred to the given arcs are y—y’=m(«— x"), y—y’ =m («— x"), x”, y’, being the coordinates of the new origin; then the values of x and y to be used in the transformation of coordi- nates would be 125 _ 2" (ax' + by'—1) px +qy—1 3 _ yf! (cx! + dy’ —1) ~ pa’ + qy’—1 In which a, 4, c, d, p, and gq, are functions of m, m, x", and y’. It is evident that the degree of the transformed equation in 2’, y’, will be the same as that of the original one in « and y. The great circle represented by the equation az + By =1, meets the arcs of reference in two points, the cotangents of whose distances from the origin are a and (; and, if the arcs of reference meet at right angles, the coordinates of the pole of this great circle are — a, and — . It appears from this, that if a and 3, instead of being fixed, are connected by an equation of the first degree, the great circle will turn round a fixed point. And, in general, if a and ( be connected by an equation of the n“* degree, the great circle will envelope a spherical curve to which z tangent arcs may be drawn from the same point. Thus, the fundamental principles of the theory of polar reciprocals present themselves to us in the most obvious manner as we enter upon the analytic geometry of the sphere. A spherical curve being represented by an equation be- tween rectangular coordinates, the equation of the great circle touching it at the point 2’, 7’, is (y — y') dz’ — (x— vx’) dy’ = 0; the equation of the normal arc at the same point is (y Pes y') [dy’ oo a! (a’dy/ =f y/dx’)| + (@ — 2’) [de' + y' (y'da’ — 2'dy’)} = 0. Now, if we differentiate this last equation with respect to 129 v and zy’, supposing x and y to be constant, we should find another equation, which, taken along with that of the normal arc, would furnish the values of x and y, the coordinates of the point in which two consecutive normal arcs intersect : and thus, as in plane geometry, we find the evolute of a spherical curve. Let 2y be the diametral are of the circle of the sphere which osculates a spherical curve at the point 2’, y’, Mr. Grayes finds that [de® + dy? + (a'dy! = y'de’)?}3 = pe ns Po A A Bi AE tany == Cl a? + 9 (dald?y’ — dy/Pa’y For the rectification and quadrature of a spherical curve given by an equation between rectangular coordinates, the following formule are to be employed :— — Vda? + dy? + (aldy —y¥de'P : ds ] +0? + y” > and ) Hubba kcl-oi-edoue YC ed boos, : (Lt) V1 +a? +9? ~ “In the’ preceding equations the radius of the sphere has been supposed = 1. The method of coordinates here employed by Mr. Graves is entirely. distinct. from that which is developed by Mr. Davies in a-paper in the 12th Vol. of the Transactions of the Royal Society of Edinburgh. Mr. Graves apprehends, how- ever, that he has been anticipated in the choice of these coordinates by M..Gudermann of Cleves, who is the author of an “ Outline of Analytic Spherics,” which Mr. Grayes has been unable to procure. ) The President communicated a new demonstration of Bourier’s theorem. 130 A letter was read from Professor Holmboe, accompany- ing his memoir, “ De Priscd re Monetarid Norvegiz,” &c., and requesting to know from the Academy whether any of the coins described in that work are found in Ireland.* July 12. SIR Wma. R. HAMILTON, LL.D., President, in the Chair. Part I. of a ‘‘ Memoir on the Dialytic Method of Elimi- nation,” by J. J. Sylvester, Esq. A. M., of Trinity College, Dublin, and Professor of Natural Philosophy in University College, London, was read, The Author confines himself in this part to the treatment of two equations, the final and other derivees of which form the subject of investigation. The Author was led to reconsider his former labours in this department of the general theory by finding certain results announced by M. Cauchy in L’ Institut, March Num- ber, of the present year, which flow as obvious and imme- diate consequences from Mr. Sylvester’s own previously pub- lished principles and method. Let there be two equations in x, U= ax" + ba" + cx" + ex" + &e. = 0, V= az™+ Ba" + ra" + &e. =¢6 and let n = m +1, where « is zero or any positive value (as may be). Let any such quantities as 2” U, a°V, be termed aug- mentatives of U or V. To obtain the derivee of a degree s units lower than V, we must join s augmentatives of U withs +.10f V. Then out of 2s + « equations * The Committee of Antiquities, having been consulted on this point, reported in the negative. ) 131 eee 0, ita, oe OH Ui. ot UO, ey =0, 20; ° #67 = 0, .... Ate". V0, we may eliminate linearly 2s + .—1 quantities. Now these equations contain no power of x higher than m+.+s—1; accordingly, all powers of x, superior to m —s, may be eliminated, and the derivee of the degree (m—s) obtained in its prime form. Thus to obtain the final derivee (which is the derivee of the degree zero), we take m augmentatives of U with n of V, and eliminate (m ++ n—1) quantities, namely, ; This process, founded upon the dialytic principle, admits of a very simple modification. Let us begin with the case where. = 0, orm=n. Let the augmentatives of U, be ; termed U,, Ui, U,, U3; sees and of V, Vo, V,, Vi, | ae ee the equations themselves being written U = ax" + ba"—' + ca"—-? + &e. V = a'x” + bx" —' 4+ c'x"—? + &e. It will readily be seen that a’.U,—a.Vo, (b/ U, — bY) + (aU, — a), (ce. U,—c.V) + (b/U, — bV,) + (a’U,—aD,), &e. will be each linearly independent functions of 2, 2”, ...... a2"—", no higher power of x remaining. Whence it follows, that to obtain a derivee of the degree (m—s) in its prime form, we have only to employ the s of those which occur first in order, and amongst them eliminate 2"—', «™—*, .... -g¢m-—stl. Thus, to obtain the Jinal derivee, we must make use of n, that is, the entire number of them. * Now, let us suppose that: is not zero, but m=n—1., VOL. Ul. M 132 The equation V may be conceived to be of » instead of m dimensions, if we write it under the form 0.2" +0.2"-! + 0.a"-7-+..... + O,amtt az” + Ba™—' + &. = 0. and we are able to apply the same method as above ; but as the first: of the coefficients in the equation above written are zero, the first 7 of the quantities (a’U 5 = aV,), (0'U, — bV,) on (aU, — aV,), &e. may be read simply —a.Vo, —b.V,— ay, —ceV,— bV, — av, &c. and evidently their office can be supplied by the simple augmentatives themselves |S ORT eal UE tl | | I md and thus « letters, which otherwise would be trre/evant, fall out of the several derivees. The Author then proceeds with remarks upon the gene- ral theory of simple equations, and shows how by virtue of that theory his method contains a solution of the identity Ay UO+ Y¥-.V = Be where D, is a derivee of the 7 degree of U and JV, and, accordingly, X, of the form eee... and Y,. of the form OO ma eS. eee and accounts a priori for the fact of not more than (m — r) simple equations being required for the determination of the (m +n— 2r) quantities A, u, v, &c. 1, m,n, &c., by exhibit- ing these latter as known linear functions of no more than (n— 7) unknown quantities left to be determined. 133 Upon this remarkable relation may be constructed a me- thod well adapted for the expeditious computation of nume- rical values of the different derivees. He next, as a point of curiosity, exhibits the values of the secondary functions a’.U,—aV,, b'.U,— bv + a’.U,— al, ce .U,—c.¥+0.U,— bY, +a’.U,—ahy, &e. under the form of symmetric functions of the roots of the equations U = 0, VY = 0, by aid of the theorems developed in the “ London and Edinburgh Philosophical Magazine,” December, 1839, and afterwards proceeds to a more close examination of the final derivee resulting from two equations each of the same (any given) degree. He conceives a number of cubic blocks each of which has two numbers, termed its characteristics, inscribed upon one of its faces, upon which the value of such a block (itself called an element) depends. For instance, the value of the element, whose character- istics are r, s, is the difference between two products: the one of the coefficient r* in order occurring in the polyno- mial U, by that which comes s“ in order in V; the other product is that of the coefficient s“ in order of the polyno- mial V, by that 7 in order of U; so that if the degree of each equation be n, there will be altogether oe ) such elements. The blocks are formed into squares or flats (plafonds) of a _ 2 n+) ; : which the number is 5 or —;— according as zn is even or ~~ ~ odd. The first of these contains n blanks in a side, the next (x — 2), the next (n—4), till finally we reach a square of four blocks or of one, according as n is even or odd. These flats are laid upon one another so as to form a regu- 134 larly ascending pyramid, of which the two diagonal planes are termed the planes of separation and symmetry respectively. The former divides the pyramid into two halves, such that no element on the one side of it is the same as that of any block in the other. The plane of symmetry, as the name denotes, divides the pyramid into two exactly s¢mélar parts ; it being a rule, that all elements lying in any given line of a square (plafond) parallel to the plane of separation are identical; moreover, the sum of the characteristics is the same, for all elements lying any where in a plane parallel to that of separation. All the terms in the final derivee are made up by multi- plying x elements of the pile together, under the sole restric- tion, that no two or more terms of the said product shall lie in any one plane out of the two sets of planes perpendi- cular to the sides of the squares. The sign of any such pro- duct is determined by the places of either set of planes parallel to a side of the squares and to one another, in which the elements composing it may be conceived to lie. The Author then enters into a disquisition relating to the number of terms which will appear in the final derivee, and concludes this first part with the statement of two general canons, each of which affords as many tests for de- termining whether a prepared combination of coefficients can enter into the final derivee of any number of equations as there are units in that number, but so connected as together only to afford double that number, Jess one of in- dependent conditions. The first of these canons refers simply to the number of letters drawn out of each of the given equations, (supposed homogeneous); the second to what he proposes to call the weight of every term in the derivee in respect to each of the variables which are to be eliminated. The Author subjoins, for the purpose of conveying a more 135 accurate conception of his Pyramid of derivation, examples of the mode in which it is constructed. Whenn=1 there is one flat, When n = 2 there is one flat, viz. viz. : 2,3 | 2,4 ! | 1,2 . 2,4 | 3,4 | | Let n = 3, there willbe two Let x = 4, there will still be flats: two flats only: . YS Say Ngee Re 2,3 2,4 | 3,4 bak Sia ds BS, eee bs, 6 eS ee 4.) Lo) 2 odo 2,5 | 3,5 | 4,5 136 Let n = 5, there will be three flats : 3, 4 137 Let » = 6, there will be three flats : ~ ~ bs ~ — oh oo + Ted o me ~ ~ ~ ~ ty or oD + Tod Yo) ~ ~ ~ = ay oy wn ool + 19 Tos) = ~ ~ fore on as wn oe a" 19 © ~ ~ a Padi aa — nN on Sn © ~ — an oy = = Thus the work of computation reduces itself merely to elements, or the n (x + 1) cross-products n+1 4 calculating n. = ee ee, 158 out of which they are constituted, and combining them fac- torially after that law of the pyramid, to which allusion has been already made. DONATIONS. First Principles of Medicine. 4th Edition. By Archi- bald Billing, M.D., &c. Presented by the Author. Bulletin de la Société Geologique de France. Tome XI. (1889 4 1840.) Presented by the Society. O'Halloran on the Air; a Manuscript, presented by Major-General Sir Joseph O’Halloran, M.R.I.A., &c. Mémoires de la Société de Physique et d’ Histoire Natu- relle de Geneve. Tome IX., lere Partie. Presented by the Society. Caicul de la Densité de la Terre, suivi d’un Memoire sur an cas special du Mouvement d'un Pendule. Par L. F. Me- nabrea. Presented by the Author. Proceedings of the Royal Society of Edinburgh. Nos. 16—i8. Transactions of the Royal Society of Edinburgh. Vol. XIV. Part 2; Vol. XV. Part 1. Presented by the So- ciety. Transactions of the American Philosophical Society. Vol. VII. Part 3. (New Series.) Presented by the Society. PROCEEDINGS OF THE ROYAL IRISH ACADEMY. 1841. No. 31. November 8. SIR Wm. R. HAMILTON, LL.D., President, in the Chair. John H. Jellett, Esq., F. T.C.D., was elected a member of the Academy. A letter was read from Dr. Orpen, stating that increas- ing ill health would not allow him to continue to discharge his duties to the Academy, and tendering the resignation of his office of Treasurer, and of his place as a member of Council. ReEsoLveD,—That the Academy have heard Dr. Orpen’s communication with much regret, and that they deeply la- ment the cause which deprives them of his valuable services. Professor Mac Cullagh read the following notes on some points in the Theory of Light. I. On a Mechanical Theory which has been proposed for the Explanation of the Phenomena of Circular Polarization in Liquids, and of Circular and Elliptic Polarization in Quartz or Rock-erystal ; with Remarks on the correspond- ing Theory of Rectilinear Polarization. The theory of elliptic polarization, which I feel myself called upon to notice, was first stated by M. Cauchy, and has been VOL, II. N 140 made the subject of elaborate investigation by other writers. That celebrated analyst, conceiving (though without suffi- cient reason, as will presently appear) that he had fully ex- plained the known laws of the propagation of rectilinear vibra- tions by the hypothesis that the luminiferous ether, in media transmitting such vibrations, consists of separate molecules symmetrically arranged with respect to each ofthree rectangu- lar planes, and acting on each other by forces which are some function of the distance, was led very naturally to imagine that he would find the laws of circular and elliptic vibrations, in other media, to be included in the more general hypothesis of an unsymmetrical arrangement. Accordingly, in a letter read to the French Academy on the 22nd of February, 1836, a letter to which he attached so much importance that he desired it might not only be published in the Proceedings, but also ‘‘ deposited in the Archives” of that body (see the Comptes rendus des Séances de l’ Académie des Sciences, tom. ii. p. 182), he gave a precise statement of his more extended views, informing the Academy that he had submitted his new theory to calculation, and that, among other remarkable re- sults, he had obtained (with a slight variation or correction) the laws of circular polarization, discovered by Arago, Biot, and Fresnel. Referring to his Memoir on Dispersion, pub- lished at Prague, under the title of Nowveaux Exercices de Mathématiques, he observes, that the results therein con- tained may be generalised, by “ceasing to neglect” in the equations of motion [the equations marked (24) in § 2 of that memoir], certain terms which vanish in the case ofa symmetrical distribution of the ether. He then goes on to say— ‘* Nos formules ainsi généralisées représentent les phé- noménes de l’absorption de Ja lumiére ou de certains rayons, produite par les verres colorés, la tourmaline, &c., le phe- noméne de la polarisation circulaire produite par le cristal de roche, l’huile de térébenthine, &c. (Voir les expériences aes ~~ i a ~ eee e ee ? 141 de MM. Arago, Biot, Fresnel). Elles servent méme a dé- terminer les conditions et les lois de ces phénoménes ; elles montrent que généralement, dans un rayon de lumiére po- lariseé, une molecule d’éther décrit une ellipse. Mais dans certains cas particuliers, cette ellipse se change en une droite, et alors on obtient la polarisation rectiligne.” ‘ Enfin le calcul prouve que, dans le cristal de roche, V'huile de térébenthine, &c., la polarisation des rayons transmis parallélement a l’axe (s'il s’agit du cristal de roche) n’est pas rigoureusement cir- culaire, mais qu’alors lellipse différe trés peu du cercle.” Thus, to say nothing for the present of the questions of dispersion and absorption, it appears that M. Cauchy con- ceived he had completely accounted for the facts of circular and elliptic polarization, and that he had deduced the for- mulas ‘‘ which serve to determine the conditions and laws of these phenomena.” But neither in this letter, nor in any subsequent version* of his theory, has he given the formulas themselves. Nor has he told us the nature of the calculations by which he was enabled to correct the received opinion, and to prove that the vibrations in a ray transmitted along the axis of quartz, or through oil of turpentine, are not ri- gorously circular, as Fresnel and others have supposed, but slightly elliptical. Now—to take the case of quartz—if we ‘consider that the vibrations of a ray passing along the axis are in a plane perpendicular to it, and if we admit, as M. Cauchy always does in the case of other uniaxal crystals, that there is a perfect optical symmetry all round the axis, we shall find it hard to conceive on what grounds he could have * From some statements that have been made within the last few days by Pro- fessor Powell (Phil. Mag. vol. xix. p. 374), at the request of M. Cauchy himself, it appears that the latter republished his views about circular and elliptic polariza- tion, in alithographed memoir of the date of August, 1836. But I do not find that he published, either then or since, the detailed calculations which he seems to have - made. NQ 142 come to the conclusion that the vibrations of such a ray are performed in an ellipse. For if all planes passing through the axis of the crystal be alike in their optical properties, there will be absolutely nothing to determine the position and ratio of the axes of the ellipse; there will be no reason why its major axis, for example, should lie in one of these planes, rather than in any other. But, whatever may be thought of this case independently of observation, it is manifestly ab- surd to suppose that the vibrations are elliptical in the case of a ray passing through oil of turpentine, or any other liquid possessing the property of rotatory polarization; for, in a liquid, all planes drawn through the ray itself are circum- stanced alike. From these simple considerations it is evident that the theory of M. Cauchy is unsound; but a closer exa- mination will show that it is entirely without foundation, and that it is directly opposed to the very phenomena which it professes to explain. To make this appear, however, in the easiest way that the abstruseness of the subject will allow, it will be necessary to advert to some former re- searches of my own, which have a direct bearing on the question. The same day on which M. Cauchy’s letter was read to the French Academy, I had the honour of reading to the Royal Irish Academy, a paper ‘“‘ On the Laws of Double Re- fraction in Quartz” (see Transactions R. I. A., vol. xvii. p- 461), wherein I showed that every thing which we know respecting the action of that crystal upon light is comprised mathematically in the following equations : 2 3 dn d*n aE ae ae de (1) which differ from the common equations of vibratory motion by the two additional terms containing third differential co- | 145 efficients multiplied by the same constant c, this constant having opposite signs in the two equations. ‘The quantities E and » are, at any time ¢, the displacements parallel to the axes of x and y, which are supposed to be the principal di- rections in the plane of the wave, one of them being there- fore perpendicular to the axis of the crystal. The constants A and B are given by the expressions A=a’, B=a’— (a*?—)’)sin*y, where a and } are the principal velocities of propagation, ordinary and extraordinary, and y is the angle made by the wave-normal (or the direction of z) with the axis of the crys- tal. The only new constant introduced is c, which, though the peculiar phenomena of quartz depend entirely on its ex- istence, isalmost inconceivably small; its value is determined in the paper just referred to. The equations are there proved to afford a strict geometrical representation of the facts ; not only connecting together all the laws discovered by the dis- tinguished observers to whom M. Cauchy refers, and in- cluding the subsequent additions for which we are indebted to Mr. Airy, but leading to new results, one of which esta- blishes a relation between two different classes of pheno- mena, and is verified by the experiments of M. Biot and Mr. Airy. Having, therefore, such conclusive proofs of the truth of these equations, we are entitled to assume them as a standard whereby to judge of any theory; so that any me- chanical hypothesis which leads to results inconsistent with them may be at once rejected. Now I assert that the mechanical hypothesis of M. Cauchy contradicts these equations, and therefore contra- dicts all the phenomena and experiments which he supposed it to represent. But before we proceed to the proof of this assertion, it may perhaps be proper to remark, that pre- viously to the date of M. Cauchy's communication, and of my own paper, I had actually tried and rejected this identical 144 hypothesis, and had even gone so far as to reject along with it the whole of M. Cauchy’s views about the mechanism of light. For though, in my paper, I have said nothing of any mecha- nical investigations, yet, as a matter of course, before it was read to the Academy, I made every effort to connect my equations in some way with mechanical principles; and it was because I had failed in doing so to my own satisfaction, that I chose to publish the equations without comment,* as bare geometrical assumptions, and contented myself with stating orally to the Academy, as I did some months after to the Physical Section of the British Association in Bristol (see Transactions of the Sections, p. 18), that a mechanical account of the phenomena still remained a desideratum which no attempts of mine had been able to supply. I am not sure that on the first occasion I stated the precise nature of these attempts, though I incline to think I did; but I have a dis- tinct recollection of having done so on the second occasion, in reply to questions that were asked me by some Members of the Association.+| Now, my first attempt to explain those equations, which was made almost as soon as I discovered them, actually turned upon the very idea which about the same time found entrance into the mind of M. Cauchy— I mean the idea of an unsymmetrical arrangement of the ether. For as it was generally believed, at that period, * The circumstances here related will account for what Mr. Whewell (History of the Inductive Sciences, vol. ii. p. 449) calls the “obscure and oracular form” in which those equations were published. Having, at that time, no good explanation of them to give, I thought it better to attempt none. But in thegeneral view which I have since taken (see p. 103 of this volume), they do not offer any peculiar diffi- culty. + At the period of this meeting, M. Cauchy’s letter on Elliptic Polarization had been published for some months; but I was not then aware of its existence. Indeed the letter appears not to have attracted any general notice; for the theory which it contains was afterwards advanced in England as a new one, and M. Cauchy has been lately obliged to assert his prior claim to it, through the medium of Professor Powell.—See notes, pp. 141, 149. 145 that the hypothesis of ethereal molecules symmetrically distributed had led, in the hands of M. Cauchy, to a complete theory of rectilinear polarization in crystals (see his Exercices de Mathématiques, Cinquiéme Année, Paris, 1830, and the Mémoires de l'Institut, tom x. p. 293), the notion of endeavouring to account for the phenomena of elliptic polarization, by freeing the hypothesis from any re- striction as to the distribution of the ether, would naturally occur to any one who was thinking on the subject, no less than to M. Cauchy himself. And though, for my own part, I never was satisfied with that theory, which seemed to me to possess no other merit than that of following out in detail the extremely curious, but (as I thought) very imperfect, analogy which had been perceived to exist between the vi- brations of the luminiferous medium and those of a common elastic* solid (for it is usual to regard such a solid as a rigid * The analogy was suggested by the hypothesis of transversal vibrations, which, when viewed in its physical bearing, was considered by Dr. Young to be “perfectly appalling in its consequences,” as it was only to solids that a “lateral resistance”’ tending to produce such vibrations had ever been attributed. (Supplement to the Encyclopedia Britannica, vol. vi. p. 862: Edinburgh, 1824). He, admits, how- ever, that the question whether fluids may not “ transmit impressions by lateral ad- hesion, remains completely open for discussion, notwithstanding the apparent diffi- culties attending it.” As far as I am aware, Fresnel always regarded the ether asa fluid. M. Poisson affirms that it must be so regarded, and attributes its apparent peculiarities to the immense rapidity of its vibrations, which does not allow the law of equal pressure to hold good in the state of motion (Annales de Chimie, tom. xliv. p- 432). M. Cauchy calls the ether a fluid, though he treats it as a solid. My own impression is, that the ether is a medium ofa peculiar kind, differing from all ponder- able bodies, whether solid or fluid, in this respect, that it absolutely refuses, in any case, to change its density, and therefore propagates to a distance transversal vibra- tions only ; while ordinary elastic fluids transmit only normal vibrations, and ordi- nary solids admit vibrations of both kinds. This hypothesis also includes the supposition that the density of the ether is unchanged by the presence of pondera- ble matter. As to M. Cauchy’s third ray, with vibrations nearly normal to the wave, there is no reason to believe that it has even the faintest existence; but it is neces- sarily introduced by his identification of the vibrations of light with those of an in- definitely extended elastic solid. 1i6 system of attracting or repelling molecules, and M. Cauchy has really done nothing more than transfer to the luminife- rous ether both the constitution of the solid and differential formulas of its vibration), still I should have been glad, in the absence of anything better, to find my equations sup- ported by a similar theory, and their form at least counte- nanced by the like mechanical analogy. Besides, I recol- lected that Fresnel himself, in his Memoir on Double Re- fraction, had indicated a “ helicoidal arrangement,” or some- thing of that sort, as a probable cause of circular polariza- tion (Mémoires de l'Institut, tom. vii. p. 73); and as this was an hypothesis of the same kind as the other, only not so general, I was prepared to find that the supposition of an arbitrary arrangement, whatever might be thought of its physical reality, would lead to equations of the same form as those which I had assumed. Upon trial, however, the very contrary proved to be the case, for though it was pos- sible to obtain additional terms, containing differential co- efficients of the third order, multiplied by the same constant C, yet this constant always came out with the same sign in both equations, whereas a difference of sign was essential for the expression of the phenomena. I had no sooner ar- rived at this result, than I perceived it to be fatal to the theory of M. Cauchy, and to afford a demonstration of its insufficiency, not only in the particular application which I had made of it, but in all its applications. For the hypo- thesis which I used was, in fact, identical with that theory, in the most general form of which it is susceptible, when un- restricted by any particular supposition as to the arrange- ment of the ethereal molecules; and therefore the funda- mental conception of the theory could not be true, as it not merely failed to explain a large and most remarkable class of phenomena—those of circular and elliptical polarization—but absolutely excluded them, and left no room for their exist- ence. It followed from this, that the mechanical explanation, a ee eee eee 147 which the same theory was supposed to have given, of the phenomena of rectilinear polarization and double refraction in crystals, could not be well founded; indeed, as I have said, I had always distrusted it, and that for various rea- sons, of which one has been already mentioned, and another was suggested by the forced relations which M. Cauchy had found it necessary to establish among the constants of his theory, and by which he had compelled, as it were, his com- plicated formulas to assume the appearance of an agreement (though, after all, a very imperfect one) with the simple laws of Fresnel. Such were the conclusions at which I arrived, and the reflections which they forced upon me, nearly six years ago. They have been frequently mentioned in conversation to those who took an interest in such matters, and their general tenor may be gathered from what I have elsewhere written (Transactions of the Academy, vol. xviii. p. 68); but I did not think it worth while to publish themin detail, because it seemed probable that juster notions would prevail in the course of a few years, and that the ingenious speculations to which I have alluded would gradually come to be estimated at their proper value. But from whatever cause it has arisen—whe- ther from the real difficulties of the subject, or the extreme vagueness of the ideas that most persons are content to form of it, or from deference to the authority of a distinguished mathematician—certain it is that the doctrines in question have not only been received without any expression of dissent, but have been eagerly adopted, both inthis country and abroad, by a host of followers; and even the extraordinary error, which it is my more immediate object to expose, has been continually gaining ground up to the very moment at which I write, and has at last begun to be ranked among the elementary truths of the undulatory theory of light. Notwithstanding my unwilling- ness, therefore, to be at all concerned in such discussions, I do not think myself at liberty to remain silent any longer. t eee 2 ie 148 There are occasions on which every consideration of this kind must give way to a regard for the interests of science. To show that the principles of M. Cauchy contradict, in- stead of explaining, the phenomenon of elliptic polarization, let us take the axes of coordinates as before; and let us sup- pose, for the sake of simplicity, and to avoid his third ray, that the normal displacements vanish. Then his fundamental equations take the form a . —;z = SfAsS+ ShAn, dt” (2) d? n {= hE, where f, g, / are quantities depending on the law of force and the mutual distances of the molecules.* If, therefore, * | have not thought it necessary to transcribe the original equations of M. Cauchy, which are rather long. He has presented them in different forms; but the system marked (16) at the end of § 1 of his Memoir on Dispersion, already quoted, is the most convenient, and it is the one which I have here used. The directions of the coordinates being arbiirary, I have supposed the axis of x to be perpendicu- lar to the wave-plane. Then, on putting = 0, A Z= 0, in order to get rid of the normal vibration, the last equation of the system becomes useless, and the other two are reduced to the equations (2), given above ; the letters /, ¢, h, being writ- ten in place of certain functions depending on the mutual actions of the molecules. It will be proved, further on, that this simplification does not at all affect the argu- ment. As the directions of a and y still remain arbitrary, I have made them pa- rallel to the axes of the supposed elliptic vibration. It may be right to observe, for the sake of clearness, that, when the medium is arranged symmetrically, it is always possible to take the directions of 2 and y such that the two sums depending on the quantity h may disappear from the equations (2), and then the vibrations are rectilinear. But when the arrangement is unsym- metrical, this is no longer possible. The equations (2) are precisely the same as those which have been employed by Mr. Tovey and by Professor Powell, the latter of whom, in his lately published work, entitled, “4 General and Elementary View of ihe Undulatory Theory, as ap- plied to the Dispersion of Light, and other Subjects,’ has dwelt at great length on the theory of elliptic polarization, which they have been supposed to afford, and which he regards as a most important accession to the Science of Light. Professor Powell has also made some communications on the subject to the British Asso- a rt cal ae tl 149 we assume that each molecule describes an ellipse, the axes of which are parallel to those of # and y; that is to say, if we make E=pceosg, n= sing, Qn (3) p = i (sd or 2), and consequently AE = p(sin 26 sin ¢ — 2 sin 70 cos 9), An= — q(sin20cos¢ +2 sin 70 sin 9), where 06= ™, we shall find, by substituting these values in the equations (2), which must hold good independently of #, soa t+ch, sop (4) Sf sin 20 — 2kSh sin*O = 0, Sg sin 20+ : Sh sin 70 = 0, wherein £ = : expresses the ratio of the semiaxes of the el- ‘liptic vibration, and r2 2 i on? =fsin 6, B = an3 dg sin *6, oe . C=7a Dh sin 26. ciation, and has written two papers about it in the Philosophical Transactions (1838, p. 253; and 1840, p. 157), besides several others in the Philosophical Magazine. He, however, always attributed this theory of elliptic polarization to Mr. Tovey, until his attention was directed, by a letter from M. Cauchy, to some investiga- tions of the latter which he had not previously seen (Phil. Mag. vol. xix. p. 374). Mr. Tovey set out with the principles of M. Cauchy, and therefore naturally struck into the same track, in pursuit of the same object, apparently quite unconscious that any one had preceded him. It was, indeed, an obvious reflection, that these prin- ciples, when generalised to the utmost, ought toinclude, not only the laws of elliptic polarization, but (as really has been thought by M. Cauchy and his fol- lowers) of dispersion and absorption, and, in short, of all the phenomena of optics. 150 Equating the two values of s*, we get, for the determination of k, the following quadratic : e442 k+1=0. (5) Now making the substitutions (3) in equations (1), page 142, we have Ope Qn. ay am C s=a——\ ch, iralle dane 7 Gi (6) and thence i r See Spams (7) a result which is perfectly inconsistent with the former, since the two roots of (5) have the same sign, if they are not imagi- nary, while those of (7) have opposite stgns, and cannot be imaginary. If, therefore, one equation agrees with the phe- nomena, the other must contradict them. The last equation indicates that, in the double refraction of quartz, the two elliptic vibrations are always possible, and performed in op- posite directions, which is in accordance with the facts ; whereas the equation (5), deduced from M. Cauchy’s theory, would inform us that the vibrations of the two rays are either zmpossible or in the same direction.* To apply the results to a particular instance, let us con- ceive a circularly polarized ray passing along the axis of quartz, or through one of the rotatory liquids, such as oil of turpentine; the position of the coordinates x and y, in the plane of the wave, being now, of course, arbitrary. In each of these cases we have f = + 1, anda = 8B = a’, so that the value of s” in equation (6) is expressed by the constant a’, plus or minus a term which is inversely proportional to the * This conclusion, which shows that M. Cauchy’s Theory is in direct opposition to the phenomena, might have been obtained without any reference to the equa- tions (1). But these equations are necessary in what follows. 151 wave-lengthA; the sign of this term depending on the direc- tion of the circular vibration. Now it will not be possible to obtain a similar value of s? from the formulas (4), unless we suppose A’ = Bb’ = a’, since it is only in the expansion of c’ that a term inversely proportional to A can be found; but on this supposition the formulas are inconsistent with each other, nor can they be reconciled by any value of k. Indeed, when a’ = v’, the equation (5) gives k= + ¥—1. Thus it appears that circular vibrations, such as are known to be propagated along the axis of quartz, and through cer- tain fluids, cannot possibly exist on the hypothesis of M. Cauchy. It was probably some partial perception of this fact that caused M. Cauchy to assert that the vibrations, in these cases, are not exactly circular, but in some degree elliptical ; a supposition which, if it were at all conceivable, which we have seen it is not (p. 142), would be at once set aside by what has just been proved; for no assumed value of k, whether small or great, will in any way help to remove the difficulty. But this is not all. Rectilinear vibrations are excluded as well as circular; for we cannot suppose / = 0 in the equa- tions (4), so long as the quantity c’, resulting from the hypo- thesis of unsymmetrical arrangement, has any existence. Thus the inconsistency of that hypothesis is complete, and the equations to which it leads are utterly devoid of mean- ing. The foregoing investigation does not differ materially from that which I had recourse to in the beginning of the year 1836. To render the proof more easily intelligible, and to get rid of M. Cauchy’s “third ray,’ which has no existence n the nature of things, I have suppressed the normal vibrations; a procedure which is not, in general, al- lowable on the principles of M. Cauchy. It will readily ap- pear, however, that this simplification still leaves the demon- stration perfectly rigorous in the case of circular vibrations, 152 and does not affect its force when the vibrations are ellipti- cal. For in the rotatory fluids it is obvious that the normal vibrations, supposing such to exist, must, by reason of the symmetry which the fluid constitution requires, be indepen- dent of the transversal vibrations, and separable from them, so that the onekind of vibrations may be supposed to vanish when we wish merely to determine the laws of the other. The equations (2) are, therefore, quite exact in this case; and they are also exact in the case of a ray passing along the axis of quartz, since such a ray is not experimentally dis- tinguishable from one transmitted by a rotatory fluid, and its vibrations must consequently be subject to the same kind of symmetry. In these two cases, therefore, it is rigorously proved that the values of 4, which ought to be equal to plus and minus unity, are imaginary, and equal to + ¥ — 1. And if we now take the most general case with regard to quartz, and suppose that the ray, which was at first coinci- dent with the axis of the crystal, becomes gradually inclined to it, the values of / must evidently continue to be imaginary, until such an inclination has been attained that the two roots of equation (5) become possible and equal, in consequence of the increased magnitude of the co-efficient of the second term. Supposing the last term of that equation to remain unchanged, this would take place when the co-efficient of & (without regarding its sign) became equal to the number 2, and the values of & each equal to unity, both values being positive or both negative. The vibrations which before were impossible, would, at this inclination, suddenly become pos- sible; they would be circular, which is the exclusive pro- perty of vibrations transmitted along the axis; and they would have the same direction in both rays, which is not a property of any vibrations that are known to exist. At greater inclinations the vibrations would be elliptical, but they would still have the same direction in the two rays. These re- sults would not be sensibly altered by regarding the equa- 153 tion (5) as only approximate in the case of rays inclined to the axis; for the last term of that equation, if it does not re- main the same, can never differ much from unity ; since it must become exactly equal to unity, whatever be the direction of the ray, when the crystalline structure is supposed to disap- pear, and the medium to become a rotatory fluid. That a theory involving so many inconsistencies should have been advanced by a person of M. Canchy’s reputation, would, perhaps, appear very extraordinary, if we did not re- collect that it was unavoidably suggested by the general principles which he had previously adopted, and which were supposed, not merely by himself, but by the scientific world generally, to have already afforded the only satisfactory ex- planation of the laws of double refraction in the common and well-known case where the vibrations are rectilinear. This supposed explanation was obtained, as has been said, by restricting the application of M. Cauchy's principles to the hypothesis of a vibrating medium arranged symmetrically, in which case it was shown that the vibrations were neces- sarily rectilinear; and of course the removal of this restric- tion was the only way in which it was possible, on those principles, to account for the existence of circular and ellip- tical vibrations. Accordingly, when M. Cauchy perceived that, on the hypothesis of unsymmetrical arrangement, the ex- istence of rectilinear vibrations became impossible, and that ° of elliptic vibrations, generally speaking, possible, he found it very easy to persuade himself that he had obtained a new proof of the correctness of his views, and a new and most important application of the fundamental equations by which his general principles were analytically expressed. To have supposed otherwise would have been to admit that his general principles were false. If the elliptical or quasi-circular vibrations which he was now contemplating were not capable of being identified with those which had been recognized in the phenomena presented by quartz and 154 the rotatory fluids—if their laws were essentially or very considerably different—his theory would be inconsistent with a wide range of well known facts, and, notwith- standing its so-called explanations of other laws, should be finally abandoned. Under these circumstances, therefore, he very naturally supposed that his new results must be in complete harmony with the phenomena discovered by M. Arago, and analysed so successfully by MM. Biot and Fresnel; although, had he taken the precaution of acquiring such a clear notion of the phenomena as would have enabled him to translate them into analytical language, he must have perceived that they were entirely opposed to his results, and that this opposition furnished an argument which swept away the very foundations of his theory. For, if the constitution of the luminiferous medium were such as M. Cauchy ‘sup- poses, the well-known phenomena of circular and elliptic po- larization would, as we have seen, be absolutely impos- sible. Thus the argument which overturns the particular theory of elliptical polarization destroys at the same time all the other optical theories of M. Cauchy, because they are all built on the principles which we have now demonstrated to be false. But though the principles of M. Cauchy are now, for the first time, formally refuted, they were objected to, on ‘general grounds, so long ago as the year 1830, by a person whose opinion, on a question of mechanics, ought to have had considerable weight. This was M. Poisson, who, having de- duced from the equations of motion of an elastic solid the con- sequence that such a body admitted vibrations perpendicu- lar to the direction of their propagation, thought it right to remark that this conclusion could not be supposed to account for transversal vibrations in the theory of light, because (as he expressed himself) ‘‘the same equations of motion could not possibly apply to two systems [of molecules] so essen- tially different from each other” as the ethereal fluid and ee 155 an elastic solid.*—(See the Annales de Chimie, tom. xliv. p- 432). The remark, however, did not meet with much attention from mathematicians, who were, perhaps, not dis- posed to scrutinize too closely any hypothesis which gave transversal vibrations as a result. Besides, the hypothesis appeared to go much further, as it offered primd facie explanations of a great variety of phenomena; it was one to which calculation could be readily applied, and there- fore it naturally found favour with the calculator; and as to M. Poisson’s objection, it was easily removed by a change of terms, for when the elastic solid was called an “ elastic system,” there was no longer anything startling in the an- nouncement that the motions of the ether are those of such asystem. The hypothesis was therefore embraced by a great number of writers in every part of Europe, who reproduced, each in his own way, the results of M. Cauchy, though some- times with considerable modifications. Every day saw some new investigation purely analytical—some new mathematical research uncontrolled by a single physical conception—put forward as a “mechanical theory” of double refraction, of circular polarization, of dispersion, of absorption; until at length the Journals of Science and Transactions of Societies were filled with a great mass of unmeaning formulas. This state of things was partly occasioned by the great number of “ disposable” constants entering into the differential equations of M. Cauchy and their integrals; for it was easy to introduce, among the constants, such relations as would lead to any de- sired conclusion ; and this method was frequently adopted by M. Cauchy himself. Thus, in his theory of double (or rather triple) refraction, given in the works already cited (p. 145), he supposes three out of his nineconstants to vanish, and assumes, sss * As the theory of M. Cauchy (Mem. de ? Institut, tom. x.) had been communi- cated to the Academy of Sciences some months before the period (October, 1830) at which M. Poisson wrote, there can be no doubt that M. Poisson’s remark was directed against that theory, though he did not expressly mention it. VOL. Il. .@) 156 among the other six, three very strange and improbable re- lations, by means of which each of the principal sections of his wave-surface (considering only two out ofits three sheets) is reduced to the circle and ellipse of Fresnel’s law; and the three principal sections being thus forced to coincide, it would not be very surprising if the two sheets were found to coincide in every part with the wave-surface of Fresnel. The coincidence, however, is only approximate; but M. Cauchy is so far from being embarrassed by this circumstance, that he does not hesitate to regard his own theory as rigo- rously true, and that of Fresnel as bearing to it, in point of accuracy, the same relation which the elliptical theory of the planets, in the system of the world, bears to that of gravita- tion (Mémoires de (Institut, tom. x. p. 313). Nor is he at all embarrassed by the supernumerary ray belonging to the third sheet of his wave-surface ; he assumes at once that such a ray exists, though it was never seen, and promises, for the satisfaction of philosophers, to make known the means of ascertaining its existence (Jbid. p. 305). But he afterwards contented himself with observing that as its vibrations are in the direction of propagation they probably make no impres- sion on the eye, and he then gave it the name of the “ invisible ray.” (Nouveaux Exercices, p. 40). In these investigations, the suppositions which M. Cauchy had made respecting the constants led to the result that the vibrations of a polarized ray are parallel to its plane of pola- rization ; but in the year 1836 he changed his opinion on this point, and then, by reinstating the constants that he had be- fore supposed to vanish, and establishing proper relations amongst them and the rest, he arrived at the conclusion that the vibrations are perpendicular to the plane of polarization (Comptes Rendus, Tom. ii. p. 242). All his other results, of course, underwent some corresponding change ; and it is this new theory which must now be regarded as rigorous, while that of Fresnel is to be looked on as approximate. But itis 157 needless to say, that if the accuracy of Fresnel’s law of double refraction is to be disputed, it must be on much better grounds than these; and the results of M. Cauchy are cer- tainly too far removed from that law to have any chance of being consonant with truth. Although, for example, his new views respecting the direction of the vibrations agree, in a general way, with those of Fresnel, there is yet, in one par- ticular, an important difference between them; for accord- ing to Fresnel, the vibrations are always exactly in the sur- face of the wave, while, according to M. Cauchy (in his old theory as well as the new), they are only soin ordinary media. In a biaxal crystal he finds—and this is one of the ways in which the “invisible ray” manifests its influence—that the direction of vibration, in each of the two rays that are visible, is inclined at a certain angle to the wave-plane; but this angle, though small, is by no means inconsiderable, as M. Cauchy seems to intimate, overlooking the fact, which appears from his own equations, that it is of the same order of mag- nitude as the quantities on which the double refraction de- pends. It is true, the deviation measured by this angle can- not, if it exists, be directly observed in the refracted light ; but its indirect effects on reflected light ought to be very great, since the action of the crystal on a ray reflected at its surface differs from that of an ordinary medium by a quantity of the same order merely as the aforesaid angle; and as the problem of crystalline reflexion has been already solved (Trans. R. I. A. vol. xviii., p. 31) on the supposition (which is an essential one in the solution) that the vibrations are ex- actly in the plane of the wave, it is highly improbable, con- sidering the complex nature of the question, that it will be solved, in any satisfactory way, on a supposition so different as that which is required by the theory of M. Cauchy. How- ever, as the laws of such reflexion are now well known, by means of the solution alluded to, it is possible that M. Cauchy may, as in the case of double refraction, succeed in deducing 02 158 the same laws, or, if not the same, what may seem to be more exact laws, from certain principles* of his own, helped out, if need be, by proper relations among his constants; espe- cially if, to allow greater scope for such relations, the number of constants be increased by the hypothesis of two coexist- * In applying these principles to the question of reflexion and refraction at the surface of an ordinary medium (Comptes Rendus, Tom. ii. p. 348), M. Cauchy has arrived at the singular conclusion, that light may be greatly increased by refraction through a prism, at the same time that it is almost totally reflected within it. Sup- posing the refracting angle of the prism to be very little less than the angle of to- tal reflexion for the substance of which it is composed, a ray incident perpendicu- larly on one of the faces will emerge making a very small angle wit the other face; and as the reflexion at the latter face is nearly total, it is self-evident that the intensity of the emergent light, as compared with that of the incident, must be very smal]. M. Cauchy, however, finds, by an elaborate analysis, that a prodigious multiplication of light [‘‘ une prodigieuse multiplication de la lumiére’’] takes place, the emergent ray being nearly six times more intense than the incident when the prism is made of glass, and nearly nine times when the prism is of diamond. This result was, in a general way, actually verified experimentally by himself and ano- ther person; soeasy it is, in some cases, to see anything that we expect to see. Had the result been true, it would have been a very brilliant discovery indeed; for then we should have been able, by a simple series of refractions, to convert the feeblest light into one of any intensity we pleased ; but the very absurdity of such a sup- position should have taught M. Cauchy to distrust both his theory and his experi- ment. Far from doing so, however, he considers the fact to be perfectly esta- blished, and to afford a new argument against the system of emission. “Ici,” says he, “un rayon, réféchi en totalité, est de plus transmis avec accroissement de Iumiére ; ce qui est un nouvel argument contre le systéme d’émission.’’ The sys- tem of emission has at least this advantage, that by no possible error could such a conclusion be deduced from it. For if all the particles of light be reflected, cer- tainly none of them can be refracted. The truth is, that M. Cauchy mistook the measure of intensity in the hypothe- sis of undulations, supposing it to be proportional simply to the square of the amplitude of vibration; whereas it is really measured by the vis viva, or by that square multiplied by the quantity of ether put in motion, a quantity which in the present case is evanescent, since the corresponding volumes of ether, moved by the ray within in the prism and by the emergent ray, are to each other as the sine of twice the angle of the prisin to the sine of twice the very small angle which the emergent ray makes with the second face of the prism. The intensity of the emer- gent light is therefore very small, as it onght to be, though the amplitude of its vibrations is considerable. : ~~ “S —— OCU elle 159 ing systems of molecules, an hypothesis which M. Cauchy bas already considered with his usual generality, but without making any precise application of it. (Eercices d’ Analyse et de Physique Mathématique, Tom. i. p. 33.) Perhaps one cause why M. Canchy’s views on the subject of double refraction have met with such general acceptance, may be found in the fact, that a theory setting out from the same principles, and leading, by the same relations among constants, to formulas identical in every respect with his earlier results, was advanced independently, and nearly at the same time, by M. Neumann of Konigsberg (Poggendorff’s Annals, vol. xxv. p. 418). A coincidence so remarkable would be looked upon, not unreasonably, as a strong argu- ment in favour of the theory ; though it must be allowed that, in the effort to extend the knowledge of any subject, there is a tendency in different minds to adopt the same errors re- specting it, as well as the same truths; a fact of which we have seen other examples in the course of the present article. According to M. Neumann (#bid. p. 454), the “ third ray,” not being perceived as light, must manifest its existence as radiant heat, or as a chemical power, or as some other agent [“‘als strahlende Warme, oder chemisch wirkend, oder als irgend ein anderes Agens”}, and he thinks that the nature of this ray will be more easily investigated, if the laws of re- flexion shall be deduced from the aforesaid theory. But we have seen that the laws of reflexion are, to all appearance, at variance with the theory, and they take no account whatever of the third ray. Besides, the discoveries which have been made of late years respecting the polarization of radiant heat, and the strong analogies that have been traced between it and light, amount to a demonstration that its vibrations are transversal, and of course essentially different from those of the supposed third ray, which are normal, or nearly so. There is every reason to believe that the vibrations of the 160 chemical rays are also transversal; and we may confidently assert, that the three species of rays—those of light and heat, and the chemical rays,—are produced not only by vi- brations of the same medium, but by the same kind of vibra- tions, propagated with nearly the same velocities. If, there- fore, the third ray of MM. Cauchy and Neumann has any existence, it must be referred to ‘‘ some other agent,” the nature of which it is impossible to conjecture. Enough has now been said to show that the optical theory which we have examined, and which has passed current in the scientific world for a considerable period, is quite inade- quate to explain the leading phenomena of light, and that it is based upon principles which are altogether inapplicable to the subject. M. Cauchy states, in the memoir so often quoted (Mem. de l'Institut, Tom. x. p. 294), that the first ap- plication which he had made of his principles was to the theory of sound, and that the formulas which he had deduced from them agreed remarkably well with the experiments of Savart and others on the vibrations of elastic solids. As I have already intimated, it is in the solution of such ques- tions (which, however, have long been familiar to mathemati- cians) that the fundamental equations of M. Cauchy may be most advantageously employed ; and had he pursued his re- searches in this direction, his labours would doubtless have been attended with more success, and with greater benefit to science. II. On Fresnel’s Formula for the Intensity of Reflected Light, with Remarks on Metallic Reflexion. When Mr. Potter discovered, by experiment, that more light is reflected by a metal at a perpendicular incidence than at any oblique incidence (at least as far as 70°), the fact was looked upon, by himself and others, as contrary to all re- ceived theories ; and certainly the universal opinion, up to that time, was, that the intensity of reflexion always increases hea ey 161 with the incidence. It may therefore be worth while to re- mark, that the formula given by Fresnel for reflexion at the surface of a transparent body, though not of course appli- cable, except in a very rude way, to the case of metals, would yet lead us to expect, for highly refracting bodies as the metals are supposed to be, precisely such a result as that obtained by Mr. Potter. For when the index of refraction exceeds the number 2 + 3, or the tangent of 75°, the ex- pression for the intensity of reflected light will be found to have a minimum value at a certain angle of incidence; while for all less values of the refractive index the intensity will be least at the perpendicular incidence. Let i and i’ be the angles of incidence and refraction, and put _ sing cost — ~ sind” "= cosa’? then if 1 be the intensity of the reflected light, when common light is incident, Fresnel’s expression . 2 (sin? (i + 7) " tan’%(2+7/)) ’ in which the intensity of the incident light is taken for unity, may be put under the form which has a minimum value when 1 1 8 p+—-=M+—-———; . e M+ a the value of 1 being in that case ¢ = sier 4 ¢ +2) 8 a een 2(m = ~). va 2(m + ty. 8 162 and the corresponding angle of incidence being given by the formula _ vu e—l| 1 Bike ied ve I’ where «= ( [ayy : 1 ioe Since « + — cannot be less than 2, it is easy to see that, when 7 : ai 1 there is a minimum, m + — cannot be less than 4, and there- M fore m cannot be less than 2 + 3, or 3.732. As an example, let m + 2 =6. Then, at a perpendicu- lar incidence, one-half the incident light will be reflected. The minimum will be when i = 65°36’, and at this angle only 55 of the incident light will be reflected. The value here assumed for the refractive index is that which Sir J. Herschel (Treatise on Light, Art. 594), assigns to mercury ; but if my ideas be correct, it is far too low for that metal. The only person who supposes that the refractive index of a metal is not a large number, is M. Cauchy. It has always been held as a maxim in optics, that the higher the reflective power of any substance, the higher also is its refractive index. But M. Cauchy completely reverses this maxim; for, as I have elsewhere shown (Comptes Rendus, tom. viii. p. 964), it follows from his theory that the most reflective metals are the least refractive, and even that the index of refraction, which for transparent bodies is always greater than unity, may for metals descend far below unity. Thus, according to his for- mula, the index of refraction for pure silver is the fraction 1, so that the dense body of the silver actually plays the part of a very rare medium with respect toa vacuum. It appears to me that such a result as this is quite sufficient to overturn the theory from which it is derived. The formulas, however, which he gives for the intensity of the reflected light, are identical with the empirical expressions which I had given long before, and are at least approximately true. In framing my own empirical theory (see Proceedings, 163 vol. i, p. 2), two suppositions relative to the value of the refractive index presented themselves. Putting m for the modulus, and x for the characteristic, I had to choose be- The latter value is that tween the values Mcosy and ro which I adopted; the former, whichis M. Cauchy’s, was re- jected because I saw that it would lead to the result above mentioned. Another result of M. Cauchy’s, which he has given twice in the Comptes Rendus (tom. ii. p. 428, and tom. viii. p. 965) requires to be noticed. When a polarized ray is reflected by a metal, the phase of its vibration is altered, and if the in- cidence be oblique, the change of phase is different, accord- ing as the light is polarized in the plane of incidence, or in the perpendicular plane. But when the ray is reflected at a perpendicular incidence, it is manifest that the change is a constant quantity, whatever be the plane of polarization. In fact, the distinction between the plane of incidence and the perpendicular plane no longer exists, and the phenomena must be the same in all planes passing through the ray. Yet M. Cauchy, in the two places above quoted, asserts it to be a consequence of his theory, that in this case the altera- tions of phase are different for two planes of polarization at right angles to each other, and that the difference of the al- terations amounts to half an undulation. The same singular hypothesis had been previously made by M. Neumann (Pog- gendorff’s Annals, vol. xxvi. p. 90), whom M. Cauchy appears to have followed; but M. Neumann has since admitted it to be erroneous (Ibid. vol. xl. p. 513). Mr. J. Huband Smith communicated to the Academy some particulars connected with the recent discovery of a cairn containing cinerary urns, which appears to have been accom- panied by some circumstances not unworthy of notice. It took place at Loughanmore, in the county of Antrim, 164 the seat of Mr. Thomas Adair, in a field which was being ploughed, in the spring of 1840. After a few urns had been found, there being some difficulty in preserving them en- tire, Mr. Adair, with a commendable desire to avoid the de- struction of remains so full of interest, caused the cairn, in which these urns were found, to be closed carefully, and re- stored the ground to its former state as nearly as might be, in order to leave it to some skilful and experienced antiquary to explore the entire ina more deliberate and scientific manner. The discovery was occasioned by one of the horses which were in the plough suddenly stumbling, one of his legs having sunk nearly up to the knee in adeep hole. Onexa- mination it was found he had put his foot into a fine sepul- chral urn, which, it need hardly be stated, was broken into shivers. On a slight further search a second urn was discovered. Every effort was made to preserve this one entire, but in vain; it fell to pieces in the hands of the person who took it up. A third urn was then exposed, when Mr. Adair finding it impossible to save them, put a stop for the time to the fur- ther opening of the cairn. The cairn in which these urns were found is situated in the townland of Loughanmore, and not far from the Loughan or lake (now drained) from which the townland de- rives its name. It lies within a field called the cove-park, there being one or more artificial caves, or coves (as they are termed by the Antrim peasantry), within it. And from a hollow sound which the ground gives, other caves, as yet unopened, are confidently supposed to exist near where the urns were found. The cairn in question is indicated by so very slight an elevation of thesurface, thatit was in course of being ploughed over without any particudar notice, till the finding of the urns drew Mr. Adair’s attention to it. This elevation was then observed to have a circumference of some twelve or fourteen * \ ) ° a 165 feet, perhaps a little more ; and on closer examination proved to be composed of loose field-stones mixed with earth, ap- parently laid in, upon, and around the urns, with just so much care as not to break them. It will not fail to be noticed, that in this latter circum- stance this cairn seems to differ remarkably from most others, for instance Deveril Barrow in Dorsetshire, which has been thought worthy of an elegant descriptive work, and many other of the Wiltshire Barrows, so carefully and scientifically opened by an eminent and accomplished English antiquary, the late Sir Richard Colt Hoare; and also from the very important cairn opened at Mount Stewart, near Grey-Abbey, in the county of Down, about the year 1807. In these the urns have almost invariably been protected by a kist or stone chest formed of flags, enclosing a considerable space. We have the authority of our distinguished Irish antiquary, Mr. George Petrie, for saying that “ the sepulchral urns of Ireland are superior in ornament to any found in England. The ornaments of gold frequently found in them are richer and more numerous.” And he does not hesitate to infer from these and other facts, that ‘‘the pagan Irish were supe- rior in the arts of civilized life to their British neighbours.” These urns found at Loughanmore were found to have been all placed with the mouth downwards. They lay rather closely together, scarce eighteen inches apart from each , other, the smaller urns appearing to surround the larger one, which was that broken by the horse. The two smaller sized urns were of the same size, and would hold probably eight or nine quarts of liquid each. No metallic remains of brass or bronze; no flint arrow- heads, stone adzes, or any other remains were found. Every probability exists of future discoveries of a most interesting description being made on a stricter examination of this cairn. Opportunities such as this daily offer themselves in this 166 country, of pursuing an inquiry of deep historical interest ; which if they were to occur at the other side of the Irish channel, would be grasped at with avidity by the untiring zeal of many an English antiquary, who, while he cultivates assiduously, and under circumstances of extreme difficulty, the meagre opportunities which England affords to the study of ancient British and Celtic remains, cannot but look with a feeling of astonishment (akin perhaps to contempt), on the apathy with which in Ireland we suffer daily the tan- gible and unquestionable proofs of the early civilization of our country, to which we have long proudly laid claim, ac- tually to perish before our eyes, from the most disgraceful negligence. The Chair having been taken, pro tempore, by the Rev. J. H. Todd, D. D., V. P., the President communicated the following proof of the known law of Composition of Forces. Two rectangular forces, 2 and y, being supposed to be equivalent to a single resultant force p, inclined at an angle v to the force x, it is required to determine the law of the dependence of this angle on the ratio of the two component forces x and y. Denoting by p’ any other single force, intermediate be- tween x and y, and inclined to a at an angle 2’, which we shall suppose to be greater than; and denoting by 2’ and y' the rectangular components of this new force p’, in the directions of x« and y, we may, by easy decompositions and ‘recompositions, obtain a new pair of rectangular forces, 2” and y", which are together equivalent to p’, and have for components wag! + Y ee P Pp x y" = —y! —_ ¥ x’; r | SS 167 the direction of a” coinciding with that of p’, but the direc- tion of y” being perpendicular thereto. Hence, a” ax + yy that is, tan—! x = tan—! y — tan! Y, x x x or, finally, S(e' —v =f (v') —f (2); (a) at least for values of v, v’, and v’— », which are each greater Ww . . than 0, and less than 33 if f be a function so chosen that the equation y — = tans (v % — tanf (0) expresses the sought law of connexion between the ratio z and the angle v. The functional equation (A) gives m Sm) = mflo) = "=f (ne), m and n being any whole numbers; and the case of equal components gives evidently £G)=% hence and ultimately, S(e) = % (8) because it is evident, by the nature of the question, that T 2’ therewith, and therefore could not be equal thereto for all while v increases from 0 to =, the function f(v) increases Pree at ] values of v commensurable with q unless it had the same property also for all intermediate incommensurable values. We find, therefore, that for all values of the component forces x and y, the equation 168 Y — tanv (c) x holds good; that is, the resultant force coincides én direction with the diagonal of the rectangle constructed with lines re- presenting a and y as sides. The other part of the known law of the composition of forces, namely, that this resultant is represented also in mag- nitude by the same diagonal, may easily be proved by the process of the Mécanique Céleste, which, in the present no- tation, corresponds to making a’ = x, y’ = Ys al!’ =p, and therefore gives 2 Pye p= = paz +7. But the demonstration above assigned for the law of the direction of the resultant, appears to Sir William Hamilton to be new. It was resolved, on the recommendation of the Council, to present a congratulatory address to His Excellency the Lord Lieutenant ; whereupon, the Academy having adjourn- ed for a short interval, an address was prepared, which was afterwards agreed to. A letter was read from M. Moreau de Jonnés, present- ing to the Academy two volumes of the Agricultural Statistics of France. DONATIONS. Comptes Rendus Hebdomadaires des Seances de l Acade- mie des Sciences. Premier Semestre. 1841. Nos. 17-24. Ordnance Map of the Queen’s County, in 39 sheets, in- cluding Title and Index. Presented by His Excellency the Lord Lieutenant. Journal of the Franklin Institute. Vol. 1. Third Series. (1841). 169 Det Kongelige Danske Videnskabernes Selskabs Natur- videnskabelige og Mathematiske Afhandlinger. 8° Deel. (1841). - Commentationes Societatis Regie Scientiarum Gottingensis recentiores. Vol. VIII. (1832-1837). Esop’s Fables in Chinese. Presented by the Rev. David Thom. An Account of the Magnetic Observations made at Har- vard University. (U. S.) Presented by the American Academy. Résumé des Observations sur la Meteorologie, sur le Mag- netisme, §c., faites a ' Observatoire Royal de Bruxelles en 1840. Par le Directeur A. Quetelet. Presented by the Author. Memoire sur la Diathermansie Electrique des Couples Metalliques : Des Travaux et des Opinions des Allemands sur la Pile Voltaique : Essai Historique sur les Phénoménes et les Doctrines de l’Electro-Chimie. Par Professeur C. F. Wartmann. Pre- sented by the Author. Oversigt over det Kongelige Danske Videnskabernes Sel- skabs Forhandlinger og dets Medlemmers Arbeider. 1 Aaret, 1839-40. Report of the Council of the Zoological Society of Lon- don. April 29, 1841. Report on the Observations by the self-registering Ane- mometer, in 1837-40. By A. F. Osler, Esq. Presented by the British Association. Abstract of the Magnetic Observations made at the Tra- vandrum Observatory in May, 1841. By John Caldecott, Esq. Presented by the Author. Extrait du Tom. VIII. No. 6, des Bulletins de Academie Royale de Bruxelles. (“ Physique du Globe.”) Presented by M. Gudele. 170 Rapport Decennal des Travaux de l’ Academie Royale de Bruxelles depuis 1830. Par M. A. Quetelet, Hon. M. RiP. A., &e. ke. Annuaire de ! Academie Royal de Bruxelles. 7” année. Annuaire de l Observatoire Royale de Bruxelles, pour V’An 1841. Par M. Quetelet. Presented by the Author. Des Moyens de soustraire 1 Exploitation des Mines de Houille aux Chances d' Explosion. Recueil de Memoires et de Rapports publié par l’ Academie Royale de Bruxelles. Presented by the Academy. Traité élémentaire des Fonctions Elliptiques. Par P. F. Verhulst. Presented by the Author. Statisque dela France (Agriculture). Tom. 1. If. Par M. De Jonnés. Presented by the Author. First Publication of the Irish Archeological Society. Presented by the Society. Memoires couronnes de l Academie Royale de Bruxelles. Tome XIV. 2™ Partie (1839-40). Nouveaux Memoires de l Academie Royale de Bruxelles. Tome XIII. (1841). Bulletins de ? Academie Royale de Bruxelles. Nos. 9, 12 (1840). Nos. 1, 6 (1841), Transactions of the Zoological Society of London. Vol. II. Part 5. Meteorological Observations made in Dublin. By Thomas H. Orpen, M.D., M.R.I.A. Presented by the Author. Journal of the Statistical Society of London. Vol. IV. Part 3. Seventh Annual Report of the Poor-Law Commissioners (1841). Report of the Poor-Law Commissioners on Medical Chari- ties in Ireland. (1841). Presented by George Nicholls, Esq. Abhandlungen der Kéniglichen Akademie der Wissens- chaften zu Berlin, (1839). PROCEEDINGS OF THE ROYAL IRISH ACADEMY. 1841. No. 32. November 30. (Stated Meeting.) SIR Ws. R. HAMILTON, LL.D., President, in the Chair. The following communication “ on the Compound Na- ‘ ture of Nitrogen,” by George J. Knox, Esq., was read by Dr. Kane. Soon after the discovery of the bases of the alcalies and earths by Sir Humphrey Davy, the compound nature of ni- trogen began to be a subject of discussion amongst chemists; but the arguments in favour of this supposition, deduced principally from the nature of the ammoniacal amalgam, led to no satisfactory physical results. The experiments of Sir Humphrey Davy on the ammo- niacal nitruret of potassium, and those of Despretz and Grove on the compounds of nitrogen with iron, copper, &c., have shown that the metals singly (even when aided by the most powerful electrical induction) have not the power of de- composing nitrogen. ‘There is one experiment, however, by Sir Humphrey Davy, from which one might deduce its com- pound nature. Upon heating ammonia-nitruret of potassium in an iron tube, he obtained more hydrogen, and less nitrogen, than the ammonia ought to have given. Again: on mixing this substance with a greater pro- portion of potassium, he obtained still more hydrogen, and VOL. II. P 172 less nitrogen; whereas, on heating the same substance in a tube of platinum, the potassium alloyed with the platinum, and the ammonia was given off almost entirely undecomposed. How can these experiments be explained except upon the supposition that the potassium and the iron had con- jointly decomposed the nitrogen ? The latest experiments which bear upon this subject, and from which | received the idea which led me to this investigation, are those of Doctor Brown, “ upon the conversion of Carbon into Silicon,” an explanation of phenomena which appears to me most un- reasonable, and contrary to all chemical analogy; whilst the supposition of the carbon having reduced the nitrogen is not only a simple but an unavoidable conclusion to arrive at, if nitrogen be a compound substance. To determine, by ex- periment, the correctness or incorrectness of this idea, it were only necessary to reduce nitrogen by some other substance than charcoal; and should silica result from its decomposition, the problem might be considered to be solved. Exp. I.—A considerable quantity of ammonia-nitruret of potassium was formed, by passing ammonia over potassium heated in an iron tube; the part which had not been in con- tact with the tube, having been examined for silica, contained none. Exp. II.—Ammonia was passed for several hours over pure iron, heated to a dull red heat ; examined for silica, it contained none. Exp. III.—Ammonia-nitruret of potassium was heated with pure iron in an iron crucible, for one half hour, over a large Rose’s lamp; the contents of the crucible, on examina- tion, gave silicon and silica, the weight of which was not re- gistered, as it might have been said to have derived a portion of silica from the inner surface of the crucible. Exp. 1V.—Twenty grains of ammonia-nitruret of potas- sium were heated with twenty grains of pure iron in the same iron vessel for one half hour; when treated with nitric 173 and muriatic acids there remained insoluble a small quantity of a brownish colour, which, when fused with carbonate of potash, gave of silica 0.10. The solution, supersaturated with potash, filtered, neutralized, evaporated to dryness, gave of silica 1.450; sum total of silica 1.550. From these experiments, together with those of Sir Hum- phrey Davy mentioned above, one might infer that nitrogen is either a compound of silicon and hydrogen, or of silicon, hydrogen, and oxygen; to determine which, synthetically, a current of dry muriatic acid gas was passed over siliciuret of potassium (formed by heating silica with potassium), placed in a bent tube of Bohemian glass, the extremity of which dipped into a cup of mercury, lying on the bottom of a vessel filled with water. The atmospheric air had been previously expelled from the apparatus by a current of hydrogen. % The gases insoluble in water having been collected, were found, on examination, to be hydrogen and nitrogen, the relative proportions of which varied in different experiments. In two experiments the proportions of hydrogen to ni- trogen were four of the former to one of the latter. In a third experiment, as six of hydrogen to one of nitrogen. In a fourth, as five of hydrogen to four of nitrogen. Observation.—White fumes appeared occasionally in the tube, indicating the presence of muriate of ammonia. Professor Lloyd exhibited a specimen of Rock from Terre Adele. . Professor Mac Cullagh communicated to the Academy a very simple geometrical rule, which gives the solution of the _ problem of total reflexion, for ordinary media and for uni- _ axal crystals. P2 174: First, let the total reflexion take place at the common surface of two ordinary media, as between glass and air, and let it be proposed to determine the incident and reflected vibrations, when the refracted vibration is known, It is to be observed, that the refracted vibration (which is in general elliptical) cannot be arbitrarily assumed; for, as may be inferred from what has been already stated (Proceedings of the Academy, vol. ii. p. 102), it must be always similar to the section of a certain cylinder, the sides of which are perpen- dicular to the plane of incidence, and the base of which is an ellipse lying in that plane and having its major axis per- pendicular to the reflecting surface, the ratio of the major to the minor axis being that of unity to the constant r. The value of 7, as determined by the general rule in p. 101, is 1 bg Papa ! n? sini’ where 7 is the angle of incidence, and z the index of refrac- tion out of the rarer into the denser medium. The ellipse is greatest for a particle at the common surface of the media; and for a particle situated in the rarer medium, at the distance z from that surface, its linear dimensions are pro- Qnrrz portional to the quantity e~ » ; so that for a very small valne of x the refracted vibration becomes insensible. Now, taking any plane section of the aforesaid cylinder to represent the refracted vibration for a particle situated at the common surface of the two media, let op and og be the semiaxes of the section, and let them be drawn, with their proper lengths and directions, from the point of incidence 0; through which point also let two planes be drawn to repre- sent the incident and reflected waves. ‘Then conceive a plane passing through the semiaxis op, and intersecting the two wave-planes, to revolve until it comes into the position where the semiaxis makes equal angles with the two inter- sections; and in this position let the intersections be made the sides of a parallelogram, of which the semiaxis oP is the 175 diagonal. Let 0A and oa’, which are of course equal in length, denote these two sides. Make a similar construction for the other semiaxis 0@, and let os, on’, which are also equal, denote the two sides of the corresponding parallelogram. Then will the incident vibration be represented by the ellipse of which 0A and oB are conjugate semidiameters, and the reflected vi- bration by the ellipse of which oa’ and oB’ are conjugate semi- diameters. And the correspondence of phase in describing the three ellipses will be such that the points , a’, P will be simultaneous positions, as also the points B, B’, a. ! The same construction precisely will answer for the case of total reflexion at the surface of a uniaxal crystal, which is covered with a fluid of greater refractive power than itself. It is to be applied successively to the ordinary and extraordi- nary refracted vibrations, and we thus get the wniradial inci- dent and reflected vibrations, or rather the ellipses which are similar to them. And as any incident vibration may be re- solved into two which shall be similar to the uniradial ones, we can find the reflected vibration which corresponds to it, by compounding the uniradial reflected vibrations. ; It may be well to mention that, in a uniaxal crystal, the plane of the extraordinary refracted vibration is always per- pendicular to the axis, and therefore the ellipse in which the vibration is performed may be easily determined by the re- mark in p. 102. The plane of the ordinary vibration has no fixed position in the crystal; but if we conceive the auxi- liary quantities &, m, 21, (p. 98) to be compounded into an el- lipse (as if they were displacements), the plane of this auxi- liary ellipse will be perpendicular to the axis of the crystal. Whether the preceding very simple construction, for find- ing the incident and reflected vibrations by means of the re- fracted vibration, extends also to the case of biawxal crystals, _ is a point which has not yet been determined, on account of the complicated operations to which the investigation leads, at least when attempted in any way that obviously suggests itself. 176 Joseph Huband Smith, Esq. was elected a Member of the Committee of Antiquities, and Dr. Aquilla Smith was elected Treasurer of the Academy, in the room of Dr, Orpen, re- signed. The following Address was presented on the 13th No- vember to the Lord Lieutenant : “ To His Excellency the Right Hon. Thomas Philip Earl De Grey, Lord Lieutenant-General and General-Governor of Ireland. ‘* May IT PLEASE YOUR EXCELLLENCY, “‘ We, the President and Members of the Royal Irish Academy, have the honour to present to your Excellency our very sincere congratulations on your arrival in our metropo- litan city, as the representative of our most gracious So- vereign. ‘*‘ It has been the pleasure of her Majesty to declare her- self the Patron of the Institution of which we are members ; and, in virtue of the charter which was granted to us by one of her royal predecessors, King George the II., the office of Visitor of the Academy has become vested in your Excel- lency, as Lord Lieutenant of Ireland. ‘* We cannot but think ourselves fortunate in an official connexion with a nobleman who, in his private career, has shown himself so much attached to arts and letters as your Excellency is known to be. “The objects of the Royal Irish Academy are Science, Polite Literature, and Antiquities ; and in the tranquil pursuit of these objects, the importance of which is appreciated by your Excellency, we have had the pleasure of seeing fos- tered within our body those feelings of mutual good-will, which are, perhaps, scarcely less highly to be prized than the pursuit of knowledge itself. (Signed) * WitttaAm Rowan Hamitton, President.” 177 To which His Excellency was pleased to return the follow- ing answer : * Mr. PresipeNtT, AND MemsBers oF THE Roya Irish AcaDEmy, ** T thank you for your congratulations on my arrival in Ireland. ** It is a source of pleasure to me to feel that a part of my public duty, as the Representative of her Majesty, will bring -me into such immediate connexion with the body of scienti- fic and learned gentlemen forming the Royal Irish Academy. ‘* The duties of a visitor lose the austerity of official cha- racter, and merge into those of friendship and association, when the person who is invested with them has the honour of being received with the warmth which has distinguished your reception of myself. ** You are pleased to estimate my fitness and talents be- yond their value; but I can assure you that you cannot attach more importance than I do to the welfare and prosperity of such institutions as yours. As you justly observe, the pur- suit of the objects principally cultivated by the Royal Irish Academy enables you to foster within your body feelings of mutual good-will; and when I see enrolled amongst your members those who conscientiously entertain a difference of opinion upon points ofthe very highest importance, I cannot withhold my conviction of the public utility of a society which affords them a point of union, and holds out to them an ob- ject upon which they can honestly coincide.” DONATIONS. Bericht iiber die zur Bekanntmachung geeigneten Ver- handlungen der Kénigl. Preuss. Akademie der Wissenschaf- ten zu Berlin. VomJuli 1840 bis Juni 1841. Transactions of the Cambridge Philosophical Society. ~ Vol. VII. Part. 2. 178 Astronomische Nachrichten. Nos. 413-432. Magnétisme terrestre. Par M.Quetelet. Extrait du tom. VIII. No. 9, des Bulletins de Academie Royale du Brux- elles. Presented by the Author. Nouveaux Memoires de l Academie Royale des Sciences et Belles-Lettres de Bruxelles. Tome. XIV. Memoires Couronnés par ? Academie Royale des Sciences et Belles-Lettres de Bruxelles. Tome XY. 1 partie 1840-4]. Memoire sur différens Procédes d Integration, par lesquels on obtient l’'attraction d’un ellipsoide homogene dont les trois axes sont inégaux, sur un point extérieur. Par M. J. Plana. Presented by the Author. The Fishes of the Dukhun. By Lieut.-Col. W. H. Sykes, F.R.S. Presented by the Author. Notes on India before the Mahommedan Invasion. By Lieut.-Col. W. H. Sykes, F. R.S. Presented by the Author. Proceedings of the Royal Society. Nos. 44-48. 1840-41. Supplemental Instructions for the Use of the Magnetical Observatories. Presented by the Royal Society. On the Character of Sir John Falstaff. By James O. Hal- liwell, Esq. Presented by the Author. A Plan of Medical Reform and Reorganization of the Pro- fession. By Richard Carmichael, Esq. Presented by the Author. December 13. SIR Wm. R. HAMILTON, LL.D., President, in the Chair. The President read the following letter from the Right Hon. Sir John Newport, Bart., presenting to the Academy a manuscript containing an account of the Loans of Money to King Charles I. eS a | a a we ee Oe ef eo 179 * New Park, *€ 12th November, 1841. * T desire, Sir, to offer for acceptance of the Royal Irish Academy, of which I have, during many years, had the honour of being a member, a volume, which, as it respects a most interesting period of British history, and materially tends to elucidate transactions which had a powerful influ- ence in producing the calamitous results, in the reign of Charles the First, that immediately succeeded, may be deemed not unworthy of admission into the Library of the Institution. ‘* The volume contains correct copies of the orders of the Lords of the Council, and letters addressed to the Lord Lieutenants of the counties of England, and others, directing the assessment and collection of what was called a voluntary loan, according to the annexed lists, from the several land- holders, merchants, and merchant strangers of England, and the citizens of the cities and towns therein, including the judges and law officers, but specially excluding all members of the peerage, ‘ with whom it was not purposed to deal for the present.’ “* The original documents, of which this volume is a tran- script, were found during the period whilst I held the office of Comptroller-General of the Exchequer, amongst a large collection of papers deposited in the Pells Office; and as I considered them to afford interesting materials to elucidate the history of that eventful period, I directed two copies to be made of them; one of these I sent to the British Museum, and now offer the other to the acceptance of the Royal Irish Academy. ** The great inequality of the extent of the demand onthe several parties thus assessed, varying in a great degree with their capacity of resistance to its enforcement, will be quite apparent on examining the lists; as will also the urgency of the measure, from the repetition of the letters from the Lords 180 of the Council, at a short interval of time, deprecating further delay, and censuring what had already occurred. One name in the list of contributors from the town of Cambridge, that of Hobson the carrier, celebrated by some lines of Milton, has, from that circumstance, attracted atten- tion, from the sum demanded and the nature of his occupa- tion. “ The original papers have been injured by damp, and rendered in some degree, but not materially, defective. ‘‘In order to render the papers more accessible for perusal, I have sketched out a table of reference which I enclose, and avail myself of the kindness of my valued friend, the Lord Bishop of Cashel, for their transmission to Dublin. * Tam, Sir, ‘* Your obedient Servant, ‘© Joun NEWPORT. Sir William R. Hamilton, President R. I. Academy, Sc. §e. Fe.” The special thanks of the Academy were voted to Sir J. Newport. A paper was read by William Roberts, Esq., ¥. E.2. Us “on the Rectification of Lemniscates and other Curves.” Let a curve be traced out by the feet of perpendiculars dropped from a fixed origin upon the tangents to a given curve: and from this new curve, let another be derived by a similar construction, and soon. Also let acurve be imagined which is constantly touched by perpendiculars to the radii vectores of the given curve, drawn at the points where it is met by these radii, and from this let another be derived by a similar mode of generation, and so on. Then if s, denote the are of the curve which is x in order in the former series, and s_, that of the n™ in the lat- ter, we shall have ad? dw dw" gla 2 Ae \at ae dea\="a) ds, = + (, =a, rdr, = dw?\t2! dr 2 F (r, w) = 0 being the polar equation of the given curve. It is convenient to distinguish the curves of the two series by calling those of the former positive, and those of the lat- ter negative; we may also generally denote their polar co- ordinates by the symbols 7,,,, 4,: If the given curve, which may be denominated the base of either system, be an ellipse whose centre is the origin, it will be found, by applying the above formula, that the nega- tive curves will in general have their ares expressible by elliptic integrals of the first and second kinds, whose modulus is the eccentricity of the base-ellipse. The arc of the first will involve only a function of the first kind: a result which has been given by Mr. Talbot in a letter addressed to M. Gergonne, and inserted in the Annales des Mathematiques, tom. xiv. p. 380. A function of the third kind, with a circular parameter — 1 + b*, where bd is the semiaxis minor of the ellipse, its semiaxis major being unity, and the modulus of which is the eccentricity, enters into the arcs of all the positive curves ; and their general rectification depends only on that of the ellipse, and of the first derived, both positive and negative. The quadrants of the ellipse, and of the first two curves, positive and negative, are connected by the following rela- tion : (s_; + $i) 8-1 = (38 — 8-2) (2s — Sp). V5—-1 —s 2 It is worthy of notice, that if the eccentricity be the functions of the third kind disappear, and the rectifica- tion of both series depends only on that of the ellipse and of the first negative curve. 182 If the base curve be a hyperbola, whose centre is the origin, the arcs of all the curves of the negative series will depend only on elliptic functions of the first and second kinds. But the general expression for the arc in the positive series contains a function of the third kind, the parameter of which is alternately circular and logarithmic: the curves of an odd order involving the same function of the circular kind, and those of an even order the same of the logarithmic kind, if the real axis of the base-hyperbola be greater than the ima- ginary, and vice versa. Mr. Roberts also shows, that besides the case of the equilateral hyperbola, in which the first positive curve is the lemniscate of Bernouilli, and which has been the only one hitherto noticed, at least as far as he is aware, there are two others, in which the arc of the first positive curve can be ex- pressed by a function of the first kind, with the addition of a circular arc in one case, and of a logarithm in the other. The first of these occurs when the imaginary semiaxis is V5—1 2 equal to (the distance between the centre and focus being unity), and this fraction is the modulus of the function. The other case is furnished by the conjugate hyperbola, and the modulus is complementary. In both these cases func- tions of the third kind disappear from the ares of the positive curves. If the hyperbola be equilateral, and its semiaxis be sup- posed equal to unity, the general equation of the derived curves of both series may be presented under the form 2 | r ‘ = 204 ae Syeogil eo el = = 2n—1 The successive curves represented by this equation are very curiously related to each other. The following property ap- pears worthy of remark : Let Pri, Pns Pn4i be corresponding points on the BO tet, 183 (n—1)", n, and (n+ 1)" curves of the positive series respec- tively, and v their common vertex, which is also that of the hyperbola, then will arc VP,»_; + right line P»_; Pn = arc VPn41 n— 2n +1 Mr. Roberts states that he has demonstrated the property in a manner purely geometrical. This equation shows that the arcs of all the curves of an odd order will depend only on that of Bernouilli’s lemniscate, or the function F § 4, ¢}, and those of an even order only on the are of the second of the series. This latter are is three times the difference between the corresponding hyper- bolic are and the portion of the tangent applied at its extre- mity, which is intercepted between the point of contact and the perpendicular dropped upon it from the centre: and the entire quadrant is three times the difference between the infinite hyperbolic are and its asymptot. Also, Sn, Sni1, denoting the quadrants of the n, and (n+ 1)” curves, the following very remarkable relation exists between them, Sn Snyi — (22+ 1) 52 The curves of the negative series enjoy analogous pro- perties. Lastly, let the base curve be a circle, the origin being within it: and it appears that the rectification of the curves of both series, which are of an even order, can be effected by the ares of circles; and that those ofan odd order, which belong to the positive series, will involve elliptic integrals of the first and second kinds in their arcs. The negative curves _ of an odd order contain a term depending on a function of _ the third kind, which is however reducible to a function of _ the first kind and a logarithm. By the particular consideration of the first negative curve in this case, Mr. Roberts was led to a very simple demon- 184 stration of the equation which results from the application of Lagrange’s celebrated scale of reduction to elliptic functions of the second kind, and which is nothing more than the analytical expression of Landen’s theorem. Professor Mac Cullagh exhibited to the Academy some Roman Denarii, from the collection of Mrs. Alexander of Blackheath (Coleraine). These coins (twenty-eight in number) were found in the year 1831, along with an immense quantity of others of the same kind, weighing altogether about eight pounds, by a labourer who was digging in a field on the Faugh Mountain, near Pleaskin, one of the headlands of the Giant’s Causeway. According to an account published at the time in the Belfast News’ Letter (June, 1831), and communicated to the Academy by the Rev. Dr. Drummond, they were found under a flat stone which was turned up by the spade. Nearly 200 of them (says this account) were sold for a trifling sum to an English gentleman at Coleraine, and some of the remainder were bought by the Rev. R. Alexander. Of the twenty-eight coins that were exhibited, only seventeen have their legends legible, and these are of the times of the emperors, from Vespasian to the Antonines. ‘The following list of them has been supplied by Dr. Aquilla Smith, with references to the catalogue of the University Cabinet, pub- lished by the Rev. J. Malet, F.T.C.D. 1. Vespasian, . . . Malet, 384. 2. Vespasian, . . . Reverse, a winged Caduceus. 3. Domitian, . . . Malet, 452. 4. Domitian, . . . Reverse, Minerva. 5. Nerva, . . . . Malet, 467. eeteoe Malet, 513. 8. Trajan, . . . . Reverse, Minerva. 9. Trajan, . . . . Reverse, a Female seated. —_ i) . Madan, .. . . Malet, 548. 185 1}. Hadrian, . . . Malet, 552, 12. Antoninus Pius, . Malet, 615. 13. Antoninus Pius, . Malet, 621. 14, "Antoninus Pius, . Malet, 623. 15. Antoninus Pius, Re. a Female holding a Cornucopia. 16. Faustina the Elder, Malet, 670. 17. Faustinathe Younger, Malet, 723. Dr. Smith remarks, that the coin of Hadrian, No. 11, is interesting, as having on the reverse a star and crescent, resembling those on the Jrish coins of King John. The Rev. Dr. Drummond then gave an account of other Roman coins that had been found in Ireland; and in some preliminary observations he dwelt on the utility of preserving a knowledge even of such an insulated fact as the discovery of a coin, for though of little importance in itself, it might prompt to farther research, and lead both the historian and antiquary to consequences which could scarcely have been anticipated. In England, almost every year is bringing to light various monuments of Roman antiquity, but in Ireland they are ex- ceedingly rare; though, perhaps, of more frequent occurrence than is generally known. Ancient coins and other articles have been repeatedly found by persons ignorant of their real value, and sold as mere metal by their weight, without re- gard to their age and character. Thus, we read in Mason’s Parochial Survey, that in the parish of Dunaghy were found a number of silver coins, which were sold at Ballymena be- fore any one had an opportunity of examining or describing them. Again, the Rev. Alexander Ross informs us, that a person on whose veracity he could depend, assured him, _ that about thirty years prior to the time of his writing, two or three men, in digging an old fort near Cashel, found an _ earthen pot, which might contain four or five quarts, filled with gold coins of different sizes (Par. Survey, II. p. 304). 186 The same writer states that “a fine copper coin of the Em- peror Nero was found some years ago, and is now in Mr. A. Ogilby’s collection, the head finely relieved, and in perfect preservation.” In the collection of the Royal Dublin Society are three Roman copper coins of the Cesars, dug up in Fer- managh, and presented by Sir C. Coote. But the most cu- rious fact in connexion with the coins exhibited by Mr. Mac Cullagh, is that of a Roman gold coin being found many years previous, nearly in the same locality. The Rev. Robert Trail, in his statistical account of Ballintoy (Mason’s Par. Survey), says, “within these few days a gold coin of Valen- tinian was brought to me in perfect preservation, and is now in my custody. It is about the size of half a guinea, and on the head side is the following inscription D. N. VALENTI- NIANUS, P. F. AUG. On the reverse RESTITUTOR REIPUBLICE. As Valentinian succeeded Jovian in 364, and died in 375, this money must have been struck during that period, but how it came into this parish I cannot conjecture.” —(II. p. 155). A single coin might be accidentally dropped and lost by some collector or virtuoso, on his tour to the Giant’s Cause- way ; but we cannot account in this way for a large collection of coins of ancient date. ‘They must have been placed where they were found, by some careful hand, probably in times of turbulence and danger, as in a place of safety, whence they might be removed at a more favourable season. A few years ago, G. Putland, Esq., of Bray, had occasion to build piers for a gate contiguous to the sea-beach, on the north side of Bray Head. His workmen, on digging for a foundation, were surprised to meet with the skeletons of se- veral human bodies, which, on farther examination, they found to be placed, not confusedly heaped together, as the slain on a battle field, but in graves placed regularly side by side, and separated each from its neighbour, by thin partitions of flag or of stone. On the exposure to the air, j 187 the bones crumbled to atoms; the teeth alone were more durable, and in tolerable preservation.* The most remarka- ble circumstance connected with these skeletons was a num- ber of Roman copper coins, one or two of which lay on or beside the breast of each. Of these coins, which were about the size of our penny pieces, some bore the image and super- scription of Adrian, and others those of Trajan, in clear and distinct relief. Several were greatly corroded, and rendered altogether illegible. A few of the best of these coins were for a short time in Dr. Drummond’s possession, He shewed them to the late lamented Dean of St. Patrick’s, who said that he had seen a coin precisely similar, which was found in the island of Lambay. As the Romans never formed any settlement in Ireland, the question naturally arises, how came these coins to be placed in this locality, and under such circumstances? The ready reply is, that the bodies here interred were probably those of mariners, the crew of some Roman galley that had been stranded and lost on the shores of Bray, and that some of the survivors who had escaped, performed the funeral rites. Among the Romans it was deemed an act of great im- _ piety to leave a corpse unburied; and hence Horace intro- _ duces the shade of the drowned Archytas, imploring the _ passer by to sprinkle a little dust on his body, which had _ been cast on the shores of Tarentum. Palinurus, in Virgil, _ makes a similar request. The coins, it is presumed, were the fee designed for the grim ferryman; a part of the funeral rites of the greatest im- portance, and by no means to be neglected, for the shades of those who had not the proper fee, as well as of those whose * Sir William Hamilton, in a paper in the Archzologia (vol. iv. p.161), observes that the teeth of some skeletons of soldiers, found at Pompeii, were remarkably ; ‘sound. “ Perhaps,” says he, “among the ancients, who did not use sugar, they “might not be so subject to decay as ours.” VOL. Il. Q 188 bodies remained unburied, were condemned to wander a hundred years on the banks of the Styx. Thus may we account for the Roman coins found at Bray; but how shall we account for those dug up at Fermanagh, or discovered at Dungiven, Ballintoy, and the neighbourhood of the Giants’ Causeway ? Though the Romans never had any permanent station in Ireland, they were well acquainted with its geographical po- sition, its passages, and its harbours, as we learn from the unquestionable testimony of Tacitus; and though this and other testimonies were wanting, it might be fairly presumed that the Roman fleets which encompassed Great Britain, sailed beyond the Orkneys, and boasted that they had ar- rived at the Ultima Thule, could not be ignorant of Ireland and its coasts, though not induced by the spirit of commerce or adventure. The mariners would sometimes be tempted to land, if not to repair their shattered vessels, to procure wood, water, and provisions. Tacitus informs us that Agricola obtained information concerning the state of Ireland, from one of its chiefs, who, for disatfection or rebellion, had been driven into exile, and sought refuge from the Roman commander. It is to be la- mented that our native Irish historians, as far as the writer has been able to ascertain, are completely dark on this sub- ject. Though an eminent Irish scholar, profoundly versed in our ancient MSS.,can produce one passage—but it is the only one he ever met with—which seems to countenance the idea that the Romans had subjected any sept of the Irish to their yoke. He states that in discussing the means bywhich Conor Mac Nesa, King of Ulster, and cotemporary with Christ, discovered the crucifixion of the Saviour, a writer, in an old Irish MS., in the library of T.C.D., says that “he learned it from the Druid Bachrach, or from Altus the Consul, who came from Octavin to ask the tribute from the Gaels.” 189 Roman coins might find their way to Ireland in the com- mon intercourse of trade. They may have been brought by the early Christian missionaries, or by men who fled hither, as to an asylum, from persecution. It is universally admit- ted, says Lanigan, that there were Christian congregations in Ireland before the mission of Palladius in 431, though it is impossible to determine who first introduced Christianity.— It is reasonably conjectured, that during the persecution of Diocletian and Maximian, the only one recorded as having extended to Britain, some Christians, and particularly those _ of the clerical order, sought refuge in Ireland ; and it is a fair presumption that they would bring with them such articles as were most precious and most easily carried, among which © coins and jewels are the chief. There is yet another mode of accounting for these remains of antiquity, not less plausible. The early Irish, like the neighbouring nations, were fond of making predatory excursions. They often landed on the shores of England and Wales, and carried off whatever spoil fell into their hands. They also assisted their friends, the Albanian Scots, whose country they colonized under Carbre Riada, in their wars with the Romans, and may have sometimes returned enriched with treasure, obtained by the sword. Of the spoils, by which they were sometimes enriched, it may suffice to mention an instance, extracted from O’Fla- herty’s Ogygia. Crimthan Nianair, the 111th Monarch of Ireland, towards the end of the first century, returned from a “ foreign expedition, in which he obtained a very rich booty; among which was a golden chariot ; a pair of tables, studded with 300 brilliant gems; a quilt, of va- rious colours; a cloak, interwoven with threads of gold; a sword, engraved with various figures of serpents, which were of the purest gold; a shield, embossed with refulgent silver studs; a spear, which always gave an incurable wound; a sling, so unerring, that it never missed ; two hounds coupled Q2 190 with a chain, which, being made of silver, was worth 500 cows, with other valuable rarities.”—Ogygia, II. pp. 182-183. The same author informs us that about the middle of the third century, Cormac, the 126th Monarch of Ireland, ‘equipped a large fleet, which he sent to the North of Britain, where he was committing depredations for three years.”—p. 208. He also states, on the authority of Ammianus Marcellinus and Claudian, that the Saxons, in conjunction with our coun- trymen the Scots and Picts, made frequent excursions to Britain a long time before they made settlements in that country. Ammianus, he says, writes that ‘ the Scots (i.e. the Trish) and Picts, not only invaded those places in Britain that were adjacent to the Roman boundaries, but that in the first year of the Emperor Valentinian, A.D. 364, acombined army ofthe Picts, Saxons, Scots, and Attacots, reduced the Britains to the utmost distress.” Hence, he concludes, there was a common league between them, with intermarriages and com- mercial intercourse. According to Dr. Drummond, when we consider the va- rious modes in which Roman coins may have found their way into Ireland, the wonder perbaps should be, not that so many, but that so few, have been discovered. The Rev. G. Sidney Smith, D.D., M.R.I. A., read “an Account of some Characters found on Stones on the top of Knockmany Hill, county Tyrone.” On the top of Knockmany bill, in the parish of Clogher, and demesne of the Rev. Francis Gervais, there are some interesting remains of ancient times. Besides two moats, one internal to the other, there is an ancient chamber or kyst- vaen, consisting of upright flag-stones, about six feet high. It includes a space fourteen feet long by seven wide. Its po- sition with respect to the moats is represented in the ground plan, fig. 1. The stones marked by a darker shade are 191 standing, and those in dotted lines have been thrown down. On five of the stones characters are found, which seemed to be well worth copying, which I have accordingly done, and represented them in the accompanying figures. The most remarkable of these characters occur on the stone marked No. 1, inthe ground plan. Those represented in fig. 2, are on the lower part of the stone, and those in fig. 3, on the up- per; there may have been other intermediate characters, but they are effaced. The spiral in fig. 2, is about nine inches in diameter, and that in fig. 3, about twelve inches. Fig. 4 represents the characters on stone No. 2, and fig. 6, those on No. 5, on the same scale as in figs. 2 and 3; and fig. 5 _ represents the stones marked 3 and 4, which are six feet high. It will be observed that in the spirals and other marks, there 3 is some resemblance to the New Grange characters, and in fig. 4, we have a close approach to the Ogham. The copies were made with great pains, and are I believe exact in the small details, On the difficult subject of these ancient characters little _can be done until a greater mass of facts shall have been col- lected ; and hitherto few have been observed in the North of Ireland. Mr.Windele and other zealous antiquarians have prosecuted the subject in Munster with great zeal and suc- cess, Mr.S. Ferguson exhibited some gold beads found in the county of Donegal. January 10. Rev. HUMPHREY LLOYD, D.D., Vice-President, in the Chair. : William Andrews, Esq., John Thomas Banks, Esq., Robert 3ateson, Esq., John Burrowes, Esq., Rev. Samuel Butcher, Fe. T. C. D., Fleetwood Churchill, M.D., Alexander Clendin- 192 ning, Esq., Rev. Reginald Courtenay, Durham Dunlop, Esq., Alexander Ferrier, Esq., Wrigley Grimshaw, M. D., Wil- liam Hogan, Esq., William John Hughes, Esq.,and William Roberts, Esq., F.T. C. D., were elected members of the Academy, REso.tvepD,—-On the recommendation of Council,—‘ That henceforth, at every annual election of officers, the President for the expiring year be considered as eligible to any one of the Committees of Council.” Mr. Ball, referring to his paper read before the Academy in November, 1839, relative to a Loligo, to which he gave the specific name of Eblane, exhibited the following Aceta- buliferous Cephalopoda, with the view of showing the increased knowledge of species of the Irish seas, and of placing on re- cord the very interesting discovery of two of the genus Rossia, which he had reason to believe had not before been noticed. He then exhibited specimens of 1. Sepia officinalis. Dublin bay. 2. Sepia Rupellaria.? A dorsal plate, being one of three specimens found by G. Hyndman, Esq., at Magilligan. See Ferussac and D’Orbigny’s Cephalopoda, plate 3 of Sepia. 3. Loligo vulgaris. Dublin, &c. 4. Loligo sagittata. Leith. Obtained by W. Baiting Ksq., of Belfast. 5. Loligo sagittata, var.? This was in the former pa- per considered as a variety, but on comparison with the true sagittata, No. 3, it seems to be a distinct species. It was obtained by G. Allman, Esq., on the coast of Cork. 6. Loligo subulata, var.? Was obtained by John Montgo- mery, Esq-, of Locust Lodge, on the coast ofthe County Down. 7. Loligo subulata, var. No. 2. Somewhat shorter than No. 5. Youghal, 1832. 8. Loligo media. Youghal, 1819, 193 9. Loligo media, var. - It approaches the form of sagit- tata in the termination of its visceral sac. 10. LoligoEblane. Ofthe former paper. Obtained byT.W. Warren, Esq., in 1836; and other specimens of greater beauty and larger size obtained in the bays of Belfast and Dublin by W. Thompson, Esq., and Mr. Ball. As it now appears that the animal possesses both eyelids and a lacrymal sinus, cha- racters not ascribed to the genus Loligo, it may require to be placed in another genus. 11. Eledone ventricosa. Youghal, 1820, and Dublin. A very fine specimen was found by Mrs. Lyle at Kingstown. 12. Octopus vulgaris. Plymouth, 1841. Mr. Ball. 13. Sepiola Rondeletii. Youghal, 1819. Dublin, 1829. Mr. Ball. 14. Rossia Owenii. Was obtained in 1839 by Mr. Ball, from a fishwoman who had found it ina Dublin bay fishing boat. It is remarkable for the great size and distinctness of its acetabula, which are placed on long peduncles, and may be compared to the pearls in a diadem: they are ranged in three rows, those of the centre row being not more than half the diamater of those on each side; on the first pair of arms the acetabula are more numerous, more equal in size, and smaller than onthe others. The specific name has been given in honour of R. Owen, Esq., the founder of the genus Rossia. 15. Rossia Jacobii. Was obtained from the same woman as the foregoing, in 1840, by A. Jacob, Esq:, M.D., who kindly sent it to Mr. Ball. It is much larger, but differs considerably in its proportions from Rossia Owenii; its ace- tabula are smaller; its arms proportionably shorter; the membrane round the mouth forms a hexagonal figure, from each angle of which a ridge runs, which is decurrent in six cases ; on the second, third, and fourth pair of arms, and in the seventh the ridge passes upon the web between the first pair of arms, where it bifurcates, and runs out on each side. ‘Its specific name is given in honour of Dr. Jacob, from 194 whom Mr. Ball has in many instances received valuable aid in zoological pursuits. The fins of both these species of Ros- sie are like in form and position to those of Sepiola Ronde- letii. 16. Spirula australis. Shell found at Youghal, 1820. The following are the Measurements of the Rossice in Inches : Length of body, . Breadth over fins,. Length of fin, .. Extreme breadth, Breadth between eyes, . Extreme breadth of head, Length of head, Length of tentaculz, , Portion of tentaculz occupied by veered bula, . Pay eS ee Length of first pair of arms, counting from’ top, of head...) <) 4+ sieacnse Ditto, second ditto, ditto, Ditto, third ditto, ditto, Ditto, fourth ditto, ditto, Depth of fin between first pair of arms, Ditto, first and second do. Ditto, second and third do. Ditto, third and fourth do. Ditto, fourth do. Rossia Owenii. ie 2°0 0-7 0:45 0-9 Te | 0°5 4-0 09 2:1 24 2-7 2:3 0-2 0:3 0-42 0-4 0-04 Rossia Jacobii. 21 27 15 0-7 1-2 1-4 0-7 a7 ~ Led 2:2 23 26 24 0-4: 0°5 0°6 0°8 0:03 William Roberts, Esq., F.T.C.D., read a paper on a class of spherical curves, the arcs of which represent the three species of elliptic transcendents. A cone of the second order, whose vertex is upon the surface of a sphere, and one of whose principal axes is a diameter, will intersect the sphere along a curve which ad- ee eee ——e 195 mits of several varieties, according to the nature of the sec- tions of the cone parallel to its principal planes, and the position of its internal axis. This curve may be made to furnish, by means of its arc, a geometrical representation of the three species of elliptic trancendents, including the two cases of the third. In the course of the investigations alluded to, Mr. Roberts was also led to consider two species of the curve called the spherical conic, which appear to possess many remarkable analogies to the properties of the equilateral hyperbola. These cases occur when the axis minor is a quadrant, and when the semi-axes a and b are connected by the relation sina = tan b. The following extract of a letter from Andrew Dur- ham, Esq., to the Marquess of Downshire, was read to the | Academy by Sir William Betham, with his Lordship’s per- mission : ** Belvedere, Lisburn, ** 29th December, 1841. “My Lorp, ** As your Lordship and party were prevented from at tending the interesting search at Drumboe Tower, I beg to inform your Lordship that about seven feet below where we commenced excavating, we found a skeleton, én situ, lying by compass N. W. by W., wanting both legs and feet from the knees, and also the right arm. The earth we removed was of a blackish colour, as if composed of decomposed vege- table matter, full of stones, many of which, from the mortar on them, must have fallen from the top and the entrance, which is about five feet from the external level; and on the eastern side, it also abounded in bones of different animals, and a few bones seemingly of black cattle. Under this earth _ we came to a surface of mortar; this induced us to proceed still more cautiously ; and immediately under this mortar we 196 first discovered the skull, in good preservation, together with the teeth ; we then laid bare the whole body, a work of no little difficulty, from the wetness and adhesiveness of the soil. We were much inclined to leave the body as we found it, but were obliged to raise it to continue our search. We excava- ted to the very foundation of the Tower, without finding any- thing else, with the exception of many pieces of charcoal. The skull was lying on the right side, and the dorsal and cer- vical vertebree were considerably decomposed. “* The diameter of the Tower inside is nine feet. The skeleton was not placed exactly in the centre, but the head was so near the side that there would have been room suffi- cient for the body with its legs and feet, had it been placed in the centre. The mystery seems increased by the want of the arm. None of the bones found had been acted on by fire. “« There was no flag-stone, nor floor either above or below the body. The layer of mortar seems intended as a substi- tute for a floor. «« There were several jawbones, apparently pigs’, from the size of the tusks; but no skulls, with the exception of one of a bird. ** The external circumference of the Tower is fifty-one feet ; the wall being four feet thick. ** T believe I have mentioned every thing of importance; I leave others to draw conclusions.” Sir W. Betham stated that he considered this tower had been opened before, and that the skeleton was then dislocated. The propensity of searching for treasure may have led to the violation of this tomb, asit had to that ofothers, as Cashel, from which the bones had all been removed; but at Ardmore and Cloyne the skeletons were found really in situ; the floor of mor- tar, both above and below, being perfect. The Tower of Aber- nethy in Scotland has also been examined with the same re- sults as at Ardmore and Cloyne. The stones, with mortar attached to them, found in Drumboe, were certainly part of 197 the concrete course of mortar covering the earth in which the body reposed, which was broken up by the violaters of the tomb. A notice of the occurrence of a Metallic Alloy in an un- usual state of aggregation and molecular arrangement, was read by Robert Mallet, Esq., M.R. I. A. Amongst the several classes of substances which chemistry at present considers as simple, the metals stand preeminently marked by their almost invariable possession of a nearly fixed and striking group of sensible qualities, which together con- stitute the well known “ metallic character.” Some of these, such as lustre and fusibility, are common to every metallic body; but by the occasional variation of nearly every other sensible quality of the metals, the law of continuity remains unbroken, which unites them in different directions with the other classes of material bodies. Thus opacity, which is pro- bably mechanically destroyed in gold leaf, is lost in selenium; and so, in this most prevalent of their properties, the metals, through tellurium, selenium and sulphur, become translucent, and mingle with the nonmetallicelements. Soalso their solidity, at common temperature, is lost in mercury; their great den- sity, in sodium and potassium ; their malleability, in bismuth, antimony, and arsenic; while in tellurium, the power to con- duct electricity is nearly wanting ; and, lastly, hydrogen, “to all intents a metal in its chemical relations, yet possesses not a single physical quality in common with these, but exists as an invisible and scarcely ponderable gas. But although different metals thus vary in sensible quali- ties, those which collectively belong to the same individual metal are as remarkable for their permanence. Unless selenium be admitted to be a metal, no approach to dimorphism has hitherto been recognized in any body of the class ; the only case recorded, that by Dufresnoy, of the occurrence of cast iron in cubes and rhomboids, not having 198 been given by him with certainty, nor since verified by other observers. Hence any instance of such acharacter, or tendency towards it,is worthy of attentive consideration ; andit was with this view that the author brought before the Academy the following notice of the occurrence of an alloy of copper, in two states, having totally different sensible and physical qualities, while identical in chemical constitution. The alloy in question, in its original or normal condition, was in fact a species of brass; and the particular specimen presented to the Academy was a portion of one of the brass bearings, or beds, in which the principal shaft of a large steam engine re- volved. The bearing, or bed of a shaft (as is generally known), consists of a hollow cylinder, generally of brass, divided in two by a plane passing through the axis ; its inner surface is finely polished, and sustains the shaft, during its revolution, which is also polished; the cavity of the brass being com- pletely filled by the shaft, which, in the present instance, was of cast iron, and about nine inches in diameter. It frequently happens, notwithstanding the polish of both metallic surfaces, and the application of oil, that the friction due to their rapid passage over each other, while exposed to undue or irregular pressure, produces a considerable rise of temperature, and the brass becomes abraded. Its particles have no coherence, and much resemble the ‘* bronze powder” used by painters. In an instance, however, which some time since came under the author’s notice, a different result took place. The minute particles of abraded brass were by the motion of the shaft, during a few hours, impacted into a cavity, at the junc- tion of the two semicylinders of the bearing, where they be- came again a coherent mass, and when removed presented all the external appearance of an ingot or piece of brass, which had been poured in a state of fusion into the cavity. On more minute examination, however, the mass was found to 199 differ much in properties from the original brass, out of which it was formed. The mass or ingot of brass, thus formed by the union of particles at a temperature which had never reached that of boiling water, and a fragment of which was presented, pos- sessed on that side which had been in contact with the shaft, a bright polished metallic surface, like that of the original metal from which it had been formed: its other surfaces bore the impress of the cavity in which it was found. It was hard, coherent, and could be filed or polished like ordinary brass. It was, however, perfectly brittle; and when broken, the frac- ture, in place of possessing asub-crystalline structure, and me- tallic lustre, like that of the normal brass or alloy, was nearly black, and ofa fine grained earthy character, and without any trace of metallic lustre or appearance. Examined with a lens, some very minute pores or cavities are found throughout its substance, which is uniformly of a very dark brown or nearly black colour, and devoid of all me- tallic character, except when cut or filed—that is, in mine- ralogical language, its colour is earthy black, and its streak metallic. The author remarked that the observed cases of aggrega- tion in solid particles, without the intervention either ofa sol- vent or of fusion, are extremely rare, and as bearing upon the little understood subject of cohesive attraction, are of much interest. The property of welding, which is possessed by all bodies, whether metallic or not, which pass through an intermediate stage of softness or pastyness previous to fusion, and is not found in any substance which readily crystallizes, and hence passes ‘‘ per saltum” from the solid to the liquid state by heat, forms a “ frontier instance” of cohesive forces, being enabled to act in the aggregation of bodies, by only an approach to liquidity, or by a very small degree of intermo- bility. 200 Aggregation may also take place between portions of a body merely softened by a solvent, which is afterwards with- drawn, as in the familiar instance of Indian Rubber, softened by naptha for the manufacture of waterproof cloths; where the former, after being moulded or united in any way re- quired, is left in its pristine condition by the evaporation of the naptha from amongst its particles. But the cases of aggregation of solids, without such elevation of temperature, or the presence of solvents, are so rare, that but two or three have as yet been observed. Of these the most remarkable is that recorded by Pouillet, of the gradual, but complete, adhesion of surfaces of clean plate-glass, when left to re- pose on each other for a considerable time. It has also been stated, that clean plates of lead or of tin, if pressed together by a considerable force when cold, require a proportionably great force to separate them. The case presented to the Academy, therefore, is another added to these rare instances of molecular aggregation in solids, independent of solution or fusion: the author therefore thought it worth while to examine with a little care the properties both of the original brass, and of the mass thus curiously formed from it, or, as he thenceforth called them, of the normal and the anomalous alloy. The normal alloy is of a bright gold colour, and sub-erysial- line in structure, and of great toughness; its cohesive force is equal to 21.8 tons per square inch, which is above the average strength of any of the alloys of copper and zinc, or copper and tin, as found by my experiments on the cohesive power of these alloys, published in the Proceedings of the Academy, and elsewhere. The cohesive force of the anomalous alloy is only 1.43 tons per square inch, or only about one-fifteenth that of the former. The specific gravity of the normal alloy is = 8.600; that of the anomalous only = 7.581. — 201 On submitting both alloys to analysis, their constitution proved identical; it is as follows: Copper. . . . . . 83,523 ree SEPA @.838s Pe gs Sr O1O Rene Tee ON, rhe Se OL0RA Bigse SePh poe oge Sip HOI 100.000 Uniting the small amount of lead with the tin, and dividing by the atomic weights, the nearest approach to atomic con- stitution is, Copper 4 26.3 atoms. Zine = 2.3 Tin in 1.5 These alloys have therefore not a strictly definite constitution, but one more nearly so than is usually found in commerce. Both alloys are equally good conductors of electricity. The author examined their relative powers of conducting heat by the method which Despretz has employed with so much accuracy, and found that of the normal to that of the anoma- lous alloy as 86: 35, numbers which are so nearly equal as to render it likely the difference is only error of experiment. He also endeavoured to determine their relative specific heats, using the method of mixture, which was the only one which the small size of the metals permitted, and eliminating the errors incident to this mode by first plunging the alloy hot into cold water, and then cold into hot water. In this way, if w and ¢ = the weight and temperature of the water, m and ¢’ = the weight and temperature of the metallic alloy, m,... . = the mean temperature of both, _s.... = the specific heat of the alloy, there are two values, one where the metal is the hotter, 202 _w(m—?t). ~ M (t/—m)’ and another where the water is the hotter body, w (t — m) St (m — t’) the mean of which is the specific heat of the alloy pretty exactly. The result gave the specific heat of the normal alloy = .0879, water as unity, and that of the anomalous alloy = .0848; both of which are below the specific heat as- signed by Dalton to brass. The normal alloy is malleable, flexible, ductile, and la- minable. In the anomalous alloy there is an absolute negation of all these properties. The normal alloy readily amalgamates with mercury, at common temperatures; the anomalous alloy will not amalga- mate with mercury even at 400° Fahr. When the anomalous alloy is heated to incipient redness in a glass tube, a minute trace of water, and of a burned or- ganic substance, probably adherent oil, are discoverable; it suffers no change, however, but a slight increase of density. The normal alloy suffers no change when so treated. The normal alloy, treated on charcoal with the blow-pipe, fuses at once into a bead. On treating the anomalous alloy so, the fragment swells rapidly to more than twice its original bulk, on becoming bright red hot; it then glows, or becomes spontaneously incandescent, in the way that hydrated oxide of chrome and some others do, and instantly contracts to less than its original bulk, and becomes a fluid bead, which, on cooling, differs in no respect from the original alloy. The anomalous alloy, when pulverized in an agate mor- tar, forms a black powder, devoid of all appearance of a metal; its filings also are quite black; while those of the normal alloy, produced by the same file, possess the usual metallic lustre. These facts, in connexion with the black 203 colour and fine earthy appearance of the fracture, bring to mind the case recorded by Sir David Brewster, of a piece of smoky quartz, the fracture of which was absolutely black, and yet was quite transparent to transmitted light, and whose blackness, he found, arose from the surfaces of fracture, consisting of a fine down of short and slen- der filaments of transparent and colourless quartz, the dia- meter of which was so small (not exceeding the one-third of the millionth part of an inch), that they were incapable of reflecting a single ray of the strongest light. In describing this, Sir David Brewster predicted, that ** fractures of quartz and other minerals would yet be found which should exhibit a fine down of different colours depending on their size.” It seems, therefore, extremely probable, that the cause of the near approach to blackness in the fracture and filings of this alloy, arises from the excessive minuteness of its parti- cles, and thus fulfils the foregoing prediction; the brownish tinge being produced by the reflexion of a little red light.* The polish and power of reflecting light of the anomalous alloy are not quite so great as those of the normal, but are still remarkable ; and, as it seemed a matter of some interest to determine whether both reflected the same quantity or in- tensity of light at equal angles, the author endeavoured to ascertain this point as respects heat, by means of Melloni’s pile for the galvanometrical determination of temperature, assuming, as suggested to him by Professor Mac Cullagh, that what would be true of heat in this respect, would also be so of light; but from the small size of the reflecting surfaces he had at his command, he found it impossible to arrive at ————— CS bce ete italia ‘ * Since this paper was read, Professor Lloyd suggested to the author, the ana- logy between the appearance of the powder and filings of the anomalous alloy and Platina Mohr, and those powders obtained by reduction of other metals by hydro- gen. None of these, however, are coherent, which constitutes the peculiarity in _ the present case. VOL, II. R 204 any trustworthy result. He is, however, inclined to believe, that both metals reflect most at a perpendicular incidence. From the foregoing detail of the properties, in several respects so different, of this substance in its normal and ano- malous states, the author thinks he is warranted in pro- nouncing it the first observed instance of an approach to dimorphism in a metallic alloy; and one, the mode of pro- duction and characteristics of which present several points of interest. The conditions under which the alloy was aggregated, involved extremely minute division of the metal, great pres- sure in forcing the divided particles into contact, and nearly the exclusion of air. Considerable electrical disturbance may have also co-operated; such, together with induced mag- netism, being the constant accompaniments of motion in heavy machinery. By re-establishing these conditions, under suitable arrangements, the author hopes to repeat the re- sults thus accidentally first obtained, and so produce possibly dimorphous states of other metals or their definite combina- tions. There is but one body which occurred to the author, presenting an analogy to this anomalous alloy, namely, indigo ; whose fracture, it is well known, is fine earthy, and of the usual blue colour, but becomes coppery, or assumes the me- tallic lustre on being rubbed or burnished. DONATIONS. Uber den Galvanismus gegen ortliche Krankheiten, von Dr. Gustav Crusell. Recueil des Acts de la Seance Publique de l Académie Im- periale des Sciences de St.Petersbourg, tenue le 29 Decembre, 1840. Memoires de ! Academie Imperiale des Sciences de St. Petersbourg. 6"° Série. Sciences Politiques, §c. TomelV. Livraison 6, and Tome V. Livraisons 1-4. 205 Sciences Mathematiques, §c. TomelV. Premiere par- tie, Livraisons 5° et 6°; Tome VI. Seconde partie, Livraisons 1-5. Proceedings of the Committee of Commerce and Agricul- ture of Royal Asiatic Society, 1841. Journal of the Royal Asiatic Society. No. 12. Prelection on the Studies connected with the School of Engineering in Trinity College, Dublin. By the Rev, Hum- phrey Lloyd, D.D. Presented by the Author. The Chronicle of William de Rishanger. By Richard O. Halliwell, Esq., Hon. M.R.I.A., &c. Presented by the Editor. Ordnance Survey of Wexford, in eighty-six sheets. Pre- sented by the Lord Lieutenant. Sketch of the Loan Fund System in Ireland. By Charles Piesse, Esq. Presented by the Author. Catalogue of the Miscellaneous Literature in the Library of the Royal Society. (1841). Proceedings of the Royal Society, 1841. Nos. 46-50. Supplemental Instructions for the use of Magnetical Ob- servatories. 1841. Phil. Transactions for 1841. Parts 1 and 2. Edinburgh Astronomical Observations. Vol. 1V: 1838. Memoires de l’ Académie Royale des Sciences de l'Institut _ de France. Tome XII. 4 Memoires présentés par divers savans a 0 Academie des Sciences Mathematiques et Physiques. Tome IV. The American Almanack for 1842. amit O Resend ¢ a " s . , ity md 4 ay + yeh ietise’ iS se £ 4G a, . f feet 4 - etil¢g Ris} wt ; Sea : } 4 " a : !! sORME Tra we EO sar A ret. 4: te wert af sna oe snaghe. herweaiae ‘ 3) PROCEEDINGS OF THE ROYAL IRISH ACADEMY. 1842. No. 33. January 24. Rrv. HUMPHREY LLOYD, D. D., Vice-President, in the Chair. Resotvep,—On the recommendation of Council,—That it shall be the duty of the Committee of Publication to report on Papers intended for publication in the Transactions. Reso.tvep,—On the recommendation of Council,—That the Treasurer be authorized to sell stock of the Academy to the amount of £300, for payment of the Printer’s bill and other arrears. The Rev. Charles Graves, F. T.C. D., read a paper “on ~ the Motion of a Point upon the Surface of a Sphere.” When the motion of a material point is limited to a given plane, the circumstances of its motion are commonly investi- gated by means of the equations, xd? = d’x, ydl? = d’y, # and y being rectangular coordinates in the given plane. Mr. Graves shows that, in like manner, the motion of a ma- terial point, constrained to move on the surface of a sphere, whose radius = 1, may be discussed by means of the similar equations, VOL, I. s 208 xit =d( Sa) (1) vd? = a(—_9 = a (2) in which x and y are used to denote the rectangular spheri- cal coordinates of the moving point (vid. page 127), and x, y, the moments, in the planes of the a and y arcs of reference, of the resultant of the forces acting upon the point. The re- action of the surface being taken into account, this resultant is tangential to the sphere, and so may be conceived to act along a great circle passing through the point. From equations (1) and (2) we derive a third, es o_ 7 ( yau — xdy ) (xy —ya) dt? =d ee ig (3) which leads to important consequences. It appears from the second formula in p. 129 that, if the equations (1) (2) and (3) be multiplied respectively by 2Qdzx 2dy ae 2(ydu—ady) l+a2°+y” l+a2?+y” 1a? +y’ they will give for the velocity, v, of the moving point, eee zdy)| anit x (ady— —yda)] _ (4) l+2°+y7/ / Now, if the resultant tangential force r act always along a great circle which passes through the origin, that is, if we consider the case analogous to that of a central force in the dynamics of the plane, +P and y = ai Set "@ 5 “@ yy) +y’)" In this case, therefore, which for simplicity we may call that of a central force, equation (3) gives ydx—axdy _ l+a°?+y? hat, (9) and equation (4) is reduced to 209 ot xdz + xdy _ 4 6 ara rar ee (6) It is easy to show that these two latter equations are equiva- lent to the two following, sin*pdw = hdt, (7) 2hrdp = 0’, (8) in which p is the vector arc drawn from the origin to the moving point, and w is the angle between it and the « arc of reference. Let us now describe the circle of the sphere which osculates the trajectory along which the point ep moves, and let c be the arc of the great circle passing through P and the origin, and intercepted within the osculating circle; then it may be shown that ee v ~ tand.c- (9) R If p denote the arc of the great circle drawn from the origin perpendicular to the arc touching the trajectory at Pp, we may deduce from (7) that 2 “fe hes (10) ~ sin? p” By the help of equation (9) it may be proved that “A material point may be made to describe a spherical conic if it be urged by a force, acting along the arc of a great circle drawn from the focus to the point, and varying inversely as the square of the sine of the vector arc p.” Also: ** A material point may be made to describe a _ spherical conic by the agency of a force, acting along the are _ of a great circle drawn from the centre to the point, and vary- ing as tanp sec’p.” In the dynamics of a point constrained to move on the surface of a sphere, we have, for the discussion of the inverse problem of central forces, the following equation, s2 210 R = A?(L +47) («+ 55), in which x is the cotangent of p. The analogy between the formulz given in this paper and those usually employed in discussing the motion of a point on a plane is very striking. The former too become identical with the latter when the portion of the sphere on which the trajectory is described becomes infinitely small in comparison with the radius. The Rev. H. Lloyd V. P. read the following paper “ ona New Magnetical Instrument, for the Measurement of the In- clination, and its Changes.” In order to know all that relates to the earth’s magnetic force, at a given place, observation must furnish the values of three elements. Those which naturally present themselves for immediate determination are, the intensity of the force itself, and the two angles (the declination and inclination) which determine its direction. We may substitute for these, however, any other system of elements which are connected with them by known relations. Thus, we have hitherto pre- ferred to observe the declination, and the two components (horizontal and vertical) of ihe intensity; and, in general, the main considerations which should guide us in our choice are, the exactness of the observed results, and the facility of their determination. In this point of view, the declination and the horizontal component of the intensity leave us nothing to desire, their determination being now reduced to a degree of precision, hardly (if at all) inferior to that of astronomical measure- ments. The same thing, however, cannot be said respecting the third element, as hitherto observed. In the Dublin Magnetical Observatory, and in the Observatories since es- tablished by order of the Government and of the East India Company upon the same plan, the third element chosen for i Be 211 observation has been the vertical component of the intensity, the instrument for the measurement of which has been al- ready submitted to the notice of the Academy. The prin- ciple of this instrument, it will he remembered, is to balance the vertical component of the magnetic force by a fixed weight, and to observe the changes of the position of equili- brium, under the action of the changing force. Unexcep- tionable as this principle is in theory, the accuracy of the results has not been commensurate with that of the other two instruments. This inferiority is to be traced to the large influence which the unavoidable errors of workman- ship must necessarily have on the position of equilibrium of a magnet supported on a fixed axle. It has been shown that the effect of magnetizing a bar, under the most advantageous circumstances of form, and at the part of the globe where the vertical component of the magnetic force is greatest, is the same (as to its position of equilibrium) as if its centre of gravity had been transferred about the 2;th of an inch to- wards the north end; so that the moment of the force, exerted by the vertical component of the earth’s magne- tism, can never exceed this small quantity multiplied by the weight of the bar. Now, in order to render the results of this instrument comparable to those of the horizontal-force magnetometer, it should enable us to measure changes of the vertical force, amounting to the >54 ‘soodth part of the whole; i. e. we have to measure effects, such as would be produced by shifting the centre of gravity through the one- millionth of an inch. It will be easily understood, from this Statement, how great must be the effect of a minute distur- bance of the relative parts of the instrument, or of inequalities in the bearing points of the axle; and experience has ac- cordingly shown that it is altogether unavailable for the de- _ termination of changes of long period. The same difficulties, and from the same source, have been found to attach to the usual method of observing the 212 magnetic inclination, and its changes, however refined the construction of the instrument. The sources of error seem, in fact, to be inherent in every direct process of determining the third element; and it is only by an indirect method that we can hope to evade them.* Of this character is the method now proposed. If a soft iron bar, perfectly devoid of magnetic polarity, be held in a vertical position, it immediately becomes a tem- porary magnet under the inducing action of the earth’s mag- netic force, the lower extremity becoming a north pole, and the upper a south pole. Accordingly, if a freely-suspended horizontal magnet, whose dimensions are small in comparison with those of the bar, be situated near, ina plane passing through one of these poles, it will be deflected from the magnetic meridian. The deflecting force is the induced force of the bar, which may be regarded as proportional to the energy of the inducing cause, i. e. to the vertical compo- nent of the earth’s force; while the counteracting force is the horizontal component of the same force, acting directly on the magnet itself, to bring it back to the magnetic meri- dian. Thus the magnet will take up a position of equili- brium, under the action of these opposing forces; and this position will serve to determine the ratio which subsists be- tween them. When the right line connecting the centre of the horizontal magnet, and the acting pole of the bar, is perpendicular to the magnetic meridian, the tangent of the angle of deflection will measure the ratio of the two forces, and will therefore be proportional to the tangent of the mag- netic inclination. Accordingly, by observing the changes of * Two such indirect methods of determining the inclination haye been pro- posed in Germany, one by Professors Gauss and Weber, the other by Dr. Sar- torius von Walterhausen. That now suggested bears a close analogy, in principle, to the former of these: it differs from it, however, not only in the means em- ployed, but also in the end in view,—the main object of the present method being the determination of the inclination-changes. 213 position of the horizontal magnet, so circumstanced, we can infer those of the inclination itself. But the iron bar may have (and generally will have) a certain portion of permanent magnetism, which will concur with the induced magnetism in producing the deflection ; and it becomes necessary to institute the observations in such a manner, as to be able to eliminate the effects of this extraneous cause. For this purpose we have only to invert the bar, so that the acting pole, which was uppermost in one part of the observation, shall be lowermost in the other. The induced polarity will, under these circumstances, be opposite in the two cases; and the acting force will in one case be the sum of the induced and permanent forces, and in the other their difference. Let x and y denote the horizontal and vertical compo- nents of the earth’s magnetic force, m the intensity of the permanent magnetism in the acting pole, and m the magnetic moment of the suspended magnet. The intensity of the in- duced magnetism is, by hypothesis, equal to ky,’ k being an unknown constant; and when this is of the same name as the permanent magnetism, the intensity of the act- ing force, at the unit of distance, is ~ ky + M. Accordingly, the moment of this force to turn the suspended magnet is (ky + m) mrcosu, u being the angle of deflection, and r a constant depending on the distance; or, making, for abridgment, kr = p, mr = q, (py +) mcosu. But this deflecting force is resisted by the earth’s horizontal force, the moment of which to turn the magnet is Xm SiN u ; 214 and the magnet will rest when these moments are equal. Hence the equation of equilibrium is pY + q=xtanw. (1) By the same reasoning it will appear, that when the induced and permanent magnetisms are of contrary names, there is pY —g=xtanv; (2) in which w’ is the new angle of deflection when the bar is inverted. And adding these equations together, and ob- serving that y = x tan 9, @ being the inclination, we have 2p tan@ = tanw + tanw’. (3) This equation would furnish at once the inclination sought, provided we knew the value of the constant £. In order to determine it, we have only to place the iron bar horizon- tally in the magnetic meridian, its acting pole remaining in the same place as before, but pointing alternately to the north and south. The inducing force is, in this case, the hor?- zontal component of the earth’s magnetic force; and it will be readily seen that the equations of equilibrium are similar to (1) and (2), substituting x for y. If therefore v and v’ denote the angles of deflection in these positions, we have 2p = tanv + tanv’; (4) and dividing (3) by this, tan w + tan w’ tanv + tan’ (5) Thus, from the deflections produced in these four positions of the bar, we obtain the inclination. In order to determine the changes of the inclination, it is tan @ = not necessary to observe the deflections in the horizontal po- sition of the bar. Let equation (1) be differentiated, x, y, and w being all variable, and let the resulting equation be divided by (3). We thus obtain the following equation, from which p and g are both eliminated : a a 215 AF 2. 2Au 2tanu Ax Y cos’u(tanu-+tanw) ~ tanuw+tanu’” x” But from the relation y = x tan@, we have Y x sin @ cos 0’ and substituting, Ad cosu/Au sin (wu — wu’) Ax ey tok hed ee Ripe. poewen a A-a), atn ac) x (6) The second term of the right-hand member of this equation contains a correction required for the simultaneous changes of the horizontal intensity ; but this correction will be gene- rally small, and, when the bar has no permanent magnetism, will vanish altogether. In this latter case, in fact, it appears from (1) and (2) that uw’ = uw; so that the preceding equation is reduced to tt sin 20 NA (7) ‘= Qu We must remember that the angle wu in the preceding formule, being the deviation of the suspended magnet from the position which it would assume under the action of the earth alone, its changes are the differences between the ob- served changes of position of the suspended magnet, and the corresponding changes of declination. Let a denote the de- viation of the suspended magnet, measured from some faced line, and a’ the corresponding angle when the iron bar is temoved; then u-a—a’, Au = Aa— Aad’. _ But Aa = kn, Ad’ = k’n’; in which x denotes the number of divisions of the scale of the instrument corresponding to the angle Aa, n’ the number corresponding to the angle Aa’, as shown by the declinometer, and & and &’ the arc-values of a single division in each instrument. Hence Au = kn— k’n’. (8) 216 I now proceed to the construction of the apparatus em- ployed in these measurements. The magnet is cylindrical; its length is three inches, and diameter one-fourth of an inch. A mirror is attached to the stirrup by which it is suspended, by means of which the varying position of the magnet may be observed with a telescope at a distance, after the method of Gauss. ‘This mirror is of course vertical; and it has a motion round a ver- tical axis, by means of which it may be adjusted to any de- sired position of the observing telescope. The mirror is circular, and is three-fourths of an inch in diameter. The moveable part of the stirrup to which it is attached has the form of a cross; and it is rendered vertical by means of three screws, near the extremities of three of the arms of the cross, the heads of which project and hold it. The mirror is maintained in contact with these heads by springs at the back. The box is octagonal; the interval between the opposite sides is four inches, and that between the top and bottom twoinches. The top and bottom, and the connecting pillars, are formed of gun-metal; the eight sides are closed by moveable pieces, three of which are of glass, and the rest of ebony. ‘To the top of the box is attached an upright tube of glass, eight inches in length, which encloses the suspen- sion thread. The suspension apparatus at the top of the tube is of the usual construction; the circular piece to which it is attached has a movement of rotation, and its outer sur- face is graduated to 5°, for the purpose of determining the effect of torsion of the suspension thread. The base of the instrument is a circle of gun-metal, six inches in diameter, graduated on the edge. ‘The box is connected with this circle by a short conical stem, forming the axis of a second plate, which revolves upon the fixed one. This moveable plate carries two verniers, by which the angle of rotation may be read off to minutes. Two 217 tubular arms, slightly inclined to one another, are attached to this plate ; and their other extremities are connected by a cross-piece, which carries a short scale at a distance of eighteen inches from the mirror. This part of the apparatus is employed in determining the total angles of deflection. The soft iron bar is a cylinder, twelve inches long, and three-fourths of an inch in diameter. One of its extremities is enclosed in a hollow cylinder of brass, connected with a horizontal pivot which revolves in a fixed socket. The axis of this pivot being in the line passing through the centre of the suspended magnet, and perpendicular to the magnetic meridian, it is obvious that the bar has a movement of rota- tion in the plane of the magnetic meridian itself. The dis- tance of the axis of the bar from the centre of the magnet is about five inches; and it is so placed that the induced pole is in the direction of the axis of the pivot, and thus remains fixed during the movement of the bar. The changes of position of the suspended magnet are observed at a distance by means of a fixed telescope and scale. The scale, whose divisions are reflected by the mir- ror, is attached above the telescope to the support near the eye-end. Dr. Fulton made some observations on Grecian and Ro- man Architecture. February 14. SIR Wa. R. HAMILTON, LL.D., President, in the Chair. Captain Stirling, 73rd Regt., Rev. Thomas Stack, F.T.C.D., Joseph Nelson, Esq., Q.C., and Rev. Robert Chatto, were elected members of the Academy. Dr. Anster read a paper, by the Rev. J. Wills, upon Mr. Stewart’s attempt to explain certain processes of the 218 Human Understanding, on the supposition that it acquires, by habit, an acceleration in the succession of ideas, so great as to escape the consciousness. After having observed that Mr. Stewart’s error consisted, not in his reasoning, but in having failed to observe that his facts are themselves complex results which demand a minute analysis, and having also dwelt upon some elementary errors to which he mainly attributed the entire of Mr. Stewart's the- ory, the author proceeded to a detailed investigation of the several examples brought forward in its support. He first stated the case of a player on the harpsichord, whose rapidity of execution is adduced to illustrate the pro- position that so many separate acts of will and attention, as it seems to involve, are so accelerated as to take place without any consciousness of their separate occurrence. On this he observed, that, to a very great extent, the separate acts assumed could have no existence, by reason of the absolute coincidence, in point of time, of the rapid and complex move- ment of the musician’s hand; from which he inferred, that some other law must be sought for to explain the phenomena. To discover this law, the author proceeded to examine the process of the mind in the acquisition of the art by which the complex and simultaneous movements are effected. These are, he observed, first separately attended to and separately executed; but so long as this separateness continues, it is evident that the required result is not attained. Slowly, however, and by frequent repetition of the same set of ideas presented in combination, this combination itself becomes the object of perception; and from being separate ideas and movements, they become simultaneous, and assume the new form of a single complex conception, executed by a complex movement. In confirmation of this inference, he observed, that the slightest attempt to attend to any of the component parts would disconcert the best skill. He also observed, that Mr. Stewart had been in some degree misled by having —_— 219 generally fixed his attention on examples in which the com- ponent ideas are successive in the order of occurrence. He observed upon a considerable class of cases which are deci- sive against Mr. Stewart, being composed of very complex acts, of which the separate parts are never recognized, such as the class of movements called ‘‘ mechanical.” The author next entered on a detailed view of Mr. Stewart’s example of a person reading, and showed that the same reasoning is applicable. He noticed the complica- tion of trains of thought, which, according to Mr. Stewart’s theory, must be simultaneously proceeding; and alsoobserved, that his theory could not stop short at any point of these; and that wherever he might attempt to stop, an explanation should be given, which ought to supersede his whole theory. He then pursued the inquiry as in the previous example, by investigating the mind’s progress in learning to read, and de- duced similar conclusions. These he also confirmed, by noticing the various errors which occur in reading and print- ing; of these he showed, that they illustrate the effect of the combinations or complex conceptions previously formed to supply even the want of many of the component parts; so that the letter is inferred from the general form of the sylla- ble, and the syllable from that of the word, rather than the contrary process. From this example he concluded, that the mind, by repeated acts of attention, acquires a stock of syl- labic and vocal associations, of which the act of reading is a combined result; that by a further extension, written sen- tences may become combined with a process of thought, and that every reader possesses some range of thought thus symbolized by habit; and finally, that the general inference to be drawn from this and other similar examples is, that by means of habit, groups of signs, of movements, facts, thoughts, sensations or phenomena, may acquire varied relations to each other; and that these being acquired, the combination alone becomes the object of notice. He then pursued the applica- 220 tion of the same reasoning to some other examples, not no- ticed by Mr. Stewart, which he observed were better adapted for illustration ; and then proceeded to notice briefly the ap- plication of the same principles to the other examples adduced by Mr. Stewart. He then reverted to an explanation of Mr. Stewart’s and of other writers, concerning the perception of the distance of visible objects; and after noticing the fallacy which it in- volved, he showed it to be explicable by the same general process as in the former cases. He next observed that the numerous errors arising from the same law of habit might be made use of to illustrate or prove the same conclusions ; and explained, at some length, the illusion of faces and other visual phenomena framed by the imagination. After several observations on the comparative difficulties of Mr. Stewart’s method and his own, the author noticed the distinction between the previous cases, in which there is an apparent character of combination, and others in which a difficulty must seem to arise from continuity. He then went at considerable length to apply the same reasoning to the case of the orator, as adduced by Mr. Stewart, and more fully de- scribed by Lord Brougham. He lastly adverted to Mr. Stewart's explanation of dreams, and showed that it involved some important contradictions and inconsistencies ; and that, contrary to Mr. Stewart’s assertion, it implies a new law of mind. He then showed that it could be explained by the same method which he had already applied to the other ex- amples. And after some explanations of the manner in which the law of suggestion operated in dreams, he observed, in conclusion, that Mr. Stewart had set out with a notion adapted to lead him astray ; which he thought to be a subject of re- gret, as the line of investigation which he had selected would otherwise have offered a clearer and better evidenced founda- 221 tion for metaphysical science than any which had been pre- viously adopted. DONATIONS. Catalogue of the Works of Art in the Possession of Sir Peter P. Rubens, atthe Time of his Decease. Presented by Dawson Turner, Esq. Ueber die Himjaritische Sprache und Schrift. Von Dr. W. Gesenius. Presented by the Author. A Descriptive Vocabulary of the Language of the Abo- rigines of Western Australia. By G. Fletcher Moore, Esq. Presented by the Author. Magnetische und M eteorologische Beobachtungen xu Prag. Vom 1 Juli 1839, bis 31 Juli 1840. By Karl Kreil. Pre- sented by the Author. Proceedings of the American Philosophical Society. Vol. II. No. 19. A Record of the Case of Mary Jobson. By W. R. Clanny, M.D., &c. Presented by the Author. February 28. Rev. HUMPHREY LLOYD, D. D., Vice-President, in the Chair. Dr. Evory Kennedy read a paper on the peculiar Sys- tem of Generation, and Habits, observed by him to prevail in certain Acephalocysts, parasitical animals inhabiting the human body, and belonging to the class of hydatid entozoa. Having considered their animal nature, and their primary formation, as involving the question of spontaneous genera- tion, he described generally the methods of reproduction adopted in this class of animals, and adduced the explana- tions and opinions offered by the best authorities on the 222 subject, but particularly those of Bremner, Lannec, and Owen, by which acephalocystic reproduction is referred to imperfect ovation or generation. Dr. Kennedy went on to show that the uterine hydatid or hydrometra hydatica of Wiesmantel, which should more correctly be termed the “ Acephalocystis Hysterobiaveluterina,” multiplies by fisstpa- rous generation, and that the creatures still continue adherent to, or connected with each other by filiform bands or elon- gations of the strictured parts of their bodies. Dr. Kennedy exhibited several preparations and drawings in which this mode of reproduction by subdivision was perceptible in dif- ferent stages of progress, and having alluded to an imperfect division, observed also to occur in infusorial animalcules, re- commended that the system of reproduction which he de- scribed should be termed “ fissiparo-coherent.” A paper “ on the colouring Matters of the Persian Berries” was read by Dr. Kane. These berries, the fruit of the dyer’s buckthorn, Rhamnus Tinctoria, are imported from the Levant, and from the south of France, for the use of dyers, to whom they furnish a yel- low colour of great brilliancy, though not so permanent as some others. The appearance of the berries, as found in commerce, varies considerably ; some samples, and those the most valuable, being larger, fuller, and of a light greenish olive colour, whilst others are smaller, as if shrivelled, and dark brown in tint. The former Dr. Kane considers to have the appearance of being gathered before complete ripening, whilst the latter owe their altered character to being allowed to remain longer on the stem, or to having been incautiously dried. The colouring matter in these two kinds is essentially different. The unripe berries yield but little colour to pure water, and when digested in ether give abundance of a rich - = 223 golden yellow substance, to which Dr. Kane has given the name of chrysorhamnine. The dark coloured berries contain little of the substance soluble in ether, but give out to boil- ing water an olive yellow material, to which, in its pure form, Dr. Kane gives the name of xanthorhamnine. This sub- stance is produced, however, only by the decomposition of the former; thus, if the unripe berries be boiled for a few minutes in water, they, when dried, yield to ether scarcely traces of chrysorhamnine, this principle being, by contact of air and hot water, changed into xanthorhamnine. Omitting the details of methods of purification, and of analysis, the properties and composition of these bodies may be expressed as follows : Chrysorhamnine is of a rich golden yellow colour, of a crystalline aspect, and may be obtained in brilliant stellated tufts of short silky needles. It is but very sparingly soluble in cold water, and when boiled with water the portion which dissolves does not separate on cooling, but is found to be changed into xanthorhamnine. It dissolves in alcohol, but is not obtained by its evaporation, without being much al- tered. In ether, however, it dissolves abundantly, and by _ the spontaneous evaporation of its solution is deposited in a pure form. It has no acid reaction, but dissolves in alkaline solutions, in which, however, it appears also to be mostly altered. Dried at 212° Fahr. it consisted of I. Il. Carbon)! 38-40) "4 ° 68,23 57.81 Hydrogen . . . 4.77 4,64 Oxygen’. 95°") 6° 37.00 © °°37.65 100.00 100.00 OO Oe ee LS ee ‘ ” ese numbers give the formula C,; H,, O,, by which there VOL, Il. y C,, = 188 58.23 Hye 4.64: O, = 88 37.13 237 100.00 On adding an alcoholic solution of chrysorhamnine to a solution of acetate of lead, a rich yellow precipitate is formed, which, when dried at 212°, was found to be expressed by the formula C,; Hj, On + 2 PbO, the numbers being as follow : Theory. Experiment. Carbon. g...¢10138.0° \.29.98).. ni -gteeeeee Hydrogen ..”. FEO BDO in oi) Sek ene Oxygen... (60> 0 288.0, 219.11): .- ees Oxide oflead. . 223.4 48.52 . . . 48.60 460.4 100.00 100.00 A little water appears to have been lost in the analysis, which, however, does not affect the formula deduced. By the decomposition of a more basic acetate of lead, a yellow precipitate is obtained, which consisted of one equi- valent of chrysorhamnine united to three equivalents of oxide of lead. The chrysorhamnine may be easily observed in its na- tural state of deposition in the berry; it lines the interior of the capsule-cells, with a brilliant resinous-looking pale yel- low, and semitransparent coating. Xanthorhamnine is formed by boiling chrysorhamnine in water, in a capsule, so as to admit of free access of air. It dissolves with an olive, yellow colour, and on evaporating to dryness, remains as a dark, extractive looking mass, quite in- soluble in ether, but abundantly soluble in alcohol and water. It may be procured also from the berries, without previous separation of the chrysorhamnine, by similar treatment, but it is then rendered impure by a gummy substance being pi 2S te cae 225 mixed with it. It is very difficult to determine when this substance can be considered anhydrous. Prepared by eva- poration over sulphuric acid in vacuo, it is quite dry, and may be powdered, but if heated it liquefies below 212°, and continues giving out watery vapour until the temperature is raised to 350°, beyond which the organic matter itself cannot be heated without decomposition. On cooling it reassumes its perfectly dry aspect, and may be easily powdered. It was hence analyzed in all these stages of desiccation, __ with the following results. It contained : Dried in vacuo. Formula deduced. Carbon ..°. . 934.74 Cog S138 34.78 Hydrogen . . . 6.93 ss Q7 6.80 Oxygen . . . - 58.33 Dw ., =. 282 5842 100.00 397 100.00 Dried at 212°. Formula deduced. Carbon. . 49.97 51.20 Ce oe as Lae 50.92 Hydrogen. 5.18 5.28 a 13 4.80 Oxygen . 44.85 43.52 Ong =. BD. aS 100.00 100.00 271 100.00 Dried in an oil bath at 320°. Formula deduced. Carbon . . =. - 52.55 Cop: ASB. 5B.67 Hydrogen . . . 5.15 Bg: 12 4.58 Oxygen... .- 42.30 Ow) 3 212 42.75 100.00 262 100.00 By adding a solution of xanthorhamnine to solutions of acetate of lead, two combinations may be formed, one by neutral acetate of lead, the other by using the tribasic salt. But it is difficult to obtain either unmixed with some traces _ of the other, and thence the analysis of both vary a little from the true atomic constitution. Thus the tribasic salt gives . 4 -° T 2 226 i Dried at 212°. Formula deduced. Carbon . . 26.58 Co rez 645.0 26.93 Hydrogen . 2.86 Heeatelbn 2.93 Oxygen. . 25.97 Oj n=: 438) 26.54 Oxide of lead 45.36 44.59 2.PbO) =., 2284 43.60 100.00 512.4 100.00 The tribasic salt gives Dried at 212°, Formula deduced. Carbon . . 21.89 22.07 Cho 1. 18680 21.20 Hydrogen . 3.06 2.82 By ass) AS 2.76 Oxygen . 23.75 23.73 O» = . 160.0 24.57 Oxide of lead 52.30 51.38 3 PbO= | 335.1 51.47 100.00 100.00 651.1 100.00 If we consider the xanthorhamnine, as dried in the oil- bath, to be then anhydrous, the bodies analyzed become Xanthorhamnine, dry = C.; Hy Oy. do. dried at 212°. = Cy, Hy Oi, + Aq. do. dried in vacuo = C23 Hy, Oi, + 15 Aq. Ist lead salt, C3 Hy O14 4 a PbO oe 3 Aq. 2nd lead salt, C2; Hy, O1, + 3 PhO +6 Ag. The xanthorhamnine is thus formed by the addition of one equivalent of water and two of oxygen to the chry- sorhamnine, as C,, H,,O,, + HO + O, = C.3H},.0O.4. And if we were to consider the substance dried in the oil-bath at 320° still to retain an atom of water, it should be simply oxidated chrysorhamnine, being, when dry, C.; Hy, On + 20. The Rev. H. Lloyd, V. P., read a supplement to a former communication “on a New Magnetical Instrument, for the measurement of the Inclination and its Changes.” — -* 227 Having, on a former occasion, explained the principle of this instrument, and given the details of its construction, it re- mains only that I should now describe the observations made for the purpose of testing its performance. I shall pass over for the present those which relate to the absolute inclination, because they have yielded results which can be regarded only as approximations to the truth, and I have not succeeded as yet in tracing the errors to their source. It is manifest, how- ever, that an instrument may be a good differential instru- ment, while it is incapable of yielding absolute results ; and there are special reasons why this should be the case with the apparatus now under consideration. Accordingly its failure in the latter respect, even though established, would furnish no ground for despairing of its success in the former. It is obvious that the apparatus is wholly free from the sources of error already noticed, belonging to magnetical in- struments moving on a fixed axle; and the only doubt of its performance must relate to the changes of induced mag- netism in the iron bar. Thus it might be questioned, before trial, whether such a bar receives in all cases an amount of free magnetism proportional to the inducing force ;—whe- ther, again, the minutest changes in the latter are accompa- nied by corresponding changes in the former ;—and whether, lastly, the changes thus produced are instantaneous, or, at least, demand no appreciable time for their development. In the first experiments which I made, for the purpose of determining these questions, the induced magnetism of the iron bar was altered by means of a permanent magnet, placed in the same right line with the bar, and at a known distance from it. The effect produced upon the position of the sus- pended magnet being observed, the distance was altered by a known amount, and a new observation taken; and so on, at many different distances. ‘Then, the law of action of the inducing magnet being known, we may calculate the changes _of deflection of the suspended magnet, on the supposition 228 that the changes of the induced force of the bar are propor- tional to those of the inducing action, and then compare them with the changes of deflection observed. The calculated and observed results of many series of observations, taken in this manner, were found to accord as nearly as the accuracy of the observations themselves allowed. In making this comparison, however, it is necessary to take into account the effect of the direct action of the fixed magnet upon the suspended one. The axis of the former magnet being not far from the vertical passing through the centre of the latter, its action upon it and upon the iron bar follow, nearly, the same law; so that its direct effects upon the position of the suspended magnet are, very nearly, pro- portional to those which it produces through the medium of the induced force of the bar. On this principle the ob- served results may be cleared, approximately, of those parts of the changes which are foreign to the question. Still it must be admitted that such a complication of the results tends to weaken their evidence; and it was therefore de- sirable to obtain further proof, in a manner less exception- able. The object being to alter the inducing action according to a known law, and to observe the changes of the induced force, as shown by the position of the suspended magnet, it is manifest that it may be attained by simply varying the angle which the iron bar makes with the direction of the earth’s magnetic force, the distance of its pole from the sus- pended magnet remaining unchanged. In fact, it will be seen, by pursuing the same reasoning as before, that if rR denote the total force of the earth, and y the angle which the bar makes with its direction, the equation of equilibrium of the suspended magnet is pReos) + q=Xtanu; the line connecting the pole of the bar with the centre of the ; 4 i - 4 | 229 suspended magnet being, as before, perpendicular to the magnetic meridian. Hence, if the bar be devoid of perma- nent magnetism (or g=0), andif the forces rR and x remain unchanged during the experiments, we have tanw = acosy, a being a constant. In order to observe whether the deflections of the sus- pended magnet obeyed this law, a small divided circle was attached to the piece upon which the iron bar moved, in such a manner that the axis of the pivot passed through its centre. The circle being fixed, and the bar connected with the moveable arm carrying the vernier, we have the means of determining the angle through which it is moved. The plane of the motion coinciding with the magnetic meridian, the inclination of the bar to the vertical was altered by 5° between the successive observations of the position of the suspended magnet. The following Tables contain the re- sults of two such series of observations. The first column of each gives the inclination of the bar to the vertical; the se- cond, its inclination (~) to the direction of the magnetic force, i. e. the former angle increased by the complement of the magnetic inclination (19° 10’). The third column con- tains the observed readings of the scale, corresponding to the positions of the suspended magnet ; the fourth, the dif- ferences between each of these readings and the reading belonging to the vertical position of the bar, converted into angular measure ; the fifth, the actual deflections; the sixth, the calculated deflections, as deduced by the formula given above; and the seventh, the differences. In order to derive the numbers of the fifth column from those of the fourth, it is necessary to know the deflection cor- responding to the vertical position of the bar. This angle is determined by placing the bar vertically, with its acting pole above and below successively, and noting the readings of the horizontal circle, when the same division of the move- 230 able scale, reflected by the mirror, was brought to coincide with the fixed wire of the telescope. The differences be- tween each of these readings, and the similar reading when the bar is removed, are double the deflections corresponding to the two positions of the bar; and, when they are nearly equal, the mean of these deflections may be taken as that due to the induced force. FIRST OBSERVATION, Acting end of bar asouth pole, reading = 14° 8’, deflection = 17° 0” 99 north pole, : 82 5l, Z ald Bar removed, . 48 ;..7,.- mean +=A701t ser ‘ | Inclination Reading Angular | . to vertical. Cf of Seale | Differenese: ibaa: Calculated. cr + 14° 30’) 33° 407 2:2 |—1956/.2 1501478 | 4-8 1501 45) +073 +10 0; 29 10 13-2 |—1 124/15 58-6/15 57-2) 4+ 1-4 + 5 0} 24 10 23-1 let 330/16 38-:0)16 37-8) + 0-2 0 0; 19 10 31-4 0-0;17 11-0 — 5 0/1410 | 375/14 943/17 353117 3671 — 14 —10 0} 910 42:38 |4+ 45-4/17 564/17 547) + 1-7 —13 30} 540 | 45-8 \+ 973/18 83/18 27) +. 56 SECOND OBSERVATION. Acting end of bar asouth pole, reading = 14° 23’, deflection = 16°36’ e north pole, ‘ 82 15, a = by 20 Bar removed, . 47 35, mean = 16 58 Inclination yp. Reading} Angular | u Z Difference. to vertical. of Scale.|Differences. Observed. u Calculated. — + 15° 0’ 34° 10’ 2-6 |— 2°1%8 14° 56-2) 14°57"8| — 16 +10 0 29 10 | 144 |—1 148 15 48-2/15 45:0} — 1-8 + 5 0; 24 10 | 248 |— 83-4 16 24-6| 16 25-2] — 0-6 0 0; 19 10 | 332 0.0 16 58-0 17 25:1|17 23:3) + 1-8 — 5 4 14 10 | 40:0 |4 27-1) In the preceding observations a telescope of low power was employed, and the arc-value of a single division of the ~ CES ay Pe 231 scale: (which was at the distance of eighteen inches from the» mirror) was 5’.98. The differences of the observed and calculated results, therefore, do not in general exceed the amount which may be fairly ascribed to errors of observa- tion; and the accordance is sufficient to establish the fact, that the changes of the induced force of the bar are, within the observed limits, proportional to those of the inducing action. It is important to observe also that the changes of the induced force, produced artificially in these experiments, are much greater than any which are likely to arise from the variations of the vertical component of the earth’s magnetic force, and therefore that the experiments may be regarded as severe tests of the performance of the instrument. The preceding observations further showed, that the changes in the inducing force were instantly followed by their effects upon the suspended magnet; so that the changes of induced force required no appreciable time for their develop- ment. It remained only to ascertain, in a somewhat fuller manner, how far the bar was susceptible of minute magnetic changes, from very small variations of the acting force. For this purpose, a series of readings of the scale was taken, the inclination of the bar to the vertical being altered by half a degree between the consecutive readings. ‘The mean diffe- rence of the successive readings was found to agree, very exactly, with the calculated difference; while the partial dif- _ ferences deviated from the mean by an amount not exceeding the limits of error of observation. It may be presumed there- fore, that the changes of the induced force in the iron bar are continuous; and, accordingly, that the sensibility of the instrument is only limited by the optical power, which is ap- plied to observe the changes of position of the suspended magnet.* In the experiments above described, the arc-value * Against this conclusion is the fact, that considerable changes in the induced force of the bar seem to be attended with some permanent changes of polarity ; and it may be presumed that the same thing will take place, in a proportionate 232 of the divisions of the scale was 3/.98; with the modifications since introduced into the reading part of the apparatus, the scale divisions have nearly the same value as in the instrument for the measurement of the declination, so that the readings may be made with certainty to less than the tenth of a minute. The present value of the inclination in Dublin is about 70° 50’; and the mean deflection produced by the iron bar in its actual position being about 19°, it follows from (7) that the changes of inclination are inferred with the same degree of precision, very nearly, as the observed changes of angle. The last test to which the instrument was subjected, was, to employ it for some time in the regular observation of in- clination changes, for which it is destined; and to ascertain how far the mean results of the observations of successive weeks agreed in exhibiting the law of the diurnal variation. The instrument was accordingly observed for five successive weeks, every second hour during the day and night, and the means calculated, omitting those days in which the series was broken by changes of adjustment during experiment. The curves now laid before the Academy represent the pro- jected results of the observations of each of these weeks, together with that of the mean ofthe whole. An inspection of them is sufficient to show that the curves of the separate weeks accord with one another, and with the mean, as nearly as can be expected in the results of such limited series, the discordances being only such as are due to the known irre- gularities in the direction of the earth’s magnetic force. A communication from the President was read, contain- ing some remarks supplementary to the account which he had given at a former meeting, of his Researches respecting Fluctuating Funetions, (see Proceedings, June 22nd, 1840). degree, with the minute changes induced by the variations of the earth’s force. It. remains for future examination to determine how far such permanent changes, if they occur, may impair the accuracy of the results. 233 The following general observations are extracted, on the nature and history of this branch of analysis :— Lagrange appears to have been the first who was led (in connexion with the celebrated problem of vibrating cords) to assign, as the result of a species of interpolation, an expres- sion for an arbitrary function, continuous or discontinuous in form, between any finite limits, by a series of sines of multi- ples, in which the coefficients are definite integrals. Analo- gous expressions, for a particular class of rational and inte- gral functions, were derived by Daniel Bernouilli, through successive integrations, from the results of certain trigono- metric summations, which he had characterized in a former memoir as being incongruously true. No further step of im- portance towards the improvement of this theory seems to have been made, till Fourier, in his researches on Heat, was led to the discovery of his well known theorem, by which any arbitrary function of any real variable is expressed, between finite or infinite limits, by a double definite integral. Poisson and Cauchy have treated the same subject since, and en- riched it with new views and applications ; and through the labours of these and, perhaps, of other writers, the theory of the development or transformation of arbitrary functions, through functions of determined forms, has become one of the most important and interesting departments of modern algebra. It must, however, be owned that some obscurity seems — still to hang over the subject, and that a further examination of its principles may not be useless or unnecessary. The very existence of such transformations as in this theory are sought for and obtained, appears at first sight paradoxical ; it is difficult at first to conceive the possibility of expressing a perfectly arbitrary function through any series of sines or cosines; the variable being thus made the subject of known _ and determined operations, whereas it had offered itself _ originally as the subject of operations unknown and undeter- 25-4 mined. And even after this first feeling of paradox is re- moved, or relieved, by the consideration that the number of the operations of known form is infinite, and that the opera- tion of arbitrary form reappears in another part of the ex- pression, as performed on an auxiliary variable; it still requires attentive consideration to see clearly how it is pos- sible that none of the values of this new variable should have any influence on the final result, except those which are extremely nearly equal to the variable originally proposed. This latter difficulty has not, perhaps, been removed to the complete satisfaction of those who desire to examine the question with all the diligence its importance deserves, by any of the published works upon the subject, A conviction, doubtless, may be attained, that the results are true, but something is, perhaps, felt to be still wanting for the full rigour of mathematical demonstration. Such has, at least, been the impression left on the mind of the present writer, after an attentive study of the reasonings usually employed, respecting the transformations of arbitrary functions. Poisson, for example, in treating this subject, sets out, most commonly, with a series of cosines of multiple ares ; and because the sum is generally indeterminate, when continued to infinity, he alters the series by multiplying each term by the corresponding power of an auxiliary quantity which he assumes to be less than unity, in order that its powers may diminish, and at last vanish ; but, in order that the new series may tend indefinitely to coincide with the old one, he con- ceives, after effecting its summation, that the auxiliary quan- tity tends to become unity. The limit thus obtained is generally zero, but becomes on the contrary infinite when the are and its multiples vanish; from which it is inferred by Poisson, that if this are be the difference of two variables, an original and an auxiliary, and if the series be multiplied by any arbitrary function of the latter variable, and integrated with respect thereto, the effect of all the values of that ; | — ry me 8s teense! 235 variable will disappear from the result, except the effect of those which are extremely nearly equal to the variable origi- nally proposed. Poisson has made, with consummate skill, a great number _ of applications of this method; yet it appears to present, on close consideration, some difficulties of the kind above alluded to. In fact, the introduction of the system of factors, which __ tend to vanish before the integration, as their indices increase, _ but tend to unity, after the integration, for all finite values of _ those indices, seems somewhat to change the nature of the _ question, by the introduction of a foreignelement. Nor is it perhaps manifest that the original series, of which the sum is indeterminate, may be replaced by the convergent series with determined sum, which results from multiplying its terms by the powers of a factor infinitely little less than unity ; while it is held that to multiply by the powers of a factor infinitely little greater than unity would give an useless or even false result. Besides there is something unsatisfactory in employ- ing an apparently arbitrary contrivance for annulling the effect of those terms of the proposed series which are situated at a great distance from the origin, but which do not them- _ selves originally tend to vanish as they become more distant therefrom. Nor is this difficulty entirely removed, when integration by parts is had recourse to, in order to show that the effect of these distant terms is insensible in the ultimate result ; because it then becomes necessary to differentiate the arbitrary function; but to treat its differential coefficient as always finite is to diminish the generality of the inquiry. Many other processes and proofs are subject to similar or different difficulties; but there is one method of demonstra- tion employed by Fourier, in his separate Treatise on Heat, which has, in the opinion of the present writer, received less notice than it deserves, and of which it is proper here to speak. The principle of the method here alluded to may be ealled the Principle of Fluctuation, and is the same which 236 was enunciated under that title in the remarks prefixed to this paper. In virtue of this principle (which may thus be considered as having been indicated by Fourier, although not expressly stated by him), if any function, such as the sine or cosine of an infinite multiple of an arc, changes sign infinitely often within a finite extent of the variable on which it depends, and has for its mean value zero; and if this, which may be called a fluctuating function, be multiplied by any arbitrary but finite function of the same variable, and afterwards integrated between any finite limits; the integral of the product will be zero, on account of the mutual destruc- tion or neutralization of all its elements. It follows immediately from this principle, that if the factor by which the fluctuating function is multiplied, instead of remaining always finite, becomes infinite between the limits of integration, for one or more particular values of the vari- able on which it depends; it is then only necessary to attend to values in the immediate neighbourhood of these, in order to obtain the value of the integral. And in this way Fourier has given what seems to be the most satisfactory published proof, and (so to speak) the most natural explanation of the theorem called by his name; since it exhibits the actual pro- cess, one might almost say the interior mechanism, which, in the expression assigned by him, destroys the effect of all those values of the auxiliary variable which are not required for the result. So clear, indeed, is this conception, that it admits of being easily translated into geometrical construc- tions, which have accordingly been used by Fourier for that purpose. There are, however, some remaining difficulties connected with this mode of demonstration, which may perhaps account for the circumstance that it seems never to be mentioned, nor alluded to, in any of the historical notices which Poisson has given on the subject of these transformations. For ex- ample, although Fourier, in the proof just referred to, of the eter ve ae 7 _ r a rn ee 237 theorem called by his name, shows clearly that in integrating the product of an arbitrary but finite function, and the sine or cosine of an infinite multiple, each successive positive portion of the integral is destroyed by the negative portion which follows it, if infinitely small quantities be neglected, yet he omits to show that the infinitely small outstanding dif- ference of values of these positive and negative portions, cor- responding to a single period of the trigonometric function introduced, is of the second order; and, therefore, a doubt may arise whether the infinite number of such infinitely small periods, contained in any finite interval, may not produce, by their accumulation, a finite result. It it also desirable to be able to state the argument in the language of limits, rather than in that of infinitesimals; and to exhibit, by appropriate definitions and notations, what was evidently foreseen by Fourier, that the result depends rather on the fluctuating than on the trigonometric character of the auxiliary function employed. The same view of the question had occurred to the pre- sent writer, before he was aware that indications of it were to be found among the published works of Fourier ; and he still conceives that the details of the demonstration to which he was thus led may be not devoid of interest and utility, as tending to give greater rigour and clearness to the proof and the conception of a widely applicable and highly remarkable theorem. Yet, if he did not suppose that the present paper contains something more than a mere expansion or improvement of a known proof of a known result, the Author would scarcely have ventured to offer it to the Transactions* of the Royal Irish Academy. It aims not merely to give a more perfectly satisfactory demonstration of Fourier’s celebrated theorem ee a * Sir William Hamilton’s Essay on Fluctuating Functions, will be found in the Second Part of volume xix. of the Transactions of the Academy. 238 than any which the writer has elsewhere seen, but also to present that theorem, and many others analogous thereto, under a greatly generalized form, deduced from the principle of fluctuation. Functions more general than sines or cosines, yet having some correspondent properties, are introduced throughout ; and constants, distinct from the ratio of the cir- cumference to the diameter of a circle, present themselves in connexion therewith. And thus, ifthe intention of the writer have been in any degree accomplished, it will have been shown, according to the opinion expressed in the remarks prefixed to this paper, that the development of the impor- tant principle above referred to gives not only a new clear- ness, but also (in some respects) a new extension, to this de- partment of science. DONATIONS. Memorie dell’ Imperiale Regio Instituto del Regno Lom- bardo-Veneto. Vols. 1-5. ; Memorie dell’ Instituto Nazionale Italiano, Vol.1, 4 Parts, vol. 2, 2 Parts. Mazxwell’s Narrative of the Prince’s Expedition. (1745). Published by the Maitland Club. Presented by John Smith, Esq., Secretary M. C. : Bibliotheca Scoto-Celtica. By John Reid, Esq. Pre- sented by the Author. Hints for the better Construction of Dwellings for small Farmers, §c. By W. J. Hughes, M.R.I. A. Presented by the Author. PROCEEDINGS OF THE ROYAL IRISH ACADEMY. 1842. No. 34. March 16. (Stated Meeting). _ SIR Wm. R. HAMILTON, LL.D., President, in the Chair. On the recommendation of Council, Charles Wheatstone, Esq., was elected an honorary member of the Academy. The Secretary of Council read the following Report, which was ordered to be entered on the Minutes : “ The affairs of the Academy during the past year will require but __ abrief review, as the interval has not been very fertile in results. The second part of the nineteenth volume of our Transactions has not yet been published ; and the Essay on the Round Towers (which is to _ make the twentieth volume) is still advancing slowly through the _ press, its progress being necessarily retarded by the great number of illustrations which are required from the nature of the work. «« The subscription which was opened last year, under the manage- ment of the Committee of Antiquities, for the purchase of the collec- tion of the late Dean of St. Patrick’s, has not hitherto answered the expectations that were formed of it. Of the sum of one thousand pounds, which the Dean’s representatives agreed to accept for the collection, little more than one-half has been raised. Notwithstand- ing this circumstance, however, the Council are persuaded that public feeling is in favour of the project, and that a little more energy, on yur part, is all that is required to ensure success. It would indeed ea disgrace to us, if, for want of proper exertions, this fine collection vould be lost to the country. VOL, Il. U 240 «« Meanwhile, the small cabinet in the possession of the Academy has been augmented by some valuable articles, from the fund of two hundred pounds set apart for that purpose. Among these are a gold torgquis, weighing upwards of twelve ounces ; and a gold collar of the most elegant form and workmanship, weighing four and a-half ounces. The latter beautiful specimen of ancient art was lately dug up in a bog, by a common labourer, and but for the existence of the fund above mentioned, which allowed it to be secured at once for the Academy, it would probably have been condemned to the crucible; the usual fate of such old ornaments as possess a high intrinsic value. «« As this fund, however, is but small, and in the present state of our finances cannot be expected to be permanent, while the re- sources of private subscription, to which we have so often had occa- sion to resort, must be considered as now almost exhausted, the Council have thought it advisable to try whether it might not be pos- sible to obtain some public assistance towards carrying out an object which is admitted to be one of great public interest. They have therefore presented a memorial to the Lord Lieutenant, praying his Excellency to recommend to her Majesty’s Government the addition of £100 a year to our usual grant, for the sole purpose of purchasing antiquities; this additional sum to be strictly accounted for every year. Should the proposal be favourably received by the Government, the Academy will be in a position to accomplish its designs in this de- partment, at a very trifling expense to the public. «In order that a greater number of the members of the Academy may be induced to take a lively interest in its affairs, by enjoying a share of its honours, the Council have thought it expedient to re- commend that there should in future be an annual change in the list of Vice-Presidents, the senior Vice-President going out of office after the stated meeting in March, and they hope that every future President will consent to act upon this suggestion in the appointment of Vice-Presidents. But as it is proposed, by this arrangement, that no person should be appointed as Vice-President more than four times successively, so it is not intended to recommend that any Vice-Pre- sident should be displaced, who may have been appointed less than four times successively. «¢ Among the deaths that have occurred in our body, during the 4 241 past year, we have had to regret that of the Very Rev. Robert Burrowes, D. D., Dean of Cork, and formerly Fellow of Trinity Col- lege. Though not an original member, Dr. Burrowes was among the very first members of the Academy. He filled the office of Secretary for several years, and contributed some very elegant papers, in the department of Polite Literature, to the early volumes of our Trans- actions. « Within the last few days we have had to lament the death of another distinguished member of the Academy and Council, the Rev. Cesar Otway, the author of several well-known works illustrative of the history and antiquities of his native country, and abounding in graphic sketches of Irish scenery, and vigorous delineations of Irish character and manners. «In the list of honorary members, we have lost an eminent Botanist, Aylmer Burke Lambert, Esq. He was the author of a magnificent work on Pines, in three volumes, the last of which, more recently published than the rest, contains some fine contributions from the Californian collections of our countryman and fellow-acade- mician, Dr. Coulter. « The other members deceased within the year are : Peter Burrowes, Esq., Q.C. Isaac D’Olier, LL. D. J. H. Blake, Esq., Q. C. « And the new members elected within the year are: William Monsell, Esq. J. H. Jellett, Esq., F.T.C.D. ~ Robert Tighe, Esq. William Andrews, Esq. W. E. Hudson, Esq. J. T. Banks, Esq. _G. Fitzgibbon, Esq. Robert Bateson, Esq. _ William Phibbs, Esq. John Burrowes, Esq. Rey. James Reid. Rey. Samuel Butcher, F.T.C.D. William Lee, Esq., F.T.C.D. | Fleetwood Churchill, M.D. Robert Jones, Esq. Alexander Clendinning, Esq. Thomas Wilson, Esq. Rev. Reg. Courtenay. _ Beriah Botfield, Esq. Durham Dunlop, Esq., Jun. , Ww. T. Mulyany, Esq. Alexander Ferrier, Esq. Oliver Sproule, Esq. Wrigley Grimshaw, M.D. ames Thompson, Esq. William Hogan, Esq. ames Patten, M.D. W. J. Hughes, Esq. v2 242 William Roberts, Esq., F.T.C.D. Joseph Nelson, Esq. Captain A. C. Sterling. Rev. Robert Chatto.” Rey. Thomas Stack, F. T.C. D. Resotvep,—That we have heard, with deep regret, of the death of our fellow Academician, the Rev. Cesar Otway, and that, while we wish to record our sense of the value of his ser- vices to the Academy, and our opinion of his merits as an author, who, possessing in his own person many of the best traits in the Irish character, has by his lively and interesting sketches powerfully assisted in drawing public attention to the history, scenery, and antiquities of his native land; we de- sire also to convey to his afflicted family the assurances of our sincere sympathy in their sorrow for one whose private vir- tues rendered him the delight of the domestic circle, as his talents and information made him valuable as a member of our Institution. Resotvep,—That the Academy have heard, with regret, that Dr. Aquilla Smith, having found his attendance on the Council inconsistent with his professional pursuits, has ten- dered the resignation of his place as a member of Council; and they desire to express their sense of the valuable assis- tance they received from him during the time they had his cooperation in advancing their objects. The ballot for the Annual Election having closed, the scrutineers reported that the following gentlemen were elected Officers and Council for the ensuing year: President—Sir William Rowan Hamilton, LL.D. Treasurer—James Pim, Jun., Esq. Secretary to the Academy—Rev. Joseph H. Singer, D.D. Secretary to the Council—J. Mac Cullagh, Esq. LL.D. Secretary of Foreign Correspondence—Rev. Humphrey Lloyd, D.D. Librarian—Rev. William H. Drummond, D.D. Clerk and Assistant Librarian—Edward Clibborn. 243 Committee of Science. Rev. France Sadleir, D.D., Provost of ‘Trinity College ; Rev. Humphrey Lloyd, D.D.; James Apjohn, M.D. ; James Mac Cullagh, LL.D.; Rev. William Digby Sadleir, A.M.; Robert Ball, Esq.; Robert Kane, M.D. . Committee of Polite Literature. His Grace the Archbishop of Dublin ; Rev. Joseph Hen- derson Singer, D.D.; Samuel Litton, M.D.; Rev. William Hamilton Drummond, D.D.; Rev. Charles Richard Elring- ton, D.D.; Rev. Charles William Wall, D.D.; Rev. Thomas H. Porter, D.D. Committee of Antiquities. George Petrie, Esq.; Rev. James Henthorn Todd, D.D.; Henry J. Monck Mason, LL.D.; Samuel Ferguson, Esq. ; Joseph Huband Smith, Esq. ; James Pim, Jun. Esq.; Cap- tain Larcom, R.E. The President then appointed, under his hand and seal, the following Vice-Presidents : His Grace the Archbishop of Dublin; the Rev. Hum- phrey Lloyd, D.D.; the Rev. James Henthorn Todd, D.D.; _ the Rev. Joseph Henderson Singer, D.D. The auditors appointed by Council to examine the Trea- surer’s accounts reported as follows : “« We have examined the above accounts,* with the vouchers pro- duced, and have found it to be correct; and we find that there is a balance in bank, amounting to £169 17s. 1d. sterling. “ (Signed, ) “ Tuomas Hotton, } “ JosEPH CARSON. ft March 16, 1842,” * Entered in Treasurer's book. 244 “« The Treasurer reports, that there is £1052 6s. 8d. in 3 per Cent. Consols, and £1609 4s. 9d., in 34 per Cent. Stock, the latter being the Cunningham Fund. “ (Signed,) ; “ AQUILLA SMITH. ‘© March 16, 1842.” April 11. SIR Ws. R. HAMILTON, LL.D., President, in the Chair. Rev. Richard Butler, Robert Law, M.D., and John Toleken, M. D., F.T.C.D., were elected members of the Academy. Mr. Ferguson read a paper by the Rev. Arthur B. Rowan, A. M., M.R.I.A., on the ancient Church of Kil- melchedor. This church stands in a small hamlet and parish of the same name, in the barony of Corkaguiny, county of Kerry, at the foot of Brandon mountain, and near the harbour of Smerwick. At the top of the neighbouring mountain is a small ruined oratory, and a well of great reputed sanctity, which are dedicated to St. Brandon, or Brendan, the founder ‘of the Diocesan Cathedral of Ardfert; and the neighbour- hood is further remarkable for some of those small stone- roofed cells or chapelries which are supposed to belong to a very remote age, and of which one that has been described and engraved by Smith, in his History of Kerry, still remains in complete preservation. The church derives its name from St. Melchedor, who is mentioned in a catalogue of saints in the book of Ballimote; also ina MS. calendar in the Library of the Academy, where, under the date May 14, he is com- memorated as “ Melchedar, son of Ronan, son of the King of Ulster, of Kilmeilche[dor?], on the sea shore, at Knock- 245 Brennaun in the west.” For this information the author ac- knowledges himself indebted to Mr. Owen Connellan. He then proceeds to the description of the church, of which plans and drawings are given. ‘The building,” he says, ** stands due east and west, and consists of two parts, the _ mave and choir, separated by a richly carved semicircular archway. The former is twenty-six feet long, by sixteen feet wide, and thirteen feet high to the springing of the stone roof. The choir is, as usual, much smaller, being but j sixteen feet long, by twelve wide, and eleven feet high to the roof, which was also of stone. There are five windows, one in the eastern gable, and -one at each side in the nave and choir; all of them having the round arch of the same style of architecture as the ornamented doorways. The entrance to the church is at the western end, through a richly orna- mented doorway of the Anglo-Norman, or, as it is more cor- rectly called, the Lombardic style of architecture. Making allowance for the greater size and profusion of ornament, I find in the arches of the western door and nave of Rochester Cathedral, the nearest model for the doorways of Kilmelche- dor church. In Ireland, the account given by Grose, in his Antiquities, of Cormac’s Chapel or Crypt at Cashel, may, pro tanto, be copied asa description of Kilmelchedor. Thus he tells us, ‘it is a stone-roofed chapel,’ with ‘a nave and _ choir, with ‘columns supporting the grand arch leading into the choir; the columns short and thick; the portal semécir- cular, with nail-head and chevron mouldings; the windows also round.’ So far the descriptions of both buildings exactly agree.” The roof of Kilmelchedor seems to have been constructed on the same principle as the roofs of the ancient and curious _ stone hermitages in its neighbourhood; one stone overlap- _ ping the other, with sufficient bearing to sustain the weight ‘as the work advanced. But the chief peculiarity of this church is the elaborate ornament of the interior nave, 246 which is of a kind to attract attention even if found in one of our most richly adorned churches, but much more so in a building in this remote situation. At the height of about four feet from the floor, the nave shows, on each side through its whole length, a series of square pannelled compartments, separated by short massive pilasters projecting from the wall. These compartments, twelve in number, are in per- fect preservation, and appear to have been originally exe- cuted in polished stone. The nave windows occupy a com- partment at each side, and are surmounted by plain round arches. Within the choir, and springing directly from each side of the doorway, there are small arched apertures, the use of which the author is at a loss to conjecture. The semicir- cular head of the western doorway is filled with a single stone, on the inner side of which is a projecting effigy, now too much defaced to admit more than a conjecture as to what it represented. In the church-yard stands a rude gigantic cross, formed of a single stone; another, less rude, lies half prostrate, and has been built into the wallofa tomb. Ogham stones are found at several places in the neighbourhood ; there is one, much effaced, in the churchyard. Having noticed the vulgar tradition that the church ‘‘ was built long ago by the Spaniards,” the author offers some conjectures as to the probable date of its erection, which he concludes to have been in the eighth or ninth century, ‘when the Danes had intercourse with this and with other parts of Ireland ;” but he supposes that it was ornamented and finished in its present style at a subsequent period. The following notice of an ancient Boat, found near Drogheda, was read by W. I. Hughes, Esq. During the progress of the works carried on by the Cor- poration of Drogheda for the improvement of the port and harbour, it was found necessary to deepen the bed of the River 247 Boyne below the bridge, towards the sea, which left that part of the river above the bridge, towards Oldbridge, quite dry. At this part (in the Summer of 1837), the boat, the _ subject of the present notice, was found by some workmen ___ who were engaged taking gravel from the river, close by the _ obelisk erected to commemorate the battle fought between ‘ James the Second and William the Third, about two miles _ from the town of Drogheda. Its extreme length is eighteen feet nine inches, and __ breadth two feet eight inches, tapering to a breadth of four- teen inches at the back, and to nine inches in the front, being flattened at either end; no oars seem to have been used in propelling it, there being no marks on the sides, or places for dowells used in modern boats to secure the oars, but at either - end a groove is perceptible where oars were placed to steer or scull with. Paddles may have been used in the same manner as the Indians manage their canoes. Some of the paddles have been found, but they are of a very rough kind, _having the appearance of the branch of a tree, feathered at one end, without any attempt at shape. Along with this cott was found what I shall call an anchor ; it is four feetin length, and three feet across, having ee. two arms, to one of which a rope was attached to secure the boat. The Royal Dublin Society have one of those ancient cotts in their possession, which differs from that now described in shape and size; the cott found at Drogheda being flattened at both ends, whilst that belonging to the Dublin Society has one end flat and the other pointed, being of the shape of a modern boat. Its length is twenty-one feet twoinches, breadth one foot, and depth ten inches; being scarcely sufficient _ for a person to sit in. There is no keel to either of the - boats. Another was found lately in a bog, on the estate of Sir Charles Kennedy, in the county of Waterford ; it is only— 248 eight feet six inches long, and two feet ten inches broad, and is round at the bottom, having a keel. Ware, in his work on the Antiquities of Ireland, states it as his opinion, that the Pheenicians were the original colo- nisers of this country, and that they used boats made of osiers or wicker work, and covered with skins, in which they navi- gated the bays and the mouths of the rivers. The ancient Irish, he says, made use of another kind of boat in the rivers and lakes, formed out of an oak wrought hollow, which is called by the Irish coé#z, and by the English coit, a vessel well known to antiquity under other names. Pliny calls boats hollowed out of a single beam, Monoxyle, from a Greek word of that import, and describes them to be— lintres ex uno ligno excavate, i. e. boats formed out of one piece of timber wrought hollow. And in another place Pliny relates that the German pirates sailed in boats hol- lowed out of single trees, each of which they made so large as to contain thirty men. April 25. SIR Wm. R. HAMILTON, LL.D., President, in the Chair. The Rev. Dr. Kennedy Bailie commenced the reading of a paper containing an Account of his Researches in certain parts of Asia Minor. The Rev. Dr. Robinson gave an account of the casting of the great six-foot Speculum by the Earl of Rosse. The publication of this account is deferred, for the pre- sent, by Dr. Robinson. On a future occasion he expects to lay before the Academy a statement of the performance of the telescope when it shall be turned, for the first time, to the heavens. The history of the casting of the specu- 249 lum, of the performance of the telescope, and of the ma- ehinery by which it is moved, will then appear in the Pro- ceedings. May 9. SIR Ws. R. HAMILTON, LL.D., President, in the Chair. 4 William Blacker, Esq. and the Rev. James Booth were elected members of the Academy. James Mac Cullagh, Esq. was elected Secretary of the Academy, in the room of the Rev. Dr. Singer, resigned ; and Dr. Kane was elected Secretary of Council. A paper, by the Rev. Dr. Hincks, ‘‘ On the True Date of the Rosetta Stone,” was read. The date usually assigned to this monument, on the au- thority of Dr. Young, is the 27th March, 196 B. c., according _ to the proleptic Julian reckoning ; the true date, as deter- _ mined by Dr. Hincks, is the 27th March, 197 8. c. Taking _ the former date for granted, M. Letronne has drawn from it a great many inferences, which the error of a single year en- tirely vitiates. These inferences relate to the history of _ Ptolemy Epiphanes, and to the mode of computing the years _ of his reign and of the reigns of other Egyptian kings; as also to the various priesthoods of royal personages that are _ mentioned on the Ptolemaic monuments. The conclusions _ of M. Letronne, and those which are to be deduced from the corrected date, are exhibited by the author in parallel columns. The President made some remarks on the day of the - Vernal Equinox at the time of the Council of Nice. - It has been stated by some eminent writers on astronomy, for example by Brinkley and Biot, and seems to be gene- rally supposed, that the vernal equinox in the year 325, a. p. 250 fell on the 21st of March. But Sir W. Hamilton finds that Vince’s Solar Tables (or Delambre’s, from which those are formed) conduct to about 2} hours before the Greenwich mean noon of the 20th of March, as the true date of the equinox in that year; which thus appears to have been as- signed to a wrong day, by some erroneous computation or report, perhaps as long ago as the time of the phenomenon in question. As this result is curious, Sir W. Hamilton conceives that it may not be uninteresting to confirm it by a very simple process of calculation, derived from the Gregorian Calendar. According to that calendar, 400 years contain 146097 days, being a number less by 3 than that of the days in four Julian centuries ; and if the farther refinement be adopted, which some have suggested, of suppressing the intercalary day in each of the years, 4000, 8000, &c., then, in the calendar thus improved, 4000 civil years will contain 1460969 solar days. Assuming then, as a sufficiently near approximation, that such is the real length of 4000 tropical years; multiply- ing by 3, and dividing by 8, we find that 1500 tropical years are equivalent to 547863 days and a fraction; which fraction of a day, according to this simple arithmetic, would be equi- valent to 9 hours. But 1500 Julian years contain 547875 days, that is, 12 more than the number last determined ; and these 12 days are precisely the difference of new and old styles in the present century. If, then, we neglect the frac- tion, the new-style date of an equinox in any year of the nineteenth century ought to be the same with the old-style date of the same equinox in the corresponding year of the fourth century; and in particular the vernal equinox of 325 ought to have fallen on the 20th of March, because that of 1825 fell on the day so named: while the fraction of a day above referred to, though not entirely to be relied on, ren- ders this result a little more exact, by throwing back the equinox from the evening to a time more near to noon. 251 The following communication from the Rev. Thomas Knox was read: ** River Glebe, Toomavara, ** April 27, 1842. ** An application of the Daguerreotype process to astro- nomical purposes occurred to me last autumn. It is well known that an inscription on a building which it would re- quire a telescope to read, from its smallness or distance, can (if a view of that building be taken in the camera on one of Daguerre’s plates) be read by a microscope, though invisible _on the plate to the naked eye; also, that the internal struc- ture of some insects can be as well studied by examining the image of the object on the plate by a microscope (that image having been formed from the oxyhydrogen microscope). ** From these known facts it is extremely probable that were an image of a double star, or of one of the nebule, taken _ ona Daguerre plate in the focus of a telescope of moderate ‘ power, but which of itself could not divide the star or resolve 7 f ——_—- ~—— SL Oa the nebula; that by then examining the plate by a strong microscope, the state of that star, &c. might be ascertained, as well as if it had in the first place been examined by a telescope of very high power. _ “That the light of the fixed stars possesses chemical rays, and would therefore affect Daguerre’s plates, there can be little doubt; and I feel certain in my own mind that the ‘image thus formed would reveal to the microscope as much as a telescope of equal power could in the first instance have _ ascertained. ‘*T am aware that theorising this way is very unprofit- able, but I do not possess instrumental means for trying the experiment myself, my equatorial not having any clock mo- tion adapted to it. On the accuracy and steadiness of the clock movement ali would depend; any small telescope, or yerhaps even a single lens, equatorially mounted, would do ‘ 252 the rest. The plates need not exceed in size the pencil of rays, and may be very small. “If this succeed, we might gain great advantages by thus mapping the stars and nebulz, and examining their state at our leisure, in our study, and being able to take advantage of what every practical astronomer knows to occur so seldom in our climate, namely, a state of the atmosphere favourable for delicate observation. “To try it, some easily divided star, such as ¢ Urse, might be first used, and, if the plate registered it as a double star, we might then proceed to other more difficult objects.” DONATIONS. A Letter on the State of Schools of Chemistry in the United Kingdom. By Wm. Gregory, M.D., M.R.1.A., &c. &c. Presented by the Author. A volume of Tracts relating to the Historical Society of Dublin. Presented by G. A. Kennedy, M.D., M.R.I. A. &e. &e. Journal of the Franklin Institute. Third Series. Vol. II. Eleventh Report of the British Association for 1841. (Plymouth). Presented by the Association. Account of the Magnetical Observatory of Dublin. By the Rev. H. Lloyd, D. D., &c. Presented by the Author. A View of the Coinage of the Heptarchy. By John Lind- say, Esq. Presented by the Author. Mémoires de la Societe Géologique de France. Tome IV. Second Part. Transactions of the Royal Society of Copenhagen. Vol. V1. (1841). On the Use and Study of History. By W. Torrens M‘Cul- lagh, LL.B. Presented by the Author. 253 May 23. SIR Wm. R. HAMILTON, LL.D., President, in the Chair. The Rev. Dr. Kennedy Bailie, late F. T. C. D., concluded a paper which he had commenced on the last meeting but one of the Academy, the subject of which was a general statement of his researches in certain parts of Asia Minor, relative to Inscriptions of the Greco-Roman era. The fol- lowing is an outline of his communication. He commenced with some brief notices of what has been done by scholars in this department of classical literature, and with remarking on its importance, as illustrative of the language, the history, and the institutions of the people who have bequeathed these monuments to after-ages. In this section, the labours of Chandler, Pococke, Spon, Clarke, and Professor Boeckh, were particularly commemorated. Next followed an account of the rules by which he was guided, in forming his collection of inscriptions, during a tour which he had recently made in the countries bordering _ on the Mediterranean. The third section embraced notices of the inscriptions _ which he copied in six of the Apocalyptic sites, namely, Ephesus, Philadelphia, Sardes, Thyatira, Pergamus, and | Smyrna, and of a few others which he found in some neigh- bouring localities, viz. two sepulchral, from the sites of the ancient Cotyaion, and three from the Turkish town of Kir- kagatch, situated on the road from Thyatira to Pergamus. The Ephesian monuments related chiefly to circumstances connected with the Artemisiac festivals. They were three in : number; one, a psephisma, or decree of the senate and _ people of Ephesus; the two remaining, honorary tituli. Of the four inscriptions found at Philadelphia, the most ‘remarkable was a fragment ofa titulus, which, in all proba- ility, had been inscribed on the pedestal of a statue of the 254 eunuch Eutropius, after the downfall of the power of that favourite of Arcadius. In support of this opinion, Dr. Kennedy Bailie entered at some length into that part of the history of the period which concerns the expedition against Trigibild the Ostrogoth, under the auspices of Eutropius, which terminated in the dis- comfiture and death of the general whom he had selected. This inscription was found in an extremely mutilated state; and an attempt has been made by the author of the paper to restore it, on the basis of the historical notices de- rivable from Claudian’s two books against Eutropius. It was metrical: the lines alternately hexameter and pen- tameter. The inscriptions found at Thyatira were nine in number, of which four at least were entaphial. The others were chiefly honorary tituli, and of these, the most perfect which Dr. Kennedy Bailie found, was one which had been inscribed on the pedestal of a statue erected in memory of the skill and prowess ofa distinguished Thyatirene athlete, Menander the son of Paullus, by the youths of the first Heraclean Gym- nasia. The most perfect amongst the sepulchral epigraphs was found on a soros which had been the property of a distin- guished citizen of Thyatira, named Fabius Zosimus. In this are recited, at full length, the intentions of the owner, the legal sanction under which they were to be carried into effect, the names of the Proconsul and Registrar, as also the date. It contains, moreover, some interesting notices relating to the astyography of the ancient site amongst the ruins of which it was found. Of the Sardian monuments, the most remarkable was one which appeared to have been destined to commemorate the munificence of Tiberius, Trajan, and, most probably, of Ha- drian also, to the citizens of Sardes. a * 255 This record was found by the author in a most mutilated state ; but sufficient of it fortunately remained, to enable him to connect its notices with the accounts given by Tacitus, Spartianus, and Dio, of the liberality of those emperors to the distressed States of the Proconsular Asia, which had been devastated by a succession of earthquakes in the region of the Katakekaumene. The most remarkable of the Pergamenian incriptions were those in honour of Hadrian, both after his assumption of the purple, and during the life-time of Trajan. One of these may be regarded as peculiarly valuable, the great pro- bability being, that it still exists amongst the inedited monu- ments of the Greco-Roman era, and that it bears most strongly on the historical doubt originated by the above- mentioned Dio, on the subject of Hadrian’s adoption. Two other inscriptions, which were copied at Pergamos, appear evidently to belong to the period of the Lower Em- pire. They have, however, been allowed a place in this collection, as tending to illustrate the taste and style of the age in such matters. Both are honorary, and one en- taphial. The Smyrnzan Tituli are five in number, viz. a fragment of a decree, or treaty; a notice of the officers of the customs of the port of the ancient city; a votive epigraph, ona stele; a fragment of an inscription from the frieze of a temple; lastly, an epitaph. On these the author of the essay dwelt at considerable length, more especially on the third, in which he pointed out a circumstance which appeared to have escaped the notice of former writers: amongst these, of Mr. Arundell, whose work on the Apocalyptic Churches appeared in 1828. This remark concerned the metre, and led to a conversation with a gentleman present, who expressed an interest in Mr. Arundell’s discoveries, and a wish to be informed on the sub- "ject of the accuracy of that traveller’s statements. VOL. Il. x 256 Dr. Kennedy Bailie’s reply was: that his sole concern, at present, was the literature of inscriptions; that therefore he felt not at liberty to venture any observation on either the style or the accuracy of the reverend gentleman’s volumes, excepting so far as related to that subject ; and that he was bound in candour to confess, that the form in which his col- lection of inscriptions has been offered to the public is not one on which any reader could rely as a scholar-like repre- sentation of the original monuments. The inscriptions of the Turkish town of Kirgagatch and Cotyaion, next occupied the author’s attention. The first of these, three in number, comprised an honorary titulus, in favour of Hadrian, inscribed on a block of marble, which was most probably brought from Stratonicea. Secondly, a de- cree of the senate and people of that city in honour of Dio- dorus Philometor, son of Nicander, in consideration of his public services. Thirdly, a dedication of a church, in the age of the Lower Empire, or what appears to have been such, for the characters had been very much effaced. Of these the author read a detailed account, and stated his reasons for supposing that the more ancient tituli had been brought from Stratonicea in Caria, thus establishing some connexion between that site and the Turkish town. This is the more remarkable, inasmuch as there exist no architectural remains in Kirkagatch to lead to the supposition that it occupied any known ancient site. Two inscriptions from Kitaiah (Cotyaion) concluded the series, both of which were copied from grave-stones in the Armenian cemetery. They were sepulchral tituli, and the stones themselves, on which they were engraved, most pro- bably fragments of Sarkophagi. The Secretary read a letter from Dr. Hunter, presenting to the Academy three mathematical works, by the Nuwab Shums-ool-oomrah of Hyderabad. 257 ** Dublin, Royal Barracks, “ May 23, 1842. *¢ Sir, ** 1 beg to present to the Library of the Royal Irish Academy the three accompanying works on scientific subjects, printed in the Persian language and character, and the composition of a native prince. “They were brought home by me three years ago, on my return from India, where I was serving with my regiment, and were given me by the Prince for the purpose of being presented to some scientific Institution. ** They are the composition of Nuwab Shums-ool-oomrah of Hyderabad, in the Nizam’s Country; a prince who has distinguished himself much by his scientific acquirements, his original genius, and general love of literature. He has great curiosity about every European invention, and his house is set round with every sort of mechanical contrivance. These works were printed by himself in his lithographic printing press. The large work is on geometry and trigo- nometry; the two smaller are on spherical trigonometry and logarithms. ~~ aaTaR” ‘*T remain, Sir, &c. ‘Tuomas Hunter, M.D., “ Assistant-Surgeon, 12th Royal Lancers. Net Be eo _ ** To the Secretary of the _ Royal Irish Academy.” DONATIONS. Three Lithographed Manuscripts in Persian, on Geo- _ metry, Trigonometry, and Logarithms. By the Prince Shums- ool-oomrah, of Hyderabad. Presented by Thomas Hunter, 'M.D., &c. Ordnance Survey of Kilkenny, in 49 Sheets. Presented by His Excellency the Lord Lieutenant. 258 Statistical Returns of the Dublin Metropolitan Police for 1841. Presented by the Commissioners. Nouveau Catalogue des principales Apparitions d’ Etoiles Filantes. Par M. Quetelet. Presented by the Author. Annuaire de lV Academie Royale de Bruxelles (1842). Bulletins de Vv Academie Royale de Bruxelles (1841), The Manuscript Rarities of the University of Cambridge. By James Orchard Halliwell, Esq. Presented by the Author. Notes on the United States of North America in 1838-9- 40. By George Combe, Esq.,Hon. M.R.I. A. Presented by the Author. iti PROCEEDINGS OF THE ROYAL IRISH ACADEMY, 1842. No. 35. June 13. REV. HUMPHREY LLOYD, D.D., Vice-President, in ty the Chair. Maria Edgeworth was elected (by acclamation) an Ho- norary Member of the Academy. Arthur B. Cane, Esq., B. J. Chapman, Esq., Francis M. _ Jennings, Esq., and Sir Thomas Staples, Bart., were elected Ordinary Members. Mr. J. Huband Smith read a paper descriptive of the recent discovery of a vast number of Cinerary Urns at the Hill of Rath, within a few miles of Drogheda, on the road to _ Collon. At the foot of the hill a quarry had been opened to pro- bs cure stones for the repair of the road. In the beginning of _ spring the tenant in the occupation of the farm proceeded to level this quarry, by carrying down the earth from the brow of the hill; and in the progress of his work he disco- _ vered from 150 to 200 urns of unbaked clay, of various sizes, j almost all placed in an inverted position, and covering, each 0 i a considerable quantity of human bones. _ As it seemed probable that a more careful examination of sf the portion of this interesting rath or tumulus which yet emained undisturbed might be productive of some discovery VOL, II. Y 260 calculated to throw light upon the still unsettled question of the date of this mode of interment, as well as “ the authors of these sepulchral memorials,” Mr. Smith was induced to undertake it, and accordingly proceeded to the spot for that purpose on the 30th of November last. The rath appears to have occupied the declivity of a hill, sloping gently to the west, and was originally enclosed by a breastwork of earth, of inconsiderable elevation, all trace of which had nearly disappeared, but which, according to report, may have once enclosed a space of five or six acres. ‘The soil upon the surface having been found to con- sist of rich clay, had been from time to time spread over the poorer land adjoining. It was not, however, till the process of levelling was begun that urns were discovered; they were then found at a depth of from four to five feet beneath the original surface, resting upon the till, or gravelly subsoil. Mr. Smith proceeded to a part of the hill pointed out to him as not having been yet disturbed, and, with the assistance of a few labourers, very soon had the satisfaction of laying bare four or five, or more urns. They were placed appa- rently without any regularity, about two or three feet asun- der, and having been imbedded in yellow clay, without any flags or other stones to protect them, had in most cases been pressed in, and broken to pieces, by the superincumbent earth. One, however, which remained whole, Mr. Smith, by the utmost care in freeing it from the moist clay which surrounded it, and by allowing it to dry for two or three hours before he ventured to move it, was enabled to carry away entire, and he now presented it, with its contents, to the Academy. These urns varied in size, and were in general from about eight to fifteen inches in height. Closely adjoining one of the larger ones, in fact crushed against it, lay two smaller, measuring probably but two or three inches each in diameter; these latter ones did not appear to haye held bones, In another instance a group of three or more urns, of a larger 261 size, appeared pressed together. On removing the broken pieces of each urn the bones appeared in a little conical heap within, in very small fragments, the larger ones having fallen to the sides, mixed at bottom with black unctuous earth, and occasionally small morsels of charred wood. In the very large and fine jurn which had been found previous to Mr. Smith’s visit to the tumulus, and which he now presented to the Academy in the name of Mr. Kelly of Drogheda, by whom it had been disinterred, some very interesting matters had been found mixed up with a very considerable quantity _ of human remains which it contained. These consisted of a flint arrow head, a curious curved needle of bone, one end of which was flattened and perforated, and some small stone tools, one of which seemed likely to have been used in making the indentations or rudely sculptured patterns by which this urn, in common with all the others, was orna- mented; and lastly, a small, thin scale of copper, pierced with ~ asmall hole. No other metallic remains of any kind were dis- covered, nor upon the closest inquiry does there seem any ground for supposing that any ornaments, either of silver or gold, such as have been so frequently obtained in barrows and other sepulchral tumuli, both here and in England, were found in this rath. This last mentioned urn, which was the largest discovered here, measures seventeen inches in height, and the same in extreme breadth; and would probably con- tain about eight gallons of liquid. _ The most remarkable differences between this tumulus and most other repositories of the ashes of our pagan pre- decessors, both in this country and in England, appear to be } the vast number of urns which were found here, in one vast _ cemetery, and the total absence of any kist of flags, or other ity formed to receive and protect the urns from the pres- of the earth either laterally or from above. Y 2 Ss Kalty 262 A paper entitled, ‘‘ An Inquiry as to the Coefficient of Labouring Force in Overshot Water-Wheels, whose diameter is equal to, or exceeds the total descent due to the fall; and of Water-Wheels moving in Circular Channels,” was read by Robert Mallet, Esq., Mem. Ins. C. E., M. R.I. A. This paper is partly mathematical and partly experimen- tal. The investigation which it describes, the results of which are given in ten tables, had in view principally to ob- tain definite experimental answers to the following ques- tions : Ist. With a given height of fall and head of water, or in other words, with a given descent and depth of water in the pentrough, will any diameter of wheel greater than that equal to the fall give an increase of labouring force (i. e. a better effect than the latter), or will a loss of labouring force result from such increase of diameter ? 2nd. When the head of water is necessarily variable, un- der what conditions will an advantage be obtained by the use of the larger wheel, and what will be the maximum ad- vantage? 3rd. Is any increase of labouring force obtained by causing the loaded arc of an overshot wheel to revolve in a closely fitting circular race or conduit, and if so, what is the amount of advantage, and what the conditions of maximum effect ? The author briefly reviews the history of our knowledge of this branch of hydrodynamics, the experimental researches of Da Borda, Smeaton, &c., and the more recent improve- ments in the theory of water-wheels, due to the analytic investigations of German and French engineers, and the admirably conducted experiments of Poncelet, Morin, and the Franklin Institute. Smeaton, in his paper on water-wheels, read to the Royal Society in May, 1759, and Dr. Robison of Edinburgh, in his treatise on water-power, lay downas a fixed principle, that no advantage can be obtained by making the diameter of an over- — 263 shot wheel greater than that of the total descent, minus so much asis necessary to give the water a proper velocity on reaching the wheel. The author, however, contends that the reasoning by which the latter writer upholds this is inconclusive,—that there are some circumstances which he points out necessarily in favour of the larger wheel, and that conditions may occur in practice in which it is desirable to use the larger wheel, even at some sacrifice of power; and that hence it is of im- ; portance to ascertain its value in use, as compared with Smeaton’s size for maximum effect. 3 The author states the general proposition, “ that the la- bouring force (travail of French authors, or mechanical power of Smeaton) of any machine, transferring the motive power of water, is equal to that of the whole moving power em- ployed, minus one-half of the vis viva lost by the water on - entering the machine, and minus one-half of the vis viva due to the velocity of the water on quitting it.” He then obtains general equations expressing the relations between the fall, the velocity, the weight of fluid, the power, &c. in overshot water-wheels, at whatever point the water may first reach the wheel, and whether the latter move naked, or in a cir- cular channel or course. From these he deduces, that— Ist. Ifthe portion of the total descent passed through by _ the water, before reaching the wheel, be given, the velocity of the circumference should be one-half that due to this height. 2nd. If the velocity of the circumference be given, the _ water must descend through such a fraction of the whole fall, _ before reaching the wheel, as will generate this velocity. ; 3rd. The maximum of labouring force is greater as the | velocity of the wheel is less, and its limit theoretically ap- _ proaches that due to the whole fall; general equations are _ then given, expressing the amount of labouring force in all the conditions considered by the author, and their maxima. One of the principal advantages of using an overshot wheel greater in diameter than the height of the fall, is the 264 capability thus given of making any additional head of water occurring at intervals, by freshes or any other cause, avail- able, by letting the water on the wheel at higher and higher levels. The first course of experiments is devoted to the deter- mination of the comparative value of two water-wheels, the one whose diameter is equal to the whole fall; the other to the head and fall, or to the total descent. By the head, the author always means the efficient head, or that due to the actual velocity of efflux at the sluice or shuttle, as determined by Smeaton’s experimental method,—this was equal to six inches in all cases. The apparatus employed in these researches consisted of two accurately made models of these wheels, with curved buckets, made of tin plate, the arms, &c. of brass, and the axes of cast iron, working on brass. Special contrivances were adopted to measure the weight of water passed through each wheel in each experiment, which was in every case 1000 lbs. avoirdupoise; and others, to preserve the head of water quite constant,—to determine the number of revolu- tions made per minute, and thence the speed of the wheels. One wheel was 25.5 inches diameter, the other 33 inches diameter. The value of the labouring force was determined directly by the elevation of known weights to a recorded height by a silken cord over a pulley ; the altitude was read off, on a fixed rule placed vertically against a lofty chimney. The relative power of the wheels was determined by the speed of rotation of a regulating fly or vane. All the principal results given in the ten tables are the average of five good experiments. From the accurate work- manship and large size of these models, the peculiar con- trivances for ensuring accuracy of observation, and the care taken in the experiments, the author reposes considerable confidence in his results as practical data. The velocity, in reference to maximum effect, isdetermined, —— or ee 265 and found to be lower than that deduced by Smeaton from his experiments, which the author presumes arises from the better construction of apparatus, and better form of bucket used in the present case. The author then ascertains, by another train of experi- ments on both wheels, the value of the circular conduit or race, and finds, in round numbers, that there is an economy of labouring force, amounting to from eight to eleven per cent. of the power of the fall, obtained by its use. This conduit acts by retaining the water in the buckets at the lower por- tion of the loaded are. The velocity of a water-wheel work- ing thus, he finds may vary through a greater range without a material loss of power than when working naked, and that a steady motion is also continued to a much lower velocity. The author arrives at the following practical conclusions : lst. When the depth of water in the reservoir is inva- riable, the diameter of the water-wheel should never be greater than the entire height of the fall, less so much of it as may be requisite to give the water a proper velocity on entering the buckets. 2nd. When the depth of water in the reservoir varies considerably and unavoidably in depth, an advantage may be obtained by applying a larger wheel dependent upon the extent of fluctuation and the ratio in time that the water is at its highest and lowest levels during a given prolonged period ; if this be a ratio of equality in time there will be no advan- tage, and hence in practice the cases will be rare where any advantage will be obtained. 3rd. If the level of the water in the reservoir never fall _ below the mean depth of the reservoir, when at the highest and lowest, and the average depth be between an eighth and a a tenth of the height of the fall, then the average labour- ing force of the large wheel will be greater than that of the _ small one, and it will of course increase this advantage at 266 Hence the author affirms that Dr. Robison’s conclusions must henceforth receive a limitation. Having shown that a positive advantage is obtained by the use of the circular conduit, amounting to about eleven per cent. of the total power, and that this value increases with an increase in the velocity of the wheel up to six feet per second, or more in large wheels, the author contends, that it is practicable to increase the efficiency of the best overshot wheels as now usually made, at least ten per cent. by this application. The only objections ever urged against the conduit were of a merely practical character, and the author shows that improved workmanship, and the modern use of cast iron, of which the conduit may be constructed, and provided with adjustments, render these no longer tenable. Drawings of the apparatus used in these researches, and the tabulated results, were exhibited to the Academy. Professor Lloyd read a paper “‘ on the Phenomena of Thin Plates in Polarized Light.” The author stated, that his attention had been drawn to this subject by a letter which he had received from Sir David Brewster, describing a large class of hitherto unobserved phenomena. Sir David Brewster having expressed his de- sire, in this letter, to know whether the wave-theory could furnish an explanation of the facts which he had observed, Professor Lloyd was thus led to undertake the investigation which formed the subject of the present communication.* Mr. Airy had long since inferred, from a consideration of the form of Fresnel’s expression for the intensity of reflected light, that when light, polarized perpendicularly to the plane * The present paper was read in the Mathematical Section of the British Association, last year; and a summary of the results was published in the dihe- neum, of August, 1841. The author deferred submitting it to the Academy, in the hope of being able to add an experimental confirmation of some of the conclusions not noticed by Sir D. Brewster. He has, however, been compelled, by the pressure of other duties, to postpone still further this branch of the investigation. 267 of incidence, was incident upon a thin plate bounded by media of unequal refractive powers, a remarkable change in the reflected light should take place, when the angle of inci- dence was intermediate to the polarizing angles of the two surfaces of the plate. This theoretical anticipation was fully verified by experiment. When a lens of low refracting power was laid upon a plate of high refracting power, the rings which were formed appeared with a black centre, when the angle of incidence was less than the polarizing angle of the low refracting substance, or greater than the polarizing angle of the high refracting substance ; while, when the incidence was in- termediate to these two angles, the rings were white-centred, and the whole system was complementary to what it had been before. At the polarizing angle itself the rings disappeared, there being no light reflected from one of the surfaces of the plate, and therefore no interference. The examination of this subject has since been re- sumed by Sir David Brewster; and he has repeated the ex- periments of Mr. Airy in a more general form, the incident light being polarized in any plane. He has thus been led to many new results. ‘The rings are found to disappear under circumstances in which light is reflected from both surfaces - ofthe plate; and there are many remarkable peculiarities in the transition of the rings into the complementary system.* It was to the theoretical explanation of these phenomena that Professor Lloyd now invited the attention of the Aca- demy. In the conduct of the investigation he has generalized _ the methods followed by M. Poisson and Mr. Airy on the same subject. The incident vibration being resolved into two, one in the plane of incidence, and the other in the per- pendicular plane, each portion will give rise to an infinite series of reflected vibrations, into which it is subdivided at the bounding surfaces of the plate. The expression of the resultant intensity, foreach portion, being then deduced, the * The researches of Sir David Brewster are now published in the Philosophical Transactions for 1841, 268 actual intensity of the reflected beam is the sum of these in- tensities. Its value is found to be expressed by the formula ecco w+2uu' cosa +u™ 4 si w? + 2ww! cosa + w? a Y 1+ 2uu'cosa + uz? YT] + 2ww'cosa+ww”’ in which z and w’ denote the ratios of the reflected to the in- cident vibration at the two surfaces of the plate, when the light is polarized in the plane of incidence; w and w’ the corresponding quantities for light polarized in the perpen- dicular plane ; anda the difference of phase of the successive portions of the reflected beam. The values of u, wu’, w’, w, are, _sin(@—0’) wis sin(@’— 0”) ght tan(0— an(O—6) _ tan(0’— 6") ~sin(+6’)’ ~~ sin(#’ + 6”)’ tan(O+0)’” ~ tan(&’ + 8”) where @ denotes the angle of incidence on the first surface of the plate; 6’ the corresponding angle of refraction, or the angle of incidence on the second surface; and @” the angle of refraction at the second. The value of a is 4 a= —T cos i; A T being the thickness of the plate, and A the length of the wave. When the obliquity of the incident pencil is not very great, the squares and higher powers of u, «, w, w’, may be neglected in comparison with unity, and the expression of the intensity has the approximate value, I= cos*y(u? + 2uu’cosa + wu”) +'sin’y(w? 4+ 2ww'cosa + w”) This quantity will be independent of the phase a, and there- fore the intensity will be constani, and the rings disappear, when uu cosy + ww’ sin’y = 0; that is, when the azimuth of the plane of polarization has the value given by the formula, uu! cos (9— 0’) cos (#’— 8”) ww cos(0 + 0) cos (0 + 0’) tan’y = — In this formula cos(@—6@’) and cos (0’—@”) are always positive ; ee ey 269 and accordingly the resulting value of tany will be real, and therefore the disappearance of the rings possible, only when cos (0+ 6’) and cos(@’ + 0”) are of opposite signs; i. e. when the angles of incidence on the two surfaces are, in the one case greater, and in the other less, than the polarizing angle. The media at the two sides of the plate, therefore, must have different refractive powers. Again, the phases of the two portions of the reflected beam, and which are polarized respectively in the plane of incidence and in the perpendicular plane, are given by the formulas, u’(1—u?) sina u(1-u?) + w(x) cosa’ w'(1—w?) sina w(1 + w”?) + w’(1+w*) cosa The phases, a’ and a’, are consequently in general different, and therefore the resulting light will be, in general, ellipti- cally polarized. The author entered into some developments connected with this part of the subject, which does not ap- pear to have been noticed by Sir D. Brewster in the course of his experimental inquiries; and he concluded by stating the important bearings which it may possibly have upon the phenomena of elliptical polarization by metals. tana’ = tana” = Professor Lloyd having, in the preceding commnnication, thrown out the idea that the elliptical polarization of metals might possibly be identified with that which is produced by a thin film on the surface of a reflecting body, Pro- fessor Mac Cullagh took occasion to observe that an analo- gous, but far more general, hypothesis had occurred to himself some years ago, among the various conjectures by which he had sought to account for the remarkable dif- _ ference between the action of metals and that of trans- parent media in reflecting light. In his theory of crystalline _ reflexion he had found it allowable to suppose that the _ change in the elasticity of the ether, in passing out of 270 one medium into the other, takes place abrupily at their common surface; and he had thought it not unlikely that the supposition of agradual change of elasticity, taking place with- in a very small space at one or both sides of the surface of a metal, might afford an explanation of the peculiar phenomena of metallic reflexion. Such a supposition would be mathe- matically equivalent to the hypothesis that an immense num- ber of films, of which the refractive powers vary between given limits according to some law, compose a very thin stratum at the surface of a polished metal; and it would be in accordance with the inference drawn by Professor Mac Cullagh from certain formulas (Transactions R.I. A., vol. xviii. p. 70) that the law of equivalent vibrations is not observed in metals; an inference which, indeed, originally suggested to him the hypothesis in question. He had not yet compared the hypothesis with his formulas, but it was easy to see that it would explain the non-existence of an angle of complete polarization for metals, as well as the ge- neral fact of elliptical polarization; and perhaps the metallic brilliancy, difference of colour, &c. might be occasioned by the great number of reflexions in the variable stratum at the surface, and the endless variety of interferences pro- duced by them. The above was only one of the conjectures which had been formerly made by Professor Mac Cullagh in relation to this subject, and it was mentioned on this occasion chiefly on account of its analogy with the view taken by Professor Lloyd. Another and very different hypothesis, which was the first that had occurred to him, as being immediately suggested by the imaginary form which he had assumed for the velocity of propagation in a metal, will be found stated in the Comptes Rendus of the French Academy, tom. viii., p. 962, in a letter to M. Arago, dated May 11,1839. It consisted in supposing the amplitude of the vibration within the metal to be propor- tional to acertain exponential of which the value is there given, accompanied with the remark that this expression for the vibra- 271 tion, if introduced into the differential equations (at that time unknown) which subsist at the confines of two media, would probably explain the peculiar phenomena of metallic re- flexion, such as change of phase, &c. Very soon after that date the equations were discovered which hold good at the common surface of two ¢ransparent media (see Proceedings R.1.A. vol.i., p.378); and it is certainly nota little singular that these equations, with the help of the aforesaid expression for the vibration, not only explain the change of phase, but lead to the precise formulas which had been previously given for the case of metallic reflexion (Transactions R. I. A. vol. xviii. p- 71). The application of the equations, however, to this case, cannot be regarded as legitimate without further proof; and the hypothesis is attended by another difficulty, the na- ture of which may be seen in the letter alluded to. On the whole, Professor Mac Cullagh did not consider him- self warranted, as yet, in choosing between his two hypo- theses, nor even in concluding that one or other of them must be the right one. Before constructing any refined theory, he thought it necessary that the formulas to which he had re- ferred, and which, if they are correct, must be the foundation of the theory, should be tested by experiments more accu- rate than any that had yet been made, and this was a task to which he hoped he should soon have leisure to devote him- self. Professor Lloyd explained, that the hypothesis which he had suggested had not been offered by him as an exact physical representation of the optical constitution of metals ; but rather as one which lent itself, with tolerable facility, to mathematical expression, and the results of which might possibly, by a suitable determination of the constants of the formulas, be found to coincide with the phenomena, and therefore with the results of a more rigid theory. _ Resotvep,—T hat, in future, when the office of Secretary of the Academy is vacant, the vacancy shall be filled up by express election. June 27. REV. J. H. TODD, D. D., Vice-President, in the Chair. H. J. Monck Mason, Esq., LL.D., read an account of a visit which he had paid to the Tomb of the Volumnii at Perugia. Mr. Mason then presented a gold fibula found in Ireland, as a contribution to the Museum of Antiquities, now in pro- cess of formation by the Academy. The thanks of the Academy were voted to Mr. Mason for the donation. A paper was read by Dr. Macartney ‘ on the minute Structure of the Brain in the Chimpanzee and the human Idiot, compared with that of the perfect Brain of Man, with some reflections on the Cerebral Functions.” The author commenced by stating, that he had disco- vered the brain of all animals to be composed of a plexiform arrangement of white (or, as he termed them, sentient) fila- ments, the most delicate of which he found to pervade all the coloured substances of the brain. He attributed the higher sensorial powers of the cerebral organ to the disposition and intercommunication of these filaments, more especially where they exist in the coloured substances. The mode he em- ploys for rendering the finer filaments evident is to moisten the different substances during the dissection with a solution of alum in water, which, causing a slight coagulation, makes the filaments opaque and visible. ‘The author accounted for the fact that the existence of the most delicate plexuses had hitherto escaped observation, from the circumstance that other anatomists had not used any fluid to coagulate them. He considers the shape and magnitude of the different parts of the brain as merely subservient to the proper arrange- ment and number of the plexuses of the sentient substance. I 273 The principal object of the paper was to point out the first gradations from the perfect structure of the brain in man, and for this purpose the author related the dissection of the brain of the chimpanzee (simia troglodytes, Lin.) and of two human idiots, from which he was led to conclude that the primary deviations in the anatomy of the brain were to be found in the essential structure of the locus niger, of the cor- pus fimbriatum, and of the corpora olivaria,—in the existence of the white strig in the fourth ventricle, of the corpora can- dicantia, and of calcareous granules in the pineal gland,—in the degree of intermixture of the white filaments of the arbor vite, the distinction of the anterior crura of the fornia, and lastly the decussations of the pyramids. By the dissections it was evident that the brain of the chimpanzee possessed a superior structure to that of the natural human idiot. As the author had previously ascertained that all the plexuses in the brain are conjoined, and all the cerebral and spinal nerves are incorporated with the parts from which they are said to arise, he was led to infer that the functions of the brain are not confined to particular parts of the surface, but that all the parts exercise a mutual influence on each other, that its powers and operation are systematic and har- monious, instead of the effect of different parts of the brain acting independently and often in opposition to each other. He stated a number of facts contradicting the opinion of the cerebellum being designed to produce the sexual instinct, as taught by Gall and his followers. He ascribed the origin of all _ instincts to the organs to the operations of which the instincts are subservient. He argued that if instinctive impulses were _ to originate in the brain, they would interfere with all its higher functions. The author further considered the per- fect continuity and incorporation of the nerves with central parts of the system, as sufficient to account for the functions of sensation and voluntary motion, without the interposition _ of nervous fluid. 274 Dr. Macartney exhibited a drawing of the base of the brain of an idiot, in which there was a singular deficiency of the cerebellum; and also a cast of the brain of the chim- panzee, and one of the human brain. These two, making allowance for the size, almost perfectly agreed with regard to external appearances. aeceeaaatenena J. Huband Smith, Esq., by command of His Excellency the Lord Lieutenant, presented to the Academy an ancient gold semilunar ornament of considerable value, found in the county of Roscommon. The thanks of the Academy were voted to His Excel- lency for this donation. A considerable number of ancient bronze articles, con- sisting of portions of chain armour, a spear head, a lance blade, with some coins, found near Headfort, County Gal- way, were presented to the Museum on the part of Richard J. Mansergh St. George, Esq. Mr. St. George received the thanks of the Academy. The collection of Antiquities of the late Dean of St. Pa- trick’s was presented to the Academy in the name of the Subscribers, Resotvep,—That the List of Subscribers be printed as an Appendix to the Proceedings.* * See Appendix, Ne. I. 275 August 4. REV. C. W. WALL, D.D., in the Chair. The President made a communication respecting a me- : thod which had been lately proposed by Professor Badano of Genoa, for the solution of algebraical equations of the 4 fifth and higher degrees.* Lagrange has shown that the function P= (a tor" +o? 2” + wa!’ 4 wx")? receives only twenty-four different values, for all possible changes of arrangement of the five quantities, x’,.. . x”, if w be an imaginary root of unity, so that wo +o +o0?+0+1=0 Professor Badano has proposed to express these twenty- four values by certain combinations of quadratic and cubic radicals, suggested by the theory of biquadratic equations, and having the following for their type: = wy be V Hot A/ Hg FV Ba + /Hs — Hs — V He eV $87 $V He + 4/ Ho V Bio + 4/ Hn — Hn — V Hi} Ae fis + V a + 8 o/s FV Bio + 8a/ tz— V this} AV {ito + V Boo + 0? 9 Hart V Hae + 8 A/ Has— V Hos 3 _ O being here an imaginary cube root of unity. He contends z that the twenty-four quantities, H,,... Ho, are all symme- _ tric functions of the five quantities 2’,...2”; and that they are connected among themselves by the sixteen relations -H3==H5, By = He, H7 = Hig = Hig, Hs = Hi4 = Hoy Ho = His — Hay Ayo = Hig Ha, Hy = Hi7 = Hog, Hig =Hig—Hs, Ho= Huy Hio= Hie REGAN 3 oy eee ee Se a * Nuove Ricerche sulla Risoluzione Generale delle Equazioni Algebriche del P. Gerotamo BapAno, Carmelitano scalzo, Professore di Matematica nella R. Universita di Genova. Genova, Tipografia Ponthenier, 1840. See also an “ Ap- pendice” to the same work. VOL. Il. Z 276 Sir W. Hamilton examines, in great detail, the composition of the two conjugate quantities H,, He, which are each of the thirtieth dimension relatively to the five original quantities a’,...a"; and arrives at the conclusion that neither Hy nor Hg is a symmetric function of those five quantities #’,...2”, though each is symmetric relatively to four of them. He finds also that these two quantities H, and Hg are not gene- rally equal to each other, but differ by the sign of an imagi- nary radical, namely, (0—6@) (w—w’®—w* + 0’) = Y —15, when they are fully developed, in consistency with Professor Badano’s definitions. Analogous results are obtained for the two quantities H3, H;; and these general results are veri- fied by applying them to a particular system of numerical values of the five quantities 2’,...a”. It is shown also that the three quantities Hy, H)3, His, are neither independent of the arrangement of those five quantities 2, nor (generally) equal to each other. And thus, although , is symmetric, and Hy vanishes, Sir W.H. conceives it to be proved that Professor Badano’s expressions, for the twenty-four values of Lagrange’s function ¢°, give no assistance towards the solution of the general equation of the fifth degree, and therefore that the same method could not be expected to resolve equations still more elevated, even if we were not in possession of an @ priori proof that no root of any general equation above the fourth degree can be expressed as a func- tion of its coefficients, by any finite combination of radicals and rational functions. DONATIONS. Three Silver Coins, found at Rockingham, the seat of Vis- count Lorton. Presented by C. T. Webber, Esq. Copper Medal, “ The glorious attempt of LXIV. to pre- 277 serve the Constitution.” MDCCXLIX. Dublin. Presented by Miss A. Clibborn. % The past and present Statistical State of Ireland exhibited ina Series of Tables. By Cesar Moreu, Esq., F.R.S. Pre- sented by James Hardiman, Esq. Proceedings of the Royal Society of Edinburgh, Nos. 19, 20, for 1841-2. Transactions of the Royal Society of Edinburgh. Vol. XV. Part 2 (pp. 265-334). Memoirs of the Literary and Philosophical Society of Manchester. Vol. VI. New Series. Statistical Returns of the Dublin Metropolitan Police for the year 1841. Presented by the Commissioners. Lecture on the Application of Science to Agriculture. By Charles Daubeny, M.D. Presented by the Author. Proceedings of the American Philosophical Society. From November, 1841, to April, 1842. The New County Book of Tipperary. By Jeffries Kings- ley, M.R.I. A. Presented by the Author. Proceedings of the Geological Society of London. Vol. Il. Part II. 1841-42. Nos. 77 to 83. Fourth Annual Report of the Commissioners of the Central Loan Fund Board of Ireland. (Act 1& 2 Vict. c. 78.) Pre- sented by Mr. Piessé. § Transactions of the American Philosophical Society held at Philadelphia. Flora Batava, door Jan Kops. Nos. 123 and 124. Niewe Verhandelingen Van het Bataafsch Genootschap der _ Proefondervindelijke Wijsbegeerte te Rotterdam. Achtste _ Deel. Tweede Stuk. Copy of an Inscription found in Babylon by Harford 278 ten Bandes Zweite Abtheilung, in der Rethe der denkschriften der XVIII. Band. Philosophical Transactions of the Royal Society of Lon- don for the Year 1842. Part I. Abhandlungen der Mathematisch-Ph ysikalischen Classe der Keeniglich Bayerischen Akademie der Wissens-chaften, Drit- ten Bandes Zweite Abtheilung, in der rethe der denkschriften der XVI. Band. Ueber das Magnetische Observatorium der Kénigl. Stern- warte bei Miinchen. Von Dr. J. Lamont. Presented by the Author. A Piece of Leather, found in taking up Part of the old City of Dublin Wall, adjoining the old Tower in the lower Castle Yard, by Mr. Johnson, and which is supposed to have lain there since the Year 1202, Presented by W. Farren, Esq. Memoires de Institut de France. Academie des Sciences Morales et Politiques. Savans Etrangers, Tome I. Academie des Sciences Morales et Politiques. Tome III. Memoires presentés par divers Savans al Academie Royale des Sciences de l'Institut de France. Sciences Mathema- tiques et Physiques. Tome VII. Memoires de l'Institut de France, Academie Royale des Sciences. Tome XVIII. Notices et Extraits des Manuscrits. Tome XIV. 2nd Partie. Archeologia. Vol. XXIX. Journal of the Statistical Society of London. Vol. V. Part 2. July to September, 1842. Archives du Musée d’Histoire Naturelle. Tome I. Liv. 1,2, 3,4; and Tome II. Liv. 1 and 2. The South Australian Almanack for 1842. By James F. Bennett. Presented by George Davies, Bag., 1: CD Proceedings of the Zoological Society of London. Part IX. 1841. PROCEEDINGS OF THE ROYAL IRISH ACADEMY. _ 1842. No. 36. : November 14, SIR Wm. R. HAMILTON, LL.D., President, in the Chair. —_———— The Secretary read a paper by Sir David Brewster, ‘ on the Compensations of Polarized Light, with a description of a Polarimeter for measuring Degrees of Polarization.” The author first directed attention to the difference of opinion between him and most other philosophers, as to the _ constitution of partially polarized light; it being generally _ supposed that such light is a mixture of common light and perfectly polarized light, whilst he considers that the entire _ quantity of light undergoes a physical change by approxima- ting more or less to the condition of light completely pola- rized. Upon this view he had long since explained the laws of polarization discovered by himself, but he had been anxious to obtain experimental evidence capable of deciding between the two ideas, and in this he considers that he is now successful. By means of experiments,—described in the paper,—-the author points out that when two portions of light oppositely polarized compensate each other, the proportions and con- litions necessary are not those which could result from mix- s of common light with fully polarized light, and hence that the pencils must be wholly in different physical These experiments led him to the invention of 2A 280 an instrument termed the Compensating Rhomb, by means of which he considers decisive evidence of the correctness of his views has been obtained. In order to determine if this principle be general, and to ascertain the laws of the compensation of polarized light, Sir David Brewster constructed an instrument for measuring the degrees of polarization. This he calls a Polarimeter. It consists of two parts, one of which is intended to produce a ray of compensation, having a physical character susceptible of numerical expression, and the other to produce polarized bands, or rectilinear isochromatic lines, the extinction of which indicates that the compensation is effected. The de- tails of the construction of the instrument are fully given in the memoir, and numerous experiments made with it, and confirmatory of the author’s views, are described. In conclusion, Sir D. Brewster points out as the general results of his inquiries, as follows: ** 1. The first and most important result of this inquiry is, that it affords a new and independent demonstration of the laws of the polarization of light by reflexion and refraction, given in my papers of 1830. As this result has been already referred to, I shall merely mention the following general proposition. ** When a ray of common light is incident at any angle upon the polished surface of a transparent body, the whole of the reflected pencil suffers a physical change, bringing it more or less into a state of complete polarization; inwirtue of which change, its planes of polarization are more or less turned into the plane of reflexion, while the whole of the re- fracted pencil has suffered a similar, but opposite change, in virtue of which, its planes of polarization are turned more or less into a plane perpendicular to the plane of reflexion. **2, Asthe light of the sky and the clouds is more or less polarized, the employment of the light which they reflect may, in delicate experiments, be a serious source of error, if —— 251 we are not aware of its properties. By the principle of com- pensation, however, we may convert this partially polarized light into common light, and thus make experiments with as great accuracy in the day-time, as we can do with the direct light of a flame. If the light from a particular part of the sky be admitted into a dark room, or otherwise employed, we have only to compensate its polarization either by reflexion or refraction, and employ, as unpolarized or common light, that part of the light which corresponds with the neutral line. “3. The laws of the compensation of polarized light enable us to investigate the polarizing structure of the atmosphere, and to ascertain the nature and extent of the two opposite polarizing influences, which I have found to exist in it, and by the compensation of which the neutral points are pro- duced. But, as I shall soon submit to the Society the results of my observations on this subject, I shall not add any thing further at present. _ “4, Inevery case where reflected or refracted light reaches the eye of the observer, whether it comes from bodies near us, or from the primary or secondary planets of our system, the doctrine of compensation enables us to obtain important information respecting the phenomena presented by light thus polarized. The nature of the reflecting or refracting surface, the angles of reflexion or refraction, and the nature _ of the source of illumination, may, in certain cases, be ap- proximately ascertained. “5. When the light of the sun, or any self-luminous body,. is reflected from the surface of standing water, such as the _ sea ora lake, it is polarized according to laws which are well known; but when the partially polarized light of the sky (light polarized in every possible plane, passing through the sun and the observer) is reflected, a variety of curious com- _ pensations take place, which, when the position of the ob- strver is fixed, vary with the season of the year, and the hour 2a2 282 of the day. In some cases, there is a perfect compensation, the partially polarized light of the sky being restored to common light by the reflection of the water. In other cases the light of the sky has its polarization increased by re- flexion from the water in the same. plane in which it was itself polarized; and in other cases, the compensation is. effected only in particular planes. At sunset, for example, the light reflected from the sea at a great obliquity in two vertical planes inclined 45° to a vertical plane passing through the sun and the observer, is compensated in these two planes, or the plane of its polarization is inclined about 45° to the reflecting surface. The same observations apply to the light of the two rainbows when reflected from the surface of water. “6. When the light of the sky, or of the rainbow, is re- flected from surfaces not horizontal, such as the roofs of houses, sheets of falling water, or surfaces of smoke and va- pour, the compensations are more varied, and a perfect neutralization of the light by the second reflexion is more frequently obtained.” Professor Lloyd mentioned some circumstances which appeared to be opposed to Sir David Brewster’s views. Professor Kane commenced the reading of a paper “ on the Tannin of Catechu, and the chemical Substances derived from it.” The abstract of this paper will be printed when the con- clusion has been read. DONATIONS. Transactions of the Zoological Society of London. Vol. III. Part1. 1842. Reports of the Auditors and Council of the Zoological Society of London, April 29th, 1842, and List of Members. 283 Proceedings of the Royal Society. Nos. 52, 53. Supplementary Appendix to the Report of the Poor Law Commissioners of the Medical Charities in Ireland, with In- dexes. 1841. Presented by the Commissioners. A pamphlet entitled, “ Is Selenium a true Element?” Pre- ‘sented by Septimus Piesse. November 30. (Stated Meeting.) SIR Wn. R. HAMILTON, LL.D., President, in the Chair. John Anster, LL. D., was elected a member of the Com- mittee of Polite Literature, in the room of the Rey. Dr. Porter, who had resigned. . Resotvep,—On the recommendation of Council,—That .. Mr. E. Curry be employed to make a Catalogue of the Irish MSS. in the Library of the Academy, for the sum of £100. The Secretary read a letter from George Birch, Esq., presenting to the Academy an ancient tombstone, from the Abbey of Mondhinchy, with an inscription in the Irish cha- racter. Resotvep,—That the thanks of the Academy be given to Mr. Birch for his donation. Rey. Dr. Todd, V.P., gave the following account of the Proceedings of the Committee for the purchase of the late Dean of St. Patrick’s collection of Irish Antiquities, which had been recently presented to the Academy. ___ “It has been thought fitting that some record should appear in e the Proceedings of the Academy of the successful efforts that have * made under the direction of the Committee of Antiquities, for _ raising the subscription, which has preserved from dispersion, and 284 placed in the safe keeping of this Society the invaluable Collection of Irish antiquities belonging to our late lamented Vice-President, the Dean of St. Patrick’s. ‘“‘ It was well known to all his intimate friends that one of the principal motives that influenced him in the formation of his Mu- seum, next to the zeal for the preservation and study of antiquities which characterized him, was a wish to have his collection pre- served for public use, under the care of the Royal Irish Academy. “« As soon as it was ascertained, therefore, that he had died intes- tate, and consequently without making any provision for carrying these his often expressed wishes into effect, many of his personal friends, knowing how deeply he would have deprecated the dispersion of his Collection, felt anxious, were it only as a testimony of respect to his memory, that the Irish part at least of the Museum should be ob- tained for the Academy; and in this they were warmly seconded by all who were aware of the value of the Collection, and who felt the great importance of a National Museum of Antiquities to the study of our ancient history. “‘ Accordingly, at the Stated Meeting of the Academy in No- vember,;- 1840, soon after the lamented death of the Dean, the sub- ject was brought forward, and the Committee of Antiquities were requested to take immediate steps towards opening a subscription for the purchase of the Irish part of the collection. “The Committee met immediately after, and their first act was to publish in the principal newspapers of Dublin a short address, for the purpose of ascertaining the state of public feeling on the subject. A circular was also prepared, and sent to the principal nobility and gentry of Ireland, to all in short, as far as they could be ascertained, who were thought likely to take an interest in the design. ‘¢ This was all that could be done at that time. The absence of Mrs. Dawson on the Continent, and the consequent difficulty of as- certaining the wishes of the Dean’s family, rendered it impossible to discover what sum they were likely to accept for that portion of the Museum which the Committee were commissioned to purchase, or indeed whether they would consent at all to separate the Irish part of the Collection from the rest. . 285 “From this unavoidable delay, the zeal of many appeared to cool, and the subscription for a time proceeded but slowly; but at length, on the 27th of March, 1841, the Committee took the bold step of authorizing Mr. Petrie and Dr. Aquilla Smith to offer £1000 for the Collection. “TI should have mentioned that this sum was decided upon after an exact valuation of the whole. The coins were valued by Dr. Aquilla Smith, and the other antiquities, at Mrs. Dawson’s special request, by Mr. Petrie; and the sum at which these gentlemen fixed _ the value of the Collection was £1060. The Committee were of opinion, therefore, that in offering the sum of £1000, they were dealing fairly with the public fund entrusted to them; while by striking off about six per cent. from the amount of the valuation, they were only allowing for the necessary expenses which would have attended the sale of the Museum had it been submitted to a public auction. “‘ It was not, however, until the 26th of June following that a final answer was obtained from the Dean’s family to the proposal of the Committee. On that day Dr. Smith reported that Mrs. Dawson had consented to accept the offered sum, and also that she was will- ing to allow three months from that date for its collection. ‘* New efforts were then made by the Committee: circulars were again sent out, and an address to the public was inserted in the newspapers ; a deputation was appointed to wait on His Excellency _ the Lord Lieutenant, who contributed £20 to the fund; and in _ short every exertion was made to rouse the friends of Ireland to the _ importance of the great national object that was in view. ____** The success that has crowned these efforts is mainly owing to a the zealous manner in which the exertions of the Committee were . seconded by some other members of the Academy, who aided them _ by their advice and counsel, and also by their invaluable and inde- _ fatigable labours. Of these it is imipousible to avoid naming Mr. _—_— = ee were most deeply indebted for the success of their un- aking ; and although it is obviously improper to allude to any individual of those who were members of the Committee itself, yet . feel sure I shall be pardoned in departing from strict propriety so 286 far as to say, that to the exertions of Dr. Aquilla Smith and Mr. Petrie, their intimate knowledge of the contents and value of the Collection, and their good offices with the family of the Dean, the Academy and the country are mainly indebted for the possession of the trea- sures which have been added to our Museum. “« Still, ‘however, the subscriptions for some time came in so slowly, that it became necessary to solicit more time for collecting the money than was originally agreed upon; and this request was acceded to by Mrs. Dawson, with a liberality for which she deserves the gratitude and the thanks of the Academy. ‘«« At length on the 9th of April of the present year, the first in- stalment of £500 was paid to Mrs. Dawson, and the Collection was soon after removed to the Academy House, under the superinten- dence of Dr. Aquilla Smith. ‘A guarantee for the payment of the remaining half of the purchase money having been given to Mrs. Dawson by certain sub- scribers to the fund, the Antiquities were at first placed under the custody of those gentlemen; who bound themselves to hand over the Collection to the Committee as soon as the debt for which they had made themselves responsible was discharged. “* On the 31st May the whole remainder of the purchase money was paid to Mrs. Dawson, and the gentlemen who had so liberally come forward to guarantee its discharge were released from their obligation. It was found also, that after the payment of all the incidental expenses, a balance remained at that time in favour of the fund to the amount of £24 17s. 6d. This balance was subsequently increased by some subscriptions that afterwards came in, and the whole overplus has been applied, under the direction of the Com- mittee, to the purchase of some valuable antiquities, which have been added to the Collection. “In recording this last stage of the proceedings of the Com- mittee it is necessary to remark, that but for the public spirit of the individuals who came forward to give their personal security to Mrs. Dawson for the payment of the purchase money, all would have been lost, and the Museum would necessarily have been sent for public sale to London. For although at that time the stipulated sum had been very nearly promised, yet many of those who had put 287 down their names had not paid their subscriptions, and the time ne- cessary for collecting the money would have exceeded the limit to which the Committee had bound themselves to Mrs. Dawson; and thus she would have been left at liberty to take other means for disposing of the Museum. It is necessary, therefore, that the Aca- _ demy should know that the gentlemen who came forward to rescue the Committee from a dilemma which would have made vain all their previous exertions, and to whom we are therefore so particu- larly indebted for the great step that has been made towards the formation of a National Museum, are George Carr, Esq., Dr. Aquilla Smith, Professor Mac Cullagh, Thomas Hutton, Esq., and Robert Callwell, Esq. *‘ The thanks of the Academy are also due to Mr. Clibborn for his invaluable services throughout the whole of these transactions, and particularly in the last stage of them, when it became necessary to make exertions to call in the subscriptions that had been pro- mised, and to take steps, after the Museum had come into our pos- session, for the arrangement and safe keeping of its contents. To _____ him also we are indebted for the ingenious plan for a new Board ~ Room, which has received the approval of the Council, and is sub- ‘mitted to your consideration this evening: a plan which will enable us to convert the room in which we are now assembled into a Mu- seum, where the treasures of which we are now the guardians, may be displayed in a manner useful to the public, and their permanent security duly provided for. “The special thanks of the Academy are also due to Messrs. Boyle, Low, Pim, and Co., who kindly permitted subscriptions to be paid at their house, without any charge whatsoever to the fund ; and whoalso offered to advance to the Committee any sum that might ‘be required as a temporary accommodation, during the necessary delay that attended the collection of the subscriptions. This liberal offer the Committee were compelled to avail themselves of, by _ drawing upon Messrs. Boyle and Co. for a sum of £53 15s. 5d. on _ the Ist of June last, a sum which was not entirely repaid for up- wards of two months afterwards. “It is proper to mention here, that His Excellency Earl De _ Grey, in addition to his subscription to the fund for the purchase of 288 the Dawson Collection, has also been pleased to present to the Academy a valuable Aision of gold, which was recently found in the county of Roscommon, and of which His Excellency became the purchaser, for the express purpose of placing it in our Museum. Mr. H. J. Monck Mason also, in addition to his subscription, presented a very beautiful gold Fibula, of considerable weight and value. ‘* Tt should be distinctly understood, that the subscriptions re- ceived have enabled the Committee to pay all the expenses attendant upon these transactions, without any charge whatsoever to the funds of the Academy. ‘** The Academy, as a body, have had nothing whatsoever to do with the purchase of the Museum, and there will be found among the subscribers very many names of gentlemen who are not mem- bers of, or in any way connected with our Society. The Museum, therefore, strictly speaking, is the property of the subscribers, and is by them presented to the Academy, to be kept by us in trust, for the benefit of the public. The Academy, as a Corporation, have contributed nothing to the purchase, except so far as their consent- ing to take the charge of so valuable a gift, and to provide a room for its exhibition, may be considered, as it doubtless is, a most im- portant contribution to the great end which the subscribers have had in view. ‘‘ The accounts of the Committee have been audited by Messrs. Callwell and Hutton; they are in the hands of Mr. Clibborn, and are open, of course, to the inspection of any of the contributors. “Tt may be well now to say a few words on the value and con- tents of the Museum of which we are thus become the guardians. “The Museum contains no less than ninety-seven ornaments of solid gold, whose total weight amounts to 98 oz. 144dwt. It pos- sesses also 252 articles of pure silver, and 1674 bronzes and other antiques, composed of pottery, amber, glass, and the baser metals. ‘* This enumeration does not include the coins and medals, which are of singular interest and value, and of which a catalogue, in the handwriting of Dean Dawson, is now on the table. ‘“* To specify the various articles of value and interest more par- ticularly, so far at least as to give any detailed account of them, would be too great a trespass on your time, even if I could feel my- ~ al ie wa self fully competent to the task; but it is impossible to close this Report without endeavouring to give you some rough and general view at least of the treasure which we have now obtained. ‘* Among the gold ornaments are twenty-seven fibulz, one of them of considerable size; three perfect torques, and fragments of some others; two gorgets; two singular hollow balls or beads of gold, which were found with eleven others in the County of Ros- common, and which the Dean saved from the crucible of the gold- smith; a most interesting collection of ancient finger rings, and _ sixteen specimens of the small solid rings of gold, which are be- lieved to have been the current money of the ancient inhabitants of 289 Ireland. “ The collection of silver finger rings and of ancient seals, is of great interest and value. Among them will be found the matrices of the seals of the O’Neills and other Irish chiefs, with several ec- clesiastical seals of various periods. “There is a remarkable collection of the ancient Irish bells, whose uses and history our friend Mr. Petrie has so ably discussed ; some of these are the large bells, which once, perhaps, were sus- : pended in the Round Towers ; others are the small altar bells, many of them exhibiting proofs of great antiquity. One of the large bells contains an Irish inscription, which proves it to be as old as the ninth century. “The collection of military weapons and other antiques con- nected with the warfare of our ancestors is of great extent and value. It contains a great variety of specimens, in excellent preser- vation, of the flint arrow heads and spear heads, which are supposed to have been the most ancient weapons in use in Ireland; a large number of the peculiar weapon, in stone and bronze, called celts, of all the sizes and forms in which they are found; and a magnificent _ collection of swords and spear heads, from many of the remarkable fields of battle recorded in the history of Ireland. “It would be drawing too much on your patience to enter _ more particularly into a description of particular objects of interest . in this Collection ; at some future time it might perhaps be an enter- taining, as well as an instructive task (if some of our antiquaries _ would undertake it), to exhibit to the Academy, from time to time, 290 the more remarkable and important articles of our Museum, with remarks on their history, and use. But a more fitting occasion for this will perhaps be found, when Tur Dawson Co.tuzction is pro- perly arranged and displayed, as I hope it soon will be, in a room fitted for its reception. “I must say a few words of the coins and medals before I can conclude this Report. ‘* They may be divided into three classes : “1. The Danish Irish coins of thé ninth and tenth centuries. ‘This series comprehends the coins of Domnald and some of the sovereigns unknown; a coin of Ivar, A. D. 872, and a large collection of the Dublin coins of Sitric, A. D. 980 and 989. Also the Dublin coins of Athelred, and some of great singularity and rarity, which bear the impress of the Dublin mint, and which the Dean, on grounds however admitted by himself to be doubtful, was at one time disposed to refer to the reign of A®thelstan. ‘© 2. The coins struck in and for Ireland by British sove- reigns. ‘‘ Among these are a magnificent series of the coins of John, minted in Dublin, Waterford, and Limerick, between the years 1177 and 1199; and a singularly perfect series of the coins struck in Ire- land from the reign of John to that of George IV., containing many varieties of great rarity and value. ‘© 3. 4 series of medals struck in Ireland. ‘‘ The most complete that has ever been collected. This series is particularly interesting to the Academy, because the late Dean, a very short time before his decease, contributed to our Transactions a valuable paper on the subject of Irish Medals, in which the most remarkable of these very medals are noticed and described. “« On the whole, I would congratulate the Academy, and not the Academy only, but the country, on the possession of this important and invaluable Collection. As one of those who enjoyed the pri- vilege of an intimate acquaintance with its late lamented owner, I cannot help expressing the gratification which I feel in the reflection that this, the national part of his Museum, is saved from dispersion, secured to Ireland, and presented to the Academy, for which he had destined it. I feel a melancholy satisfaction, in which his 291 friends will sympathize with me, in having (in however humble a degree) taken a part in bringing about the fulfilment of the wish I have often heard him utter, that his Museum might be here; and __ in the assurance that here his name will live as a benefactor to his country, and an example to our gentry, by whom the study and preservation of our antiquities have been (I must say) disgracefully neglected. “« But on public grounds, most of all, I would congratulate the Academy on having now laid the foundation of a National Museum, which will doubtless be the means of preserving many articles of value and interest from destruction—of bringing together the many curious relics of the past, which are now in the hands of private families or individuals, and perhaps also of awakening the attention of the Government of the country, to the importance (too long for- gotten or overlooked) of forming, upon a liberal and extensive basis, a really National Museum of the Antiquities of Ireland.” Resotvep,—That this Report be entered on the Minutes, and published in the Proceedings. _ Resotvep,—That the special thanks of the Academy be given to those subscribers to the Dawson Fund who are not _ members of the Academy.* Resotvep,—On the recommendation of Council,—That _the plan of the new Board Room proposed by Mr. Murray _ and Mr. Owen, be approved of by the Academy. ; f December 12. SIR Wu. R. HAMILTON, LL.D., President, in the Chair. _ Rev. Dr. Todd, V. P. on the part of the Knight of Glin, pre- sented to the Academy a gold coin, with an Arabic inscrip- ion, found in the wall of a house in the townland of Killeny, * See List of Subscribers in Appendix No. I. 292 The thanks of the Academy were presented to the Knight of Glin for his donation. Dr. Apjohn read a paper by Dr. Andrews, “ on the Heat developed during the Formation of the Metallic Compounds of Chlorine, Bromine, and Iodine.” The author confines his attention in the present paper to the combinations of zinc and iron, which metals, he shows, will not combine at ordinary temperatures with chlorine, bromine, or iodine, unless water is also present. The re- actions which take place when an excess of iron in a state of fine subdivision is agitated with any of the three elements just mentioned, are rather complicated,—a sesqui-compound (Fe, Cl;, Fe, Br3, Fes 1;) being first formed, which afterwards combines with an additional atom of iron, and becomes con- verted into a proto-compound (Fe; Cl;, &c.) The heat de- veloped during this process consequently arises from three distinct causes:—first, the union of Fe, with Cl;; secondly, the solution of the compound so formed in water ; and thirdly, its conversion into Fe; Cl; by its combination with Fe. The heat arising from the two latter causes being determined by separate experiments, and taken from that obtained during the original reaction, the remainder will be evidently the heat due to the union of Fe, and C];; and by a similar method, the heat developed during the union of Fe, with Br, and of Fe, with I;, may also be determined. Referred to the num- ber of degrees of Fahrenheit’s scale, through which one grain of water would be heated by the combination of one grain of iron in each case, the heat evolved during the formation of Fe, + Cl, is 3246°; during that of Fe, + Brs, 2302°; and of Fe, + I,, 834°. The reaction which occurs when zine is treated in a similar manner is much simpler, and the heat developed, referred to the zine as unit, is 2766° for Zn + Cl; 2284° for Zn + Br; and 1474° for Zn + I. The author also proves, by direct experiments, that when 293 solutions of the sesqui-chloride, sesqui-bromide, or sesqui- iodide of iron are converted into the corresponding proto- compounds of iron, by combining with iron, the heat in all cases is the same for the same quantity of iron dissolved. The method by which these numerical results were ob- tained, and the apparatus employed, are minutely described in the original communication. Dr. Kane inquired how far he considered the final results obtained by Dr. Andrews to affect the ideas of thermo-che- mical combination, founded on the experiments of Despretz ~ and Dulong? Dr. Apjohn stated that the results of Dr. Andrews were quite opposed to their experiments, as he found the quanti- ties of heat not to bear any relation to the atomic weight of the combining bodies. The Secretary read a paper by the Rev. Edward Hincks * on the Chronology of the Eighteenth Dynasty of Manetho.” The object of this paper is to determine the period at which the eighteenth dynasty of Manetho flourished, by the recorded dates, in months of the wandering year, of facts, which must, from their nature, have occurred at known sea- sons of the solar year. Three such dates are brought for- ward: two of them relating to the time of the commencement of campaigns; and the third, to that of the inundation: and they all concur in depressing the epochs of the eighteenth dynasty about 350 years below those, which the Cham- pollions and Rosellini have adopted. An approximation to the dates of the accession of many monarchs of the dynasty is - attempted. For example, the year B. C. 1278 is fixed upon as very nearly, if not exactly, that of the accession of Ame- _ nothph III. Mr. Mallet having become acquainted with the recent 294 making, for optical and other purposes, gave a short account of them to the Academy. The improvements consist chiefly in— Ist. The use of platina bottoms to earthen melting pots, and heating these in improved furnaces from below, so as to produce circulation in the fluid glass. 2nd. In preserving the liquid glass from all contamina- tion from without by “tears,” &c. and from the dome of the furnace, as well as from deoxidation of the lead salts by contact of carbon. 3rd. In an improved mode of cutting off, by a platina blade, the upper portion of the fluid glass, without distur- bance of the remainder; thus separating the whole of the impure dross at top, which was heretofore stirred down into the mass just previous to casting. 4th. In a beautiful and effective mode of removing the air bubbles, or “ seeds,” as they are called, from the liquid glass, by placing the ignited glass pot of liquid metal within an exhausted receiver, so contrived that it can be rapidly placed within, and withdrawn from the vacuum vessel. Mr. Mallet was not aware that as yet any specimen of glass prepared by these improved processes had been wrought for any optical purpose, the inventor’s efforts having been as yet principally directed to the manufacture of plate glass; but he considered that the practical nature of these improve- ments, and their capability of being applied upon a large scale, gave good hope of their extension to the making of optical glasses also. Rev. Dr. Robinson made some remarks with reference to Mr. Faraday’s experiments on the manufacture of glass for optical purposes, and described the processes adopted at Munich in selecting the portions of glass of which lenses are formed. PROCEEDINGS OF THE ROYAL IRISH ACADEMY. ree te tie al) alow) piney wsibivous vitouys 1843. No. 87. ae en ee SR Rar aes January 9. SIR Ws. R. HAMILTON, LL.D., President, in the Chair. Stewart Blacker, Esq., Thomas Cather, Esq., William V. Drury, M.D., William Gore, M.D., Thomas Hodder, Esq. R.N., Rev. John Homan, Henry Hutton, Esq., Robert Leslie Ogilby, Esq., the Hon. Frederick Ponsonby, and George Sal- ‘mon, Esq., F.T.C.D., were elected members of the Academy. Rev. H. Lloyd, V. P., read a paper “ on the Determina- tion of the Intensity of the Earth’s Magnetic Force in abso- lute Measure.” The means of determining the intensity of the earth’s mag- _ netic force in absolute measure consist, it is well known, in _ observing the time of vibration of a freely-suspended_hori- _ zontal magnet, under the influence of the earth alone, and _ then employing the same magnet to act upon another, which is also freely-suspended, and noting the effects of its action combined. with that of the earth. From the former of these _ observations we deduce the product of the horizontal com- ponent of the earth’s magnetic force into the moment of free n agnetism of the first magnet,—from the latter, the ratio of the same quantities; and, the product and the ratio being thus known, the two factors are absolutely determined. The former part of this process involving no difficulty which may VOL. It 2B 296 not be overcome by due care in observing, we shall confine our attention, in the present communication, to the latter. Two methods have been proposed for this second obser- vation, one by Poisson, and the other by Gauss. The me- thod of Poisson consisted in observing the time of vibration of the second magnet, under the combined action of the first and of the earth, the acting magnet having its axis in the magnetic meridian passing through the centre of the sus- pended magnet. In the method of Gauss, which is now universally adopted, we observe the position of equilibrium of the second magnet, resulting from the action of the same forces. The acting magnet being placed transversely with respect to the suspended one, the latter is deflected from the meridian, and the amount of this deflection serves to deter- mine the ratio of the deflecting force to the earth’s force. The position chosen by Gauss for the deflecting magnet is that in which its axis is in the right line passing through the centre of the suspended magnet, and perpendicular to the magnetic meridian, in which case the tangent of the angle of deflection is equal to the ratio of the two forces. From this ratio it remains to deduce that of the magnetic moment of the deflecting bar to the earth’s force. The difficulty of this process arises from the form of the expression of the force of the deflecting bar. This force being expressed by a series descending according to the negative odd powers of the distance, with unknown co- efficients, it is evident that observation must furnish as many equations of condition, corresponding to different distances, as there are terms of sensible magnitude in the series; and from these equations the unknown quantities are to be deduced by elimination. Now, the greater the num- ber of unknown quantities thus eliminated, the greater will be the influence of the errors of observation on the final re- sult; and if, on the other hand, the distance between the magnets be taken so great, that all the terms of the series a 297 after the first may be insensible, the angle of deflection be- comes very small, and the errors in its observed value beara large proportion to the whole. It fortunately happens, that at moderate distances (dis- tances not less than four times the length of the magnets) all _ the terms beyond the second may be neglected. The ex- pression for the tangent of the angle of deflection is thus reduced to two terms, one of which contains the inverse cube of the distance, and the other the inverse fifth power; that is, if w denote the angle of deflection, and p the distance, , Q Q tanu = — =} a + De in which @ and @/ are unknown coefficients, the former of which is double of the ratio sought. Accordingly, the me- thod recommended by Gauss consists in observing the angles of deflection, u and uw’, at two different distances, p and p’, and inferring the coefficient @ by elimination between the two resulting equations of condition. ' It is evident, however, that if the coefficient of the in. _ verse fifth power of the distance be evanescent,—or, more _ generally, if the ratio of the two coefficients be known @ _ priori,—the quantity sought may be obtained, without elimi- nation, from the results of observation at one distance only. _ For if a = ha, h being a known quantity, the preceding ex- _ pression becomes h and accordingly the value of @ is obtained, from the result of observation at a single distance, by the formula te. D*tanw — ~ l+hpo-? not only is the labour of observation thus diminished, but (which is of more importance) the accuracy of the re- 2B2 298 sult is increased. In order to show this, the author en- tered into an examination of the amount of the probable error in the two methods, from which it appeared that the probable error of a, arising from an error in the observed deflection, will be less than in the usual method in the ratio of 1 to 5.563, even when the latter is employed in the man- ner most conducive to accuracy. In fact, the ratio of the probable error to the entire quantity is found to be ex- pressed, in the two cases, by the formule Age Au Ae v ge +t Au ce ae Ra ae g—l «uw where q denotes the ratio of the two distances; and the least Vq°+1 value of the factor — is 5.563, and corresponds to the ratio g = 1.32. In order to know the ratio hf, it is necessary to de- termine the moment of the force exerted by the deflecting magnet upon the suspended magnet, extending the approxi- mation to the terms involving the fifth power of the distance. The axis of the deflecting magnet being supposed to lie in the right line joining the centres of the two magnets, and the axis of the suspended magnet forming the angle y with that line, this moment is found to be 2mm’ Dp? : M3 w’;\ 1 sin) 91+ (2— 5cos*y —1 =) aa ; vg 1+ (2% +8 (5e0s4y—1) 2) LE, in which m and wm’, m; and m’;, denote certain integrals de- pending on the distribution of free magnetism, in the deflect- ing and suspended magnets, whose values are l l M = . mrdr, M3 = iv mr°dr, a4 La m being the quantity of free magnetism in any transverse section of the magnet, r its distance from the centre, and J half the length ofthe bar. The form of this result exhibits 299 the advantage of the method of deflection recently proposed by Professor Lamont, in which y = 90°, or the deflecting bar | perpendicular to the suspended bar. In the ordinary method, £ = 90° — uw; and, the moment of the force exerted by the earth being xm’ sinu, where x de- notes the horizontal component of the earth’s magnetic force, the equation of equilibrium is 2m § 1 M M3 ; M,’\ l tanu = 314 (et —s%t 4 15sintwt) f. D The angle of deflection, w, being small, the term involving the square of its sine may be neglected, in comparison with the others; and the equation assumes the form already ad- verted to, namely, Q h tanu = 53 (1+ 5)5 in which we have made, for abridgment, , = a ee 4 = _ ma i In order to apply this result, we must know, at least ap- proximately, the law of magnetic distribution, or the function of r by which m is represented. Almost the only knowledge which we possess on this subject is that derived from the researches of Coulomb. From these researches M. Biot has inferred, that the quantity of free magnetism, in each point _ of a bar magnetized by the method of double touch, may be represented by the formula m= Au — pl"); p being a quantity independent of the length of the magnet, and 4 a function of » and/. M. Biot has further shown, that when the length of the magnet is small, the relation between _m and r is approximately expressed by the simple formula ‘% Ss up re 555 ~2 300 the curve of intensities becoming, in that case, very nearly a right line passing through the centre of the magnet. Employing then this approximate formula, we have mM=3m'?; mM3;= 2m'l'. : *,° - M ° The ratio of these quantities is = = 27, a value indepen- dent of m’; and substituting in the expression of h above given, and designating the half lengths of the deflecting and of the suspended magnets by / and /’, respectively, h=2(2?—3/*); an expression whose value may be exactly known, indepen- dently of experiment. This value vanishes, when J? = 327, or i= 1-224/'; and in this case, therefore, the quantity sought is given by the simple formula Q = D’tanu. The author concluded his paper with an account ofa series of deflection experiments, instituted for the purpose of confirming these results. The magnets employed were cylindrical, their lengths being 3 inches and 33 inches, and their diameter 3-10ths of aninch. The observations were made with every precaution necessary to insure exactness, and at times when the fluctuations in the direction and in- tensity of the magnetic force were very small; and their re- sults verify the conclusions above obtained, as applied to the case of small magnets. Dr. Apjohn next read the following letter, which he had received from Captain Boileau, superintendent of the Mag- netic Observatory at Simla, in India. ** Simla, March, 7, 1842. ‘¢ My pear Sir, “‘T have the pleasure of forwarding to you, through the Government of India, a complete set of hygrometric tables, 301 : computed by my assistant, from your last formula, to which I have added a vapour table, computed by Biot’s formula, from Dalton’s experiments, which is the same that Pouillet has used in the last edition of his Traité de Physique, that I have seen. Every one of the numerical values in this table (No. 3) has been computed directly from the formula to seven places of decimals, five of which only have been retained. In like manner, in part 1, each of the numerical values for depressions to one-tenth of a degree Fahrenheit, has been directly computed for twenty and for thirty inches of | pressure, and the intermediate values obtained by addition. All the work has been checked by differences, and examined by three separate computors. “© Accompanying, are also sent the separate observations of the wet and dry bulb thermometers, of Daniell’s hygro- meter, and of the standard barometer, with notice of the : weather for the twelve term days of 1841, which have been ; taken specially for your own use, and which you will, I think, find to confirm the views you had already taken upon the subject. There is one point which strikes at first sight, viz., that with very few exceptions, the dew-point, by the hygro- meter, is too high. It is a difficult instrument to use. It requires the observer to approach near to it; and, even with the utmost care, it is difficult to prevent an effect sensible at times to a prejudicial extent, upon the hygrometric condition of the surrounding air. None of these difficulties occur with the wet and dry thermometers, which have one still greater advantage, viz., the ease with which the wet ball can, under almost any circumstances, be moistened. ** During several months, we observed the hygrometer hourly on term days, but finding that this gave much trouble, _ and was likely to prejudice the readings of the magnetome- ter, I discontinued the practice, and had since but one ob- _ servation every two hours. During this year, I regret to say, that a failure in ether 302 has prevented any readings on either January or February term days, and of a supply of five pints just had up under order of Government, nearly three and a-half pints have evaporated on the journey. So much for an Indian climate, and bottles not hermetically sealed. You will oblige me by acknowledging the receipt of this packet, either through our -mutual friend Professor Lloyd, or through the Military Se- cretary at the East India House, Philip Melvill, Esq.; and if you wish me to alter the system adopted, you have only to say so, and I will endeavour to meet your views. I hope to continue the regular series from this month again without interruption. “ Believe me to remain, with kind regards, “« My dear Sir, “Yours very truly, * S. Borteavu. “ P. S.—You can make any use of the accompanying do- cument you may please to do.” Dr. Apjohn then observed, that availing himself of the per- mission given him by Captain Boileau, he would make a few remarks upon the hygrometric observations made on the mag- netic term days for 1841. These observations were highly in- teresting to meteorologists, having been made by an officer of great scientific attainments, of extensive experience as an observer, and with the aid of first-rate instruments: but his (Dr. Apjohn’s) reason for considering them particularly im- portant was, that they furnished the means of estimating the relative merits of the two hygrometric processes at present in use, viz., that according to which, the dewpoint is directly got by the aid of Mr. Daniell’s instrument, and that which conducts to the same conclusion through the application of the well known formula, Pat! 1 ee v4 SF es f’ =f' — 01147 (t—t’) x 30 * In this expression 7’ is the force of vapour at dew-point, /” the force of 303 to the temperatures indicated by a wet and dry thermo- meter. The observations for the April term day, were those to which it was his intention to advert, as they exhibited higher values for ¢—7’, than those made in any other month. Now upon looking through these which amount to 24, the first fact which at once presents itself is, that in every in- stance but two, the observed dew-points are higher than ob- tained by the formula, and in some instances, by as many as nine degrees Fahrenheit. One or other series, therefore, must be erroneous. That the observed dew-points are inac- curate, Dr. Apjohn inferred, on the ground of their being in- consistent with each other ; for he held it as quite certain, whe- ther the hygrometric expression be correct or not, that when in the case of any two distinct observations, ¢ and ¢’ have the same values, that upon both such occasions the air includes the same amount of moisture, or has the same dew-point. Tried by such a criterion, the results obtained with Daniell’s instrument are defective, as is well illustrated by the follow- ing extract from the April observations. q : ; t t’ t" ob. = t" cale. 10670 5143.5 $4.7) seis spongy saciggg § OP:.i24;4 7 yee 47 31 31.6 17 €62 47 36.6 32.8 2 §55 42.5 30.5 an 24 Ye 42.2 33 28 Sebi ' 6G). .1.2 From what has been just said, it is obvious, that observa- tions 10 and 11 should give nearly the same dew-point. This is true of the dew points got by the formula, but not at all of the direct determinations by the hygrometer, as those _ _ vapour at ¢’, the temperature by the wet thermometer, and ¢ the temperature of jt the air, 304 differ 9°.5. In 7 and 17, the dew-points are necessarily nearly the same. The results got by the formula differ by only 1°.2, while the instrumental ones differ by 6°.6. Again, 2and 24 should give g.p. the same dew-point. This is true of the formula, but not at all of the hygrometer, as the tem- peratures it yields differ by 2°.5. The preceding instances, the number of which might be greatly augmented, were, Dr. Apjobn conceived, quite sufficient to show, that even in the hands of Captain Boileau, Daniell’s instrument has not given correct conclusions; and that, therefore, generally it cannot be relied upon for determining, accurately, the hygrometric relations of the atmosphere. With respect to the column of results obtained by Cap- tain Boileau, from the wet bulb process, Dr. Apjohn could not entertain the slightest doubt of their exactness, having found that his formula stood the severest experimental tests to which he could subject it. These experiments, however, (see Transactions Royal Irish Academy, vol. vi.) were, he admitted, all made under pressures, at or about 30: and hence it always appeared to him desirable, that they should be repeated at such diminished pressures, as are met with at elevated points on the earth’s surface. In this point of view, the Simla observations appeared at first highly impor- tant, the pressure there being but little over 23; but as no reliance can be placed on the dew-points directly got, they cannot be used to test the accuracy of the hygrometric ex- pression. Dr. Apjohn then expressed a hope, that no one who heard him would misunderstand him to assert, that the dew- point could not be accurately got by Daniell’s instrument. He knew it could, and he had explained elsewhere how to use it, so as to arrive at a correct result. What he had, however, asserted before, and would again repeat, was, first, that it was an instrument very difficult to observe accurately with ; and second, that when Mr. Daniell’s rule is attended 7 305 to, namely, to take asdew-point, the mean of the temperatures indicated by the inner thermometer at the instant of the de- position of the dew, and at that of its disappearance, the result is necessarily higher than the truth. Dr. Apjohn concluded, by drawing attention to the great value of the other tables alluded to in Captain Boileau’s letter, the construction of which, must have been a work of immense labour. Two of these greatly simplify the calcula- tions necessary in applying the hygrometric formula, as the arithmetical operations are thereby reduced to mere addition and subtraction. The third table gives the force of vapour to tenths of a degree Fahrenheit, throughout the entire range included between —3° and + 146, Fahrenheit, calculated de novo by the well known method of Biot, from the experiments of Dalton and Ure. It does not materially differ, except in its greater extent and minuteness, from the table of the tension of aqueous vapour which Dr. Apjohn has hitherto used, and the superior accuracy of which, as compared with the table of Kaemtz, and that not long since published by the Meteor- ological Committee of the Royal Society, has been rendered highly probable by Professor Lloyd. Professor Mac Cullagh read a paper on the Catalogue of Egyptian Kings, which is usually known by the name of the Laterculum of Eratosthenes. This Catalogue, which the distinguished mathematician and philosopher whose name it bears drew up by com- mand of Ptolemy Euergetes, contains a long series of kings who reigned at Thebes in Upper Egypt; and has been pre- served to us in the Chronographia of Georgius Syncellus, a _ Greek monk of the eighth century. It is a document which has been made much use of by chronologers; by some of whom, as by Sir John Marsham for example, who calls it -“ venerandissimum antiquitatis monumentum,” it has been _ reckoned of the very highest authority; but it is extremely 306 corrupt in the latter part, owing to the carelessness with which it was transcribed either by Syncellus himself or his immediate copyists. ‘The writers on Egyptian antiquities have in consequence been much perplexed in settling the chronology of the reigns in which the errors exist, and the attempts that have been made to remove the confusion have only served to increase it. It was the object of the author to restore the document to its original state, and he showed that this might be effected, with complete certainty, by a pro- per attention to the manuscripts of Syncellus. Ofthese only two are known; one has been used by Father Goar, the first editor of the Chronographia (Paris, 1652); the other, which is a much better one, has been collated by Dindorf, the se- cond and latest editor. Dindorf’s edition was published at Bonn, in the year 1829, as part of the Corpus Scripto- rum Historie Byzantine, and on its first appearance Mr. Mac Cullagh had satisfied himself as to the original readings of the Catalogue, and had seen how to account for the errors which, probably from Syncellus’s own negligence, had crept into it; but he did not publish his conclusions at the time, thinking that similar considerations could not fail to occur to some of the numerous writers who were then giving their especial attention to such subjects. This, however, has not been the case. Chronologers have continued to follow in the footsteps of Goar, a man of little learning, and of no critical sagacity, who corrected the Catalogue most injudiciously, and whose corrections, strange to say, are left without any remark by Dindorf. Thus Mr. Cory, in his Ancient Frag- ments, a work much referred to, merely transcribes Goar’s list; and Mr. Cullimore, in attempting to reconcile ancient authors with each other and with the monuments, has adopted an hypothesis respecting the identity of two sovereigns, which is not tenable when the true version of the Catalogue is known. Even in Goar’s edition, however, there was quite enough to have led a person of ordinary judgment to the a i Oe 307 correct readings of the Catalogue, though perhaps they could not be said to be absolutely certain without the additional light obtained from that of Dindorf. The Catalogue in question professes to contain the names of thirty-eight sovereigns, with the years of their reigns; the whole succession occupying, as is stated, a period of 1076 years; but it is only in the last eight reigns that the errors and inconsistencies occur. The thirty-second prince is called Stamenemes 3, that is, Stamenemes the Second, though there is, at present, no other of that name in the list; and the beginning of his reign—as appears from the years of the world, which Syncellus has annexed according to the Con- stantinopolitan reckoning—follows the termination of the preceding one by an interval of twenty-six years. Jackson, in his Chronological Antiquities, is positive that this prince is called the Second by a mistake, and adds the years that are wanting to the reign of his predecessor, as Goar had pre- viously done. In the first part of this view all authors, with- out exception, are agreed, though they do not explain howa mistake, so very odd, could have originated; but the learned Marsham,—who, having adopted the short chronology of the Hebrew Bible, is so hard pressed to find room for the Egyp- tian dynasties that he is obliged to begin the reign of Menes the very year after the Deluge,—is glad to omit the twenty-six years altogether, thus reducing the sum of all the reigns to 1050 years, contrary to what is expressly stated by Syncellus. The natural inference from the state of the MSS, is, however, simply this: that the thirty-second king was Stamenemes I., that he reigned twenty-six years, and was succeeded by Stamenemes II. We may easily conceive that the eye of the transcriber, deceived by the identity of names, passed over the first, and rested on the second, thus occa- sioning the error. Indeed there can now be no doubt that this was the fact; because, in the MS. marked (B) by Dindorf, the next king is numbered as the thirty-fourth, the next but 308 one as the thirty-fifth, and so on; which shows that a name had dropped out, and this name could be no other than that of Stamenemes I., who must have filled the vacant interval, and must consequently have reigned the number of years that has been assigned to him. As neither Goar nor any other writer perceived this omis- sion, the successor of Stamenemes II. has always been rec- koned as the thirty-third in the list, and the next following as the thirty-fourth, &c. But as one error begets another, the omission was compensated by the insertion of an anonymous king, who is placed thirty-sixth in the list, with a reign of fourteen years; the insertion being necessary to complete the number (thirty-eight) which the Catalogue ought to con- tain. And, by a further error, these fourteen years are taken out of the reign of the thirty-seventh sovereign, who ought to have nineteen years instead of the five that have been hitherto assigned to him. This last error was occasioned by an ignorant correction of a mistake which is found in both the MSS., and which therefore probably arose from the care- lessness of Syncellus himself. The thirty-seventh king and his predecessor are stated to have begun to reign in the same year of the world, and to have reigned the same num- ber of years (five). Now from what goes before it is plain that both these numbers belong to the thirty-sixth king; and from the year of the world in which the thirty-eighth and last king began to reign, it is clear that the thirty-seventh reigned nineteen years. The mistake in the MSS. is one which might easily be made by a thoughtless writer; for the Catalogue is given in detached portions—a few reigns at a time—separated by a great quantity of other matter, and the name of the thirty-sixth king ends one of these portions, while that of the thirty-seventh begins another; so that, not having both before his eyes at the same moment, a person so careless as Syncellus might, without being conscious of it, attach the same reign and date to the two names, by tran- 309 scribing twice over the same line of numbers in the Catalogue which he was copying; the whole of which Catalogue, in all likelihood, he had previously drawn up ina tabular form, with the years of the world annexed according to his own chro- nology, that it might be ready, as any portion of it was wanted, for immediate transference to his pages. Such seems to be the natural account of the matter; but, as usual, it does not occur to Goar, who takes the opportunity, which the confusion affords him, of foisting in his supplementary king between the two last mentioned, giving each of these five years, as in the MS., by which means he obtains room for him, while on the other hand he alters the year of the world attached to the thirty-seventh king, so as to make it suit his hypothesis. The following is a view of the last eight reigns, as they appear to have stood in the original document, compared with the erroneous list of Goar. The years of the world are omitted, as being of no importance, except so far as they are useful in the preceding argument. I, Goar’s List. II. Correcrep List. Years. Years. 31. Peteathyres reigned 42 31. Peteathyres reigned 16 32. Stamenemes air eo 82. Stamenemes I. ,, 26 _ 983, Sistosichermes ,, 35 33. Stamenemes II. ,, 23 _ 84, Maris ee ae 34. Sistosichermes ,, 55 _ 85. Siphoas “4 5 35. Maris » 48 * 36. Anonymous ohm Ah 36. Siphoas s 5 87. Phruoro : 5 37. Phruoro 3°46 88. Amutharteus 1, eo 38. Amutharteus ,, 63 The interval of time which has been shown to belong to the first Stamenemes, and which was added by Goar to the reign of Peteathyres, is differently disposed of by Mr. Cul- -limore, i in a chronological table which he has given in the o volume of the Transactions of the Royal Society of - Literature. His object being to compare the lists of Eratos- 310 thenes, Manetho, &c., with the supposed hieroglyphical series, he makes Saophis, the fifteenth in Eratosthenes’ Ca- talogue, the same as a king whose name is read Phrathek Osirtesen; but the forty-third year of the latter is mentioned on the monuments, whereas Saophis has only twenty-nine years in the Catalogue. To escape from this difficulty, therefore, Mr. Cullimore adds the unappropriated interval to the reign of Saophis, thus giving him fifty-five years instead of twenty-nine. But it now appears that such a supposition is altogether inadmissible, and consequently the two per- sonages in question cannot be identified; a circumstance which proves that there is some fault in Mr. Cullimore’s assumptions, and that his other conclusions, at least in this part of his table, cannot be relied on. The corrections here given do not interfere with the in- ferences drawn by Professor Mac Cullagh from the Cata- logue of Eratosthenes ina former paper on Egyptian Chrono- logy (Proceedings of the Royal Irish Academy, vol. i. p. 66), because the portion of the Catalogue with which he was there concerned terminates with the reign of Queen Nitocris, the twenty-second in the list. The corrections, indeed, though not hitherto published, were made long before the date (April, 1837) of that paper, but not before he had adopted the hypothesis therein proposed, as an answer to the old and ever-recurring question—Who were the Egyptian sove- reigns that were contemporary with Moses? For it was in consequence of this hypothesis, which had suggested itself to him at a very early period, that he was led to examine the Catalogue minutely, in order to discover whether his chro- nology was affected by its errors. Having been led to refer to his hypothesis, Mr. Mac Cul- lagh took occasion to observe that, in the interval which had elapsed since it was published, he had not met with any facts that were opposed to it: on the contrary, the more he considered it, the more he was inclined to believe in its Sil reality ; though it was entirely different from every other that had been proposed, either by modern chronologers or by the early Fathers of the Church, in their manifold attempts to connect the narrative of Moses with the remaining fragments of Egyptian history. The hypothesis, indeed, is the only one which, while it gives a probable date for the Exodus, also satisfies what Mr. Mac Cullagh conceives to be the ne- cessary conditions of the question; namely, a very long reign —of at least eighty years—during which the Israelites were persecuted, succeeded by a very short one—apparently not more than a year—during which their deliverance was wrought; and it is interesting in itself, on account of the remarkable connexion which it establishes between sacred and profane history, and the highly dramatic character of the events which are thus, for the first time, brought into view. Mr. Petrie exhibited a drawing, on a large scale, of an ancient inscribed grave stone at Clonmacnoise, which he con- sidered as interesting, not only as a characteristic example of the usual sepulchral memorials of the Irish, from the sixth to the twelfth century,—and of which Mr. Petrie has col- lected upwards of three hundred examples,—but also as a monumental record of a person very eminently distinguished _ for his learning in Ireland in the ninth century. This stone, which is about four feet in length, and three . in breadth, though never squared or dressed, exhibits a very 1 richly carved cross, and the following simple inscription : SVIOINE. m maizae hvmdt!: SUIBHNE, THE SON oF MAILZHUMAI. _ Of the celebrity, in his day, of the person who is thus recorded, the Irish Annals, as well as those of England and VOL, II. 2c 312 at the year 890: Suibne mec Maoilhuma, anconiza Cluana mac nowy, oes. Thus also in the Annals of Ulster at the same year, or more correctly 891: Suibne mac Maele huma, Cnconiea, ez pepiba opzimup Cluana mac nop, vopmiuic. To the latter entry, Doctor O’Conor, in his Rerum Hib. Scriptores, appends the following note: ‘© Suibneum hune Annales Anglosaxonici Suifnethwm ap- pellant.—Vide Chron. Saxon. ad ann. 891, ‘ Tres Scoti de Hibernia, ad A‘lfredum regem Anglorum venerunt, Dubsla- nus, Maccebethus, et Melinmunus, Swifneth etiam, precipuus doctor qui inter Scotos fuit, decessit,—concordat Fabius Aithelwerdus, qui tertium appellat— Magilmumenum artibus frondentem, littera doctum, magistrum insignem Scotorum.’— Chron. 1. 4, c. 3. Eadem habet Wigorniensis ad ann, 892, et Matheus Florilegus,ad ann. 891. Huc etiam referenda sunt quz habet Caradocus ad ann. 889, ‘ Suibnion Cubin Doc- torum Scotiz maximus obiit.’” Sir James Ware, in his Jrish Writers, tells us, that “ his works, and the titles of them, are lost.” Mr. Griffith presented, on the part of the Shannon Com- missioners, a collection of antiquities discovered in the Shan- non, and gave the following account of the locality and other circumstances attending the discovery. The object of my present communication is to notice the discovery of certain ancient arms in an excavation made in the bed of the river Shannon at the ford of Keelogue, four miles below Banagher, in the King’s County. The ford at Keelogue, and that of Meelick, which is im- mediately below it, is the first point of the river Shannon which was anciently passable except by boat, above the falls at Killaloe, a distance of thirty British, or nearly twenty-five Irish miles; and consequently, previously to the construction of roads, and the erection of bridges at Portumna and Ba- 313 nagher, this ford must have been the main pass between the northern portion of the county of Clare, and the southern portion of the county of Galway, with the counties of Tip- : perary, King’s County, &c. &c. Hence it is probable that at a former period the ford at Keelogue, which is the shal- lowest on the river, and much better than that of Banagher, was the principal point of communication between the dis- tricts above enumerated ; and even in modern times, in com- mon with the passes by the bridges of Banagher, Shannon Bridge, and Athlone, the defence of the pass at Keelogue and Meelick was considered of sufficient importance to induce the British Government to erect two towers, mounted with cannon, on the King’s County side, to guard the passes of the river from the west. The fall of the river Shannon at Keelogue and Meelick amounts to ten feet; and to render the river navigable, the commissioners appointed to direct the improvements of the navigation of the Shannon, have agreed with contractors for the construction of a lock of very large dimensions, a stone weir to regulate the discharge and the level of the water, and for the deepening of the river at Keelogue ford, by ex- cavating the bed to the depth of six feet below the present bottom, so as to give a depth of full seven feet six inches for navigation when the works shall have been completed. Towards deepening this ford the contractors dammed off -aportion of the river 100 feet in width, and 700 feet in length, and have commenced an excavation of nearly six feet in a depth ; the material to be excavated consisted at the top of _ two feet of gravel, loose stone, and sand, and at the bottom __ of four feet of a mass, composed of clay and rolled limestone, which in some parts was found to be so solid and compact, ‘that it became necessary to blast it with gunpowder, in . _ preference to excavating, according to the ordinary system, hrough detrital matter. This compound of clay and rolled limestone, and lime- 314 stone gravel, is similar to that which forms the bed of the Shannon at all the other fords over which bridges have been erected, as at Banagher, Shannon Bridge, Athlone, &c., and these gravel banks in most cases are in connexion with, and in fact form a part of those low, but steep, ridges or hills, composed of clay and rolled limestone, which occur so abundantly in the King’s, Queen’s County, and the counties of Westmeath and Longford, on the east side of the river, and in the counties of Clare, Galway, and Roscommon, on the west. These gravel ridges, or eskers, as they are generally called, usually affect an east and west, or north-west and south-east direction, and consequently cross the river Shannon, whose direction between Athlone and Killaloe is north-east, south- west, nearly at right angles; hence the fords, which, particu- larly at Athlone, Shannon Bridge, &c., are merely gaps cut through the eskers by the action of the water, run directly -across the river, and present shallow, having deep ponds of water on either side, so that when the falls are not consider- able, as at the fords of Banagher, Shannon Bridge, &c., the excavation of the bed of the river at the ford will bring the water on both sides to a level, and there will still remain ample depth above for the purposes of navigation. But to return to Keelogue, I have already mentioned that the upper part of the excavation consisted of two feet of loose stones, gravel, and sand, and the lower part of four feet of a very compact mass, composed of indurated clay and rolled limestone. In excavating in the loose material of which the upper two feet was composed, the labourers found in the shallowest part of the ford, a considerable number of ancient arms, consisting of bronze swords, spears, &c., in excellent preservation, which are similar to those which have been frequently discovered in other parts of Ireland; and to- wards the lower part of the upper two feet they discovered a great number of stone hatchets, also similar in many respects to those which have been so frequently met with in different 315 parts of this country. In regard to the stone hatchets, I would merely observe, that the greater number, which are black, are composed of the siliceous rock called Lydean Stone, which occurs in thin beds, interstratified with the dark gray, impure limestone called Calp, which is abun- dant in the neighbourhood of Keelogue and Banagher ; but the others, some of which present a bluish gray, and some a yellowish colour, are composed of a subcrystalline, and ap- parently igneous porphyritic rock, none of which occurs in the neighbourhood, or possibly in the south of Ireland. Hence it is probable that the latter, which are much more perfectly executed than the black, or those composed of Lydean Stone, were brought from a distance, and probably from a foreign country. q The important and interesting subject for consideration in the antiquities before us is, that they are evidently the relics of very different, and probably distant periods. Owing to the rapidity of the current at Keelogue ford, it is extra- ordinary that any comparatively recent deposit should have been formed, and at all events the annual increase must have been inconsiderable; hence, though not more than one foot of silty matter may be found between the stone weapons of a very remote age, and the swords and spears of another period still remote from us, yet under the circumstances de- scribed centuries may have intervened between the periods of mortal strife which must have taken place in the river probably between the Leinster men and Connaught men of old, disputing the passage of the river at two distinct and no doubt very distant periods. I am not sufficiently versed in the ancient Irish history to _ say whether any records are in existence of a battle having been fought at the fords of Meelick and Keelogue; but if any such exist I have no doubt that many members of the _ Academy, and lovers of ancient lore, will be enabled to en- lighten us on the subject. Ihave only further to mention, 316 that I have been deputed by my brother Commissioners for the improvement of the Shannon Navigation to present these ancient relics to the Royal Irish Academy, for the purpose of being added to their already important and valuable col- lection of Irish antiquities. DONATIONS. Supplementary Appendix to the Report of the Poor Law Commissioners of the Medical Charities in Ireland, with In- dexes. 1841. Presented by the Commissioners. A pamphlet entitled, “ Is Selenium a irue Element?” Pre- sented by Septimus Piesse. Transactions of the Zoological Society of London. Vol. III. Partl. 1842. Reports of the Auditors and Council of the Zoological Society of London, April 29th, 1842, and List of Members. Su la Falsita dell’ Origine Scandinava di Jacopo Graberg di Hemso. Sunto della Letteratura Svezzese. Degli Ultimi Progressi della Geografia (two copies). Saggio Istorico su Gli Scaldi 0 Antichi Poeti Scandinavi. Occhiata Sullo stato della Geografia nei Tempi Antichi e Moderni. Specchio Geografico, e Statistico dell Impero di Marocco. Presented by the Author. A copy of the Ordnance Survey of the County of Water- ford, in forty-two sheets, including the Title and Index. Pre- sented by His Excellency the Lord Lieutenant. Extraits du Tome XV. et XVI. des Memoires de? Academie Royal de Bruxelles, with Notes. Presented by the Academy. Examinations at the University of London for M.D., B. M., B. L., M. A., and B. A., (six pamphlets). Presented by the University. Memoires de l' Institut Royal de France. ‘Tome Quinzieme. Presented by the Institute. 317 Specimen de l' Imprimerie de Bachelier. Presented by the Author. Memoirs of the Royal Astronomical Society. Vol. XIV. Presented by the Society. Memoire sur la Chaleur des Gas Permanens. Par Jean Plana. Presented by the Author. Proceedings of the Royal Society, $c. 30th Nov. 1842. Presented by the Society. Revista de Espana y del Estrangero. B. Fezuier Gon- zalo Moror. Tomol. Presented by the Author. Geological Report of Londonderry. By Captain Port- lock, M.R.I.A., &c. Presented by the Master General and Board of Ordnance. Archives du Muséum a’ Histoire Naturelle de Paris. Tome Il. Liv. 1 and2. Presented by the Museum. Address to the Geological Society of London. By Rode- rick Impey Murchison, F.R.S., &c. Presented by the Au- thor. Report of the Twelfth Meeting of the British Association, held at Manchester in 1842. Presented by the Association. Statutes relating to the Admiralty, to the eighth Year of George III. Presented by Captain Portlock. Ancient Irish Pavement Tiles, with Introductory Remarks. By Thomas Oldham, Esq. Presented by the Author. Proceedings of the Glasgow Philosophical Society, 1841, 1842. Presented by the Society. Memoires publies parla Société Hollandaise des Sciences. Second Serie. Tome II. Presented by the Society. Proceedings of the American Philosophical Society. Vol. II. Nos. 24 and 25. Transactions of the American Philosophical Society. Vol. VIII. Newseries. Parts 2 and 3. Presented by the Society. Fifth Annual Report of the Loan Fund Board of Ireland. 1843, Presented by the Commissioners. a Communication to the Right Hon. Sir Robert Peel, Bart. 318 By Jeffries Kingsley, Esq., M.R.I.A. Presented by the Author. Bulletin des Séances de la Société Vaudoise des Sciences Naturelles. Nos. 1-4. Presented by the Society. Sur les Figures Roriques et les Bandes Colorées produites par I’ Electricité. Par M. P. Riess. Presented by the Author. Expériences sur la non caloricité propre de U Electricité. Sur les relations qui lient la lumiere a I’ Electricité. Sur les travaux récents qui ont eu pour objet Vetude de la vitesse de propagation de l’Electricité. Par M. le Prof. Elie Wartmann. Presented by the Author. Journal of the Franklin Institute. Vols. I. and IV. Third Series. Presented by the Institute. Proceedings of the Zoological Society of London. Part 10. 1843. Presented by the Society. OF PROCEEDINGS 4 THE ROYAL IRISH ACADEMY. 1842. No. 88. January 23. Rev. JAMES H. TODD, D. D., Vice-President, in the Chair. Mr. G. J. Allman, read the following paper on the Mus- cular System of certain fresh water ascidian Zoophytes, being the first of a series of memoirs which he proposed present- ing to the Academy on the physiological and zoological his- tory of the zoophytes of fresh water. “The subject on which I have now the honour of ad- dressing the Academy, belongs to a hitherto but little inves- tigated department of zoology, the structure of the ascidian zoophytes* of fresh water. Our present knowledge of these minute creatures is chiefly due to Raspail, the distinguished _ French naturalist and chemist, whose researches into the structure of Alcyonella Stagnorum, are characterized by - much patient observation,} while in these countries the sub- ject has been totally neglected. Not so, however, with the ascidian zoophytes of the ocean; these interesting animals have had both here and on the continent some able investi- gators, among whom none deserve to be mentioned before a ©The zoophyta ascidioida of Johnston are synonymous with the bryozoa of Ehrenberg, and the ciliobrachiata of Farre, and include all those zoophytes whose organization is referrible to the molluscan type. ~ $ Compte rendu des seances de I’Academie des Sciences. 4 Fevrier, 1839. 320 Milne Edwards, and Farre, and it is especially to the latter indefatigable and accurate observer that we are indebted for a knowledge of the minute anatomy of these most curious and highly organized polypes. Though in my own investi- gations into the anatomy of the fresh water zoophytes of this order, I have not restricted myself to any particular struc- tures, I yet intend, in the following remarks, confining my observations to their muscular system; reserving for some other occasion the pleasure of directing the attention of the Academy to those points of their anatomy not dwelt upon in the present paper. “In the remarks which I am about to offer, it will be seen how closely the ascidian zoophytes of our fresh waters correspond in organization with the marine species; and though in minute anatomical detail certain differences will be observed, yet these differences are far from invalidating the unity of the type of structure,—a unity which will be found from the following observations to pervade, in a re- markable degree, the entire order. I would wish it to be understood too, that if I should in any respect differ from the statements of Dr. Farre, I offer no opposition whatever to his observed facts, but solely to one or two of the conclu- sions to which they have induced him to arrive. ** The animal of the present order, to the muscular ana- tomy of which I have chiefly attended, is one which has not as yet been recorded as a native of the British Islands. About two years since I was sent, by Mr. William Thompson of Belfast, to whose researches into the natural history of this country we are so much indebted, a small portion of the dried polypidom of a zoophyte, which he found, in Sep- tember, 1837, cast upon the shore of Lough Erne. From the dried condition of the fragment,—a condition in which the fresh water zoophytes lose all their most interesting characters,—I was unable at the time to arrive at any- thing satisfactory in the investigation of the species; I —— 321 therefore contented myself by sketching in my note-book, the few imperfect external characters which continued visi- ble on the dry and shrivelled zoophyte. No farther than this did my knowledge of Mr. Thompson’s discovery extend, when an opportunity fortunately occurred in October last, of obtaining living specimens of the animal. These I dis- covered in the Grand Canal, near Dublin, and have thus been enabled to pursue my investigations, from which I find the species to be one of great interest. I find, more- over, that although it has been hitherto unnoticed, as a British animal, it is identical with the alcyonella articulata of Ehrenberg, for which Gervais, who found the animal near Paris, subsequently constituted anew genus, under the name of Paludicella.* It is also noticed by Van Beneden, who met with it near Louvain, and gives a figure of it,t which, though not very good, will yet be found of use in the iden- tification of the species. ‘Though Ehrenberg’s appellation possesses the claim of priority, yet, as it refers the zoophyte to a genus into which its structure will not admit it, it must be rejected, and I shall accordingly adopt the name Palludi- cella, by which it has been designated by Gervais. ‘In the following remarks upon the muscular system of the fresh water ascidian zoophytes, my description of this system is chiefly derived from observations made upon Palu- dicella articulata, as there are certain points in the muscular anatomy of other species, upon which I cannot as yet speak with certainty, and for completing my observations on which, I must wait until the approaching Spring shall afford me fresh objects for investigation. **In describing the muscles of these animals, I have availed myself of Dr. Farre’s phraseology, applying to the q several sets of muscles in the fresh water ciliobrachiate zoo- _ © Bulletin de l’Acad. Roy. de Bruxelles, an. 1839. + Mem. de la Société d’Hist. Nat. de Paris, tom. 4. » rap a 322 phytes, the same terms which Farre has given to the analo- gous sets in the ciliobrachiates of the sea. ‘© In Paludicella then, three groups of muscles may be detected. These are strictly analogous to muscles which have been demonstrated in the salt water zoophytes of the same order, and for a description of which, we are indebted to an admirable paper of Dr. Farre, in the Philosophical Transactions, an. 1837. The first of these groups to which I shall direct your attention, corresponds with the anterior set of retractor muscles of Farre. It may be observed (fig. 3 and 4, h, h) to take its origin from the internal surface of the walls of the cell near the middle, and thence to pass upwards in order to be inserted into the margin of the tentacular disk, and upper part of the pharynx. The action of this group is obvious, it is the true retractor apparatus of the polype, and it is worthy of remark, that neither in this nor in any other fresh water zoophyte whose anatomy I have studied, could 1 detect muscular fibres analogous to those described by Farre, as inserted into the remote extremity of the stomach in those zoophytes of the sea which had come under his observation. ‘*The second set of muscles to be described in Paludi- cella, consists of four bundles of fibres (fig. 3 and 4, 2, 2, 2) which arise from the inner walls of the cell near the top, two at each side, having the tubular orifice between them. From this origin, they pass towards the aperture of the cell, slightly converging, and are inserted by distinct at- tachments, which are all placed in the same plane, into the inner surface of the tube near the margin of the orifice. These are in every respect analogous to the muscles which Farre describes under the name of opercular, and to which he ascribes the office of assisting in the inversion of the polype tube drawing in its margin after the retreating po- lype, and by their continued action, closing the orifice of the cell. Reasons will presently be given for dissenting from this view of the action of the opercular muscles, and in the , 323 4 meantime I shall proceed to the description of the third group. “The third groupis analogous to one detected by Dr. Farre, in the ascidian zoophytes of the sea, and to which he has given the name parietal. The parietal muscles take a transverse course, and originate and terminate in the internal membrane of the cell. In paludicella (fig. 3 and 4, h, k, k, k) they are rather numerous, and consist of short fibres of variable length, which pass transversely round the internal tunic, being capable of detection through nearly the entire length of the cell, and sometimes passing one another in their course, they may be seen to surround the cell with a contractile tissue. Dr. Farre is of opinion, that these muscles in the zoophytes which he has examined, are attached by their extremities only, being free in the intermediate space. In paludicella __ however, I saw nothing which would lead me to suspect, that in this zoophyte such was their disposition. I shall not here, however, speak positively, as it will require more ex- tensive observations before any decisive conclusion can be arrived at. “ Such are the three great groups of muscles which I have succeeded in detecting in paludicella, and so far as my obser- vations have gone, analogous groups are to be found in the other fresh water ciliobrachiates. It will at once be seen, by 4 any one acquainted with Dr. Farre’s paper, that while the - muscles just described correspond in all their important features with those of the ascidian zoophytes of the sea, thus beautifully demonstrating the unity of type by which the order is characterized, yet in the details of the several groups, some remarkable modifications will be found to exist. _ “The first thing which strikes us is the absence, probably among all the fresh water ascidian zoophytes of that well- developed fasciculus of muscular fibres, which is observed in e of the sea, to arise from the bottom of the cell, and a 324 pass upwards to be inserted into the fundus of the stomach. It is true, that Trembley describes in alcyonella stagnorum, a certain appendage to the fundus of the stomach, to which he assigns the office ofa retractor muscle; ‘“ J’ai vu,” says Trem- bley, ‘‘ distinctement, lorsque les polypes 4 panache etaient bien au dehors de leur cellules un fil qui tenait d’un cété a l'extrémité inferieure de ’estomac et de l’autre au fond dela cellule.”* Raspail supposes this an erroneous observation, and conceives that Trembley mistook for a distinct organ, the appearance presented under the microscope, by a fold of the reflected tunic.| Notwithstanding, however, the criti- cism of Raspail, I believe the observation of the celebrated historian of the green polype to he perfectly correct, though his reasoning is erroneous. ‘**T have myself witnessed in Plumatella repens, an organ in every respect corresponding to Trembley’s description; I believe this organ to be an ovary, though from its position and attachments, Trembley’s opinion might at first appear correct, and the structure in question might be supposed analogous to the posterior set of retractor muscles in the ciliobrachiate zoophytes of the sea. This supposition, how- ever, is untenable, and I have satisfied myself by repeated observations, that no such function is performed by it; it is observed to undergo no contraction, and its motions are en- tirely passive and dependant on those of the body of the polype. ‘* Inthe same animal, Trembley also describes as retractor muscles, filaments attached by one extremity to the base of the plume of tentacula, and by the other to the bottom of the cell;{ but this, likewise, is considered by Raspail as an error, and referrible to the same source as the former. Here again I must dissent from the French naturalist; the fila- * Hist. des Polypes d’Eau douce, p. 216. t+ Mem. de la Soc. d’Hist. Nat. de Paris, tom. 4, p. 92. } Op. cit. p. 216. 325 ments alluded to by Trembley correspond closely with fas- ciculi described above, as existing in paludicella, and which I have also witnessed in other fresh water zoophytes; and I cannot but think, notwithstanding the high authority of Raspail, that they are really such as Trembley describes them. It is worth remarking, that Raspail denies the exis- tence of retractor muscles in alcyonella, believing that, with the general contractility of the animal, such a contrivance would be superfluous. I have not yet succeeded in obtaining any specimens of alcyonella, so that upon this point I cannot speak from direct observation. Since these muscles, how- ever, are particularly well marked in all the fresh water ascidian zoophytes, whose anatomy I have studied, as well as in those of the ocean, I must still adhere to the original observation of Trembley ; for it can hardly be supposed, that a genus so nearly allied to those in which the system in question is well developed, and which Raspail, by the way, would consider but as a different grade of evolution, should be altogether destitute of them. “ In Plumatella repens I have examined, with much care, the retractor apparatus. In this species it consists of two fasciculi of muscular fibres, which arise from the sides of the cell near the bottom; and thence passing upwards symmetri- cally, one along each side of the body of the polype, receive an extensive attachment, being inserted into the wide part of the tentacular crescent, into the pharynx for its entire length, and into the upper part of the stomach ; a few fibres appear detached at each side from the main fasciculus, to be inserted more externally near the base of the tentacular lobes. The function of these muscles is evident, acting from their more fixed attachment to the side of the cell, they become power- ful retractors, by which the body of the polype is drawn _ inwards and concealed in the more internal parts of the poly- ~ pidom. “In the_opercular muscles, paludicella offers no remark- 326 able deviation from the general arrangement of these muscles in the salt water species. In plumatella repens, however, and perhaps in most other species of fresh-water ciliobra- chiates, their arrangement is very peculiar. In this zoo- phyte, they consist of a series of about twenty-five distinct delicate fasciculi, which arise from the internal surface of the cell at regular intervals, and in a plane perpendicular to its axis, and thence radiating inwards are inserted into the op- posed surface of the reflected tunic. * In assigning their proper office to the muscles which have been already described as the true retractor apparatus of the polype, no difficulty whatever is met with; neither can we be at a loss in discovering the true function of the parietal muscles, for these acting upon the flexible internal tunic of the polype cell, must necessarily, by their contraction, dimi- nish transversely the space included between this tunic and the body of the polype, a function the great importance of which, in the economy of the little animal, will presently be apparent. When, however, we attempt to explain the action of the opercular muscles, the task will perhaps be found not quite so easy. It has been stated that Dr. Farre assigns to these muscles the office of drawing in the flexible portion of the polype tube after the retreating polype, and by their con- tinued action closing the orifice of the cell. I cannot help thinking, however, that in ascribing this office to the oper- cular muscles, Dr. Farre is correct but to a very limited extent, and that their chief use is directly opposite to that assigned to them by this excellent observer. The use which I would assign to the opercular muscles is, first, that of assisting the polype in its protrusion, an office which they accomplish by fixing and preserving in the axis of the polype tube that portion of the reflected tunic (fig. 4, ¢, ©) which is included, during the retracted state of the animal, between the summit of the fasciculus of approximated tentacula, and the orifice of the cell; and, secondly. what is a still more 527 important function, that of affording to the respiratory sur- face, when the polype is retracted within the recesses of its cell, a constant supply of fresh water, of which the little animal would be deprived, were it not that some means existed of dilating the tubular reflection of the tunic, an office to the performance of which these muscles are fully adequate, acting then in a state of antagonism to the parietal | muscles, which tend to keep the orifice of the tube closely shut. , ** My objections to Dr. Farre’s view of the function per- formed by the muscles in question are referrible to three heads: first, want of necessity in ascribing to them the office for which this anatomist believes them destined; secondly, their inability to perform the function which he ascribes to them; and thirdly, the possibility of assigning to them another office in full accordance with the necessities of the animal. ‘* That we are not obliged to seek for opercular muscles, in order to account for the closing of the orifice when the polype has retired into the recesses of its cell, is evident, if we give the slightest consideration to the action of the true retractor muscles. It is quite plain that the retraction of the polype itself, which is effected by the muscles which act di- rectly &pon it, is amply sufficient to produce the complete invagination of the flexible termination of the cell; and, ac- cordingly, observation will convince us that this invagination follows exactly the retraction of the polype, and is evidently related to the latter action as an effect to acause. That the opercular muscles cannot, except in a very partial manner, produce the effect ascribed to them by Dr. Farre, is also evident, when we reflect upon their course and attachments. Avising from the circumferential portion of the cell, and _ thence passing inwards, to be inserted into a point nearer to the axis, they must, after the invagination of the tunic has _ proceeded beyond the plane of their insertion, possess upon the reflected tunic a decidedly délatable action,—an action —L— ee - er 328 which is antagonized, first, by the parietal muscles, as will be presently explained, and, secondly, by the true retractor muscles; for these muscles, acting through the medium of the polype, in most instances nearly centrally, or in the axis of the tube, will not, in their ordinary action, possess any di- lating power, but, on the contrary, will tend to close the aperture by approximating the sides of the tubular reflection of the cell. «‘ Since we have thus seen that the opercular muscles are incapable of producing the closure of the orifice, it becomes an interesting subject of inquiry to determine by what means the act in question is performed, and indeed a slight consi- deration will render manifest the simple yet effective mecha- nism appropriated to this purpose. The great agents by which the closure of the cell is effected are to be found in the parietal muscles, for these fibres, by pressing the fluid of the cell against the tube of invaginated membrane (fig. 4, ¢, ¢), will approximate the sides of this tube to one another, at the same time that the membrane will be thrown upwards against the aperture of the cell, thus completely closing the orifice, and enabling the little animal to rest secure fromall intrusion in the recesses of the polypidom. ‘* After this account of the muscular system of the polypes, the mechanism will now be easily understood by which the animal is protruded from its cell when hunger calls it forth to seek its food in the surrounding medium, or when desirous of exposing its respiratory surface still more per- fectly to the vivifying influence of the aerated water. “‘ Previously to the discovery of the parietal muscles no satisfactory explanation had been given of the protrusive act of the polype, and even since the detection of these muscles by Dr. Farre, their share in effecting the protrusion of the animal would appear to be underrated. Dr. Farre considers their influence in this respect as of secondary importance, and would seem to attribute the act in question mainly to the ———— 529 straightening of the cesophagus, which in the ciliobrachiates of the sea is bent upon itself during the retracted state of the polype. In none of the fresh water species, however, which I have examined, with the exception of Paludicella articulata, does this curvature of the cesophagus appear to exist; we therefore cannot in these instances have recourse to its agency in accounting for the phenomenon now under consideration, and we are consequently driven to the parietal muscles, or to the general contractibility of the internal tunic, as the only provision by which this important act can be effected. I mention the general contractibility of the internal tunic as a probable agent in protrusion, for I do not think the existence of the parietal muscles throughout the entire order as yet sufficiently established. “ We shall now suppose the polype withdrawn into the recesses of its cell, and that hunger or some other stimulus impresses on it a desire of protrusion. The parietal muscles, which appear to me to be the direct agents in effecting the protrusive act, now begin to contract, and thus exercise a pressure on the fluid which surrounds the polype, and is in- cluded between the latter and the internal membrane of the cell. The compressed fluid in its turn acts upon the polype, and by its upward pressure against that portion of the flexi- ble tunic which is carried in by the animal during its re- treat, will tend to produce an eversion of this membrane, which, in the completely retracted state, constitutes a tube of some length between the summit of the fasciculus of ap- proximated tentacula and the orifice of the cell. The oper- cular muscles at the same time coming into play will, by their nicely adjusted action, keep the invaginated tunic exactly in the axis of the orifice, and thus materially assist in effect- ing the necessary protrusion, which, by the continued action of the parietal muscles, will go on increasing till the com- plete evagination of the reflected membrane has taken place. This, then, I conceive to be the true account of the protru- 330 sive act, and that the apparatus just mentioned is amply sufficient for the purpose, without having recourse to the agency of the bent cesophagus,—an agency which in pluma- tella repens, and other fresh water zoophytes, which I have examined, assuredly does not exist, as in these the cesophagus is straight during the retracted state of the animal. In the remarks now offered, however, I do not deny that some in- fluence is exercised by the straightening of the cesophagus in those species in which this tube is bent upon itself pre- viously to the commencement of protrusion; I merely wish to assert that we are not necessarily obliged to have recourse to this agency, but that in some instances, at least, the pa- rietal muscles, or, in their absence, the general contractility of the internal tunic, are agents perfectly effective. “Such are the observations which I have had an oppor- tunity of making on the muscular system of the ascidian polypes of fresh water. Iam fully aware that they are far from being perfect, but for this my excuse must be found in the extreme difficulty of such investigations, made, as they all necessarily are, under a high power of the microscope, with an illumination most carefully adjusted, and which can by no means be at all times obtained, in order that structures of such extreme tenuity and transparency may not entirely escape detection. The observations have all been made on the living animals, and no one who has not devoted himself to such investigations can form any idea of the close and pa- tient attention which they require,—the constant watching to obtain the animal in the exact condition or position, in which alone certain peculiarities of structure are apparent; and, finally, the mortification of finding the conclusions to which we had arrived on one day, after hours of painful at- tention, invalidated by some more favourable observation on the next. ** In the present communication I have confined myself to the muscular system; on some other occasion I may perhaps | 331 again entreat the indulgence of the Academy, while I lay . before it my observations upon other not less interesting z, parts of the structure of these curious animals.”* DESCRIPTION OF THE PLATE. Fig. 1. Paludicella articulata; natural size. Fig. 2. Portion of the polypidome magnified. Fig. 3. A cell with the polype exserted, a, a, a. The polype cell. b. The orifice of the cell. ce. That portion of the internal tunic which is carried out by the polype during its egress from the cell. d. The stomach of the polype. e. The rectum. J. The cesophagus. g. The crown of tentacula exserted and expanded. h,h. The proper retractor muscles of the polype; they are now relaxed, and carried out by the animal in the act of protrusion. 2,2. Two of the four sets of opercular muscles, also in a state of relaxation. k,k, k, k. The parietal muscles, preserving, by their contrac- tion, the membrane ¢, in a state of tension, and thus maintaining the exserted condition of the polype. * After the present account had been written, 1 happened to meet with a paper by M. Dumortier, in the Bul. Ac. Brx. an. 1835, on the Polype a Panache _ of Trembley, a polype belonging to the order now under consideration, and for which M. Dumortier constitutes a distinct genus under the name Lophopus, characterized by the tentacula, being destitute of cilia. So remarkable an ex- ception, however, would this character offer to that of the entire order, that I cannot but suppose Dumortier in error; an opinion in which I believe myself fully born out by the phenomena subsequently described by this naturalist, and _ which are evidently the result of imperfectly observed cilia. ist Dumortier details, at considerable length, the anatomy of the zoophyte, and _ has witnessed fibres corresponding with the retractor and opercular muscles “described in the present communication. His paper is well worth perusal, though _ some of his statements will require further corroboration. 332 Fig. 4. A cell with the polype retracted. a, a, a. The polype cell. b. The orifice of the cell. c, c. The inverted membrane, which, in the completely re- tracted condition of the polype, consists of that portion of the internal membrane which had been carried out in the act of exser- tion, together with the more flexible termination of the external tunic of the cell. d. The stomach of the polype. e. The rectum. J. The esophagus. Both rectum and cesophagus are here curved upon themselves, and thus accommodated to the retracted state of the polype. 9,g. The crown of tentacula retracted, and the tentacula approximated into a close fasciculus. h, h. The proper retractor muscles of the polype in a state of contraction. i, i, 7. The opercular muscles also contracted. k, k, k, k. The parietal muscles relaxed. Dr. Robinson gave a brief account of meteors observed at Armagh on the 10th of August, 1842, apologizing for the imperfect nature of the observations, while he felt that it was desirable that they should be placed on record. The sky had been overcast, but became clear a little after ten, of which Dr. R. was availing himself to try an eye- piece of a peculiar construction, when the appearance of two large meteors, travelling in nearly the same direction, re- minded him of the peculiar character of the 10th, and in conjunction with T. F. Bergin, Esq. and another observer, he proposed to watch for others. The roof of the dwelling- house afforded an excellent position. Mr. Bergin looked south-west; he (Dr. R.) east; and the third north. From 10,55". Armagh time, till 12", seventy-eight were seen; of which about twenty were in Dr. Robinson’s district, and fifty in Mr. Bergin’s. With scarcely any exception, their ten- 333 dency was in tracks converging at € Ophiuchi. The greater part of them were larger than ordinary falling stars, and left a red train; in some instances a luminous cloud marked for a few seconds the place of their disappearance, and then was faint Aurora towards north-west. The night was occa- sionally cloudy, and after twelve became completely overcast. DONATIONS. Report of the Limerick Philosophical and Literary Society. Presented by Dr. Gore. Supplementary Appendix to the Report of the Poor Law Commissioners on the Medical Charities, Ireland. Presented by the Commissioners. February 13. SIR Wm. R. HAMILTON, LL.D., President, in the Chair. Robert Culley, Esq., James Magee, Esq., and H. L. Renny, Esq., were elected members of the Academy. A paper on the Action of certain Salts as Manures, by the Rev. Thomas Knox, was read by the Secretary of Council. ‘¢ A small meadow, containing about an English acre, was divided into six plots, and in last Spring, were manured as follows: Ist. 2nd. 3rd. 4th. 5th. 6th. Ashes. | Stable | Burned | Muriate of ammo- | Guano, | 2} barrels of manure. | gypsum, | nia, 6 lbs.; pearl | 2 stone. | lime mixed 4 stone. | ash, 6 lbs. ; 8 lbs. of with earth. bones, burned and dissolved in half a pint of sulphuric acid, and diluted largely. 33 b Plots Ist, 2nd, 3rd, and 6th, were top dressed in March; plots 4th and 5thin April. Mr. Knox first remarks, about the composition of No. 4, that the quantity of muriate of ammo- nia was calculated (according to Liebig) on the supposition that the decomposition of the ammonia furnished all the nitrogen required for the plant, and was sufficient to give a heavy crop with the addition of the ammonia derived from the rain. The quantity of bones was sufficient to furnish all the phosphates required, at the rate of from three to four tons to an acre, and were, as Liebig suggested, first dis- solved in sulphuric acid, and having been mixed with a large quantity of water, were sprinkled evenly over the land. At first, plots Ist and 2nd, those manured with ashes and stable manure, appeared much the most luxuriant, and even up to the time of cutting, that top dressed with manure seemed far a finer and heavier crop, and had a richer colour. When ripe, the plots were mowed and saved quite separately, and that there might be no mistake, pegs had been driven down deep into the ground at the time of laying on the top dressing. When the hay was quite dry and saved, the pro- duce of each plot was weighed separately, and I was then surprised to find, that though the stable manure was to all appearance the best, yet the plot manured with the mixed salts and dissolved bones much surpassed it; also that on which the ashes had been used. This, in case of plot Ist, I consider to be due to the potash (which the ashes contain), enabling the plant to take up more silica from the soil; and in the case of plot 4th, to the potash and phosphates, by which greater firmness of stalk was acquired by the plant, and it was prevented from losing weight in drying, as the one that was top dressed with the stable manure did. I was prevented at that time from determining this analytically, which might have been done, simply by weighing the ashes resulting from burning equal weights of hay. I here give the weights of hay, the exact quantity of land, which was re- 535 gularly surveyed, and also the weight of hay calculated at what it would be per acre. ee Ist Plot. 2nd Plot. 3rd Plot. 4th Plot. 6th Plot. 6th Plot. | Hay, 8} cwt. | Hay, 9} cwt. | Hay, 8hcwt. | Hay, 8 cewt. Hay, 6 cwt. Hay, 5 ewt. Land, 24} perch| Land, 274 perch| Land, 253 perch} Land, 22 perch.) Land, 212 perch] Land,20 perch. } Produced at the Rate per Acre, Ton Cwt. St. | Ton Cwt. St.| Ton Cwt. St. |} Ton Cwt. St. Ton Cwt. St. | 7 ie” A 2 int 2 9 7 2 2 2 0 0 Ton Cwt. St. 18 2 4 6 “The results of the above experiments point out the ad- vantage of the salts of ammonia and potash when combined with dissolved bones, but the nature of the land and crop to which it is applied, must be considered, as it might be posi- tively injurious in some cases. In the instance given above, the meadow was an old one, which had not been broken up for many years, and the grass was close and fine in texture, so that great advantage was gained by the additional silica and phosphate of lime; but in the case of a new meadow, the hay is often, for the first year or so, too strong and wiry. In such a case, were the same applied, it would be rendered too coarse for the use of horses or cattle; it might, therefore, be found better, for the first two seasons, to apply simply the salts of ammonia, which would increase the sappiness of the plant and the general growth, without adding to the harsh- ness of texture. ‘ ‘“‘Thope to be able, on some future occasion, to lay before the Academy the result of further experiments on the sub- ject, and (should time permit me) accompanied with an accurate analysis of the ashes of the plant in each case.” Mr. Webber made an inquiry as to the cost of the ma- nures mentioned, and suggested that Mr. Knox should be requested to annex to his paper, a statement of the relative expenses of the manure employed. Dr. Kane and Dr. Apjohn made some remarks on the general subject. VOL. II. 2E 536 Mr. J. Huband Smith gave an account of some ancient tiles found in the ruins of Bective Abbey, near Trim, and exhibited specimens of some raised and incaustic tiles, with drawings of others. Dr. Todd, V. P., gave an account of an ancient Irish MS. preserved in the Bodleian Library, Oxford. This MS., which is a large quarto on vellum, was formerly in the collection of Archbishop Laud, by whom it was pre- sented to the Bodleian. It was also once in the posses- sion of Sir George Carew, as appears from the autograph **G. Carew” on the margin of the first page. It contains a large collection of miscellaneous pieces, historical, genealogi- cal, theological, and poetical, in different hands, and of diffe- rent dates ; such a collection was called by the ancient Irish “a Psalter,” and in an entry, which shall be considered presently, this volume is called “ the Psalter of Mac-Richard Butler.” Pasted down on the inside of the cover is the following note: * Oxford y° 9" of August 1673. ‘‘ This booke is a famous coppie of a greate part of Salcaip Capit, the booke of St Mochuda of Rathin & Lismore, and the chronicles of Conga; wherein is contained many divine thinges, and y® most part of y° Antiquities of y® ancientest houses in Ireland, a Cathologue of their Kings, of the coming in of y° Romans vnto England, of y* coming of y* Saxons, and of their lives and raygne; a notable Calender of the Irish Saints composed in verse eight hundred yeares agoe, w™ the Saints of ye Romane breviary vntill that tyme; a Cathologue of y° Popes of Roome; How y° Irish and English were con- verted to y° Catholique faith; w‘ many other things as the reader may finde, and soe understanding what they containe lett him remember *‘ 'TuLtLy Conry. “ Tuleagna o Maolconaipe.” alts fe . M's 357 This account of the contents of the volume is very in- adequate, as well as erroneous. There seems but little reason to think that the book contains a copy of any part of the Psalter of Cashel, although that celebrated Collection is sometimes referred to or quoted; no traces of the book of St. Mochuda, or the Chronicles of Cong, are now to be found in the volume; if Tully Conry therefore was not mistaken, there is ground to suspect that the MS. may have lost something since the foregoing account of its contents was written. On the upper and lower margins, in several places, there are entries and memorandums by various possessors of the book, which serve to give us its history, and to fix the date of a great part of the documents of which it consists. The most remarkable of these entries must now be noticed. 1. On the lower margin of fol. 4, 6, there is the following note, which is here given in the original, with a translation: ee On anoro vo pigpaid m*. pean, m°. copna, m°*, mhaorlin moip ui mail-conaine, pil ag lepugav an libaippe vo muipip m*. comaip .1. 1apla vepmuyhan, sur pe an eargeibeimea.... caici na beallcame cap eip veipceant epinn oa planugao icep gallagurp gaeroil, A prayer here for Sighraidh son of John, son of Torna, son of Mailin Mor O’Mulconry; who is restoring this book for Mau- rice, son of Thomas, i. e. the Earl of Desmond, who is now residing at Askeaton..... at the beginning of May, after the south of Ireland has submitted to him both English and Irish. 2. Another entry of a similar kind occurs on the lower margin of fol. 34, as follows: Op. npo vom recip 1. Mui m* comaip, m° pemay, in cI o’ap lempugiup an becpo cuarp Le opoc _ mpepumencaib. A prayer here for my patron (?), i. e. Maurice, son of Thomas, son of James, the person for whom I am restoring the little portion above, with bad instru- ments. The Maurice mentioned in these extracts was the tenth 338 Earl of Desmond, who succeeded his elder brother James in the Earldom in 1481. He was the son of Thomas, the eighth Earl, who was beheaded at Drogheda, 5th February, 1467. He died 1497, according to O’Clery’s book of Pedigrees: and as the foregoing entries were manifestly made during his life-time, it is evident that this volume was of some anti- tiquity, so as to require the ink to be revived and restored, in the latter end of the fifteenth century. This was a process very common with Irish scribes, as is evident from the in- spection of our ancient vellum MSS., many of which have suffered great damage by ignorant attempts to restore them. 3. A memorandum of peculiar interest oecurs on the up- per margin of fol. 110, 5. It is as follows: : Salzaip m¢ purpoepo burzilep This Psalter was the Psalter of ..€momn buizilep, ino c-palzain peo, no Fo v-cucad mardin barle m ppoill ap iapla upmuman agup ap m® puipoeno buizilen le 1apla vepmuman .1, tomar, agup vo bainead mleaban po agup leaban nacappuigi ap pu- apglad m* puipoeno, agur Ip pe mm m®° puipoepo pin vo chuip na leabaip pin oa pepibad vo fem, no gup bain Tomar [ve ia0]. Mae Richard Butler, i. e. Ed- mond Butler, until after the de- feat at Bally-in-spoill, of the Earl of Ormond and of Mae Richard Butler, by the Earl of Desmond, i, e. Thomas; and this Book and the Book of Carrick were given in ransom of Mac Richard, and itis this Mac Richard that caused these books to be transcribed for himself, until Thomas took them from him. Thus it appears that this book, and the book of Carrick, (now unknown) were in the fifteenth century considered as a sufficient ransom for the person of a great chieftain,—a re- markable proof of the preservation of a love of literature amongst the native Irish nobles, in the midst of all their war and faction at that period. Nor is this a solitary instance in Irish history. The Leabhar na h-Uidhri, a manuscript of the twelfth century, in the collection of Messrs. Hodges and Smith, contains an entry of a similar kind. 339 The foregoing memorandum, however, shows that this volume was written originally for Sir Edmund, son of Richard, Butler, commonly called Mac Richard ; and that on his de- feat by Thomas, eighth Earl of Desmond, who, as we have already seen, was beheaded in 1467, it passed into the hands of the Desmond family. In the book of Pedigrees of the O’Clerys, an unpublished work, of which the autograph MS., in the original Irish, is in the Library of this Academy, the following account of Thomas, eighth Earl of Desmond is given (p. 247): “The fate of Thomas, son of James, Earl of Desmond, i.e. the ninth [eighth] Earl. Thus did it happen unto him, viz. John Tipto [Tiptoft] Earl of Worcester, came into Ireland as Lord Justice, called by proclamation of the English of Ireland to the great Council at Drogheda. And bad was the counsel there agreed upon, viz. to behead Thomas, son of James, the Earl, without impeachment of crime, right, or law, but merely from envy and hatred; the man of best mien and form, wisdom, and intelligence of either English or Irish of his time. No praise bestowed upon him could be too high. The sorrow and affliction of that death was felt equally by the English and the Irish. This Thomas the Earl invariably overthrew and put down his enemies and op- ponents on every occasion whenever he fought with them. Great indeed was the battle in which he overthrew the But- lers, on the Suir, and innumerable were the hosts of them that were slain and drowned on that occasion. He likewise gave several overthrows besides, that are not here enume- rated. A Lord intellectual and learned in Latin, English, and ancient Irish writings, was that Thomas. It was he that gave the great overthrow to the Mac Carthys at Reidh- an-Eich-bhuidhe. The 5th day of February the Earl was beheaded, and 42 years was his age at that time. At Tralee was he buried, 1467.”* * This is a strictly literal translation of the original Irish.—See Grace’s 340 This extract, taken in connexion with the entry in the Oxford MS., is exceedingly curious, as it notices the fact that Thomas Earl of Desmond was learned in ancient Irish writings ; and therefore incidentally confirms the probability of his accepting ancient MSS. as a ransom for the Mac Richard. The place called Bally-in-spoill is now unknown ; but from the record in the Book of Pedigrees it seems pro- bable that it was a village on the banks of the Suir. 4. Another interesting entry, which enables us to date one portion of the volume, occurs on fol. 86, a, in the hand- writing of the original scribe, at the end of a very valuable fragment of Cormac’s Glossary : ly h-e analao in agepna in uaip vo pepibad in panaran po na palcnac, «1. mile bliadan agup ceitm .c. bliadan agup zp bladna vec, agup oa x. In cuiced la vo mi Febna agurp in The year of our Lord when this Glossary of the Psalter was written, was 1453; on the 5th day of the month of February, and the eighth day of the moon. I am John Boy O’Clery who wrote it, and for Edmund Butler Mac Richard was it written. coctmav la von epea. Mins reaan bud: o clei vo pemb, agup o’emann buizilep m° pip- zepo vo pepibad. lt appears therefore that this portion of the volume was transcribed (doubtless from much more ancient documents, perhaps from the veritable Psalter of Cashel itself) in the middle of the fifteenth century for Sir Edmund Butler, commonly called Mac Richard; and that it subsequently passed into the family of Desmond, having been received in ransom of Mac Richard by Thomas Earl of Desmond. This MS. having been for the last two centuries in Eng- land, appears to be wholly unknown to our historians. The rules of the Bodleian Library do not permit its MSS. to be lent, and as there is no accurate catalogue of the valuable, Annals, printed by the Irish Archeological Society, p. 165, note °, for a further mention of Earl Thomas, 541 but unknown, and, in Oxford, unappreciated collection of Irish MSS. which it contains, the MSS. there preserved are almost as inaccessible for the purposes of Irish historical research, as those of the Vatican or the Escurial. Dr. Todd did not pretend to give a complete account of } . the contents of the “ Psalter of Mac Richard,” as it may per- haps for convenience be called. He was able only to carry away a very few memoranda of such articles as appeared, on a very hasty inspection, likely to prove most interesting. On fol.’7 is a religious tract, known as the Life of St. Margaret, a work of no value, except to the philologist. Fol. 9. The Genealogy of St. Mochoemog. Fol. 11, d. A religious tract, entitled, in Irish, “ The History of the Image of our Lord,” and also, in Latin, “ In- cipit Libellus Anastasii [Athanasii] Archiepi Alexandriz urbis, de passione imaginis Dni. nri. Jhu. Xi.” This is pro- bably an Irish version of the tract attributed to St. Athanasius at the second Council of Nice, although now admitted to be spurious. It is published in Greek and Latin in the Bene- dictine edition of the works of St. Athanasius, Fol. 14, a. A curious legend of Donogh O’Breen, abbot of Clonmacnois. The story is, that having gone on a pilgri- mage to Armagh, he was miraculously detained there until his death, A. D. 987. He is said to have been the last of the Irish saints who performed the miracle of raising the dead.—See Annals of the Four Masters in an. 987. Fol. 15. An account of the ancient tract called the Felire, or Festilogium, of Angus the Culdee; being a Mar- tyrology, or Calendar of the Saints’ days observed in the ancient Irish Church, compiled in the eighth century. Fol. 18, 6. “ The Destruction of Jerusalem by Titus, son of Vespasian, in revenge for the Blood of Christ.” There is a copy of this tract in the Leabhar Breac in the _ Library of the Academy, and a fragment of it in the Book of Lismore. _ 342 Fol. 23. A legend of the Infancy and Life of Christ, as revealed by the Virgin Mary to St. Bernard. Fol. 29. A sermon in Irish on the text, “Omnia que- cunque vultis ut faciant vobis homines, et vos facite illis.” ‘Fol. 30, 6. A sermon on the text, ‘‘ Cum ergo facies elimosinam.” There are copies of these sermons in the Leabhar Breac. Fol. 33, a. The celebrated Chronological Poem of Giolla Ccemgin, beginning with the Creation, and carried down to the year 1072, when its author flourished.—See O’Reilly’s Irish Writers (Trans. Hiberno-Celtic Soc. vol. i.), p. Ixxx. There is a very ancient copy of this poem in the Library of Trinity College Dublin, MS. H. 2, 18. Fol. 38 to 42. Genealogies of the Irish Saints. Fol. 43, a. The three sons of Moses, &c. b. ‘* Incipit inventio sanctz crucis.” Fol. 57, 5. A tract containing the fabulous history of Ireland before the Deluge, as related by Fintan, one of the ante-diluvian colonists of Ireland, who, under various trans- migrations, is supposed to have survived the deluge. This work ends with an account of a convocation of the states of Ireland held at Tara, in the sixth century, under Dermot M‘Cearbhaill (Carroll). There is a fine copy of it in the Library of Trinity College, MS. H. 2, 16. Fol. 58. The history of Mac Datho’s hog. Mac Datho was king of Leinster in the first century. He invited the kings of Connaught and Ulster to a feast, with a view to sow dissensions between them for his own political ends. At this feast there was served up an enormous hog, the cutting up of which, and the assigning to each chieftain his proper share, became a matter of fierce contention between the guests, and produced the effect intended by their crafty en- tertainer. There are two copies of this legend in the Library of Trinity College, MS., H. 2, 18, and H. 3, 18. 343 Fol]. 59. A very fine and ancient copy of the Felire, or Festilogium of Angus the Culdee. This part of the volume is much more ancient than the rest, and was probably written in the twelfth century. It ends fol. 72, a. There is a fine copy of this work, with the gloss, in the Leabhar Breac. Fol. 72, 6. A poem addressed to Cormac Mac Cuil- lionan, king and bishop of Cashel, in the ninth and Bepaning of the tenth century, on the duties of a king. There are good copies of it in the Library of Trinity College, MS., H. 2, 18, and H. 3, 18. Fol. 73, 6. A poem on the sons of Oillil Olum, king of Munster in the third century. There is a good copy of it in the Library of Trinity Col- lege, MS., H. 2, 18. Fol. 74, a. A poem on the succession of the kings of Emania, by Cinaeth O’Hartigan, who died A.D. 975. It begins Fianna bacan n emam. This poem appears to have been unknown to O’Reilly.— Irish Writers, p. \xii. Fol. 75,a. A tract beginning ‘ Hibernia insola inter duos filios principales Militis, i. e. Herimon et Eber, in duas partes divisa est.” The remainder is in Irish. Fol. 81, 6. An account of the great plague in A. D. 633, beginning Cnno vommice incapnationip oc.xxm. =Opa mona hi faxain cuaipcent ond anbchme pucav paulinup eoilbepza iWluing co canzia agup po haipimed co hononach. “ In the year of our Lord’s incarnation 633, a great mortality in North Saxony, to avoid which Paulinus Edilberta was carried away in a ship to Kent, and was there honourably received.” After this are a number of short poems. Fol. 83. An imperfect but very ancient copy of Cormac’s _ Glossary, beginning with the word Minvech, which is thus explained, quar menvic ab eo quoo ere menoicur. It ends - fol. 86, a; after which is the entry already quoted, from VOL. I. 2F 344 which we learn a very remarkable fact, hitherto I believe unnoticed by our historians, that Cormac’s Glossary was compiled from the notes or glosses added by Cormac Mac Cuilionan, the celebrated king and bishop of Cashel, to the miscellaneous compilation called the Psalter of Cashel. Cor- mac was killed in the battle of Belach Mughna, now Ballagh- moon, in the County of Kildare, near Carlow, A. D. 903. Fol. 93, b. A tract, with the following Latin title, ‘‘ De causis quibus exules aquilonensium ad mumonienses adducti sunt,” beginning Iped cecamurp focono comps, &e. Fol. 94, b. The history of the war between Oilill Olum and Mac Con. This is a most valuable document. Oilill Olum was king of Munster in the third century. He de- prived Mac Con, his stepson, of his lawful inheritance. Mac Con rebelled, assembled his followers, but was defeated by Oilill at the battle of Ceannabrat, a place on the borders of the counties of Cork and Tipperary. The defeated prince fled to Scotland, where he had influence enough to raise a large force of foreign adventurers, with whom he returned to Ireland, and again encountered the troops of his step- father in the bloody battle of Moy Mocroimhe, in the county of Galway. In this battle Oilill was aided by Art, son of Conn of the hundred battles, then monarch of Ireland; but was defeated. Art was slain, and with him the six sons of Oilill,with the flower of the Irish chiefs. Mac Conn assumed the sovereignty of Ireland, and continued to reign until driven back to Munster by Cormac Mac Art, several years after- wards, who thus revenged the death of his father. There is an imperfect copy of this tract (a MS. of the early part of the twelfth century) in the Library of Trinity College, Dublin, H. 2, 18. Fol.96,a. The history of the battle of Mucruimhe, be- ginning @uro eugan mop vo cach mucpuime. Fol. 99, 6. The Expulsion of the Decies from Tara by Cormac Mac Art. 345 Fol. 102, a. The coming of St. Finian from abroad into Ireland with the Gospel. Fol. 104. The History of Oriell, with the genealogies of many Irish families. Fol. 109, a. A poem on the sons of Conor Mac Nessa, king of Ulster in the first century; by Mongan, a celebrated poet. Fol. 109, b. Pedigrees of the families of Fermoy, County Cork. Fol. 111, a. Pedigree of O’Dunlevey. Fol. 112. Lists of Roman emperors, kings of Egypt, Assyria, and Israel; bishops of Rome, Armagh, &c. In the margin of fol. 117, b, there is written in faint red ink, pale. capil: by which we may infer that the tract there tran- scribed was preserved also in the Psalter of Cashel. This is apparently the only reason for supposing that the present MS. contains extracts from the Psalter of Cashel. Fol. 118. The actions and deeds of Finn M‘Cumhaill. Fol. 122. A very important tract, which appears from the handwriting to be much more ancient than any other part of the volume, containing the derivation of the names, local traditions, and other remarkable circumstances of the hills, mountains, rivers, caves, rocks, carns, and monumental remains in Ireland: more especially such as relate to the deeds of Finn Mac Cumhaill and his heroes. There is an imperfect copy of this tract in the Book of Lismore, in the possession of His Grace the Duke of Devon- shire, of which a copy was lately made for the Academy by Mr. Curry. Fol. 127, a. A Finian tale, entitled, “‘ The Elopement of the Daughter of the King of Munster with Oisin.” The remainder of the volume is occupied with a series of these tales, which are of great interest and importance. Many modern copies of them on paper are preserved, espe- ‘ cially in the valuable collection of Messrs. Hodges and Smith, 345 which is particularly rich in this branch of Irish literature: but with the exception of the fragment in the book of Lis- more, the present volume is the only vellum MS. of such tales whose existence is known. The special thanks of the Academy were voted to the Board of Ordnance and to Captain Portlock for the presen- tation of the Ordnance Geological Survey of Tyrone, Lon- donderry, and Fermanagh. DONATIONS. Abhandlungen der Akademie der Wissenchaften zu Ber- lin, 1840, Presented by the Academy. Bericht tiber die zur Bekanntmachung geeigneten Verhand- lungen der Kénigl. Preuss. Akademie der Wissenschaften xu Berlin. Presented by the Academy. ; Account of the Induction Inclinometer and of its Adjust- ments. By the Rev. H. Lloyd, D.D., F.R.S., V.P.R.LA. Presented by the Author . Regulations of the School of Engineering in the University - of Dublin, with a Syllabus of the Course. Presented by Pro- fessor Lloyd. PROCEEDINGS OF THE ROYAL IRISH ACADEMY. a... 1843. No. 39. February 27. SIR Ws. R. HAMILTON, LL.D., President, in the Chair. Sir William Betham exhibited to the Academy an ancient shoe, found in a bog on the property of Sir Nicholas Fitz- simon, in the King’s County. Professor Lloyd read a supplement to a former paper “on the Determination of the Intensity of the Earth’s Mag- netic Force, in Absolute Measure.” In a paper recently communicated to the Academy, the author had shown that the ratio of the coefficients of the first two terms, in the expression for the moment of the force exerted by a deflecting upon a suspended magnet, was gene- rally given by the formula M. M’ ae eee —; M M in which m and m; denote certain integrals depending on the _ law of distribution of free magnetism in the deflecting mag- net, and m’ and w’; the corresponding quantities for the sus- _ pended magnet. It was further shown, that when the mag- nets were small, this formula was reduced to | h=3(22~ 82%); VOL. Il, ; 26 348 / and /’ denoting the half lengths of the two magnets. This ratio being thus known @ priori, the two unknown quantities in the equation of equilibrium of the suspended bar are re- duced to one; and we are thus enabled not only to dispense with the observations of deflection at two separate distances, but also to infer the quantity sought with much greater ac- curacy than in the received method, by superseding the pro- cess of elimination. The preceding value of the ratio, h, has been derived from an approximate law of magnetic distribution, which can be regarded as physically exact only in the case of very small magnets; and the truth of the formula has been veri- fied, in that case, by direct experiment. It was interesting to inquire, therefore, how far the same formula represented the law of action of large magnets, and whether, by any mo- dification, it might be applied to the results obtained with such instruments. For this purpose the following deflection experiments were made:—The magnets employed were rectangular bars, 12 inches, 9 inches, and 7} inches, in length; % of an inch in breadth; and { of an inch in thickness. The observations were made with the aid of the Unifilar Magnetometer of the Magnetic Observatory, which has been elsewhere described ; and simultaneous observations were taken with the Declino- meter, in order to eliminate the changes of declination which occurred in the interval of the opposite deflections. In the first and second series, the position of the suspended bar was observed by means of a collimator attached; in all the rest, it was observed by the help of a mirror connected with the stirrup, which reflected the divisions of a scale placed at a distance of nearly six feet. The angles of deflection were calculated, in the case of the collimator bar, by the formula tan uw = 4 (nme — nw)k ; where », and m» denote the observed readings of the scale, : 349 with the marked end of the deflecting bar to the East and to the West respectively. The value of the constant & is given by the formula = (1 +") tan6; F 6 denoting the angle corresponding to one division of the scale, and ~ the ratio of the torsion force to the magnetic force. When the mirror is employed, the formule of re- duction are similar, if only we substitute 2u and 20 for u and @. The following Table gives the values of the constants employed in the reduction: l | 6 ‘5 (coll.) 49-158 6°37795 ‘5 (mirr.) 58-766 6°75643 Pet ~~] = amatyenoeny 6°75684 Spel hat nits . 6°75700 The following Tables contain the calculated results: the values of }(”-—w) are corrected for the changes of declination which occurred in the interval of the two readings m, and ny. Series l.and II. 7=/=°5. u 3 (%e—Nw) uw 4 2039 45” 194-22 2° 39/18” lo 7/43” 82:26 1° 7305 Series III. and IV. 2—°5, l’ =-375. u 3°56 25” 3°56 38” 2° 0/53” 2° 1" 4” 1° 10/45 1°10’ 3” 26.2 350 Series V. and VI. J=°5, ’ =°313. Vv. 3 (Me — Mar) u 3 (%e — Nw) ” 4:0005 243-58 3°57! 44-5 242-74 3°56! 56” 5:0008 123°65 BEG Do 123-36 2° 0/585 6:0010 7141 LTO?! G5 71-25 To O'57e Series VII. and VIII. 2=:°375, ’= "5. 1 (me — re) u 4 (Me — nw) u 3°3762 211°18 3° 26/ 10/5 210°50 3° 25/ 30/5 43754 97°88 1935/50" 97°56 1°35’ 36/5 5:3757 63°24 0°.52/ 13” 52°88 0° 51/515 SERIES PMVend x. P= =<37b. A ee ea dD. 3 (Ne — me) % 4 (ne — nw) | uu 33766 | 212:37 | 3027/31” 212:52 | 3027/40” 4:37 60 97°52 | 1035/3975 | 97:55 | 1°35/41-5 SERIES 5 ta HMR £1 See XI. 3 (me — mw) sd 3 (Me — Nw) u 213°83 3°29! 1” 97:90 1°36/ 3/5 52°82 0°51/52” 3°3766 21416 3° 29/ 21” 4-3760 98-05 1° 30/137 5°3765 52°85 0°51/54” The following Table contains the calculated results of the foregoing observations. The values of the coefficients, @ and Q’, are deduced from the formula Gh mm’ tanu = —+--; a a by the method of least squares. 351 Q’ ‘ a! wah 4-2800 — 0-824 —0:193 4-2662 ~ 0-790 — 085 43934 4 0-293 + 0-067 4-3976 + 0-293 + 0-067 43791 +0887 | 40-202 43760 + 0°692 + 0158 § 23830 — 0-823 ~ 0345 ) 23702 ~ 0-761 ~ 0-321 2-3407 — 0-161 — 0-069 2-3402 — 0135 — 0-058 2-3456 + 0-027 40-012 2-3428 +. 0-005 + 0002 The values of 4 thus obtained are not adequately re- presented by the formula which has been already deduced for the case of small magnets, the differences between the calculated values and the means of the two observed results . being, in general, greater than the differences of the latter inter se. It was accordingly natural to inquire whether the agreement might not be rendered more complete by pushing farther the approximation in the value of the function which represents the law of magnetic distribution. This was found to be the case on trial. But it was also found that the observed results were represented, with nearly equal exactness, by the empirical formula, h=2(1—c)?—3(l—c); a formula which agrees with the hypothesis, that the whole force of each magnet is concentred in two points, or poles, at given equal distances from the ends. If we expand the pre- ceding formula, and add together the resulting equations, we have for the determination of c, 6c? + 23(21—3l')e + Sh—3B(2/?—3l”) = 0; or, substituting the numerical values of the coefficients de- duced from the preceding Table, 352 c?— 0°625c + 0°0125 = 0; from which we deduce c = ‘078. The following Table contains the values of / thus calcu- lated, together with the means of the observed results. The differences barely exceed the probable errors of the latter; and the corresponding error in the calculated value of @ is less than the probable error of the same quantity, as deduced in the ordinary method from the observed deflections at two distances. j V h (obs.) Dif, 5 5 — 0-189 +011 | 5 375 + 0-067 + -025 5 313 + 0-180 +011 ‘375 | +5 — 0°333 — -025 375 | 375 — 0:063 — 025 ‘375 | -313 + 0:007 + -004 It follows from the preceding formula, that the relation between the half lengths of the two magnets, which will cause the coefficient of the fifth power of the distance to vanish, is l—ce = 1:224(’—c); or, substituting for ¢ its value, 2+ 0175 = 1:2241. It will appear evidently from the foregoing results, that on account of the large probable error of h, its value should be determined in each case from the mean of a much greater number of observations, before we can obtain thereby a sa- tisfactory verification of any formula for its calculation. As far as the comparison has been here carried, the results ap- pear to indicate that the value of # cannot be obtained a priori, in the case of large magnets, with that precision which would justify us in superseding observation, although we may obtain thereby an approximate value, comparable in exactness with the result of a single observation. 353 Mr. T. Oldham read a paper “ on the Tiles found in the ancient Churches in Ireland.” Mr. Oldham commenced by drawing attention to speci- mens of old tiles, from various places, which were on the table; and having alluded to the fact, that there has hitherto been no published representation of these tiles from any place in Ireland, proceeded to show that there were three distinct varieties :—l1st. Impressed or indented, in which the pattern is formed by being sunk below the general surface of the tile. 2nd. Encaustic, in which the pattern is produced by a differently coloured substance inlaid; and 3rd. Tiles in re- lief, or embossed, in which the pattern is raised above the general surface or ground. QL Vy VE (URS a From the great simplicity of the patterns in the indented tiles, from their interlacing character (Fig. 1), and from the fact, that several of these patterns occur also in the more carefully formed encaustic tiles, it was shown that the im- pressed variety was the earliest in date ; and, from a conside- ration of the history of the establishments where they occur, probably belonged to the twelfth century ; that the encaustic variety was a subsequent improvement on this more simple form, and that the embossed tiles belonged to an era when the knowledge of the arts had very much declined. This 354 was proved by several from Bective Abbey, the date of which was fixed by the occurrence of the tudor, or double rose, and by an heraldic tile from the same place, representing the arms of the Fitzgeralds, having the motto, “ Crom abo—Si Dien plet,” and the initials G. E. It was shown, from the history of this family, that the tile could only be referred to a date subsequent to 1496 (in which year the Earls of Kil- dare, previously attainted, were restored to their honours, and again allowed to use their motto), and to either Gerald the eighth or Gerald the ninth Earl, both of whom had wives whose Christian name was Elizabeth, corresponding to the initials G. E.—Gerald and Elizabeth. The identity of several of the patterns from different places in Ireland, and the strong resemblance of many to those found in England and Normandy were then alluded to, and several peculiarities in the Irish pattern, which tended to prove that they were manufactured on the spot, were pointed out. Speaking of the comparative cost of these tiles now and formerly, Mr. Oldham showed from the account of the re- pairs at Hampton Court in 1536, and allowing for the diffe- - 355 rence in the value of money, that the price at present charged was somewhat less than in the sixteenth century; and concluded by soliciting the assistance of the members in bringing together as complete a series as possible of the pat- terns still remaining in many of the ruined churches of Treland. The President read a Supplementary Notice of his Exa- mination of Signor Badano’s Memoir on the Resolution of Equations of the Fifth Degree, and described the successful 4 application to cubic and biquadratic equations of the method proposed by Badano, but which had been shown to be un- ; successful with equations of higher degrees than the fourth. r “7 * Rev. Dr. Marks, on the part of the Bishop of Cashel, presented the seal used by the latter as Dean of St. Patrick’s. 356 March 16. (Stated Meeting). SIR Wm. R. HAMILTON, LL.D., President, in the Chair. The Secretary of Council read the following Report, which was ordered to be entered on the Minutes : “The affairs of the Academy during the past year have been, for the most part, of a similar character to those which have formed the subjects of former Reports. It is, however, satisfactory to the Council to be able to state, that our proceedings have been distin- guished by still increasing activity and zeal among our members, and that some important measures have been entered upon, and others brought to completion, which it is to be expected will tend permanently to sustain the reputation of the Academy, and extend its useful influence. “‘ The second part of the nineteenth volume of the Transactions of the Academy is now printed, and the Council is enabled to place before the Academy an early copy. In a few days it will be ready for distribution among the members. ‘* The twentieth volume, which will altogether consist of Mr. Petrie’s Essay on the Round Towers, is progressing through the Press; and a portion of the twenty-first volume is in the hands of the printer. “The Council have with great pleasure to report, that the va- luable collection of Irish antiquities amassed by the late Dean of St. Patrick’s, having been purchased by a subscription, has been presented by the subscribers to the Academy. The amount sub- scribed having slightly exceeded the cost of the Collection, the balance was applied to the purchase of some other valuable relics of antiquity, which were also presented to the Academy, and now form part of its Museum. The detailed circumstances connected with the collection and application of this subscription, and the eminent services rendered to the Academy and to Irish Archzeology by various gentlemen, to whose exertions final success was mainly due, have already been brought under your notice in the Report drawn up by the Committee of Antiquities, and presented to the Academy in November last by Dr. Todd. The Council have there- f 4 357 fore, on the present occasion, only to congratulate the Academy and the country on the acquisition of this Collection, which it is to be hoped will prove a centre to which may be attracted the various objects of antiquarian interest now scattered through the country, or which may hereafter be discovered, and thus be laid the foun- dation of a truly national Museum of Antiquities. ‘* Besides the actual Dawson Collection, our Museum has been enriched by donations from His Excellency the Lord Lieutenant, and from various private individuals, to whom on the several occa- sions of presentation well merited thanks were voted by the Aca- demy. ‘* The necessity of arranging our Museum in such a form as should do justice to its intrinsic value, and adapt it for those pur- poses of reference and exhibition on which much of the influence it is calculated to exert must depend, has rendered the present ac- commodation of the Academy House totally inadequate to our wants, and the Council has consequently directed its attention to ascertaining how far our accommodation in rooms can be extended. It has been found that at a moderate cost the present Board Room may be converted into a Museum Room sufficient for our objects, and that under the Library and the adjoining spaces, there exists ground now of little use, on which a Board Room, rather larger than the present, may be constructed. A model and drawings of the ar- rangement proposed have been already laid before the Academy, and met with its approval, but circumstances connected with our te- nure of this house have induced the Council to postpone for a short time entering upon any outlay in building. “In the Report of the last Council, the Academy was informed that an application had been made to His Excellency the Lord Lieutenant, that he might recommend tothe Government to increase our Annual Grant by the sum of £100, or to allow that sum per year, specially for the purchase of Irish antiquities. No decisive answer has been as yet received to that application, but it is to be hoped that as we have now made so excellent a beginning to our Museum, and that the sphere of our public utility has thus been much extended, so small an increase to our exceedingly scanty means may not be finally refused. 308 ‘“‘ In November last, the Academy authorized the Council to employ Mr. Curry to draw up a Catalogue Raisonné of the Irish manuscripts in the Library of the Academy. This work has been ever since in progress, but will still require some months for its completion. ‘« Some time ago the Council became aware that it was contem- plated by Her Majesty’s Government to withdraw from the Irish branch of the Ordnance Survey those grants of money which have hitherto been made to the departments of Geology and Natural History, as well as of Topographical Antiquities and Statistics, so that the future operations of the Survey should be limited to the completion of the Maps. Sensible of the great benefit that must accrue to the country at large by the continuance of those depart- ments, for which already a vast body of materials have been col- lected, which, if publication were now abandoned, may be totally lost, and feeling that independent of its interest, as positively extend- ing the domain of science, and of which so brilliant an example has been already presented to the Academy, on the part of the Board of Ordnance, by Captain Portlock, the Geological branch of the Sur- vey is of the highest practical importance to Ireland, as making known the true position and limits of our mineral wealth, and guarding enterprize from those latent perils on which, from want of such scientific knowledge, it has been so often wrecked, the Council did not hesitate to interpose its voice against the relin- quishing of that undertaking. A deputation of the Council waited on His Excellency the Lord Lieutenant with a memorial, in which the more evident reasons in favour of the continuation of this truly national work were embodied. His Excellency received the depu- tation with his usual courtesy, and was pleased to express his sym- pathy with its objects. He undertook to forward the memorial to the heads of the Government in London, and the Council is not without: sanguine hopes that the Memoir of the Ordnance Survey may be finally continued on its original extended scale. “In obtaining this result, the Council believe that the voice of the Royal Irish Academy will have afforded some assistance. “Since the date of the last Report, the Library of the Academy has been increased by numerous donations of books, for which 359 thanks have been voted to the donors, at the meetings of the Aca- demy. The Academy continues in communication with the prin- cipal scientific bodies of Europe and America, with which an inter- change of Transactions and other publications is kept up. “ During the past year the accession of new members to the Academy has been such as to show, that notwithstanding the usually abstract nature of its proceedings, its importance is fully recog- nized. As honorary members, two have been elected on the recom- mendation of the Council: the one a philosopher of European eminence, Professor Wheatstone; the other, an Irish woman, whose name adorns the roll of the Academy, as her works have long shed lustre on the literature of her country, Miss Edgeworth. The names of the gentlemen who have been elected ordinary members of the Academy are : Rev. Richard Butler. W. V. Drury, M.D. Dr. Robert Law. W. R. Gore, M. D. John Toleken, Esq., F.T.C.D. J. E. Hodder, Esq., R. N. William Blacker, Esq. Rev. John Homan. Rev. James Booth. H. Hutton, Esq. Arthur Cane, Esq. R. Leslie Ogilby, Esq. B. J. Chapman, Esq. Hon. Frederick Ponsonby. F. M. Jennings, Esq. George Salmon, Esq., F.T.C.D. : Sir Thomas Staples, Bart. Robert Culley, Esq. a Stewart Blacker, Esq. James Magee, Esq. } Thomas Cather, Esq. H. L. Renny, Esq. ‘* In a body so numerous as ours, it could not be expected that a year should pass away without the loss of some from amongst our ranks. Unhappily within the last twelve months we have had oc- casion to deplore the deaths of several valued members. “From the list-of honorary members three have been removed, Sir James Ivory, Mr. Allan Cunningham, and Professor Heeren. Of our ordinary members we have lost the Hon. J udge Foster, the Right Rev. Charles Dickenson, late Lord Bishop of Meath, Dr. Macartney, Mr. David Aher, and Mr. Bowles. It is fit to notice _ briefly their career and their connexion with this Academy. ' “ Sir James Ivory was a native of Dundee, and studied in the University of St. Andrew’s, where he first distinguished himself in 360 those mathematical studies on which the elements of his subsequent distinction rested. Although intended for the Church, circum- stances threw him into the totally different career of managing an extensive flax and spinning concern. But even the engrossing na- ture of commercial industry could not wean him from scientific pursuits, and on the dissolution of the company he devoted himself exclusively to mathematical investigation. He passed to London, and was appointed Professor in the Military College of Sandhurst, which he retained until ill health, occasioned by his untiring re- searches, obliged him to resign. His merits were so well recog- nized that he received the retiring pension, although he had not served the time required by the War Office. Subsequently a royal pension was conferred upon him, and at the same time he received the honour of Knighthood of the Guelphic Order of Hanover. ‘‘ Sir James Ivory was elected by this Academy an honorary member on the score of his eminent mathematical discoveries. These it is unnecessary to detail. They embraced the solution, in abstract mathematics and in physical astronomy, of problems of the greatest difficulty and importance; and the Royal Society of London sufficiently indicated their opinion of his merits by award- ing to him at different periods the Royal and the Copley medals. ‘Mr. Allan Cunningham, although occupying a totally different field of intellectual exertion from that trod by Ivory, and cultivating rather the faculties of imagination and invention than those of logical thought, is also an example of learning, pursued as an en- joyment in the first instance to relieve the weary practice of a mechanical trade, and finally adopted as a profession. Born in Scotland, he was early apprenticed to a stone-mason, for whom he worked many years. His mind, imbued with the traditions and tales of the Border district in which he resided, soon applied its vigorous though somewhat rugged poetic faculties to their arrange- ment; and although it is said that many of the traditions he has rendered popular, had their first origin in his own fertile brain, yet there is no doubt but that his verses have preserved a great body of popular Scottish story, that otherwise might have been lost. Would that the abundant sources of poetical composition which the earlier chronicles of this country present were similarly utilized. The 361 varied results of Mr. Cunningham’s literary life need not here be detailed. He subsequently became connected with Sir Francis Chantrey, in whose workroom he acted as manager and superinten- dant. Called thus to intimate association with the most elevated in art, all his subsequent literary works had for object, more or less, its illustration, and his final labour, concluded but a few days be- fore his death, was the life of his countryman and friend, Sir David Wilkie. Mr. Cunningham was elected an honorary member of this Academy on the score of his various literary merits. ‘The death of Professor Heeren of Gottingen is felt through Europe as the removal of one of the brightest luminaries of classical literature. A reputation, already brilliant, bequeathed to him by his father, received additional lustre from his elaborate investiga- tions into the commerce and social condition of the nations of an- tiquity. He was appointed first Professor of Philosophy, and after- wards of History, in the University of Géttingen; and his decease in the past year has added another to the crowd of illustrious dead, by whose memory that seat of learning is rendered sacred.” “Our recollection of those members whom we have lost from the ordinary roll of the Academy during the past year is yet so fresh, the time that has elapsed since they assisted at our meetings is so short, that the notice, necessarily so brief, that can be here made of their career must be imperfect, and may appear unjust. In the in- stances, however, of two eminent members, whose recent loss we all deplore, the Right Rev. the Lord Bishop of Meath, and the Hon. Justice Foster, it may be said, thatalthough numbering them among its members, this Academy was not the scene of their labours or their glory; devoted to the pursuit of most important and engross- ing professions, in which by their varied talents they attained the highest dignities, time was not available for the prosecution of any of those objects which this Academy has more especially in view. Neither contributed to our Transactions, but the purposes of this Institution, and its progress, were always subjects of their warm approbation and support. «Mr. Bowles, a young member of the Academy, must be deeply regretted, as from his extensive knowledge of languages, and the enlightened assiduity with which he was, up to the period of his death, engaged in acquiring statistical information, much was to be expected. 362 “In Mr. David Aher the country has lost one well conversant, as a civil engineer, with its physical circumstances, and anxious and effectual in promoting industry. He was principally engaged in the working of the coal district of Kilkenny and the Queen’s County, but was concerned in many other engineering operations in that neighbour- hood. He supplied a great deal of valuable information embodied in the Reports onthe Irish Bogs, drawn up by order of Government; and recently, I believe his last work, at the time when the plans for railway intercourse through Ireland were much discussed, he sur- veyed and proposed a line extending from Dublin to Kilkenny. Owing to the purely practical nature of Mr. Aher’s labours, he did not contribute any memoirs to our Transactions, but his career was not on that account the less valuable. This Academy, necessarily limited in its scope to the more general and abstract contemplation of scientific questions, is still most fully cognizant of the merit, and anxious to express its admiration of those men, who practically developing the sources of useful employment and industrial wealth which our country holds, may become important agents in increasing the comfort and happiness of our people. ‘* Dr. James Macartney was born in March, 1770, in Armagh, where his family had long been resident. He was educated in the country, where he received the rudiments of an ordinary education, but was not at college, nor was he intended for a profession. Forced, however, in 1790, by the death of his father, to decide upon his future course of life, he chose the profession of surgery, ‘ not,’ as he used to say, ‘ because he had any peculiar aptitude for the business, but that he thought it would harden his feelings, which he had found on many occasions painfully acute.’ In 1794 he was apprenticed to Dr. Hartigan, who was at that time Professor of Anatomy to the Royal College of Surgeons in Ireland. Passing to London for the completion of his professional studies, he was ap- pointed, in 1798, Demonstrator of Anatomy at Bartholomew's Hos- pital ; and in 1800, having become a member of the Royal College of Surgeons in London, he began to lecture on Comparative Anatomy and Physiology, which he continued up to 1810. During the greater p 363 part of this time he was Surgeon to the Radnorshire Militia, which office, however, was not allowed to interfere with his scientific or professional pursuits. In 1811 he accompanied that Regiment to Treland, and in 1813, the Professorship of Anatomy and Surgery in Trinity College having become vacant by the death of Dr. Hartigan, he presented himself as a candidate, and was elected. ‘* For twenty-four years Dr. Macartney discharged the duties of that important office with unexampled zeal and industry, and used his utmost exertions to improve medical education. He endea- voured to establish a course of lectures on Comparative Anatomy, but circumstances prevented his plan being at the time carried out. He was, however, successful in arranging a separate course on Pa- thology, and in conjunction with Dr. Jacob, then his Demonstrator, he instituted a dispensary for the special treatment of diseases of the eye andear. As a lecturer, his manner, though unadorned by the arts of verbal eloquence, became highly popular from the sound ideas which he imparted, and the distinct and logical language in which they were clothed. His classes were always very large, and by his means the reputation of the Medical School of the University of Dublin was materially elevated. ** He resigned his Professorship in 1837, but still continued his application to scientific pursuits. On the 5th of the present month (March) he was seized with apoplexy, and died on the following morning. “‘In a literary point of view, Dr. Macartney’s contributions to medical and zoological science were numerous and important. In 1803 he commenced writing for Rees’ Cyclopedia, to which he supplied the articles—‘ Comparative Anatomy. Vegetable Ana- tomy. Bezoar. Anatomy of Birds. Classification of Animals. Anatomy of the Egg. Anatomy of Fishes. Incubation. Ana- tomy of Mammalia.’ In the Philosophical Transactions he pub- lished a memoir on Luminous Animals, and contributed many minor papers to the British Association, and to the Academie de Medicine of Paris. His large work on Inflammation, containing his chief _ discoveries in physiology and surgery, was published in Dublin _ in 1838; and in the Transactions of this Academy there are by him two valuable memoirs, the first in vol. xiii, on Curvature of the a VOL. II. 2H — a 364 Spme, and the second, on the Anatomy of the Brain of the Chim- panzee, inserted in the second part of the nineteenth volume, which has been this evening laid before the Academy, but of which, un- fortunately, he did not live to witness the formal publication. ‘* Dr. Macartney was a Fellow of the Royal Society, and of the Linnean Society of London, and an Honorary Fellow of the King and Queen’s College of Physicians in Ireland. He was also a Fo- reign Associate of the Academy of Medicine of Paris, and member of many of the most eminent scientific societies of the Continent of Europe and of America. “* The Reverend James Horner, D. D., engaged in the constant practice of the sacred duties of his profession, did not take any part in the proceedings of the Academy, but will be long remembered by many amongst us for the interest he always manifested in our suc- cess, the amenity of his manner, and the benevolence of his heart. “* The engrossing occupations of an active political life had also so completely removed the Right Hon. Sir John Newport, Bart. from the pursuits to which this Academy is devoted, that it is only necessary formally to record his loss, and that he had not contri- buted to our proceedings.” The Treasurer presented the following Abstract of his Account with the Academy for the year ending this 16th of March, 1843: “dadnspasy “NOP ‘WId SUWVE ‘paubigy fo LI LO6OF f9 LU LO6F FE GM Se ee ee ee ‘syuware Ay &ansvary, “ TE SI-18) Sa OS ORD ange tea Dee wl 9 €£9G ‘* * * * + + *y903g yue0 10d fg uo spuopraig “ 00 1% °° * * + * + ‘aeek euo 103 9[qQuU7g Jo yoy * ¥ L£1.9 * unoosoy jo sounpeg ‘0g 3 ou00g aed ‘ysug ‘* Oe Be OED shh" St ev Sa re SES a ee eer Oe Mimeantar ae 0 SI 66 OR eth SS ste ew Par eee oF ee ‘suorjtsodu0g Os “ $6 IL eee eee, SOINBvOLT, UL “OCT “ 0: Oe ee ee ee ‘suorydrsosqng yenuay “ OL TE 886 * * * * + + * ‘puvjeay jo yoeg ur ooumeg “ | fr of, * * + + + + = = *peatooox sorzpuns soy yseg “ Met geg ss ts st sss ss pred sorspung ge |} 1 2 69 °° * “BPeT “qoue_E MOT QIpNe aod se ‘ooneug oF, OSS, po F 49 “a "Sh8L ‘HOUVNN Ht9T ‘AWACVOW SIU] IVAOY 977 YpM JUNOIOP U2 ‘waunsva4y, “NAP ‘WIG SINVE 366 The auditors appointed by Council to examine the Trea- surer’s accounts reported as follows : “‘ We have examined the original Account,* with the vouchers produced, and found it to be correct; and we find that there is a balance in bank of £288 lls. 10d., and in the Treasurer’s hands, £2 11s. 94d., making a total balance of £291 3s. 7}d. “ (Signed,) “Franc SADLEIR. “ Samven Lirron.” “‘ March 16, 1843.” ‘“« The treasurer reports that there is £1085 17s. 1d. in 3 per Cent. Consols, and £1665 4s. 2d. in 34 per Cent. Government Stock, to the credit of the Academy in the Bank of Ireland; the latter known as the Cunningham Fund. He also reports, that eleven members owe their annual subscriptions, due 16th March last, and that two members are owing their two years’ subscriptions to the same date. There are no other arrears due. He has also to report, that the Annual Parliamentary Grant for the current year, amount £300, has not yet been placed to the credit of the Academy in the Bank of Ireland, but that there is no reason to doubt that it will be done within a few days. “* (Signed,) “ James Pim, Jon., ‘¢ Treasurer.” The ballot for the Annual Election having closed, the President requested the Rev. Charles Strong and Mr. Call- well to assist the officers in examining the balloting lists. The Scrutineers reported that the following gentlemen were duly elected Officers and Council for the ensuing year: President—Sir William Rowan Hamilton, LL.D. Treasurer—James Pim, Jun., Esq. Secretary to the Academy—J. Mac Cullagh, Esq. LL.D. Secretary to the Council—Robert Kane, M. D. * Entered in Treasurer’s book. , 367 Secretary of Foreign Correspondence—Rev. Humphrey Lloyd, D.D. Librarian—Rey. William H. Drummond, D.D. Clerk and Assistant Librarian—Edward Clibborn. Committee of Science. Rev. Franc Sadleir, D.D., Provost of Trinity College; Rey. Humphrey Lloyd, D.D.; James Apjohn, M.D.; James Mac Cullagh, LL.D.; Rev. William Digby Sadleir, A.M.; Robert Ball, Esq.; Robert Kane, M.D. Committee of Polite Literature. His Grace the Archbishop of Dublin ; Rev. Joseph Hen- derson Singer, D.D.; Samuel Litton, M.D.; Rev. William Hamilton Drummond, D.D.; Rev. Charles Richard Elring- ton, D.D.; Rev. Charles William Wall, D.D. ; John Anster, LL.D. Committee of Antiquities. George Petrie, Esq.,R.H.A.; Rev. J.H. Todd, D.D.; Henry J. Monck Mason, LL.D.; Samuel Ferguson, Esq. ; Joseph Huband Smith, Esq. ; James Pim, Jun. Esq. ; Cap- tain Larcom, R.E. The President then appointed, under his hand and seal, the following Vice-Presidents : Rev. Humphrey Lloyd, D.D.; Rev. James Henthorn Todd, D.D.; Rey. Joseph Henderson Singer, D.D.; James Apjohn, M.D. 368 April 10. RICHARD GRIFFITH, Ese., in the Chair. George James Allman, Esq., Henry Lindsay, Esq., John M‘Mullen, Esq., Hon. and Very Rev. Henry Packenham, Dean of St. Patrick’s, Goddard Richards, Esq., and John Wynne, Esq., were elected Members of the Academy. Dr. Todd, V.P., read a translation of an Ivish deed or agreement made in the year 1526, between Conla Mac Geo- ghegan, chief of the Kinel Fiacha, and Breasal Sionnach, alias Fox, chief of the Clan Tadgan,—both of Westmeath. The agreement was, that Mac Geoghegan should be lord over Fox and his country under certain conditions, which are specified, and of which the principal is, that Mac Geoghegan is to do his best for the protection and defence of Fox and his country. The deed adds, “‘ if Mac Geoghegan should on any occasion fail to do his best for the protection and sustainment of the Fox in his lordship, that he would do for himself; that he no longer have rent, nor privilege, nor lordship over him, but every one be for himself.” One passage proves that the custom of holding the half yearly assemblage (o'peaczar) on the Ist of November and the Ist of May was then kept up. ‘‘ Every general assembly of Samhan [All Saints’ day] or of Bealtine [May day] that shall be in Mac Geoghegan’s country, shall be held at Baileath-an- Urchair, or at Corr-na-Sgean, and the Fox and the nobles of his country shall attend.” It is known from other sources that the Brehon laws, and the authority of the hereditary Brehons, were kept up in many parts of Ireland to a much later period: the following passage therefore, which contains an allusion to the Brehon, is not surprizing. ‘ And whenever either an Englishman or an Irishman sues the Fox or any one of his country, they ess reer ree 369 shall submit to pay whatever is decided upon by Mortogh Mac Egan, or whoever may be the Brehon at the time, &c.” The original of this deed, which is in Irish, is in the pos- session of Sir Richard Nagle, the lineal representative of Mac Geoghegan, who has kindly permitted a copy of it to be taken and deposited in the Library of the Academy. The great body of the document is uninjured and legible ; the only imperfection which occurs is in the following pas- sage at the end, which contains the signatures and date of the agreement. ** These are they of the Foxes’ country who are present with us, viz. the Fox himself, and the two sons of Edmund, viz. Murtogh and Phelim; and the two sons of Brian Fox, viz. Breasal and Cucogry ; and Murtogh, son of Owen, son of. .... i.e. the Ollamh (poet or historian) of Fox... . and myself James O’Cionga [or king] the son of Carbry O’Cionga, who was present at the making of this agreement, and who wrote it. And it was on the Fast [i. e. the Eve] of St. Adamnan this agreement was made; and particularly on Wednesday; and it was on a Friday it was written. And this is the year of the Lord at this time, viz. six years, and twenty, five hundred and one thousand years [1526], and the 22nd day of the month of August. ‘* + Tam the Mac Geoghegan. > Iam the Fox.” [Here follows a line in the characters of the consonant Ogham, but so much effaced that although the key is known, it has been found impossible to decipher it. The last word only is le- gible, which is Graine, or Grace, a woman’s name: then follows] ‘‘are in Ireland.» We are the sons of Edmund Fox. »& We are the sons of Brian Fox.” Mr. Mallet gave a notice of recent improvements in the formation of Mosaic pavements. April 24. SIR WILLIAM BETHAM, in the Chair. The Chairman informed the Academy, that Sir Richard O’Donnell had consented to deposit the Cathach, containing a MS. of the Psalms in Latin, by St. Colombkill, in the Mu- seum of the Royal Irish Academy. Resotvep,—That the marked thanks of the Academy be returned to Sir Richard O’Donnell for his kindness. Read, a letter from the Rev. T. R. Robinson, accom- panying a box containing an original Pyrometer of Wedge- wood, presented to the Academy by Miss Edgeworth, (H. M. R.1. A.) ‘© Dear Mac Cutaen, “ Our friend, Miss Edgeworth, has requested me to present from her to the Academy a Wedgewood’s Pyro- meter, which, as unfortunately I cannot attend this evening, I commit to your care. This instrument is remarkable, as being the first attempt to place within reach of the manu- facturer and the chemist an easy method of measuring, at least approximatively, the temperature of their furnaces. It consists, as is well known, of a pair of converging bars, which measure, by a graduation on them, the contraction of clay cylinders that have been heated; this remains permanent, and were it, as Mr. Wedgewood supposed, a function of temperature alone, would suffice for all practical purposes. Many circumstances, however, have interfered with its gene- ral employment. The set of clay pieces which were used in the first instance were made of natural clay found in Corn- wall. By these the numbers given in treatises of chemistry for the fusing points of the more refractory metals were de- termined, and I think it probable that Mr. Kirwan used them in his researches; Sir James Hall, [ think, did not. Mr. 371 Wedgewood had stated in his memoir that the supply of the clay was inexhaustible; but when the stock first made was disposed of, he was unable to find the identical spot where it had been obtained, and the contraction of the new speci- men was different. Had he used it as he did the other, and merely directed the employment of a number by which to multiply the indications of the scale, no inconvenience would have resulted ; but he thought he might bring it to an iden- tity by adding ‘earth of alum,’ obtained by precipitating alum by carbonate of potassa; a product which Apjohn or Kane will tell you is very far indeed from being pure alumina. This unhappily made the contraction irregular, and the clay pieces much less capable of resisting a high heat. Its indi- cations were found to differ from those of the first set, and it fell into disuse, especially for two reasons. The first that Wedgewood had assigned to his degrees, a value enormously too large, so that he supposed the extreme heat of a furnace to be about 30000 of Fahrenheit, when it is only 4000. Many years since, in our Transactions, I had pointed out this error, and corrected it, with tolerable success, as was long afterwards confirmed by Daniell and Prinsep. The se- cond, that a long exposure to a low heat produces the same contraction as a short exposure to a high. This is said by Sir James Hall to have been established by Dr, Kennedy, whose experiments, however, are no where published; and I confess that I doubt the fact, Guyton De Morveau has even made an observation which may account for the mistake. He found that similar pieces exposed for half an hour in a powerful furnace, one surrounded by siliceous sand, the other by powdered charcoal, marked 90 and 60, in conse- quence of the different conducting powers of these media. Now it is possible that the Scotch philosopher may have overlooked this influence, and not allowed time enough for ‘the higher temperature to be fully transmitted. The py- rometers of Daniell and others which have since been con- VOL, Il. I 372 trived, are so much more cumbrous and elaborate than this, that I hope it may yet be revived; and if so, the chemists, who may construct pieces for themselves, would find it useful to compare them with Wedgewood’s old standard. A single cylinder is sufficient for this, as after measuring a compara- tively low temperature, it will still contract when submitted toahigher. This I know to have been one of the original and genuine set presented to the late Mr. Edgeworth by its inventor, and therefore, independent of its probable utility, precious asa relic of two such men, and still more so as the gift of our illustrious countrywoman to a body, of whose scientific triumphs she is proud, and in whose welfare I know her to be deeply interested. « T. R. Roprnson. * April 24, 1843.” ResoLtveD,—That the letter be referred to Council, for special notice and attention. H. Smith, Esq. exhibited an ancient dress, found in a bog at a considerable depth, near the Abbey of Kilkenny. A number of interesting antiquities, found at Ballyrowan, in the Queen’s County, by Mr. Harrison, were presented by the Rev. B. I. Clarke, to the Academy. The thanks of the Academy were presented to Mr. Clarke for his donation. Sir Wm. Betham made a communication on the antiquity of certain languages. DONATIONS. Astronomical Observations made with Ramsden’s Zenith Sector, and Catalogue of the Stars which have been observed at the different stations of the Ordnance Survey in England 373 and Scotland. London, 1842. Presented by the Master General of the Hon. Board of Ordnance. Ordnance Survey of the County of Clare, in seventy-seven sheets, including the Title and Index. Presented by His Ex- cellency the Lord Lieutenant. Battle of Magh Rath. Presented by the Irish Archeolo- gical Society. Memoires de la Société de Physique et d'Histoire Natu- relle de Genéve. Ninth volume. 1841, 1842, Presented by the Society. On the Publie Institutions for the Advancement of Agri- cultural Science which exist in other Countries. By Charles Daubeny, M.D. Presented by the Author. Transactions of the Camlnidge Philosophical Society. Vol. VII. Part 3. Presented by the Society. Proceedings of the Academie Royale de Bruxelles. Nos. 1 to9 inclusive. Vol. IX. Comptes Rendus des Seances de l' Acudemie des Sciences. Nos. 1 to 7 inclusive, from 2 Janvier to 13 Fevrier, 1843. Presented by the Academy. Annales del Observatoire Royale de Bruxelles. Tome Il. Presented by M. Quetelet. Archives du Museum d’ Histoire Naturelle de Paris. Liy- raison 3. Presented by the Museum. _e PROCEEDINGS OF THE ROYAL IRISH ACADEMY. 1843. No. 40. May 8. SIR Ws. R. HAMILTON, LL.D., President, in the Chair. I. G. Abeltshauser, Esq. was elected a member of the Academy. The special thanks of the Academy were voted to Miss Edgeworth for her donation of Wedgewood’s Pyrometer. Professor Mac Cullagh read the following communication. On the Laws of Metallic Reflexion, and on the Mode of making Experiments upon Elliptic Polarization. Several years ago, as the Academy are aware, I made an attempt to investigate the laws according to which light is reflected at the surfaces of metals, and I then proposed cer- tain formule which represented, with sufficient accuracy, all the facts and experiments which I was able to collect upon the subject (see the Proceedings of the Academy, vol. i. p. 2, October, 1836; Transactions, vol. xviii. p. 71, note). But in order to test these formule satisfactorily, it was neces- sary to obtain measurements far more exact than any that had previously been made; and for this end I devised an instrument, which was constructed for me by Mr. Grubb, and of which a brief description has been given in the Pro- ceedings, vol. i. p. 159. I regret to say, however, that no- - VOL. IT. 2K 376 thing of much consequence has yet been done with the instrument. Some preliminary trials of its performance were indeed made in the summer of 1837, and the results of one of these shall presently be given; but an accidental strain which it suffered, while I was preparing to undertake a series of experiments, caused me to discontinue the observations at the time; and being then obliged to superintend the printing of my essay on the Laws of Crystalline Reflexion and Refraction (Transactions R. I. A., vol. xviii. p. 31), my attention was drawn afresh to this latter subject, respect- ing which some new questions suggested themselves, which I thought it right to discuss in notes appended to the essay. I was not afterwards at leisure to take up the experimental inquiry, until the beginning of the year 1839, when I began to think of putting the instrument in order for that purpose. The strain which it had suffered rendered some slight alte- rations necessary ; and I now resolved to make additions to it also, with the view of operating upon the fixed lines of the spectrum, as a few trials had convinced me that measures sufficiently precise could not be obtained without employing light of definite refrangibility. I wished, moreover, to take the opportunity which the nature of the proposed experi- ments presented, of verifying the theory of Fresnel’s rhomb, or rather of verifying, by means of the rhomb, the formule which Fresnel has given for computing the effects of total reflexion, when it takes place at the common surface of two ordinary media. I wrote therefore to Munich for se- veral articles which I wanted; among others, for a set of rhombs cut at different angles, out of different kinds of glass. But while I was waiting for these some months elapsed, and in the meantime I got sight of a new theory, which, from its connexion with my former researches, pos- sessed more immediate interest, and the pursuit of which, in conjunction with other studies and various engagements, caused me again to suspend the inquiry respecting the laws of metallic reflexion. I allude to the Dynamical Theory 377 of Crystalline Reflexion and Refraction, communicated to the Academy in December, 1839 (Proceedings, vol. i. p. 374). This was followed soon after by a general Theory of Total Reflexion (Proceedings, vol. ii. p. 96), founded on the same principles. The latter theory, forming a new department of physical optics, and involving the solution of questions not previously attempted, was analytically complete when it was communicated to the Academy in May, 1841; but its geometrical development has since required my attention from time to time, and has not yet been brought to that de- gree of simplicity of which it appears to be susceptible (see Proceedings, vol. ii. p. 174). Indeed I have found that, in this instance, the geometrical laws of the phenomena are by no means obvious interpretations of the equations re- sulting from the analytical solution of the problem; and in endeavouring to verify such supposed laws I have often been led to algebraical calculations of so complicated a nature that it has been impracticable to bring them to any conclusion, and I have been obliged, from mere weariness, to abandon them altogether. On returning, however, to the investigation, after perhaps a long interval of time, I have usually per- ceived some mode of eluding the calculations, or of directly deducing the geometrical law; and when the theory comes to be published in its final form, no trace of these difficulties will probably appear. , ‘ From the causes above-mentioned, combined with fre- J quent absence from Dublin, the researches which I had entered upon, respecting the action of metals upon light, have been hitherto interrupted ; and as it may still be some time before they are resumed, I venture, in the meanwhile, ‘to submit to the Academy the results already spoken of, which were obtained on the first trial of the instrument, and which afford the best data th can yet be had for compari- son with theory. The results, it must be confessed, are those of very 2K2 378 rough experiments, made one evening (about the month of July, 1837) in company with Mr. Grubb, before I had received the instrument from his hands, and merely with the view of showing him, when it was finished, the kind of phenomena that I proposed to observe with it, and the mode of observing them. But the instrument was so far superior (in workmanship at least) to any apparatus previously em- ployed for this sort of experiments, that it was impossible, without great negligence in using it, not to obtain measures of considerable accuracy. I did not, however, at the time, set much value on these measures, because I expected shortly to possess a series of observations made with every possible precaution ; but having chanced to preserve the paper on which they were noted down, I was tempted, a few days ago, to try how far they agreed with my formule; and the agree- ment turns out to be so close, that I think myself justified in publishing them. Besides, it will be curious hereafter to compare them with more careful measurements. Before we proceed, however, to the details of the experi- ments, it may be well to give the formule in a state fitted for immediate application. The light incident on the metal being polarized in a certain plane, let a denote the azimuth of this plane, or the angle which it makes with the plane of incidence; and as the reflected light will be elliptically pola- rized, or,in other words, will perform its vibrations in ellipses all similar and equal to each other, as wellas similarly placed, put @ for the angle which either axis of any one of these ellipses makes withthe plane of incidence, and let {3 be another angle, such that its tangent may represent the ratio of one axis of the ellipse to the other. Then when the optical con- stants M and y (of which I suppose the first to be a number greater than unity, and the second an angle less than 90°) are known for the particular metal, the angles 6 and ( may be computed for any value of a, at any given angle of inci- dence, by the following formule : 379 (v’—yv) sin 2a tan 20— ++) a? (A my ici 2g sin 2a v’+v+ 2fcos 2a’ in which f and g are constant quantities given by the expres- sions 1 EN*, fi ( _ =) ne (x + =) sin x, (B) and v, v’ are quantities depending on the angle of incidence i, in the following way.. Let é’ be an angle such that sin @ M sind’ ~ cosy’ ) and put : : cosz | cosa’ (>) then will mieenitte 7 pee («) The angles @ and £3 are given by ciinibastig observation with the instrument; and from their values at any incidence, and for any azimuth a of the plane of primitive polarization, we can find the constants m and x, which we may afterwards use to calculate the values of 0 and [3 for all other incidences and azimuths, in order to compare them with the observed values. It is indifferent, in the formule, whether @ be re- ferred to the major or the minor axis of the elliptic vibration, as also whether tan 3 be the ratio of the minor to the major axis, or the reciprocal of that ratio; but in what follows we shall suppose @ to be the inclination of the plane of inci- dence to that axis, which, when a is 45° or less, is always the major axis; and {3 shall be supposed less than 45°, in ‘order that its tangent may represent the ratio of the minor axis to the major. When the sinc ais as to 45°, the formule (a) become Ia n9Q.— = - tan20 = ~ F° in 2B = eye (F) from which we may deduce the remarkable relation tan 23 cos 20 — A ay (6) 380 showing that, in the case supposed, the ratio of tan? to cos 26 is independent of the angle of incidence. In the ex- periments which I made with Mr. Grubb this azimuth was always 45°; and the following Table contains the results of observation compared with those obtained by calculation from formule (Fr). The experiments were made upon a small disk of speculum metal; and in the calculations I have taken mM = 2.94, y = 64° 25’. Value of 0. Value of 6. Observed. 27° hae. 15 41 — 8 45 —350 15 Calculated. 27% G3! 15 44 — 9 16 —29 25 Observed. 28° 0’ 33 (7 34 10 27 0 Calculated. 28° 0’ 331 34 6 26 53 —37 22 | =—37 25 16 47 Ve ¥ The light used in these observations was that of a candle placed at a short distance, and was admitted through small apertures at the ends of the tubes. (See the description of the instrument in the Proceedings, vol. i. p. 159). The Nicol’s prism inthe first tube having been secured in a position in which its principal plane was inclined 45° to the plane of incidence, and the two arms having been set at the proper angle with the surface of the metal, the Fresnel’s rhomb and the Nicol’s prism in the second tube were moved simultaneously, until the image of the candle became as faint as possible. Had light perfectly homogeneous been employed, the image could have been made to vanish altogether; but instead of vanish- ing, it became highly coloured, and our rule in observing was to make the blue at one side of it, and the red at the other, equally vivid, so as to get results which should belong, as nearly as possible, to the mean ray of the spectrum. When this was done, the angles @ and [3 (subject however to certain corrections which will be hereafter explained) were respec- tively read off from the divided circles belonging to the thomb and the prism. The observations were made at large 381 incidences, because it is within the last thirty degrees of incidence that the phenomena go through their most rapid changes. If we now cast our eyes on the above table, making due allowance for the uncertainty arising from the dispersion of the metal, we shall be struck with the agreement between the calculated and observed numbers. The differences are greatest in the last two observations, which however were really the first; for the observations were made in the in- verse order of the incidences, and their accuracy may have improved as they went on. However that may be, the dif- ferences are quite within the limits of the errors of observa- tion; and they are actually less than those which Fresnel found to exist between calculation and experiment in the much simpler case of reflexion at the surface of a transparent ordinary medium, when he proceeded to verify the formula which he had discovered for computing the effect of such reflexion.—See the Table which he has given in the Annales de Chimie, tom. xvii. p. 314. It may seem extraordinary that these experiments should have been in my possession for nearly six years, before I be- came aware of their close agreement with my formule; but the fact is, that I did not regard them with much interest, ‘because, from the circumstances in which they were made, I did not expect more than a general accordance with theory. ‘And even now, I am in no haste to infer the absolute exac- titude of the formula, though they are found to represent the phenomena so well. It was far more allowable to infer that the formula of Fresnel was exact in the case just men- tioned, though it appeared to represent the phenomena less perfectly. For, to say nothing of the small number of our ex- periments, the present is a much more complicated case, and the phenomena depend on two constants instead of one, so that the formule might be slightly altered, and yet perhaps con- tinue to agree very well with rough experiments. Where there is only one constant this is not so probable. Again, 382 there is one of the quantities in the preceding formule which may be greatly altered without producing more than a slight effect on the values of @ and 3. This quantity is the ratio of sinz to sin z’, which, according to the value in formula (c), is a number so large as to make the angle ¢’ always small, so that its cosine never differs much from unity; and therefore if the above ratio were taken equal to any other large num- ber, the value of » in formula (Dp) would remain nearly the same, and consequently the values of # and (3 would be but slightly changed. - It is with regard to the value of jm as a function of the incidence that I entertain the greatest doubts, and if any defect shall be found in the formule I think it will be here. The relations (c) and (p), from which » may be deduced in terms of 2, were not indeed adopted without strong reasons ; but I am not entirely satisfied with them, because, when we reverse the problem, and seek to determine the constants M and y from the observed values of 0 and (3 at a given inci- dence, the results are rather. complicated and involved, though the approximate determination is easy enough. As the formule are in a great measure built upon conjecture, we must not be disposed: to receive them without the strongest experimental proofs; and it will certainly require experiments of no ordinary accuracy to decide some of the questions which may be raised respecting them. When plane-polarized light is incident on a metal, if its vibrations be resolved in directions parallel and perpendicu- lar to the plane of incidence, the effect of the reflexion is to change unequally the phases of the resolved vibrations; and it may be useful to have the formule which express the diffe- rence of phase after reflexion, and the ratio of the amplitudes of vibration. Put @ for the difference of phase; and sup- posing, for simplicity, the incident light to be polarized in an azimuth of 45°, let o be angle less than 45°, such that tano may represent the ratio of the reflected amplitudes 383 respectively perpendicular and parallel to the plane of inci- dence; then we shall have ily od Sha tan an ee cos2o = aca (H) from which we may infer that . sind tan 2o= 2n . (1) I or that the product on the left side of the last equation is independent of the angle of incidence. It is to be observed that the relations (c) and (1) are independent of the value of p, and may hold good though that value should require to be changed. All the preceding formule are merely mathematical con- sequences of those which I published long ago in the Tran- sactions of the Academy (vol. xviii. p. 71). The formule which I had previously given in the Proceedings (vol. i. p. 2) are slightly different, and, I think, less likely to be exact, because they are less simple, and do not lead to any of the remarkable relations which may be deduced from the others, Having had occasion, in the course of the few experi- ments which I made with the instrument before mentioned, to study the nature of Fresnel’s rhomb, which constitutes an important part of it, I shall here describe the method which must be followed in order to obtain true results, when the rhomb is employed in observations on light elliptically pola- rized. A ray in which. the vibrations are supposed to be elliptical is given, and what we want is to determine the ratio of the axes of the elliptic vibration, and their directions with respect to a fixed plane passing through the ray; in other words, to determine the angles which we have denoted by 6 and @ in the case of a ray reflected from a metal. For this purpose the ray is admitted perpendicularly to the sur- face at one end of the rhomb, and after having suffered two total reflexions within, passes out perpendicularly to the sur- 384 face at the other end. Then causing the rhomb to revolve about the ray, we shall find two positions of it in which the emergent light will be plane-polarized, these positions being readily indicated by a Nicol’s prism interposed between the rhomb and the eye; for such a prism, by being turned round the ray, can make the light totally disappear when it is plane-polarized, but not otherwise. These two positions of the rhomb will be exactly 90° from each other; in one of them the principal plane of the rhomb (the plane of reflexion within it) will be parallel to the major axis of the elliptic vi- bration, and the angle which it makes with the plane of in- cidence on the metal will be equal to 9: while in the same position the angle which the principal plane makes with the plane of polarization of the emergent ray (as given by the Nicol’s prism) will be equal to (3. In the other position, the principal plane will be parallel to the minor axis of the elliptic vibration, and the corresponding angles will be equal to 90°—6 and 90°—f3 respectively. This, however, proceeds on the supposition that the rhomb is exact. When it is not so, which is of course the proper supposition, and a very ne- cessary one in the experiments with which we are concerned, there will still be, generally speaking, two positions of it in which the emergent ray will be plane-polarized, or in which a disappearance of the light may be produced by the Nicol’s prism; but these positions will no longer be 90° from each other, nor will the principal plane, in either of them, coincide with an axis of the elliptic vibration. If we now measure the angles between the different planes as before, and denote them by 6’, 3’ in the first position, and by 90°—6”, 90°—3” in the second, we shall find that @’ and 0” are unequal, but we shall have ’ equal to 8". The values of @ and # will then be given by the formule / “ i : i ; cos 23 = ae (k) The error of the rhomb may easily be found. Supposing 385. the vibrations to be resolved in directions parallel and per- pendicular to its principal plane, the rhomb is intended to produce a difference of 90° between the phases of the re- solved vibrations, or to alter by that amount the difference of phase which may already exist; but the effect really pro- duced is usually different from 90°, and this difference, which I call ¢, is the error of the rhomb. ‘The value of ¢ is given by the formula _ sin (0/— 0") . tane = tan 2B 3 (t) and as the error of the rhomb is a constant quantity, we have thus an equation of condition which must always sub- sist between the angles 0’—@” and 3. For any given rhomb the sine of the first of these angles is proportional to the tangent of twice the second, and therefore 0’— 6" constantly increases as (3 increases towards 45°, that is, as the axes of the elliptic vibration approach to equality. When 3 is equal to 45°— 4, we have 0’— 0’=90°; and for values of 3 still nearer to 45°, the value of sin (0’/— 0”) becomes greater than unity, that is to say, it becomes impossible, by means of the rhomb, to reduce the light to the state of plane-polarization.. This is a case that may easily happen with an ordinary rhomb in making experiments on the light reflected from metals; because at a certain incidence, and for a certain azimuth of the plane of primitive polarization, the reflected light will be circularly polarized. The rhomb which I used in the experiments tabulated above, was made by Mr. Dollond, and was perhaps as accu- rate as rhombs usually are; it was cut at an angle of 544°, as prescribed by Fresnel. Its error was about 3°, and the value of 0’—0”, at the incidence of 75°, was about 7°. But in another rhomb, also procured from Mr. Dollond, and cut at the same angle, the value of #’—6”, under the same circum- stances, was about 20°, and the value of < was therefore 386 about 8°. The angle given by Fresnel was calculated for glass of which the refractive index is 1.51; and the errors of the rhombs are to be attributed to differences in the re- fractive powers of the glass. I was not at all prepared to expect errors so large as these when I began to work with the rhomb, and they perplexed me a good deal at first, until I found the means of taking them into account, and of making the rhomb itself serve to measure and to eliminate them. The value of the rhomb as an instrument of research is much increased by the circumstance that it can thus de- termine its own effect, and that it is not at all necessary to adapt its angle exactly to the refractive index of the glass. It may also be remarked, that this circumstance affords a method of directly and accurately testing the truth of the formule which Fresnel has given for the case of total re- flexion at the separating surface of two ordinary media; for we have only to measure the angle of the rhomb and the refrac- tive index of the glass, and to compute, by Fresnel’s for- mula, the alteration which the rhomb ought to produce in the difference between the phases of the resolved vibrations ; which alteration of phase we may then compare with that deduced, by means of the formulz (xk) and (x), from direct experiment. If, in each position of the rhomb, we measure the angle which the plane of polarization of the emergent ray makes ‘with the plane of incidence on the metal, and call the two angles respectively y’, y”, we shall have 7 et eae p’, y =O’ 4+ B’; (m) and therefore y/ ue 7! — @/ + 6” = 26, 2p’ = yy’ A. 0’—6": (x) from which it appears that if the rhomb were perfectly exact, that is, if 6’ and 0” were equal to each other, the angle 0 would be half the sum of y’, y", and the angle (3 half their difference. It would then be sufficient to measure the angles y and y”, in order to get # and 3 accurately. And if the 387 rhomb were erroneous, the true value of @ would still be half the sum of y’, y’; but the true value of 3 would not be discoverable without measuring the angles 6’, 0", by the help of which it can be deduced from the second of formule (x), combined with the second of formulz (k). Nor can we dis- cover whether the rhomb is erroneous or not, without mea- suring the angles 0’, 0”; and therefore as these angles must be measured in any case, the former method of determining 0 and 3 is to be preferred. In making experiments on elliptically polarized light, a plate of mica or any other doubly refracting crystal, placed perpendicular to the ray, may be used instead of Fresnel’s rhomb. If the thickness of the crystalline plate be such that the interval between the two rays which emerge from it is equal to the fourth part of the length of a wave, for light of a given refrangibility, the plate will, for such light, per- form all the functions of the rhomb; the principal plane of the rhomb being represented by the plane of polarization of one of the emergent rays. But unless the light be perfectly homogeneous, this method is liable to great inaccuracy in practice, since the effect of the plate in producing or altering the difference of phase between the two rays which interfere on their emergence from it, is inversely proportional to the length of a wave, and will therefore be extremely different for light of different colours, and will change very per- ceptibly even within the limits of the same colour. Itis true, the effect of the rhomb also varies with the colour of the light: but this variation is trifling compared with that which exists in the other case. It was for this reason that I em- ployed the rhomb in my experiments, instead of a crystalline plate. The apparatus, however, is much simplified by using such a plate; and if any one chooses to do so, and to work with homogeneous light, he must take care to follow, in every respect, the directions which I have given for conducting experiments with the rhomb. The two cases are precisely 388 similar; and if it be necessary not to neglect the errors of the rhomb, it is certainly not less necessary to take into ac- count those which may arise from a want of accuracy in the thickness of the plate, considering how difficult it is to make the thickness correspond exactly to the particular ray which we wish to observe. I have been induced to enter into these particulars, re- specting the mode of making experiments on elliptic polari- zation, because the subject is one which has not hitherto been studied ; nor does it seem to have occurred to any one that any precaution was requisite beyond that of getting the rhomb cut as nearly as possible at the proper angle, or the crystalline plate made as nearly as possible of the proper thickness. This, indeed, was quite sufficient for ordinary purposes. For example, light polarized in a plane inclined 45° to the principal plane of the rhomb or of the plate, would, as far as the eye could judge, be circularly polarized after passing through either of them. Notwithstanding a certain error in the angle of the one, or in the thickness of the other, such light would, when analysed by a rhomboid of Iceland-spar, give two images always sensibly equal in inten- sity. But an error which could not be at all detected in this way, might produce a very great effect in such experiments as those upon the metals, and, for the purpose of comparison with theory, might render them entirely useless, if in the first method of observing we relied upon one set of obser- vations, taking (suppose) the values of 6’ and 3’ for the true values of 0 and (3; or if, inthe second method, we contented ourselves with merely measuring the angles y’ and 7”. ; The necessity of attending to the foregoing rules and re- marks will appear from an examination of the experiments of M. de Senarmont, published in the Annales de Chimie, tom. Ixxiii. pp. 351-358. In these very elaborate experi- ments, which were made upon light reflected at various inci- dences from steel and speculum metal, the author followed 389 a plan similar to that which I have adopted, and which, in a general way, I had previously sketched in the Proceedings of the Academy (vol. i. p. 159). There was this difference, however, that he used a plate of mica instead of Fresnel’s rhomb. Now as he worked with common white light, the use of the mica plate must have rendered two kinds of errors unavoidable. In the first place, it would be impossible always to take the observations for the same ray of the spectrum; and next, as a consequence of this, the thick- ness of the plate would be generally inexact for the particu- lar ray to which the observations happened to correspond. If the thickness of the plate were exact for a certain ray, it would be very sensibly inexact even for the neighbouring parts of the spectrum; and as the part of the spectrum to which the observations belonged was continually changing, the results obtained for different incidences and azimuths would not be comparable with each other, even though, in each separate case, the error of the plate were allowed for and eliminated. The values of 0, however, as determined by M. de Senarmont, would be correct, so far as this error is concerned ; those of (3 alone would be erroneous. For the values of @ were determined in two ways: by measuring the angles 0’, 0”, and taking their sum for 20; also by measur- ing the angles y’, y’, and taking their sum for the same quan- tity. Now each of these methods gives a true value of 6, because by the preceding formule we have 20 = #’ + 9” = vy + 7’; and this accounts for the agreement, shown by the tables of M. de Senarmont, between the values* of 20 ob- tained by these different methods. But the values of B were deduced from the angles y’, y’, by simply making their dif- * Or rather the values of 180° + 26; because the angle w, the double of which appears in the tables of M. de Senarmont, is equal to 90°-++ 6. The angles which he calls y, and y, are equal to 90°-++- y” and 90° + y’ respectively. It therefore comes to the same thing, whether the one set of angles or the other is supposed to be measured. The letter 6 has the same signification in both notations, 390 ference equal to 2/3; and we see by the second of formule (x) that, when the plate is not of the proper thickness, this value of 2 is erroneous by the whole amount of the angle 0’ — 0”, the difference between ’ and (3 being supposed so small that it may be neglected. As M. de Senarmont proceeded on the common assumption that when the thickness of the plate has been adjusted to that part of the spectrum to which the ob- servations are intended to refer, it may afterwards, through the whole series of experiments, be regarded as exact, he necessarily conceived @’ and 6” to be the same angle; and it was on the principle of taking an average between two mea- sures of the same quantity, that he made the supposition 20 = 6’ + 6”, which happened to be correct. When there- fore he found 6’ and 0” to be different, he of course looked upon the difference as merely an error of observation, which it would be superfluous to tabulate. Not having the values of this difference, therefore, we have not the means of im- mediately correcting the values of 2/3. But as observations were made for several azimuths at each angle of incidence, we may use the values of @ to determine those of 3; for when at any incidence (except that of maximum polarization, where 6=0 for all azimuths) the values of @ are known for two given values of a, we can deduce the corresponding values of 3, with- out any other theory than that of the composition of vibrations. The values of (3 so deduced must indeed be expected to be very inaccurate, partly because of errors in the observed values of 0, partly because the observations in different azimuths do not answer to the same ray of the spectrum; but they will be accurate enough to show the great amount of the error committed by neglecting the difference # — 6”. For ex- ample, putting 0) and /3) for the values. of @ and 3 when a = 45°, M. de Senarmont gives, at the incidence of 60° upon steel, 20, = 64° 15’ (taking the mean of his two determina- tions), and for the azimuths 55°, 30°, 25°, he gives 20 equal to 88° 5’, 37° 2’, and “9° 36’ respectively. Combining these Pre i 391 values of 20 in succession with that of 20), we get for 2B the series of values 32° 38’, 33° 28’, 34° 30’; the differences between which are to be attributed to the causes above stated. The mean value of 28, thus found is 33° 32’; while its value, as given by M. de Senarmont, is only 28° 41’, The difference 4°51’ is the value of § — 6”, which, divided by the tangent of 2,, gives 7°19’ for the mean value of ¢, the error of the ‘mmica-plate corresponding to that part of the spectrum which was observed at the incidence of 60°. At incidences nearer the angle of maximum polarization, the errors are probably much greater. Beyond that angle they again diminish, and in some cases they almost vanish. Thus, at the incidence of 85° upon steel, with the value of 20) and the value of 20 corresponding to a = 20°, we get, by computation, a value of 2(5 which differs only by a few minutes from that given by M. de Senarmont. Nearly the same thing happens at the same incidence when we take a= 25°. In these cases therefore the results belong to that particular ray for which the thickness of the plate was exact. The observations of M. de Senarmont on speculum metal were not carried beyond the incidence of 60°. He states that he was unable to observe at higher incidences, on ac- count of the uncertainty arising from the dispersion of the metal; but though this cause operated in some degree, his embarrassment must have been really occasioned by the in- creasing magnitude of the difference & — 0”, as he approached the angle of maximum polarization; that difference being perhaps twice as great as in the case of steel. My own ex- periments on speculum metal were all made, as has been seen, at incidences greater than 60°. The experiments of M: de Senarmont do not at all agree with the formule ; and therefore I have been obliged to ana- lyse his method of observation, and to show that it could not lead to correct results. It is to be regretted that his VOL. II. 2. 392 method was defective, as the zeal and assiduity which he has displayed in the inquiry would otherwise have put us in possession of a large collection of valuable data. I shall conclude by saying a few words respecting the in- tensity of the light reflected by metals. The formule for computing this intensity have been given in the Transactions of the Academy, in the place already referred to; but they may be here stated in a form better suited for calculation. If we suppose y and y/ to be two angles, such that M cotany = -, cotan y/ = Mu, (0) be and then take two other angles w, w’, such that cosw = sin2y cosy, cosw’ = sin2wW’ cos, (Pp) we shall have 7 = tan3o, 7’ = taniw’, (a) where is the amplitude of the reflected rectilinear vibration, when the incident light is polarized in the plane of incidence, and 7’ is the amplitude of the reflected vibration when the incident light is polarized perpendicularly to that plane; the amplitude of the incident vibration being in each case sup- posed to be unity. Hence when common light is incident, if its intensity be taken for unity, the intensity 1 of the reflected light will be given by the formula 1= }(tan*}w + tan*} w’). (Rr) If with the values of m and x determined by my experi- ments we compute, by the last formula, the intensity of re- flexion for speculum metal at a perpendicular incidence, in which case x = 1, we shall find 1 = .583. This is consider- ably lower than the estimate of Sir William Herschel, who, in the Philosophical Transactions for 1800 (p. 65), gives .673 as the measure of the reflective power of his specula. The same number, very nearly, results from taking the mean of Mr. Potter’s observations (Edinburgh Journal of Science, New Series, vol. iii. p. 280). It might seem therefore that oes a” ie = = = 393 the formula is in fault ; but I am inclined to think that the metal which I employed had really a low reflective power. Its angle of maximum polarization was certainly much less than that of the speculum metal used by Sir David Brewster (Phil. Trans. 1830, p. 324), who states the angle to be 76°, whereas in my experiments it was only about 733°; and any increase in this angle, by increasing the value of m, raises the reflective power. On the other hand, the maximum va- lue of 3 (when a = 45°) was greater than that given by Sir David Brewster, namely, 32°; and any increase in 6 tends also to increase the reflective power. Now it is not unrea- sonable to suppose that the highest values of both angles may be most nearly those which belong to the best specula; and accordingly if we take 76° for the incidence of maximum po- larization, and retain the maximum value of 3, namely 34° 37’, which results from my experiments, we shall get m = 3.68, x = 66° 16’, and the value of 1 at the perpendicular incidence will come out equal to .662, which scarcely differs from the number given by Herschel. It is clear from what precedes that the optical constants are different for different specimens of speculum metal, and this is no more than we should expect, from the circum- stance that the metal is a compound, and therefore liable to vary in its optical properties from variations in the pro- portion of its constituents; but I am disposed to believe that the same thing is generally true, though of course in a less degree, of the simple metals, so that in order to render the comparison satisfactory, the measures of intensity should always be made on the same specimen which has furnished the values of Mand yx. There is one metal, however, with respect to which there can be no doubt that the experiments of different observers are strictly comparable, when it is pure, and at ordinary temperatures; I mean mercury. For this metal Sir David Brewster states the angle of maximum’ pola- 394 rization to be 78° 27’, and the maximum value of 8, when a = 45°, to be 35°; from which I find m=4.616, y = 68° 13’, and, at the perpendicular incidence, 1=.734. Now Bouguer observed the quantity of light reflected by mercury, but not at a perpendicular incidence. His measures were taken at the incidences of 69° and 783°, for the first of which he gives, by two different observations, .637 and .666; for the second, by two observations, .754 and .703, as the intensity of reflexion. (See his Traité d’Optique sur la Gradation de la Lumitre, Paris, 1760; pp. 124, 126). If we make the computation from the formula, with the above values of m and x, we find the quantities of light reflected at these two incidences to be, as nearly as possible, equal to each other, and to seven-tenths of the incident light, the intensity of reflexion being a mini- mum at an intermediate incidence; and if we suppose these quantities to be really equal at the incidences observed by Bouguer, we must take the mean of all his numbers, which is .69, as the most probable result of observation. This result differs but little from one of the two numbers given by him at each incidence, and scarcely at all from the result of calculation. The angle at which the intensity of reflexion is a mini- mum, when common light is incident, may be found from the formula («+ ) @ + 7) = (1 — 4 Vv (f? +. g°)—4cosx, (s) which gives the value of u,and thence that of 7. This incidence for mercury is, by calculation, 75° 15’, and the minimum va- lue of 1 is .693, which is less than its value at a perpendicular incidence by about one-eighteenth of the latter. According to the formule, the reflexion is always total at an incidence of 90°. Rev. Charles Graves communicated certain extracts from ne 395 a work of the late Dr. Cheyne, on a Deranged State of the Faculty of communicating by Speech or Writing.* Dr. Allman read a paper ‘*©on a New Genus of Hydra- form Zoophytes.” The author discovered the animal on which he founded the new genus in the Grand Canal near Dublin, in October, 1842. The genus of which this zoophyte constitutes as yet the only known species, will finda place in the family of the tubulariade, and occupies a position between coryne and tubularia, differing from the former in the possession of a polypedome, and from the latter in the scattered arrange- ment of its tentacula. The tentacula, as in both the last mentioned genera, are filiform; and in this character a point of distinction is at once found between the new genus and ‘Hermia, Johnst. To the new zoophyte Dr. Allman assigned the name Cordylophora lacustris. May 22. SIR Wa. R. HAMILTON,LL.D., President, in the Chair. Right Hon. the Earl of Dunraven was elected a member of the Academy. Dr. Osborne read some observations on the deprivation of the faculty of speech while the intellect remains entire, and in which the defect does not arise from paralysis of the - yocal organs. The communication was intended as a sequel Seo O19 W OUN His Eto sil to sitios aly hire acelin * This work having been since published, the extracts are not here given. 396 to Dr. Cheyne’s observations read at the last meeting, and was chiefly intended to refer to a case published by Dr. Os- borne, which afforded some peculiar opportunities of inves- tigating the nature of this affection. The subject of this case was a gentleman of about 26 years of age, and of very considerable literary attainments. He was a Scholar of Trinity College, and also a proficient in the French, Italian, and German languages. When re- siding in the country, one morning, after bathing in a neigh- bouring lake, he was sitting at breakfast, when he suddenly fell in an apoplectic fit. A physician was immediately sent for, and after being subjected to the appropriate treatment, he became sensible in about a fortnight. But although re- stored to his intellects, he had the mortification of finding himself deprived of speech. He spoke, but what he uttered was quite unintelligible, although he laboured under no pa- ralytic affection, and pronounced a variety of syllables with the greatest apparent ease. When he came to Dublin his extraordinary jargon caused him to be treated as a foreigner in the hotel where he stopped; and when he went to the College in quest of a friend he was unable to express his wish to the gate-porter, and succeeded only by pointing to the apartments which his friend had occupied. ‘The circum- stance of his having received a liberal education, and his tractable disposition, rendered this case peculiarly favour- able for ascertaining the true nature of the affection, and the result of Dr. Osborne’s observations during several months were as follows: 1. He perfectly comprehended every word said to him, and his conduct and habits were those of a man in a sound state of mind, and were exactly those which his friends stated to be peculiar to him before the seizure. He had no pa- ralysis, and the motions of his mouth and tongue were exe- cuted with the force and rapidity of ordinary health. 397 2. He perfectly comprehended written language. He con- tinued to read his newspaper every day, and when passing events were spoken of, proved that he hada clear recollection of all that he read. Having procured a copy of Andral’s Pathology in French, he read it with great diligence, having _ lately intended to embrace the medical profession, 3. He expressed his ideas in writing with considerable fluency, and when he failed it appeared to arise merely from the want of the association with spoken language, which caused confusion and uncertainty, the words being ortho- graphically correct, but frequently not in their proper places. He translated Latin sentences accurately, and also wrote correct answers to historical questions. 4, His knowledge of arithmetic was unimpaired, he added and subtracted numbers of different denominations with un- common readiness ; also played well at the game of drafts. 5. His recollection of musical sounds appeared to be un- a impaired, for when the tune of Rule Britannia was played he ___ pointed to the shipping in the river. 6. His power of repeating words after another person _ was almost confined to certain monosyllables ; and in repeat- ing the letters of the alphabet he could never pronounce k, q,u, v, w, x, and g, although he often uttered those sounds in attempting to pronounce the other letters. The letter i also he was very seldom able to pronounce. 7. In order to ascertain and place on record the peculiar imperfection of language which he exhibited, the following sentence from the By-laws of the College of Physicians was selected, viz. “ It shall be in the power of the College to exa- mine or not examine any Licentiate previously to his admission to a Fellowship, as they shall think fit.” Waving set him to read this aloud, he read as follows: ‘‘ An the be what in the __ temother of the trothotodoo to majorum or that emidrate ein -einkrastrai mestreit to ketra totombreidei to ra fromtreido as _ that kekistret.” ‘The same passage was presented to him in 398 a few days afterwards, and he then read it as follows: “ Be mather be in the kondreit of the compestret to samtreis amtreit emtreido am temtreido mestreiterso to his eftreido tum bried rederiso of deid dat drit destrest.” We observe here those monosyllables which are of most frequent use in our language, as the, be, what, in, that, his, and was, along with several syllables almost peculiar to the German language, which he was engaged in studying at the time of the apoplectic seizure; but the main feature in the case was, that although he knew when he spoke wrong, yet that he was unable to speak right, notwithstanding he arti- culated very difficult and unusual syllables. As in this case the recollection of the meaning of words was retained, and it was proved that there was no paralytic affection interfering with pronunciation, but that even in the act of endeavouring to imitate another person, he could not pronounce the right word, Dr. Osborne concluded that the affection was not (as has been usually described) a loss of the faculty of language or of the memory of names, while the memory of things remains, but that it consisted in a loss of the recollection how to use the vocal apparatus. In stammering it is obvious that the patient knows the mode in which the word is to be pronounced ; he begins it rightly, but is prevented from finishing it by debility or spasm on the part of the muscles, causing them to resist his efforts.. In this patient, on the contrary, the words which he could write, and understood perfectly, he was unable to com- mence the first syllable of, and instead of them uttered words compounded from other languages. His ear afforded him very little assistance, as his attempts to repeat what had been read were scarcely better than his reading. The or- gans were not paralysed, neither were they affected by spasm, nor was he ignorant of the sounds to be uttered: it only remains then that he was ignorant of the art of pro- 399 ducing those sounds, and as he was previously in possession of this art, we are justified in asserting that he forgot it. It may appear unaccountable why we should be liable to forget the use of the vocal organs, but never forget the use of the other voluntary muscles. Thus while we have those i instances of persons pronouncing one word when they in- tended another, we have no instance of an individual running when he wished to stand, or leaping when he wished to sit down. This, however, admits of being adequately explained, | by the nerves concerned in the muscular apparatus of speech being derived from the brain and highest portions of the spinal cord, and consequently liable to be disturbed by apo- plectic affections ; while the nerves of the limbs being derived from the cervical plexus, or lower portions of the spine, are unaffected, except by such causes as may produce paralysis. Dr. Osborne referred to the Ephimerides Curtose for a ease in which the art of writing was retained, while that of speaking was lost; and also alluded to that of Zacharias in the Sacred Scriptures, who, although deprived of speech, is related to have written “‘ The child’s name is John.” Those instances which have been recorded of persons after wounds or apoplectic seizures ceasing to speak their usual language, and resuming the use of some other lan- guage with which they had been familiar at a former period, appear to be of the same nature as the present. The recol- lection of one language, and its train of associate actions being lost, it was most probable that the vocal organs should move in that train to which they had formerly beenaccustomed, and fall into the use of another language. It is highly pro- bable that a similar occurrence would have taken place in _ this patient if he had only cultivated one language besides English, but having been conversant with five languages, __ the muscular apparatus ranged among them, forming a kind of polyglot jargon, which was formed without any rule, was inconsistent with itself, and wholly unintelligible. VOL. 11. 2M 400 Although Dr. Osborne did not enter upon the medical treatment of the case, yet he considered that the effect of the plan adopted to recover his speech afforded an additional proof that this patient had not lost the faculty of language, but only the art or knack of speaking. He commenced learning to speak de novo like a child, by repeating after another person first the letters of the alphabet, and subse- quently words. This was avery laborious task. Sometimes he was able to pronounce words which at other times he found impracticable, but his progress may be estimated by his repeating after another the same By-law of the College of Physicians in the following terms: ‘‘ It may be in the power of the College to enhavine or not ariatin any Licentiate seviously to his amission to a spolowship as they shall think jit.” A month or two afterwards he repeated the same By- law perfectly well, with the exception of the word power, which on this occasion he called prier. This gentleman soon afterwards went to the country, where in a few months he was carried off by a fever, and Dr. Osborne learned no further particulars respecting him after he left Dublin. Sir William Hamilton remarked that Dr. Robinson’s mean refractions, published in the second Part of the Nineteenth Volume of the Transactions of the Academy, might be re- presented nearly by the formula, rR = 57,546 tan (0—4” xr); (1) or by this other formula, R cot @+R? sin 3”,8 = 57,346 ; (2) r being the number of seconds in the refraction correspond- ing to the apparent zenith distance 0, when the thermometer is 50°, and the barometer 29,60 inches. The first formula seems to give a maximum positive de- viation from Dr. Robinson’s Table, of about a quarter of a second, at about 80° of zenith distance; it agrees with the dj 401 Table at about 83° 10’; is deficient by a second at about 84° 30’; and by #” at 85°. The second formula, which may be reduced to logarithmic calculation by the equations, log tan 29 = log tan 8 + 2,81296, t (3) logr = logtanp + 3,24657, does not agree quite so closely with Dr. Robinson's Table, — in the earlier part of it; but the error, positive or negative, seems never to exceed half a second, within the extent of the Table, that is, as far as 85°. It appeared to Sir W. H. worth noticing, that the results of such (necessarily) long and complex calculations, as those which Dr. R. had made, could be so nearly represented by formulz so simple: of which, indeed, the first is evidently analogous to Bradley’s well known form, but differs in its coefficients. The second form is more unusual, and gives (approximately) the mean refraction as a root of a quadratic equation. It has been used (with other logarithms) by Brinkley, for low altitudes. DONATIONS. Address to the Geological Society of London. By Rode- rick J. Murcheson, F.R. S.A. Presented by the Author. Report of the Meeting of the British Association held at Manchester in 1842. Presented by the Association. Statutes relating to the Admiralty, to the 8th of Geo. IIT. Presented by Captain Portlock. Proceedings of the Glasgow Philosophical Society. 1841- 1842. Presented by the Society. Memoirs published by the Society of Sciences in Holland. _ Wol. Il. Second Series. Proceedings of the American Philosophical Society. Vol. Il . Parts 24 and 25. me ‘Transactions of the American Philosophical Society. Vol. ‘a viol. New series. Parts 2.and3. Presented by the So- 402 Fifth Annual Report of the Loan Fund Board in Ireland for 1843. Presented by the Commissioners. Communication to the Right Hon. Sir Robert Peel, Bart. By Jeffries Kingsley, Esq. Presented by the Author. Bulletin des Sciences de la Societé Vaudoise des Sciences Naturelles. Nos.1-4. Presented by the Society. Sur les Figures Roriques et les Bandes Coloriées produites par l’ Electricité. Par M. P. Riess. Presented by the Author. Expériences sur la non caloricité propre de I Electricité. Sur les relations qui lient la lumiere a l Electricité. Sur les travaux recents qui ont en pour objet letude de la vitesse de propagation de (Electricité. Par M. Le Prof. Elie Wartmann. Presented by the Author. Memoirs of the Literary and Philosophical Society of Manchester. New Series. Vol. VII. Part 1. Presented by the Society. List of Premiums of the Society for the Encouragement of Arts, Manufaciures, and Commerce, for 1843-45. Presented by the Society. Transactions of the Geological Society of London. Se- cond Series. Vol. VI. Part 2. Presented by the Society. PROCEEDINGS OF THE ROYAL IRISH ACADEMY. 1843. No. 41. June 12. SIR Wm. R. HAMILTON, LL.D., President, in the Chair. Sir William Betham read the following letter from Sir Richard O’Donel, Bart. : ** April 24th, 1848. ** My pear Sir WILLIAM, ** I have to apologise for all the trouble I have given you about the Caah, but several circumstances have come to my knowledge within the last few days, which induce me to desire that it should be placed in the Royal Irish Academy, next to the Cross of Cong; but I would not take any step in the matter without first consulting you, and having done so, I write you this note to request you will be so good as to make known my wishes to the Dublin Society upon the subject, and to have it removed to the Royal Irish Academy, upon their taking charge of it as my property, placing it during the day beside the Cross of Cong, and having it each night placed in a fire proof box. “I again beg leave of you to pardon me for all this trou- ble, and to accept my thanks for your kindness at all times, and believe me, * Dear Sir William, “Very sincerely yours, *“* Ricuarp O’Donet. "i _ Record Tower, Castle.” VOL. Il. 2N 404 Resotvep,—That the thanks of the Academy be given to Sir Richard O’Donel, Bart., for his valuable deposit, and that the custody of it be accepted by the Academy on the terms proposed by him. Sir Wm. Betham gave an account of the Caah. Professor Kane read a notice of some recent Determina- tions of the Heat developed during the Formation of certain Compounds of Chlorine, by Dr. Andrews. The present results were obtained by a similar method to that described in the last volume of the Transactions of the Academy. The chlorine, however, was employed in the dry state, and the compounds being formed without the pre- sence of water, the heat of combination was deduced from a single direct experiment. In the case of potassium, an im- portant modification of the apparatus was required, which will be described when the full details of the experiments are communicated to the Academy. The numbers in the first column are the immediate results of experiments, and ex- press, in degrees of Fahrenheit’s scale, the heat produced during each reaction, in reference to the chlorine as unit, that is, the degrees through which a weight of water equal to that of the combining chlorine would be raised by the heat developed in the formation of each compound. The num- bers in the second column express the same heat, referred to the combining metal as unit, and are deduced by calcula- tion from the others. K + €l .. 5879° .. 5954°, Sn + Cl... 1621°.. 1346°. Sb, + Cl;.. 1570° .. 1145°. As, + Cl;..1268°.. 898°. Dr. Allman read a notice of a new species of Linaria. This plant was discovered growing on the banks of the River Bandon, and Dr. Allman considered it sufficiently dis- { a al Ts, hae ¥ 7 é _ eleganter signati: labium inferius diluté luteum, striis pa- 405 tinct to entitle it to rank as a new species. Specimens of the plant collected by Dr. Allman were seen in London by Mr. H. C. Watson, who recognized them as identical in species with a Linaria, gathered by himself in two English localities, and, moreover, that they corresponded with the Antirrhinum Bauhin of Gaudin’s Flora Helvetica, LZ. Italica, Koch. In accordance with these views, a paper by Mr. Watson ap- peared in the second Number of Sir W. J. Hooker’s London Journal of Botany, adding L. Bauhini to the Flora of Britain. To the claim, however, of L. Bauhini to be admitted into the British Flora, Dr. Allman could not assent; so far at least as this claim depended on the identity of the Irish with the Continental plant. He had carefully examined the Irish Linaria, and convinced himself not only of its distinctness from L. Bauhini, but of its claim to rank as a new species. To Linaria repens it is closely allied, indeed there is some difficulty in separating it from this plant as a distinct species. Dr. Allman, however, conceived that specific characters would be found in the flowers, which not only differ in colour from those of L. repens, but also in their larger size, and in the greater relative as well as absolute length of the spur. To the new Linaria he gave the specific name sepium, and described it as follows: Linaria sepium. Lin. radice repente, foliis subglaucis lineari-lanceolatis, caleare incurvo corollam zquante, semi- nibus trigonis. Radix repens. Caulis erectus simplex v. subramosus, Paniculatus. Folia subglauca, lineari-lanceolata, sparsa, inferiora sepe verticillata. Bractee lanceolate, pedicello breviores, Calycis lacinie lanceolate. Flores in paniculam ex racemis erectis constantem dispositi, et odorem suavem at tenuem exhalentes. Calcar incurvum corollam zquans, la- bium superius, tubus et calcar grisei, striis palidé purpureis lidé purpureis et parum distinctis notatum: palatium villis 2N2 406 saturaté luteis vestitum, villis purpureis quemque marginem investientibus, Capsula globosa, dehiscens superne pluribus valvulis lanceolatis. Semina nigra, trigona, lateribus inzequa- libus muricatis, marginibus in alas tres productis. A L. repente differt hee species calcare longiore, corolla majori et labio inferiori luteo; a L. vulgari discrepat floribus minoribus corolla striis signata et toto flore, preter labium inferius et palatium, coloris lutei experti: ad hoc semina tri- gona signum certum prestant quo hee species a L. vulgari dignosci potest ; ab Antirrhino Bauhini differt caule erectiori, foliis angustioribus, colore florum pistillo glabro et seminibus trigonis. Habitat in sepibus juxta flumen Bandon. —Florebat Junio, Julio et Augusto 4. Rey. Dr. Kennedy Bailie commenced the reading of a paper on “ Certain Greek Inscriptions copied on the Sites of Ancient Teos and Aphrodisias in Asia Minor.” DONATIONS. Journal of the Franklin Institute. Vols. Il]. and IV Third Series. Presented by the Institute. Proceedings of the Zoological Society of London. Part 10. 1843. Presented by the Society. Tribes and Customs of By-Many. By John O'Donovan, Esq. Presented by the Irish Archzological Society. Astronomische Nachrichten. Nos. 462-477. Annales des Sciences Physiques et Naturelles d Agriculture et d’ Industrie, publiées par la Société Royale d' Agriculture, &e. de Lyon. Tomes I. II. and III. Presented by the So- ciety. Second Mémoire sur les Kaolins. Par M. Brongniart. Presented by the Author. JS eee ae 407 June 26. SIR Ws. R. HAMILTON, LL.D., President, in the Chair. Present, His Excellency Earl De Grey, Lord Lieutenant, Visitor of the Academy. : : 4 Dr. Kennedy Bailie read in continuation the Account of his Researches in Ancient Teos and Aphrodisias, in Asia Minor. Previously to entering on his selection of notices with respect to the Teian, &c. inscriptions, he thought it proper to offer a few remarks on that part of his former essay which relates to the subject of the inscriptions from Sardes and Pergamus. The passages more particularly referred to are those in pages 132-4, and 149-50, on which certain observations were made either explanatory of, or modifying, the author’s con- clusions, as expressed therein. The result in the case of the Sardian titulus has been, that it must no longer be consi- dered as referrible to the ages of Hadrian or of the Antonines, as he was at first led to suppose; and in that of the Perga- menian, that the document may be so interpreted as not to be in anywise connected with the question of Hadrian’s adoption by Trajan. The new readings illustrative of these points were sub- mitted to the notice of the Academy. The authorthen proceeded to a detail of his researches on the sites of the ancient Teos and the neighbouring port-town of Cherrzidz, which is mentioned by Strabo. This last he considers as occupied by the modern village of Sighadjék. The most interesting of the inscriptions which he brought _ from these sites is a fragment of one of an early date, at _ least coeval with those which Chishull has published in his celebrated work on the Antiquities of Asia, from copies 408 made by the late Sir William Sherard in 1709 and 1716. It related, as far as can be collected from the extremely muti- lated state of the monument, to a treaty of Asylumship (aovAla) between the inhabitants of this district of Asia Minor and certain other States of Greek origin, amongst which there are fragments of the names of the Agrigentines, the Coans, the Polyrrhenians (of Crete), also of the people of Delphi. This notice was concluded with a translation of the Titulus, which contained such supplementary matter as the author deemed requisite to complete the sense. He then proceeded to notice two other inscriptions, one of which he regarded as marking the site of the Temple of Bacchus, in Teos, of which Vitruvius has made mention; and the other as a remnant of the inscribed monuments of the ancient Chalcis, which lay contiguous to Teos. The first of these is remarkable, from its containing a notice of the election of a female of rank to serve the office of High Priestess of Asia. The second informs us of the existence of a Gerusia, or House of Assembly for the Seniors, in the city to which it belonged. Whether this was Chalcis (as conjectured above), or Teos, is uncertain. In proceeding to Gheyerah (the representative of Aphro- disias in Caria), the site of Tralles was noticed ; as also were the Tituli, which Pococke and others have copied from the ruin at present existing in the ancient acropolis. The Temple of Aphrodite, extensive remains of which still exist, in Aphrodisias, was then noticed ; as also the probable site of the Agora. Near this the first of the Aphrodisian in- scriptions was copied, which is remarkable from its contain- ing notices of a gradation in dignity amongst the Archons of the city, as also amongst the Neopei, or Trustees of the Temple of Aphrodite. The inscription in honour of Constantius and one of his colleagues, over the west portal, was next explained, and 409 reasons were assigned for supposing that the name of Julian, the Apostate, had been erased by the Christian inhabitants of the city, from this monument. The next inscription which was noticed contains an allu- sion to the office of Asiarch, which led the author of the Memoir to offer some explanations in reference thereto, prin- cipally on the mode of election to, and the duties, of, that station. The next brought under consideration was a fragment, ca- pable of being restored so as to present the first two petitions of the Lord’s Prayer; a supposition in perfect consistence with the history of the town. Several others were also noticed ; the most remarkable and interesting of which was a tomb-inscription of consider- able length, copied from the eastern side of the rampart. The discussion of this led to many remarks on the mode adopted amongst the Greek colonists of Asia Minor to ex- press degrees of descent, on the terms of their sepulchral architecture, and on the laws regulating tomb-property. Connected with this subject was a series of observations on the office of the Stephanephore. ‘This appears to have been partly of a civil nature, partly pontifical, in accordance with which the right of wearing diadems was granted to functionaries of this class, as to the FJamines amongst the Romans. The Memoir closed with some details respecting a series of reliefs, which the author discovered on the exterior of the southern wall. These, though placed in juxta-position, did not all refer to the same subject. There are two interposed, which appear to be altogether symbolical in their meaning, or at least to possess a mythical character, and to have been intended as illustrations of some mythical circumstance. . A suggestion was offered, that perhaps it would be worthy the attention of archeologists, to adopt means to have these sculptures removed from their present position, 410 and deposited in some museum. ‘They appeared to the au- thor to be curious and valuable specimens of ancient art, and are, in all probability, connected with the mythical legends of the Cretan people, with whom the early inhabitants of Aphrodisias were closely connected. The Rey. Dr. Todd, V. P. gave an account of a Stone with an Ogham Inscription, which was found with many others in a cave at Fortwilliam, in the county of Kerry, and sent up to the Provost and Senior Fellows of Trinity Col- lege. After having given a short account of the different kinds of Ogham spoken of by Irish grammarians, and exhibited the key usually given for reading the particular kind of Ogham to which the inscription on the stone found at Fort- william belongs, Dr. Todd proceeded to show the inapplica- bility of this key to the interpretation of the inscription. The whole subject of the Ogham inscriptions, he stated, was one which was involved in great obscurity, and although very abundant materials exist for investigating it, it has never yet been fairly examined. Several treatises on the subject are to be found in our ancient MSS., but no Irish scholar seems as yet to have had the courage to enter upon the study of them. Numerous inscriptions on stones, similar to that now exhibited to the Academy, are also to be found, particularly in the south and west of Ireland, but accurate copies of these inscriptions are no where accessible. Dr. Todd suggested this as a suitable subject for a prize, if ever the Academy should return to the former practice of offering a prize for an essay on a given subject. In this case, how- ever, he recommended that the prize should be offered, not for the best essay or theory for the explanation of the Ogham character, but, in the first instance, for the most accurate and best authenticated collection of copies, or fac similes, of the inscriptions themselves. The following engraving gives a correct view of the stone, 411 which is four feet five inches high, and in its broadest part at the base four feet six and a half inches in circumference, and an exact copy of the inscription : 00 06 . 2) ee TL ee veces DaonnyZuitO op 0000 SSP wo onoofy Nl, Mr. Griffith read a notice by Mr. Hemans, of a Disloca- tion in the Calp near Killester. _ The President, on presenting to Dr. Kane the Cunning- ham Medal, awarded to him for his Researches on the Nature of Ammonia, gave an account of the progress of his dis- coveries. 412 It is now my duty to inform you, that a Cunningham Medal has been awarded by the Council to Dr. Robert Kane, for his Researches on the Nature and Constitution of the Compounds of Ammonia, pub- lished in the First Part of the Nineteenth Volume of the Transac- tions of this Academy. It would, indeed, have been much more satisfactory to myself, and doubtless to you also, if one of your Vice-Presidents, who is himself eminent in Chemistry, had under- taken the task which thus devolves upon me, of laying before youa sketch of the grounds of this award; but at least, my experience of your kindness encourages me to hope, that while thus called upon officially to attempt the discharge of a duty, for which I cannot pretend to possess any personal fitness, or any professional prepara- tion, I shall meet with all that indulgence of which I feel myself to stand so much in need. Although, in consequence of the variety of departments of thought and study which are cultivated in this Academy, and the impossibility of any one mind’s fully grasping all, it is likely that many of its members are unacquainted with the details of chemistry, yet it has become matter of even popular knowledge, that in general the chemist aims to determine the constitution or composition of the bodies with which we are surrounded, by discovering the natures and proportions of their elements. Few need, for instance, to be told that water, which was once regarded as itself a simple element, and which seems to be so unlike to air, or fire, or earth, has been found to result from the intimate union of two different airs or gases, known by the names of oxygen and hydrogen, of which the one is also, under other circumstances, the chief supporter of com- bustion, is an ingredient of the atmosphere we breathe, and is closely connected with the continuance and healthful action of our own vital processes, by assisting to purify the blood, and to maintain the animal heat; this same gas combining also, at other times, with some metals to form rusts, with others acids, with others again alkalies and earths, entering largely into the composition of marble and of limestone, and, in short, insinuating itself, with a more than Protean ease and variety, into almost every bodily thing around us or within us; while the other gas which contributes to compose water, though endowed with quite different properties, is also ex- 413 tensively met with in nature, especially in organized bodies, and in particular occurs as an element in that important substance, on the confines of the mineral and organic kingdoms, to which the Re- searches of Doctor Kane relate; ammonia being, as all chemists admit, a compound of hydrogen and nitrogen, which last-named gas is well known as being the other chief ingredient (besides oxy- gen) of atmospheric air. Again, it is generally known, to those who take an interest in physical science, as a truth which is almost the foundation of modern chemistry, that the elements of bodies of well-marked and definite constitutions, such as pure (distilled) water, or dry (anhy- drous) ammonia, are combined, not in arbitrary, but in fixed and determined proportions; for example, the oxygen contained in any quantity of pure water weighs exactly, or almost exactly, eight times as much as the hydrogen contained in the same quantity, but occupies (when collected and measured) a space or volume only half as great ; and the nitrogen contained in any given amount of dry ammoniacal gas, is to the hydrogen with which it is combined, by weight as 14 to 3, and by volume in the proportion, equally fixed, of 1 to 3. Yet such results as these, respecting the constitution of com- pound bodies, however numerous and accurate they may be, are still not sufficient to satisfy the curiosity, or to terminate the re- searches of chemists. They aspire to understand, if possible, not only the «timate constitution of bodies, or the elements of which they are composed, and the proportions of those elements, but also the proximate constitution of the same bodies, or the manner in which they arise from other intermediate and less complex com- pounds. Water, for instance, is believed to enter, in many cases, into composition with other bodies, as water, not as oxygen and hydrogen. Has ammonia any such component, which itself is composite? It is admitted to consist of one volume of nitrogen, combined with three of hydrogen. Can any order be discovered in this combination, any proximate constituent, any simpler and earlier product, from which the ammonia is afterwards produced? Until _ experiments decide, it appears not impossible, may seem even not unlikely, that nitrogen may combine (more intimately than by mere 414 mixture) not only with thrice but with twice or once its own volume of hydrogen, and that thus other substances may be formed, from which, by the addition of new hydrogen, ammonia may result. It is interesting, therefore, to inquire whether either of these conceived possibilities is actually realized in nature; whether these two im- portant gases do ever actually combine with each other in either of these two proportions. In the symbolic language of chemists, as usually written in these countries, the compound NH, is well known, being no other than ammonia ; but does NH* or does NH, exist? An eminent French chemist, M. Dumas, in examining a sub- stance, which he called oxamide, and which was one of the results of the action of oxalic acid on ammonia, was led to the conclusion, that the last mentioned compound of nitrogen and hydrogen, name- ly NH,, does really exist in nature, and he proposed for it the name of amide. The same chemist considered it also to exist in the substance formed by heating potassium in ammoniacal gas; and the same combination, amide, had been (I believe) regarded as a proximate constituent of certain other compound bodies, such as urea, sulphamide, and carbamide, before Dr. Kane’s researches on the White Precipitate of Mercury. Yet it has been judged by Berzelius, that the investigations of Dr. Kane have assisted in an important degree to establish the actual existence (der wirklichen existenz) of amide, or of amidogene (as Kane prefers to call it, from its analogy with oxygen and cyanogen), and have thrown much light upon its chemical history and relations. In fact, the body oxamide, which seems to have first led Dumas to infer the existence of amide, was one of those organic com- pounds, respecting which it has often been found difficult, by che- mical inquirers, to pass with confidence from the empirical to the rational formula; from the knowledge of the z/¢imate elements (or of those which are at present to be viewed as such), and of the proportions in which they combine, to a satisfactory view respecting the proximate elements, or intermediate and less complex combi- Pee eee ve UPe aes eer eee * The compound NH, or as it is otherwise better written, HN, has been sus- pected to exist, as one of the proximate elements of melamine and of some con- nected bodies. See Gregory’s edition of Turner’s Chemistry, 1840, page 757. 415 nations on which the final result depends. Oxamide may be, and was considered to be, probably composed of amide and carbonic oxide (in the foregoing notation, NH,4+C,0O,); but it was perceived to admit also* of being possibly compounded of nitric oxide and a certain combination of carbon and hydrogen (NO,+C,H,); or of cyanogen and water(C,N+H,O,). And even the amidides of potas- sium (KNH,) and of sodium (NaNH,), have, from the energetic affinities of those metallic bases, been thought to prove less decisively the existence of amidogene itself, than the amidide of mercury (HgNH,) discovered by Dr. Kane, in his analysis of the white preci- pitate of the last mentioned metal. (Trans. R. I. A., vol. xviii. part iii.) Although this precipitate had been long known, and often ana- lyzed, erroneous views (as they are now regarded) were entertained respecting its composition, and it had, for instance, been supposed to contain oxygen, till Kane pointed out the absence of this element, and showed, with a high degree of probability, that the proximate elements were the chloride and the amidide of mercury; white pre- cipitate being thus a chlor-amidide of that metal (HgC1+ HgNH,, if the Berzelian equivalent of mercury be adopted, instead of its double). Uligren, a friend of Berzelius, obtained the chemical prize from the Swedish Academy of Sciences, for the year 1836, for a paper in which, having with great care repeated and varied the experiments, he confirmed this and other connected results of our countryman; and Berzelius himself, in his Report read to the above-mentioned Academy in 1837, on the recent progress of the Physical Sciences in Europe (to which Report allusion has been made above), ex- pressed his opinion that these researches of Kane were among the most important of the preceding year. In the essay for which your Council have awarded the present * L’Oxamide peut donc, a volonté, étre considérée comme un composé de cyano- géne et d’eau, ou bien comme un composé de deutoxide d’azote et d’hydrogéne bicarboné, ou bien enfin comme un composé d’oxide de carbone et d’un azoture @hydrogéne différent de ’ammoniaque.—Dumas, sur l'Oxamide, &c. Annales de Chimie et de Physique, tome xliv. page 142. + Diese Untersuchungen von Kane gehéren meiner Ansicht nach zu den wich- ‘eu tigeren des verflossenen Jahres.—Wohler’s German Translation of Berzelius’s j Pr Report, Jahres-Bericht iiber die Fortschritte der physischen Wissenschaften, ‘17th year, page 179. (Tiibingen, 1838). 416 prize, Dr. Kane has pursued his researches on ammonia, and has shown, with apparently a high probability, that there exist ami- dides (though not yet insulated) of other* metals besidesm ercury, especially of silver and copper; that is, combinations of these me- tals with the proximate element amide or amidogene. He has also given, in great detail, a series of analyses performed by him on a large number of compound bodies, of which some had been imper- fectly examined before, while others were discovered by himself. But as it would lead into far too great length, and too minute detail, if any attempt were made at present to review these laborious pro- cesses of analytical chemistry, and as indeed they derive their chief philosophical interest from the views with which they have been associated, it may be proper to attempt no more than a very brief (I fear that it will also be a very inadequate) sketch of those views. Dr. Kane considers that in ammonia, which, in the usual lan- guage of chemists, is said to consist of one atom of nitrogen and three atoms of hydrogen, one of these atoms of hydrogen is more loosely combined than the two others with the nitrogen, so as to be capable of a comparatively easy replacement, by many, perhaps by all, of the metals, as well as by organic radicals; the other two atoms of hydrogen being already, in the ammonia itself, and not merely in the products of such replacement of hydrogen by metals, combined in a particular way with the one atom of nitrogen, so as to form that substance named amide or amidogene, which was de- tected by Dumas (as has been mentioned) in performing the analysis of oxamide, From Dr. Kane’s own study of the combinations of this substance amidogene (H, N), with metals, he infers it to bea compound radical of feebly electro-negative energy, analogous to that important one cyanogen (C, N ), of which the discovery by Gay- Lussac has exercised so powerful an influence on modern chemistry. He considers this radical, amidogene, as existing ready formed, in combination with hydrogen, in ammonia; which latter substance is thus, according to him, to be regarded as amidide of hydrogen ; and as, in this respect, analogous to water, and to the hydro- eyanic, hydro-sulphuric, and muriatic acids, that is, to the oxide, * Dr. Kane has since made it probable that there exist amidides of palladium and platinum also. (Phil. Trans. 1842, part ii.) as 417 cyanide, sulphuret, and chloride of hydrogen; from all of which bodies it is possible, as from ammonia, to expel an atom of hydro- gen, and to replace it by an atom of metal,—if indeed hydrogen be not (as there seems to be a tendency to believe it to be) itself of metallic nature, notwithstanding its highly rarefied form. By de- veloping this view of the constitution and function of ammonia, Dr. Kane has offered explanations of a large number of replacements of that substance by others, some of which replacements (I believe) were known before, while many have been discovered by himself. One of the most remarkable points in Dr. Kane’s views is the way in which he considers the ordinary salts of ammonia. Many of these are known to contain an atom of water, the existence of which led to the proposition of the very remarkable theory by Ber- zelius, of the existence in them of a compound metal ammonium, which has not indeed been insulated, but has been found to form, in combination with mercury, a certain metallic amalgam. Dr, Kane looks upon these salts as double salts of hydrogen. He con- siders them to containammonia ready formed, united with a hydrated acid or with a hydrogen acid. He seeks to establish the similarity of the common ammoniacal salts to those complex metallic ami- dides, whose nature he has developed by analysis. Thus, for example, the well-known body, sal-ammoniac, is, in the Berzelian view, regarded as chloride of ammonium; but, in the view put forward by Dr. Kane, it is chlor-amidide of hydrogen. The former view supposes that the ammonia robs the hydrochloric acid of its hydrogen, to form, by a combination with it, a metallic base, NH,, with which the chlorine unites ; as this last element com- bines with the metal sodium, in the formation of common salt. The latter view supposes that in the action between hydrochloric acid and dry ammoniacal gas, thereis no separation of the chlorine from the hydrogen,—no breaking up of a previously existing union,—no overcoming of the affinity which these two elements (chlorine and hydrogen) have for each other; but an exemplification of a general tendency of chlorides, oxides, and amidides of the same or similar radicals, to unite, and form chlor-oxides, chlor-amidides, or oxami- dides. Sal-ammoniac is, according to Kane, a double haloid salt ; he looks upon it as being a compound exactly analogous to the white mercurial precipitate, which was first accurately analyzed by 418 himself; the one being HCl + HAd (if Ad be the symbol of amido- gene), while the other is HgCl + HgAd, so that the mercury in the latter takes the place of the hydrogen in the former. It was, however, in the oxysalts, such as the sulphate of am- monia, that the presence of an atom, or equivalent, of water, or at least of the elements required for the composition of such an equivalent, appears to have suggested to Berzelius the theory, that what seemed to be hydrate of ammonia (NH,+ HO) was really oxide of ammonium (NH,-+ 0). There are, undoubtedly, many tempta- tions to adopt this view, besides the high reputation of its pro- pounder. One is, that it assimilates the constitution of sulphate of ammonia to what seems to be regarded by the greater number of modern chemists, as the probable constitution of other sulphates, nitrates, &c., for example, the sulphate of iron. When green vitriol is to be formed by the action of sulphuric acid upon iron, it is requisite to dilute the acid with water, before the action will take place. The hydrogen of the water then bubbles off, but what becomes of the oxygen which had been combined with it? Does it combine immediately, and as it were in the first instance, with the iron, to form oxide of iron, on which the anhydrous sulphuric acid may act, to produce sulphate of owide of iron, according to the view which seems, till lately, to have been adopted: or does this oxygen, from the water, combine rather with the sulphuric acid to produce a sort of oxide thereof, and does this su/phat-oxygen act on the pure metallic iron to form with it a sulphat-oxide, as many eminent chemists now appear to think? Whatever may be the final judgment of those who are entitled to form opinions on questions such as these, it cannot, I conceive, be justly said, that the questions themselves are unimportant. They touch on points connected with the philosophy of chemistry, are essentially con- nected with its theory, and cannot always be without an influence upon its practice. Now according to the Berzelian view of sulphate of ammonia, that is the salt produced by the mutual action of sulphuric acid, water, and ammonia, this salt is properly a sulphat-oxide of the compound metal ammonium (NH,+S0,), inthe same way as green vitriol, on the view last mentioned, is sulphat-oxide of iron =e ii K : 419 (Fe + SO,), or as sulphate of potash is sulphat-oxide of potassium (K + SO,), and this analogy is doubtless pleasing to contemplate. Dr. Kane does not entirely reject this Berzelian theory of ammo- nium; he acknowledges that the substance NH,, which he regards as subamidide of hydrogen, and compares to some suboxides, pos- sesses metallic properties, and is a proximate constituent of certain compounds, especially of the ammoniacal amalgam; but he con- ‘%teives that the evidence for the existence of ammonia itself, in many of the ammoniacal salts, is too strong to be resisted: and he looks upon the hydrated ammonia, which is found to combine with sulphuric and other oxacids, as being not, in general, oxide of am- monium, but oayamidide of hydrogen ; the sulphate of ‘ammonia being thus a bibasic compound, of which one base is ammonia, while the other base is water. } Between the conflicting opinions of such men, supported each J by powerful arguments and analogies,—and it will easily be con- ceived that in so short a sketch as this, and upon such a subject, it has been found impossible by me to mention even the names of all the eminent chemists whose experiments and writings should be studied, by persons inquiring for themselves,—not only do I not ven- ture to express any judgment of mine, but I conceive also that your Council did not desire to express on their part any decision. To jus- tify the present award, it was, I believe, deemed by them sufficient, that great research and great talents had been brought, in the inves- tigations of the author to whom that award has been made, to bear on an important subject, which has derived, from those investiga- gations, an additional degree of importance. Whatever may be the final and unappealable judgment of those persons who shall, at some future time, be competent and disposed to pronounce it, we need not fear that the honour of this Academy shall have been com- ’ promised by the recognition which the Council have thought it right on the present occasion to make, of that combination of genius and industry, which has already caused the researches of Kane to _ influence in no slight degree the progress of chemical science, and has won for him an European reputation. : = ‘ The President then presented the Gold Medal to Dr. : Kane, and the Academy adjourned for the summer. a VOL. II. 20 420 July 31. (Extraordinary Meeting.) SIR Wm. R. HAMILTON, LL.D., President, in the Chair. Resotvep,—On the recommendation of Council,—That the Treasurer be empowered to sell stock in the 3 per cent. Consols, to the amount of £300, in order to pay Mr. Gill’s bill for printing Transactions to March 16, 1843, amount £264 10s. 4d., and the rent of the Academy House to 81st July, 1843. Resotvep,—On the recommendation of Council,—That the Treasurer be empowered to sell such 3} per cent. stock, being the Cunningham Fund, as shall amount to £50, to- wards defraying the cost of medals. Sir William Betham presented to the Academy certain casts from the sculptures on the inside of the tower of Ardmore. Dr. Lloyd having taken the Chair, the President gave an account of some researches in the Calculus of Probabilities. Many questions in the mathematical theory of probabili- ties conduct to approximate expressions of the form p =—-\, dt e*; that is, p = (i), 0 being the characteristic of a certain function which has been tabulated by Encke in a memoir on the Method of Least Squares, translated from the Berlin Ephemeris, in vol. ii. part 7 of Taylor’s Scientific Memoirs; p being the proba- bility sought, and ¢ an auxiliary variable. Sir William Hamilton proposes to treat the equation p = 9%) as being in all cases rigorous, by suitably determining the auxiliary variable ¢, which variable he proposes to call the ee ———— 421 argument of probability, because it is the argument with which Encke’s Table should be entered, in order to obtain from that Table the value of the probability p. He shows how to improve several of Laplace’s approximate expressions for the argument #, and uses in many such questions a trans- formation of a certain double definite integral, of the form, 4sicr ¢? ue ) ar | du e-*" u cos (2s'ruv) Tv o o = O(r(l+n 51 +257% + ...)); in which u=lt+awv+a.u'+... vr=1+fhiw+Pou'+... while vj; v.,...depend on a,...(3;,... and on; thus vy, = Fa, — Pir. The function @ has the same form as before, so that if, for sufficiently large values of the quantity s (which represents, in many questions, the number of observations or events to be combined), a probability p can be expressed, exactly or nearly, by the foregoing double definite integral, then the argument t, of this probability p, will be expressed nearly by the formula, t=r(1+v,:57 +5). Numerical examples were given, in which the approxi- mations thus obtained appeared to be very close. For in- stance, if a common die (supposed to be perfectly fair) be thrown six times, the probability that the sum of the six numbers which turn up in these six throws shall not be less _ than 18, nor more than 24, is represented rigorously by the integral 2 \ sin 7x (aie 6 =-\ dx — — ) ion 22448 : p= — _ On \eaaeane OF by the fraction 23448 ; while the approximate formula deduced by the foregoing method gives 27449 for the numerator of this fraction, or for _ the product 6° ; the error of the resulting probability being _ therefore in this case only 6°. The advantage of the method 422 is that the quantity which has here been called the argument of probability, depends in general more simply than does the probability itself on the conditions of a question; while the introduction of this new conception and nomenclature allows some of the most important known results respecting the mean results of many observations to be enunciated in a simple and elegant manner. DONATIONS. Historias e Memorias da Academia Real des Sciencias de Lisboa. Tome XII. Parte 2. Discurso lido em 22 de Janeiro de 1843 na sessao pub- lica da Academia Real des Sciencias de Lisboa. Por J.J. da Costa de Macedo. Presented by the Academy. Le Petit Agriculteur. Par N.C. Seringe. Presented by the Author. Astronomical Observations made at the Radcliffe Obser- vatory, Oxford, in 1840. By M.J. Johnson, Esq. Presented by the Governors. Archives du Museum d'Histoire Naturelle. Tome III. Liv. 3, et Tome II. Liv. 4. Presented by the Museum. Remarks on Safety Lamps. By Doctor Reid Clanny, H.M.R.I.A. Presented by the Author. Transactions of the Royal Society of Edinburgh. Vol. XV. Part 3. Presented by the Society. Proceedings of the National Institution for the Promotion of Science at Washington. D. C. for 1840 and 1842. Parts 1 and 2. Presented by Thomas Sewall, M. D., Professor of Medicine in Columbia College, U. S. Memoirs of the Chemical Society of London for 1841-3. Vol. I. Presented by the Society. Numismatic Chronicle. No. XXII. Presented by the Numismatic Society. Statistical Returns of the Dublin Metropolitan Police for 1842. Presented by the Commissioners. Seas PROCEEDINGS OF THE ROYAL IRISH ACADEMY. * 1843. No. 42. November 13. SIR Ws. R. HAMILTON, LL.D., President, in the Chair. Dr. Allman drew the attention of the Academy to cer- tain undescribed peculiarities in the anatomy of Anthoce~ phalus, a genus of Entozoal worms. The points especially dwelt upon by Dr. Allman were the remarkably definite ar- rangement of the hooks with which the proboscides are fur- nished, and the singular apparatus destined to effect the retraction and exsertion of the latter organs. The probos- — cides were described as communicating each with a distinct tube, which extending through the entire length of the ani- mal, terminates posteriorly in an oval dilatation, with thick- ened walls. The retraction of the proboscides consists in an inversion, by which they become invaginated in the tu- bular appendage. This invagination is effected by means of a muscular filament, which is attached by one extremity to the internal surface of the cud de sac of the proboscis, and may be thence traced through the tube as far as the oval body in which the latter terminates. The mode by which the exsertion of the proboscides is effected would appear to be as follows:—These organs, together with their tubular prolongation through the ver- micular body of the Entozoon, are filled with a transparent fluid, which during the inversion of the proboscides is ex- VOL, Il. 2P 424 pelled into the more posterior parts of the tubular prolon- gations, and into the oval bodies in which these terminate. Mr. Bergin had pointed out to Dr. Allman the existence of muscular fibres in the walls of the oval dilatations. The contraction, therefore, of these muscles, will cause the con- tained fluid to impinge upon the inverted extremity of the proboscis, which will thus be forced outwards, and the pro- boscis injected with the fluid. The source of this fluid would appear to be in the oval bodies themselves, whose structure is, in all probability, glandular, and which, besides possessing a contractile power, by which the contents of their cavities are expelled, would seem also to be the secerners of the fluid which plays so important a part in the protrusion of the proboscides. The Chair having been taken pro tem. by the Rev. H. Lloyd, D. D., Vice-President, The President read a paper on a new Species of Imagi- nary Quantities, connected with a theory of Quaternions. It is known to all students of algebra that an imaginary equation of the form 27= —1 has been employed so as to conduct to very varied and important results. Sir Wm. Ha- milton proposes to consider some of the consequences which result from the following system of imaginary equations, or equations between a@ system ofthree different imaginary quan- tities : Ne (a) wok jk=i, ki=j; (a) ji=—kh, kj=—i, itk=—j; (c) no linear relation between 2,7, k being supposed to exist, so that the equation e= 4, in which =w+iet+yjyths, QQ = w + ial + ijy! + ke’, 425 and w, x, y,2, w’, x’, y’, x’ are real, is equivalent to the four separate equations, wow, =a, yay’, 2=8. Sir W. Hamilton calls an expression of the form @ a qua- ternion; and the four real quantities w, x, y, = he calls the con- stituents thereof. Quaternions are added or subtracted by adding or subtracting their constituents, so that et evawtw tilCeto'ytily ty) Fhe +2’). Their multiplication is, in virtue of the definitions (a) (B) (c), effected by the formule ee! = Q! = ww! + ix” + jy" + ke", w! = ww! — axa’ —yy’—22', | a’ wa +aw +y2 —2y’, y =wy yw! + x2’ — xe’, e/a we +euw+ay — yx’, which give w!? + a!? + y/? + 3? = (w? +a? + y? +27) (w? + a? + y? + 2), and therefore (0) Me w= we, (z) if we call the positive quantity B= VCO +7 +2, the modulus of the quaternion e@. The modulus of the pro- duct of any two quaternions is therefore equal to the product of the moduli. Let w= pcos 8, 1 x =psin0@ cos ¢, y = msin @ sin ¢ cosy, x = psin@ sing sind; (F) then, because the equations (D) give ww! + wv’ a!’ + yy" + 2'2" = w (w”? + a’? + y? + 2”), ww! + va” + yy tex w' (w? + ety + 2°), 2Pe2z 4:26 we have cos 0” —=cos@ cos 6’ — sin@ sin @’ (cos¢ cos¢’ + sing sing’ cos (W) —W’)), cos@ =cos 6’ cos 6” + sin’ sin 8" (cos¢’ cos¢” + sing’ sing” cos wv} (Gc) cos 8’ = cos 6" cos 8 + sin 8" sin O (cos $"'cos@ + sing” sind cos (W"— W)). Consider 2, y, = as the rectangular coordinates of a point of space, and let r be the point where the radius vector of x,y, x (prolonged if necessary) intersects the spheric surface described about the origin with a radius equal to unity; call Rr the representative point of the quaternion @, and let the polar coordinates ¢ and %, which determine rk upon the sphere, be called the co-latitude and the longitude of the re- presentative point Rr, or of the quaternion @ itself; let also“ the other angle @ be called the amplitude of the quaternion; so that a quaternion is completely determined by its modulus, amplitude, co-latitude, and longitude. Construct the repre- sentative points r’ and r”, of the other factor Q’, and of the product @”; and complete the spherical triangle rr’ Rr”, by drawing the arcs RR’, R’R”, RR. Then, the equations (a) become cos0” = cos@ cos’ —sin@ sin@’ cosrR’, cos@ = cos@ cos 6” + sin # sin 0” cos R’R”, cos 0’ =cos@”cos6 + sin @”sin@ cosr’R, and consequently shew that the angles of the triangle Rr’ r” are BO, RE 6, a See (H) these angles are therefore respectively equal to the ampli- tudes of the factors, and the supplement (to two right angles) of the amplitude of the product. The equations (p) show, further, that the product-point rR” is to the right or left of the multiplicand-point x’, with respect to the mul- tiplier-point R, according as the semiaxis of + x (or its in- tersection with the spheric surface) is to the right or left of the semiaxis of + y, with respect to the semiaxis of + 2: that is, according as the positive direction of rotation in longitude is towards the right or left. A change in the 427 order of the two quaternion-factors would throw the pro- duct-point kr” from the right to the left, or from the left to the right of rR’. It results from these principles, that if rr’R” be any spherical triangle; if, also, a B y be the rectangular coordi- nates of r, a’ By’ those of Rr’, and a” B” y” of R", the centre of the sphere being origin, and the radius being unity ; and if the rotation round +2 from + y to +2 be of the same (right-handed or left-handed) character as that round Rr from r’ to Rr”; then the following formula of multiplication, ac- cording to the rules of quaternions, will hold good : fcosr+(iat+jsB+hy)sinr} §cosr’+(ia’ +jP’+ky’) sinR’ } = — cosr”+(ia”+j7P"+hy”) sink”. (1) Developing and decomposing this imaginary or symbolic formula (1), we find that it is equivalent to the system of the four following real equations, or equations between real quantities : —cosR” = cosR cosk’ —(aa'+ BB’ + yy’) sinRsinR’; a” sink" =asinRcosk’ + a’ sink’ cosR + (By — yf’) sink sink’ ; B”’ sink” = 8B sinr cosr’ + PB’ sink’ cosR + (ya’ — ay’) sinksinR’; (k) y" sink” = y sink cosr’ + y’sink’ cosR + (a8 — Ba’) sink sink’. Of these equations (xk), the first is only an expression of the well-known theorem, already employed in these remarks, which serves to connect a side of any spherical triangle with the three angles thereof. The three other equations (x) are an expression of another theorem (which possibly is new), namely, that a force = sink”, directed from the centre of the sphere to the point Rr”, is statically equivalent to the sys- tem of three other forces, one directed to R, and equal to sink cosr’, another directed to rR’, and equal to sin R’ cosR, and the third equal to sink sinr’ sinrr’, and directed to- wards that pole of the arc rr’, which lies at the same side of this arc as rR”. It is not difficult to prove this theorem other- wise; but it may be regarded as interesting to see that the four equations (kK) are included so simply in the one formula 428 (1) of multiplication of quaternions, and are obtained so easily by developing and decomposing that formula, accord- ing to the fundamental definitions (a) (B)(c). A new sort of algorithm, or calculus, for spherical trigonometry, appears to be thus given, or indicated. And by supposing the three corners of the spherical triangle rR’ R” to tend indefinitely to close up in that one point which is the intersection of the spheric surface with the positive semiaxis of aw, each coordi- nate a will tend to become = 1, and each (3 and y to vanish, while the sum of the three angles will tend to become = 7; so that the following well known and important equation in the usual calculus of imaginaries, as connected with plane trigonometry, namely, (cosr +ésin R) (cosR’ + ésinr’) = cos(R+R’) + zsin(R +R), (in which 2? = — 1), is found to result, as a limiting case, from the more general formula (1). In the ordinary theory there are only two different square roots of negative unity (+ ¢ and — 2), and they differ only in their signs. In the present theory, in order that a qua- ternion, w+zx + jy + kz, should have its square = — 1, it is necessary and sufficient that we should have w=0, #P+7+2—+1; we are conducted, therefore, to the extended expression, Y —1 =icos¢+jsin¢ cosy +h sing siny, (L) which may be called an imaginary unit, because its modulus is = 1, and its square is negative unity. To distinguish one such imaginary unit from another, we may adopt the nota- tion, i, = ia +8 + ky, which gives % = — 1, (L’) k being still that point upon the spheric surface which has a, B, y (or cos¢, sing cosy, sing siny) for its rectangular coordinates; and then the formula of multiplication (1) be- <2 9 af el 429 comes, for any spherical triangle, in which the rotation round R, from R’ to R”, is positive, (cos R+2, sin R) (cos rR’ + i, sin RK’) = — cos R”+é,, sink”. (1’) If Pe” be the positive pole of the arc rx’, or the pole to which the least rotation from r’ round R is positive, then the product of the two imaginary units in the first member of this formula (which may be any two such units), is the fol- lowing : dy tp’ = — cos RR’-+ Zp sin RR’; (m) we have also, for the product of the same two factors, taken in the opposite order, the expression dy, = — COSRR’ — 2p SINRR’, (x) which differs only in the sign of the imaginary part; and the product of these two products is unity, because, in gene- ral, (w + tx+ jy +hz) (w—ix—jy—kz)=w?+2°?+y7?4+2°; (0) we have, therefore, tn Age dp’ tn = i (P) and the products é, x and iyi, may be said to be reciprocals of each other. In general, in virtue of the fundamental equations of de- finition, (a), (B), (c), although the distributive character of the multiplication of ordinary algebraic quantities (real or imaginary) extends to the operation of the same name in the theory of quaternions, so that Q@(e’+0”) = ed’/+a0”, &e., yet the commutative character is lost, and we cannot gene- rally write for the new as for the old imaginaries, ad’ = ea, since we have, for example, ji = — ij. However, in virtue of the same definitions, it will be found that another important property of the old multiplication is preserved, or extended 430 , to the new, namely, that which may be called the associative character of the operation, and which may have for its type the formula Mi Q. Q’Q”. rege Ql’ _ QQ’. Q! Ql Qi’. thus we have, generally, a. ea" = aa’. Q’, (Q) a. aaa” = aa’. Qe” =a 9’Q". a”, (@’) and so on for any number of factors; the notation @ @’ 9” being employed to express that one determined quaternion, which, in virtue of the theorem (Q@), is obtained, whether we ~ first multiply @” as a multiplicand by @’ as a multiplier, and then multiply the product @/@” as a multiplicand by @ as a multiplier ; or multiply first @’ by @, and then Q” by ea’. With the help of this principle, we might easily prove the equation (P), by observing that its first member = ¢,% ig = == It In the same manner it is seen at once that ts apy ‘ dp? den ° dni dan sie ete tx(n—1) ip = (— Ly; (P’) whatever ” points upon the spheric surface may be denoted by Rk, RR”; BR”, ... R\—"): and by combining this principle with that expressed by (m), it is not difficult to prove that for any spherical polygon, rr’...r—"), the following for- mula holds good : (cos R + 2, sin R) (cosR’ + @y sink’) (cosr” + 4,7 sin R”) »+-(cosxk®) + 74» sink’) =(—1)*, (R) which includes the theorem (1’) for the case of a spherical triangle, and in which the arrangement of the » points may be supposed, for simplicity, to be such that the rotations round rR from rR’ to R”, round R’ from R” to rR”, and so on, are all positive, and each less than two right angles, though’ it is easy to interpret the expression so as to include also the cases where any or all of these conditions are violated. When the polygon becomes infinitely small, and therefore 431 plane, the imaginary units become all equal to each other, and may be denoted by the common symbol 7; and the for- mula (R) agrees then with the known relation, that T—R+7—R’+7—R" +... +7—R"") = 2. Again, let r, rR’, rR” be, respectively, the representative points of any three quaternions Q, Q’, @”, and let R,, R,, R, be the representative points of the three other quaternions, QQ, a”, aaa”, derived by multiplication from the former , then the algebraical principle expressed by the formula (a) may be geometrically enunciated by saying that the two points r, and r, are the foci of a spherical conic which touches the four sides of the spherical quadrilateral Rr’ Rr” R,, ; and analogous theorems respecting spherical pentagons and other polygons may be deduced, by constructing similarly the formulz (@’), &c. In general, a quaternion @, like an ordinary imaginary quantity, may be put under the form, Q = p(cos@ + (—1) sin#) = w + (—1)r, (s) provided that we assign to (—1)3, or VY —1, the extended meaning (L), which involves two arbitrary angles; and the same general quaternion @ may be considered as a root of a - quadratic equation, with real coefficients, namely, e’—2we+ 22 =0, (s’) which easily conducts to the following expression for a quo- tient, or formula for the division of quaternions, Q!! e 2 w—eQ hi cts " " £ Sg ah, Q'; (s”) ‘ Q! P , if we define Q~'Q" or “to mean that quaternion Q’ which gives the product Q”, when it is multiplied as a multiplicand by @ asa multiplier. The same general formula (s”) of di- vision may easily be deduced from the equation (0), by writing that equation as follows, 432 i t —ix—jy—kez i, (w+ ix + jy ths) = en — rae + (0’) or it may be obtained from the four general equations of multiplication (p), by treating the four constituents of the multiplicand, namely, w’, 2’, y 2’, as the four sought quan- tities, while w, x,y,z, and w”, a” y”, x”, are given; or froma construction of spherical trigonometry, on principles already laid down. The general expression (s) for a quaternion may be raised to any power with a real exponent q, in the same manner as an ordinary imaginary expression, by treating the square root of — 1 which it involves as an imaginary unit 7, having (in general) a fixed direction; raising the modulus yp to the proposed real power; and multiplying the amplitude @, in- creased or diminished by any whole number of circum- ferences, by the exponent q: thus, (4 (cos 8+ i,sin 8))! = p41 (cos g (0+ 2n7) + igsing(8+2n7)), (7) if g be real, and if x be any whole number. For example, a quaternion has in general two, and only two, different square roots, and they differ only in their signs, being both included in the formula, (u(cos 0 +¢é,sin @))? = p3(cos G+nn)+igsin es nz), (t’) in which it is useless to assign to m any other values than 0 and 1; although, in the particular case where the original quaternion reduces itself to a real and negative quantity, so that 0 = z, this formula (1’) becomes (—pn)i= + pity, or simply (—p)? = pik, (v7) the direction of 7, remaining here entirely undetermined; a result agreeing with the expression (t) or (u’) for /—1. In like manner the quaternions, which are cube roots of mcs are included in the expression, Qur sa co mt 13 = cos —— 3 + i, sin —— 3 (2) 433 é, denoting here again an imaginary unit, with a direction altogether arbitrary. If we make, for abridgment, 2 Fe)=1+ 2+ 2 4 2 4 &e,, (v) the series here indicated will be always convergent, whatever quaternion @ may be; and we can always separate its real and imaginary parts by the formula, JS (w+ ir) =f (w) (cosr +4, sinr) ; (v’) which gives, reciprocally, for the inverse function f-', the expression S-"(u(cos@ + i, sin8)) =logu+i,(@4+2n7), (v”) « being any whole number, and logy being the natural, or Napierian, logarithm of , or, in other words, that real quan- tity, positive or negative, of which the function f is equal to the given real and positive modulus ». And although the ordinary property of exponential functions, namely, S(2) -F(@’) = fete), does not in general hold good, in the present theory, unless the two quaternions Q and @’ be codirectional, yet we may raise the function f to any real power by the formula (f(wtinr)!=f(qwtizr+2nn), (v”) which it is natural to extend, by definition, to the case where the exponent g becomes itself a quaternion. The general equation, Qf = Q/, (v) when put under the form (Sw tin)! =f w' + ivr’), (v’) will then give — twtin(r' — eee) i twit, (r +2nz)} + (r+ 2nryP and thus the general expression for a quaternion g, which is (v”) 434 one of the logarithms of a given quaternion Q’, to a given base @,, is found to involve two independent whole numbers m and n’, as in the theories of Graves and Ohm, respecting the ge- neral logarithms of ordinary imaginary quantities to ordinary imaginary bases. For other developments and applications of the new theory, it is necessary to refer to the original paper from which this abstract is taken, and which will probably appear in the twenty-first volume of the Transactions of the Aca- demy. November 30. (Stated Meeting.) REV. H. LLOYD, D.D., Vice-President, in the Chair. The Rev. Dr. Todd, V.P., presented to the Academy, in his name and that of Mr. O'Donovan, a volume containing tracings made from Irish MSS. preserved in the College of St. Isidore at Rome, by the Rev. Dr. Lyons, who had sent them from Rome, some to Mr. O'Donovan, and the re- mainder to Dr. Todd. The thanks of the Academy were voted to Mr. O’Donovan and also to the Rev. Dr. Lyons, for the important service he has rendered to Irish literature, by making known the existence of these MSS. The Rev. Dr. Todd made some remarks on the progress of the Catalogue, made by Mr. Eugene Curry, of the Irish MSS. in the Library of the Academy. The miscellaneous character of the MSS., almost every volume of them containing tracts or poems, wholly uncon- nected with each other, rendered it impossible to attempt any previous classification. Mr. Curry, therefore, took the MSS. in the order in which they stood on the shelves of the Library, hoping that all the important objects of a classifica- 435 tion might be attained by the means of proper Indexes after the work is completed. The method pursued was to give a description of the contents of each volume, enumerating the several tracts of which it consists, describing its state of preservation, no- ticing, as far as possible, its defects or imperfections, and identifying, whenever it could be done, the handwriting of the scribe or scribes by whom it had been written. Particular attention has been paid to the history of every important MS. ; the quotations made from it by historians or lexi- cographers have been verified, and, where practicable, the various hands through which it has passed, and the means by which it became the property of the Academy, have been accurately detailed and recorded. In this way many opportunities have occurred of correcting mistakes which have been made by various writers on Irish subjects—mistakes, which must always be numerous in the history of a people, whose ancient literature is still in manu- script, and in a language which is every day becoming more obsolete and obscure. ‘These mistakes Mr. Curry has always corrected with temper, and with due allowance for the diffi- culties under which the authors to be corrected must neces- sarily have laboured; although it must be confessed that sometimes blunders may be found of a nature well calculated ‘to try the patience or rouse the indignation of an Irish scholar. Another object of great importance which Mr. Curry has kept steadily in view during the progress of the Catalogue, has been the noticing of other copies of the tracts or poems described, whenever the existence of such copies was known to him: and his accurate acquaintance with the contents of the Irish MSS. of Trinity College, and those in the posses- sion of Messrs. Hodges and Smith,* the only two great col- lections accessible to him for this purpose, rendered Mr. Curry peculiarly well qualified for such a task. * Since purchased by the Academy. 436 In reference to the history of the MSS., of such of them, at least, as are of any high antiquity, it was of great im- portance to collect together the numerous memoranda, short scraps of poetry, dates, signatures, and other entries, which are frequently to be found on the margins of MSS. These are often mere scribbling, and often written from pure wantonness, or for the purpose of trying a pen; but they very frequently contain information of singular interest, shewing who were the ancient owners or possessors of the MS., and sometimes giving facts and dates of which we have no other record. A most remarkable example of the value of these apparently trifling scribblings will be found in Mr. Curry’s account of the Leabhar Breac, upon whose history the most important light has been thus thrown. The autograph volume of the Four Masters, which is one of the glories of the Academy’s Library, may also be mentioned as a MS., whose history Mr. Curry’s researches have greatly illustrated. By a comparison of it with the MS. (also an autograph) in the Library of Trinity College, Mr. Curry has succeeded in identifying the handwritings of its different compilers, and to assign to each the portion of these Annals which he appears to have compiled, or at least to have transcribed. When any document occurred of peculiar interest, as an historical tale, or ancient deed, or singular narrative, Mr. Curry has very generally given an abstract of its contents. This has been sparingly done, from a wish to avoid swelling the Catalogue to too great a bulk; but it is of more im- portance than it might seem to be at first view, especially if the Catalogue should ever be published, as furnishing to those who are at a distance, the means of identifying the works described with MSS. in other collections. Dr. Todd having read some extracts from Mr. Curry’s Catalogue in illustration of the foregoing remarks, concluded by stating, that about five volumes still remained to be cata- a ee er Sp RN A ALI PED NI RIES ABR IAT 2 cali pres 5 ‘oi id - aw. a nt RS 437 logued, including the important volumes, the Books of Lecan and Ballymote, whose examination would take some months, and that the Council have therefore been under the necessity of applying to the Academy for a further grant of money to enable Mr. Curry to complete the work. It was resolved by the Academy that the sum recom- mended by the Council be granted for this purpose. December 11. SIR Ws. R. HAMILTON, LL.D., President, in the Chair. Matthew Dease, Esq., William M‘Doughall, Esq., Sir Montague Chapman, Bart., James H. Pickford, M. D., Ed- ward Bewley, M.D., and James S. Eiffe, Esqrs., were elected Members of the Academy. Professor Kane read a paper on the Chemical Compo- sition of the plants of Flax and Hemp. In those plants which are cultivated for the purpose of being ultimately employed as food, it is found that certain consti- tuents are withdrawn from the soil, partly of an organic and partly of an inorganic character, which give to the plant, or to certain portions of it, the constitution that adapts it for sustaining the animal organism. Thus nitrogen, alkalies, and lastly, phosphates, &c., are found as components of plants, and the value of the crop yielded by a certain surface of ground is proportional, generally speaking, to the materials which the crop has taken up. If, therefore, wheat, or oats, or potatoes exhaust a soil, the agriculturist does not suffer thereby, for he is paid for the materials of which they have exhausted it, and when he replaces that loss of material by fresh manure he but invests a certain capital, to be delivered at a profit in the next season. Many plants not employed as food, but ancillary to our civilization as luxuries, or as utilized in the arts, are similarly el? 438 circumstanced. ‘Thus when indigo or tobacco is grown, the object is to obtain the greatest possible development of the co- louring or of the narcotic principle. For this purpose, elements are necessary of which the soil is thereby deprived, but the impoverishing of the soil is paid for, by its materials being sold as the valuable portion of the plant. In such cases, therefore, to sustain the fertility of the soil, a continued sup- ply, from external sources, of the materials which the plants take up is required. The farmer must supply in the manure the elements which he sends to market in the grown plants. Dr. Kane then proceeded to point out that this principle was limited as to certain classes of plants, by the fact, now clearly established by the concurrent investigations of vege- table physiologists and of chemists, that certain vegetable substances, and those of high importance to mankind, were not formed of materials abstracted from the soil, but were produced by the vital action of the plant upon the consti- tuents of the atmosphere. This class of bodies he charac- terized as being constituted, generally, of carbon, united with hydrogen and oxygen in the proportions which form water. The carbonic acid of the atmosphere, with the watery vapour constantly existing in it, supplies the elements of sugar, gum, starch, and ligneous fibre, and the oxygen of the carbonic acid, evolved by the vital action of the plants, tends, as it is well known, to ameliorate the air we breathe. When, there- fore, we take the sugar, or the woody fibre of a plant, we have a material, formed, as to its elements, independent of the soil. For its formation is required a plant in healthy vegetation, and for the plant to be in healthy vegetation, it may require to abstract from the soil various materials, so that the crop may actually be of a highly exhausting nature. Still those materials do not go to the sugar or to the fibre; they exist in other portions of the plant; and if the sugar or fibre be the valuable portion of the crop, as in reality usually oc- curs, the elements which render its production costly are re- jected, and let to waste; they do not subserve any future ee oS se ee 439 useful purpose, although nothing should be easier than to apply them thereto. Such is actually, according to Dr. Kane’s idea, the con- dition of the growth of one plant of the highest importance to agricultural industry in Ireland—that of flax, and also of ano- ther, which although not now grown here, has been grown with success, and, as he conceives, might still be cultivated with con- siderable advantage, the hemp. In flax and hemp the valuable portion of the plant is ligneous fibre ; the purer this fibre is, the more its value increases; yet the pure fibre contains no ele- ment derived from the soil. It is well known to be produced solely by the atmospherical constituents. Hence the intense exhausting nature of the flax and hemp crops, which makes them be dreaded by agriculturists, notwithstanding the high money value of the crops, arises, according to Dr. Kane, from causes of which the effects may be obviated by attention to the true conditions of the growth and composition of the plants, so that those fibre-crops, such as flax and hemp, from being the most exhausting and expensive, may be ren- dered the least injurious to the land, and perhaps amongst the cheapest that can be grown. As the chemical composition of these plants had never been examined, Dr. Kane devoted himself to the determina- tion, as well of their organic as of their inorganic constituents, and from an extensive series of analyses, of which the de- tails are given in the memoir, arrived at the following results: Composition of the stem of hemp, dried at 212°. F. Darbom i Miate eo. yi5 2. 3094 erydrogen ili. hoe ed a Ge Oxygen! aw. es eae Tiitrogen 9 oe ig See ae Aeos 0 Re Sa ees Se 100.00 VOL. Ul. 2a 440 Composition of the leaves of hemp, dried at 212°. Gavbon io.) Sere 2 ae Hydrogen’. . ©.) 9988 S71 °6.88 Nitrogen) 2 eo Be Oxygen . © . «+ - - + 29.70 Ashes 540 sgours ee ho ay eae 100.00 The ashes of the hemp plant were found to consist of Pstashiee.|) axiy od). ¢ bot. Oe eae Sida rca te ov das stake iiak 72 BGS hE | toey ct Teeiiee Soh ots eee Magnesiay << )s) 1s py stots on!) vs ES Alana \iie.tos SNM. th. By | Bligaitil. (ask. eswie igs at ae Ge Phosphoric acid . . - - + + 3.22 Sulphuricacid . . ...- - 41.10 Ghiarines ais eee eee aS IS 1.53 Catbonie acid at. eeeer ier Jere BNO 100.00 Dressed hemp fibre was found to give but 1.4 per cent. of ashes, when dried at 212°. Its organic composition need not be given, as it is identical with that of ordinary woody fibre, which is well known. It therefore contains no ni- trogen. The characteristic constituents of the hemp plant are seen to be nitrogen and lime. In these it is peculiarly rich, and with these it is the duty of the agriculturist abundantly to supply it. When hemp is steeped in order to separate the fibrous bark from the internal stem, it is known that the water dis- solves certain substances out of the plants, and thereby ac- quires narcotic properties. Dr. Kane evaporated a quantity of the hemp liquor to dryness, and analyzed the extract so 44] obtained, in order to trace what action the steeping had ex- erted on the plant. He found the composition of the hemp extract, dried at 212°, to be, SOOM Fee oy Se ae Deveepear 2 Ue ee Pemmeer seh or <> aria SE Sree se ee TS orga peter maar te. 0 100.00 If we exclude the ashes, the organic part consisted of Ce te ier joi ol ie eel PIS BOUE i ti. i nts via casa eel 1 an aa od Peale Suan? ea i ond isi take Solids sil BOGE 100.00 This composition approaches to that of the azotized ani- mal substances, and surpasses the animal manures usually sold. The water in which hemp has been steeped contains thus most of the nitrogen of the plant, and if poured over the soil should serve efficiently to restore its fertile powers. The ashes of the hemp extract require also to be noticed, for the plant, in steeping, gives up to the water especially its soluble constituents. The ashes of the leaves of hemp con- tain in 22 parts only 1.77 soluble in water, or 8.05 per cent., whilst the ashes of the hemp extract contain in 49.2 parts, 29.70 parts soluble in water, or 60.4 per cent. Thus almost all the alkaline constituents of the ashes are dissolved out by the water, whilst the earthy materials remain associated with the residual portions of the stem. Dr. Kane next examined the stem, as it remains after treatment for the fibre, by steeping and peeling. Dried at 212° this hemp residue consisted of 2Q2 442 Cambor?) nde: A a S680 Bivdrogen) 3)u.iy fie WES DS ee Gas Battogen: >< jis) aS Bae 43 Oxy Pen yeas! Gel iio. Ses iie*) ogee YN cl eg oe a ee ee mS 100.00 The ashes contained but a trace of alkali, and itis seen that the nitrogen has almost disappeared. From these researches it is plain that, by the quantity of nitrogen, of phosphoric acid, of potash, of magnesia, and of lime, which the hemp takes from the soil, it must be, as ex- perience proves it, a highly exhausting crop; but as the ma- terials so abstracted are not found in the valuable fibre, but in the residual stem, the chaff, and the steeping liquor, all these are available for the purpose of restoring to the soil what had been taken up, and in fact, if it were possible to carry on the processes of the preparation of the fibre without loss, the same nitrogen and inorganic constituents might, as it would appear from these chemical inquiries and from phy- siological researches, serve for any number of successive crops of hemp; the fibre alone, generated at the expense of the atmosphere, being sent out and sold, and thus the crop be absolutely deprived of all exhausting quality to the soil. Dr. Kane’s inquiries regarding the flax plant were of a precisely similar character to those described already in the case of hemp, and have led him to similar conclusions affect- ing the practical culture of this important plant. The gene- ral results of his analyses are as follows: Stem of flax dried at 212°; the plant had its usual amount of leaves, but the seed vessels had not ripened. Carbone i. diet olin Me aes i Se Hydrogen’. + (54.475 etre fee ie Nitgopent) shicn nts 4 scala: 56 OxyeeN 2A Deitch RD Ashesi’ 2. lo ape <. B00 100.00 -_ A ; : 443 There is a great difference here shewn between the com- position of the plants of hemp and flax, though they resemble each other so much in their uses. The hemp contains a large amount of nitrogen, the flax very little. The hemp contains more oxygen than would form water with the hy- drogen. Flax, on the contrary, contains an excess of hydro- gen. The difference is also remarkable in the composition of the ashes. The ashes of the flax plant consist of in) ai UR en! 5, POE Posts ie ee PU Oe, ta eee MMS Er. Pees, Lee Premesia | TPs oe EE heh ie a”. ee GD SM Te Oe gh It on, Ye ee Phosphoric acid . . . . . . 10.84 orpniiic acid ye Tne BG SEEN Breet res eee ee RES ae Carponie acid’ 6s oA ROR 100.00 The great quantity of lime which characterized the hemp here disappears, and the peculiar quality of the ash is the presence of soda and potash in equal quantities, much mag- nesia, and especially the large proportion of phosphoric acid. Dr. Kane has not met with any analysis of the ash of a plant yielding the same amount of phosphoric acid, and hence the exceedingly exhausting power of the flax crop is easily understood. Dr. Kane notices in this ash of flax, that the potash, soda, sulphuric acid, and chlorine are in a very simple rela- tion to each other, the numbers given above coinciding closely with those of two atoms each of sulphuric acid and chlorine, six of potash, and nine of soda. So that if (in the ash) all the soda be taken as carbonate, the potash will be 444 divided equally among sulphuric, muriatic, and carbonic acids. Dr. Kane thinks that this simplicity is probably acci- dental, but suggests it for attention in subsequent analyses of flax ashes from other localities. The steeping of flax to loosen the coat of fibrous bark is accompanied by the solution of certain censtituents of the plant, as in the case of hemp. The extract of the steeping water was analyzed ; it yielded, dried at 212°, Carbon) .1). 820) lite, RPE OED Hydromen-.¢. °. «3°. °.. eee Nitfogen .. -... °°... .-. Wee OxVeens. 2°. ee ae PS) CE ea aia ei ae 5 100.00 The organic part of this extract consisted therefore of Garner. dh ciel. obese EL VERON ais (ies) sks eel eek ae Nitgoreniiiits he | pe ngs deride ee Oxyren .. ) ict ') oad i 2 > = 3 O, = 451 and eliminating 2, y; in like manner, we get K = A(l—a) ay” + B(1—B)y,’; (7) from which expressions it appears that, every thing else re- maining, the focus and directrix may be changed without changing the surface described. For in order that the sur- face may remain unchanged, it is only necessary that K should remain constant, since A and B are supposed constant. This condition being fulfilled, the focus may be any point F whose coordinates x, y, satisfy the equation (6), and A (the foot of the directrix) may be any point whose coordinates a, y2 satisfy the equation (7); it being understood, however, that when one of these points is chosen, the other is determined. The locus of F (supposing k not to vanish) is therefore an ellipse or a hyperbola,* which may be called the focal curve, or the focal line; and the locus of A is another ellipse or hyperbola, which may be called the dirigent curve or line: the centre of each curve is the centre of the surface, and its axes coincide with the axes of the surface which lie in the plane of zy. Moreover, as the quantities 1 — a and 1 — B are essentially positive, the two curves are always of the same kind, that is, both ellipses, or both hyperbolas; and when they are hyperbolas, their real axes have the same direction. The directrix, remaining always parallel to the axis of z, describes a cylinder which may be called the dirigent cylinder. Since, by the relations (4), the corresponding coordinates of F and A have always the same sign, these points either lie within the same right angle made by the axes of « and y, or lie on the same axis, at the same side of the centre. And as these relations give B A y— Ly = i—are R- "n= 1-3?" (8) * In the Proceedings of the Academy, vol. i. p. 90, it was stated inadver- tently that ‘if we confine ourselves to the central surfaces, the locus of the foci will be an ellipse.” 452 it is easy to see that the right line AF is a normal to the focal curve; for the quantities 7, — a and y2 — y, are pro- portional to the cosines of the angles which that right line makes with the axes of x and y respectively, while the values just given for these quantities are, in virtue of the equation (6), proportional to the cosines of the angles which the nor- mal to the focal curve at the point F makes with the same axes. It may also be shown that if the directrix prolonged through A intersect a directive plane in a certain point, and if a right line drawn through F, parallel to the directrix, intersect the same plane in another point, the right line join- ing those points will be a normal to the curve described in that plane by the first point. § 3. Tofind in what way the focal and dirigent curves are connected with the surface, let the equations (5), (6), (7) (when xk does not vanish) be put under the forms x? y = a ~ 4% 4251, ©) ay yn xy ys —4+--=1, —+4+- —I1, 10 Pi ide Q1 Po + Qo ( ) so that the quantities Pp, 9, R may represent the squares of the semiaxes of the surface, and Pj, Q), Pa, Q the squares of the semiaxes of the curves, these quantities being positive or ne- gative, according as the corresponding semiaxes are real or imaginary. Then we have K K P= 7 hei R =k; Pp; = P(l — 4), Q, = e(l— B), (11) otae8 de MIs 5a a 1a’ haar ae whence it follows that PiPo = P?, 391 Qa = ?, (12) ¢ 453 and also that P} = P—R, Q; = Q—R. (13) From equations (12) we see that p, and P, have always the same sign, as also Q, and Q; and that, neglecting signs, the semiaxes of the surface are mean proportionals between the corresponding semiaxes of the focal and dirigent curves. These curves are therefore reciprocal polars with respect to the section made in the surface by the plane of xy; and it would be easy to show that the points F and A are recipro- cal points, or that a tangent applied at one of them to the curve which is its locus has the other for its pole. The focal curve, when we know in which of the principal planes it lies, is determined by the conditions (13), and as it depends on the relative magnitudes of the quantities P, a, R, it will be convenient to distinguish the axes of the surface, with relation to these magnitudes. Supposing, therefore, the quantities Pp, @, R to be taken with their proper signs, as they are in the equation (9), that axis to which the greatest of them (which is always positive) refers, shall be called the primary axis; and that to which the quantity algebraically least has reference, shall be termed the se- condary axis; while the quantity which has an intermediate algebraic value shall mark the middle or mean axis. Then, since both P, and Q, will be negative, ifr be the greatest of the quantities aforesaid, the focal curve cannot lie in the plane of the mean and secondary axes. Its plane must there- fore pass through the primary axis; it will be the plane of the primary and mean axes, if R be the least of the three quantities ; but the plane of the primary and secondary axes, if rR be the intermediate quantity. In the former case the curve will be an ellipse, in the latter a hyperbola ; and we shall extend the name of focal curves to both the curves so determined, though it may happen that only one of them can be used in the generation of the surface by the modular method, as the method of which we are treating may be 454 called, from its employment of the modulus. A focal curve which can be so used shall be distinguished as a modular fo- cal; but each focal, whether modular or not, shall be sup- posed to have a dirigent curve and a dirigent cylinder con- nected with it by the relations already laid down. Since Pp, — Q, = P— Q, the foci of a focal curve are the same as those of the principal section in the plane of which it lies, and they are therefore on the primary axis of the sur- face. It will sometimes contribute to brevity of expression, if we also give the name of primary to the major axis of an ellipse and to the real axis of a hyperbola. We may then say that the primary axes of the surface and of its two focal curves are coincident in direction; and that (as is evident) the foci of either curve are the extremities of the primary axis of the other. If x be supposed to approach gradually to zero, while a and B remain constant, the focal and dirigent ellipses will gradually contract, and the focal and dirigent hyperbolas will approach to their asymptotes, which remain fixed. When k actually vanishes, the surface becomes a cone; the two ellipses are each reduced to a point coinciding with the ver- tex of the cone, and each hyperbola is reduced to the pair of right lines which were previously the asymptotes. The diri- gent cylinder, in the one case, is narrowed into a right line ; in the other case it is converted into a pair of planes, which we may call the dirigent planes of the cone. § 4. We have now to show how the different kinds of sur- faces belonging to the first class are produced, according to the different values of the modulus and other constants concerned in their generation. I. When m is less than cos ¢, the quantities a, B, K, P, @, R are all positive, and @ is intermediate in value between P and rR. The surface is therefore an ellipsoid, and its mean axis is the directive. As the quantities 1—a and 1 —B are always positive, the focal and dirigent curves are ellipses. ae © 455 Here we cannot suppose k to vanish, as the surface would then be reduced to a point. When ¢ = 0, that is, when the directive planes coincide with each other, and therefore with a plane perpendicular to the directrix, so that SD is the shortest distance of the point S from the directrix, the surface is a spheroid produced by the revolution of an ellipse round its minor axis, and the focal and dirigent curves are circles. II. When m is greater than unity, a and B are negative ; and if k be finite, it is also negative; whence P and Q are po- sitive, and R is negative. Also, supposing ¢ not to vanish, Qis greater than p. - The surface is therefore a hyperboloid of one sheet, with its real axes in the plane of ry; and the directive axis is the primary. The focal and dirigent curves are ellipses. But when ¢ = 0, the surface is that produced by the revolution of a hyperbola round its imaginary axis, and the focal and dirigent* are circles. If k= 0, which implies, since a and B have the same sign, that 2, 1, Yo, ¥ are each zero, the surface is a cone having the axis of z for its internal axis; and the focal and dirigent are each reduced to a point. The focus and di- rectrix are consequently unique ; the focus can only be the vertex of the cone, the directrix can only be the internal axis ; and the directrix therefore passes through the focus. The directive axis, which coincides with the axis of y, is one of the external axes; that one, namely, which is parallel to the greater axes of the elliptic sections made in the cone by planes perpendicular to its internal axis. This is on the supposition that ¢ is finite; for, when ¢ = 0, the cone be- comes one of revolution round the axis of z. III. When m is greater than cos ¢, but less than unity, we have a positive and B negative, and the species of the * When the term dirigent stands alone, it is understood to mean a dirigent line. VOL. II. QR 456 surface depends on K. It is inconsistent with these condi- tions to suppose # = 0, and therefore the surface cannot, in this case, be one of revolution. The value of k may be supposed to be given by the formula l—a l—B pets ee K= 7 (ao x;) + = (y2— %)"s (14) which contains only the relative coordinates of the focus and the foot of the directrix, and is a consequence of the equa- tions (6) and (8). 1°. Ifk is a positive quantity, the surface is a hyperboloid of one sheet, with its secondary axis in the direction of 2; the primary axis, as before, is the directive, but the focal and dirigent are now hyperbolas. 2°. If k is a negative quantity, the surface is a hyperbo- loid of two sheets, having its primary axis coincident with that of z The secondary axis is the directive; the focal and dirigent are hyperbolas. 3°. Ifx = 0, the surface is a cone, having the axis of x for its internal axis; the directive axis being, as before, that external axis to which the greater axes of the elliptic sec- tions, made by planes perpendicular to the interna] axis, are parallel. The axis of = is the other external axis, which may be called the mean azis of the cone, because it coincides with the mean axis of any hyperboloid to which the cone is asymptotic. As aand B have different signs, it is evident, from the equations (6) and (7), that the focal and dirigent are each a pair of right lines passing through the vertex, each pair making equal angles with the internal axis. Two planes, each of which is drawn through the mean axis and a dirigent line, are the dirigent planes of the cone. The corresponding focal and dirigent lines are those which lie within the same right angle made by the internal and directive axes; and since by the equations (6) and (8) the value of k may be written ——— ew FNP ee eee eee ee eee eee eee 457 K=a(@— xm) +n(y—~), (15) we see that, as K now vanishes, the right line joining corres- ponding points F and A upon these lines is perpendicular to the focal line. Of the two sides of the cone which are in the plane of xy, one lies between each focal and its dirigent ; and it may be inferred from the equations, that the tangents of the angles which the internal axis makes with a focal line, with one of these sides of the cone, and with a dirigent line, are in continued proportion, the proportion being that of the cosine of @ to unity. And hence it follows, that these two sides of the cone, with a focal line and its dirigent, cut harmonically any right line which crosses them. § 5. From this discussion it appears, that the ellipsoid and the hyperboloid of two sheets can be generated modularly, each in one way only, the modular focal being the ellipse for the former, and the hyperbola for the latter; but that the hyperboloid of one sheet can be generated in two ways, each of its focals being modular, and each focal having its proper modulus. The cone also admits two modes of gene- ration,* in one of which, however, the focus is limited to the vertex of the cone, and the directrix to its internal axis. * The double generation of the cone, when its vertex is the focus, may be proved synthetically by the method indicated in the Examination Papers of the year 1838, p. xlvi (published in the University Calendar for 1839). Supposing the cone to stand on a circular base (one of its directive sections), and to be cir- cumscribed by a sphere, the right lines joining its vertex with the two points where a diameter perpendicular to the plane of the base intersects the sphere, will be its internal and mean axes. Thenif P be either of these points, V the vertex, C the point where the axis PV cuts the plane of the base, and B any point in the circumference of the base, the triangles PVB and PBC will be si- milar, since the angles at V and B are equal, and the angle at P is common to both triangles; therefore BV will be to BC as PV to PB, that is, in a constant ratio. It is not difficult to complete the demonstration, when the focus is sup- posed to be any point on one of the focal lines. 2r2 458 But when the hyperboloid of one sheet, or the cone, is a surface of revolution, it has only one mode of modular ge- neration. In cases of double generation, the directive planes of course remain the same, as they have a fixed relation to the surface. A modular focal, it may be observed (and the remark applies equally to surfaces of the second class), is distinguished by the circumstance that it does not intersect the surface. The only exception to this rule are the focal lines of the cone, which pass through its vertex. A focal which is not modular may be called wmbilicar, because it intersects the surface in the umbilics; an umbilic being a point on the surface where the tangent plane is parallel to a directive plane. Thus the focal hyperbola of the ellipsoid, and the focal ellipse of the hyperboloid of two sheets, are umbilicar focals, and pass through the umbilics of these surfaces ; but the hyperboloid of one sheet has no umbilics, and accordingly both its focals are modular, and neither of them intersects the surface. The umbilicar focals and di- rigents have properties which shall be mentioned here- after. An umbilicar focal and the principal section whose plane coincides with that of the focal are curves of different kinds, the one being an ellipse when the other is a hyperbola; but a modular focal is always of the same kind with the coinci- dent section of the surface, being an ellipse, a hyperbola, or a pair of right lines, according as the section is an ellipse, a hyperbola, or a pair of right lines; and when the section is reduced to a point, so likewise is the modular focal. The plane of a modular focal always passes through the directive axis. When the directive axis is the primary, as in the hyperboloid of one sheet, both focals are modular. But in the ellipsoid and the hyperboloid of two sheets, where the primary axis is not directive, only one of the focals can be modular. The plane of an umbilicar focal is Se ie ee ee ee i 2 rs 459 always perpendicular to the directive axis; and therefore, when that axis is the primary, there is no umbilicar focal.* When the surface is doubly modular, the two moduli m,m’ are connected by the relation cos*@ sin’h _ m? m!2 aaa 1; (16) where @ is the angle made by a directive plane with the plane of the focal to which the modulus m belongs. One modulus is greater than unity; the other is less than unity, but greater than the cosine of the angle which the plane of the corresponding focal makes with a directive plane. In the hyperboloid of one sheet, the less modulus is that which belongs to the focal hyperbola. In the cone, the less modulus belongs to the focal lines. Of the two moduli of a cone, that which belongs to the focal lines may be termed the linear modulus; and the other, to which only a single focus corresponds, may be called the singular modulus. § 6. Second Class of Surfaces.—In this class of sur- faces, one of the quantities a, B vanishes, or both of them vanish. I. When m = cos 9, and ¢ is not zero, A vanishes, but B * If the first of the equations (10), when Pp, and q, are both negative, be supposed to express an imaginary focal, there will, in a central surface, be three focals, two modular and one umbilicar; the two modular focals being in the principal planes which pass through the directive axis, and the umbilicar focal in the remaining principal plane. Then, when we know which of the axes is the directive axis, we know which of the three focals is imaginary, because the plane of the imaginary focal is perpendicular to the primary axis. A modular focal may be imaginary, and yet have a real modulus; this occurs in the hyperboloid of two sheets. In the ellipsoid, the imaginary focal has an imaginary modulus. In all cases the two moduli are connected by the relation (16). It will appear hereafter, that the vertex of the cone is an umbilicar focus. The cone has therefore three focals, none of which is imaginary; but two of them are single points coinciding with the vertex. 460 does not; and the surface is either a paraboloid or a cy- linder. 1°. If the surface is a paraboloid, we may suppose the origin of coordinates to be at its vertex, in which case pec H and xk vanish, and we have the relations Gro=%— 2%, Yi = Y2 Cos” ds 2 2 2 2 2 as (17) La” + Yo cos’ p — a> — y,? = 0; the equation of the surface being y’ sin? @ + 2? 4+ 26x =0, (18) which shews that the paraboloid is elliptic, having its axis in the direction of x, and the plane of zy for that of its greater principal ‘section. From the relations (17) we obtain the following, yy tan*¢? + 2ca,+e67=0, (19) Ys’ sin? p cos’ ¢ + 2ca,— = 0; from which we see that the focal and dirigent curves are parabolas, having their axes the same as that of the surface; and their vertices equidistant from the vertex of the surface, but at opposite sides of it. The concavity of each curve is turned in the same direction as that of the section vy. The focus of the focal parabola is the focus of the section xy, and its vertex is the focus of the section xz of the surface; its parameter being the difference of the parameters of these two sections. The parameter of the section vy is a mean proportional between the parameters of the focal and diri- gent parabolas. 2°. If the surface is a cylinder, we may make c@ and u vanish, by taking the origin on its axis. We then have et oF = y2C0s" p, K ae tan? d mg a ue $3 (20) the equation of the cylinder, which is elliptic, being y’ sin? @ +22 =k. (21) Here the focal and dirigent are each a pair of right lines 461 parallel to the axis of the cylinder, and passing through the foci and directrices of a section perpendicular to the axis. The corresponding focal and dirigent lines lie at the same side of the axis. II. When m =1, and ¢ is not zero, B vanishes, but a does not. 1°. If the surface is a paraboloid, and the origin of co- ordinates at its vertex, the quantities c and k vanish; same the equation of the surface becomes x’ tan? ¢ — 2? = 2Hy, (22) and we have the relations — 5 = 2 K=>%—- 7s @, = @28ec ps x? sec? + yo — a2 — yy = 0. (23) The paraboloid is therefore hyperbolic, its axis being that of y, which is also the directive axis; and as the tangent of ¢@ may have any finite value, the plane of zy, which is that of the focal curve, may be either of the principal planes passing through the axis of the surface. The relations (23) give 1 x, sin? ¢ — 2uy, — Hn” = 0, 2” tan? @ sec? @ — 2uy. + H’ = O, Sl for the equations of the focal and dirigent, which are there- fore parabolas, having their axes the same as those of the surface, and their concavities turned in the same direction as that of the section xy; their vertices being equidistant from the vertex of the surface, and at opposite sides of it. The focus of the focal parabola is the focus of the section «wy, and its vertex is the focus of the section yz, its para- meter being the sum of the parameters of these two sections. The parameter of the section wy is a mean proportional between the parameters of the focal and dirigent parabolas. _ 2°. If the surface is a cylinder, and the origin on its axis, G@ and H vanish, and we have 462 &, = asec? g, Ni = Y,> F —K = 2,’sin’ ¢ = 2,” tan* ¢ sec’ ¢; ) the equation of the cylinder, which is hyperbolic, being x tan? @— 2? = — kK. (26) The focal and dirigent are each a pair of right lines pa- rallel to the axis of the cylinder; the corresponding lines passing through a focus and the adjacent directrix of any section perpendicular to the axis. The directive planes are parallel to the asymptotic planes of the cylinder. In this case, if k = 0, the surface is reduced to two di- rective planes, and the focal and dirigent to the intersection of these planes. III. When m= 1, and ¢ = 0, both a and B vanish, and the surface is the parabolic cylinder. If, as is allowable, we suppose G and k to vanish, the equation of the cylinder becomes =? + 2uy— 0, (27) and we have H>=hf—- Ys; t= L225 Ly + ys — 2 — vc 0; (8) whence n=—h, y=dn. (29) The focal and dirigent are each a right line parallel to the axis of x, the former passing through the focus, the latter meeting the directrix of the parabolic section made by the plane of yz. The plane of zy is the directive plane. § 7. We learn from this discussion, that, among the surfaces of the second class, the hyperbolic paraboloid is the only one which admits a twofold modular generation; the modu- lus, however, being the same for both its focals. In the elliptic paraboloid the modular focal is restricted to the plane of that principal section which has the greater parameter ; we shall therefore suppose a parabola to be described in the plane of the other principal section, according to the 463 law of the modular focals; the law being, that the focus of the parabola shall be the focus of the principal section in the plane of which the parabola lies, and its vertex the focus of the principal section in the perpendicular plane. The parabola so described will have its concavity opposed to that of the surface ; it will cut the surface in the umbilics, and will be its umbilicar focal, the only such focal to be found among the surfaces of the second class. We shall of course sup- pose further, that this focal has a dirigent parabola connected with it by the same law as in the other cases, the vertices of the focal and dirigent being equidistant from that of the surface and at opposite sides of it, while the parameter of the dirigent is a third proportional to the parameters of the focal and of the principal section in the plane of which the curves lie. The two focals of a paraboloid are so re- lated, that the focus of the one is the vertex of the other. The cylinders have no other focals than those which occur above. § 8. In this, as in the first class of surfaces, the right line FA, joining a focus F with the foot of its corresponding directrix, is perpendicular to the focal line ; and the focal and dirigent are reciprocal polars with respect to the section zy of the surface. These properties are easily inferred from the preceding results; but, as they are general, it may be well to prove them generally for both classes of surfaces. Supposing, therefore, the origin of coordinates to be any where in the plane of wy, and writing the equation of the surface in the form (e— ax)? +(y— nP+2?=1L(e — 2)? +M(y—y2), (80) which, when identified with (3), gives the relations A=1-—1, B—1—umM, G > L%— 2X; H >= Mj2—-%> (31) K = La,” + My.” — 2)? — ys 464 we find, by differentiating the values of the constants @, H, and kK, Lda. = dx, Mdy2 = dy, Lt dz + MY2 dz —%, da, — y, dy, =0. (32) Hence we obtain (x2 — a) da, + (y2— 91) dps = 0; (33) an equation which expresses that the right line joining the points F and A is perpendicular to the line which is the locus of the point F. Again, the equation of the section xy of the surface being Aa’? + By? + 2ex + 2Hy=K, (34) the equation of the right line which is, with respect to this section, the polar of a point A whose coordinates are x2, Y2, is (av, + G)a+(By¥.+ H)Y¥=K—Ga.— Hy; (35) but the relations (31) give Ate +G=%y—XN, BYo + H=Y2— Yi; K — GX — HY. = 2 (%.— 2) +91 (Yo— Y1)3 one and hence the equation (35) becomes (a2— %)(w@—m)+Y%—-ynly—-y)=9, (3%) which, as is evident from (33), is the equation of a tangent applied to the focal at the point F corresponding to A. This shows that the focal and dirigent are reciprocal polars with respect to the section xy, and that in this relation, as well as in the other, the points F and A are corresponding points. Supposing FE’ and A’ to be two other corresponding points on the focal and dirigent, if tangents applied to the focal at F and F’ intersect each other in T, the point T will be the pole of the right line AA’ with respect to the section xy, as well as the pole of the right line FE’ with respect to q , 465 the focal ; and hence if any right line be drawn through T, and if P be the pole of this right line with respect to the section, and N its pole with respect to the focal, the points P and N will be on the right lines AA’ and FF’ respectively. Now it is useful to observe that the distances AA’ and FF’ are always similarly divided (both of them internally or both of them externally) by the points P and N, so that we have AP to A’P as FN to F’N. This property may be proved directly by means of the foregoing equations; or it may be regarded as a consequence of the following theo- rem:—If through a fixed point in the plane of two given conics having the same centre, or of two given parabolas having their axes parallel, any pair of right lines be drawn, and their poles be taken with respect to each curve, the dis- tance between the poles relative to one curve will be in a constant ratio to the distance between the poles relative to the other curve.* In fact, the poles of the right lines TF, TF’, with respect to the focal, are F, F’; and their poles with respect to the section xy are A, A’; therefore, since the focal and the section xy may be taken for the given curves, and the point T for the fixed point, the ratio of FF’ to AA’ is the same as the ratio of FN to AP or of F’/N to A’P, and consequently the distances FF’ and AA‘ are si- milarly divided in the points N and P. §9. In the equation (30), considered as equivalent to the equation (1), the constants L and Mm are both positive ; but the properties which have been deduced from the former equation are independent of this circumstance, and _ * There is an analogous theorem for two surfaces of the second order which have the same centre, or two paraboloids which have their axes parallel. If through a fixed right line any two planes be drawn, and their poles be taken with respect to each surface, the distance between the poles relative to the one surface will be in a constant ratio to the distance between the poles relative to the other. 466 equally subsist when one of these constants is supposed to be negative (for they cannot both be negative). This leads us to inquire what surfaces the equation (30) is capable of representing when the constants L and m have different signs; as also, for a given surface, what lines are traced in the plane of zy by points F and A, of which ax,, y, and x», 2 are the respective coordinates. After the ex- amples already given, this question is easily discussed, and the result is, that the only surfaces which can be so repre- sented are the ellipsoid, the hyperboloid of two sheets, the cone, and the elliptic paraboloid—that is to say, the um- bilicar surfaces together with the cone; and that, for an umbilicar surface, the locus of F is the umbilicar focal, and therefore the locus of A is the corresponding dirigent ; while for the cone the points F and A are unique, coinciding with each other and with the vertex of the cone. A geometrical interpretation of this case is readily found; for as L and m have different signs, the right-hand member of the equation (30), if m be the negative quantity, is the product of two factors of the form S(e—%)+E8y—y), f(e— %2)—sY¥—y), in which f and g are constant; and these factors are evi- dently proportional to the distances of a point whose coordi- nates are x, y, 3, from two planes whose equations are f(e— x) + 8y-y=0, f(e—m)—sy—y)=0, which planes always pass through a directrix, and are in- clined at equal and constant angles to the axis of 2 or of y. Therefore, if F be the focus which belongs to this directrix, the square of the distance of F from any point of this surface is ina constant ratio to the rectangle under the distances of the latter point from the two planes. And these planes are di- rective planes; because, if a section parallel to one of them be made in the surface, the distance of any point of the sec- tion from the other plane will be proportional to the square 467 of the distance of the same point from the focus ; and, as the locus of a point, whose distance from a given plane is pro- portional to the square of its distance from a given point, is obviously a sphere, it follows that the section aforesaid is the section of a sphere, and consequently a circle; which shows that the plane to which the section is parallel is a directive plane. Thus,* the square of the distance of any point of ] 4 ; : * In attempting to find a geometrical generation for the surfaces of the se- cond order, one of the first things which I thought of, before I fell upon the modular method, was to try the locus of a point such that the square of its dis- tance from a given point should be in a constant ratio to the rectangle under its distances from two given planes; but when I saw that this locus would not represent all the species of surfaces, I laid aside the discussion of it. Some time since, however, Mr. Salmon, Fellow of Trinity College, was led inde- pendently, in studying the modular method, to consider the same locus; and he remarked to me, what I had not previously observed, that it offers a pro- perty supplementary, in a certain sense, to the modular property; that when the surface is an ellipsoid, for example, the given point or focus is on the focal hyperbola, which the modular property leaves empty. This remark of Mr. Salmon served to complete the theory of the focals, by indicating a simple geometrical relation between a non-modular focal and any point on the surface to which it belongs. In a memoir *‘ On a new Method of Generation and Discussion of the Sur- faces of the second Order,” presented by M. Amyot to the Academy of Sciences of Paris, on the 26th December, 1842, the author investigates this same locus, conceiving it to involve that property in surfaces which is analogous to the property of the focus and directrix in the conic sections; and the im- portance attached to the discovery of such analogous properties induced M. Cauchy to write a very detailed report on M. Amyot’s memoir, accompanied with notes and additions of his own (Comptes rendus des Séances de l’ Académie des Sciences, tom. xvi. pp. 783-828, 885-890; April, 1843); and also occa- sioned several discussions, principally between M. Poncelet and M, Chasles, relative to that Memoir (Comptes rendus, tom. xvi. pp. 829, 938, 947, 1105, 1110). But the property involved in this locus cannot be said to afford a ‘method of generation of the surfaces of the second order, since it applies only _ to some of the surfaces, and gives an ambiguous result even where it does apply. It is therefore not at all analogous to the aforesaid general pro- -perty of the conic sections, and moreover it was not new when M. Amyot 468 the surface from an umbilicar focus bears a constant ratio to the rectangle under the perpendicular distances of the same brought it forward. Mr. Salmon had in fact proposed it for investigation to the students of the University of Dublin, at the ordinary examinations in October, 1842; and it was published, towards the end of that year, in the University Calendar for 1843, some months before the date of M. Cauchy’s report, by which the contents of M. Amyot’s memoir were first made known. The parallelism of the two given planes to the circular sections of the surface is also stated in the Calendar; but this remarkable relation is not noticed by M. Amyot, nor by M. Cauchy. (See the Examination Papers of the year 1842, p. xly, quest. 17, 18; in the Calendar for 1843.) It is scarcely necessary to add, that the analogue which M. Amyot and other mathematicians have been seeking for, and which was long felt to be wanting in the theory of surfaces of the second order, is no other than the modular property of these surfaces, which appears to be not yet known abroad. M. Poncelet insists much on the im- portance of extending the signification of the terms focus and directrix, so as to make them applicable to surfaces; and he supposes this to have been effected, for the first time, by M. Amyot. These terms however, applied in their true general sense to surfaces, had been in use, several years before, among the mathematical students of Dublin, as may be seen by referring to the Calendar (Examination Papers of the year 1838, p.c; 1839, p. xxxi). The locus above-mentioned, being co-extensive with the umbilicar property, does not represent any surface which can be generated by the right line, except the cone. To remedy this want of generality, M. Cauchy proposes to consider a surface of the second order as described by a point, the square of whose distance from a given point bears a constant ratio either to the rectangle under its distances from two given planes, or to the sum of the squares of these distances. This enunciation, no doubt, takes in both kinds of focals, and all the species of surfaces; but the additional conception is not of the kind required by the analogy in question, nor has it any of the characters of an elementary prin- ciple. For the given planes, according to M. Cauchy’s idea, do not stand in any simple or natural relation to the surface ; and besides there is no reason why, instead of the sum of the squares of the distances from the given planes, we should not take the sum after multiplying the one square by any given positive number, and the other square by another given positive number ; nor is there any reason why we should not take other homogeneous functions of these dis- tances. This conception would therefore be found of little use in geome- trical applications; while the modular principle, on the contrary, by employing a simple ratio between two right lines, both of which have a natural connexion 469 point from two directive planes drawn through the diree- trix corresponding to that focus; and it is easy to see that this ratio, the square root of which we shall denote by pu, is equal to L — M, or, neglecting signs, to the sum of the nu- merical values of L and m. Of course, if the distances from the directive planes, instead of being perpendicular, be measured parallel to any fixed right line, the ratio will still be constant, though different. For example, if the fixed right line for each plane be that which joins the corres- ponding umbilic with either focus of the section wy, the ratio of the square to the rectangle will be the square of the number msec ¢, where m is the modulus, and ¢ the angle which the primary axis makes with a directive plane. When the umbilicar property is applied to the cone, the vertex of which is, as we have seen, to be regarded as an umbilicar focus, having the directive axis for its directrix, it indicates that the product of the sines of the angles which any side of the cone makes with its two directive planes is a constant quantity. It is remarkable that the vertex of the cone affords the only instance of a focal point which is at once modular and umbilicar, as well as the only instance of a focal point which is doubly modular. This union of properties it may be con- ceived to owe to the circumstance that the cone is the asymptotic limit of the two kinds of hyperboloids. For ifa with the surface, lends itself with the greatest ease to the reasonings of geometry. Indeed the whole difficulty, in extending the property of the directrix to surfaces of the second order, consisted in the discovery of such a ratio inherent in all of them; a ratio having nothing arbitrary in its nature, and for which no other of equal simplicity can be substituted. It may be proper to mention that the term modulus, which I have used for the first time in the present paper, with reference to surfaces of the second order, has been borrowed from M. Cauchy, by whom it is employed, however, ‘in a signification entirely different. Several other new terms are also now in- ‘troduced, from the necessity of the case. *¥ 470 series of hyperboloids have the same asymptotic cone, and their primary axes be indefinitely diminished, they will ap- proach indefinitely to the cone; and, in the limit, the focal ellipse and hyperbola of the hyperboloid of one sheet will pass into the vertex and the focal lines of the cone, thus making the vertex doubly modular, while the focal ellipse of the hyperboloid of two sheets will also be contracted into the vertex, and will make that point umbilicar. When the two directive planes coincide, and become one directive plane, the umbilicar property is reduced to this, that the distances of any point in the surface from the point F and from the directive plane are in a constant ratio to each other; and therefore the surface becomes one of re- volution round an axis passing through F at right angles to that plane, the point F being a focus of the meridional section, or the vertex if the surface be a cone. When the directive planes are supposed to be parallel, but separated by a finite interval, we get the same class of surfaces of revolution, with the addition of the surface produced by the revolution of an ellipse round its minor axis; the point F being still on the axis of revolution, but not having any fixed relation to the surface. § 10. If in the equation (30) we supposed the right-hand member to have an additional term containing the product of the quantities « — x, and y — y, with a constant coeffi- cient, all the foregoing conclusions regarding the geometrical meaning of that equation would remain unchanged, because the additional term could always be taken away by assigning proper directions to the axes of x andy. If, after the re- moval of this term, the coefficients of the squares of the aforesaid quantities were both positive, the locus of F would be amodular focal of the surface expressed by the equation; but if one coefficient were positive and the other negative, the locus of F would be an umbilicar focal. The equation in its more general form is evidently that which we should 471 obtain for the locus of a point S, such that the square of its distance SF from a given point F should be a given ho- mogeneous function of the second degree of its distances from two given planes ; the plane of ry being drawn through F perpendicular to the intersection of these planes, and 2, Y2 being the coordinates of any point on this inter- section, while 2, y, are the coordinates of F. The point F might be any point on one of the focals of the surface de- scribed by 8; the intersection of the two planes (supposing them always parallel to fixed planes) being the correspond- ing directrix. These considerations may be further guneeitiieds if we remark that the equation of any given surface of the second order may be put under the form (e— 2)? +(y— 91)? +(2—21)? =L(@— x9)? + M(y— Yo) +-N(z—20)" AL'(y— Y2)(8—82) + M'(w— X2)(2#— 22) +N'(L—22)(y—Y2), (38) where L, M, N, L’, M’, N’ are constants, and 2, Yi, 2 are con- ceived to be the coordinates of a certain point F, and %2, Y2, % the coordinates of another point A. The con- stants L’,M’,N’ may, if we please, be made to vanish by changing the directions of the axes of coordinates ; and when this is done, the new coordinate planes will be parallel to the principal planes of the surface. Then, by proceeding as before, it may be shown that, without changing the surface, we are at liberty, under certain conditions, to make the points F and A move in space. The conditions are ex- pressed geometrically by saying that the two surfaces, upon which these points must be always found, are reciprocal polars with respect to the given surface, the points Fand A being, in this polar relation, corresponding points ; and that the surface which is the locus of F is a surface of the second order, confocal with the given one, it being understood that confocal surfaces are those which have the same focal lines. The surface on which A lies is therefore also of the second VOL. II, 2s rid order, and the right line AF is a normal at F to the sur- face which is the locus of this point. Moreover, if through the point A three or more planes be drawn parallel to fixed planes, and perpendiculars be dropped upon them from any point S whose coordinates are 2, y, 2, the right-hand member of the equation (38) may be conceived to represent a given homogeneous function of the second degree of these perpendiculars; and the given surface may therefore be regarded as the locus of a point S, such that the square of the distance SF is always equal to that function. § 11. In the enumeration of the surfaces capable of being generated by the modular method, we miss the five follow- ing varieties, which are contained in the general equa- tion of the second degree, but are excluded from that me- thod of generation by reason of the simplicity of their forms—namely, the sphere, the right cylinder on a circu- lar base, and the three surfaces which may be produced by the revolution of a conic section (not a circle) round its primary axis.* These three surfaces are the prolate sphe- roid, the hyperboloid of two sheets, and the paraboloid of revolution; and the circumstance that the foci of the generating curves are also foci of the surfaces, renders it easy to investigate their focal properties.t In point of sim- plicity, the excepted surfaces are to the other surfaces of the second order what the circle is to the other conic sections, the circle being, in like manner, excepted from the curves which can be generated by the analogous method én plano; and the geometry of the five excepted surfaces may therefore be regarded as comparatively elementary. These five surfaces * The case of two parallel planes is also excluded, but it is not here taken into account. The case of two parallel right lines is in like manner excluded from the corresponding generation of lines of the second order. _ + A paper by M. Chasles, on these surfaces of revolution, will be found in the Memoirs of the Academy of Brussels, tom. v. (An. 1829). —— ss rr ™rlté~ (x — &)? +n? (y — yo)’ cos? o; and if we suppose to remain finite and constant, while ¢ approaches to 90°, and m indefinitely diminishes, this quan- tity will approach indefinitely to n°(w — a,)’, which will be its limiting value when ¢ = 90°. But 2 — ay is the distance of the point S from a fixed plane intersecting the axis of x perpendicularly at the distance x, from the origin of coordi- nates ; and therefore, in the limit, the equation expresses that the distances of any point S of the surface from the focus F and from this fixed plane, are to each other as n to unity, that is, in a constant ratio; which is a common pro- perty of the three surfaces in question. This property also belongs to the right cone, but the right cone does not rank among the excepted surfaces. “ § 12. We have seen that, when the modulus is unity, any plane parallel to either of the directive planes intersects the surface in a right line; whence it follows, that through any point on the surface of a hyperbolic paraboloid two right > a. : . | | 475 lines may be drawn which shall lie entirely in the surface. The plane of these right lines is of course the tangent plane at that point, and therefore every tangent plane intersects the surface in two right lines. This is otherwise evident from considering that the sections parallel to a given tan- gent plane are similar hyperbolas, whose centres are ranged ona diameter passing through the point of contact, and whose asymptotes, having always the same directions, are parallel to two fixed right lines which we may suppose to be drawn through that point. For as the distance between the plane of section and the tangent plane diminishes, the axes of the hyperbola diminish ; and they vanish when that dis- stance vanishes, the hyperbola being then reduced to its asymptotes. The tangent plane therefore intersects the surface in the two fixed right lines aforesaid. The same reasoning, it is manifest, will apply to any other surface of the second order, which has hyperbolic sections parallel to its tangent planes; and therefore the hyperboloid of one sheet, which is the only other such surface,* is also intersected in two right lines by any of its tangent planes. These right lines are usually called the generatrices of the surface. From what has been said, it appears that the generatrices of the hyperbolic paraboloid, and the asymptotes of its sec- tions (all its sections, except those made by planes parallel to the axis, being hyperbolas), are parallel to the directive planes. The generatrices of the hyperboloid of one sheet, and the asymptotes of its hyperbolic sections, are parallel to the sides of the asymptotic cone ; because any section of the * The double generation of these two surfaces by the motion of a right line has been long known. It appears to have been discovered and fully discussed by some of the first pupils of the Polytechnic School of Paris. This mode of generation had, however, been remarked by Wren, with regard to the hypre- boloid of revolution. It does not seem to have been observed, that the existence of rectilinear generatrices is included in the idea of hyperbolic sections parallel to a tangent plane. 476 hyperboloid is similar to a parallel section of the asymptotic cone, and when the latter section is a hyperbola its asymp- totes are parallel to two sides of the cone. PART II.—PROPERTIES OF SURFACES OF THE SECOND ORDER. § 1. In the preceding part of this paper it has been ne- cessary to enter into details for the purpose of communicat- ing fundamental notions clearly. In the following part, which will contain certain properties of surfaces of the se- cond order, we shall be as brief as possible; giving demon- strations of the more elementary theorems, but confining ourselves to a short statement of the rest. Many consequences follow from the principles already laid down. Through any directrix of a surface of the second order let a fixed plane be drawn cutting the surface, and let S be any point of the section. If the directrix and its focus F be modular, and ifa plane always parallel to the same directive plane be conceived to pass through S and to cut the direc- trix in D, the directive distance SD will be always parallel to a given right line, and will therefore be in a constant ratio to the perpendicular distance of S from the directrix. This perpendicular distance will consequently bear a given ratio to SF, the distance of the point S from the focus. And the same thing will be true when the directrix and focus are umbilicar, because the perpendicular distance of the point S from the directrix will be in a constant ratio to its distance from each directive plane drawn through the directrix. The fixed plane of section will in general contain another directrix parallel to the former, and belonging to the same focal ; and it is evident that the perpendicular distance of S from this other directrix will be in a given ratio to its dis- tance SF’ from the corresponding focus F’, the ratio being the same as in the former case. Hence, according as the point S lies between the two directrices, or at the same side ee ae? ee ee ee ee . 7 477 of both, the sum or difference of the distances SF and SF’ will be constant. If the plane of section pass through either of the foci, as F, this focus and its directrix will manifestly be the focus and directrix of the section. In this case the plane of section will be perpendicular to the focal at F. And if the surface be a cone, the point F being anywhere on one of its focal lines, the distance of the point S from the directrix will be in a constant ratio to its perpendicular distance from the dirigent plane which contains the directrix, and therefore this per- pendicular distance will be in a given ratio to the distance SF. Now calling V the vertex of the cone, and taking SV for radius, the perpendicular distance aforesaid is the sine of the angle which the side SV of the cone makes with the dirigent plane ; and SF, which is perpendicular to VF, is the sine of the angle SVF. Consequently the sines of the angles which any side of a cone makes with a dirigent plane and the corresponding focal line are in a given ratio to each other. § 2. Conceive a surface of the second order to be inter- sected in two points S, S’by aright line which cuts two parallel directrices in the points E, E’, and let F, F’ be the foci corresponding respectively to these directrices. The perpendicular distances of the points S, S’ from the first di- rectrix and from the second are to each other as the lengths SE, S’E, SE’, S’E’ respectively, and therefore the ratios of FS to SE, of FS’ to S’E, of FS to SE’, and of F’S’ to S’E’ are all equal. Hence, the right line FE bisects one of the angles made by the right lines FS and FS’; and the right line F’E’ bi- sects one of the angles made by F’S and F’S’. When the points S,S/ are at the same side of E, the angle supplemental to SFS’ is that which is bisected by the right line FE. Now if the point S be fixed, and S/ap- proach to it indefinitely, the angle SFE will approach inde- 478 finitely to a right angle. Therefore ifa right line touching the surface meeta directrix in a certain point, the distance between this point and the point of contact will subtend a right angle at the focus which corresponds to the directrix. And ifa cone circumscribing the surface have its vertex in a directrix, the curve of contact will be in a plane drawn through the cor- responding focus at right angles to the right line which joins that focus with the vertex. When the surface intersected by the right line SS’ is a cone, suppose this line to lie in the plane of the focus F and its directrix, that is, in the plane which is perpendicular at F to the focal line VF (the vertex of the cone being de- noted, as before, by V); the angles made by the right lines FE,FS, FS’, are then the same as the angles made by planes drawn through VF and each of the right lines VE, VS, VS’; and the last three right lines are the intersections of a plane VSS’ with the dirigent plane on which the point Ei lies, and with the surface of thecone. ‘Therefore if a plane passing through the vertex of a cone intersect its surface in two right lines, and one of its dirigent planes in another right line, and if a plane be drawn through each of these right lines respectively and the focal line which belongs to the di- rigent plane, the last of the three planes so drawn will bisect one of the angles made by the other two. And hence, if a plane touching a cone along one of its sides intersect a diri- gent plane in a certain right line, and if through this right line and the side of contact two planes be drawn intersecting each other in the focal line which corresponds to the dirigent plane, the two planes so drawn will be at right angles to each other. Let a right line touching a surface of the second order in S meet two parallel directrices in the points E, E’, and let F, F’ be the corresponding foci. Then the triangles FSE and F’SE’ are similar, because the angles at F and F’ are right angles, and the ratio of FS to SI. is the same as the ratio of F’S 479 to SE’. Therefore the tangent EE’ makes equal angles with the right lines drawn from the point of contact S to the foci F,F’. When the surface is a cone, let the tangent be per- pendicular to the side VS which passes through the point of contact ; the angles FSE and F’SE’are then the angles which the tangent plane VEE’ makes with the planes VSF and VSF’, because the right line FE is perpendicular to the plane VSF, and the right line F’E’ is perpendicular to the plane VSF’. Therefore the tangent plane of a cone makes equal angles with the planes drawn through the side of con- tact and each of the focal lines. Supposing a section to be made in a surface of the second order by a plane which cuts any directrix in the point E, if the focus F belonging to this directrix be the vertex of a cone having the section for its base, the right line FE will be an axis ofthe cone. For if through FE any plane be drawn cutting the base of the cone in the points S, S’, one of the angles made by the sides FS, FS’ which pass through these points will always be bisected by the right line FE; and this is the characteristic property of an axis. § 3. Two surfaces of the second order being supposed to have the same focus, directrix, and directive planes, so that they differ only in the value of the modulus m, or of the umbilicar ratio (see Part I. § 9), let a right line passing through any point E of the directrix cut one surface in the points S, S’, and the other in the points So, S,, and conceive right lines to be drawn from all these points to the common focus F. Since, if ratios be expressed by numbers, the ratio of FS to SE (or of FS’ to S’E) is to the ratio of FS, to SyE (or of FS, to S,E) as the value of m for the one surface is to its value for the other, when the focus is modular, or as the value of « for the one surface is to its value for the other when the focus is umbilicar, the sines of the angles EFS, and EFS (or of the angles EFS, and EFS’) are in a con- stant proportion to each other, because these sines are pro- 480 portional to those ratios. And since the right line FE bi- sects the angles SFS’ and S,FS,, both internally or both externally, in which case the angles SFS, and S’FS, areequal, or else one internally and the other externally in which case the angles SFS, and S’FS, are supplemental, it is easy to infer, from the constant ratio of the aforesaid sines, that in the first case the product, in the second case the ratio of the tangents of the halves of the angles SFS, and S’FS, (or of the halves of the angles SFS, and S’FS,) is a constant quan- tity. If the point S’ approximate indefinitely to S, the right line passing through these points will approach indefinitely to atangent. ‘Therefore when two surfaces are related as above, if a right line passing through any point E of their common directrix intersect one surface in the points So, Si, and touch the other in the point S, the chord S,S, will sub- tend a constant angle at the common focus F, and this angle will be bisected, either internally or externally, by the right line FS drawn from the focus to the point of contact. And the angle EFS being then a right angle, the cosine of the angle SFS, or SFS, will be equal to the ratio of the less value of m or » tothe greater.* § 4. Among the surfaces of the second order the only one which has a point upon itself for a modular focus is the cone, the vertex of which is such a focus, related either to the in- ternal or to the mean axis as directrix. In the latter rela- tion the vertex belongs to the series of foci which are ranged on the focal lines. ‘To see the consequence of this, let V be the vertex of the cone, and VW its mean axis perpendicular to the plane of the focal lines. On one of the focal lines and its dirigent assume any corresponding * See Exam. Papers, An. 1839, p. xxxi. questions 9, 10. These and some of the preceding theorems were originally stated with reference to modular foci only, They are now extended to umbilicar foci. 481 points F and A, and let AD be the directrix passing through A. ‘Then if a directive plane, drawn through any point S of the surface, cut this directrix in D and the mean axis in W, the ratio of SF to SD will be expressed by the linear modulus, as will also the ratio of VF to WD, since V isa point of the surface, and WD is equal to the directive dis- tance of Vfrom AD. But since V is a focus to which the mean axis is directrix, the ratio of SV to SW is expressed by the same modulus. Thusthe triangles SVF andSW Dare simi- lar, the sides of the one being proportional to those of the other. Therefore the angle SVF is equal to the angle SWD; that is to say, the angle which the side VS of the cone makes ’ with the focal line VF is equal to the angle contained by two right lines WD and WS, of which one is the intersection of the directive plane with the dirigent plane VWD corres- ponding to VF, and the other is the intersection of the di- rective plane with the plane VWS passing through the mean axis and the side VS of the cone. Hence it appears that the sum of the angles (properly reckoned) which any side of the cone makes with its two focal lines is constant. For if; F’ be a point on the other focal line, and D’ the point where the directrix correspond- ing to F’ is intersected by the same directive plane SWD, it may be shown as above that the angle SVE’ is equal to the angle SWD’, that is, to the angle made by the right line WS with the right line WD’ in which the directive plane in- tersects the dirigent plane corresponding to VF’. Conceiv- ing therefore the points F, F’, S, and with them the points D, D’, to lie all on the same side of the principal plane _ which is perpendicular to the internal axis, the right line WS will lie between the right lines WD and WD’, and the sum of the angles SVF and SVF’ will be equal to the ~ angle DWD’, which is a constant angle, being contained by the right lines in which a directive plane intersects the two a dirigent planes of the cone. This constant angle will be 482 found to be equal, as it ought to be, to one of the angles made by the two sides of the cone which are in the plane of the focal lines, namely to the angle within which the inter- nal axis lies. If we conceive the cone to have its vertex at the centre of a sphere, and the points F, F’,S to be on the surface of this sphere, the arcs of great circles connecting the point S with each of the fixed points F, F’ will have a constant sum. The curve formed by the intersection of the sphere and the cone may therefore, from analogy, be called a spherical ellipse, or, more generally, a spherical conic, because, by removing one of its foci F, F’ to the opposite extremity of the diame- ter of the sphere, the difference of the arcs SF and SF’ will be constant, which shows that the spherical curve is analo- gous to the hyperbola as well as to the ellipse. Either of these plane curves may, in fact, be obtained as a limit of the spherical curve when the sphere is indefinitely enlarged, ac- cording as the diameter along which the enlargement takes place, and of which one extremity may be conceived to be fixed while the other recedes indefinitely, coincides with the internal or with the directive axis of the cone. The fixed extremity becomes the centre of the limiting curve, which is an ellipse in the first case, and a hyperbola in the second. The great circle touching a spherical conic at any point makes equal angles with the two arcs of great circles which join that point with the foci, because the sum of these ares is constant. This is identical with a property already de- monstrated relative to the tangent planes of the cone. In- deed it is obvious that the properties of the cone may also be stated as properties of the spherical conic, and this is frequently the more convenient way of stating them. § 5. If the sides of one cone be perpendicular to the tangent planes of another, the tangent planes of the former will be perpendicular to the sides of the latter. For the plane of two sides of the first cone is perpendicu- Vo er cai ta 1 idlat ee ee PL OE eee 483 lar to the intersection of the two corresponding tangent planes of the second cone; and as these two sides ap- proach indefinitely to each other, their plane approaches to a tangent plane, while the intersection of the two correspond- ing tangent planes of the second cone approaches indefi- nitely to aside of the cone. Thus any given side of the one cone corresponds to a certain side of the other; and any side of either cone is perpendicular to the plane which touches the other along the corresponding side. This rea- soning applies to cones of any kind. Two cones so related may be called reciprocal cones. When one is of the second order, it will be found that the other is also of the second order, and that, in their equations relative to their axes, which are obviously parallel or coinci- dent, the coefficients of the squares of the corresponding va- riables are reciprocally proportional, so that the equations 2 2 2 Px? + ay? + ra? = 0, T+th+—=0, (1) express two such cones which have a common vertex. These cones have the same internal axis, but the directive axis of the one coincides with the mean axis of the other, and it may be shown from the equations that the directive planes of the one are perpendicular to the focal lines of the other. The two curves in which these cones are intersected bya sphere, having its centre at their common vertex, are reciprocal spherical conics. In general, two curves traced on the sur- face of a sphere may be said to be reciprocal to each other, when the cones passing through them, and having a common vertex at the centre of the sphere, are reciprocal cones. Any given point of the one curve corresponds to a certain point of the other, and the great circle which touches either curve atany point is distant by a quadrant from the corresponding point of the other curve. By means of these relations any property of a cone of the second order, or of a spherical conic, may be made to produce 484 a reciprocal property. Thus, we have seen that the tangent plane of a cone makes equal angles with two planes passing through the side of contact and through each of the focal lines; therefore, drawing right lines perpendicular to the planes, and planes perpendicular to the right lines here men- tioned, we have, in the reciprocal cone, a side making equal angles with the right lines in which the directive planes of this cone are intersected by a plane touching it along that side. It is therefore a property of the cone, that the inter- sections of a tangent plane with the two directive planes make equal angles with the side of contact; a property which it is easy to prove without the aid of the reciprocal cone. The two directive sections drawn through any point S of a given surface of the second order may, when they are cir- cles, be made the directive sections of a cone, and this may obviously be done in two ways. Each of the two cones so determined will be touched by the plane which touches the given surface at the point S, because the right lines which are tangents to the two circular sections at that point, are tangents to each cone as well as to the given surface; there- fore the side of contact of each cone bisects one of the an- gles made by these two tangents; and hence the two sides of contact are the principal directions in the tangent plane at the point S, that is, they are the directions of the greatest and least curvature of the given surface at that point; for these directions are parallel to the axes of a section made in the surface by a plane parallel to the tangent plane, and the axes of any section bisect the angles contained by the right lines in which the plane of section cuts the two directive planes. . § 6. It has been shown that the sum of the angles which any side of a cone makes with its focal lines is constant. Hence we obtain the reciprocal property, that* the sum of * This property, and that to which it is reciprocal, as well as some other properties of the cone, were, together with the idea of reciprocal cones and of 485 the angles (properly reckoned) which any tangent plane of a cone makes with its two directive planes is constant. This property may be otherwise proved as follows. Through a point assumed anywhere in the side of con- tact, let two directive planes be drawn. As the circles in which the cone is cut by these planes have a common chord, they are circles of the same sphere; and a tangent plane ap- plied to this sphere, at the aforesaid point, coincides with the tangent plane of the cone, because each tangent plane contains the tangents drawn to the two circles at that point. _ The common chord of the circles is bisected at right angles ___ by the principal plane which is perpendicular to the direct- ive axis, and therefore that principal plane contains the centres of the two circles and the centre of the sphere. Now the acute angle made by a tangent plane of a sphere with the plane of any small circle passing through the point of contact, is evidently half the angle subtended at the centre of the sphere by a diameter of that circle; therefore the acute angles, which the common tangent plane of the cone and of the sphere above-mentioned makes with the planes of the directive sections, are the halves of the angles subtended at the centre of the sphere by the diameters of the sections, But the diameters which lie in the principal plane already spoken of, and are terminated by two sides of the cone, are chords of the great circle in which that plane intersects the . ; spherical conics, suggested by my earliest researches connected with the mechani- cal theory of rotation and the laws of double refraction. I was not then aware that the focal lines of the cone had been previously discovered, nor that the spherical conic had been introduced into geometry. Indeed all the properties of the cone which are given inthis paper were first presented to me in my own investiga- tions. Its double modular property, related to the vertex as focus, was one of the propositions in the theory of the rotation of a solid body, and was used in finding the position of the axis of rotation within the body at a given time. But the modular property common to all the surfaces of the second order was not discovered until some years later. 486 sphere ; and the halves of the angles which they subtend at its centre are equal to the angles in the greater segments of which they are the chords, and consequently equal to the two adjacent acute angles of the quadrilateral which has these chords for its diagonals. Hence, as two opposite angles of the quadrilateral are together equal to two right angles, it follows that the four angles of the quadrilateral repre- sent the four angles, the obtuse as well as the acute angles, which the tangent plane of the cone makes with the planes of the directive sections; the two angles of the quadrilateral which lie opposite to the same diagonal being equal to the acute and obtuse angles made by the tangent plane with the plane of the section of which that diagonal is the diameter. ‘Thus any two adjacent angles of the quadrilateral may be taken for the angles which the tangent plane of the cone makes with the directive planes. If we take the two adja- cent angles which lie in the same triangle with the angle « contained by the two sides of the cone that help to form the quadrilateral, the sum of these two angles will be equal to two right angles diminished by «; and if we take the two remaining angles of the quadrilateral, their sum will be equal to two right angles increased by x; both which sums are constant. But if we take either of the other pairs of adja- cent angles, the difference of the pair will be constant, and equal to x. ‘The same conclusion may be deduced as a property of the spherical conic. Let a great circle touching this curve be intersected in two points, one oneach side of the point of contact, by the two directive circles, that is, by two great circles whose planes are directive planes of the cone which passes through the conic and has its vertex at the centre of the sphere. Since the right lines in which the tangent plane of a cone intersects the directive planes are equally inclined to the side of contact, the arc intercepted between the points where the tangent circle of the conic intersects the directive ad ed 487 circles is bisected in the point of contact ; therefore, either of the spherical triangles whose base is the tangent arc so in- tercepted, and whose other two sides are the directive circles, has a constant area; because, if we suppose the tangent are to change its position through an indefinitely small angle, and to be always terminated by the directive circles, the two little triangles bounded by its two positions and by the two indefinitely small directive arcs which lie between these posi- tions, will have their nascent ratio one of equality, so that the area of either of the spherical triangles mentioned above, will not be changed by the change in the position of its base. But in each of these triangles the angle opposite the base is constant; therefore the sum of the angles at the base is constant. From this reasoning itappears that if a spherical triangle have a given area, and two of its sides be fixed, the third side will always touch a spherical conic having the fixed sides for its directive arcs, and will be always bisected in the point of contact. § 7. The intersection of any given central surface of the second order with a concentric sphere is a spherical conic, since the cone which passes through the curve of intersection and has its vertex at the common centre, is of the second order. The cylinder also, which passes through the same curve and has its side parallel to any of the arcs of the given surface, is of the second order; and the cone, the cylinder, and the given surface are condirective, that is, the directive planes of one of them are also the directive planes of each of the other two. This may be seen from the equations of the different surfaces; for, in general, two surfaces, whose principal planes are parallel, will be condirective, if, when their equations are expressed by coordinates perpendicular to these planes, the differences of the coefficients of the squares of the variables in the equation of the one be pro- VOL. Il, 2T 488 portional to the corresponding differences in the equation of the other. If any given surface of the second order be intersected by a sphere whose centre is any point in one of the principal planes, the cylinder passing through the curve of intersection, and having its side perpendicular to that principal plane, will be of the second order, and will be condirective with the given surface. This cylinder, when its side is parallel to the directive axis, is hyperbolic; otherwise it is elliptic. If a paraboloid be cut by any plane, the cylinder which passes through the curve of section and has its side parallel to the axis of the paraboloid, will be condirective with that surface ; and it will be elliptic or hyperbolic, according as the para- boloid is elliptic or hyperbolic.* If two concentric surfaces of the second order be recipro- cal polars with respect to a concentric sphere, the directive axis of the one surface will coincide with the mean axis of the other, and the directive planes of the one will be perpen- dicular to the asymptotes of the focal hyperbola of the other. When one of the surfaces is a hyperboloid, the other is a hyperboloid of the same kind ; the asymptotes of the focal hy- perbola of each surface are the focal lines of its asymptotic cone; and the two asymptotic cones are reciprocal. When any number of central surfaces of the second order are confocal, or, more generally, when their focal hyperbolas have the same asymptotes, it is obvious that their reciprocal surfaces, taken with respect to any sphere concentric with them, are all condirective. § 8. Ifa diameter of constant length, revolving within a *T have introduced the terms directive and condirective, as more general than the terms cyclic and biconeyclic employed by M. Chasles. The latter terms suggest the idea of circular sections, and therefore could not properly be used with reference to the hyperbolic paraboloid, or to the hyperbolic or parabolic cylinder, in each of which surfaces a directive section is a right line. 489 given central surface, describe a cone having its vertex at the centre, the extremities of the diameter will lie in a sphe- rical conic. And if the cone be touched by any plane, the side of contact will evidently be normal to the section which that plane makes in the given surface, and will therefore be an axis of the section. As the axes of a section always bi- sect the angles made by the two right lines in which its plane intersects the directive planes of the surface, and as the cone aforesaid has the same directive planes with the given surface, it follows that theright lines in which a tangent plane of a cone cuts its directive planes are equally inclined to the side of contact ; a theorem which has been already obtained in another way. If a section be made in a given central surface by any plane passing through the centre, the cone described by a constant semidiameter equal to either semiaxis of the sec- tion will touch the plane of section; for if it could cut that plane, a semiaxis would be equal to another radius of the section. Denoting by r,7’ the semiaxes of the section, con- ceive two cones to be described by the revolution of two constant semidiameters equal to ry and r’ respectively. These cones are condirective with the given surface, and have the plane of section for theircommon tangent plane. Supposing that surface to be expressed by the equation xr y? am er ae (2) and the directive axis to be that of y, the axis of «x will be the internal axis of one cone, say of that described by r, and the axis of z will be the internal axis of the other cone. Let « be the angle made by the two sides of the first cone which lie in the plane xz, and «’ the angle made by the two sides of the second cone which lie in the same plane; the former angle being taken so as to contain the axis of z within it, and the latter so as to contain within it the axis of z. 2T2 490 Then, considering 1,7’ as radii of the section vz of the sur- face, we have obviously 1 __cos*4« | sin?4 Mia ce hat a= zoey Sas 4 (24 =) + 4(2~2) cone, 1 cos?4x’ | sin? 4x’ ie 2) (2 1 ) —_ = —_ eT an Ge 0 | eae Oy Eee /. = aes + Z het o 2 \>—= Jeosk’; (3) observing that when these formule give a negative value for r? or 7”, in which case the surface expressed by the equation (2) must be a hyperboloid, the direction of r or 7’ meets, not that surface, but the surface of the conjugate hyperboloid expressed by the equation 2 2 x er ei ~t2 425-1. (4) Now calling 6 and 6’ the angles made by the tangent plane of the cones with the directive planes of the given surface, which are also the directive planes of each cone, the angles x, «’ depend on the sum or difference of 0 and 6’. Ifthe latter angles be taken so that their sum may be equal to the supplement of «, their difference will be equal to x’, and the formule (3) will become oe = (542) —2 (1!) cos 046% fila dietek ais 6) va=4(5 +5) -3 (5 — {) e080 - 0%, by which the semiaxes of any central section are expressed in terms of the non-directive semiaxes of the surface, and of the angles which the plane of section makes with the direc- tive planes.* * See the Transactions of the Royal Irish Academy, vol. xxi., as before cited. The formulw (5) were first given, for the case of the ellipsoid, by Fresnel, in his Theory of Double Refraction, Mémoires de 1’Institut, tom. vii., p: 155. 491 § 9. From the centre O of the surface expressed by equa- tion (2) let a right line OF be drawn cutting perpendicu- larly in = the plane which touches the surface at S. Let o denote the length of the perpendicular O3, and a, GB, y the angles which it makes with 2, y, z. Then o* = Pcos7a + Qcos 73 + RCos *y. (6) From this formula it is manifest, that if three planes touching the surface be at right angles to each other, the sum of the squares of their perpendicular distances from the centre will be equal to the constant quantity p + @+ R, and therefore the point of intersection of the planes will lie in the surface of a given sphere. If another surface represented by the equation be touched by a plane cutting OS perpendicularly in 2, and if oo be the length of O,, then oo” = Py Cos "a + Qo cos 7B + Ry cos *y; and therefore when the two surfaces are confocal, that is, when P—Pyp—Q—Q%=R— R= f, we have o? — a,” = fk, which is a constant quantity. Hence if three confocal surfaces be touched by three rectangular planes, the sum of the squares of the perpendiculars dropped on these planes from the centre will be constant, and the locus of the intersection of the planes will be a sphere. The focal curves of a given surface are the limits of sur- faces confocal with it,* when these surfaces are conceived, * It was by this consideration, arising out of the theorems given in this and the next section about confocal surfaces, that I was led to perceive the na- ture of the focal curves, and the analogy between their points and the foci of 492 by the progressive diminution of their mean or secondary axes, to become flattened, and to approach more and more nearly toa plane passing through the primary axis. And it will appear hereafter, that if a bifocal right line, that is, a right line passing through both focal curves, be the inter- section of two planes touching these curves, those two planes will be at right angles to each other. Therefore the locus of the point where a tangent plane of a given central surface is intersected perpendicularly by a bifocal right line is a sphere. The primary axis of the surface is evidently the diameter of this sphere. Hence we conclude that the locus of the point where a tangent plane of a paraboloid is intersected perpendicu- larly by a bifocal right line is a plane touching the parabo- loid at its vertex. For a paraboloid is the limit of a central surface whose primary axis is prolonged indefinitely in one direction, and a plane is the corresponding limit of the sphere described on that axis as diameter. As this consi- deration is frequently of use in deducing properties of para- boloids from those of central surfaces, it may be well to state it more particularly. It is to be observed, then, that the indefinite extension of the primary axis at one extremity may take place according to any law which leaves the other extremity always at a finite distance from a given point, and gives a finite limiting parameter to each of the principal sec- tions of the surface which pass through that axis. The simplest supposition is, that one extremity of the axis and the adjacent foci of those two principal sections remain fixed, while the other extremity and the other foci move off, with the centre, to distances which are conceived to increase with- out limit. Then, at any finite distances from the fixed conies. And I regarded that analogy as fully established when I found (in March or April, 1832) that the normal at any point of a surface of the second order is an axis of the cone which has that point for its vertex and a focal for its base. i 493 points, the focal curves approach indefinitely to parabolas, as do also all sections of the surface which pass through the primary axis, while the surface itself approaches indefinitely . to a paraboloid; so that the limit of the central surface is a paraboloid having parabolas for its focal curves. The limit of an ellipsoid, or of a hyperboloid of two sheets, is an ellip- tic paraboloid, having one of its focals modular and the other umbilicar, like each of the central surfaces from which it may be derived; and the limit of a hyperboloid of one sheet is a hyperbolic paraboloid, having, like that hyberbo- loid, both its focals modular. § 10. Let the plane touching at S the surface expressed by equation (2), intersect the axis ofa in the point X, and let the normal applied at S intersect the planes yz, zz, xy, in the points L, M, N respectively. Since the section made in the surface by a plane passing through OX and the point S has one of its axes in the direction of OX, it appears, by an elementary property of conics, that the rectangle under OX and the coordinate x of the point S is equal to the quantity Pp; but that coordinate is to LS as OS ora isto OX, and therefore the rectangle under o and LS is equal to pr. Simi- larly the rectangle under o and MS is equal to a, and the rectangle under o and NS is equal to rR. Thus the parts of the normal intercepted between the point S and each of the principal planes, are to each other as the squares of the semiaxes respectively perpendicular to these planes; the square of an imaginary semiaxis being regarded as negative, and the corresponding intercept being measured from S in a direction opposite to that which corresponds to a real semiaxis. The rectangle under o and the part of the normal inter- cepted between two principal planes, is equal to the difference of the squares of the semiaxes which are perpendicular to these planes. This rectangle is therefore constant, not only 494. for a given surface, but for all surfaces which are confocal with it. Hence the part of the normal intercepted between two principal planes bears a given ratio to the part of it inter- cepted between one of these and the third principal plane, whether the normal be applied at any point of a given sur- face, or at any point of a surface confocal with it. If therefore normals to a series of confocal surfaces be all parallel to a given right line, they must all lie in the same plane passing through the common centre of the surfaces, because otherwise the parts of any such normal, which are intercepted between each pair of principal planes, would not be in a constant ratio to each other. The point S being the point at which any of these paral- lel normals is applied, the plane touching the surface at S is parallel to a given plane, the perpendicular OS dropped upon it from the centre has a given direction, the plane OS® is fixed, and the directions of the lines OL,OM, ON in which this plane intersects the principal planes are also fixed. And as the angle OSS is always a right angle, and the normal at S is always parallel to O%, the distance SE bears a given ratio to each of the distances OL, OM, ON, and therefore also to each of the intercepts MN, LN, LM. Hence, since the rectangle under O% and any one of these intercepts is constant, the rectangle under OF and S2 is constant. Therefore if a series of confocal central surfaces be touched by parallel planes, the points of contact will all lie in one plane, and their locus, in that plane, will be an equila- teral hyperbola, having its centre at the centre of the sur- faces, and having one of its asymptotes perpendicular to the tangent planes. This hyperbola evidently passes through two points on each of the focal curves, namely the points where the tangent to each curve is parallel to the tangent planes. If a series of confocal paraboloids be touched by parallel . . > ; 495 planes, it will be found that the points of contact all lie in a bifocal right line, and that the normals at these points lie in a plane parallel to the axis of the surfaces; so that the part of any normal which is intercepted by thetwo principal planes is constant. This theorem may be proved from the two follow- ing properties of the paraboloid:—1l. A normal being ap- plied to the surface at the point S, the segments of the normal, measured from S to the points where it intersects the planes of the two principal sections, are to each other in- versely as the parameters of these sections. 2. Supposing the axis of x to be that of the surface, the difference between the coordinates x of the point S and of the point where the normal meets the plane of one of the principal sections, is equal to the semiparameter of the other principal section. § 11. Let a tangent plane, applied at any point S ofa surface of the second order, intersect the plane of one of its focals in the right line ©, and let P be the foot of the per- pendicular dropped from S upon the latter plane. The pole of the right line ©, with respect to the principal section lying in this plane, is the point P. Let N be its pole with respect to the focal. Then if T be any point of the right line ©, the polar of this point with respect to the section will pass through P, and its polar with respect to the focal will pass through N; and if the former polar intersect the dirigent curve in A, A’, and the latter intersect the focal in F, F’, the points F, F’ will correspond respectively to the points A, A’,and the distances AA’ and FF’ will be similarly divided by the points P and N (See Part I. § 8). But since the point S is in the plane of the two directrices which pass through A and A’, the lengths AP and A‘P, which are the perpendicular distances of S from the directrices, are pro- portional to the lengths FS and F’S. Therefore FN is to F’N as FS is to F’S, and the right line NS bisects one of the angles made by the right lines FS and F’S. Andas thisholds wherever the point T is taken on the right line ©, that is, 496 in whatever direction the right line FF’ passes through the point N, it follows that the right line NS is an axis of the cone which has the point S for its vertex and the focal for its base. Further, if FE’ intersect © in the point Q, we have FN to F’N as FQ is to F’Q, because N is the pole of © with respect to the focal; therefore FQ is to F’Q as FS is to F’S, and hence the right line QS also bisects one of the angles made by FS and F’S. The right lines NS and QS are therefore at right angles to each other, and as the latter always lies in the tangent plane, the former must be perpendicular to that plane. Consequently the normal at any point of a surface of the second order is an axis of the cone which has that point for its vertex and either of the focals for its base. It is known that when two confocal surfaces intersect each other, they intersect everywhere at right angles; and that through any given point three surfaces may in general be described, which shall have the same focal curves. If three confocal surfaces pass through the point S, the normal to each of them at S is an axis of each of the cones which stand on the focals and have S for their common vertex. The normals to the three surfaces are therefore the three axes of each cone. If the points at which a series of confocal surfaces are touched by parallel planes be the vertices of cones having one of the focals for their common base, each of these cones will have one of its axes perpendicular to the tangent planes. Therefore when an axis of a cone which stands on a given base is always parallel to a given right line, the locus of the vertex is an equilateral hyperbola or a right line, according as the base is a central conic or a parabola. § 12. A system of three confocal surfaces intersecting each other consists of an ellipsoid, a hyperboloid of one sheet, and a hyperboloid of two sheets, if the focals be central conics; but it consists of two elliptic paraboloids ee as 497 and a hyperbolic paraboloid, if the focals be parabolas. In the central system, the ellipsoid has the greatest primary axis, and the hyperboloid of two sheets the least; and the focal which is modular in one of these surfaces is umbilicar in the other. The asymptotic cones of the hyperboloids are confocal, the focal lines of each cone being the asymptotes of the focal hyperbola. In the system of paraboloids, the two elliptic paraboloids are distinguished by the circum- . stance that the modular focal of the one is the umbilicar focal of the other. The curve in which two confocal surfaces intersect each other is a line of curvature of each, as is well known ;* and a series of lines of curvature on a given surface are found by making aseries of confocal surfaces intersect it. Now ifa series of the lines of curvature of a given surface be projected on one ofits directive planes by right lines paral- lel to either of its non-directive axes, the projections will be a series of confocal conics ; and when the surface is umbili- ear, the foci of all these conics will be the corresponding projections of the umbilics.| When the surface is not um- bilicar, its directive axis will be parallel to the primary axis of the projections. The same line of curvature has two projections, accord- ing as it is projected by right lines parallel to the one or to the other non-directive axis. In the ellipsoid these projec- tions are always curves of different kinds, the one being an ellipse when the other is a hyperbola; but in a hyperboloid the projections are either both ellipses or both hyper- bolas. In the hyperbolic paraboloid the projections are parabolas. In the elliptic paraboloid, one of the projections is always a parabola, and the other is either an ellipse or a hyperbola. * See Dupin’s Développements de Géométrie. + Exam. Papers, An. 1838, p. xlvi., quest. 4; p. xcix., quest. 70. 498 The corresponding projections of two lines of curvature which pass through a given point of the surface, are confo- cal conics intersecting each other in the projection of that point, and of course intersecting at right angles. § 13. A bifocal chord is a bifucal right line terminated both ways by the surface.* In a central surface, the length of a bifocal chord is proportional to the square of the dia- meter which is parallel to it; the square of the diameter being equal to the rectangle under the chord and the pri- mary axis. More generally, if a chord of a given central surface touch two other given surfaces confocal with it, the length of the chord will be proportional to the square of the parallel dia- meter of the first surface, the square of the diameter being equal to the rectangle under the chord and a certain right line 2/, determined by the formula aves WEE = GP) P49’ wherein it is supposed that the equation (2) represents the first surface, and that p’, P’’ are the quantities corresponding to Pp in the equations of the other two surfaces. In any surface of the second order, the lengths of two bifocal chords are proportional to the rectangles under the segments of any two intersecting chords to which they are parallel. In the paraboloid paren: by the eee 2? x r= dB if x be the length of a — chord making the angles 6 and y with the axes of y and z respectively, we have 1 _ cos ie 4. £08 7 (8) x - q * The theorems in § 13 are now stated for the first time. 499 § 14. At the point S on a given central surface expressed by the equation (2), let a tangent plane be applied, and let k, k’ be the squares of the semiaxes of a central section made in the surface by a plane parallel to the tangent plane ; each of the quantities /, k’ being positive or negative accord- ing as the corresponding semiaxis of the section is real or imaginary, that is, according as it meets the given surface or not. Then the equations* of two other surfaces confocal with the given one, and passing through the point S, are a y? 2? 2 y 2? ae tae eg ee te The given surface is intersected by these two surfaces re- spectively in the two lines of curvature which pass through the point S; the tangent drawn to the first line of curvature at S is parallel to the second semiaxis of the section, and the tangent drawn to the second line of curvature at S is parallel to the first semiaxis of the section. When two confocal surfaces intersect, the normal applied to one of them at any point S of the line of curvature formed by their intersection lies in the tangent plane of the other, aud is parallel to an axis of any section made in the latter by a plane parallel to the tangent plane. Sup- posing the surfaces to be central, if two normals be applied at the point S, and a diameter of each surface be drawn pa- rallel to the normal of the other, the two diameters so drawn will be equal and of a constant length, wherever the point S is taken on the line of curvature; the square of that length being equal to the difference of the squares of the primary axes of the surfaces, and the diameter of the sur- face which has the greater primary axis being real, while that of the other surface is imaginary. As the point S moves along the line of curvature, each constant diameter * Exam. Papers, An. 1837, p.c., quests. 4, 5, 6 ; An. 1838, p.c., quests. 71, 72. 500 describes a cone condirective with the surface to which it belongs ; the two cones so described are reciprocal, and the focal lines of the cone which belongs to one surface are perpendicular to the directive planes of the other surface. When two confocal paraboloids intersect, if normals be applied to them at any point S of their intersection, and a bifocal chord of each surface be drawn parallel to the nor- mal of the other, the two chords so drawn will be equal and of a constant length, wherever the point S is taken in the line of intersection of the surfaces ; that constant length being equal to the difference between the parameters of either pair of coincident principal sections. § 15. The point S being the common intersection of a given system of confocal surfaces, of which the equations are x? yp. 2 e igeie oz — — — => ==, a y? 2? peeks fee ee STL Fae ey , suppose that another surface A confocal with these, and ex- pressed by the equation z Ro a xy Pr Po se oR +S, (11) is circumscribed by a cone having its vertex at S. Ifthe normals applied at S to the given surfaces, taken in the order of the equations (10), be the axes of new rectangular coor- dinates &, n, Z, the equation of the cone, referred to these coordinates, will be* * The equation (12) was obtained in the year 1832, and was given at my lectures in Hilary Term, 1836. The most remarkable properties of cones circumscribing confocal surfaces, are immediate consequences of this equation. That such cones, when they have a common vertex, are confocal, their focal lines being the generatrices of the hyperboloid of one sheet passing through the ver- ——— 34 i? ag ate Po +. Fe A = 0; (12) The surfaces of the given system, in the order of their equations, may be supposed to be an ellipsoid, a hyperbo- loid of one sheet, and a hyperboloid of two sheets; the axes of x, y, z being respectively the primary, the mean, and the secondary axes of each surface. Then P is greater than pr’, and p’ greater than Pp”. The normals to the given surfaces are the axes of the cone expressed by the equation (12); and if the surface A be changed, but still remain confocal with the given system, it is obvious from that equation that the focal lines of the cir- cumscribing cone will remain unchanged, since the differences of the quantities by which the squares of &, n, ¢ are divided are independent of the surface A. As pP’ is intermediate in value between P and Pp”, the normal to the hyperbo- loid of one sheet is always the mean axis of the cone; the focal lines lie in the plane &Z, and their equation is 35 Sk a = quae ——— a U, (13) which shows that they are parallel to the asymptotes of a central section made in the hyperboloid of one sheet by a plane parallel to the plane &Z, since the quantities p’ — p and p’ — p” are (including the proper signs) the squares of the semiaxes of the section which are parallel to € and Z re- SS a a a ee eae ee eee tex, was first stated by Professor C. G. J. Jacobi, of Konigsberg, in 1884, See Crelle’s Journal, vol. xii., p. 137. See also the excellent work of M. Chasles, published in 1837, and entitled ‘* Apercu historique sur l'Origine et le Développement des Méthodes en Géométrie ;” p. 387. The analogy which exists between the focals of surfaces and the foci of curves of the second order was supposed by M. Chasles to have been pointed out in that work for the first time (Comptes rendus, tom. xvi., pp. 833, 1106); but that analogy had been previously taught and developed in the lectures just alluded to. 502 spectively. The focal lines are therefore the generatrices of that hyperboloid at the point S. When pr, = 0, the equation (12) becomes 2.) ot. (14) which is that of the cone standing on the focal ellipse and having its vertex at S. When e = 0, the same equation becomes a ae xe which is that of the cone standing on the focal hyperbola, and having its vertex atS. The normal to the hyperboloid of one sheet at the point S is the mean axis of both cones; the normal to the ellipsoid is the internal axis of the first cone and the directive axis of the second, while the nor- mal to the hyperboloid of two sheets is the directive axis of the first and the internal axis of the second. The three surfaces expressed by the equations Eine SF at cae P pal, tig he l, eee Beit 8 et wtee! (16) are a confocal system, having their centre at S, and being respectively an ellipsoid, a hyperboloid of one sheet, and a hyperboloid of two sheets. They intersect each other in the centre of the system expressed by the equations (10), and their normals at that point are the axes of z, y, z respectively. The relations between the two systems of surfaces are there- fore perfectly reciprocal. From the equations (14) and (15) it is manifest that the asymptotic cones of the hyperboloids of one system pass through the focals of the other. § 16. The point S being the intersection of a given sys- tem of confocal paraboloids whose equations are E 503° where p—p'=¢ a q’ = 4(h— h’), and p — p” =q- q”’ = 4(h —h’); suppose that another paraboloid A confocal with these, and expressed by the equation 2 2 0 is circumscribed by a cone having its vertex at S. Then if the normals applied at Sto the given system of surfaces, taken in the order of their equations, be the axes of the coor- dinates &, n,Z respectively, the equation of the circumscribing cone will be 4 n 2 p—p tp pt Pp i showing that those normals are the axes of the cone, and that the focal lines of the cone are independent of the sur- face A, provided it be confocal with the given surfaces. If the hyperbolic paraboloid be the second surface of the given system, the parameter p’ will be intermediate in value be- tween p and p”, and the equation of the focal lines of the cone will be ay °° ne Be i, =0, 20 BaP ot oP wit which is the equation of a pair of right lines parallel to the asymptotes of a section made in the hyperbolic paraboloid by a plane parallel to the plane &Z, since the quantities p’— p and p’ — p” are proportional to the squares of the semiaxes of the section which are parallel to € and Z respectively. The focal lines are therefore the generatrices of the hyperbolic paraboloid at the point S. VOL, I. 2u 504 Putting po and q alternately equal to zero in the equa- tion (19), we get Eto Fe eee iets Pe ane q Ts £ the equations of two cones which have a common vertex at S, the first of them standing on the focal which lies in the plane «xz, the second on the focal which lies in the plane zy. The mean axis of each of these cones is the normal at S to the hyperbolic paraboloid; the internal axis of either cone is the normal to the elliptic paraboloid which has the base of that cone for its modular focal. =0, (21) As the cones which have a common vertex, and stand on the focals of any surface of the second order, are confocal, they intersect at right angles. ‘Therefore when two planes passing through a bifocal right line touch the focals, these planes are at right angles to each other. And as cones which have a common vertex, and circumscribe confocal surfaces, are confocal, two such cones, when they intersect each other, intersect at right angles. Therefore when a right line touches two confocal surfaces, the tangent planes passing through this right line are at right angles to each other. § 17. When two surfaces are reciprocal polars* with re- spect to any sphere, and one of them is of the second order, the other is also of the second order. Let the surface B be reciprocal to the surface A before mentioned, with respect to a sphere of which the centre is S; and suppose R’ and R,,to be any corresponding points on these surfaces. ‘Then the plane which touches the surface A at the point R, intersects the right line SR’ perpendicularly in a point K, such that the rectangle under SR’ and SK is constant, being equal to the * Transactions of the Royal [rish Academy, vol. xvii., p. 241 ; Exam. Papers, An, 1841, p, cxxvi., quest. 4. —— — = 505 square of the radius of the sphere. Now if the point K approach indefinitely to S, the distance SR’ will increase without limit, the surface B being of course a hyperboloid ; and if through S any plane be drawn touching the surface A, aright line perpendicular to this plane will evidently be parallel to a side of the asymptotic cone of the hyperboloid. The asymptotic cone of B is therefore reciprocal to the cone which, having its vertex at S, circumscribes the surface A. Hence, as the directive planes of a hyperboloid are the same as those of its asymptotic cone, it follows that the direc- tive planes of the surface B are perpendicular to the gene- ratrices of the hyperboloid of one sheet, or the hyperbolic ~ paraboloid, which passes through S, and is confocal with the surface A. And this relation between two reciprocal surfaces ought to be general, whatever be the position of the point S with respect to them;* for though it has been de- duced by the aid of the circumscribing cone aforesaid, it does not, in its enunciation, imply the existence of such a cone. This conclusion may be verified by investigating the equation of the surface B in terms of the coordinates &, n, Z. Suppose o to be the radius of the sphere with respect to which the surfaces A and B are reciprocal. Then if A bea cen- tral surface expressed by the equation (11), and having Eo, no, So for the coordinates of its centre, the surface B will be represented by the equation (P — Po) E? + (RP! — Po) n? +(e” — Po) 2? = 20° (Eo E + no n+ 20%) — 0°; but if A be a paraboloid expressed by the equation (18), the equation of B will be (p — po) 5° + (p! — po) n° + Cp” — po) &” = 4p” (Ecos a + n cos B + Z cos ), where a, (3, y are the angles which the axis of « makes with (22) (23) * This relation was first noticed by Mr. Salmon. 506 the axes of &, 1, Z respectively. In the first case, the equation (22) shows that the directive planes of B are perpendicular to the right lines expressed by the equation (13); in the second case, the equation (23) shows that the directive planes of B are perpendicular to the right lines expressed by the equation (20). When the surface A is a paraboloid, and the distance of the point R from its vertex is indefinitely increased, the plane touching the surface at R approaches indefinitely to parallelism with its axis, and the right line SK, perpendicu- lar to that plane, increases without limit. Therefore the surface B passes through the point S, and is touched in that point by aplane perpendicular to the axis of A. When the point S lies upon the surface A, the coefficient of the square of one of the variables, in the equation (22) or (23), is reduced to zero, and the surface Bisa paraboloid hav- ing its axis parallel to the normal applied at S to the surface A. This also appears from considering that when § is a point of the surface A, the normal at that point is the only right line passing through §, which meets the surface B at an infinite distance. Ifa series of surfaces be confocal, their reciprocal sur- faces, taken with respect to any given sphere, will be condi- rective. When the equations of any two condirective surfaces are expressed by coordinates perpendicular to their principal planes, the constants in the equations may be always so taken that the differences of the coefficients of the squares of the variables in one equation shall be equal to the corresponding differences inthe other. ‘Then by subtracting the one equa- tion from the other, we get the equation of a sphere. There- fore when two condirective surfaces intersect each other, their intersection is, in general, a spherical curve. But when the surfaces are two paraboloids of the same species, their intersection is a plane curve. 507 § 18. Through any point S of a given surface four bifo- cal right lines may in general be drawn. Supposing the surface to be central, let a plane drawn through the centre, parallel to the plane which touches the surface at S, intersect any one of theseright lines. Then the distance of the point of intersection from the point S will always be equal to the primary semiaxis of the surface.* If through any point S of a given central surface a right line be drawn touching two other given surfaces confocal with it, and if this right line be intersected by a plane drawn through the centre parallel to the plane which touches the first surface at S, the distance of the point of intersection from the point S will be constant, wherever the point S is taken on the first surface. If this constant distance be called Z, and the other denominations be the same as in the formula (7), the value of Z will be given by that formula.+ Professor Mac Cullagh communicated the following note relative to the comparison of arcs of curves, particularly of plane and spherical conics. The first Lemma given in my paper on the rectification of the conic sections (Transactions of the Royal Irish Aca- demy, vol. xvi., p. 79) is obviously true for curves described on any given surface, provided the tangents drawn to these - curves be shortest lines on the surface. The demonstration remains exactly the same; and the Lemma, in this general form, may be stated as follows. Understanding a tangent to be a shortest line, and sup- posing two given curves E and F to be described on a given * Exam. Papers, An. 1838, p. xlvii., quest. 9. Tt In the notes to the last mentioned work of M. Chasles, on the History of Methods in Geometry, will be found many theorems relative to surfaces of the second order. Among them are some of the theorems which are given in the present paper ; but it is needless to specify these, as M. Chasles’s work is so well known. 508 surface, let tangents drawn to the first curve at two points T, ¢, indefinitely near each other, meet the second curve in the points P, py. Then taking a fixed point A on the curve E, if we put s to denote (according to the position of this point with respect to T) the sum (or difference) of the arc AT and the tangent TP, and s + ds to denote the sum (or difference) of the arc A¢ and the tangent ¢p, we shall have ds equal to the projection of the infinitesimal are Pp upon the tangent; that is, if a be the angle which the tan- gent TP makes with the curve F at the point P, we shall have ds equal to Pp multiplied by the cosine of a. Now through the points P, p conceive other tangents T’P, t’p to be drawn, touching the curve E in the points T’, ¢’; and let s’ and ds’ have for these tangents the same signification which s and ds have for the former tangents. Supposing the nature of the curve F to be such that it al- ways bisects, either internally or externally, the angle made at the point P by the tangents TP and T’P, it is evident that ds = + ds’, and therefore either s + s’ or s — s’ is a con- stant quantity. A simple example of this theorem is afforded by the plane and spherical conics. If the curves E and F be two confocal conics, either plane or spherical, and tangents TP, T’P be drawn to F from any point P of E (the tangents being of course right lines when the curves are plane, and arcs of great circles when they are spherical; in both cases shortest lines) it is well known that the angle TPT’ made by the tangents is always bisected by the conic E. The angle is bisected internally or externally according as the conics intersect or not. Hence we have the two following properties* of confocal conics :— * The first of these properties was originally given for spherical conics by the Rev. Charles Graves, Fellow of Trinity College, in the ‘notes and addi- tions” to histranslation of M. Chasles’s Memoirs on Cones and Spherical Conics, ; ; 4 é 509 1. When two confocal conics do not intersect, if one of them be touched in the points T, T’ by tangents drawn from any point P of the other, the sum of the tangents TP, T’P will exceed the convex arc TT’ lying between the points of contact, by a constant quantity. 2. When two confocal conics intersect in the point A, if one of them be touched in the points T, T’ by tangents drawn from any point P of the other, the difference between the tangents TP, T’P will be equal to the difference be- the arcs AT, AT’. These properties give the readiest and most elegant so- lution of problems concerning the comparison of different arcs of a plane or spherical conic. Any are being given on a conic, we may find another arc beginning from a given point, which shall differ from the given are by a right line if the conic be plane, or by a circular are if the conic be sphe- rical. DONATIONS. Memoires de la Société Géologique de France. Tom. 5. Parts 1, 2. Presented by the Society. The Tenth Annual Report of the Royal Cornwall Poly- technic Society. (1842.) Parts 1 and 2. Presented by the Society. Bulletin de ? Academie Royale de Bruxelles, from 5th of November, 1842, to 8th of July, 1843. p- 77 (Dublin, 1841). Mr. Graves obtained it as the reciprocal of the pro- position, that when two spherical conics have the same directive circles, any tangent arc of the inner conic divides the outer one into two segments, each of which has a constant area. Both properties, with the general theorem relative to curves described on any surface and touched by shortest lines, were after- wards givenin the University Calendar. See Exam. Papers, An. 1841, p. xli., quests. 3-6; An. 1842, p. Ixxxiii., quests. 30-34. These two properties of conics were communicated, in October 1843, to the Academy of Sciences of Paris, by M. Chasles, who supposed them to be new. See the Comptes rendus, tom. xvii. p. 838. 510 Ordnance Survey of Tipperary, in 93 Sheets, including Title and Index. Presented by His Excellency the Lord Lieutenant. Oberon’s Vision in the Midsummer Night’s Dream. Wlus- trated by the Rev. N. J. Halpin. Presented by the Author. Oversight over det Kongelige Danske Videnskabernes Selskabs Forhandlinger og dets Medlemmers Arbeider, 1 Aaret, 1841. By Professor Oersted. Presented by the Author. The Numismatic Chronicle and Journal of the Numisma- tic Society of London for July, 1843, (No. 21). Presented by the Society. PROCEEDINGS THE ROYAL IRISH ACADEMY. 1844. No. 43. January 8. SIR Wm. R. HAMILTON, LL.D., President, in the Chair, William Henry and John Neville, Esquires, were elected Members of the Academy. The President read a letter from the Rev. James Ken- nedy Bailie, D.D., presenting his “ Fasciculus Inscriptionum Grecarum.” The special thanks of the Academy were given to Dr. Bailie for his donation. Robert Ball, Esq., read a notice of the Means used by the Ancients for attaching Handles to the Stone and Meta Implements called Celts. Mr. Ball stated that many years since, the lamented Dean Dawson proposed to him to put handles to the four most re- markable forms of celts, witha view of discovering the probable manner in which these instruments were used. He accord- ingly did affix the handles (exhibited to the Academy), and they appeared satisfactorily to answer the question: but re- cent observation has convinced him that in two at least of these hypothetical mountings he was incorrect, as proved, he thought, by a stone celt mounted, which was a short time since brought from a mine in Mexico, and an iron one—a war weapon—brought a few weeks since from Little Fish Bay in Africa. As he deemed the subject one of interest to VOL, Il. 2x 512 antiquarians, he described as follows the mounting of the recent implements alluded to, which, he conceived, may fairly be assumed as the manner used in olden time for celts of similar form. 3 INCHES. The Mexican stone celt (No. 1) (whichis the property of Mrs. Lyle) was mounted by placing a slender rod ateach side se 513 of it, in the direction of its length, so that the larger ends of the rods would have overlapped each other about two inches, had they not been separated by the body of the instrument ; a small cord was then loosely wound round the ends of the rod and the included celt: when thus arranged, the smaller ends of the rods were brought together and tied, forming what sailors call a Spanish Windlass, The elasticity of the rods keeping a constant strain, makes a more effective handle than it would appear possible to form by ordinary tying, and with much less expense of time and trouble. The iron celt (No. 2) kindly given to Mr. Ball by Captain Adams, R.N., is fixed in the bend of a club formed like a Scotch golf stick ; by this arrangement, while the iron is so fixed that a stroke serves to make it only the faster, the effectiveness of the weapon is much increased by the weight of the knob at its end. The accompanying figures illustrate the foregoing. Mr. Ball observed that these were, he thought, proofs of the value of seeking explanation of antiquarian difficulties, by observing the analogies afforded by the less civilized por- tions of the human race, rather than by indulging in hypo- thetical fancies. Mr. Oldham read a brief notice of a stone with Ogham characters in the County of Waterford. The stone referred to (fig 1) is well known throughout that portion of the country, by the name of Ballyquin stone. It stands on the road to Curraghmore from Carrick-on-Suir, about three miles and a half from that town. This road is comparatively a new one, and the stone has been left standing about three feet from the ditch on the south side. It isa single block of the hard and coarse red conglomerate, so abundant in the neighbourhood, and in the adjoining range of the Commeragh mountains. In height it is eight feet, and tapers gradually but irregularly from about four feet at the base, to about one foot three inches at the top, and is about 2x2 514 one foot or a little more in average thickness. The sides of the stone are rough, and do not exhibit any trace of chisel- ling or tooling, further than possibly a rude dressing with Fig. 1. the hammer; but along the south east corner of the stone (as it now stands), and extending from the summit to near the base, are a series of Ogham characters of peculiar interest. ‘These have been carefully worked, the bottom of 515 the cuts or grooves which form them being quite smooth and even, notwithstanding the very unfavourable texture of the stone, composed as it is of pebbles varying in size, compo- sition, and hardness. Some of these markings or letters are imperfect, from injuries which the stone has received, or from wear by exposure, but the drawing (fig. 1) gives a tolerably accurate idea of its present state. This Ogham differs in some respects from any with which Mr. Oldham was acquainted. There is no combination of more than four letters or grooves in it, and if the corner of the stone be considered the centre line, to which these let- ters should be referred, several of them do not come up to that line, and in one case two appear interrupted or discon- tinued in the centre; that is, there are portions of the cut or groove corresponding to each other at both ends, but they do not pass over the corner or central line. Mr. Oldham’s object was, however, more particularly to add another to the collection of Ogham inscriptions, and thus increase the data from which some clue to these now unknown quantities might perhaps be obtained. He was the more anxious to do this, as this stone had been altogether omitted on the Ordnance Maps of the County of Waterford recently published. This stone is mentioned by Ryland in his History of Wa- terford, who merely notices the existence of some defaced markings. He alludes to the occurrence of caves in the fields adjoining. Ballyquin is also the name of the town- land in which the stone stands. Mr. Oldham also presented drawings of some Oghams now in the Cork Institution, and remarked how very desirable it was that they should be published at once, the originals being so liable to injury, either from accident or design. Fig. 2, is a block of sandstone, very rough and unhewn, the surface on which the letters or marks are cut being the only flat one on the stone. It is about four feet six inches in 516 length, of which the letters extend two feet ; one foot ten inches broad at the top, and tapers rudely to the base. Fig. 3 was “ dug out of an ancient fort or rath at Burnt- fort, near Mallow, in the County of Cork, on the property of H. Purcell, Esq.” It is of taleose mica slate, coarse-grained ; the broad face is exceedingly rough and uneven; the nar- row one more smooth and regular, being the natural cleavage of the rock. It is nearly seven inches wide on the narrow side, and fifteen on the broad, and about five feet high along, being nearly a parallelogram. The cuttings are nearly similar throughout in depth and care of execution. Fig. 4 was found at Glounaglough, parish of Aghabolloge. The entire stone is five feet seven inches long ; eleven inches and a-half broad at top, and nearly nine at the bottom. It is of a clayey-slate rock. The letters do not extend further down the stone than one foot ten inches; it is nearly of the same thickness all through, forming a thin slab. On the face of the stone there are scrapings, and the lower letters are a ee EE ——— 517 not formed by a regular groove, as the upper are, but have all the characters of such scratches as would be formed on a stone by sharpening knives or other edged tools. Fig. 4. ~ Fig 5. ret) 4%, HWM, Mi Fig. 5 is of sandstone, rudely chiselled on the faces and sides, and roughly rounded on the corners of the back, the back itself being flat. It is two feet eight inches high; eleven inches and a-half at the broadest part, and about seven inches thick. In shape it has a rude resemblance to the ordinary form of a coffin. The letters are distinct grooves, but they do not appear to be all of the same age, as some are very evidently new or recent, and, as in Fig. 3, very similar to the scratches formed by sharpening tools. The Cork Institution is indebted to the zeal of Messrs. Windele and Abel for these valuable Ogham stones. Dr. Apjohn read a notice, by the Rev. Thomas Knox, on Cyanogen, as a Food for Plants. 518 Liebig having proved in his work on Agricultural Che- mistry that the nitrogenous compounds of vegetables are de- rived principally from the decomposition of ammonia, and that the carbon is derived from the carbonic acid of the at- mosphere, it occurred to me to try (while experimenting on some manures) whether a source of each might not be found in some salt of cyanogen (c,n). This, I think, the following facts will make probable. The salt I used for this purpose was the ferro-cyanuret of potassium, (K, Cfy = Ce N; a Fe + Ks EXPERIMENTS. A piece of grass was selected in the garden, as being as even and equal as possible, and five plots were marked out on it, side by side, each containing exactly ten square yards; they were marked out by pegs in the corners, and a line put round each while the salts were putting on, and during the cutting of the grass. They were then manured as follows, on the 17th of June last: No. 1. Muriate of Ammonia, 3 oz. 2, Aqua Ammonia of the shops, 3 a pint; with Linseed Oil, 4 pints. 3. Nothing. 4. Yellow Prussiate of Potash, 3 oz. In the usual state, as sold by druggists, in crystals. Phosphate of Soda, 13 oz. Pearl Ash, 3 oz. Sulphate of Magnesia, 13 oz. Carbonate of Ammonia, 3 oz. The salts on these two last plots were not laid on till the 26th of June, which gave them a slight disadvantage. They were all mown on the 25th of September, and weighed fresh the moment they were cut, when the weights were as fol- lows: 519 No. 1. 23% lbs. when dry 7% lbs. 2. 19 9 53 3. 213 Me 6} 4. 325 7 93 5. 283 “ 83 I cannot depend on the dry weight, nor draw any conclu- sions from it, though it follows nearly the same proportion as the fresh grass; the weather had been very wet, and it had been left too long exposed to it. The great advantage of the plot manured with the prus- siate of potash over the others is very remarkable; for about a month it seemed rather inferior to that manured with the muriate of ammonia; but after that time the difference be- came very perceptible to the eye or foot. The final advantage of No. 4 above No. 1 is at the rate of 38 cwt. of fresh grass, or 8} cwt. of dry grass to the acre. The reason of this superiority cannot arise from the nitrogen alone, as the quantity of it in the three ounces of muriate of ammonia (applied to No. 1) actually exceeds that in the three ounces of ferro-cyanuret of potassium, in the proportion of 13 to 11. It must, therefore, be sought for in the other ele- ments of the salt. Supposing this salt to be absorbed by the plant, and decomposed in the same manner as the ammoniacal salts, the plant will then obtain carbon and potash, as well as the nitrogen, in the nascent state, which seems to be the only way in which carbon can be assimilated. In fact almost every element required by the plant is contained in this one com- pound, and obtained by one and the same decomposition. I beg leave to lay these facts before the Academy, as they may prove interesting to those engaged in the subject of manures, and may tend to throw a little further light on the subject of the food of plants, should they be confirmed on repe- tition ; but I fear they can be of no service to the practical agri- 520 culturist, from the high price of all the compounds of cyanogen. Mr. George Yeates read a paper containing the results of a Meteorological Journal for the year 1843.—See Appen- dix V. The Rev. H. Lloyd communicated a letter written many years ago to his father, the late Dr. Lloyd, Provost of Trinity College, by Mr. Mac Cullagh, who was then a Fellowship-Candidate in the College. It relates principally to a mechanical theory (that of the rotation of a solid body) which Mr. Mac Cullagh was occupied with at that period, and which he had occasion to allude to at the last meeting of the Academy. The following is an extract from the letter. The beginning and the date are wanting. «“ THEoREM I.—If a rigid body, not acted on by any extraneous forces, revolve round a fixed point O, and if an ellipsoid be described having its semiaxes in the direction of the principal axes passing through O, and equal to the radii of gyration round them ; thena perpendicular to the invariable plane being raised from O to meet the surface of the ellipsoid in I, the line OI (which is fixed in space, as the ellipsoid revolves with the body) will be of a constant length during the motion ; and a perpendicular from O upon the plane which touches the surface at I, will always be the axis of rotation, and will vary inversely as the angular velocity. ‘ “ Corollaries. “<1. Since every radius which is nearly equal to the greatest or least semiaxis of an ellipsoid must lie near that semiaxis, it appears that if, in the beginning of the motion, the point I be near the vertex of either of these semiaxes, it will always be near it, since OI remains constant ; and therefore, by the preceding construction, the axis of rotation will always remain near the same semiaxis. Hence the ro- tation about the axes of greatest and least moment in any body is stable. The rotation about the axis of mean moment is unstable, because the radii of an ellipsoid, which are nearly equal to the mean semiaxis, do not alllie near that semiaxis. ° ~ eT So ee 521 ‘« These things are evident from considering the trace of the con- stant line OI on the surface of the ellipsoid, and observing that, in general, its projection on the plane of the greatest and least axes is a hyperbola, and its projections on the other two planes ellipses. “2, Butif OI be equal to the mean semiaxisb(aand c being the greatest and least) it will always intersect the body in the same plane, and the ellipsoid in a circle. For there are two circular sections through the mean axis; and therefore if the point I be at any instant in either of them, it will remain in it during the motion. It would be easy to show also, that the axis of rotation, connected with OI by. the construction in the proposition, will in this case always remain in a given plane within the body. «3, If two axes (or moments) of the ellipsoid are equal, OI will describe in the body a conical surface round the third, and the axis of rotation will always be in the same plane with OJ and that third axis, and these three lines will make constant angles with each other ; also the perpendicular on the tangent plane, and therefore the - angular velocity, will be constant. These things are evident merely from considering that the ellipsoid becomes one of revolution. “4, Whatever be the forces applied to the body, the varying plane of the maximum of areas and the axis of rotation are always con- nected by the construction in the proposition. But the angular velocity is no longer inversely as the perpendicular, « To find the axis about which a body restrained by a fixed point O, and acted on by given forces, will begin to revolve, is usually considered a problem of great complexity. But it may be elegantly solved by means of the ellipsoid described above. Reduce the given forces to a single one through the fixed point O, and a pair; raise a " perpendicular to the plane of the pair from O to meet the ellipsoid in I; a perpendicular from O to the tangent plane at I will be the initial axis of rotation. “« The construction is true whether the forces that set the body in motion be impulses or pressures. If they be impulses, and ro external forces subsequently act on the body, the axis of rotation will vary its position both in the body and in space ; its course in the body is determined by the preceding theorem, as well as the variation of the angular velocity. The motion of the body in space depends mainly on the two following theorems and the rectification of the ellipse. 522 Let the principal axes of the ellipsoid (or c Q a,b, c) be OA, OB, OC. “ Turorem IJ.—If a perpendicular IP * , be let fall from I on any of the principal \ planes (as AOC), the areolar velocity of P = round O will be proportional to the perpendicular IP. «« By areolar velocity I mean the increment of the area (as POp) divided by the increment of the time when taken indefinitely small. «Since IP = »/(OI* — OP”), the position of OI, and therefore of the axis of rotation at any given time, may be determined from this~ theorem by the method of quadratures; and it may be reduced to the rectification of the ellipse. « TueoreEM .III.—Let a plane passing through the fixed line OI and any of the principal axes (as OB), intersect the plane AOC in OQ, and the invariable plane (to which O1 is perpendicular) in a straight line which may be called OR; the angular velocity of OR is inversely as the square of OQ; and hence if OR be always taken equal to OQ, the point R will describe in the invariable plane areas proportional to the times. “ Since OQ is known at any time by the preceding proposition, the position of OR at any time will be known from this by the me- thod of quadratures. Also the inclination of the plane AOC to the invariable plane is known, since it is equal to the angle OIP. Hence the position of the body at any instant is completely deter- mined. ‘“‘ For an application of the theoremslet us take the following prob- lem :—-The body revolving round a line indefinitely near the greatest or least of the principal axes, to find the time of an oscillation. By the time of an oscillation I mean that in which OI, and consequently the axis of rotation, returns to the same position within the body. ‘« Let the axis of rotation be indefinitely near OA. Then a, y, 2 being the coordi- nates of I, we have 2? + y? + 2 = OP = RF’, a y 2 and 7 + - + a> 1. Therefore (p= a)r+(g-s)eni-$ Hence the locus of P is an ellipse whose semiaxes a/ and b/ are by (at — ie ang 2. (@ — #) (a — V@—e)’ and therefore its area abe (a* — k*) ral = « But I ought to have mentioned, as part of Theorem II., the me- thod of determining in general the areolar velocity of P. Let the angular velocity multiplied by the cosines of the angles which the axis of rotation makes with OA, OB, OC be denoted (as is usual) by P,%,7- These have constant ratios to the perpendiculars, as 1P drawn in that proposition ; and in that case the areolar velocity of P is equal to 4 (b? — k*)g: and similarly when AOC is any of the other principal planes. Hence, in the present instance, the areolar velocity = 4(a* — k*)p; and therefore the time of an oscillation 2Qxrbe ~ pV —Be— a) from the above value of the area of the ellipse, and observing that, since OI is indefinitely near OA, IP and therefore p may be re- garded as constant. “If T denote the time of one revolution of the body round its axis, then ultimately T = = and therefore the time of an oscilla- tion is to the time of a revolution as the rectangle under the semiaxes of the section BOC is to the rectangle under the eccentricities of the other two sections. A similar theorem holds when the body re- volves round a line indefinitely near the least principal axis. The times of small oscillations of different magnitudes are equal, as in the pendulum. ‘* Many particular consequences might be deduced from what has been said; but it will be better to mention some new theorems about moments of inertia and centrifugal forces. 524 “‘ The forces resulting from the centrifugal forces of abody of any figure, revolving round an axis passing through a fixed point O, may be found elegantly by the ellipsoid of which we have already made so much use. Leta plane at right angles to the given axis OK, and cutting it in K, touch the ellipsoid : in I; the centrifugal forces will be re- duced to a pair whose moment is OK X KI x «®* (# being the angular velocity), whose plane is OKI, and direction as marked in the figure ; and a single force equal to Mpa*, p being the distance of the centre of gravity from OK. « If OK pass through the centre of gravity, there remains only the pair. The perpendicular OK is the radius of gyration for the axis OK. Particular consequences of these things are numerous. « Any line, taken at random in a body, may not be a principal axis. All the principal axes parallel to a given line lie in the same plane; and the points of their lengths which must be fixed, in order that they may be principal axes, will lie in a hyperbola. Suppose in this case the point O (preceding fig.) to be the centre of gravity, and OK to be parallel to the given line, and describe through I an equilateral hyperbola whose asymptotes are OK and OL; then all the principal axes, as O/K’, O”K", parallel to OK, lie in the plane OKI, and the points O’, O” of their lengths, which must be fixed, are at their intersections with the hyperbola. «By means of theorems of this nature, all of which are proved geometrically, without any calculation, I have been able to give a complete geometrical solution of the problem of the motion of a solid body not acted on by any forces. If it be acted on by given forces, the differential equations in A, B, C and p, g, 7, which are given by all the writers on mechanics, are direct consequences of the first principles, without the intervention of any calculation. * * * * * * ~« « Another thing with which I had occupied myself is the attrac- * Multiplied by the mass of the body, or by M. ee ET Pe A Tr s eee ee or 525 tion of ellipsoids. Having written out a simple demonstration of a very elegant known theorem relating thereto, I shall subjoin it sepa- rately. * * * * * * * * « The proposition above alluded to depends on the following theo- rem, which may be very simply proved :—If from the extremities A, B, C of the semiaxes of an ellipsoid whose centre is O, there be drawn three parallel chords Aw, Bg, Cy, meeting the surface of the ellipsoid in «, 6, y; and if a perpendicular from « on OA meet it in 7, a perpendicular from 6 on OB meet OB in s, and athird from y on OC meet OC in ¢; then will Ar . Bs. Ct Aa’ * BB t+ to AA’, BB’, CC’ are the whole axes. “ The proposition itself is this :—If the particles of a homogeneous ellipsoid attract inversely as the square of the distance, and if a, b, c be the semiaxes, and A,,B,,C, its attractions on points placed at their vertices, then will =e! Ao By Cy = ig tin te FH “ The attractions are here, as is usual, represented by lines; the attraction of an indefinitely small part of the solid being represented by its volume divided by the square of its distance from the attracted point. « The attraction being thus measured, it is evident that if from the vertex of a pyramid, whose transverse sections are indefinitely small, as a centre, with any radius, a sphere be described whose surface is penetrated by that of the pyramid, the attraction of the pyramid on a point at its vertex will be to its length, as the intercepted surface of the sphere is to the square of its radius. ‘Let A, B,C be the three vertices of the axes, and from them let parallel chords Az, Bg, Cy be drawn; from whose extremities a, 8, y let perpendiculars be let fall on the respective axes, meeting them in r, s,t; then by the preceding theorem 526 Ar Bs Ct AA BB. eo Let now two other chords be drawn from A making with Aw very small angles, so as to form with it the edges of a very small pyramid, and let other chords parallel to them be drawn from B and C, forming also with Bg and Cy the edges of two other small pyramids, Ima- gine a sphere fixed in space, from whose centre are drawn three lines parallel to the three chords drawn from A, or from B, or from C, and conceive the surface of the pyramid, of which they are the edges, to penetrate that of the sphere ; then will the attractions of the three py- ramids, reduced each to the direction of the axis passing through its vertex, be to Av, Bs, Ct as the intercepted surface of the sphere to the square of its radius ; and therefore the sum of each of those at- tractions, divided respectively by AA’, BB’, CC’, will be to unity in the same ratio. Conceive pyramids thus related to be multiplied in- definitely, and the spheroid will be exhausted at once from each of the three points A, B, C, while half the surface of the sphere is exhausted by the parallels drawn from its centre. Hence it appears that the sum of the whole attractions at A, B, C, divided respectively by AA’, BB’, CC’, is to unity as the surface of a hemisphere to the square of its radius, or as 24 to 1; and therefore Ay By Cy acta 5 + eal January 22. REV. James H. TODD, D. D., Vice-President, in the Chair. Mr. W. H. Hudson exhibited specimens of Irish books, now in the course of publication in Cork, which are litho- graphed. He described the advantages which that process presents over types, for composition in the Irish character. Dr. Kane read a paper on the Chemical Composition of the different kinds of fuel found in Ireland. 527 Although this country is recognized as destitute of the great development of the coal strata, which has proved so important an element in the industrial progress of Great Britain, yet there are known to exist several coal districts, some bituminous and some anthracitous, as well as deposits of wood coal, which, with the great extent of turf-bog occu- pying the surface in many places, may be considered as stores of fuel, available and sufficient for the supply of the interior of the country for a very long time. In order, however, to be able to calculate the economic value, or calorific power*of any of these Irish fuels, and so to compare them with the corresponding fuels in other countries, it was necessary to know their elementary composition ; and hence, in order to lay the basis of a true estimate of the worth of our native fuels, Dr. Kane commenced the series of analyses which formed the present communication. In order to exhibit all the relations of the composition of these fuels, that might be useful in drawing practical con- clusions, Dr. Kane adopted two distinct modes of analysis: one, exhibiting the real elementary composition; the other, which he terms the practical analysis, representing the rela- tion of the ashes, and of the fixed and volatile constituents of the fuel. He also in each case ascertained the quantity of oxygen which the fuel was capable of taking up, in order to be perfectly consumed. As the analysis of fuels is known to present some difficulty, it is necessary to mention briefly the precautions taken in order to secure accurate results. The point first determined was in each case the quantity of ashes present. To effect this a certain weight of the fuel was burned in a current of hot air, until all traces of organic material disappeared. The residual ash was then weighed. To conduct the determination of the carbon and the hydrogen of the fuels, the methods were varied according to the nature of the substance, with turf, lignite, and the bitu- minous coals. The proper weight of the material having VOL, II. 2Y 528 been dried at 212° F., was in some cases mixed with chromate of lead, and the analysis conducted in the ordinary manner ; in other cases, the substance was mixed with black oxide of copper, and some chlorate of potash having been placed in the end of the analysis tube, the operation was conducted in the usual way to near the termination, when the chlorate of potash being heated, a stream of oxygen gas passed through the apparatus, and burned out the last traces of the organic substances. “These two modes gave almost identical results with the same fuel, and there is no necessity for distinguishing amongst the analyses, of which the results follow, those that were done in the one way or in the other. It was found, however, that the anthracite could not be perfectly analysed by either of these modes: the difficulty of burning away the last portions of the carbon was so great. Hence a totally different plan was adopted for that variety of fuel. An analysis tube of Bohemian glass having been taken about a foot long, the substance to be analysed was placed in a little boat of platina foil, and introduced into the tube nearone end. ‘To this end was fitted a tube containing dry chloride of calcium to collect the water ; then the potash absorbing apparatus, then another potash absorbing appa- ratus, and finally a tube containing dry potash. These three were for the purpose of separating the carbonic acid perfectly from the excess of oxygen, and also to prevent the oxygen from carrying away any moisture from the potash liquor. The other end of the tube was connected with a gazometer full of pure oxygen gas, which, streaming over a large sur- face of fused chloride of calcium, was rendered perfectly dry. The apparatus being so adjusted, the analysis tube was heated to redness by charcoal, so that the oxygen gas passed through five or six inches of red hot tube before coming to the ignited anthracite. The analysis was thus conducted, as it were, with the hot blast, and the combustion was in all cases quite perfect. This kind of process would 529 only answer with such fuels as anthracite, which contains very little hydrogen, but with those it succeeded perfectly. Such were the means taken for the organic elementary analysis. The nitrogen was not separately determined, as the results were only required for economic calculations, and the minute trace of nitrogen does not there become impor- tant. Its weight (in all cases very small) is included in the number assigned tooxygen in the results of the analyses. The practical analysis was conducted by very strongly igniting a weighed portion of the fuel in a platinum crucible the cover of which fitted so closely as to prevent any sensi- ble combustion of the residual coke. The weight of ashes being known, the pure coke was then found. The determination of the reducing power of the fuel by means of litharge, requires very considerable care in prac- tice in order to get satisfactory results. The principal point to be attended to, is to use a roomy crucible, and to apply a quick and strong heat, so that the litharge shall at once run thin. When this is done, the results with the same fuel are very uniform, and with different fuels are fully comparable ; although in no case is so much lead got as should be in theory obtained from the conversion of the carbon and hydrogen of the fuel, minus its oxygen, into carbonic acid and water. The deficiency is usually proportional to the quantity of volatile matter in the fuel, and is not in any case large, provided proper care be taken. Hence Dr. Kane considers, and the opinion is also held by Berthier, that the result is so near the truth as to be quite available as a prac- tical and ready measure of the heating power of the fuel. The general nature of the inquiry, and the methods em- ployed, having been thus described, it is only necessary to add the numerical results of the analysis. In order that the results might represent as far as prac- ticable the average composition of the fuel, in each case rather a large mass was broken up, and its coarse powder 2x2 530 well mixed. Some ounces of this were then reduced to impalpable powder, and from this all the portions to be operated upon were taken. I. ANTHRACITES OF THE SOUTH OF IRELAND. Three specimens of this kind of coal were analysed: 1, from the Rushes Colliery, Queen’s County ; 2, ,, the Pollough Vein, Castlecomer, Co. Kilkenny; 3, 5, the Sweet Vein, Kanturk, County Cork. The anthracites have no tendency to froth or cake in cokeing. They give off little or no inflammable gas on being ignited, but usually the masses break up quite small, espe- cially if the heat be suddenly applied. The ashes are almost always red, owing to peroxide of iron remaining after the combustion of the iron pyrites, which the anthracite gene- rally contains. Rushes anthracite—0.375 grammes gave: Water: 2 filets pectt-cgagp Qh ls Carbonic acid. . . . 1.238 Light red ashes . . . 0.014 The Pollough anthracite. 0.364 grammes gave : TV BN cat cents wot oe eee Carbonic acid . . . . 1.086 Brownashes . .. . 0.036 The Sweet Vein anthracite—0.293 grammes gave : WW akee oo) elite £°.) 4) OES Carbonic acid. . . . 0.928 0.305 gave . . . 0.026 ashes, white. These coals consisted, therefore, of : Rushes. Pollough. Sweet Vein. Carbon. . =. s; . 90.04 81.36 86.37 Hydrogen. . . 3.50 2.41 3.71 yren. oe. tp aS 6.34 1.40 Ue OES ae ae ee ' 9.89 8.52 100.00 100.00 100.00 531 Of these coals the Sweet Vein was perfectly free from sulphur; the Rushes coal contained but a minute trace ; but the Pollough coal contained a good deal, and as the sulphurous acid produced during its combustion should be absorbed by the potash, and counted as carbonic acid in the analysis, it was necessary to correct the above result by a direct determination of the sulphur. For this purpose 3.526 grammes of the coal were boiled with aqua regia, and the liquor precipitated by chloride of barium. ‘The sulphate of barytes obtained weighed 1.589 grammes, corresponding to 45.07 per cent., containing 6.18 of sulphur. Now, 6.18 sulphur give 12.36 sulphurous acid, and sub- tracting that from the carbonic acid obtained in the elemen- tary analysis, then converting the sulphur into bisulphu- ret of iron, and subtracting the pyrites from the ash, there comes out, as the true composition of the Pollough coal : Ash, free fromiron . . . 2.19 Bi-sulphuret ofiron . . . 11.58 Carbon | sie ah) ars ened a FEAR Hydrogen ..... . 24 Guymon: (C3620) cat. sess B40 ] giving of pure an- thracite 86.23. 100.00 It is interesting to contrast the composition of the really organic part of these three varieties of coal. Rushes. Pollough. Sweet Vein. Carbon. . . . 93.53 87.46 94,39 Hydrogen. . . 3.63 2.79 4.05 Oxygen... 2.84 9.75 1.56 100.00 100.00 100.00 By the praetical mode of analysis these coals were found to give, per cent. : . 532 Rushes. Pollough. Sweet Vein. Volatile matter . . 9.85 10.40 10.35 Pure coke . . . 86.42 19.71 81.138 esis. oes Ps ot aiken 9.89 8.52 100.00 100.00 100.C0 The result of ignition with litharge was, that One part of Rushes coal gave . 31.8 of lead. EGUOU CIE ob -o b es 6G «yep Mad hae Sweet Vein eh ere ee Hence they correspond respectively. 100 parts of Rushes to. . 93.5 of pure carbon. 100;.""~, fp 2 “salon... Acad sis 100 ,, Sweet Vein . 85.3 * And in average 100 parts of Irish anthracite may be consi- dered to possess a calorific power equal to 84 parts of pure carbon. II. COAL OF THE CONNAUGHT BASIN. The coals examined were all from the collieries of Brah- lieve mountain, forming the western division of the Lough Allen coal field. The specimens were furnished through the kindness of Colonel Jones, member of the Shannon Com- mission. The results were as follow : AUGHABEHY COAL, A rich, black coal, easily broken. Sp. gr. 1.274. When heated, it gives off a good deal of inflammable gas, and leaves a light grey, porous, coherent coke. Its elementary analysis was effected : 0.472 grammes gave: Carbonicacid . .. . . 1.379 grammes. Whaver sot seams rte te) te Cees a 0.921 grammes gave of white ashes, 0.099, or 10.75 per cent. . ——— lience it contained: SN ORR eee etter AE aaa werner FP . ROOD sc ne 8 tee, ae Pa ss se 8 ee a 100.00 ROVER COAL. This coal is rather brown in aspect, and splits easily into cubical fragments. On ignition it gives out gas, but does not froth. Its coke is porous, slightly coherent. Its elementary analysis was : 3.196 grammesgave . . . 0.237 of ashes, equivalent to 7.41 per cent. 0.489 gramme gave: MRR 0) ale Pinca A sia tk i: e4 Mee lO Curie ein. Ge. 3 se fl ROS Hence it contained : IT! eve a a. ea au EIyGrOHe es en ok ee WRT eS et ce es es eee Ashes 14 od aN es, alias aN ge MRA CE 100.00 The practical analysis of these two coals gave the follow- ing results : Aughabehy Coal.—13.418 grammes gave on ignition 10.340 of coke. Rover Coal.—14.300 gave on ignition 11.770 of coke. Hence they consisted of : Aughabehy. Rover. Volatile matter . . . 23.10 . . 17.70 Pore coke. SS Pe. PEBAB OT *. 74.89 Reties 2 0%" eee eo “ewan uid at da 100.00 100.00 534 Specimens of coal from the Celtnaveena and the Meena- shama collieries were also examined in this manner, with the following results : Celtnaveena Coal.—l4.772 grammes gave by ignition 11.960 of coke. 1,091 gramme gave 0.164 of white ashes. Meenashama Coal.—6.280 grammes gave 5.095 coke. 3.778 gave 0.742 of ashes. Hence they consist of— Celtnaveena. Meenashama. Volatile matter . . . 19.10 . . 18.90 Pure Coke... «sos OBST... Sole Wale © eth ck co eae ee 100.00 100.00 Each of these varieties of coal was examined as to the quantity of oxygen it absorbed by reducing litharge. 1 part of Aughabehy coal produced 26 parts of lead. 1 part of Rover coal produced 284 parts of lead. 1 part of Celtnaveena coal gave 26 of lead. ] part Meenashama coal gave 25 of lead. 100 parts are therefore equivalent Of Skea to . 77 parts of pure carbon. Rover... . 84 - Celtnaveena . . 77 BA Meenashama . . 73 * These coals are similar in appearance to the Aughabehy, but are more slaty. When ignited they give off inflammable gas, but donot froth. Their coke is dense. It is thus seen that the Aughabehy is the most bitumi- nous of these coals, whilst the Rover is the least so, and that in fact the latter approaches closely in its composition to the anthracite of the Munster coal field. Ne ee ee ee SE Sle 535 Ill. COAL ON THE TYRONE BASIN. Of this locality two kinds of coal were examined, from opposite sides of the field, the new Drumglass Colliery, and the colliery at Coal Island. COAL ISLAND COAL. It is slaty in structure, dull coloured; sp. gr. 1.267. On ignition it gives off much gas, froths, and leaves a very porous coke. 2.814 gave 0.328 of ashes almost white. 8.830 grammes gave after ignition 5.390 of coke. It hence consisted of Volawle tustter .). . 4} 3 %..5 +- (88.06 RR Go ah ode Kah kody os ipo: MOE RN ie ad Marl Fada lira: va Shae 100.00 In its elementary analysis, 0.563 gramme gave: WIRE er di cee ee eee ee Ogee WApeemtG AGM SOc es ee ke oe Whence results the composition Carton tests Bo ieee Gel Uses) C808 PU VOROBEM Hines fou Sate tat ns ly ee Oxyoen ear ee es NSA 1 ed a ae ee aera a SA 100.00 On ignition with litharge, one part of this coal gave 264 of lead, hence 100 parts correspond to 78 of pure carbon. NEW DRUMGLASS COLLIERY. This coal is brilliant, black, friable, frequently mixed with pyrites, which oxidize on exposure to the air. Its ashes are consequently reddish. On ignition it gives off much gas, froths, and produces a light porous coke. Its practical analysis was as follows : 536 1.977 grammes gave of brown ash 0.342. 11.540 gave on ignition 5.920 of coke. It consisted hence of — Volatile matter . 2. -bs » «© > 48:70 Pure coke Sear tute Acard 1) secs Oa Ashes Reichs Vina coi) os | Abo 100.00. When ignited with litharge, one part produced 22 parts of lead. 100 parts of it are therefore equivalent to 65 parts of pure carbon. IV. COAL OF THE ANTRIM DISTRICT. The coal of Ballycastle is dull, black; sp. gr. 1.279. On ignition it gave out much gas, frothed, and left a porous coke. On its practical analysis it gave in 100 parts Volatile matter sn6 he. a.) eo Pre eee. 3h Nias GPS Rs ip Sa bos he MGenreag ee) Fe ila e@, fet ne, sets ie = yee La One part of it produced 25 of lead, and 100 are therefore equivalent to 715 parts of pure carbon. V. LIGNITES OF LOUGH NEAGH. Having thus determined the composition, and more im- portant practical relations of the coals from the several coal districts of Ireland, Dr. Kane proceeded to examine the nature of the deposit of lignite which is found among the tertiary beds along the southern extremity of Lough Neagh. As these investigations had solely a technical object, the silicified wood of that district did not require any notice, but only such wood-coals as were capable of use as fuel, Two specimens were examined. They retained all the structure of wood, and were of a deep brown colour. When ignited they gave off gas, which burned brilliantly, and left a dense black charcoal. On elementary analysis, they gave the following results : 537 No. 1.—1.887 gave 0.163 of a reddish ash containing much iron. 0.489 grammes gave: Water Gb wait KE. SG Cavboniciacid « .))0) 28) oa. od 050 No. 2.—3.393 grammes gave of slightly reddish ashes 0.550. 0.648 gramme gave RR, SO Se A ae & Fy) Carbonicacid . .. . - 1,220 These lignites consequently donetaesl of No. 1. No, 2. Capbony. Gf« fe is ke. BSG. cg BISG Ey ARO OR Yon vice, oss ern cl cane 7.33 Omggee 2 ib. wey tl, 26.85 25.08 AMES. VAY. | FR . SBF 16.21 100.00 100.00 The results of the practical analyses were as follows: No. 1. No. 2. Volatile matter .. . .. . 57.70 53.70 Pure charcoal . . . . . 83.66 80.09 AACS | ovens ee ee | 16.21 By ignition with petted No. 1 gave 194 parts of lead, and No. 2 gave 16.7 parts. They hence were equivalent in 100 parts. No. 1.—To 58 parts of pure carbon. No. 2.— ,, 50 os VI. TURE. The specimens of turf were selected from Cappoge, in Kildare, and Kilbeggan, in Westmeath, on different sides of the great Bog of Allen, and from Kilbaha, in Clare. When ignited, turf gives off inflammable gas, and leaves a light, easily combustible charcoal. The elementary analyses were as follows : KILBEGGAN TURF. .383 grammes gave : 538 WVaGeE hd gah RS eon y 300280. Carbonic avidhes woe dS... OBS Ashes® © c-> s4¢¢022 8 ee eo CR KILBAHA TURF. 3.435 grammes gave 0.277 of a light reddish ash. 0.663 gramme gave: Neier ee 2 Seo ts et Oseeees Oarboute acid)... syne sepeyihete CAPPOGE TURF. 10.566 grammes gave 0.270 of ashes. 0.500 gramme gave : Waiters. C9 UI A as Carbonie acid. « - . = + «,. 0.955 From these results follow the composition : Kilbeggan. Kilbaha. Cappoge. Carbon . . 61.04 51.13 51.05 Hydrogen . 6.67 6.33 6.85 Oxygen . . 80.46 34.48 39.55 Ashes. . . 1.83 8.06 2.55 100.00 100.90 100.0 In the practical analysis of turf it is necessary to attend to the physical constitution of the fuel, as, even with the same chemical elements, the heating power, and the proportion of fixed and volatile parts, will vary with the denseness of tex- ture of the fuel. Important differences exist also in the characters of the turf taken at different depths below the surface of a bog. These circumstances require to be care- fully attended to in practice. When ignited, there were obtained from specimens of light surface turf : Cappoge. Kilbeggan. Volatile matter. . . 73.63 75,50 Pure charcoal . . . 23.82 22.67 ARTES a7 Beal 8) needs Ameen 1.83 100.00 100.00 539 and from deep-seated turf, Kilbaha. Cappoge. Volatile matter . 72.80 70.10 Pure charcoal . 19.14 23.66 Mehbweigiers o>. 8:06 6.24 100.00 100.00 Of these varieties of turf it was found that on ignition with litharge, 1 part light Cappoge turf gave 13.0 of lead, l is Kilbeggan turf ,, 14.2 ,, 1 = Kilbaha turf ba > ROMER: oc, aS and hence that 100 parts corresponded, of Cappoge turf to 37 of pure carbon. Kilbeggan ,, 41 ,, 5, Fexthalias\)-., °° 40555, 0° 3 By means of these investigations Dr. Kane trusted that the chemical nature, and economic value of the fuels of Ire- land might be considered as established, and thus one step made towards a correct knowledge of the circumstances un- der which this country is placed as to those important mate- rials of industry. The question as to the extent of those deposits, the real quantity of each fuel available in practice, as well as the mode in which those deposits have had their origin, pass from the domain of chemical inquiry, and hence have been left by Dr. Kane to those geological philosophers whom the Academy proudly enumerates amongst its mem- bers. Dr. Apjohn and Mr. R. Mallet made some observa- tions. a PROCEEDINGS OF THE ROYAL IRISH ACADEMY. 1844, No. 44. February 12. REV. James H. TODD, D. D., Vice-President, in the Chair. Henry Clare, Esq., was elected a member of the Aca- demy, and the Rev. Charles Graves was elected a member of the Committee of Polite Literature. ¥ > Mr. Ball made a communication on a collection of the Irish names of animals, which he had been for many years collecting from ancient manuscripts, dictionaries, persons speaking the Irish language at present, &c. He stated that for one important addition he was indebted to Mr. Curry, who pointed out in a manuscript poem, said to be of the fifth century, ascribed to Caoilte, one of Finn Mac Coole’s heroes, and which is certainly older than the year 1000, a portion, in which the names of one hundred animals are recorded in a list of the ransom paid for the celebrated Finn Mac Coole, when a prisoner. Some of the names mentioned have not yet been translated. Mr. Ball observed on the value of such a collection as a means of throwing light on the names of places in Ireland, and urged the interest that naturalists of other countries felt, in preserving the names by which animals were known in their native places, as a sufficient reason for desiring to preserve those of Ireland. He stated his inten- tion of having the collection he had made properly digested 542 and arranged by a competent person, and that he would then offer it tothe Academy for publication. Professor Mac Cullagh made some remarks, of which the following is the substance, concerning the letter communi- cated by Mr. Lloyd at a former meeting (see Proceedings, p- 520). The letter read by Mr. Lloyd at alate meeting of the Academy, was written by me immediately after the examina- tion for Fellowships, which was held in Trinity College, in the year 1831. Ihad been a candidate on that occasion; and Dr. Bartholomew Lloyd, to whom the letter was ad- dressed, had been one of the examiners. The letter con- tains, among other things, several theorems taken froma geo- metrical theory of Rotation, with which I had been previously occupied. Soon after it was written, I returned to that theory, for the purpose of improving it in one part where I felt it to be defective, and where, indeed, I experienced the chief difficulty ; I mean the part which relates to finding the position of the body at any giventime. The method given in my letter for doing this by quadratures, had occurred to me in 1829 ; but I was, of course, not satisfied with it, and I had in the interval made some attempts to find a method more elegant, and, as far as possible, really geometrical. In the autumn of 1831 I succeeded completely in this, and no further additions of any consequence were made to the theory. The position of the line OI within the body, at any given time, was found by an elliptic function of the first kind, the modulus and amplitude of which are given immediately by geometrical considerations; the modulus of the function being in fact the ratio of the two moduli of the cone which that line, stationary in space, describes within the body. This result was deduced from Theorems I. and II. of the let- ter. Thecone reciprocal to that just mentioned was used to find the position of the body in space. This reciprocal cone, —_ i j 543 carried about with the body, always touches the invariable plane ; the side of contact, at any instant, being that which corresponds to OI, and which therefore lies in the plane passing through OJ and the axis of rotation. The angle de- scribed in the invariable plane by the side of contact is the sum or difference of two angles, one of which is proportional to the time, and the other is the angle described by that side in the surface of the cone. As the latter angle is measured by the are of a spherical conic, it followed, on comparing this result with the integral given by Legendre in his dis- cussion of the question of rotation, that the are of a spheri- cal conic represents an elliptic function of the third kind with a circular parameter. The curve described by the point I on the surface of the ellipsoid, is a spherical conic; and it now appears in what way the consideration of this mechanical question led to the study of the properties of cones and spherical conics. From theorems relating to centrifugal forces and principal axes of rotation, I was further led to consider systems of ellipsoids and hyperboloids having the foci of their principal sections the same; and then the focal curves presented themselves as the limits of these surfaces. The properties of the focal curves and of confocal surfaces occupied me, at intervals, in the year 1832 ; but in the latter part of that year my atten- tion was diverted from these subjects, and it was not until 1834 that I began to think of writing down and _ publishing the results of my inquiries respecting them. In doing so, I wished to be able to assign a geometrical origin to the sur- faces of the second order, the theory of these surfaces being intended to precede that of rotation; and in seeking for such an origin, I found the modular property. But not long after (in the summer of 1834) happening to look into a French scientific journal, I learned that M. Poinsot had just read to the Academy of Sciences of Paris a memoir in which he treated the question of rotation geometrically, by a method VOL. Il. 22 544 substantially the same as mine. This caused me to give up the design of writing on that subject; and, my thoughts then turning to the theory of light, the subject of surfaces of the second order was also dropped. Another form of Theorem I. is given by the property of reciprocal ellipsoids. Ifa second ellipsoid be constructed, having its centre at O, and its semiaxes coincident with, and inversely proportional to those of the first, and if this ellipsoid be touched by a plane parallel to the invariable plane, it is obvious, from the relations of reciprocal ellipsoids, that the tangent plane will be fixed in space, and that the right line which joins the point of contact with the point O, will always be the axis of rotation, and will be proportional to the angu- lar velocity. This form of the theorem, though not men- tioned in the letter, was nevertheless employed in my theory of rotation. Itis the form given by M. Poinsot, who uses only the second ellipsoid ; and it has the advantage of de- termining geometrically (as M. Poinsot has remarked) the successive positions of the body in space, independently of the consideration of time; for the ellipsoid evidently rolls upon the fixed plane which it always touches. ‘This advan- tage, however, though evident when stated, I do not recol- lect that I had distinctly perceived. The theorem mentioned in my letter, for finding the mo- ment of the centrifugal forces, is the same (making allowance for the difference of the ellipsoids) with one given by M. Poinsot, which he speaks of as ‘‘ a simple and remarkable theorem, containing in itself the whole theory of the rotation of bodies ;” and of which he further observes, as I have done, that “‘ translated into analysis, it gives immediately the three elegant equations which are due to Euler, and which are usually demonstrated by long circuits of analysis.” It was, in fact, from this theorem, by means of the principle of the composition and resolution of rotatory motions, that my theory, as well as that of M. Poinsot, was deduced. I may 545 add, that I also employed M. Poinsot’s beautiful theory of couples, which has introduced so much clearness into the fundamental doctrines of mechanics. Mr. G. Wilkinson read a paper on the existence of the pointed arch in the early buildings of Ireland, prior to the introduction of Gothic architecture. Mr. Petrie offered some remarks on Mr. Wilkinson’s com- munication. Dr. Allman noticed the occurrence in Ireland of Frederi- cella Sultana, and entered into certain details of its zoological and anatomical characters. This zoophyte has been very imperfectly described, and is moreover burthened with a dis- cordant synonomy which has involved its history in no small obscurity. The difficulty which is thus necessarily con- nected with the attempt to determine the true Fredericella Sultana, Dr. Allman endeavoured to remove, by reducing to some sort of order the mass of synonymes in which it is in- volved. It would appear to be the Tubularia Sultana of Blumenbach, its original discoverer; the Plumatella Gelat- énosa of Dr. Fleming; the Plumatella Sultana of Sir J. G. Dalyell; and the Fredericella Sultana of Gervais. It would appear also that the zoophyte described by Mr. Varley, in a late number of the London Physiological Journal, is the same as the present. By some singular oversight, Dr. Fleming, in the descrip- tion of his Plumatella Gelatinosa, refers to the Tubularia Gelatinosa of Pallas, described in the “ Elenchus Zoophy- tarum.” The Tubularia Gelatinosa of the Elenchus, how- ever, is quite a different animal; it belongs to the group with crescentic disks, and is identical with the free variation of Plumatella repens. The author, in entering into the details of its anatomical structure, drew attention to the high ascidiform type which 22z2 546 it presented. He also noticed a hyaloid membrane of great tenuity which surrounds the base of the tentacular plume, and extends upwards for about the fourth of the length of the plume, being adherent to the tentacula, and constituting a kind of calyciform appendage to the base of the crown. He mentioned the existence of this calyciform membrane in Plumatella and Cristatella, but would not speak positively as to its presence in Alcyonella ; from Paludicella it is cer- tainly absent, a fact which, along with several others, tends to approach this elegant zoophyte to the marine Ciliobrachi- ates. Dr. Allman also alluded to a singular valve-like organ with which the mouth is furnished, exactly similar to that found in Plumatella, and described by the Author at the late meeting of the British Association. This organ he has also detected in Cristatella. Through the external tunic of the polypidom will be found scattered, numerous silicious particles of no definite figure, and the Author considered himself justified, from the observations which he had made upon the fresh-water zoophytes, to come to the general conclusion that in the corneous polypidom of these animals, silica replaces the cal- careous deposits of the marine species. February 26. ROBERT BALL, Ese., Treasurer, in the Chair. The Secretary read a paper by the Rev. Dr. Hincks, « On the Defacement of Divine and Royal Names on Egyp- tian Monuments.” An attempt is made in this paper to specify the several occasions, on which the principal defacements of Egyptian 547 monuments took place; mentioning the principal ones which suffered on each occasion. The occasions specified are four. I. The dethronement or death of Q. Amuneth (circa 1325, B.C.), when her monuments were defaced by her brother Thothmos III. The propylon at Elassassif is the principal one defaced on this occasion. II. The change in the religious views of Amenothph IV. (the sun-worshipper of El Tell) (circa 1250, B. C.), which led him to deface all the figures and titles of the God Amoun, and all names of which his name formed a part. The monuments defaced on this occasion are referred to three classes. 1. Those which were never restored, as the lesser obelisks at Karnac. 2. Those in which the sun-worshipper substituted another name for what he defaced ; as ina cartouche of his own cited by M. Prisse, and in those of his supposed grandfather Amenothph III., where he substituted a repetition of the pranomen for the defaced phonetic name. 3. Those in which the names and figures that were de- faced have been restored by subsequent kings. Instances of this are the Lateran Obelisk at Rome, the great obelisks at Karnac, and those cartouches in which the name of Ame- nothph III. appears cut over the repetition of his przno- men; the latter having been previously substituted for the original name. III. The overthrow of the sun-worshippers and restora- tion of the worship of Amoun, on which occasion all the monuments of the intrusive worship were destroyed, as at Karnac, Gebel Tounh, and Ell Tell (a few years after the preceding occasion). The tomb of the king called Skhai, the father of the sun-worshipper, was violated at this time; and this was probably the occasion on which the royal name on the lion, presented by Lord Prudhoe to the British Museum, was obliterated. It was that of Amenothph IV. 548 IV. The hostility to the god Seth, Nahas, or Noubti, which arose in the minds of the Egyptian priests, and which led to the defacement of all monuments in which he appears as a beneficent god, and of his name when forming a part of names of kings. The time when this hostility arose, and the cause of it, are yet unexplained ; but it could not have led to this defacement sooner than 1100, B.C. This defacement is conspicuous on the statues of Menephthah III. at Turin and London, and the Flaminian Obelisk of Menephthah I. at Rome, and frequently at Karnac. It is incidentally mentioned that Pone, or Penne, is Lower Egypt; its extremities being mentioned in a papyrus in the British Museum in connexion with Ebo, or Elephantine, as the limits of Egypt. And the titles ‘‘ King of Penne,” ‘‘ King of the Pure Country,” which occur in the second car- touches of many Egyptian kings, are shewn to imply that the kings bearing those titles were only kings of parts of Egypt; a King of Penne, or Lower Egypt, like Horus, always imply- ing a King of Keme, or the pure country, #.e. of Upper Egypt, as Skhai and Amenothph IV. were. Mr. E. Clibborn made a communication respecting the Hycsos, or Shepherd Kings, tending to shew that they were descendants of Isaac. March 16, (Stated Meeting.) SIR Wm. R. HAMILTON, LL. D., President, in the Chair. Resotvep,—That the Rev. J. D’A. Sirr’s collection of Irish Antiquities be purchased on the terms recommended by Council. The terms being a payment of £350, the 549 cancelling of his arrears, and his being made a Life Member of the Academy. The Secretary of Council read the following Report : In presenting to the Academy the Report of Proceedings during the past year, the Council does not find it necessary to enter into much detail, as the events of that period have not been of any con- siderable importanceor unusual character. The Second Part of the 19th Volume’ of our Transactions has been published and distributed to the members of the Academy. The 20th volume, which will be altogether occupied by Mr. Petrie’s Essay on the Round Towers, is still at press. The delay in its pub- lication arises mainly from the number and importance of the artistic illustrations; and it is expected that the retarded progress of this work will be fully compensated for, in the opinion of the Academy, by its excellence, when brought out. Several Memoirs are already prepared and printed for the 2st Volume of the Transactions, and the Proceedings of last Session, which compose Part VIL. have been lately distributed to the mem- bers. Since the date of the last Report the attention of the Council has been given to the means of providing for the exhibition and guarding of the collection of Irish Antiquities. The plans proposed for this object have been already submitted to the Academy, but are not as yet in any way carried into effect; the Council being, on the one hand, restricted by want of funds, and, on the other, as it was found that the duration of tenure of the Academy House becomes uncertain after a few years, it was thought advisable not to expend much money on alterations in the building, until some definite ar- rangement had been made concerning its future tenure. For this purpose the Council have been in communication with the law agents of the Academy, but no decisive result has been as yet arrived at. It is a question of great importance to the Academy, for, at present, from the want of place for exhibition, the antiquarian treasures which we possess, and to which, we trust, each year will make large additions, are practically inaccessible to the public. Some of the 550 best evidences of the activity and utility of this Institution are hidden from the public eye, and thus the influence of the Academy, and its claims for public sympathy, are narrowed, and deprived of force. The Donations to the Antiquarian Museum during the past year have been few in number, most probably owing to the circum- stances just now described. The work of cataloguing the Irish Manuscripts in the library of the Academy is still in progress, but is expected to be terminated in a few weeks. The time occupied in this work, and the extent, three vols. folio, to which the Catalogue has gone, will be understood when it is considered that, not merely the name, but also an abstract of the contents of each MS. are inserted in the Catalogue, which will thus in itself become a very valuable addition to our library. About a year ago the Council received a communication from the Booksellers to the Academy, Messrs. Hodges and Smith, regard- ing the purchase of a collection of Irish Manuscripts in their pos- session. A Committee of Council, appointed for the purpose, re- ported that the Manuscripts were of much interest, and worth the price which Messrs. Hodges and Smith had set on them, The funds of the Academy did not, however, admit of the Council taking any direct steps for their purchase, but an application has been made, through his Excellency the Lord Lieutenant, for some assistance towards their purchase from the Government. His Excellency has expressed on this, as on all occasions, the greatest anxiety to advance the ob- jects of the Academy, but as yet no final answer has been received from the heads of the Government in England. The Library of the Academy has been increased during the past year, by numerous donations of scientific and literary works, for which, at the several meetings, thanks have been voted to the donors. An interchange of Transactions has been kept up with most of the eminent scientific institutions of Europe and America, there having been added during the past year: The Academy of Sciences of Metz, the Royal Academy of Amsterdam, with whom we did not previously correspond, and the Museum du Jardin des Plantes, at Paris, the correspondence with which had been accidentally interrupted. 551 During the past year seventeen new members have been elected into the Academy. Their names are as follows, viz.: George J. Allman, M.D. Rt. Hon. The Earl of Dunraven. Rev. Francis Crawford. Matthew Dease, Esq. Henry Lindsay, Esq. William M‘Dougall, Esq. John M‘Mullen, Esq. Sir Montague L. Chapman, Bart. Hon. and Very Rev. Henry Pak- James H. Pickford, M.D. enham, Dean of St. Patrick’s. Edward Bewley, M.D. Goddard Richards, Esq. James S. Eiffe, Esq. John Wynne, Esq. William Henry, Esq. He George Abeltshauser, A.B. John Neville, Esq. Out of our list of members we have to deplore the loss of several since the date of our last Report; most of them, certainly, persons whose energies, being devoted to other spheres, rendered their connexion with this Academy only nominal: but some, and especially one, whose connexion with us was of the closest and most endearing kind, whose scientific labours in various climates were of an extent and diversity which, while they created for him a dis- tinguished reputation, unfortunately sapped the foundations of his health. List of Members of the Royal Ivish Academy deceased since the 16th of March, 1843. Robert Bateson, Esq. Major-General Sir Joseph O’ Hal- Thomas Coulter, M.D. loran, K.C.B. Right Hon. William Vesey Lord Rev. Thomas Prior, D.D. Fitzgerald and Vesci. Rt. Hon. John Radcliffe, LL.D. Arthur Hume, Esq. Honorary Members deceased: His Royal Highness the Duke of Professor Wallace. Sussex. Amongst the honorary members had been reckoned his Royal Highness the Duke of Sussex. His exalted rank removed him from in any way personally contributing to the advancement of knowledge, but he favoured its cultivation by his august patronage, and filled for many years the office of President of the Society of Arts, having a decided taste for practical mechanics, and leaving behind him, at his 552 death, a very valuable and numerous collection of clocks and watches. In the year 1830 he was elected to the Presidency of the Royal Society of London, and was present at the meetings of that illustrious assemblage, whenever his health, which, unfortunately, was delicate, or the other demands upon his time, unavoidable from his exalted rank, admitted of his so doing. He was nominated an honorary member of this Academy, of course not for any special scientific merits, but that we might show some consonance of feeling with the scientific men of London who elected his Royal Highness to the most exalted sci- entific position of the British Empire, the chair of Newton. Professor Wallace, of Edinburgh, was known to the mathema- tical world for various memoirs, into the details of which it is not necessary to enter. His works were not of a character to influence the progress of general science in any material degree, although they manifested powers of inquiry and analysis of a very creditable amount. Of the ordinary members of the Academy whom we have lost during the past year, the Lord Fitzgerald and Vesci, the Right Hon. Judge Radcliffe, Arthur Hume, Esq., the Rey. Thomas Prior, D.D., and Major-General Sir Joseph O’Halloran, do not require special notice. They were all men publicly known, and recognized as of eminent ability in the various professional pursuits to which they had devoted themselves. Success of no ordinary kind was the result of their exertions, and has connected the names of some permanently with history. It can hence be understood that, except by a general desire to promote the objects of this Academy, by which, we trust, every member is actuated, they were not able to take any part in our proceedings, We cannot, however, pass so briefly from the name of Robert Bateson, late M.P. for Derry. Separating himself from the whirl of merely trivial and political pursuits, to which young men of his age and station are unfortunately in this country almost exclusively de- voted, he engaged in the cultivation of literature and antiquities with a zeal and ability which promised to bear the best fruit. The ancient monuments and history of his native country specially oc- cupied his attention, but not exclusively; and whilst travelling in Palestine, for purposes of literary inquiry, amongst those scenes in —— a4 553 which the most important acts of human history have been per- formed, he was seized with fever, and expired in Jerusalem. The position which Dr. Coulter occupied in this Academy, in our University, and in science generally, rendered it the duty of the Council to prepare, with more than ordinary care, a sketch of his life and labours, such as might not be derogatory to his fame ; and, hap- pily, the task was undertaken by one who, from long acquaintance and intimate friendship with the deceased, was enabled to speak mi- nutely of his personal career; and whose own extensive and profound acquaintance with almost every department of knowledge, which this Academy has had so often occasion to admire, enabled him to judge correctly of the aspects in which the labours of Doctor Coulter should be placed. The following biography of Doctor Coulter has been drawn up for this Report by the Rev. Dr. Robinson. ‘It is an old saying, that science has its martyrs as well as reli- gion ; we may add that it has its Forlorn-hope as well as war, urged to the adventure by loftier and nobler impulses, encountering in its pursuit even a greater amount of suffering and danger; but too often unnoticed and unrewarded. Its heroism is of too high an order to be appreciated by vulgar minds ; the wise and good, who alone value it, are comparatively few and powerless, and the triumphs which it achieves are not in unison with the evil tendencies and passions which unhappily predominate among mankind. Therefore it finds, in the Present, neglect, perhaps scorn or contemptuous pity of the folly which wasted on such unprofitable pursuits the powers that, if otherwise directed, might have commanded wealth, rank, and power. But the Present ere long becomes the Past ; all of its glittering ar- ray which is not based on the eternal and immutable principles of virtue and truth moulders to dust; the stream of time in its flow washes all that is earthy from the ruin, and leaves in imperishable brightness the grains of gold and gem which it contained, the trea- sure of the Future. In this sacrifice of self to science, few have sur- passed the associate, whose loss, during the last year, it is my painful duty to announce to you; and a brief notice of his history may therefore be permitted: “ Thomas Coulter was born in 1793, near Dundalk. His parents died during his childhood, but the loss was in part supplied by the 554 guardianship of a good and intelligent uncle. From an early age he was devoted to field sports, which he followed with a minute at- tention to the habits of his game, that belonged more to the natu- ralist than to the sportsman. Bees were another favourite object ; and he possessed that remarkable power of handling these irritable insects with impunity, which attracted so much notice in Wildman and others. He had in after-life the same privilege as to serpents ; of which some members may recollect an amusing exhibition in this room ; his secret being the union of gentleness and courage. «« He was prepared for college by Dr. Neilson, the author of a well-known Irish Grammar, from whom, perhaps, he derived that intense interest in the antiquities of our native land, which charac- terized him to the last. One proof of it deserves to be recorded for example’s sake. There stood on his property an ancient building, described in Wright’s Louthiana, as a Ship Temple, which the te- nant was converting into lime. The young landlord had him prose- cuted and punished for the trespass, to the surprise of many who were in the practice of similar misdeeds. In the University he had the good fortune to be placed under the care of the late Dr. Lloyd, whose esteem and regard he possessed in a high degree; though the prevailing bias of his mind prevented him from equalling in mathe- matical attainments some of his fellow-pupils. He pursued that science only so far as it ministered to other objects. But in practi- cal mechanics, in Chemistry, Physiology, and above all, in Entomo- logy and Botany, he far outstripped his college contemporaries, and while yet an undergraduate, his collections of Irish insects and mosses were such as might have been owned with credit by a veteran. But his success made him only the more conscious of his deficiencies, and determined him to seek abroad the means of supplying them. Having spent one or two summers in Paris, where he made very ex- tensive dried collections of the plants of the Jardin des Plantes, he established himself in 18—, at Geneva, where, under the auspices of De Candolle, he found all that he could desire. How well the three or four years which he spent there were employed, appears from the memoir on the Dipsacez, which he then published, and still more from his Herbarium, of which the European part was then formed, and compared with De Candolle’s own collection; a work, which when — 555 considered as the result of almost unaided individual exertion, may well be called gigantic.* The consciousness of power excited him to en- terprize, and on his return from the Continent, in 1824, he arranged an expedition to explore a considerable portion of America. His intention was to commence at Buenos Ayres, cross the great plains to Mendoza and Chili, to explore the western side of the Cordilleras, and the Lake of Titicaca; thence to California, and to return by Mexico, or by the Columbia river and Canada. For this he had actually made arrangements, and it is to be regretted that he did not execute it, He had every requisite for success among half civilized or savage races: a noble and commanding person; great Stature, ’ strength, and dexterity in the use of arms; good temper, courage, and presence of mind: a combination of qualities, which Bruce only, of modern travellers, possessed in the same degree, while he was far behind him in practical science. “« He was, however, induced to change part of his plan, and com- mence with Mexico, engaging as medical attendant to the establish- ment of the Real del Monté Mining Company for three years, during which time he hoped to complete the Mexican Flora, and afterwards to resume his original design.t *¢ But in that unhappy country, there was found neither probity nor peace. The English companies were regarded as legitimate ob- jects of plunder, and several of those whom they employed retired in sickness or despair from their posts. * Under such circumstances he felt himself called to go beyond his peculiar duty, and undertook the charge of one of the company’s principal mines, the Veta Grande, though such work was entirely new — o_o ee *His Herbarium (including the Mexican and Californian plants), contains about 150,000 specimens. T ‘‘ While in Mexico he collected, at a very great expense, plants of seventy species and varieties of Cacti, and sent them to the late Provost, the Rey. Dr. Lloyd, then Bursar, to be presented to the College for their botanic garden, He sent, at the same time, a similar collection to his friend, the late Professor De Candolle, for the Geneva Botanic Garden. Many of them were then very valuable, and unknown in European collections. One of them, a fine tall-grow- ing species, has been named Cereus Coulteri, and may now be seen, as well as other interesting species, in the College Botanic Garden. 556 to him; he, however, soon acquired the necessary knowledge, and under his management the concern became productive. This mea- sure was fortunate for his employers, but not for himself. It dis- tracted his attention from his primary object, detained him for more than a year in a district barren and uninteresting to the botanist, and, above all, mixed him up with the cabals and personal feelings which seem inseparable from such corporate bodies, and in which the high-minded and open-hearted always have the worst. At the close of his engagement he passed to California, where, and in Sonora, he spent four years, always actively employed on his primary objects,* and involved in spirit-stirring adventure; at times exposed to the Indian arrows, or compelled to defend his countrymen from the at- tacks of revolutionary patriots; exploring a burning waste of sand, when the thermometer reached 140, or nearly perishing by the bites of poisonous but almost invisible insects. At one time his metal- lurgic skill had acquired for him considerable wealth, which, during a botanical excursion, was plundered in some political convulsion. ‘¢ The industry and energy with which he carried on his botanical inquiries, is abundantly shewn by the fact,that the herbarium which he collected under such circumstances contains upwards of 50,000 speci- mens of 10,000 to 11,000 species, the far greater proportion of which was collected and preserved by himself; aud that in connexion with the herbarium he had gathered specimens about the size of a 16mo. book of nearly 1,000 descriptions of woods, most, if not all of which are accompanied by dried specimens of the foliage and inflorescence * «* One of his most interesting discoveries in California is a tall-growing pine, having cones a foot or more in length, and six inches in diameter. This has been named by the late Professor Don, at the desire of Mr. Lambert, Pinus Coulteri. It is quite hardy, and plants of it may now be seen in various collec- tions in England and Ireland. It was found in the mountains of Santa Lucia, near the mission of San Antonio, in lat. 36°, within sight of the sea, and at an elevation of 3,000 or 4,000 feet above its level, growing intermixed with another fine species, Pinus Lambertiana, also introduced, and rising to the height of from 80 to 100 feet, with large permanent spreading branches, and a trunk three or four feet in diameter. There are two small plants of it in the College Botanic Garden, and the cones may be seen in the College Her- barium,” ——— =” 557 of the trees from which they were taken ; the whole gathered by him- self, and being, perhaps, the largest collection of this particular kind ever made by any unaided individual. « At the end of this period he returned to Europe with an im- mense increase to his collection, but with a constitution irreparably injured by the hardships which he had encountered ; and even at home he was destined to meet a severe loss. In the transport from London to Dublin, a case containing his botanical manuscripts, and the materials ofa personal narrative, disappeared, and could never be traced; so that of the latter, nothing remains except a brief account of Upper California, published in the 5th volume of the Journal of the Geographical Society, and the former are totally lost, except some communications to De Candolle and Lambert. After this his chief anxiety was to secure the herbarium, which had cost him so much, from dispersion or neglect; and in this at least he was not disap- pointed. It has become the property of our University, and the task of arranging it was the employment of his few remaining years, which were devoted to that work with a concentrated energy that shewedhis consciousness of his days being numbered. It wascompleted for the European part, and about 8,000 ofthe American specimens ; but the remaining packages are well furnished with memoranda, so that for them also the arrangement is practicable. That the posses- sion of this invaluable treasure must give a powerful impulse to the study of Botany among us is sufficiently obvious; but it is doubly interesting to a scientific body like this, as an evidence of the increas- ing importance attached to the study of Natural History in the highest and most influential quarter. That important branch of knowledge has hitherto been too much neglected in university edu- cation; but better prospects are opening; and to this the influence of one so good and highly gifted as Dr. Coulter seems mainly to have contributed. Should our hopes -be realised, there is no doubt that he would have regarded it as an ample compensation for all his suf- ferings.” The ballot for the annual election having closed, the Scrutineers reported that the following gentlemen were elected Officers and Council for the ensuing year : 558 President—Sir William Rowan Hamilton, LL. D. Treasurer—James Pim, Jun., Esq. Secretary to the Academy—James Mac Cullagh, LL. D. Secretary to the Council—Robert Kane, M. D. Secretary of Foreign Correspondence—Rev. Humphrey Lloyd, D. D. Librarian—Rev. W. H. Drummond, D. D. Clerk and Assistant Librarian—Edward Clibborn. Committee of Science. Rev. Franc Sadleir, D. D., Provost of Trinity College ; Rev. Humphrey Lloyd, D.D.; James Apjohn, M.D. ; James Mac Cullagh, LL. D.; Robert Ball, Esq.; Robert Kane, M. D.; G. J. Allman, M. B. Committee of Polite Literature. His Grace the Archbishop of Dublin; Samuel Litton, M. D.; Rev. William Hamilton Drummond, D.D.; Rev. Charles Graves, A. M.; Rev. Charles W. Wall, D. D; John Anster, LL. D.; Rev. S. Butcher, A. M. Commitiee of Antiquities. George Petrie, Esq.; Rev. James H. Todd, D.D.; Henry J. Monck Mason, LL.D; Samuel Ferguson, Esq. ; J. Huband Smith, A. M.; James Pim, Jun., Esq. ; Captain Larcom, R. E. The President then appointed, under his hand and seal, the following Vice-Presidents : The Rev. James Henthorn Todd, D. D.; James Ap- john, M. D.; the Rev. Charles W. Wall, D. D.; and George Petrie, Esq. The Auditors appointed by Council to examine the Treasurer’s accounts reported as follows: 559 “We have examined the above Account,* with the vouchers produced, and have found it to be correct ; and we find that there is a balance in bank, amounting to £203 18s. 3d., sterling, and in the Treasurer’s hands, 6s. lid” “ (Signed, ) «« JosepH Carson. “Tuomas A. Larcom.” “ March 15th, 1844.” “ The Treasurer reports, that there is £1117 10s. 10d. in 8 per Cent. Consols, and £1643 19s, 6d. in 34 per Cent. Stock, the latter known as the Cunningham Fund. He also reports that there are due this 16th March, 1844: ‘ 2 Entrance fees, at £5 5s.per . . .. =. =. +£1010 0 6 Arrears of two years, at £4 4s.per. . . . 25 4 0 25 Do. oneyear, . £2 Qs. 3 alia leer a 52 10 O 170 Subscriptions for the past year, now due, at PED Serper ONY TF ype gd stsey )), Balance unappropriated in the Bank of Ireland, £203 18 3 Balance in Treasurer’s hands, . . 0 6 14 £204 4 43 357 0 O £649 8 43 “Signed for James Pim, Jun., Treasurer. “ EpwarD Cupsorn, Clerk, §c.” April 8. JAMES APJOHN, M.D., Vice-President, in the Chair. The Marquis of Kildare and William Smith O’Brien, Esq., M. P., were elected Members of the Academy; and * Entered in Treasurer’s book- VOL, Il. OA 560 Robert Ball, Esq., was elected Treasurer of the Academy, in the room of James Pim, Jun., Esq., who resigned. Dr. Apjohn read a paper by Mr. Thomas Knox, “On the Purification and Ventilation of Vessels from bad Air.” In reperusing lately Professor Daniell’s interesting re- searches* ‘‘on the spontaneous evolution of sulphuretted hydrogen in the waters of the western coast of Africa and of other localities,” a method occurred to me of purifying the cabins of vessels, and the sleeping apartments in houses, which would be as efficacious as Professor Daniell’s, with- out being liable to the objection of having free chlorine always present producing its enervating effects. The method I propose is this: to have air pumped through tubes extending from the steam engine to the cabins. The extremities of the tubes should dip into vessels contain- ing solutions of chlorine or metallic solutions; the last solu- tion, being of lead, would indicate when the solutions were to be renewed, by the black precipitate of sulphuret of lead. At the further end or top of the cabins there should be cor- responding tubes to allow the foul air to be removed ; these latter would be unnecessary when there was a fire, the draft being sufficient to remove the foul air. As we can absorb or destroy all vapours, miasma, &c., this method would apply to all unhealthy regions of the world, and would render habitable parts of the world which at present lie deserted and waste. Sierra Leone would cease to be the grave of Europeans, and the Pontine Marshes would no longer exhibit a ghostlike peasantry. EXPERIMENTS. Chambers made of wood, with air-tight windows, having apertures in the sides, into which the tubes would fit, could * Phil. Mag., July, 1841. —e 561 be made at little expense, and sent to Sierra Leone and the Pontine Marshes; in the latter place the pumps might be worked by water conveyed from the mountains or other cheap motive power. Dr. Apjohn read a paper ‘‘ On the hygrometric Cor- rection in barometric Formule for the Measurements of Heights. If the atmosphere were of one uniform temperature throughout, destitute of moisture, or in a constant hygrome- tric condition, and if the intensity of gravity were also con- stant, it is well known that the difference of the altitude of any two points in the atmosphere would be represented cor- rectly by the formula p = m x log. nt m being a constant quantity, and p and p’ being the respective pressures at the lower and upper stations, as measured by the barometer, or in any other way. A correction for temperature has been long applied by augmenting or diminishing the approximate height, or m X log. 7 by the amount that a column of air of this length would expand or contract if its temperature were changed from 32° to ot , t being the temperature of the lower, and @ that of the upper extremity of the rial column, by which the expression becomes D =m X log. — x +5 —). ae Such is, I believe, a correct account of the present form of the barometric formula, at least when we neglect the cor- rection for variations of gravity, which is, however, in gene- ral so small as to be safely negligible. The presence of moisture in the air, or rather its varying amount, must ob- viously exercise some disturbing effect on this formula; but 3A2 562 though this has been generally admitted by those who have turned their attention to the subject, I am not aware that any attempt at estimating its exact amount has been as yet made; and as the correction for moisture is frequently of considerable magnitude, and may, in my opinion, be applied with as much accuracy as that for temperature, I have taken the liberty of occupying, for a few moments, the time of the Academy with an explanation of the method which it has oc- curred to me to devise, and with which, from some trials I have made of it, I have every reason to be satisfied. Let p be the pressure, and ¢ the temperature of the air at the lower station, ¢” the dew point of the air, and f” the force of the included vapour ; and let p’, 0, 0’ and r” represent the corresponding quantities at the upper station. This being understood, a little consideration will suffice to shew that the presence of the aqueous vapour produces on the for- mula a twofold deranging effect. It augments the values of p and p’ beyond what they would be in dry air, and it pro- duces an alteration in the length of the column of air between the two stations additional to that which results from the dif- ference between its mean temperature and 32°, or the freez- ing point. The first of these is obviated, or, in other words, the correction for it is made, by substituting for p and p’ in the approximate formula, p — /” and p’ — Pr”, by which it becomes Pp —f” > = mx log. cme Having thus eliminated the effects of the tension: of aqueous vapour upon the pressures, we have next to esti- mate the conjoint influence of it and temperature, in elon- gating the pillar of air between the two stations. The theory of mixed gases and vapours enables us to do this, provided we can assign proper mean values to the temperature, the pressure, and the force of vapour of the aerial column in ques- 563 t+0 2 this must be very nearly its true value. For the same reason, f' + pr” 2 let us assume the mean value belonging to the pressure as Vp —F) X @ 1). Nowa volume v of dry air at 32° undera pressure 7, if raised to a temperature ¢’’, becomes a 461 + at 493 and if saturated with vapour at this temperature, the tension of such vapour being s”, it will become $ 461 + ¢t”’ ot age 493 rs’ This is the volume of the air when raised to ¢” and satu- rated with vapour at this temperature ; and if this volume of air have its temperature further changed, we shall say to ¢, then its bulk will be represented by the expression 461 +t” Cy 461+ ¢ 461 +¢ 7 0X “998 * ae’ ™ S140" ° S493 * a substituting, then, in this expression instead of v the value of the length of the column of air between the two sta- tions supposed dry, and at 32°, viz. : — f” — FP? tion. The mean temperature its usually taken as , and ; and the mean force of vapours may be set down as’ m x lo BT and for z, ¢, and s” their proper mean values as already ex- plained, the barometric formula finally becomes p—f" 461 + 49 b=m xX log. 5 oa x pT Vv (p—f") x aa —F’) V (p—f) ¥ (p'=B) — P48") I may add here, that the correction for moisture is far from being insignificant in its amount, as may be seen by 564 the following example. Let us suppose, that when the ap- proximate height, corrected for temperature, amounts to 2700 feet (a height reached by several of our Irish moun- tains), the mean value of 7, or the pressure to be used in the final factor of the formula, is 27.3, and of the force of va- pour, 0.3 of aninch, its value when the dew point is 43.6, then the elongation of the aerial column resulting from mois- ture is 935 = goth of 2700 = 30 feet. It will, of course, have been observed that the correction for aqueous vapour differs from that for temperature in the circumstance of being always positive ; and this coincides perfectly with the obser- vation I have had frequent occasion of making, namely, that in damp states of the atmosphere heights calculated by the formulz in general use are all appreciably less than the truth. And here I may be permitted to observe, that the great Laplace, in discussing the barometric formula, in his “ Sys- téme du Monde,” has fallen into a slight oversight; for as a rude method of compensating for the effect of the aqueous vapour present in the atmosphere, he proposes, that in ap- plying the correction for temperature the coefficient of the expansion of gases should be augmented from .00375, its value for one degree Centigrade, to .004. Now this would certainly produce the desired effect at.all temperatures above 32°; but as below 32° this equation is subtractive, the aug- mentation of the coefficient, instead of diminishing, would increase the error. The following is the passage referred to: “Les vapeurs aqueuses répandues dans |’atmosphére, etant moins denses que I'air, a la méme pression et ala méme temperature, elles diminuent la densité de l’atmos- phére; et comme, tout étant égal d’ailleurs, elles sont plus abondantes dans les grandes chaleurs; on y aura égard en partie, en augmentant un peu le nombre .00375 qui exprime la dilatation de lair pour chaque degré du thermometre. Je trouve que l’on satisfait assez bien a l'ensemble des ob- servations, en le portant a 0,004; on pourra donc fair usage a: 565 de ce dernier nombre, du moins jusq’a ce que l’on soit par- venu par une longue suite d’observations sur I'hygrométre, a introduire cet instrument dans la mesure des hauteurs par le barométre.”* I may in conclusion observe, that in assuming, with the view of calculating the expansion produced by moisture, that the pressure to be employed is the geometric mean of the corrected pressures given by the barometer at the two sta- tions, I am quite aware that I am assigning to it but an ap- proximate value. An exact expression for the pressure to be employed admits of being investigated ;} but its intro- duction into the formula, while it would give the latter com- complexity of form, and thus render it less suited for prac- tical use, would conduct to results not appreciably different from those given by the more simple methods just ex- plained. Mr. Clibborn presented to the Academy an ancient stone image, called in some places a Shela-na-gig; and read the following extract from a letter from Dr. Charles Halpin: ‘«‘ About two years ago, as I drove past the old grave- yard of Lavey Church, I discovered this curious figure, laid loosely, in a half reclining position, on the top of a gate pier that had been built recently, to hang a gate upon, at the an- cient entrance of the old church-yard. I believe the stones used in building those piers were taken from the ruins of Ne Taree * Systeme du Monde, p. 89. log. P + Let a , m being the modulus of the common system of logarithms, up ‘=p. Thenifv be the column of dry air, and that, when saturated with mois- ture whose force is f, it becomes v’, we will have Gas 0 3 P rp—f : For the very elegant expression for P I am indebted to my friend, Professor Renny. 566 the old church of Lavey (there is scarcely a trace of the old church on the site it occupied); and I think probable, that this figure was found amongst them, and laid in the position in which I found it, by the masons employed at the work. I was not aware of its real value, until apprised of it by my brother, the Rev. N. J. Halpin. He immediately re- cognized it as a ‘ Sheela-na-gig,’ and the most perfect of any he had seen. I thought it my duty to protect this pre- cious relic from the hammer. *‘ Lavey church lies about fifty miles north-west of Dub- lin, on the mail-coach ann There is a neat new church near the site of the old one. Mr. Petrie having expressed a desire that some further information should be given about this figure, and others, of the same kind, of which, he understood, there were two in the museum of the Academy, which had belonged to the late Dean Dawson: Mr. Clibborn explained that he had received notices or outlines of ten other figures, of the same kind, which had been found in old churches and castles, and from their posi- tion in the walls, sometimes hid in the course, and from the difference of the stone, it was probable they had been used in older buildings, so that their actual antiquity could not be determined by the age of the buildings in which they had been found. From the form of the stones on which several of these figures were carved, it was surmised that some of them had been originally used as grave-stones, and proba- bly intended to act as charms to avert the evil eye, or its influence, from the place. ‘These figures have a great simi- litude to others used elsewhere for this purpose formerly, as well as at present, by the natives of the east coast of Africa. He also explained that, about five years ago, when, in company with several advocates of the O’Brien theory of the Round Towers of Ireland, he was led to express an opinion that, possibly, these buildings, though erected subsequently 567 to the introduction of nominal Christianity into Ireland, might still have, to a certain extent, some analogies to views entertained by the African and Asiatic ascetics, and which might have been imported into Ireland by the first Chris- tians, in the third century ; who, if from Africa or Spain, may have brought with them more or less of Gnosticism (or views analogous to it), and with it notions and practices not very unlike, apparently the same originally with those, by which the author above-mentioned endeavoured to explain the nature and origin of the Round Towers. The first no- minal Christians, if he had been correctly informed, who came to Ireland, were lay ascetics ;* and, like the ascetics of Egypt and the East, they selected secluded valleys in the mountains, or islands in lakes, where they gave themselves up to those penitential observances calculated, according to their views, to destroy the ‘“ Hylic, or material,” to. humble and conquer the “ psychic, or animal,” and to elevate and culti- vate the “‘ pneumatic, orspiritual,” principle of their natures. It was argued that, if the tower was the residence of the Irish ascetics during their lives, it may have been con- sidered the type of the plus, male, ‘‘ pneumatic,” or spiritual principle; and so the earth, grave, crypt, or church near it, in which were deposited the bodies, or material principles of the deceased, originally derived from mother earth, may have been considered the type of the negative female, hylic, or material principle, and have been considered analogous to Ge, or De-meter, to whom the body of the dead returned, by interment ; and, hence, it was argued that, if O’Brien’s theory were true in this qualified sense, it should apply to the churches or graves near the towers or residences of the ascetics, where we should find types or indications of the negative principle. Mr. R. P. Collis, who was present, im- * See Moore’s Hist. p. 221. The extract from St. Patrick’s letter: ‘“‘ubi nun- quam pervenerat qui baptizaret, aut clericos ordinaret, aut populos consummaret.” 568 mediately mentioned the female figure at Rochestown, and stated that he had heard of several others in the same neigh- bourhood, and he recommended an inquiry into the subject, which led to the discovery of several more figures of the same kind in different places. The ‘‘hylic principle,” including the materials composing the body, was little more than the locus, where the battle of the two other principles was fought during the life of the as- cetic;* and if he persevered to death in the practices pre- scribed for the evolution of the pneumatic principle, and lost his life in these observances, or in the fulfilment of the duties which belonged to this system, his victory over the hylic or psychic principles was complete, and he was said to have arrived at ‘* perfect virtue,” and consequently became, ac- cording to Asiatic views, an inferior, or little Bauddha, which may, possibly, give us an original of the name of Monaster- boyse; in Irish, the monastery of Boaithin, or the little Bauddha. The legend of St. Colum Cille, who struck his crosier against the glass ladder, by which he went to heaven, which belongs to this place, and which strongly corroborates a Ceylonese legend, increases the suspicion, that the system which was called here Christian, originally may have been analogous to that ascetic system which existed under the same name in Egypt and the East, and was closely allied to Bauddhism, which was, and is, a system of Asceticism,} and * This doctrine is the same, or nearly the same, as that which is called Dualism, which attributes creation and life to the action and reaction of two principles, plus and minus, or positive and negative, which were personified by the ancients under every species of antagonism. The fighting dogs and serpents of the Irish are, apparently, manifestations of it, applied specially to the daily strife, or ‘‘ cross,’ of these two principles in the body of the ascetic. { When O’Brien’s book was written our knowledge of the Bauddist system was very limited. Now its antiquity, history, principles, and corruptions, are better understood, through the labours of Mr. Princep, Fa-hian’s Travels, The Mahavansa, &c. 569 mixed up with more or less pure Gnosticism; for, “ the greatest part of the Gnostics adopted very austere rules of life, recommended rigorous abstinence, and prescribed severe bodily mortifications, with the view of purifying and exalt- ing the mind,” like the Irish ascetics. ‘‘ These tenets were revived in Spain, in the fourth century, by a sect called Priscillianists,” where they may have been, to a certain de- gree, suppressed by the instrumentality of missionaries and seculars from Rome. The same system which existed in Spain previously, and which planted those views there after- wards, may have also planted them here; and the same means which suppressed them there for a time, may have here suppressed them; or there may have been, to a certain degree, for several centuries, a compromise between the ad- vocates of both systems, and that which was finally adopted here, and éalled Christianity, may have, in a covert way, contained much Gnosticism, particularly that branch of it which was adopted by the ascetics, or Culdees, and small religious communities, and by whom the first towers may have been originally built.* It is a curious circumstance, not hitherto noticed by any writer on the Round Towers, that the technical term for a Bauddist monastery in the East, is a tower; no matter whether it be a cave in the earth, or a cabin or palace on its surface. We may add to these notices another notion of the pene oe ie eS * The following extract, from the very old Irish MS. called the Speckled Book, in the Academy, will explain and confirm what I have stated concerning Irish asceticism: ‘‘ When, then, said St. Bartholomew, the Son of God was born, he was tempted by the Devil, but Christ overcame, by fastings in the wil- derness, him who overcame Adam, in Paradise, through gluttony ; for it was meet that Christ, the son of the Virgin, should overpower him who overpowered Adam, the son of the virgin, i.e. the son of holy earth; for the (mother) earth of which Adam was formed was virgin, because it had not then been polluted by iron, nor by the blood of man, nor had it been opened for the interment of man in it at that time.” 570 Gnostics, which was, ‘that malevolent genii presided in nature, and occasioned diseases and calamities, wars, and desolations; induced them to apply themselves to the study of magic, in order to weaken the powers, or suspend the in- fluence, of these malignant agents.” This doctrine of their’s was, no doubt, extended and carried out fully in every mode and form, and led them to consider themselves, and all things living on the earth, to be under the influence and subject to the evils caused by the instrumentality of these evil genii, who, in some cases, attached themselves to individuals, who were then said to have the evil eye, or who became afflicted with what is termed “ covetousness,” which blasted everything which they desired, and made it unlucky; andits possessor was shunned and avoided, as he was subject to that malign influence which is technically termed the ‘‘ evil eye.” This influence was greatly dreaded by the living, for themselves, their children, cattle, and goods, and their houses; and in many places, even now, people put up over their doors, over their hearths, and in many other places, talismans, to give them good luck, or to take away or neutralize the evil look, which brings them bad luck, by averting the evil eye, also con- sidered to bea distinct individuality, or genius. The term ** eood look,” or “luck,” is incorporated into the English lan- guage, though the belief of the evil eye is nearly lost in Eng- land, where it was universal. It still exists in Scotland, and we find it also in Ireland, where various methods are still practised to avert its influence from children, cattle, churns of milk, houses, &c. One of the most efficacious is the horse shoe, which is called “the lucky horse-shoe” for this reason, and it is ‘nailed to doors and gateways for luck,by people who have no notion that they are, probably, putting up equivalents for those hideous figures which the people cal] shela-na-gigs, one of which was lately discovered at Kiltynan Castle, by 571 Mr. Thomas Oldham, which held the lucky horse-shoe in one hand, and a cross, or dagger, in the other. _ The horse-shoe, and the triangle, A, or A, &c., and the trefoil, are all, apparently, emblems for the same antidote, which the evil eye abhors, and by which the mechanic’s wife was not only able to identify the evil genius himself, but to eject him from her house, and save her husband’s body and soul, the stake which he proposed to play for. In this coun- try the peasantry are said to entertain similar notions of the great efficacy of the same means, which is said to be ** capable of driving the Devil away,” the use for which, it is surmised, these figures were intended. Mr. William Hackett, the moment he saw a drawing of one of the figures, declared it was a “ fetish;” the African name of a figure which closely resembles the shela-na-gigs, and is commonly used for the purpose of averting the evil eye, and giving good luck. On the north coast of Africa certain emblems, carved in stone, are placed over the doors for this purpose; and formerly it would appear that certain parts of animals were used instead. In Italy the peasantry, in the neighbourhood of Naples, have a complete system “of magic” for averting the evil-eye, which consists, to a great extent, of exposures and practices, which are com- pared to the ancient orgies, and calculated to eject or avert the evil eye, or genius, from a place, and drive him and his colleagues, and their influence, beyond certain limits. These figures were, probably, intended as Jelishes, or charms, to keep off the evil eye, or its influence; and, con- sequently, they are found placed over doors of churches and castles, &c. In many instances they are evidently much older, and of a totally different material and style of art, to the building in which they are found. ‘The workmanship is quite unequal, and the style of the figures differ very much. They are not copies of a common original, but, generally, 572 the most hideous and frightful-looking female figure which the stonecutter could devise. There is, however, in the - best sculptured figures a certain expression of countenance which resembles that of death. In these the hair is very long, and there is no appearance of the tonsure, which occurs in others. The former have a strong resemblance to a Mith- raic figure, published in the Archzologia, XIX. p. 74, and also to another figure, in Ingrami ‘“‘ Monumenti Etruschi,” T. 3, Tav. XXIII. Both of these, it is thought, were also used as fetishes, or figures intended to drive away the evil influence, and obtain good luck instead. The hair of some of the figures appears to be intended to represent a peculiar tonsure, and the persons of women repre- sented are apparently attenuated by fasting and thatcourse of life which the Gnostics and ascetics so strongly insisted on, as the means of gaining the victory over the hylic or psychic (together, the evil principle) in themselves, and what St. Bridget so ably contended for in herself, and those who placed themselves under her rules. In these almost skeleton figures we have an analogy between the rule of abstinence of the Gnostics, and also their notion about amulets, abraxes, fetishes, and the evil genius; and hence the probability, that the use to which they have been assigned is the correct one, independent of any other considerations which arise from the practices now said to be efficacious in Ireland, &c., in ejecting the evil genius, or averting the evil eye; and which formerly, as well as at present, were common in Africa, Italy, Spain, Ireland, &c. With the ancient Egyptians the crux ansata appears to have been the great emblem of good luck, prosperity, and soforth. It appears to have been the antidote to the evil eye which we find mentioned in Prov. xxiii. 6, and xxviii. 22, and the Gnostics and early Egyptian Christians appear to have adopted it, without any alteration or change in its form from that used by the old Egyptians. The erwx ansata ap- 573 pears to have been a substitute for the gesture called the fico of the ancient Romans and modern Neapolitans, which combined the Dualism, or positive and negative principle. It is still used, according to the Canon De Jorio, when a lay Neapolitan wishes another good luck, when he is going on an expedition, &c. And we find the jico, combined with other emblems into the form of the cruz ansata, in the mu- seum at Naples, where there are many examples analogous to many Gnostic emblems, which are well known; some of which have been published by the Rev. Dr. Walsh. One found in the baggage of Prince Charles Edward, after the battle of Culloden, has on it a woman, in a better style of art than that of the shela-na-gigs; but, probably, intended for the same purpose, “‘ as a charm” to avert the evil eye, and gain the good luck instead. The crosses which are placed round certain enclosures in Ireland, and act as termini, or boundary marks, had pro- bably the same use formerly, to keep off the evil-eye and its influence from the enclosure, so that the sleep of the dead might not be disturbed ; hence the request to pray for the re- pose of the soul of Bran, on the tombstone in the museum, and the usual “may he rest in peace”; terms calculated to neutralise the disturbing influence of the evil- eye principle. In Asia and Africa things owned by individuals are frequently tabooed, or marked with the cross, or circle, crescent, or both combined, which, it is believed, protects them from the evil-eye, and consequently from being coveted by people, or rendered unlucky. This practice, or the notions which caused it, appears to be almost as old as man himself, and is found incorporated into the language, and occupying a greater or less proportion of the popular belief in every country. The pattern which composes the tracery on our cross of Cong, and other old Irish shrines, reliquaries, and the tomb at Cashel, which represents an animal like a dog or serpent always worrying itself, or another creature of the 574 same kind, may probably be a type of the doctrine of absti- nence or mortification of the flesh,* which to the ascetic was his daily cross, and antidote to the hylic or evil principle, which he considered himself bound to bear, and which his master before him had borne victorious to death, and by which he became exalted to the highest rank in heaven, con- sistent with our extract from the Irish MS., in which we find at least one of the doctrines mentioned, which the ascetics magnified into a constant rule of life, and made it the means of conquering the evil principle in themselves, to which these figures, it is thought, may have been charms or external an- tidotes, like the cross and bells, &c., which they ornament, which are covered with dog and knotted serpent patterns, crossing each other continually, and supposed to be emble- matic of the ascetic principle, or daily cross, and antidotes of the evil eye or principle. By this rule the stone in the museum presented by Mr. Webber, which apparently re- presents two dogs fighting, may have been an ingenious device to hide from common eyes, but to exhibit this princi- ple where it would be understood, instead of a shela-na-gig of the common form, and so it may have been intended originally as a fetish or charm to the house or castle from whence it was removed. Besides the three figures now in the Museum, I have been informed of the existence of many * The emblem, or device, for Christianity on the Roman medals, given by the Rev. Dr. Walsh, is analogous to the monstrous figures of the double dog and serpent patterns referred to, which, it is surmised, may be emblems of the ascetic principle. He observes: ‘It may be that Dioclesian wished to repre- sent only the depraved and corrupt sectarians, of which this figure (in his plate) is the emblem; and that his more atrocious colleague, careless of distinction, exhibited the genius of Christianity, under any form, as equally the object of his persecution.” There is a figure called the Idol, at Cashel, with fish-tail ex- tremities, with a face like the shela-na-gig presented by Mr. Halpin. It ap- pears to connect, or identify, the designs on the Roman medals with those Irish figures, 575 Shela-na-gigs in different parts of Ireland ; but have received drawings and exact descriptions of five others only. 1. The first discovered and described by Mr. R. P. Collis. It is in the gable of an old church at Rochestown, County Tipperary. This figure is called a Shela-na-gig, by the country people, and as it was the first found it has sup- plied the name to all the others. 2. In the church at Dowth there is a Shela-na-gig, carved in stone quite different to that which composes the walls of the church. This figure appears to have been originally a head or foot-stone of a grave. It was said to be a figure of St. Shanahan, by the person who shewed me the place. At Lusk there was a figure called the Idol, which was buried by the late Rev. Mr. Tyrrell. It appears to have been a Shela-na-gig also. 3. Found over the door of the keep of Ballinahinch Castle, near Cashel. In this figure there is an appearance of the tonsure. It was the opinion of the person who ex- amined it, that it had been inserted in the wall, and might have been taken from the ruins of the church, which are quite near the Castle. 4. Found in the south front of Moykarkey Castle, County Tipperary. This figure has a more finished and modern air than any other of which I have drawings. The country people have a legend, and call it Cathleen Owen.* It also appears inserted into the wall, and there is a ruin of a church quite near, from whence it might have been procured, to bring ‘ luck about the house.” 5. Found in the wall of the old church on the White Island, Lough Erne, in the demesne of Colonel Archdall. This figure occurs lying on its side, and is in the course low down near the door, and appears to have been a part of the * This legend may be equally authentic as that about the dog and wolf stone, presented by Mr. Webber. VOL, Il. 3B 576 materials of an older building, which were used in the build- ing of the church now inruins. In the same way one of the figures in the Museum, from the Dawson collection, appears to have been built into the wall of the church where it was found. Under such circumstances, the actual antiquity of these curious figures is quite problematical. The subject is a new one, and well deserving of the attention of antiqua- ries, to whom this notice is submitted more as a suggestion for consideration than as an opinion. The number of facts known are few, and probably it may be premature to attempt a generalization. April 22. SIR Wm. R. HAMILTON, LL. D., President, in the Chair, Reap,—a letter from the Secretary of the Lord Lieu- tenant, presenting to the Academy the stones containing the inscription from the old bridge of Athlone. Resotvep,—That the thanks of the Academy be given to His Excellency the Lord Lieutenant for his donation. The Rev. Professor Graves read a paper on the Alge- braic Geometry of Curves traced upon given Surfaces. Let u = 9 (2, y,z) = 0 be the equation of a surface re- ferred to ordinary rectangular coordinates. Its complete differential will be pdx + ady + rdz = 0. Making P Q x =—, ang ¥ —-—, R R Mr. Graves denominates x and y the normal coordinates of a point on the surface. When they are known, the 2, Yo & of the point are determined by the three equations 577 P Q u = 0, - =x, and—=y. R R As P, Q, R, are proportional to the cosines of the angles which the normal at the point (x, y) makes with the axes ; it is easy to shew that if we describe a sphere with its centre at the origin and radius = 1, x and y will be at the same time the rectangular spherical coordinates of that point on the sphere at which the tangent plane is parallel to the plane touching the surface u=o at the point (x, Y). Thus, to every point on the latter corresponds a point on the former : and a succession of points, or a line of any kind, on the sur- face u=o is in general represented by a succession of points, or a line upon the auxiliary sphere. As plane curves have been classed according to the de- grees of the equations by which they are represented, so curves traced on any given surface may be advantageously distinguished by the degrees of the equations in x and y which define them. For the properties of a curve, traced on the surface u=o, and characterized by an equation of the nth degree between x and y, are, so far as we regard only the relations of normals or tangent planes along it, identically the same as those of the spherical curve which has the same equation. But the analogy between spherical and plane curves of the mth degree has been already estab- lished. Instead, then, of looking upon the shortest lines ona surface as analogous to the right line, Mr. Graves directs his attention to the line defined by the equation ax + by+1=0, (A) the geometrical character of which is, that the normal at any point on it is always parallel to a fixed plane. Systems of such lines upon any surface possess, in general, those pro- perties of right lines which have been termed projective. Thus, for instance: “If four lines of the first degree, di- verging from the same point on a given surface, be cut in 578 four points, a, b, c, d, by another line of the same kind, we shall have sin [a, d]. sin [5, c] Bs sin [a, 6]. sin [e, d] eS aiiaastant, [a, b] being used to denote the angle between the normals to the surface at the points a and b. The normals along the line (A) are all parallel to the tangent plane at the point whose normal coordinates are a and b. Mr. Graves designates this point the pole of the line. And if a and 6 be connected by an equation, so that the pole describes some curve of the mth degree, the line (A) will always touch another curve to which m tangent lines of the first degree may in general be drawn from the same point. This relation between the curves being obviously reciprocal, Mr. Graves calls them reciprocal curves. Here is laid the foundation of a theory of polar reciprocals for curves traced upon any given surface. Amongst other exemplifications of this method, Mr. Graves employs it to discuss the lines of greatest and least curvature on the surface of an ellipsoid. ‘Their equation in normal coordinates is 2 2 2 a hee ee ee where a’, 6%, c? are the squares of the semi-axes of the ellipsoid, and /” is indeterminate. Now, from the mere fact of this equation being of the second degree, it follows that the sum or difference of the angles between the tangent plane at any point ona line of curvature and two fixed planes is constant. But further, all the spherical curves of the second de- gree represented by the preceding equation are biconfocal : and it is easy to shew that their common foci are the points on the sphere which correspond to the umbilici of the ellip- soid. Hence, the sum or difference of the angles between 579 the tangent plane at any point on a line of curvature, and the tangent planes at two umbilici, is constant ; or, as the tangent planes at the umbilici are parallel to the planes of circular section, we have the following elegant theorem: “The sum or difference of the angles between the tan- gent plane at any point along a line of curvature on an ellip- soid, and the two planes of circular section, is constant.” The proposition just mentioned was, it is believed, first published by Sir William Hamilton, in the Dublin University Review, part (3) ; the short article which contains it being dated June, 1833. It has also been published by Dr. Joachimsthal, in a paper printed in the 26th vol. of Crelle’s Journal, and dated January, 1842, where that geometer claims it as “ novum neque inelegans.” The reciprocal of the line of curvature has for its equa- tion a? — h? b? — k? c? — kh? a x? + B y? + a = 0; in which if we make x= = and y = 4, we shall get the equation of the cone, whose generatrices are parallel to the normals along the reciprocal of the line of curvature, and whose vertex is at the centre of the ellipsoid. After this substitution the last equation becomes > 2 2 2 etre M(S+$+2)=0 from the form of which it is evident that the cone passes through the intersection of the given ellipsoid, and a con- centric sphere having # for its radius. The properties of this cone, and its relation to the lines of curvature, were first noticed by Professor Mac Cullagh.* * Proceedings of the Academy, vol. ii. p. 499. 580 For the quadrature of areas on the surface of the ellip- soid Mr. Graves gives the following formula: aye (1+x?+y¥°)idxdy area = a’b°c \ epa pare PY The President made some observations on the communi- cation of Professor Graves. Mr. Clibborn read a notice of certain points in Egyptian History. Reap,—The following Report’ from the Council : « That the Council do recommend to the Academy, at its next meeting, to carry into effect the following recommendations of the Committee of Antiquities, and to request a vote of the Academy of £100 for the fitting-up of the Museum. «1. That the resolution of the Academy, of the 30th of Novem- ber, 1842, for making a new Board Room in the lower part of the house, be carried into effect. «© 2, That the present Board Room be converted intoa Museum. «« 3, That, for this purpose, two tables be provided, to stand across the new Museum, opposite the piers. The present glass cases, ex- cept that containing the Cross of Cong, to be placed on those tables, and flat glazed cases to be added; the Cross of Cong to stand ona separate pedestal between the tables, ¢. ¢. in the centre of the room. “ The Council having taken into consideration the best means of exhibiting the antiquarian treasures contained in the Museum of the Academy, and thus giving proper importance and utility to that department, appointed a Committee, which recommended the adop- tion of the resolutions of the Committee of Antiquities. These have been adopted by the Council, and are now proposed for the adoption of the Academy.” ResotveD,—That this Report and Recommendation of the Council be adopted, and that £100 be placed at the dis- posal of the Council for the purpose specified. 581 DONATIONS, Annuaire del Académie Royale de Bruxelles. Néuvieme Année 1843,—Annuaire de l’ Observatoire Royalde Bruxelles, 1843. Dixiéme Année.—Rapport sur l’Etat et les Travaux de Observatoire Royal, pendant ) Année 1841 et 1842.— Résumé des Observations magnetiques et meteorologiques faites a des Epoques determinees, (Extrait du tome XVI. des Memoires.—Observations des Phenomenes periodiques (Extrait des tomes XV., XVI. des Memoires).—Jnstructions pour l’ Observation des Phenomenes periodiques.—Memoires Couronnés et Memoires des Savans Etrangers. Publiés par YAcademie Royale. Tome XV. partie 2.—Nouveaux Me- moires de 1 Academie Royale de Bruxelles. Tome XVI. Pre- sented by the Academy of Brussels. Memoires de la Société Geologique de France. Tom. V. Parts 1, 2. Presented by the Society. Memoires de l Academie Imperiale des Sciences de St. Petersbourg. Sixth Series.—Sciences Mathematiques et Phy- siques. Tom. XIII. Livraisons 1, 2, 3.— Sciences Politiques. Tom. VI. Livraisons 1, 3.—Sciences Naturelles. Tom. V. Livraisons 1, 2.— Recueil des Actes des Seances Publiques, tenues le 31 Decembre, 1841, et le 30 Decembre, 1842.— _ Memoires presentes al’ Académie. Par divers Savans. Tom. XVI. Livraison 5. Presented by the Academy of St. Peters- burgh. Sur [Emploi de la Boussole dans les Mines. Par A Que- telet. Presented by the Author. Erster Zusaiz, zu der Schrift Ueber den Galvanismus. Von Gustav. Crusell. Presented by the Author. Ninth Annual Report of the Poor Law Commissioners, for 1843. Presented by the Commissioners. Catalogue of the Museum of the School of Medicine, Park-street, Dublin. By John Houston, M.D. Presented by the Author. 582 Faune Ornithologique de la Sicile. Par Alfred Malherbe. Presented by the Anthor. ; Annales des Sciences Physiques et Naturelles, §c. Par la Société Royale d’Agriculture, &c., de Lyon. Tom. IV. 1841. Presented by the Society. Proceedings of the American Philosophical Society, May 25-30, 1843. Presented by the Society. Transactions of the American Philosophical Society. Vol. VIII., new Series, Parts 2,3. Presented by the Society. PROCEEDINGS THE ROYAL IRISH ACADEMY. 1844. No. 45. May 13. SIR Wm. R.HAMILTON, LL. D., President, in the Chair. Wn. H. Harvey, M.D., was elected a Member of the Academy. Reap,—A recommendation of Council to the Academy, to open a subscription list for the fund required to complete the sum necessary for the purchase of Hodges and Smith’s Irish MSS., and that the Academy be recommended to head the list by a subscription of £100. Reap,—A letter from Lord Adare to Mr. Petrie, regard- ing a Grant from Government to the Academy, for the said purchase ; and also a letter from Sir Robert Peel to Lord Adare, in which he stated that he was “willing to recom- mend to the Treasury to grant £600 for the purchase of the MSS.,” ‘‘ on the condition that the whole collection shall be purchased, and that the sum required to complete the pur- chase of the whole shall be raised from other sources.” Resotvep, on the recommendation of Council,—That the Academy do open a Subscription list for the fund above mentioned, and that it do head the list by a donation of £100. Wm. R. Wilde, Esq., read a paper on the Pharos of Corunna. VOL. I. 3c 584 Mr. Wilde prefaced his observations by stating that he had already published an account of this celebrated building, which is situated at the extremity of the peninsula, on which the town of Corunna stands, wherein he had cursorily men- tioned, that independent of the architectural beauty of its structure, its inestimable value as a beacon to mariners crossing this portion of the Bay of Biscay, and its marking the common entrance to the harbours of Corunna and Fer- rol, what added “ still greater interest to it in the eye of the traveller, was the fact of its enclosing within its massive walls one of the most interesting monuments of antiquity— the Pharos of Hercules—the oldest existing specimen of this kind in Europe, and amongst the very few now anywhere to be found.”* These observations were those of an ordinary traveller, who had no particular theory to support, and no peculiar object in view, save that of eliciting truth, and recording, with fidelity, what passed under his notice. Since then Sir William Betham having, in his ‘‘ Etruria Celtica,” questioned some of the statements put forth in this quotation, and find- ing, as he states, some incongruity between the accounts given by Mr. Wilde and Laborde, appears to have come to the conclusion that the ancient Pharos is no¢ included, as is stated, within the walls of the modern Tower. Mr. Wilde went on to say, that ‘being about to repub- lish the original notice of this building, and feeling somewhat piqued at the assertion of Sir William Betham, who, never having seen the locality, laboured, I conceive, under such dis- advantages as hardly entitled him to criticise, although, it must be said, in the most kindly spirit, the description which I had given from a personal examination on the spot, * Narrative of a Voyage to Madeira and the Mediterranean, 2 vols. 8yo. 1st edition, 1840, pp. 12-14. 585 I have, however, to thank him for having noticed the subject, even in the manner which he did, for it has led to the disco- very of a most interesting manuscript and two drawings, the only ones, I believed, in existence, of the ancient and modern Towers, which I beg leave to lay before the Academy, and which I procured in the following manner : ‘When Sir William’s book appeared I wrote to the British Consul at Corunna, requesting him to procure me some information upon the subject of the ‘ Hercules Light,’ as well as plans or drawings of the ancient and modern tower; and also to have made for me a copy of, or extracts from, any work or archive, either in manuscript or print, which might be still extant at Corunna, Betanzos, or Brigantia, or any of the towns bordering the splendid harbour of Ferrol, and where such a record would be most likely to have been preserved; at the same time, from the present unsettled state of Spain, and the various revolutions with which that un- happy country has been visited, I hoped for, more than anti- cipated, a favourable answer to my communication. After the lapse of a considerable length of time I have received the most confirmatory proof of my original position in these two drawings, together with the Spanish manuscript, which I now exhibit to the Academy, and which were discovered in the bureau of an old architect in Corunna. This document, en- titled, ‘ Copia de la representacion y mas documentos que con fha de 16 de Marzo de 1786, dirigio, esta Junta de Go- bierno condor Planos al Ecmo Sr. Marques de la Sonora,’ appears to be a Report presented to the Marquis De La So- nora by a Government Commission, empowered to inquire into and report upon certain improvements destined to be put in force in the harbours of Corunnaand Ferrol, in 1786. In this ‘ Memoria Sobre la antiquedad de la Torre de Her- cules,’ it is recommended to repair the ancient Tower or Pharos standing at the extremity of the peninsula, ‘ the 3c 2 586 only notice of which,’ says the writer of this Report, ‘is, that it was in existence at the beginning of the fifth century,’ and was originally intended for the same purpose, namely, a signal for the ships going to England. It may be remarked, that so advantageous was the post considered, that in 1684 the Consuls of England, Holland, and Flanders, entreated of the Spanish authorities to have the building repaired, and stated that their Governments would, at their own expense, defray the cost of keeping up a light on it. “The preceding representations faithfully exhibit the condition of the original Tower, as it stood in 1786, and also that of the present modern casing of granite with which it is surrounded. “ The wood-engraving to the left represents the original ancient Pharos, a square, hollow tower, surmounted by a rotundo, which was crowned by a large flag, bearing evident 587 marks of the long-continued action of fire upon its surface. At each of the corners there was a small square turret; one of these is represented as still existing when this drawing was made, but evidently of a much more modern construc- tion than the rest of the building. At foot of the drawing we find the following inscription: ‘ Fecit Trueva Alumnus Academia ex Civitate portus Brigantini, anno 1797.’ «« An external winding staircase led to the top, and per- mitted ingress to its internal apartments, through the small apertures still existing in the tower. A small square but- tress at each corner, portions of which were in existence when this drawing was made, seems to have supported the stair or external winding passage at the angles; and the groove in the masonry still shews the position which such originally occupied. We read of a similar mode of access being employed on the exterior of the celebrated Pharos at Alexandria, probably for the purpose of carrying up the fuel, which was used to light the beacon that was placed at top. «‘ The mode of construction of this Tower is decidedly an- tique, although the general architecture and stone-work does not point out a period older than that of the Romans; and the masonry, composed of stones of comparatively small size, is cemented together by a lime-concrete, similar to that known to haye been employed, if not introduced, by this people. The height of the Tower, from the base to the rotunda at the top, was 82 royal Spanish feet, and the rotundo itself was 11 more, making in all about 132 feet English. It was 31 feet broad on each side, and in the interior were two walls crossing in the centre, each 44 feet in thickness. The Tower was divided into chambers or compartments by three stone floors, originally without any apertures in them, so that these apartments could only have been entered from without. The outer winding stair having been removed at some pe- riod long prior to the date to which we now refer, apertures 588 were made in these stone floors, and ladders leading from one flight to another, enabled persons to ascend to the top from within. It is stated in this Spanish document that the outer staircase was pulled down to build a convent in the neighbourhood, but at what precise period history does not record. The small Towers at the top are believed to have been erected subsequent to the removal of the outer stair, perhaps in 1684, when the British, Dutch, and Flemish Consuls relighted this wide-spreading beacon. ‘* With regard to the precise date ofits destruction, all that we can learn from Spanish authorities is, that when Molina De Malaga wrote his description of Galicia, in 1549, this staircase did not exist; for in this old poetic work we find some rhymes referring to it, thus: ‘ Pues la Cortina tampoco la deso, Gran Puerto do numa fortuna le corre. Y hablo de aquerte por sola una Torre Antiquo Castillo que aman el Vieso ; Aquerte es do dicen que estaba el eyrep, Mas es fabuloso sabido lo que era Estaba cereada de grand escalera Que quien la deshiro no tubo consep.’ Of which the following exceedingly rough, but literal trans- lation, may afford the English reader some idea: But Corunna I do not like, A Great Port where no fortune runs. I speak of this only on account of a Tower, An ancient Castle, which was called le Vieso (the old) ; This is where they say lived the witch, But it is a fabulous saying—whatever it was Was surrounded by a large staircase, Which whatever mounted could not find its way down. “The origin of the original Tower, and its name, are involved in much obscurity. Galician tradition assigns it to the workmanship of Hercules himself. Some characters, scarcely legible, on one of the stones, says the writer of this i ——— 589 Spanish manuscript, states that it was erected in honour of some of the Cesars. Near its base was discovered a stone bearing the following inscription: the translation of which is attended with some difficulty from de- MARTI facement, as well as the number of AVG x S ACR : contractions of the ap SEVIVS text. In any at- . : tempt at doing so it should be com- pared with the in- scription at p. 593. Baron Humboldt statesthat Laborde, who furnished him with a copy of these aaa lines, likewise in- formed him, I suppose from the inscription, that ‘ this Pharos was constructed by Caius Sevius Lupus, architect of the city of Aqua Flavia (Cheves), and that it was dedicated to Mars.’ “ Strabo, indeed, affirms that Galicia had been peopled | by Greek colonies, and according to an extract from the Geographies of Spain, by Asclepiades, the Myrlean, an ancient tradition, stated that the companions of Hercules settled in these countries. Very few Spanish authorities mention this ancient ‘ Torre del Pharo, or, as it is some- times called, The Iron Tower; and the appearance which it must have presented when originally built, accords precisely with the descriptions which we read of the ancient Pharos at Messina, and also that at Alexandria, around which we know there wound an external spiral staircase, so broad and so gentle in ascent that it is recorded a car and* oxen could with facility pass to the top. The Spanish manuscript, which 590 I now lay before theAcademy, refers its construction (in all likelihood) to the time of Trajan, because none of the geo- graphers who lived before this emperor mention it, not even the accurate Mela, who alludes to other particularities on this coast. This, however, is but a negative proof; and even among later geographers the same silence is preserved. There is, however, one record extant in a stanza to be found in the old Spanish geographer Ororio, or Orosirus, who lived in the beginning of the fifth century, to this effect : ‘Ubi Brigantia Calletce Civitas Sita Altissimum pharum & inter pauca Memorandi operis ad speculam Britanice Erigit .... “« Here we have the first notice of one of the purposes for which this Tower was supposed to be erected, and also of the ancient tradition, existing both in this country and in Spain, of the British Isles being seen from the Pharos of Hercules. Without, however, attaching any weight to the story of our island being seen from this Tower, it may be remarked, that if the ancients sailed directly zorthward from it they would, owing to the concavity in the Bay of Biscay in which the harbour of Corunna is placed, arrive at Cape Clear, instead of Cornwall. “The early writers upon Irish history and Irish tradi- tions have made frequent allusions to this ancient struc- ture, as the ‘Tuir Breoghan.’ It is mentioned under this head in the Leabhar Gabhaltas, or Book of the Con- quests, a translation of which was made by Henry O’Hart about the year 1686, and the original, which is now in the pos- session of Sir William Betham, contains this notice of it: ‘Then Lughaigh, the son of Ith, went to Tuir Breoghan, or Corunna, and shewed his father’s dead body unto the posterity of Breoghian,’ &c.; and from this Breoghain is, in 591 all probability derived the name of Brigantia, one of the oldest cities in this part of Europe. “ Sir William Betham has, with great labour and ingenu- ity, searched out and recorded, in his ‘ Etruria Celtica,’ the various Irish authorities that refer to this building, and says, that he has discovered references made to it in the Eugubian Tables, which, he believes, speak of the early navigators steering by the fire set up on the land when the ship left the coast of Spain for the Turn or Carne; and in the same pas- sage the triple-pointed hill of Cape Ortugal, the next most prominent headland, appears to him to be referred to. ‘In another place Sir William Betham says: ‘ The name of Corunna and the Groyne are both derived from the river upon which the town stands,—Garonne, the rough or boisterous river, as the Garonne of France.’ On this passage, however, I may remark, that I cannot agree with my brother Academician, for Corunna does not stand on any river, and the only one in its neighbourhood, and that too at a considerable distance across the harbour, is not the Groyne or Garonne, but the Rio Burgo. The term Groyne, however, is constantly applied by the early Spanish writers to the Bay itself. ‘** The term Corunna, or Colonna, may have been applied in after-times by the Romans, from the circumstance of find- ing the Tower or Column upon this headland, in the same way that the appellation of Cape Colunna has been applied to the island in the Grecian Archipelago on which was erected the celebrated Suniam temple, the remarkable co- lumns or pillars of which are still standing. “‘ Again: ‘ There is,’ says Sir William, ‘ some incongru- ity between the accounts of Mr. Wilde and Laborde. The latter says, the lighthouse is situated ‘‘ upon a very high mountain, a league from the harbour;” and Mr. Wilde has stated its position to be ‘‘ about a mile to the S. W. of the town, on a rock by the water’s edge.” Any one, however, 592 at all acquainted with the locality, knows that there is no such mountain in this vicinity as that described by Laborde, and the-position of the Hercules Tower can easily be ascer- tained by those who have not seen it by referring to any of the Admiralty’s charts of the coast; and, moreover, a light on “‘a very high mountain a league from the harbour” would be of little service for nautical purposes.’ ‘I find, however, on again referring to the work of La- borde, that it consists of two parts—an itinerary, or journal, which appears to have been written from personal observa- tion, and a running comment, in the form of notes, and printed in a smaller type, on the population, commerce, ad- ministration, natural history, &c. &c. of the countries visited, and which is evidently derived from other sources, and com- piled from different authorities. It happens that this latter is the part quoted by Sir William, and not the text of the Jour- nal, where, at p. 435, speaking of the harbour, he says : ‘ The harbour is in the form of a crescent; at the two points are the castles of Sainte-Clare and Saint Martin, which defend it, and a little island which shelters it from the north wind. All travellers have mentioned the ancient tower which ex- cites admiration from its height, and its strong and solid walls. The Galicians declare that it was built by Hercules, whose name it still bears; this is to attribute it to the Phe- nician merchants who frequented this coast; but a Roman inscription has been found near this tower, which ascribes it to the god Mars. If itis really the work of the Phcenicians, as its antiquity and the tradition lead us to believe, this ac- count may be reconciled by supposing that the Romans, wishing to preserve this monument, and in gratitude for their victory over the Carthaginians, who sprung from the Phee- nicians, consecrated it to their tutelary deity.’ ** As this was a matter of some popular interest in connex- ion with the antiquities and early history of this country, Mr. Wilde quoted several extracts from what Sir William 593 Betham has put together upon this subject, trom Giolla Keavin, an Irish poet, who lived about a. p. 1072, in a poem called Reim re Riogh, or the Race of Kings—from the An- nals of the Four Masters—and from the Book of Ballymote ; from all which it would appear that the Irish poets and annalists were well acquainted, not only with the existence of this Tower, but with many of the ancient bardic traditions assigned to it: such as its being built as a watch-tower by Breogin, the son of Braha, who is also said to be the founder of the city of Brigantia, &c. &c. “In the Spanish manuscript it is recorded that a stone bearing the following inscription was found built into the wall of an old house in the town of Corunna. IVPVS CONSTRVXIT EMV LANS MIRACVLA MEMPHIS GRADIBVS STRAVIT YLAM. LVSTRANS| CACVMINE NAVES 8 f) XD DVDV. “The writer of the manuscript thinks that the dilapidation of the Hercules commenced in the middle ages, when it was converted into a castle or fortress belonging to the Arch- bishop of Santiago; that the stones and material of the outer staircase were at this time removed, and that some trace of them may still be found in the fortifications of the old town. *'The result of the commission to which allusion was made at the commencement of this notice, was, that the Spanish . Government determined to leave. the ancient Pharos in ex- 594 istence, but to envelope it within the present modern granite building, which was commenced in 1797, and is represented in the right-hand figure of the engraving at page 586. Itis a handsome square tower, built of close-grained white granite, and not only contains between its massive walls the original Pharos, but is made to resemble it as much as possible; and on its exterior a projecting band of masonry exhibits the line of the original external staircase. ** No doubt can now any longer exist with regard to the position and preservation of this most interesting remain, the Pharos of Hercules. At foot of the drawing which Mr. Wilde exhibited, the following inscription is decisive: ‘ Per- spectiva que de muestra el estado de la terre antiqua lamada de Hercules quando de emprendio sure edificacion y revesti- mento de canteria por orden del Real consulado du la Coruna.” ** To establish this fact, and to record some additional no- tice regarding the traditions and early history of one of the most interesting structures at present remaining in Europe, must apologize for this lengthened notice.” Col. Jones made a communication concerning the disco- very in the River Shannon, of a large collection of ancient bronze and iron weapons and utensils, &c., which he pre- sented to the Museum of the Academy, on the part of the Shannon Commission. List of Antiquities found in the River Shannon at the under- named places. KEELOGUE. 150 Elfstones. 8 Small Brass Spear-heads. I piece of soft Stone (petre- | 8 Do. Iron do. faction). 2 Tron Sword Blades. 10 Sword and Brass Spear- _10 pieces of Teeth. heads. 1 piece of Deer’s Horn. 595 1 piece of Wood, partly pe- heads, Spurs, Ornaments trefied. of Scabbards, Druid’s 3 Iron Battle-axes, or Toma- Rings, &c., &c. hawks. 3 parts of a Matchlock, Bar- 10 Brass do. do. rel, and Tube. 41 sundry broken Spear- BANAGHER, 4 Lead Moulds, one with 2 Iron Spear-heads. stamp of Coins. 3 Brass Tubes or Pipes 1 Brass Dial. (ornaments). 3 Brass Spear-heads. 1 piece of Deer’s Horn. | SHANNON BRIDGE. DERRYHOLMES. 1 Brass Pin. | 1 Iron Sword-blade. BISHOP’S ISLAND. PORTUMNA. 1 Brass Vessel. 3 Pieces of Deer’s Horn. 3 Do. of Teeth. ATHLONE. 6 Elf-stones. 1 Tin Box containing Coins. 1 Two-edged Sword and 1 Grape Shot. Handle. 1 Corroded Padlock. 2 Spear-heads. Sundry small articles, Pipes, 5 Brass Pins. &c. (in a small Box). Resotvep,—That the special thanks of the Academy be returned to Col. Jones and the Officers of the Shannon Commission, for the collection of Antiquities now pre- sented. 25/0 “f : ; 1 pea SH hee pF SAP ah vets PROCEEDINGS OF THE ROYAL IRISH ACADEMY. 1844. No. 46, May 27. SIR Ws. R. HAMILTON, LL. D., President, in the Chair. Captain O’Connor exhibited two twisted gold rings, brought from Africa and there used as current money. The President communicated a method of mentally ap- proximating to the calculation of ancient eclipses, and applied it to the eclipse of the moon recorded by Tacitus as having happened soon after the death of Augustus. Mr. J. Huband Smith drew the attention of the Aca- demy toa report, that there was in contemplation the remo- val of a portion, if not the whole of the celebrated mound of New Grange, near Drogheda, to be broken up for the re- pair of the roads. ResoLtveD,—That it be referred to the Council to take steps to ascertain the truth of the report, and in the event of its proving true to take proper means to ensure the preservation of this great and important national monu- ment. 598 June 10. SIR Wm. R. HAMILTON, LL. D., President, in the Chair. Charles Hanlon, Esq., Maxwell M‘Master, Esq., Thomas Oldham, Esq., Philip Read, Esq., Henry Roe, Esq., and Robert Wilson, Esq., were elected Members of the Aca- demy. Dr. Apjohn read an account of the constitution of Jade, and also of two ores of Manganese from the South of Cork. Dr. Apjohn observed that these minerals had been re- cently analysed in his laboratory, and as the results were somewhat novel, he thought he might mention them to the Academy ; his principal object being that they might appear in the Proceedings, for the information of mineralogists and chemists. The Jade submitted to analysis was wrought into orna- ments of various kinds, which were brought to Europe by Captain Baddeley, who was engaged in several of the opera- tions of the recent Chinese war. Its colour is white, with a tinge of yellowish green. It has a splintery fracture, and is highly translucent. S.G.=2, 965. Hardness over 7, or be- tween rock crystal and topaz. Alone before the blowpipe it glazes, but with great difficulty, on the surface. By exposure to a strong red heat, it gives off a little water, and becomes opake. Fluxed in the usual manner with carbonate of barytes, it was found to include no al- kali. Another portion of it fused with a mixture of the car- bonates of potash and soda, yielded the following quantitative results : 599 (1) (2) (3) SE a eee es? ae | 21.10 Alumina and trace of Oxide of Chrome . -. . - 2.980 0,058 1.00 Dhak hawtteiae (edie ye 14160 hy | =1.572 27.10 Magnesia . . . + + - 22.275 1.076 ; Re oh a Fontan ne ell O20~ 0.180 3.10 Loss Ee hamatiava S BOSe 100.000 From the numbers in columns (2) and (3), which, calcu- lated in the ordinary manner, represent the relative numbers of atoms of the various constituents, it is obvious that the empirical formula of this mineral is MgO CaO Now, these atoms may be grouped so as to form a tersilicate of alumina, and a subsesquisilicate of lime and magnesia; so that the following may be considered as the rational formula of Chinese jade: MgO Ac: 03,3 Si0s-+9(3 ee In looking into works on mineralogy, I find that nephrite or jade has already been at least twice analysed, first, by Saussure, and secondly by Kastner; and, from the account given by Beudant, of the specimen examined by the latter, it would appear to be the Chinese. variety. The result, however, obtained by these chemists are quite irreconcileable with each other, and with mine. Thus, Saussure found his specimen to contain 3 per cent. less silex than I have de- tected in mine, to include no magnesia, but instead thereof, the oxides of iron and manganese, and about 20 per cent. of mixed soda and potash. Kastner obtained 6 per cent. less silex, about 7 per cent. more alumina, and 8 per cent. more VOL. II. 3D 21 SiO, + Ac. O; + 27 +3 HO. 2 Si Os) + 3HO. 600 magnesia, but no lime. The three specimens, therefore, differ as to the nature and relative proportion of their con- stituents. I may add, that it is not possible to represent the composition of any two of them by the same formula; so that, admitting the correctness of the published analyses, we are entitled to conclude that minerals really different are, in works upon mineralogy, confounded together under the name of Jade or Neptrite. Of the ores of mangeneus, the first I shall notice is a spe- cimen of psilomelanane, the black hematite of the older mi- neralogists, which I received some months since from R. W. Townsend, Esq., and which occurs a little to the north of the village of Glandore, in a mixed schistoze and arenaceous rock, which is coloured by Mr. Griffith, as old red sand- stone. S.G.=4.071. Hardness between fluor spar and apa- lite, occurs massive, but more generally in botryoidal and concretionary forms. The following are its constituents, determined by an analysis very carefully conducted : Q) (2) SU eia ut, cine Me je ia ale oo sgn BRAT y SG! bone sh ei a ie es atonal tS en Oxide Copper . . . - » «+ 1.254 0.031 Red Oxide Mang. (Mn,0,) 74, ora oe 31.241 0.393 Len a a Ad Be Perox. 50.545 1.152 Te eas ete, os atc oat aren Confining our attention to the oxides of manganese and the water, it is obvious, from the quotients in column (2) that the composition of the ore is very accurately represented by the formula Mn, O;, HO+3 Mn O,, or that it isa compound of one atom of manganite and three of pyrolusite. In the psi- lomelanite analysed by Turner, there were 4 atoms of ses- quioxide to 15 of peroxide; in that analysed by Berthier, 3 of sesquioxide to 17 of peroxide. It is obvious, therefore, 601 that the specimen I have examined is a new variety. But it is also peculiar in other respects. 1. It contains oxide of copper in appreciable quantity, a substance not occurring in the other psilomelanes, though it was found by Professor Davy, of the Dublin Society, to the amount of 4.5 per cent. in a Swedish ore of manganese, which he considered to be a braunite (see Journal of Geol. Society of Dublin, vol. i. part 3.) 2. The amount of barytes included by it is but about one-third of that found in the ores examined by Ber- thier and Turner. As respects the manner of the existence of the barytes always found in psilomelane, and in small quantity in some of the other ores of manganese also; I may observe that it is the opinion of some high authorities in science, of M. Beudant, for instance, that ¢¢ and the dentoxide are chemi- cally united, the latter performing the function of an acid. If this idea be correct, it will follow that they are capable of combining in at least two widely different proportions, for the psilomelanes of Berthier and Turner -will, upon this view, be represented by the formula 2 Bo O, 3 Mn, O3;, and that which I have analysed by the formula Bo O, 6 Mn, O3;, so that the latter contains, combined with the same quantity of barytes, four times as much sesquioxide of manganese as the former. This Cork psilomelane is obviously a rich ore of manga- nese, though of course inferior to the purer forms of pyro- lusite. It exists in quantity in the district which I have mentioned, and some cargoes of it have been brought into the Dublin market, but have, I am told, been objected to by the manufacturers of the bleaching salt of lime, in conse- - quence of its excessive hardness, and the consequent diffi- culty of reducing it to a fine powder. About three years ago, I received from Captain Kitto, a Cornish miner, long resident in the south of Cork, an ore of manganese, which appeared so different from those with: 602 which I was previously acquainted, that I was induced to submit it to analysis. It occurs in the locality already men- tioned, at Rowry, a little to the east of Glandore, in lumps’ of variable size, which, when broken, exhibit, though but iF developed, the faces of crystals belonging apparently to the right prismatic system, mixed, however, here and there with what would appear to be a brown hematite. Some of the crystalline portion of the ore, very carefully selected, gaves upon analysis, the following constituents: Sy aati Siegert <<]: ip mangps te guile Sa Vue, 9BGOS Perox. Iron. . . . . . - 8488 0.486 20 Red Ox. Mangan. 50. 67) _Sesquioxide 5.25 0.066 3 Oxygen . . . 6.52 ~ Peroxide 51.94 1.188 54 Water 2%, ocegtetyh yy Gin gear) Oe RNSD URED aas 100.00 These results do not conduct to any very probable formula. But if we suppose that what is set down as sesquioxide is really present as peroxide, a supposition which accords sufficiently well with the analysis, then the composition of this ore becomes very simple, being represented by the formula Fr. O;, HO+3 Mn Oz, that is by one identical with that which we have found for the psilomelane, when we substitute sesquioxide of iron for the sesquioxide of man- ganese. I have no doubt that this represents its real constitution, so that it may be safely set down as a new and very distinct species. I may observe that this mineral answers well for yielding oxygen, but is uneconomical as a source of chlorine, in consequence of the wasteful consump- tion of acid, in order to the saturation of the peroxide of iron; one-half in fact of the acid is uselessly expended. Mr. William Andrews, Secretary to the Dublin Natural History Society, read a paper upon the genera of Ferns 603 Trichomanes and Hymenophyllum. His remarks were chiefly directed to the species of Trichomanes discovered by him in September, 1842, in the western part of the County of Kerry, and which presented a variety of growth and state of fructification so much more developed and characteristic of the genus of that beautiful fern than had hitherto been met with in Ireland, that determined him to examine its affinities with some of the exotic ferns, particularly with those of the West India Islands. The Trichomanes was first discovered in Britain, by Dr. Richardson, at Belbank, near Bingley, Yorkshire, a wretched specimen of which is in the Banksian Herbarium, now in the British Museum : a figure of a barren frond is given in Dill. in Raii Syn. S. p. 127, t. 3. This specimen, however, not having been found in fructification, was supposed to be identical with the Filix (Trichomanes) pyxidifera of Plu- mier, and was described as such by Hudson, in his Flora Anglica, p. 461: and this name it retained until its disco- very, in the month of October, 1804, at Turk Waterfall, near Killarney, by Mr. Mackay, Curator of the Botanic Garden of Trinity College. Mr. Mackay obtaining this beautiful fern in fructification, forwarded specimens to Sir James Edward Smith, who at once decided its distinctness from Plumier’s plant, and considered it to be a new species, which he named and figured in English botany as Hymenophyllum alatum, from its winged stipe. The distinguished Robert Brown, the first physiological botanist of the day, corrected this specific appellation to that of brevisetum (Br. in Hort. Kew. ed. 2, 5, p. 529), from the short and barely exserted state of the receptacles that the Killarney plants generally presented. Mr. E. Newman, who has devoted so much at- tention to the specific characteristics of the British ferns, formed the first view, that the Killarney species perfectly agreed with Willdenow’s description (Sp. Plant. 5, p. 514) of the Speciosum of Teneriffe, and published it as such, in 604 his first edition of the History of British Ferns. The speci- fic name brevisetum, however, was still retained through the several editions of the British Flora, until the discovery by Mr. Andrews, in September, 1842, in a wild and wooded glen in the western part of the County of Kerry. The striking characters and fine state of fructification exhibited by these splendid plants, the most rare and most beautiful of British ferns, and now altogether confined to the south- western parts of Ireland, led Mr. Andrews to examine mi- nutely, and to trace their affinities with the numerous exotic species of that beautiful genus; and from communications with Sir William J. Hooker, and to the great kindness of that most excellent botanist and encourager of science, and the reference to his very extensive fern herbarium, it was traced and detected to be the true Trichomanes radicans of Swartz, setting aside the species brevisetum of the English flora, and the Speciosum of Willdenow. Thus the mild temperature of the south-western parts of this country pro- duced, in the utmost luxuriance of tropical growth, a plant pe- culiar to the West India Islands, and to the western coast of South America. To Dr. Scouler’s kindness Mr. Andrews was also much indebted for specimens of Trichomanes radicans, and T. Scandens, collected by Dr. S. in Brazil, and which enabled many doubts to be cleared. Mr. Andrews noticed a very remarkable character of fructification in the new variety from Kerry, ‘ that the cap- sules formed around the base of the receptacles within the cylindrical involucres, and as the receptacles elongated and became exserted considerably beyond the involucres, the capsules continued forming in an even dense mass to the ex- tremity of the receptacles.” This is described as of rare occurrence in Trichomanes. The Trichomanes reniforme of New Zealand, and the Hymenophyllum fuciforme of Chiloe, are noticed as having the capsules external to the involucres, but their being exposed to view was supposed 605 merely to result from the spreading and shrinking of the valyes. Loxsoma appears to be the only recorded genus as possessing that peculiarity of fructification. The specific descriptions of Trichomanes radicans and its synonyma, are fully given in part 2, p. 125, of that invalu- able work, Species Filicum, by Sir J. W. Hooker, recently published. Professor Allman made some observations on Mr. An- drews’s paper, in corroboration of its principles. — DONATIONS. Proceedings of the Geological Society of London. Vol. IV., Part 1. (1843). Presented by the Society. Bulletin der Kénigl. Akademie der Wissenschaften zu Munchen. Nos. 1 to 55. Abhandlungen der Philosophisch. Philologischen Classe der Kéniglich Bayerischen Akademie der Wissenschaften zu Munchen. Dritten Bandes dritte Abtheilung, in der Reihe der Denkschriften der XVIII. Band. Abhandlungen der Mathematisch. Physikalischen Classe der Kéniglich Bayerischen Akademie der Wissenschaften zu Munchen. Dritter Band. Die Abhandlungen von den Yahren, 1837, bis 43, enthaltend. Presented by the Aca- demy of Munich. Versuch einer objectiven Begriindung der Lehre von der Zusammensetzung der Krifte. Von Dr. Bernard Bolzano. Presented by the Author. ‘Prodromus zu einer neuen, verbesserten Darstellungsweise der héhern analytischen Dynamik. Vom Grafen G. Von Buquoy, Ph. D., &c. Presented by the Author. ek + on i. te a a 4 = ee ceo “tai age DR. PROCEEDINGS OF THE ROYAL IRISH ACADEMY, 1844. No. 47. June 24. SIR Ws. R. HAMILTON, LL. D., President, in the Chair. REso.veD, on the recommendation of Council—That the Academy do pay Mr. E, Curry £41 13s., for completing the Catalogue of the Irish MSS. of the Academy, this sum in- cluding the money due to him at present. Sir William Betham gave notice that, at the next meeting of the Academy, he would move for— Ist. A list of all papers or essays read before the Aca- demy, in the departments of Belles Lettres and Antiquities, which were referred to Council for publication, from the 17th of March, 1828, to the 17th of March, 1844, containing the dates of such reading, the names of the authors, whether ordered by the Council for publication, and, if published in the Transactions, with the dates of the Council's order for publication. 2nd. An account of all sums of money expended for en- graving copper-plates or wood-cuts, or making lithographs, to illustrate such essays or papers, which, ordered by Coun- cil to be published, have or have not yet appeared in the Transactions of the Academy. 3rd. An account of all sums of money expended on ac- count of paper and printing of any such essay or essays, or VOL. Il. 3 E 608 papers, which have been commenced, and are now in pro- gress of printing; with the amount of liability of the Aca- demy for what has not yet been paid. 4th. A statement of the terms of any agreement or con- tract entered into by the Council, with the author or authors of any such paper or essay, and the sum or sums of money advanced on that account. 5th. An account of all medals and rewards adjudged by the Council, and paid to any author for papers and essays, during the said period, from the 17th of March, 1828, to the 17th of March, 1844, with the dates of such payments and «elivery. 6th. An account of the debts and liabilities of the Aca- demy at this time, and also of their available assets. It was moved by Dr. Apjohn,—That the Secretary of Council be requested to provide the Academy, at the next meeting, with the information required in Sir William Betham’s notice. The motion, after discussion, was withdrawn. The Rev. H. Lloyd laid upon the table of the Academy a magnetical instrument, which had been recently constructed under his direction by Mr. Jones of London, and which he proposed to denominate the ‘‘ Theodolite Magnetometer.” Much attention had of late been given to the construc- tion of small magnetical instruments, for the use of travel- ling observers, and many improvements in their form had been effected by Prof. Weber, Mr. Fox, and Lieut. Riddell. Prof. Lamont had also recently adopted magnets of a very small size in all the instruments employed by him in his magnetical observatory, and had stated his conviction of their superiority over the larger magnets hitherto in use. Without entering at present into the grounds of this convic- tion, in the unlimited form in which it had been asserted Tee eee 609 by Prof. Lamont, Mr. Lloyd said that, as respects certain instruments intended for observations of a particular kind, there seemed now to be a pretty general agreement on the subject. He had himself proposed an instrument for the de- — termination of the changes of the Magnetic Inclination, in which the magnet was necessarily a small one; and the ad- vantages of small magnets, in the delicate observation of the absolute Horizontal Intensity, seemed now to be fully recognized. While engaged in considering the best form of an instru- ment intended for observations of the latter class, Mr. Lloyd was led to perceive, that the same apparatus might be made te serve also in the determination of the Absolute Declina- tion ;* and, by a few slight additions in the details of its construction, in that of the variations of the three magnetic elements. It may likewise be employed for all the usual pur- poses of a Theodolite ; and thus, with the addition of an or- dinary Inclinometer, a Chronometer, and a Sextant, consti- tute a complete magnetical equipment for the use of the tra- velling observer. The following is a brief description of the instrument. A divided circle, similar to that of a Theodolite, is sup- ported on a tripod base, with levelling screws. This circle is nine inchest in diameter ; it is divided to 10’, and subdivided by two verniers to 10’. The upper plate of the circle has twot projecting arms, each carrying a pair of adjustable Y sup- ports for the reading telescope, at a distance of six inches from the centre. The telescope rests in these supports on a tran- * It may be proper to observe that this arrangement had occurred to the writer before he had seen Prof. Lamont’s account of his magnetical Theodolite, an instru- ment in which the same end is obtained, although by different means. + A circle six inches in diameter, and read to 20", is sufficient for all the pur- poses of a travelling observer. : { One is sufficient, and the instrument will be so modified in all future construe- tions on the same plan. 610 sit axis, which is rendered horizontal by the help of a riding level. The aperture of the object glass is eight-tenths of an inch; a glass scale, divided to the ;},5th of an inch, is fixed in its focus; and the eye tube is made to move across the scale in a dovetail slide. The magnets are hollow cylinders, each furnished as a collimator with an achromatic lens, and a fine line cut on glass in its focus. There are four such magnets: two of them being 33 inches long, and half an inch in exterior dia- meter, and two 3 inches long, and three-eighths of an inch in exterior diameter. The larger magnets are furnished with a Y stirrup, in which they may be inverted ; the smaller magnets have the ordinary tubular stirrup, with a suspension pin and screw socket. A hollow brass cylinder, of the same dimensions as the larger magnets, and carrying a small hol- low cylindrical magnet within, serves to determine the amount of torsion of the suspension thread; it is likewise fitted up as a collimator. There are two boxes, within which the magnets are to be suspended. That belonging to the smaller magnets is a rectangular box of copper, closed by mahogany sliding sides, and having a circular aperture at each end filled with paral- lel glass. It is 3} inches long, 14 inches wide, and 1 inch deep, internally; and the thickness of the metal is a quarter of an inch, so that it may act powerfully as a damper. A suspension tube of glass, eight inches long, is screwed into an aperture in the top of the box; and is furnished with a graduated torsion cap at top, and a sliding suspension pin. This box is made to fit on the centre of the upper plate of the circle, and is capable of removal at pleasure. The box employed with the larger magnets is of wood, and of the same form as the copper box, but somewhat larger. It is detached from the instrument, but may rest on the same stand, A small wooden piece with a mirror serves to illumi- nate the magnet collimator, either from above or from the 611 side, according as the light of day, or that of a lamp or candle, is employed. The measuring rod employed in deflection experiments is a compound bar of gun metal, formed of two bars, the lower of which has its surface horizontal, and the upper ver- tical. It is three feet in length,* and is graduated on its ver- tical surface. It is placed upon the upper plate of the circle, beneath the box, and at right angles to its longer sides; and _ itis so fixed that it may be removed with ease, and replaced exactly in the same position. The support of the deflecting magnet slides upon the upper bar, and is furnished with a vernier, by means of which the distance of the two magnets may be determined with accuracy and ease. The apparatus is furnished with two soft-iron hollow cylinders, nine inches long, and three-fourths of an inch in diameter, which fit in vertical sockets attached to the upper plate of the circle. By this addition the instrument is con- verted into an Induction Inclinometer, for the measurement of the changes of the Inclination. By a slight addition to the suspension apparatus, the instrument may likewise be used as a Bifilar Magnetometer, for the measurement of the changes of the Horizontal Force. These adaptations are, however, of minor importance to the travelling observer, whose main con- cern is with the absolute determinations ; and in a fixed ob- servatory it is essential that there should be separate instru- ments for the separate purposes. The most convenient order of the observations to be made with this apparatus, when employed by the travelling ob- server, is the following. 1. Measurement of Absolute Declination. The copper box and measuring rod being removed, one * For the purposes of the travelling observer, it will be more convenient that this rod should be in two pieces. Two single bars, placed edgewise, will suffice. 612 of the larger magnets is to be suspended within the wooden box, which should be placed on the same stand with the di- vided circle, at a distance not less than one foot from its centre. The optical axis of the telescope, and that of the magnet-collimator, are then to be brought nearly into the same right line, by an azimuth movement of the top of the stand, and by a small parallel movement of the box. The torsion of the suspension thread is then to be determined by the help of the brass cylinder, and to be removed by means of the torsion cap. The magnet being then replaced, the coinciding division of the scale is noted, with the magnet di- rect and inverted, and the mean of the two readings is the division corresponding to the magnetic axis. The verniers of the circle being then read, the telescope is to be turned until the division so found coincides with a fixed mark, whose azimuth is to be determined at leisure. The latter deter- mination is made by the help of the same Theodolite, used in combination with the Chronometer or Sextant, 2. Observation of Vibration. The upper plate of the circle is to be moved to its original position, and clamped there. The coefficient of torsion of the suspension thread being determined, by the help of the torsion cap and glass scale, the magnet is to be set in vibration, and the time of 200 vi- brations determined in the ordinary manner. The are of vibration should be noted, by the help of the glass scale, at the commencement and end of the observation, and the tem- perature recorded at the same times. 3. Observation of Deflection. The wooden box being removed, the metal box and the measuring rod are to be attached to the upper plate of the instrument. One of the smaller magnets is then to be sus- pended; and the larger magnet being transferred to its sup- port upon the measuring rod, at a fixed distance, the upper plate and telescope are to be turned until the collimator line — 613 of the suspended magnet is seen to coincide with the central division of the scale of the telescope. The verniers of the circle being then read, the deflecting magnet is reversed, and the telescope is moved until there is a new coincidence. The verniers being again read, the difference of the two readings - is double the angle of deflection sought. It is necessary to eliminate the changes of the Magnetic Declination, which may occur between these two readings; and for this purpose the wooden box and one of the spare magnets may be employed by asecond observer. But the same elimination may be made as effectually by a single observer, by taking a series of readings with the deflecting magnet alternately in the two positions. Finally, the observation is to be repeated with the deflecting magnet at the same distance on the other side of the suspended magnet, and the mean of the two results taken as the deflection corresponding to that distance. The quantity sought may be inferred from the angle of deflection at a single distance, with as much accuracy as is generally attainable in observations made in the open air, or in a tent; and, in such cases, it will generally be found more advantageous to multiply the observations at the same dis- tance, in the manner already mentioned, than to repeat them ‘at two or more distances. The distance should be about Jive times the length of the magnets. The preceding arrangement is suggested chiefly in regard to the economy of time. But, when the observer has suffi- cient leisure, it is desirable that the time of observation of the two elements should be as near as possible to the epochs of their principal maxima or minima, the periodical variation being then least. For this purpose the observations should be so arranged, that the middle of the observation of Inten- sity may fall between 10 and 103 a. M.; and that of the ob- servation of Declination between ] and 13 p.m. In this case, then, the preceding arrangement should be nearly reversed. The observer should commence with the observation of de- 614 flection ; proceed at once to the observation of vibration, determining the coefficient of torsion at the end ; and, lastly, make the preliminary arrangements (of detorsion, &c.), for the determination of the Declination, deferring the observa- tion itself until 1 p.m. If there be a second observer, he should undertake the observation of Inclination, and such sextant observations as may be required for the determination of the Latitude, the Time, or the true Meridian. The obser- vation of Inclination should be simultaneous with that of the Horizontal Intensity ; the astronomical observations may be made whenever most convenient. The Theodolite Magnetometer may likewise be employed with advantage in a fixed observatory, especially in observa- tions of the absolute Intensity; and it is worthy of remark, that if the differential instruments used in connexion with it be small ones, the circle of this instrument may be em- ployed in their adjustments, and their construction thus re- duced to the simplest possible form. Mr. Wm. R. Wilde read a notice of the opening of some Tumuli, by Mr. Nugent, and the Rev. Dr. Todd (V. P.) on the part of Mr. Nugent, presented a stone of a peculiar form, found in one of the Tumuli described. : The thanks of the Academy were given to Mr. Nugent, for his communication and donation. Mr. R. Mallet presented the results of his analysis of a porcelain clay, discovered some years ago by him, at Howth, and since extensively brought into use for the manufacture of crucibles. The clay is found upon the southern side of the penin- sula of Howth, which consists principally of quartz rock ; it exists in large concretionary masses, or highly irregular beds, and appears to have reached its present position by _— 615 the transport of water. It is found of every degree of fine- ness, from a coarse gritty mass of decomposing pebbles, with occasional large nodules of friable felspar, to that of an im- palpable colourless clay, like that of Dorsetshire, known as pipe-clay. This is soft, sectile, adheres to the tongue, and forms a strongly adhesive and plastic mass with water, capa- ble of being moulded upon the potter’s wheel into the finest forms. It bakes perfectly white, or occasionally of the slightest possible rosy tint of white. Some of the masses of this mineral are strongly disco- loured by iron and manganese, and imbedded in the finest parts are occasionally found a few fragments of marine shells, and bits of wood. By washing with abundance of water, a fine quartzose sand is separable from even the finest portions of this clay. This sand is white, but water separates from it a little sand of a darker colour, like common sea sand of the Dublin coast, and a few microscopic flakes of mica. A singular minute black worm is found in this clay, which may be worth the attention of naturalists. The clay, as dug out, does not efferversce with acid, and is insoluble in them; it yields no soluble matter to water, and appears to contain no alkali in any specimens yet ex- amined. Mr. Mallet, however, has reason to think that the less fully decomposed portions of the clay may contain alkali in a soluble condition, and hence render the material valuable as a manure. Some of the finest portion of the clay, washed from the sand, and dried at a temperature of 212° Fah., was found by Mr. Mallet to have the following composition. The analysis having been conducted in the usual way, and with the usual precautions, it does not seem necessary to detail its steps: VOL. Il. SF 616 DAC, eee eee) ae. es oO Alumina, . SO ae = eae Pepe. es) sake Sle yo eee, Oreo WeGRESIa, 2 eke sie ee OOo Oxide of irda. “Mtoe steer ETO Wate wi te a a eee ee 93:01 As no washing completely removes the presence of sand from this clay, which always feels gritty to a glass rod, and as it contains comminuted mica, it could not be expected that its analysis should present a precisely mineralogical result. From the close analogy, however, which the above figures present to the composition of various felspathic rocks, as analysed by Beudant, Berthier, &c., there can be little doubt but that the geothetic origin of this clay is the decomposition of felspar, or other allied granitic minerals. In fact the re- sults approximate to the formula (taking the iron and mag- nesia together). (Al, + Sis + Ca + Mg + FeO) + HO, or, 3(Al + Si;) + (Ca + Sis) + (Mg + FeO) +Si,) + HO. This clay is of very great economic value, and capable of being used for the manufacture of the finer descriptions of pottery or even of porcelain; it has, however, hitherto only been brought into use for the manufacture of crucibles, by Mr. Mallet. The President read a paper on an improvement in the double achromatic object glass. DONATIONS. Life of W.V. Morrison, Esq., M.R.JI.A. By John Morrison, Esq. Presented by the Author. 617 Bericht iiber die zur Bekanntmachung geeigneten Ver- handlungen der Kénigl. Preuss. Akadémie der Wissenschaf- ten zu Berlin, 1842-1843. Abhandlungen der Kéniglichen Akademie der Wissen- schaften zu Berlin (1841). Presented by the Academy. Abhandlungen der Kéniglichen Gesellschaft der Wissen- schaften zu Gottingen. Erster Band. Von den Jahren 1838- 1841. Presented by the Society. Almanach der Kéniglichen Bayerischen Akademie der Wissenschaften zu Miinchen (1843). Presented by the Aca- demy. Leitfaden zur Nordischen Alterthumskunde herausgege- ben von der Kéniglichen Gesellschaft fiir Nordische Alter- thumskunde (1837). Die Kénigliche Gesellschaft fiir Nordische Alterthums- kunde xu Kopenhagen (Jan. 27, 1842). Memoires de la Société Royale des Antiquaires du Nord 1840-1843. - Presented by the Society. Fasciculus Inscriptionum Grecarum. Edidit Jacobus Kennedy Bailie, S.T.P. Presented by the Author. Proceedings of the Chemical Society of London. Part 6. Presented by the Society. Journal of the Statistical Society of London. Presented by the Society. Literarische Sympathien oder industrielle Buchmacherei. By Dr. J. G. Fliigel. Presented by the Author. Bjorgynjar Hatfskinn. Presented by Dr. Robt. Graves, M.R.I.A. The Numismatic Chronicle for April, 1844. Presented by the Numismatic Society. Journal of the Franklin Institute. 5th Volume, 8rd Series. Presented by the Institute. An Olia Podrida, or Scraps Numismatic, Antiquarian, - 618 and Literary. By Richard Sainthill. Presented by the Author. Journal of the Geological Society of Dublin. Vol. II. Part 1, No. 2. Presented by the Society. Sixteen Specimens of Chinese Cash. Presented by Robert Mallet, Esq. Archives du Museum d'Histoire Naturelle. Tome III. Livraison 4. Presented by the Directors. Memorie deli I. R. Istituto Lombardo di Scienze lettere ed Arti. Vol. 1. Presented by the Institute. Edinburgh Astronomical Observations. Vol. V., 1839. Presented by the Royal Astronomical Society. Greenwich Magnetical and Meteorological Observations, 1840-1841. Presented by the Royal Astronomical Society. L’ Art de connaitre les Pendules et les Montres. Par J. B. A. Henri Robert. Presented by T. Hutton, Esq. Puits Artesien de 0 Abattoir Grenelle. Presented by T. TIutton, Esq. On the Industrial Resources of Ireland. By Robert Kane, M.D. Presented by the Author. APPENDIX. No. I. LIST OF SUBSCRIBERS TO THE FUND FOR THE PURCHASE OF THE COLLECTION OF IRISH ANTIQUITIES, COINS, AND MEDALS OF THE LATE VERY REV. HENRY R. DAWSON, DEAN OF ST. PATRICK'S, DUBLIN. —__—_—_@——_- The Names marked thus rs are Members of the Royal Irish deademy. d. | £ | Brought forward 68 * Adare, Edwin Visct., M. P., Bennett, Robert, Esq. oar Waterloo Crescent, Dover, Mio Dirc 0 Armagh, Archbp. of, Rt. Hon. (Recorder), 1 and Most Rev. Lord J. G, Butt, Isaac, Esq., LL. D., 1 De la Poer Beresford, . 5 0 0 | * Ball, Robert, Esq... . - 1 Alley, George, Esq, - . 1 1 0 | * Banks, John T., M.D...” “tT Adair, Thos. Benjamin, Esq., 1 0 0 Barrington, Edward, Esq.,_ 1 * Anster, John, Esq.,LL.D., 1 0 0 Barrington, Richard, Esq., 1 * Apjohn, James, Esq., M.D., 10 0 Barlow, Wm. Thos., Esq., . 1 * Bateson, Robert, Esq., . 1 * Brady, Rt. Hon. Maziere, | * Beatty, Thomas Bs Pity Ne (Chief Baron of the Ex- "GP hae 1 chequer), ; 5 90 0 | * Beauchamp, H. C., ” Esq., “9 * Brisbane, Sir Thomas M. adie er nOoy Oy} M.iD.5.. » 1 * Beaufort, Captain R. N., 5 0 0. Bellingham, O’ ‘Brien, Eeq,, Beat * Barrington, Matthew, Esqi, 5.0, 0 | * Benson, Chas., Esq., M.D., 1 * Bolton, Chichester, Esq, . 5 0 0 Bewley, Henry, Esq., . 1 * Borrowes, Robert, Esq., 5 0 0 Blacker, William, Esq., . 1 * Botfield, Beriah, Esq.,M.P., 5 0 © Blair, James K., Esq., Tem- * Bailie, Rev. Jas. Kennedy, ple, London, . . - + 1 1).,: «Poo ,sihvord eee O Bland, F., Esq, «- + - 1 * Blood, Bindon, Esq., Edin- Boileau, G. W., Esq., 1 burgh, . - - + i 8indhe 0 Boileau, S.,Esq., . - + 1 Brooke, William, Esq.,. ata 3 0 O|* Bolton, W. E.,Esq, . . 1 Bernard, Lord, . . . »- 2 0 0 Bottomley, William, Esq,, 1 Barton, John, Esq... - + 2 0 0 | * Bowles, John A., Esq., 1 * Bergin, Thomas F., Esq., . 1 10 0 Boyle, James, Esq., 1 68 14 0 90 Ss, 1 | | -_ a So cococoocococor} cooco ooooocoo oooocoocoo ococcco So ooocoocco os o Brought forward, Brocas, Henry, Esq., Brocas, William, Esq., . * Burrowes, John, Esq., . * Burton, F. W., Esq., . * Butcher, Rev. S., F.T.C.D., * Butler, Rev. Richard, Trim, Butler, Colonel, Butler, Rev. Wm. Recer * Bruce, Haliday, Esq., Blacker, Stewart, Esq., * Cooper, E. J., Esq., M. P., * Callwell, Robert, Esq., . * Courtenay, H., Esq., * Caulfield, Hon. Henry, Cane, Richard, Esq., * Cane, Edward, Esq., * Carr, George, Esq-, - - Clibborn, Edward, cgi ; Close, Colonel, * Conway, F. W., Esq-, - * Cooper, J. Sisson, Esq., * Cusack, James, Esq., M.D., Clogher, Bishop of, The Hon. and Rt. Rev. Lord Robert Ponsonby Tot- tenham,D.D., . .- Curran, W. H., Esq., Caledon, Countess of, Chapman, Benjamin James, Esq., M.P.,_ - * Chetwode, Edward Wilmot, Esq. * Gisndioning, Alex, Esq. =a * Croker, Charles P,, cae M. D., Calvert, Adam, Eiq., os * Cane, Arthur, Esq.,. - * Carmichael, Richard, Esq, ; M.D., + Patmectiaet, Avdvew: Esq., a * Carter, S., Esq., « * Cash, George, Esq., - Cather, Thomas, Esq., . * Churchill, Dr., - “ * Clarke, Thomas, Esq., . Close, J. S., Esq., : * Cole, Owen Blayney, Eeq., ; * Colomb, Lieut.-Colonel, * Combe, George, Esq., . - Conyngham, Wm. iti Esq., - ; Cooke, J. R., Esq,, - * Corballis, John R., Esq., Corballis, James, Esq., ear: * Coulter, Thos., Esq., M. D., Ly 89a. 90 16 0 P10: at iL 20? Oo) iyo. 30 Lo 0: Le Oy 10 KO) OH id Aw 120; JO 1 0. Ty0y0 20 O 10 0 10 0 Le 5 1p nO 5 0 ee, 5 0 > mp Sing O a @ 3) 6...0 oe > 20: 0 Zt 0 20 0 geo 0 Ze 0 To 0 70-0 1. 0 Leo © 1 0 0 re 0 og U reg? 0 nor 0 EO" 0 10 0 Lorie, 0 1 0 0 "0" 0 Ler 0 ree 0 arto" ‘0 iO Rio 219 16 O cooooocecece me i Cramer, Maurice, Esq., Crosthwaite, Leland, Esq., Curry, William, Esq., Clinche, H. O. B., Esq., Curry, Eugene, Esq., De Grey, Thomas Philip Earl (Lord Lieutenant), and Donation of a large | Gold. Collar, “. © <> = | Dunraven,Wyndham Henry | Wyndham, Earl of, . | Downshire, Arthur Blundell / Sandy Trumbull, pager Of; 3 : Dick, Asinton, Hig ¢ “M. Pe London,. . * Darley, Frederick; Esq., - * Doyne, Charles, Esq.,. . Digby, Thomas G., Esq., . Daly, James, Esq., . - * Davidson, John, Jun., Bsa. of Armagh, . * Davy, Edmund, Esq. er Deane, Sir Thomas, * Dixon, Rev. R. V., . Dobbs, Joseph, Esq., Doherty, John, Esq., Donegan, John, Esq., * Downes, George, Esq., . * Drummond, Rev. Dr., . Duke, Jemmet, Esq., * Dunlop, Durham, Esq., * Elrington, Rev. Dr., . . Enniskillen, William Wil- loughby, Earl of, Eliot, Lord, 3 5 * Edington, William, Esq. Lip Eustace, John, Esq., M. D., Edgeworth, M. P., Esq., Fitzwilliam, Chas. William Earl, ° Fortescue, Hugh, Earl “? * Foster, Hon. Justice, Ferrier, James, Esq, -. - * Fitzgibbon, Gerald, Esq., . Fortescue, Esq., * Ferrier, Alex. Jun., Esq., . * Ferguson,Hugh, Esq.,M.D., | * Ferguson, Samuel, Esq.-, Ferrier, Alexander, Esq., - | * Finlay, John, Esq., LL. D., Finn, Rev. Charles, P. P. .- Corrigan, D. J., Esq., M. D., Brought forward, 219 16 fig: i at had I i. 0 0 10 0 10 20 0 20 0 10 O 10 0 5 60 2 40 110 1 0 LEG es | 1- 0 1 a , Lid 1 0 AsO Lied Lot® Ly ae 10 0 ae 5 (0 a0 140 0 10 272018 20 0 tO 20 2 0 2 6 110 0 1.0. 1 0 1.8 1s 389 6 i — i — i — rr) ccoocoooo® coocoooocecso — oocco cooceocoocoooeo £ Brought forward, 389 Fitzgerald, John, Esq., Fitzpatrick, P. V., Esq., * Foot, Simon, Esq., . . Foot, Lundy E., Esq., . Forster, Robert, Esq., « Fox, Rev. J. W. . * Goff, Rev. Thomas, . Goold, Thomas, Esq., . . * Graves, Rev. C., F. T. C. D., Guinness, Arthur, Esq., Gordon, Robert, Esq., . . Gordon, R., Esq., Chelten- ham, . Gosford, Archibald Earl of, * Graves, Robert J., Esq. Ma Metis | Sette * Grierson, G. A., Esq., a * Grubb, hice Esq., - Guinness, Ben. Lee, Esq., Guinness, A. Lee, Esq., * Graham, Professor, Ciates burgh, . * Grimshaw, Wrigley, Esa, is 11) 0 Sls la a Gill, M. H., Esq,, . Goold, Braniis, Esq, Gordon, R. H., Esq.,_ . * Griffith, Richard, Esq., Guinness, W.N., Esq., . . Gilmore, J. B. Esq., Q.C., Garrett, Henry, Esq., Herbert, Hon. Sydney, . * Hume, A. Esq., .« 2 * Hutton, Thomas, Esq. . * Hill, Lord George, A., . * Hudson, Henry, Esq., M. D. * Hudson, William Elliott, Esq,, - * Hamilton, Sir W. R., ae ‘D. PCR, Az, °.7 Hutchins, Samuel, Esq., : Hall, Lieut.Colonel H., Lon- don, aneks : Homan, Sir W. J, Bart. * Hart, A. Searl, LL. D., F.T.C.D., - : Haughton, James, Esq., ata Haughton, William, Esq., . Hone, Joseph, Esq., . . * Hope, Thomas C. Esq., M. D., Edinburgh, * Horner, Rev. James, Herrick, J. E., Esq., Hutton, Mrs. Thomas, . 1 — te et ht NNWwNwty ww wo woo a _ — ee — — bO DO cocococaj” wmoceoso cocoo w i] — a) ocoooco —— i) _ o _ ceoccococor ooococsc oocooco cooocooococeo o o oso oo — i] £ Brought forward, 517 Hackett, Michael, Esq., Haffield, Arthur, Esq., - Hall, S. C., Esq., . - Hall) MraiS8: Gin, << * Hamilton, John, Esq., « * Hamilton, Chas. W., Esq., Hamilton, Dacre, Esq., . * Hanna, Samuel, Esq., M.D., Hanna, William, Esq., . | * Hardiman, James, Esq., * Harrison, R., Esq., M. D., - Hewson, John, Esq., * Hill, William, Esq., * Hincks, Rev. Thomas, LL.D. | * Houston, John, Esq., M. D., Hunt, Percival, Esq., M. D., | * Hutton, E., Esq., M. D., Hutton, Henry, Esq., . Hutton, Rev. Joseph, Hyndman, George C., Esq., * Hemans, G. W., Esq., .- Healy, F. W., Esq,, . Irwin, Rev. Alexander, * Jones, Robert, Esq., * Jones, Colonel Harry D., | * Johnson, Hon. Justice, * James, Sir J. K., Bart., * Jellett, John H.,F.T.C. D., Johns, Alexander, Esq., Johnson, Edmund, Esq., Johnston, Rev. Richard, Jacob, John, Esq., M.D., . Kildare, Marquis of, * King, Hon. James, . Kemmis, Henry, Esq., . * Knox, G. James, Esq., . * Kent, William T., Esq., Kinsella, Rt. Rev. Dr., —. * Kennedy, George A., Esq., M. D., * Kerry, Knight of, (Right Honourable Maurice Fitz- gerald), P * Kane, R. J., Esq., M. D., . 5 * Kyle, William C., exp “9 LL.D., . Kane, William, Esq. | * Kelly, T. F., Esq., | * Kelly, D. H. Esq., Kerr, Doctor, . . Leinster, Augustus Frede- rick, Duke of, . — i ed ew le ee ee ee _ wNananaco i) —) mooccoocoow _— i) iw) wmwococe cococso 0 614 11 moocooscsceoscsooosoosooooocoers ecooocoeocecsecosoeoesoeocoeecooooon —) eococeccoco coeococso o Brought forward, 614 11 * Leitrim, Rt. Hon. Natha- niel Earl of, 5 Lorton, Robert Bdverd Viscount, : * Larcom, Captain R. E., . * Lloyd, Rev. Hamphrey,D.D De Lod VGH De Lucas, Edward, Esq, : Lismore, Very Rev. Henry Cotton, LL. D., Dean of * Lyle, Acheson, Esq., . . Latham, Oliver, Esq., Lindsay, John, Esq., * Lambert, Rev. Charles J., * La Touche, G. D., Esq., * Lee, Rev. Wm., F. T.C.D., Lees, Doctor, . . “ * Lenegan, J., Esq, - . * Litton, Samuel; Esq., M. D., i * Lloyd, William T., Esq., .« * Longfield, William, Esq., - * Mac Cullagh, James, Esq., i Lig Ds, Boutin kot Des: fe oe Midleton, Goes A., Vis- count, . * Marsh, Sir H., Tere ‘M. D., * Macartney, J. Esq-, M. D., * Monsell, William, Esq., Moore, Edward, Esq., . * Murchison, Rod‘. Impey, Esq., F.R.S., V. P. G.S. * Mollan, John, Esq., M. D. Macdonnell, Alex., Esq. * Magrath, Sir George, M.D., * Maguire, William, Esq., Molyneux, Sir G. Bart., M ‘Carthy, Alexander, Esq., Maturin, Edmund, Esq., Macan, John, Esq... . - Mac Clean, Samuel, Esq., - M‘Carthy, Justin, Esq., Mac Donnell, James, Esq., M.D Betfast® s05), * Mac Donnell, J., Esq., M. D. * Mac Donnell, Rev. Dr., det Gla ages mare) ae M‘Glashan, cecal Esq. ead * M‘Neece, Rev. T., F.T.C.D., * Mallet, Robert, Esq. BA Martin, John, Esq., - * Mason, H. J. M., Esq. LL. D. (and donation f a gold Fibula), Massy, Hugh, Esq., * Mayne, Rev. Charles, : - 20 £28: 0 titpy KY) 5. 0 Beet tite) 3. 0 2, 2 Ae) 2 0 a) i Nea) roe tag) iT a0 1 30 1 AG LE A0 21. 60 2220) 10 Sees 5 60 a 3 0 5 0 3 0 2. 0 2 0 2 0 2 0 eal Ee ap | 1 0 10 1 0 1 1 x. vO d Laie 1) eo 1 0 1 haa 1) 10 i; -0 Up lt) cooocooococeocoooo oo i) ooococo oooocecocoo eoooco £ Brought forward, 764 Meiklam, John, Esq, * Montgomery, Wm. F., ie ss Mullen, ieenxce, Est: na ame * Mulvany, W. T., Esq., * Murray, William, Esq., * Mackay J. T., Esq.. « . * Newport, Sir John, Bart., . *® Nelson, Joseph, Esq., Newman, Miss, . Norreys, Sir Chas. Denham Orlando Jephson, Bart., * Newenham, Thomas, Esq., * Napier, Jeseph, Esq., Nicholson, Mrs... . . Nicholson, G. A., Esq., * Nicholson, J. A., Esq., . Nolan, James Joseph, Esq., Nugent, Daniel, Esq., . - Nugent, William, Esq., . * O'Halloran, Major Gen. Sir Joseph, K.C. B., O’Connell, Daniel, MAR cay. O’Hara, C. K., Esq... . * O'Grady, M. M., Esq., M. D. By * O’Brien, Sir Lucius, Bart., * O'Ferrall, J. M., Esq., M.D. O’Brien, A. S., Esq., M. P. O’Brien, W. S., Esq., M.P. O’Callaghan, Isaac, Esq-, . * O’Conor, Matthew, Esq., O’Dwyer, Andrew C., Esq., * Orpen, T. H., Esq., M. D., * Orpen, C. H., Esq., M. D., * Owen, John U., Esq., M.D. * Owen, Jacob, Esq., . . O’Donovan, John, Esq., : Esq, * Pim, James, Jun., Esq., Perry, John, Esq-, * Pim, George, Esq., « * Portlock, Captain R. E., Pakenham, Hon. and Rev. Archdeacon, * Petrie, Geo., Esq., R. H. x: * Phibbs, Willian, Esq., - Purser, John, Esq., . * Parker, A., Esq. . Patterson, Chas., Esq., M. D, Patterson, R., Esq. és ; Pepper, Colonel, Perry, James, Esq., Pim, W. H., Esq., te et et et ee BD DO bo OO Or oO OO et tt et tt DD CO CO wwao te eee bo to ooo wmooco oof cooocoocoeceo i} oooo ecocoooocooooorrooSo eooococecocoeoco coocoo cof ooocoococeceo ooo f—) ecoococococeoscococoecocn“c[ ocooco occocoeoceco 849 17 0 - * Smith, Aquilla, Eeq,, be M.D. £ Brought forward, 849 Pollock, G. A., Esq, . ~. 1 Porter, ‘Charles, LL. D., « 1 * Porter, Rev. Thomas, D.D., 1 * Rosse, William Earlof . 10 * Robinson, Rev. T. ora D.iD., «2 ++ Rossmore, W. Wm. Lord, ard Reid, Alexander, Esq., . 2 * Reid, Rey. James, . - «. 1 * Radcliffe, Rt. Hon. John, DE. Di. sore dtes vd" ao Ray, T. M., Esq., « « Richardson, Miss, Roberts, Marmaduke C., Esq., Roberts, Wm. B. C., Esq., * Roberts, W., Esq., £-T.C.D., Roe, George, Esq., - + + Roe, Henry, Esq., « Rothwell, R., Esq... .« * Roberts, Rev. J.C., F.T.C. D., Radley, John, Esq. "9 adn en ee | * Stokes, Wm., Esq., M.D., . St. George, Richard ee Mansergh, Esq.,( with do- nation of Bronzes § Coins.) * Singer, Rev. Dr., F.T.C.D., Smith, George, Esq.,_ .- * Strong, Rev. Charles, .« Sweetman, Walter, Esq., . * Smith, Joseph H., Esq., . * Sadleir, Rev. Dr., F.T.C.D. (Provost), . .« * Sedgwick, Professor, (Cam- bridge), . - J St. George, Charles Man- sergh, Esq., .- - + = Sherrard, D. H., Esq., - * Smyth, Capt., R. N. (Car- BA aw atone Somers, John, Esq... + + * Sadleir, Rev. William D., BRC. Dig. 22-8) ‘s Sainthill, Rd., Esq.) Cork, Scully, Joseph, Esq., - « Sharpe, Charles, Esq.,. . Shirley, E. P. Esq., M. P., Shortall, Lieut. Gen., . Smith, ae Esg., « « * Smith, Rev.G.S., . . . * Smith, R. W., Esq. se * Sterling, Cap., "A.C. , (75th), to wr co oO oo wana nan | el eel cee eel ee eel el el el 963 = & -oOooo o — i — I ooooocococo i a ov oo o woooccoce - coocoocococo cooof occocoococoeco oocoo o —] otocooooeocooso oo oo — i) o cooocococo < £ Brought forward, 963 Stewart, Henry, Esq., . 1 Stewart, Colonel, 1 Stokes, J., Esq., . 1 Stokes, Miss, . eae Se | Stubber, R. H. Esq, . . 1 Stopford, Captain, w 0 Templetown, John wd Lord, -.*« 10 * Todd, Rev. Dr., F.T.C.D., 10 Tomb, George, "Esq. my BAGO s 2 * Thompson, J., Esq., . . 1 * Thompson, David P.,Esq., 1 Thompson, J., Esq., LL.D., Glasgow, . . * Thompson, Thomes, M. 'D., Glasgow, . . ° Thompson, Wm., Esq.,, si Tickell, Edward, Esq., * Tighe, Robert, Esq., 7 ® Toleken, J., Esq., F.T.C.D. Turner, Dawson, Esq., Todd, W.G., Esq... . —— ee ee * Vignoles, Rev. Doctor,. « 1 * Wall, Rev. Dr., S.F.T.C.D. 10 * Williams, Richard P., Esq., * Wilson, Thomas, Esq., . * Whiteside, J., Esq., A.M., * Wilkinson, George, Esq., . Wilson, L. P., Esq., Lond., * Westenra, Hon. H. R., M.P., * Walker, R. Chambers, Esq., * Webber, Chas. T., Esq., Wypbrants, Robert, Esq., Wood, Thomas, Esq., M.D., West, Henry, Esq.,. . * Wall, Rev. Rd. H., D.D., * Wallace, W. B., Jun., Esq., * Wallace, R. hee Esq., * Warburton, Elliot, Esq., * Webb, William, Esq., . Whitla, Francis, Esq., . * Wilde, William R., Esq., . * Wilson, Rev. James, Woodward, Rev. F. B., Wright, Edward, Esq., Wynne, John, Esq., Webb, P. R., Esq., . P Wood, William C., Esq., . ee we * Young, John T., Esq., are Allen, Edward, Esq, . . 1 -_ a ececocoocco o omococ eocoocooc#* ~ o _ mMmoccococoeocoececorrwosoocnwrnnwnooceoe alco ecocoocoof —) eoooceco eceoocooececece|ce|ceocecseoceoococeso —] else vi ADDITIONAL SUBSCRIPTIONS. £ eit. | ZL yeeck de Brought forward, 1051 8 0} Brought forward, 1060 13 0 Baker, A. W.,Esq., . = 3 5 0) (Knox, ©. C.,,Esq.,,-..- - 4OAL0 0 Benn, Edward, Esq., . 1 0 0} M‘Master, Maxwell, Esq., t0it-0 Graham, F. R., Esq., . 010 0| Otway, C.G., Esq, . 10 0 Griffith, Henry, Esq... - 2 0 O| Pope,J. W., Esq, . - . 0 5 O Henn, Thomas R., Esq.,. 1 0 0} Ray, T.M.Esgq.,collectedby 2 0 0 Hughes, W. J., Esq., . 10° 0 | Reade, W. M., Esq., ..... 2 2000 90 Knox, R. J., Esq.,. 010 0 | Sharp, Richard Esq., . De5)1 0 £1060 13 0° Total collected, £1067 13 0 No. I. ACCOUNT OF THE ROYAL IRISH ACADEMY, FROM Isr APRIL, 1841, TO 31st MARCH, 1842. THE CHARGE. sae tal adds: Balance in favour of the Public. as ne last “ Audit, . ° e ow 9 whit bl ae 59 l 4 Parliamentary Grant for 1841, ae ata (> 2 UR | al Quarterly Warrants from Treasury, ea EO. tae Total from Treasury, . |) 446 Las 3 THREE PER CENT. CONSOLS SOLD. om 61641. ae a? June 8, 9, £55 18s. 8d. at 88iy, 49 7 3 4 Interest, 154days, 014 3 | 50) 16 Brokerageyt i..5-.0:,,1 .6 1841. ee ee OE VL OB 0 July, 20, 21, £238 11s.6d.at893, 213 16 6 i Interest, 16 days, 0 6 3 ald. 2" 9 Brokerage,. . . 0 6 O . 1842, | 2S Be Feb. 9, 10, £300 at 883, . . 266 5 0 r Interest, 36 days, 017 9 267. 33:.9 Brokerage, . REF Nae (Cael 2° Se) ae Total proceeds Consols sold, . . . |__| 530 12 0 1036 11 0 Vill £ sires Brought forward, 1036 11 0 INTEREST ON STOCK: Septet aE Half year’s,on 1553 10 11, 33 per cents., Ditto: 5, 1581 34. Ly SE e A Dittor: +3 1525402) 95 3 # Ditto® %; 1286) UL... 3;°3 : Total Interest on Stock, 5 97 0 8 PuBLICATIONS AND BoOoKs soOLD: Boone, Messrs., balance of their account to 4th January, 18422) 90% Clibborn, E., for Benanc Memoirs, es 16th June, 1841, Ditto, ditto, 6th N ov. "1841, Ditto, Transactions and Faopeenes 16th sane; VS4 ec oe Ditto, ditto, 28th N ov. "1841, Ditto, Wolf’s Letter, ditto, . Total Publications sold, 37 19 O One year’s rent of stable, to Nov. 1, 1841, 21/700 LirE Compositions: ‘Lhomas WW ison, Wise, <3... erate 21 OHO jg ag RS Ee ae Oe 21. “O06 Bran OGROSS: Yes ee egg ee eee eee 2)" CA aS eotueld, Sia 6's Ec. ih tees Se ie ek Gua danes Thompson, Esq, “% 3’). 8299 BL “Oe mamnendinning. Mag ey Pe ‘such 21) 3030 op l ell EC Be Se ai ik, Coe cca 18 18 0 G. S. Gough, Esq., . . 18 18 O J. T. Mackay, Esq. (having subscribed twenty years),. . 6; 6° 0 Total Life Composition, 170-30 ENTRANCE FEEs: William Monsell, Esq., . ee He Tighe, Bag.) 5°.» 5 5 0 W. E. Hudson, Esq., a oe GO G. F. Fitzgibbon, Esq., 6. o'N@ William Phibbs, oe Aa tetas She tee gh ar oreG Rey. J. Reid, : eB en eee Co Al Maes mene W. Lee, Esq. . eee ane eel i Ore. mee R. Jones, Esq., Oo 6" 0 Thomas Wilson, Esq., otek) Sena eee oe | hi OO (VES bene Prin MBS ed me So See, | 5 Seng 52.10 07/1362: 12758 ix SPE Same 2 1362 12 8 — eo eo es Brought forward, . O. Sproule, Esq,., . Pepe La ane James Patten, M. D., J. G. Jellett, Esq., J. Banks, M.D., W. Andrews, Esq. John Burrowes, Esq., . F. Churchill, M.D.,. .- ; Alexander Ferrier, J un., Esq. a William Hogan, Esq., . : W. J. Hughes, Esq., . Rev. Samuel Butcher, . W. Grimshaw, M.D., Durham Dunlop, Esq., ys Alexander Clendinning, Esq. 4 William Roberts, Esq., . é Robert Bateson, Esq., . . Rev. Reginald Courtenay, . Captain Stirling, . “itis Rev. R. Chatto, Joseph Nelson, Esq., Rev. Thomas Stack,. . . Potaar Total Entrance Freea, ot eee a ol ee | AnAARAMMAAAAAAMAAAAAM EAD? eoooocececece|ecoeooocoooeocooon _ ANNUAL SUBSCRIPTIONS AND ARREARS: M. Longfield, Esq., . se Wm. Stokes, M.D., . W. R. Wilde, Esq., . Earl of Ross, . J. Kingsley, Esq. . John Davidson, Esq., Rev. M. M‘Key, . William Hill, Esq., . A.Smith,M.D,... Sampson Carter, Esq., . Rey. C. Otway,» . W. Edington, Esq., . E. Hutton, M.D., _ Bishop of Meath, . M. M. O’Grady, M.D., Sir R. Morrison, . J. Mollen, M.D., Charles W. Hamilton, Bs, « ; Hon. James King, ; ¢ John Ball, Esq., . . G. 8. Gough, Esq., . W. Hemans, Eeq., _ NNW NMNNYNNYNNNYNNNNNNN LABS NWNNMNNNNNYNNNNNNNNNK KR KS SS ocooocececoeocococococeco 56 14 0 {1525 7 8 ¥. W. Conway, Esq, . . W. T. Mac Cullagh, Esq., . G. D. La Touche, Esq., Lord Chief Baron, . F Right Hon. the Lord Mayor, : C. E. H. Orpen, M.D., : W.B. Wallace, Jun., Esq., : George Carr, Esq., . : Rev. F. C. Logan, General O’Halloran, R. Dickenson, Esq.,. . Charles Vignoles, ae C. E., Do Aber, Esq.,' ”. : Archbishop of Dubs} Rev. J. D. Sirr, G. A. Kennedy, M.D., R. A. Wallace, Esq., . Thomas F. Kelly, Esq., W. Longfield, Esq., . G. Wilkinson, Esq.,. . . Sir Philip Crampton, Bart., Thomas Newenham, Esq,., . Thomas E. Beatty, M.D., . Jacob Owen, Esq., R. C. Walker, Esq, . : Sir Lucius O’Brien, Bart., W. T. Lloyd, Esq., . M. O’Conor, Esq., J. Hart, M.D., R. Mallet, Esq. ae George MDowell, Esq, 5 Professor Davy, . Rev. James Wills, J. T. Young, Esq., J. Anster, LL. D., J. H. Smith, Esq., F. Barker, M. D., R. Reid, M. D., G. Levinge, Esq., . . Thomas Grubb, Esq., - J. 8. Cooper, Esq., - Rev. E. Marks, D.D., James Pim, Jun., Esq., R. W. Smith, Esq., . J. Osborn, M.D., R. Adams, Esq., Brought forward, . 56 14 WN NYYNYNNNYNNYNNNNYNYNYNNNNNYNNYNNNNNYNNNNNNNNNNYNNNYNNNNNYDND eSesesssesssoooescoseossessescososeososcoosocoosesescsesseeossoessooooen xi Brought forward, . Hon. Judge oe James Apjohn, M.D., W. Murray, Esq., . . Rev. Charles Vignoles, D. 1%. : W. F. Montgomery,M.D., . . R. J. Kane, Esq., ne A. Lyle, Esq., J. Finlay, LL.D, . . Sir Edward Borough, Bart., A. Jacob, M.D.,. .« Charles Doyne, Esqs, 1840, Ditto, 1841, E. J. Cooper, Esq,, . E. Cane, Esq., G. Cash, Esq., . W. avian. M.D., anes Eliott Warburton, Esq. ae Rev. R. Knox, . . Robert J. Graves, M. D., Edward 8. Clarke, Esq., . J. D’ Alton, Esq., a a P. D. Hardy, Esq., . Rey. James Gregory, . Sion: ‘ William Gregory, M.D., . Abraham Palmer, Esq., 1840, Ditto, 184], Archdeacon Disney, 1840, Ditto, 1841, W. Farran, Esq... James O’Grady, LL. D., A. E. Gayner, Esq., 8. Ferguson, Esq, . . Rev. R. V. Dixon, Esq., F. W. Burton, Esq... H. Watson, Esq., 184i.” James Whiteside, Esq., 1841, H. H. Joy, Esq., 1841, . W. Armstrong, Esq., 1841, G. G. Otway, Esq., 1841, P. M. Murphy, Esq., 1841, W. T. Kent, Esq., 1841, E. Hutton, M.D., 1842, C. T. Webber, Esq., 1842, A. Abell, Esq., 1841, Rev. James Carson, 1840, . Total Annual Subscription and Arres ‘rears, THe Torat CHARGE, . ; or WKY NN NN NNYNY NHN NNNNNYNYNNNNNYNYNYNNNNNNNNNNNNNNNNNNNWNNO™ G. Gilt £ ea 6). Or |\1625: 7 8 2 0 2 0 20 2 0 2 0 2 0 2.0 2 0 2 0 2 0 2 0 2 0 2 0 yA nO) 2 0 2,0 2 0 2.0 2 0 2 40 2 0 2'-0 2 0 2 0 2 0 2 0 20 2210 2 0 2 0 2 0 2 0 2 0 2 0 2 0 2 0 2:0 2 0 2 0 2 0 2 0 2 0 2 0 2 0 247 16 O £1773 3 8 xii THE DISCHARGE. ANTIQUITIES PURCHASED AND REPAIRED. £3. "a: Geraghty, for silver ornaments, 3rd May, 1841, . . Ube oo: Bambery, for gold torque, 7th dune: Lelia 5 |: - 00° '0' 0 Peters, for repairs of do., 10th do. 2 Tao Smith, for fragment of cold, 12th dG.c) 1 70 °.8 Donegan, for fragments of do., 20th July, 1841,. . . oo a OO aaa for gold fibula, "4th Nov. Leahy. i. bee Do., do., 18th Jan. 1842, 12 12 0 ee for et) ‘collar, 3rd Feb. ithe Sd ee Hogarth, unrolling papyrus, . Total ‘Antiquities purchased and repaired, Books, Printine, STATIONERY, &c. Allen, J.W., lithography, to 19th July, 1841, Branston, F. W., wood engravings for Pro- ceedings, 23rd March, 1841, ae J Ditto, ditto, Ist October, 1841, Du Noyer, G., for drawing on wood-block, 5th March, 1841, . Duncan, J., engraving belle, 12th Feb. 1841, Graisberry "and Co., printing, balance of ac- count, 3lst Dec. 1839,. . Ditto, ditto, ‘29th March, 1841, Hope, stationery, 16th Dec. 1841, : Healy, ditto, 26th Jan. 1842, Hodges and Smith, books, &c., 31st Dee. 1840, Ditto, ditto, 2nd Dee. 1841, Kirkwood, engraving, on account, 26th April, 1841, eS Sh Ey A eee Ditto, ditto, in full, 13th July, 1841, Ditto, ditto, 15th Jan. 1842, . Morrison, ditto, 13th May, 184], . Mullen, bookbinding, 3rd Jan. 1842, . a LO ee 12 0 mt . i an} — _ DOMrMMDwoo 10 14 d. E ape alee 7 f 6 113 11°°6 0 0} 0| / 0 | Oo 0 | 1 | 4 | 0 | re 11 | 6 0 0 0 4 6|113 11 6 Williams, Thos., and G Co., ‘carriage ‘of books, Xili £ Brought forward, . . 715 Oriental Translation Fund Subscription, Ist Jan. 1841,. . 10 Pettigrew and Oulton, Directory, 28th Jan. | a : 0 Ponsonby, stationery, 28th Dee, 1841, ee. 0 Taylor, Messrs., Scientific Memoirs, 16th March, 1841, cs sh hae 6 Ditto, ditto, 20th Sept. 1841, 6 Yeates, letter balance, 27th Jan. 1840, 0 Total Books, Printing, Stationery, &c., Coats, CANDLEs, OIL, &c. Allen, William, oil, to 26th June, 1841, 6 Ditto, ditto, 6th Jan. 1842, 4 Daly, John, bogwood, 24th Feb. 1842, wis 0 Kenny, M., for coal, 14th Dec. 1841, ee 10 Rathborne, for candles, 8th Feb. 1841, a Total Coals, Candles, Oil, &e., oa ee ConTINGENCIES, &c. Clibborn, E., incidentals, to 26th June, 1841, Ditto, ditto, 25th Sept. 1841, Ditto, ditto, 31st Dec. 1841, . Ditto, ditto, 9th March, 1842, Hodges and Smith, engrossing Address, 18th Jan. 1841, . . Johnston and Co. advertising, Ist Jan. 1841, Ditto, ditto, 8th Dec. 1841, Mallet, Robert, postage, 10th Jan. 1842, Nash, P., carriage to Park, 13th Nov. 1841, Roberton, J. D., oe of parcels, 15th May, 1841, . . Smith, J. HL, expenses to Drogheda, 18th Jan. 1842,. . — te bo &c., 4th June, 1841, . Treasurers for stamps, &c., 7th Feb. 1842, Ditto, ditto, 4 Total Contingencies, . : oon Tt oooor} Repairs oF House, Furniture, &c. Acheson, J eri drugect, &c., to 3rd Nov. ne40,. . Ditto, repairs, 22nd Oct. 1841, won| o~- wl on d. Se ya 6 | 113 11 0 6 6 0 0 0 739 12 ll 0 0 0 6 24 17 0 10 2 7 0 0 6 0 6 0 T 5 9 9 35 0 4 0 4/913 2 8 1 Xiv Brought forward, . ‘ Blackwall and Co., lamps and repairs, 30th Nov: 1840, U.. >. 4 aoe ne Hughes, H., a hemp mat, 2nd Sept. 1841, . Kane, M., washing down house, 3rd Nov. TAA uF te ieee Re. umes wok Kane, C., washing rollers, &c., lst June, 1841, Ditto, ditto covers, 29th Nov. 1841, Keough, F., beating carpets, &c., 4th Sept. ROE Te cs Reee on, at hence | one ge a Mullen, Wm., cleaning chimneys, 9th June, hey eo ay He MS rd oe eh ee es ee Ditto, repairs of ditto, 17th July, 1841, Nannetti, G., plaster casts, &c., 11th May, 1841, 225 Ber OP. can ee Re Perry and Co., furniture, &c., 1 1th Nov. 1841, Surman, G., repairs, &c., 14th Nov. 1841, Travell, G., matting and repairs, 3rd Nov. POdi,-. 8. (ROR: A a ee eet Walker, Wm., repairs, stove, &c., 26th Oct. PS4ile 25 Ge Bait ean 8 ek Total Repairs of House, Furniture, &c., Rent, TAXEs, AND INSURANCE. H. Truel, one year’s rent, to lst Feb. 1842, . Grand Jury cess, one year, Michaelmas, 1841, Wide street tax, ditto, ditto, 1841, Police tax, ditto, ditto, 1841, Pipe-water, ditto, lst June, 1841, Ministers’ money, ditto, Michaelmas, 1841, Parish cess, ditto, ditto, 1841, Paving and lighting, ditto, 5th Jan. 1842, Watering street, ditto, ditto, 1841, Insurance at Globe, £5 6s. 3d.) Ditto, National, 5 6 3 Total Rent, Taxes, and Insurance, — 11 24 iva} Ge ~ Os — re oe ol=) WOON S a) Nw wo or — a) CO nw wo — — rs = — womonatst-10 0 pal i) AR OUWONDBDAOCOS Ee oY O13 S22) wal 7 Mi a 0, 147 11 10 1133 5 5 eee ite XV G8 et BO ge Brought forward,... .). i. . 111383 6 § = =). ns gg ate iy Sa.aries, SERVANTS’ WaGEs, &c. peeing Edward, salary for three quarters of ear, as assistant librarian and clerk, to ) Aéth ica IMI. Gi ae Agere! te GON a Bl Hamilton, William., salary and al- £8. d. ) lowances as porter, from 27th Mar. 1841, to 12th Mar. 1842, Se eee viz., 26th ‘Tune, 1841, PR is Ditto, . 08 8| / 25th Sept. 1841, 8 2 6 ) Ditto, > 08 8 ) . 31st Dec. 1841, 8 11.2 | : 12th March, 1842, 7 410 Christmas allowances, 27th Dec. 1841, . 2-2 0 Livery cloth from An- drews, 15th Dec. 1841, 4 5 0 Ditto, making, Dunn, 17th Jan. 1842, 2 0 5h Ditto, buttons, Wood- house, 18th Dec. 1841, 016 6 Barragon coat, Simpson, 17th Feb. 1842, . . 10 0 Hat, Wright and Oxley, 17th June, 1840, . . 016 O Ditto, ditto, 21st Dec: IStle 2s. t1..8 8/0, 16". 0 Aprons, St. Peter’s Repo- sitory, 31st Dec. 1841, Kane, B., as extra porter at Meetings, 28th PERT De Sie ey Be Pad state oe ee Ditto, ditto, 28th Feb. 1842, Orpen, Dr. Thomas H., salary as Treasurer, for eight months and two ge to 30th Nov. 1841, Ditto, commission as Trcasunery on £320 Be. at 5 per cent., ‘Smith, Dr. A., salary as Treasurer, Cebes 30th Nov. 1841, ‘to 16th March, 1842, . . Wisehart, James, salary as clerk at Meetings, from 12th April, 1841, to 28th sagt 1842, . . Total Salaries, Servants’ Wages, &e., Xvi oS Brought forward, . ae. THREE AND A HALF PER CENT. GOVERNMENT STOCK PURCHASED. Lane. A eles .. 2: Gost: "Sx vee es Bee ee 7 aes | een: Byte meee hae ge ee eT 1S oo) * Total cost of Three and £55 13 10 a half per Cent. pup —— se chased, . THREE PER CENT. CONSOLS PURCHASED. 25 oS eae & Ga 5: "8S Vebst sare eee Roe. Te re a. 5o0o ge 7 > oe ae he ee eee ge et 17-10) 0104 SO iy ee | a 93°58 WOU ee ie: et he ae: epee Bi A A OE OO iy i A aera Se AL te ew an othe anne hecdeenalae ee Total cost of Three per £232 11-11 Cent. Consols pi Ses chased, . ti THE TOTAL DISCHARGE, - Balance in favour of the Public, °. The Charge as above, STATE OF THE BALANCE. 1842. 31st March. In Bank of Ireland, . In Treasurer’ s hands, as per this Account, dN Lae 1310 14 32 9 5 J) Bae 0 0 0 0 0 0 0 208 19 O . (1574 10 53 198 13 23 : | LL one Pee Meas Bn et de | 7 16. Balance as above,. . - £198 13 24 The Treasurer reports, that there is to the credit of the Academy in the Bank of Ireland, £1052 6s. 8d. in Three per Cent. Consols, and £1609 4s. 9d. in Three and a half per Cent. Government Stock, the latter known as the Cunningham Fund. 31st March, 1843. (Signed), James Pim, Jun., : Treasurer. No. III. ACCOUNT. OF THE ROYAL IRISH ACADEMY, FROM Isr APRIL, 1842, TO 3ist MARCH, 1843. THE CHARGE. = Balance in favour of the Public, as corrected | £ 8. d.| £ 8 d. by the Commissioners (£198 13s. 23d., less Buia: 10d:);,.. oP oP ADSI GOR ae _ Parliamentary Grant for 1842 (paid 16th ; March, 1843), . . 300 0 0 eel Warrants from Treasury; tn: to 1 LAG ET ae Total from Treasury, . . - |——————| 446 17 8 a "prereset on STOCK: . OW A Half year’s on 1609 4 5, 33 per Cents, | 28 2 Ditta, 269618 5,3 5 * “| 28 “Ditto, 4, 1052 6 8, 3 yt) ed iitto, +. \,./..2069" 0. 6, AS Total Interest on “Stock (exclu- sive of brokerage 5s. 3d.), . \ Aanoe 88 7 4 _ PUBLICATIONS AND Books soup: Boone, Messrs., balance of their account to 2nd January, 1843, . . He sesh One year’s rent of Stable, to Nov. ‘ 1842, cee a,2) Lae - on bo oe, x: ee ee a as ee we ‘3 = COMPOSITIONS : _ Henry Hutton, Esq, . . . . + + -| 21 0 ss wr BoteonKeq, gs . oo. | 2EO = _ W.V. Drury, Esqy,- . - + + + = 15 15— Stewart Blacker, Esq,. . . - +--+ -{| 21 0 pt he enh Hea Ret a LO a Total Life Compositions, Por ooooco d be XVili ; 8. Brought forward, .°5 .| . - . . | 863 6 ENTRANCE FEEs. John roleken, MoD: * 3°. ° 2°.) 2/1842? iRopertuaw, M.D: 2°. Evie aos Rey. R. Butler, ay W. Blacker, Esq., B. J. Chapman, Esq. . . Sir Thomas Staples, Bart., Arthur Kane, Esq., F. M. Jennings, Esq., Rey. James Booth, y LOT, ae Thomas Hodder, Esq., R. N,, De Paes lis: 3 P Henry Hutton, Esq, . . - - + 5 Hon. Frederick Ponsonby, . - . ,, Thomas Cather, Esq... > /- 55 W. V. Drury, M.D, 2 Se) eo) ts estas Opry, Meda. <>< ~ 3 gy G. Salmon, Hsq-)- 3 + [+ -aorah om 99 W.R. Gore, M. D., « MSOs Stewart Blacker, Esq... . - «+ 34 R.- Cally, Esq, 2 se 6 6.6 Bie) SS Ss SS SS, es es oe on ecooooqoooooocococeocoooeco H.L. Renny, Esq... - » - + 5 James Magee, Esq., . Sw, Total Emeabe Pees, og ge! Ife eee I ares ANNUAL SUBSCRIPTIONS AND ARREARS. Hugh Ferguson, M. D., due March 16, 1842, J. Davidson, Jun., Esq... + ,, re G. Downes, Esq., . na Bae he 3 M. Barrington, Esq,. . . 5, 1841, S. Hardy, Esq, - . - = 2» Pe J. F. Lynch, Esq... - + 5 ” John Mollan,M.D., . . . 4, 1842, W. Drennan, Esq., . . - » #8 Archdeacon Disney, . . - 355 ; W. F. Conway, Esq, . - s G. D. La Touche, Esq., . ~ ;, + WDNNNNNNNNNNNNNNNNNNW ecoooococooecoocooocoeoceo E, Davy, Esq... - + + & 9 5 G. A. Frazer, Esq, . - « » ‘ Sir L. O’Brien, Bart. -. - 5, #3 KE. Cane, Esq.. «= + + + + 9 fs James Apjohn, Esq, . - + 5 = fe Tithe, Begs ei f=) oso, * W. Edington, Esq, . . - 5, ss William Hill, Esq, . . . » ne meme ST), se |e ing * —~ «| WNHNWNNWNNNNNNNNNNNNNNNY WD 973 11 8} cS o W. Monsell, Esq., . W. B. Wallace, Esq., R. Jones, Esq., . . John Hamilton, Esq., G. Wilkinson, Esq., G. W. Hemans, Esq., M. M. O'Grady, Esq., William Murray, Esq., _ Hon. James King, Rev. James Reid, . George Carr, Esq., Rev. H. F. C. Logan, Charles Vignoles, Esq., _ John Hart, Esq., . . Sir William Betham, . Chichester Bolton, Esq., Godfrey Levinge, Esq., C. E. H. Orpen, M. D., E. J. Cooper, Esq., _ §. Carter, Esq., . MM. Longfield, Esq., Sir J. K. James, Bart., Hon. P. C. Crampton, Rev. James Wills, James Patten, M. D., _ W. T. Mulvany, Esq _ ©. Sproul, Esq., . Rev. John West, D. D., Thomas Newenham, Esq. R. Dickinson, Esq., R. Kane, M.D., Baie. W. Lee, _ R.Reid, M.D. . _ RA. Wallace, Esq., . Sir B. Boruagh,. Bell Thomas Fortescue, Esq., aR. Adams, Esq., | Tacob Owen, Esq,., . Brought forward, . . due March 16, 1842. William Gregory, Esq., . Gerald Fitzgibbon, Esq.) Charles W. Hamilton, Esq. % ” ” 3 His Grace the Abp. of Dublin, ,, ” Thomas F. Kelly, Esq., . - Hon. M. Brady (Lord Chief Baron), i 4 pte | ” _ - W. T. Lloyd, Esq., . . «JH. Smith, Esq, | ” ” =: Wales ”? + | ae e bs ” ” ” ” 138 12 WN NNNNNNNNNNNNNNNNNYN NNN NN NN NNN NNNNNYNNYNNNNNNNNNO® ‘ae 83 d 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 973 11 8h xx Brought forward, . . 1 M. Barrington, Esq., due March 16, 1842, J. Finlay, LL.D. . . an 3 A. Palmer, Esq., sae AS eeises: oo James Pim, Jun., Esq. . . ,, OS Mathew O’Conor, OL i ae “2 Arthur Jacob,M.D., . . ,, » W. Barker, M. De Meal < a3 “A F. Barker, M. D.< ee." 9459 ~ Thomas E. Beatty, M.D., . ,, es Bev. Dr. Virmoles, © 2. ..,, “ Simeon Hardy, Esq... ... ,, S e-aosporne, M! Dy &. S|. . ty, - Go. dellett, Hsqe,. >...» +55 s ey). Snath sg. Sos |. teas a Beigrubbe lisa, SS. B.S) sas =e BAPE. DO dg ee ka dy ia a qunpter, LAD. Sts} tesy + Ba Ny -courton, Bisa... So. ergs es LE Re Goh ae Oa rr = George M‘Dowell, Esq., . . ,, a William Stokes. M.D., . . ,, 9 Bea Mallet, Beg 2 f. Ss vagy oe John Ball, Esq., . . er ” W. F. Montgomery, M. D, inks 9 G. A. Kennedy,M.D:, . ...,, ” WW Ts Kent Wis Soc ctys » Acheson Lyle, Esq., . . ..,, <3 mers. Cooper; Hed: Sef - teay n General O'Halloran, . . ..,, ue Ae Aaayer, LAD..." 6. ns , om. Walker,’Hsq.™. | . .:5, .. WY. ueWalde Visa. *. 2). ita ae Rev. Dr. Marks, . . sass > Elliott Warburton, Esq.,_ a ee oh H. Coulson Beauchamp, M. D. ,, 3 William Farran, Esq.. . x s James Whiteside, HGS c_ sletss te Ps Ot. Murphy, Tsqy=. *5- sSery5 5 S. Ferguson, Esq... . . .-,, = B. J. Chapman, Esq. . . ,, 1843, Charles Doyne, Esq, . . . ,, 1842, mirth. Morrison, 2+. 5°. +3, sae Wy ludson, Meq.* . £. os '+-55 x Ditto. ditto. Sot Marks 1843, Robert Graves, M. D., vai, 1842, NNW NNNNNNNNNNNNNNN NY NNN NNNYNNYN YN NNN NNNNYNNYNNNNNYNNYNNDB? WN NNNNNNWNNNNNNNNNYNNNNNN NNN NN NNN NY NNYNYNYNNYNNNYONNNNND? Very Rev. Dean Gregory, es ~ no (ot) or — 973 11 8h gl IC eM Ee eee , xxi ‘ iB d * Brought forward, .D. Hardy, Esq., . due March 16, 1842, De Ge Otway; Haqy, 8... 5, a — 3. 0°Grady. LL.D. . . . BS: John Dalton, Esq, Eat) Para» S de ma, Gash, Bag.0 se 2. John Burrowes, Se ! Sohn Hamilton, Esq, . . ,, _ Frederick Darley, Esq... . ,, 1841, Ditto, PO Ce 2? i Rag. pe Ferguson, M. D, tad Satin, sn fe Sy ey Downes, Esq. i, Sir P. Crampton, Bart., William Murray, Esq., + A. B. Cane, Esq., . John Davidson, Esq., _ Rev. 8S. Butcher, 7... * Durham Dunlop, . duke tees ‘ _E.S. Clarke,Esq., . . . ,, +1842, Ww. T. Mac ‘emai sd f Ditto, . : : WwW. Edington, Esq.,_ bs RK. Kane, M.D. . _ C. Bolton, Esq. ‘Dr. O’Grady, . . Captain Sterhag, ~. 1. 02), _ Sir E. Borough, Bart, . . Thomas Fortescue, Esq... . io Hutton, MDa. 3 J. . G. Carr, Esq., . 2 eS Total Annual Subscriptions and Arrears, br] - Tue Torat CHARGE, . NNN NYNNYNYNYNYNYNNNNNNNNYNNNNNYNNNNYNWHH WDNNYONYNYNYNYNYNYNYNNYNNNNYNNNNNNYNNNNNNYNN PS coooocoocoeoocoocooocooocoooscooocoocoocooococors ———— 296 2 a? 1269 13 XXxil THE DISCHARGE. ANTIQUITIES PURCHASED AND REPAIRED, £0 SES eee Broderick, for two gold fragments, 17th Nov Peet tte eel mee Non bp ia 5 One Donegan, for gold cup, 15th Feb, 1843, . 4 4 0 Edwards, for warrant, 30th May, 1842, . Lal? 26 Maguire, for silver pin, 8th April, 1842, 8 2 2 J. H. Smith, for seal, 31st March, 1842, . 0. 5-40 Underwood, for silver seal, 2nd April, 1842, 2 Omne Ditto, tracery, 28th May, 1842, Owdi 20 Ditto, crozier, 15th Nov. 1842, 2p On Ditto, silver relic, 14th Sept. 1842, i) Total Antiquities purchased and repaired, |——_——_ 20 8 8 Books, PRINTING, STATIONARY, &c. Allen, engraving, to 27th July, 1842, . ; Zager) Ditto, lithography, 2nd Feb., WAS i Rect 619 6 Betham, Sir W., for Dunop’s Book, 4th July, PHAM M nth te ely |. she, “nate od BOG Camden Society, subscription to, 27th July, Fe ich BM ey (Re seed Oar eam Curry, Catalogue of Manuscripts, 16th Jan. FR Wigs eee fed ad, Sap Ee Oe Ditto, ditto, 6th March, 1843, 12 19 O Du Noyer, lithographs, to 5th Oct. 1842, . 2°10" 8 Hanlon, wood-cuts, Ist Aug., 1842, . . - 12 eg Hely, envelopes, 22nd October, 1842, . . £7200 Johnston and Co., advertisements, 26th July, le. Wasa Mice tage he a (ee ee Taylor, R. and J. E., twenty Scientific Me- moirs, Part 10, 2nd May, NSaease. Serial ys 6 0 0 Total Books, Printing, Stationary, &c., | SA ee Coats, CANDLES, OIL, &c. Allen, William, oil, to 9th Dec., 1842, : 8 0-0 Kenny, M., coke and coal, to 9th April, 1842, 318 0 Ditto, coal, to 26th Jan., 1843, see 3.156 0 Rathborne, candles, to 16th March, 1842, 6.5) 2 Wilson, T. P., coals, to 5th August, 1842, . 7 OO Total Coals, Candles, Oil, &c., . +» |—— 38 18 2 _——___—= PLS 10> ea ae Brought forward, 113 10 4 ConTINGENCIEs, &c. 4 Clibborn, E., incidentals to May, 1842, Ditto, ditto, 29th July, 1842, a Ditto, ditto, 21st Nov. 1842, ‘ag ‘Ditto, ditto, 5th Jan. 1843, . ee _ Ditto, ditto, 6th March, 1843, _ Post Office orders, Ist August, 1842, . _ Robertson, teat of parcels, 29th July, meis42, . — Rorke, for stamps, Ist Oct. 1849, oie _ Stamp on treasury warrant, 16th March, 1843, o om Cc@anrow®D o NO Cor NN KW “Total Contingencies, &0., ; 19 3,8 Repairs oF Houss, &c. ve ea? Je ses windows to 2nd June, 42, Z Ditto, ditto, to 2nd Dec., 1842, Casey, S., iron works, &c., 16th J uly, 1842, libborn, E., sundries used in cleaning house, ~ &c., 16th July, 1842, . . . Ditto, ditto, to 16th Sains, 1843, q Flinn, B., cleaning ash pit, 10th May, 1842, Mullen, W., pie sas 1 i 3rd May, 1842, .. i ditto, 14th July, 1842, ditto, 2nd Nov., 1842, Total Repairs of House, fle eco occ C'eom 16.3.6 Repairs oF Furniture, &c. - Barrington, F., iron door, to 1st Aug., 1842, _ Ditto, o eit on safe, 14th Dec., 1842, Blackwell an ’Brien, repairs of lam > globes, &ec., 12th Nov., ie, fea eg J. hinds, to 25th Den, a _ Ditto, frame and glass, 14th Feb., 1843, ‘ ne, C., washing rollers, 2nd July, 1842, ne, B., beating carpets, 21st July, 1842, ttledale, J., iron chest, 4th July, 1842, ee G., scales and letter one, 25th Nov., 1842. Aooeoernd OF So omoooo OOo _ ; = _ Total Repairs Bs Beritars ai: 17 li G 166 15 0 xXiv Brought forward, . . .| . . Bork 166 15 Rent, Taxes, InsurANcE, &c. Truell, R, H., half-year’s rent, to £ s. d. het Aug, 1842 61.1 - |. Beat SBoGaa6 Ditto, ditto, lst Feb., 1843, 52 4 6 104 9 O Grand Jury cess, half-year, Easter, 1842,. . os ARAL 3 Ditto, ditto, Mecteetnas. 1842, St5.2°0 o- _ @ © vo Wide street tax, Easter, 1842, « eet Police tax, 25th March, 1842, . 2 3 9 Ditto, 29th Sept., 1842, . 7A 3 4 Pipe water, 24th June, 1842, .. . 1 Ministers’ money, 29th Sept., 1842, . ) Parish cess, 29th Sept. 1842, . . .. . 2 Paving and lighting, 5th Jan., 1843, . . . 12 Watering street, . . . . 1842,. 0 Poor rate, 24th March, 1842,. . 2 10 Ditto, 10th Nov. 1842,.<:. 2.10 WOWONAWD 0 0 Insurance at Globe, . . . . . 513 6 Ditto, Nationaly,... i 32% .igloust Ditto, CItLO, ft). <0 les. CO Sao Ditto, dilta, a newalde Spt. Died ———— 18 410 Total Rent, Taxes, Insurance, |__| 159 17 11 SALARIES, SERVANTS’ WacGEs, &c. Clibborn, Edward, salary for one year and a uarter as assistant librarian and clerk, 46 16th March, 8435 et OF 50": O10 Hamilton, William, salary and al- lowances as porter, from March £ 3s. d. 12th to March 26th, 1842, . I-62 todune 25th; 1849 oer eT oed to Sept. 24th, 1842, . . 811 2 to Dec. 31st, 1842, 95° 4 to March 11th, 1843, 6vrins Christmas Sas ahaa Dec. 25th, 1842, wn, Pee od 36 6 8 186 6 8 — | 326 12 11 XXV Brought forward, . Smith, John, assistantporter, from £ s. d. 18th June to 18th July, 1842, 1 2 6 to 30th July, 1842, 010 0 16th March, 1842, to 27th ca tae 1842, Corcoran, messenger, to 15th March, 1842, . Sinton, T., assistant clerk, to 24th Dec. 1842, _ Wisehart, James, salary asclerk £ s. d. “ at meetings, to 23rd May, 1842, : 5 0 to 10th Jan., 1843, 110 0 Kane Robert, M.D., Secretary of Council, to 16th March, 1843, we Pim, James, 5 un., shi to 16th March, Boao, te = JES Mac Cullagh, J ames, Esq. ‘4 ’ Secre- _ tary of Council, to 16th March, £ s. d. ic aa .21 0 0 Ditto, of ‘Academy, 1 16th March, 034355". Wimmced OG Drummond, Rev. W.H., Libra- £ s. d. rian, to 16th March, 1842,. .21 0 0O Singer, Rev. J. H., Secretary to Academy, to 16th March, 1842, .» THREE AND A HALF PER CENT. GOVERNMENT STOCK PURCHASED. Alga Ske & |. 2713 8 cost eee OD ye ee ee pe! Total cost of Three and | «£55 19 5 a half per Cent. un _ chased, .. to 27th Feb., 1843, 015 0 Ditto, ditto, 1843,. .21 0 0 Total Salaries, Servants” Wages, hers, 5 \—— 21 21 42 42 21 28 Ccoar 2 28 11 oon eae 326 12 11 343 18 8 56 13 5 a 5.0 XXVi i £8. d. | Ee ae A Brought forward, . & RR. AS THREE PER CENT. CONSOLS PURCHASED. ea 8: Wid. ee SEs O PORE ie: wc ke a vate AR Ae rs ds 35 | a as eee ee 15 19 6 ah gpa: (Men serie cyt | S00, Ox 0 —_—_—_—_ Total cost of Three per £342 11 O Cent. Consols put 351,145 15 —~ chased, og cee ee pans THE TOTAL DiscHARGE, + °./|. . 5 ~. £/1058 19 11 Balance in favour of the Public ./... . 210 13 gt The Charge as above, (p. xxi.). «|. . . . £1269 13 83 STATE OF THE BALANCE. 1843. Elia as 31st March, In the Bank of Ireland, . . . . . . 208 610 In Treasurer’s hands, as per this Account, 2 6 114 Balance as above, . . . £210 13 94 The Treasurer reports, that there is to the credit of the Academy in the Bank of Ireland, £1394 17s. 8d. in Three per Cent. Consols, and £1665 4s. 2d. in Three and a half per Cent. Government Stock, the latter known as the Cunningham Fund. (Signed, ) JAMES Pim, Jun., 31st March, 1843. Treasurer. ——————E————————————— eer No. IV. ACCOUNT OF THE ROYAL IRISH ACADEMY, FROM Isr APRIL, 1843, TO 31st MARCH, 1844, THE CHARGE, Balance in favour of the Public, as Par Toast] £0 se deh ta Audit, : » + + - | 210 13 9} Parliamentary Grant for 1843 (paid Jan. o" Bias. /u:f?. Quarterly ‘Warrants from Treasury, . : Total from Treasury, . THREE PER CENT. CONSOLS SOLD: 1843, August 12, 14, £300, at 94% 4 per, Interest 40 days, aa 446 17 8 283 10 11 Brokerage, . ty Oe Total Proceeds Consols sold, Oxp 33 PER Cent. STOCK SOLD: 1843, August 12, 14, £50, at 1014 Per, sel aO.dlG Interest 40 days, " 0 3 283 3 5 3 10 i. Gceka Brokerage, . . i 0; fg Total Proceeds old 34 per | cent. Stock sold, . s sh 50 18 10 INTEREST ON STOCK: £8: Half year’s on 1665 4 3 33 eS Cents, | 29 1 4 Ditto, ,, 164319 6, 34 28 13 11 Wet: «55 1394 17 8,3 “ 2047 Fs Ditto, ,, TEL7, 10,4 ite 16 13 10 Total Interest on Stock (ex: } clusive of brokerage, 5s. 67.,) | 95 6 4 | 1087 0 OF XXVill Brought forward, . PUBLICATIONS AND Books soLpD: Boone, Messrs., balance of their account. to 31st.December, 1843, One YEAR’s Rent OF STABLE to Nov. 1,1843, Lire CoMPosITIoNs: J. Pickford, M. D., ENTRANCE FEEs: Hon. and Very Rey. the Dean of St. Pa- EEICK? Seen 2 ~. 22-1843. Goddard "Richards, Esq. 5 ie Rey. F. Crawford, : J. Wynne, Esq., . : J. George Abeltshauser, Esq er G. J. Allman, MDs 412 H. L. Lindsay, Esq., Rey. John Homan, . John M‘Mullen, Esq., . Matthew Dease, Esq., . J. Pickford, M.D., . Sir M. Chapman, Bart., E. Bewley, M.D., J. Neville, Esq., . Henry Clare, Esq., . William Henry, Esq.,. . William M‘Dougall, Esq., ; Total Entrance Fees, ANNUAL SUBSCRIPTIONS AND ARREARS: W. Andrews, Esq., due March 16, 1843, Cal: Webber, Esq., . = The Archbishop of Dublin, +5 William Hill, Esq., . Sir Thomas Staples, Bart., F. M. Jennings, Esq., James Pim, Jun., Esq., Rev. William Lee, : William Gregory, M.D., W. Longfield, Esq., - Rev. R. V. Dixon, Ditto, Rey. Richard Butler, J. Nelson, Esq., . . G. D. La Touche, Esq, = 9 14 6 3 21 0 0 1515 0 5° Bo 6 Sa 5.50 BT lg 5.5.0 6) 15 00 5-8 6 5 Gi 5 s6 e BS) 9608 5 i660 55.200 : 5 6 0 : 5 Gud | 5 nae 5 3bant a wer tie | 220 22 0 22 0 22 0 22 0 22 0 220 220 22 0 22 0 220 220 22 0 22 0 22 0 3110 0 |1227 6 32 XXix th — @ Ws _~ NWNNWNNNNNHONNYNNHYNYNNNNYNNYNNNNNNNNNNNNNNNNNNNNHNNNNYNWYYeY Brought forward, . . J. T. Banks, M. D., due March 16, 1843, A. Smith, M.D... Thomas N: eomenbetn: Esq, . a Tees F. W. Conway, Esq, . . 5, W. Blacker, Esq, . . . Sir J. K. James, Bart... . ,, Jacob Owen, Esq., . Sir W. Betham, Knt., William Hogan, Esq, . . ,, W. Drennan, Esq., . . a Hon. Justice Crampton, Li D., G. Fitzgibbon, Esq., . . Rev. James Wills, . . . ,, W. B. Wallace, Esq., W. T. Mulvany, Esq., . F. Churchill, M.D.,. A. Ferrier, Esq,, . J. 8. Cooper, Esq., . John Mollon, M.D., . F. W. Burton, Esq., W. T. Lloyd, Esq., . G. Wilkinson, Esq,, . J. Wynne, Esq., . Thomas F. Kelly, LL. D., Sir L. O’Brien, Bart., Charles Vignoles, Esq, Edward Cane, Esq,., G. W. Hemans, Esq., John Finlay, LL.D., Charles Doyne, Esq., Rev. Thomas Stack,. . . R. A. Wallace, Esq, . . 5, Thomas Grubb, Esq., . Rev. R. Chatto. (4: iti. Rev. James Reid, . . . John Toleken, M.D., . James Patten, M. D., Right Hon, Chief Baron, . Edmund Davy, Esq. . C. W. Hamilton, Esq., . J. H. Jellett, Esq, . . James Apjohn, M.D., . E. J. Cooper, Esq., . R. Adams, Esq... . . C. E. H. Orpen, M.D., . — — WNW NWNNHNNNDNNNNNNNNNNYNNYNNNNW NH NH NNN NNYNYNNNNYNNNNYNNHNNWNO®* _ to rr) —) coooCoCOoOOoOC OSC OCSOOSOOCSOSCSOSCSCSOSSOSCSSOSCSOSCSCSSSCSCSOSCSOSOSCSSSSSCSOR Xxx Brought forward, . . Hon. James King, due March 16, 1843, M. Longfield, LL. D., ° Rev. H. F. C. Logan, DoD; J. Osborne, M.D., . . . J. Huband Smith, Esq., G. A. Frazer, Esq., Eider Abraham Abell, see: . Ditto; as William Batker: M. D., Robert Tighe, Esq., . eeaws MDS sie; Rey. John West, D. D., R. Graves, M.D., . . John Ball, Esq.,. ; T. E. Beatty, M. D., . H. C. Beauchamp, M. D., R. C. Walker, Esq,, . W. Monsell, Esq., William Stokes, M. D.,. J. T. Young, Esq., RoRed i. Dp eae: Rey. Matthew Horgan, . Oliver Sproul, Esq., Arthur Jacob, M. D., J. F. Lynch, Esq., é R. W. Smith, Esq., . Wrigley Grimshaw, M. Ds. John Hart, M.D., M. Barrington, Esq., H. H. Joy, Esq,, . J. Anster, LL. D., . W. R. Wilde, Esq., . W. T. Kent, Esq., R. Dickinson, Esq., . R. Mallet, Esq., . S. Carter, Esq., M. O’Conor, Esq.. . . . W. F. Montgomery, M. D., G. M‘Dowell, Esq., . : Ditto; - Rev. Edward Marks, Dy De G. A. Kennedy, M.D., A. Lyle, Esq., . : F. Churchill, M. D..,. B. J. Chapman, Esq., 9 1 LS) NNN NNO NY NNN NNN NNN NNNNNNNNYNNYNNNNNNYNNNNNNNNNNNNNN RS NNYNNNYNYNNYNYNNNYNNNYNNNNNNYNNNNYNNNNNNNNNYNNNNNHONNNNNWNOY | 220 10 — i) LN) ~I DI iS) bol XXXi Mita Lice ek 4 . + oy Brought forwar 220 10 O }12 3 liam ie Esq., due March ma 1843, yA ee E ry Clarke, Esq. . . «6s Pe 2.2.0 oy pRalionp Esq., 2 20 al Annual Subscriptions and Arrears, abet 220.16 -'6 | Tue Toran Cuarcz,. . .|. . . £|1454 2 34 { } : ; ; OoRf Up = teen | es, parti G's a te : t : » ‘ ’ Joe, ’ : 4 Mio ~~ Ww j bth * Ve +) te a. Vu a ; we Sd ; itt nt ' . Tass ‘ Pd 4 ~ Fe sei XXXil THE DISCHARGE. ANTIQUITIES PURCHASED AND REPAIRED. Armstrong, Robert, drawing of the Magrath tomb, 18th October, 1844, . . Davis, E., great seal of George L., Nov. 13th, 1843, : Donegan, John, for antique ‘gold eneentatt Feb. 19th, 1844, Gerin, Michael, a bronze antiquity, to June 3rd, 1843, Glennon, Richard, spear, Oct. 12th, 1843, Reilly, Peter, shoes, &c. to May 20th, 1843, Ditto, a brass vessel, June 13th, 1843, Ditto, sundries, Oct. 11th, 1843, Sharkey, William, gold cinerary boxes and fibule, : Underwood, J., “for bell, to August 11th, 1843, . Ditto, cel, Oct. "10th, 1843, Ditto, dirk, Nov. 3rd, 1843, Total Antiquities purchased and repaired, ooo o ooococo Oo i=) Oo Booxs, Printinc, STATIONERY, &Xc. Allen, J. W., Lathog DRY, &c., to July 4th, Tees 9 | Curry, Eugene, "Catalogue of Manuscripts, : to April 7th, 1843, 0 Ditto, ditto, sans 5th, 1843, 0 : Ditto, ditto, July 17th, 1843, 0 Ditto, ditto, Nov. 6th, 1843, 0 : Ditto, ditto, Nov. 13th, 1843, 0 : Ditto, ditto, from 11th Dec., 1843, to Feb, 19th, 1844, ; 2) Ow Dalton, John, for book on Drogheda, to Dee. 21st, 1843, 1 4 0 Gill, M. H., printing Proceedings ‘and Cir- culars, Dec. 31st, 1842, : Ditto, ditto, ‘Tjaneactions: Match 16th, 1843, =e a XXxili Brought forward, . Hanlon, George, for woodcut of i stone to Nov. 18th, 1843, . . Hodges and Smith, books, hos to J wie, 1843, Johnson and Co., advertising Transactions to June 30th, 1843, , Kirkwood, John, printing and engraving, March, ‘24th, 1843,.6 ses Mullen, G., book binding, to March 20th, ts a : Ditto, Bitto, June 30th, 1843, Ditto, ditto, Jan. 3lst, 1844, Oriental Translation Fund, subscription for 1842 and 1843, . : Perry and Co., paper, to June 28th, 1843, Plunket, James, 24 sheets of drawings for Catalogue of Antiquities, to Dec. 24th, 1843, Reilly, John, done ‘volumes of the Transac- tions, Feb. 5th, 1844, : Taylor, R. and J. E., twenty Scientific Me- moirs, Part II., i Jan. 31st, 1843, - Total Books, Printing, Stationery, &e., Coaus, CANDLEs, OIL, &c. Kenny, M., for stove coals, to July 20th, 1843, Rathborne, J. & H., for candles, to May ai, UG! Ss Sas Todhunter, J., eee ra March 30th, 1843, Total Coals, Candles, Oil, &e., ConTINGENCIES, &c. Carriage of parcels, to Nov. 28th, 1843, Clibborn, E., incidentals, to a ha 3rd, a3, . hh Ditto, per treasurer, : Clifford, for gum, to Oct. 23rd, 1843, Declaration in Court of Exchequer, and car hire, to Dec. 6th, 1843, . . Elliot, carriage of parcels, to May 29th, 1843, Fannin, ditto, May 22nd, 1843, Ditto, ditto, Jan. 22nd, 1844, Ditto, ditto, ditto, Maguire, twine, June 16th, 1843, 17 19 on — —= — or oooooo ooo Ora nD wo Oa — — i=) — a coooocoonm OFF 8 | 672 12 5 ee 718 15 10 XXXIV Brought forward, . Pamplin, William, carriage of par cels, June 26th, 1843, 3 : Patten, J., aio, Dee. ‘27th, 1843, Postages, to June 23rd, 1843, . : Ditto, Dec. 31st, 1843, Ditto, ditto, Postage stamps, to March 25th, 1843, Power of attorney to Boyle and Co., to sell Stock, Stamp on Government ‘Grant, paid Jan. 4th, 1844, q Subscription to Mr. Ryland, to reimburse his expenses in carrying the Act of 6 & 7 Victoria, : : Total Contingencies, So. . Repairs OF Hovss, &c. Brown, J., cleaning windows, to June ah 1843, . . Ditto, glazing ditto, Feb. 3rd, 1843, Clibborn, Edward, sundries used in cleaning house, to July 16th, 1843, Mullen, Wm., sweeping chimneys, to May 17th, 1843, : : Total Repairs ‘of House, &e. REPAIRS OF FURNITURE, &c. Allen, E., towels, to April 28th, 1843, Casey, Paul repairing locks, to ‘March 20th, 1843, . Duffy, John, altering kaple, to March 10th, 1843, . Edmundson and Co., for lamps, &e., “to March 11th, 1843, Kane, B., removing and cleaning carpet J uly Ist, 1843, . ‘ Perry and Co., locks, to J uly 6th, 1842, Ditto, ditto, June 28th, 1843, Sharp and Co., ie sa" of clocks, &c., March 7th, 1843, : Surnam, George, repairs, to April Ist, 1843, Total Repairs of Furniture, &c., Ee 3. a. any 8 Ogiaré GO Le 1010 8 Lahé 1 OPIO 5 Ly 40-70 10? 30 O 2590 10 10 O 100 OO x 0:40 0 FE iG jl) AL Js) ol! ora 4 14; 0 Bl 289 On hie 0 18 10 Ler?) ted 015 6 i. Wail £. Cpe od. : 718 lo. 10 -J @ lor) XXXV Cae d. £ Rd) ies POU JOTWATT, yi Vine ve es Ate & I Rent, Taxes, Insurance, &c. Borough rate, made 30th Sept. 1842, ... 110 0 Boyle and Co., allowance for poor rate paid by them on "stable, to Nov. Ist, 1843, . . r- 62 Grand Jury cess, half year, Easter, 1843, F 3.15. 0 ce sai Insurance at Globe, Dec. 25th, 1844, 5 13 6 Ditto, National, Dec. 26th, 1844,5 13 6 Ditto, ditto, Dec. 25th, 1844,4 2 6 ——| 15 9 6 Ministers’ money, to Sept. 29th, 1843, . . 2°15 ‘5 Parish cess, to Sept. 29th, 1843, . . . . 117 6 Pipe water, to June 24th, 1843, . . . . jy Police tax, to March, 25th, 1843, 2 3 9 Ditto, to Sept. 29th, 1843, 117 6 ——/| 41 38 Truell, R. H., half year’s “ie to Aug. Ist, 1843, - b2 4 6 Ditto, ditto, Feb. Ist, "1844, 52 4 6 1049.0 Wide street tax, Easter, 1843,. .. . Lelf,. 36 Total Rent, Taxes, Insurance, 323 GR Gio I Savarigs, Servants’ WacEs, &c. Clibborn, Edward, for one year’s salary as Assistant Librarian and Clerk, to March 16th, 1844, . . . .| 120 0 O Conroy, P., delivering notices, to x une 8th, i) SAMs ees ; 01 6 Drummond, Rev. W. HL, Librarian, year? 8 salary, to 16th March, 1844, ... ./| 21 0 0 Hamilton, Wm., wages and al- lowance as porter, to April 29th, 1843," . . bit, 442.2 Ditto, to July 15th, 1843, om a ae ae Ditto, to Nov. 18th, 1843, . . 1117 0 Ditto, Christmas allowances, to Dec. 25th, 1843, 2

+——_—_ THE accompanying paper is a Meteorological Journal, shewing the maximum and minimum points the Thermome- ter indicated, the Height of the Barometer, and the Amount of Rain. The first column gives the thermometric results; the second gives the barometric pressure, in inches and thou- sands of-an inch; the third gives the amount of rain that has fallen, in thousands of an inch. These observations have been made as nearly as possible to 10 o’clock, a.M., each day throughout the past year. They are tabulated each month, so as to shew the quantity of rain that has fallen during that period. Twelve months are then made up, which shews the year’s rain to be 23.440 inches. It may not be out of place to mention the description of instruments which were made use of on the occasion. The temperature was observed with a pair of Dr. Ruther- ford’s self-registering thermometers. The barometer is simi- lar to one first made by me for Dr. Apjohn, and under his directions ; it is a very simple instrument, and extremely con- venient for daily or rapid observations ; there is no floating gauge used, nor is it necessary to make any observation at the cistern; the fluctuations in the height here are nearly all avoided, by very much increasing the area of the cistern over h xl that of the tube; in this instance it is as 1 to 500, the diameter of the tube being ;3, ; it is graduated to the five-hundredth of an inch, and reads as 1000. From this arrangement it is evi- dent that any deviation produced in the surface of the cis- tern, from the rise or falling of the mercury in the tube, will be inappreciable, and does not amount to the errors of observation. The rain-gauge is also similar to one which I made for Dr. Apjohn at the same period. In superficial area it measures 1000 inches; the rain is collected in a vessel which is graduated into cubic inches, consequently, when one inch by measure is indicated by the graduations, it de- notes that z,)5 of an inch of rain has fallen on the surface above, and as the receiver is graduated into cubic inches all the way, it gives at once the decimal, until you come to 1000 cubic inches, which is equivalent to 1 inch ofrain: this gauge admits of the most simple verification. a aan ale iat a mie OanNooaurh WON = © xli JANUARY. Thermometer. Barometer. | Rain. ! Max, Min. 520° 33° 30.350 40 34 30.150 43 32 30. + te 46 29 29.950 151 40 35 30.104 -080 47 35 30.150 -030 48 39 29.820 -009 44 32 29.260 -150 4l 30 29.470 -050 44 32 29.100 -200 36 29 29.010 .075 36 29 29.016 1.050 38 31 28.100 385 37 30 28.726 -080 35 26 * 28.950 i oF 37 26 29.850 -100 44 30 30.100 -030 48 42 30.314 49 42 30.400 48 4] 30.120 46 38 29.500 48 42 29.755 o 49 40 29.580 004 49 td 29.610 -100 49 4l 29.960 Cie’ 30.050 .035 29.864 Arey ee 29.770 .025 29.850 035 29.750 29.550 h2 Wind. x23 xn NM == 435 ZAAZAzAY dmnas Mee E nn zz AZ sa" sae Nn a < io 2 42 xhii FEBRUARY. : Thermometer. Barometer. Rain. Wind. Max. Min. 1 49° 39 29.650 060 W.byS 2 | 47 | 36 29.600 095 Ww 3 41 35 29.300 130 N. W 4 40 25 30.000 003 N. by W 5 39 32 29.970 008 N. W 6 1.40} 88 30.150 N. by W if 43 33 30.200 040 N.E 8 43 40 30,154 N. E 9 43 38 30.162 Big oR N. E. 10 42 35 30.146 -008 E. N. E. 11 40 35 30.140 .006 E 12 40 34 30.170 - .020 E. 13 42 36 30.120 Biers A E. 14 40 33 29.860 Sas ie E. N. E. 15 35 24 29.530 Free ae N. E. 16 32 21 29.284 a ace N. E. 17 36 25 29.596 Set ot nce N.N. E. ‘ 18 | 39 | 80 SOGOG Ader! . E. by N. 19 40 32 29.446 .020 E. 20 40 34 29.224 -675 S. E. 21 45 37 29.252 .145 S. E. 22 47 39 29.348 .090 E. 23 42 38 29.440 -210 E. 24 45 40 29.610 15 E. S.E. 25 47 41 29.716 E. S. E. 26 | 41 35 29.700 E. 27 39 35 28.371 te E. 28 Al 35 29.420 .010 E. : — mpeoeoesecoanouruvnrnnm t tH wp MH HOOD eH ee SE Soap enveHeSoarnannr & 27 Thermometer. Max. 43° 45 44 42 39 Min. 84° 28 32 27 33 32 33 30 39 35 35 dt 38 39 38 39 40. 41 xiii MARCH. Barometer. Rain. 29.350 100 80.070 é 80.216 srt 30.468 Sela 29.970 .008 30.150 80.200 80.150 30.160 kc 30.140 -060 30.140 -040 29.793" -025 29.650 ae 29.518 .430 29.900 .070 29.826 ‘ 29.620 29.892 ab «6 29.846 055 29.480 : 29.250 .085 29.200 .160 29.410 .380 29.562 .100 29.850 .130 29.900 ; 29.750 AAA 29.328 Spe" 29.976 29.478 - 29.320 : xliv APRIL. Thermometer. Barometer. Rain. | Wind Max. Min. 1 39° 47° 29.250 015 S. E. 2 58 46 29.350 145 W. 3 62 44 29.700 -030 4 58 40 29.200 .130 W. 5 58 47 29.300 -002 W. by S. 6 64 47 29.600 .006 W. 7 56 46 29.320 .465 S. W. 8 61 42 29.500 -100 W. 9 59 42 29.774 .090 W. 10 46 32 30.040 .002 N. W. ll 49 33 30.150 .090 N. W. 12 50 33 30.050 NeW: 13 54 32 30.076 4 N. 14 53 40 29.950 .010 N. W. 15 61 42 29.500 -100 « ANGE 16 54 44 29.950 N. W. 17 67 40 30.050 N.E: 18 62 44 30.050 E. 19 64 48 29.900 - E. by N. 20 67 48 29.650 .020 E. 21 65 46 29.750 .055 N. W. 22 54 44 29.760 .025 Ww. 23 55 40 30.010 .020 ) W. 24 62 42 29.970 .350 N. E 25 53 46 29.620 -270 W. by N 26 53 35 29.600 SUS N. by W. 27. 58 36 29.850 .195 W. by S. 28 58 41 29.650 340 W.byS 29 55 42 29.720 .030 E. by N 30 63 43 30.020 E. by N xlv MAY. Thermometer. Barometer. Wind. Max. Min. 1 66° | 438° | 30.250 E. by N 2 67 47 30.250 arte N.E. s | 69 | 44 29.960 .020 E. 4 63 | 42 29.700 .060 WwW. 5 64 | 37 20.578 . Ww. 6 60 | 38 29.600 Berwin N.W 7 | 58 | 41 29,600 016 E. 8 | 59 | 42 29.716 -002 N. E. 9 | 62 42 29.950 N. E. 10 | 67 46 30.150 N. E. il 62 45 30.150 : . N. E. 12 64 | 50 39.250 .140 S. by E 13 | 62 | 50 29,826 .205 S. 14 67 43 29,750 E.by N 15 | 64 49 29.500 E.byS : 16 67 49 29.600 ae E.byS : 17 54 | 47 29.800 .200 E. by N 1s | 60 | 44 30.050 .180 E. 19 66 | 46 19.968 .080 N. 90 | 64 | 45 29.620 .900 N.E. 21 51 46 09.560 1.320 E. by N 22 55 | 47 29.700 .130 E. 93 | 59 | 47 29.722 .026 E. by N 24 62 | 43 29.570 .120 E.by N 25 60 44 29.964 645 E.N. E. 26 | 638 | 50 29.550 205 S. 27 60 48 29.530 ‘Shee Ww. 28 | 60 48 29.750 .140 E. by N 29 | 62 45 30.050 5 E. by N 30 63 46 30.016 iat a, Ww. 31 62 50 29.800 140 Ww JUNE. Thermometer. Barometer. Rain Wind. Max. Min. 1 65° | 540 29.468 .300 E. 2 63 52 29.270 .268 S. W. 3 62 50 29,370 024 N. W. 4 53 45 29.700 240 W. 5 54 44 29.814 590 Ww. 6 54 42 30.038 035 N. W. 7 59 46 29.600 015 Ww. 8 59 49 28.900 125 W. 9 61 49 29.400 .080 N. W. 10 62 48 29.944 ll 63 49 30.210 N. W. 12 63 45 30.200 N. E. 13 71 50 30.128 Be Pa 14 70 49 30.050 .360 E. by N, 15 65 53 30.050 .240 E. 16 65 53 30.114 E. 17 72 51 30.150 E. 18 70 53 30.128 E. 19 80 57 30.050 N. E. 20 72 51 30.250 N. E. 21 74 55 30.150 Ww. 22 65 55 30.150 N. 23 69 49 30.150 E. 24 74 52 30.130 Ww. 25 80 56 30.074 SE: 26 74 52 30.300 S. E. 27 75 50 29.900 N. E. 28 78 55 29.850 W. 29 77 50 29.950 ° WwW. 30 65 52 29.950 S. W. xlvi xl vil JULY. Thermometer. Barometer. Rain. | Wind. Max. Min. 1 68° | 55° 30.000 pls, cr. S. W. 2 72 56 29.864 .080 W. by S. 3 73 57 29.850 seat E. 4 74 54 30.000 ee ba E. 5 74 53 29.700 .120 W. 6 63 52 29.720 110 S. E. 7 70 53 29.760 .020 S. E. 8 70 54 29.050 .020 W. 9 63 51 30.150 N. 10 71 54 80.250 N. E. ll 69 49 80.564 ig: ae N. W. 12 71 53 30.250 .120 W. 13 67 56 30.200 -380 W. 14 68 53 30.200 -105 W. 15 65 58 30.140 W. 16 70 53 80,250 OES Ea W. 17 71 58 30.250 .012 W. e 18 76 58 29.950 -106 S. W. 19 74 54 29.850 “se N. W. H 20 79 50 29.800 = te W. 21 65 53 29.800 Kies W. 22 65 55 29.760 Cae ie Ss. W. 23 66 50 29.750 .020 N. W. 24 69 48 30.160 N. W. 25 69 54 30.250 ee Ss. W. 26 72 61 30.250 .060 W. by S. 27 72 54 30.150 .030 N. W. 28 | 67 | 58 30.006 115 W. by S. 29 | 66 | 55 29.684 315 W. by S. 30 68 52 29.700 .050 i wes 31 68 52 30.000 110 N. W. xviii AUGUST. Thermometer. Barometer. Rain. Wind. Max. Min. 1 66° 57° 29.900 : Ss. W. 2 70 56 29.500 220 W. 3 70 54 29.420 170 S. W. 4 68 53 29.560 -280 W. 5 64 51 30.000 080 W. 6 75 54 30.100 018 W. 7 74 62 30.150 ie Ss. W. 8 70 54 30.200 110 s. by W. 9 73 50 30.250 : W. 10 74 55 30,324 S. W. 1 Kae | 955 30.350 S. by E. 12 73 55 30.270 E. 13 73 55 30.250 - S. E. 14 73 54 30.050 mee | ae E. 15 67 57 30.000 .040 E. 16 65 57 30.108 5 N. E. 17 74 54 30.200 ° E. 18 78 57 30.200 S. E. i9 | 78 | 56 29.950 an E. by S 20 78 57 29.908 060 N. E 21 71 54 29.600 : N. E. 22 74 44 29.370 195 S. W. 93 73 45 29.750 . Ss. 24 71 56 29.700 ml A S. W. 25 70 56 29.850 .090 S. W. 26 71 58 29.750 Ss. 27 71 54 30.660 - Ss. 28 72 56 29.700 .030 S. EB. 29 71 4 50.078 073 N. W. 30 70 50 30.200 N. E. 31 73 52 30.200 S. W. xlix SEPTEMBER. Thermometer. Barometer. Rain. Wind. Max. Min. 1 72° 48° 30.250 E. 2 72 68 30.410 E. 3 74 61 30.300 S. E. 4 74 51 30.500 : N. E. ‘5 73 48 30.500 Ss. 6 74 49 30.370 4 W. 7 76 50 30.300 W. 8 80 56 80.272 ; E. 9 76 58 30.200 3 E. 10 75 59 30.000 010 E. 11 67 53 29.950 270 S. E. 12 70 46 30.400 Ss. W. 13 72 51 80.220 E. 14 66 50 29.958 ces N. E. 15 66 57 29.850 .065 W. 16 65 57 80.000 A W. 17 64 57 80.150 E. 18 68 55 80.100 mer N. E. 19 70 55 30.300 .035 E. 20 69 53 30.150 S. 21 69 58 30.300 N. E. 22 67° | 56 30.522 W. by S. 23 64 45 30.624 N. 24 61 53 30.600 W. 25 62 48 30.450 N. W. 26 60 46 30.300 N. W. 27 57 Al 29.900 p N. W. 28 54 35 30.000 .007 W. 29 54 45 30.100 Fee W. 30 62 48 29.950 .250 Ww. OCTOBER. Thermometer. Barometer. Rain. Wind Max. Min. I 63° 56° 30.050 Fite W. 2 64 51 30.150 240 W. 3 61 49 30.100 - 004 Ww. 4 62 53 30.200 010 W. 5 69° |" ae 29.950 he W. by S 6 68 57 29.500 - 060 W. by S. 7 | 70 | 57 29.500 025 N. W. a es Pa 29.850 510 N. 9 | 66 | 44 29.520 145 Ww. 10 58 40 29.870 025 Ss. W. 1] 56 46 29.760 330 W. 12 54 38 29.410 250 N. W. 13 50 37 29.690 040 S. W. 14 50 32 29.810 008 N. W. 15 | 49 | 33 29.870 W. by N. 16 49 33 29.750 oe N. W. 17 46 30 29.664 005 N. W. 18 46 35 29.618 140 W. 19 45 30 30.122 W. by N. 20 66 30 30.412 =a W. 21 52 40 30.050 -130 W. 22 55 44 29.810 025 S. W. 23 58 46 30.050 ° W. 24 55 48 29.600 -060 S. W. 25 54 37 29.430 -.600 W. 26 47 34 29.610 ° W. by N. 27 47 31 29.400 - E. 28 46 31 29.460 .420 W. 29 46 31 29.500 : W. by S 30 44 32 29.400 075 Ai 31 44 30 29.550 -200 W. NOVEMBER. | Thermometer. Barometer. Rain. Wind. 1 29.650 2 29.800 3 29.400 4 29.500 5 30.030 6 29.820 7 29.700 8 29.716 9 29.916 10 29.400 11 30.050 12 30.120 13 30.250 14 30.320 15 30.150 16 30.150 17 29.600 18 29.330 19 29.460 20 29.580 21 29.350 22 29.350 23 29.490 24 29.470 25 29.450 26 29.300 27 29.450 28 30.100 29 30.450 30 30.100 lii DECEMBER. Thermometer. Barometer. Rain. Wind. Max. Min. 1 51° 39° 30.120 splot, We 2 50 39 30.170 004 W. 3 51 44 30.350 -004 S. W. a 52 43 30.270 .003 S. W. 5 | 52 | 45 SOOT GCA. mah. W. by S. 6 51 41 30.350 -040 W. by S. 7 4 %53 1 43 30.100 .012 W. by S. 8 53 44 30.300 -012 W. 9 49 45 30.296 a W. 10 52 46 30.150 ee Wes 11 49 36 30.100 -002 S. E. 12 50 45 30.350 -050 E. by S. 13 50 43 30.320 .003 W. by S. 14 51 45 30.430 > Posh Ss. W. 15 -¥i SF. | 47 S0:85086 tii. al. S. by W. 16 50 48 30.450 Tees ht W. by S. 17 54 45 30.460 -004 Ss. W. 18 50 43 30.450 a ae W. by S. 19 49 44 30.300 -ieok Ss. W. 20 52 46 SOMLSO yiees | os Ss. W. 21 53 41 30.300 aes oe E. by N. 29); (i 5eh | 42 30.300 Cidees E. by N. 23 54 45 30.250 b matte. S. by W. 24 57 53 30.400 -004 S. W. 25 56 48 30.310 eat Ie E. 26 51 41 30.350 Anns IN Ves 27 50 42 30.424 Anh 2 Was: we 28 51 47 30.460 i © S. E. 29 50 46 30.350 ag W. S. W. 30 46 44 30.150 + 5S W.S. W. 31 50 43 30.100 S ghee W. S. W. January, February, . . March,. . . ‘a May, . GS hal July, . . 4 August, . September, . October, November, December, iii GENERAL RESULTS. Amount or Ran. Inches. AS Cen ae Pe ae OL et a ee tS Ditige sty worms «te ED Ge etddep er we aloe! a. Sn Oee PE a Cee ee ne he tie wader eer ae AS Capra kes he: DES Sarace oir autre P| Sea Te See Can aie uae aS Le eee Sa en! | a “ORE Wer oct ss piensa ae 138 23.440 BAROMETER. Greatest pressure, August 27, Lowest point, January 13, . THERMOMETER. Maximum, September 8, . Minimum, February 16, . . - ..-: . 2, Grafton-street. Mean Temp, 420 34 38 4]1 614 674 68 70 67 56 49 51 30.660 28.100 80° 21 SP LPR Ae . vy ; : . , bagi ne 4. a pane ‘i 4 FP Bx yy ia oe ‘ f o Ta ar eal een - a . e - 3 ‘ hd 4 y- “ d + Oot s oS aes aie. / F ’ yi « 7 ms (ORB Solin oa ed ek ed ¥ ' ‘ - ‘ 5 ” i : - oe he i ’ & a 4 ct Ki fe eee eens i! ine bedi a " ¥ apne alt et RM oe a ee ee eae a A ea Ve eRe HT at i . ’ : 4 ae FTG RRR et Ie ee) Sa tn A. : Te ? a Beh one ene _ MAH Lv * ‘fel ; a ¢ ( J : 4" ies t a ‘ os mn Ae ory eh foe fy . A Pel ath aa Bro) 2180” Se AE Dae teen ioe ac Bator ae? ihe nt 10 Sree v7 ‘alee THE ROYAL IRISH ACADEMY, Marcx 16, 1843. Watroness: HER MOST SACRED MAJESTY THE QUEEN. Visitor : HIS EXCELLENCY THE LORD LIEUTENANT OF IRELAND. President : SIR WILLIAM ROWAN HAMILTON, LL. D. DY ice-JPresivents. Rev. Humesrey Luoyp, D. D. Rev. James Hentuorn Topp, D. D. Rev. JosepH HENDERSON SINGER, D. D. James Apsonn, M. D. COUNCIL. A Committee of Science. e Rev. Franc Sapiei, D. D., James Mac Cutzaes, LL. D. Provost. Rev. Wm. D. Sapuem, A. M. _ Rev. HuMPaReY Lioyp, D.D. | Rosert Batt, Esa. _ JAMES Apsoun, M.D. © Rosert Kane, M.D. a ee = A Committee of Polite Literature. His GRACE THE ARCHBISHOP OF | Rev. Wm. H. Drummonp, D. D. DUBLIN. Rev. Cuas. R. Etrineton, D.D. Rev Josepu H. Srincer, D. D. Rey. CHartes W. WALL, D. D. SamveE. Litton, M, D. Joun AnsTER, LL. D. Committee of Antiquities. GEORGE PETRIE, Esq., R.H.A. | Josepn H. Smiru, Esa. Rev. James H. Topp, D. D. JAMES Pio, Jun., Esa. Henry J. Monck Mason, LL.D. | Caprain Larcom, R. E. SamvueEt Fercuson, Esa. @ fficers. Treasurer.—J AMES Pim, Jun., Esa. Secretary of the Academy.—J ames Mac Cutuaeu, LL. D. Secretary of Council—Rosert Kane, M.D. Secretary of Foreign Correspondence.—Rev. Humpurey Luoyn, D.D, ' Librarian.—Rev. WittiamM H. Drummonp, D. D. Clerk and Assistant Librarian —EpDWArpD CLIBBORN. Notre.—The Members of the Academy are particularly requested to communicate to the Assistant Librarian, any corrections in this list which they may consider necessary. a MEMBERS. The Names of Life Members are marked with an Asterisk. * Adare, Edwin Viscount, M. P. F.R.S. F.R.A.S. Dun- raven Castle, Glamorganshire, and 76, Eaton-square, London. * Andrews, Thomas, M.D. 65, Chester-square, Belfast. * Armstrong, Andrew, Esq., A. M. 17, College. * Arthur, Thomas, Esq. * Ashburner, John, M.D. 55, Wimpole-street, London. Abell, Abraham Esq. Cork. Adams, Robert, Esq. V.P. Royal College of Surgeons. 11, Great Denmark-street. Allman, George James, Esq. Grattan-street. Andrews, William, Esq., Sec. Natural History Society. 18, Leinster-street. Anster, John, LL.D. 5, Lower Gloucester-street. Apjohn, James, M. D. Professor of Chemistry, Royal Col- lege of Surgeons. V. P. Geological Society of Dublin. —Vicr-Presipent. 28, Lower Baggot-street. Armstrong, William, Esq. 5, Lower Dominich-street. * Bailie, Rev. James Kennedy, D.D. Ardtrea, Stewarts- town. * Bald, William, Esq., F. R. S. E. _ * Ball, Robert, Esq. Sec. Royal Zoological Society of Ireland. Local See. Botanical Society of Edinburgh. 3, Granby-row. * Bateson, Sir Robert, Bart., M. P. Belvoir Park, Belfast. * Bateson, Robert, Esq., D.L. Belvoir Park, Belfast. b iv * Beaufort, Francis, Esq., F.R.S. F.G.S. F. R.A.S., &e. Captain R. N. Admiralty, London. * Benson, Charles, Esq., M.D. Professor of Physic, Royal College of Surgeons. 34, York-street. * Bergin, Thomas F., Esq., 5, Westland Row. * Blacker, Stewart, Esq. 20, Gardiner’s-place. * Blood, Bindon, Esq. Edinburgh. * Bolton, William Edward, Esq. 5, Nelson-street. * Botfield, Beriah, Esq., M.P. London. * Boyton, Rev. Charles, D.D. Tullyagnish, Letterkenny. * Boyle, Alexander, Esq. Killiney, and 35 College-green. * Bruce, Haliday, Esq. 37, Dame-street. Ball, John, Esq. 85, Stephen’s-green, South. Banks, John T., M.D. 8, Lower Merrion-street. Barker, Francis, M.D. Professor of Chemistry, Univer- sity of Dublin. 22, Lower Baggot-street. Barker, William, M. B. 8, Hatch-street. Barrington, Matthew, Esq. 50, Stephen’s-green, East. Beatty, Thomas E., M.D. 17, Merrion-square, North. Beauchamp, Henry C., M.D. 114, Lower Baggot-st. Betham, Sir William, Knt. Ulster King of Arms. F.S. A., F.R.A.S., V. P. Royal Dublin Society. Stradbrook House, Black Rock. Blacker, William, Esq. Armagh. Bolton, Chichester, Esq. 1, Upper Merrion-street. Booth, Rev. James, A.M. Bristol. Borough, Sir Edward, Bart. 18, Leinster-street. Brady, Right Hon. Maziere, A.M. Lord Chief Baron. 61, Harcourt-street. Burrowes, John, Esq. 1, Herbert-street. Burton, Frederick W., Esq., R.H.A. 65, Harcourt-street. Butcher, Rev. Samuel, Fellow of Trinity College. College. Butler, Rev. Richard. Trim. * Callwell, Robert, Esq. 22, Herbert-place. Vv * Campbell, William W., M.D. Port Stewart, Coleraine. * Carmichael, Andrew, Esq. 24, Rutland-square, North. * Carmichael, Richard, Esq. 24, Rutland-square, North. * Carne, Joseph, Esq., F. R.S. F.G.S. Penzance. * Carson, Rev. Joseph, A. M., Fellow of Trinity College. College. * Caulfield, Hon. Henry. Hockley, Armagh. * Chamley, George, Esq. 6, Belvidere Place. * Charlemont, Francis William Earl of. Charlemont House. * Chetwode, Edward Wilmot, Esq. Woodbrook, Portarlington. * Clare, John Earl of. Mount Shannon, Killaloe. * Clarkes Thomas, Esq. 123, Lower Baggot-street. * Clendinning, Alexander, Esq. Westport. * Colby, Lieut.-Colonel Thomas, Royal Engineers, LL. D. F.R.S. L. and E. F.G.S. F. R.A.S. &e. Ordnance Survey. Office, Phenix Park, and Tower, London. * Cole, Owen Blayney, Esq. Merrion-square, North. * Colvill, William C., Esq. 6, Bachelor’s Walk. * Conroy, Edward, Esq. Kensington, London. * Corballis, John R., Esq. 15, Baggot-street. * Cork, Cloyne, and Ross, Right Rev. Samuel Kyle, D. D., Lord Bishop of. Cork. * Coulter, Thomas, M.D. College. * Courtney, Henry, Esq. 24, Fitzwilliam-place. * Croker, Thomas Crofton, Esq., F.S. A. London. * Croker, Charles P.. M.D. 17, Merrion-square, West. * Cubitt, William, Esq., F.R.S. F.R.A.S. 8, Great George-street, Westminster, London. * Cusack, James W., Esq., M.D., Sec. Royal College of Surgeons. 3, Kildare-street. Cane, Arthur B. Esq. 60, Dawson-street. Cane, Edward, Esq. 60, Dawson-street. Carr, George, Esq. 18, Mountjoy-square, South. Carter, Samson, Esq. Kelkenny. Cash, George, Esq. Broomfield, Malahide. b2 * = 3 Vi Cather, Thomas, Esq. 20, Blessington-street. Chatto, Rev. Robert, A.M. Whickham Cottage, Gates- head. Chapman, B.I., Esq. Kéllua Castle, Athboy. Churchill, Fleetwood, M.D. 136, Stephen’s-green, West. Clarke, Edward S., Esq. 18, York-street. Conway, Frederick W., Esq. Rathmines, and 11, Trinity- street. Cooper, Edward J., Esq. M. P. Markree Castle, Colooney. Cooper, Jonathan Sisson, Esq. 15, Upper Merrion-street. Courtenay, Rev. Reginald. Crampton, Hon. Justice, LL. D. 50, Baggot-street. Crampton, Sir Philip, Bart. President, Royal Zoological Society of Ireland. 3, Merrion-square, North. Crawford, Francis, Esq. 51, Harcourt-street. Culley, Robert, Esq. Aingstown. Davis, Charles, M.D. 33, York-street. D’Olier, Isaac M., Esq. Booterstown. Drummond, Rev. William Hamilton, D. D.—Lrprarian. 28, Lower Gardiner-street. D’ Alton, John, Esq. 48, Summer-hill. Darley, Frederick, Esq. 25, Lower Fitzwilliam-street. Davidson, John, Jun., Esq. Armagh. Davy, Edmund, Esq., F.R.S. Professor of Chemistry, Royal Dublin Society. Dickinson, Robert, Esq. 79, Lower Gardiner-street. Disney, Ven. Brabazon William, Archdeacon of Raphoe. 16, Fitzwilliam-square, South. Dixon, Rev. Robert Vickers, A.M. Fellow of Trinity College. 10, College. Downes, George, Esq., A.M. Black Rock. Doyne, Charles, Esq. Newtown Park, Black Rock. Drennan, William, Esq. 4, Eccles-street. Drury, William V. M.D. Edinburgh. vii Dublin, Most Rev. Richard Whately, D. D. Archbishop of. V.P. Royal Zoological Society of Ireland. Pa- lace, Stephen’s-green, North. Dunlop, Durham, Esq. 6, Lower Abbey-street. _* Elrington, Rev. Charles Richard, D. D., Regius Professor of Divinity, University of Dublin. Trinity College. Edington, William, Esq. Treasurer of the Geological So- ciety of Dublin. 18, Leinster-street. * Fitzgerald and Vesci, Right Hon. William Vesey Lord, D.C.L. F.R.S. Merrion-square, North. * Fitzgerald, Rev. Michael. * Fitzgerald, Right Hon. Maurice, Knight of Kerry. * Fitz Wygram, Sir Robert, Bart. Connaught-place, London. * Fortescue, Thomas, Esq., M.P. Ravensdale-park, Flurry Bridge. * Foot, Simon, Esq. Hollypark, county of Dublin. * Frazer, R. Murray, Esq. Fitzgibbon, Gerald, Esq. 29, Gloucester-street, Upper. Farran, William, Esq. 76, Abbey-street. Ferguson, Hugh, M.D. 62, Sackville-street. Ferguson, Samuel, Esq. 56, Lower Dominick-street. Ferrier, Alexander, Jun., Esq., A.M. Rathmines. Finlay, John, LL.D. 31, North Cumberland-street. Frazer, George Alexander, Esq. Lieutenant R.N. * Goff, Rev. Thomas. Black Rock. * Gough, George Stephens, Esq., A. B. * Graves, Rev. Charles, A. M. Fellow of Trinity College. 2, College. * Grierson, George A., Esq. Queen’s Printing Office, 19, Essex-street, West. * Griffith, Richard, Esq., F.R.S.E. F.G.S. V.P. Geolo- gical Society of Dublin. 2, Fitzwilliam-place. vill Gayer, Arthur E., LL.D. 47, Upper Mount-street. Gore, William R., M.D. Limerick. Graves, Robert J., M.D. King’s Professor of the Insti- tutes of Medicine. 4, Merrion-square, South. Gregory, William, M.D. F.R.S.E. Aberdeen. Gregory, Very Rev. James, A. M. Dean of Kildare. 17, Fitzwilliam-street, Upper. Grimshaw, Wrigley, M.D. 11, Molesworth-street. Grubb, Thomas, Esq. 1, Upper Charlemont-street. * Hamilton, Sir William Rowan, Knt., LL.D. F.R.A.S. Astronomer Royal of Ireland, and Andrews’ Professor of Astronomy in the University of Dublin.— Presipenrt. Observatory, Dunsink. * Hanna, Samuel, M.D., A.M. 18, Granby-row. * Hardiman, James, Esq. Galway. * Harrison, Robert, M.D. Professor of Anatomy and Surgery, University of Dublin. 1, Hume-street. * Hart, Andrew Searle, Esq., LL.D. Fellow of Trinity Col- lege, College. * Haygarth, William, Esq. * Hill, Edward, Colonel. * Hill, Lord George A. Updown House, Sandwich. * Hincks, Rev. Thomas, LL.D. Belfast. * Houston, John, Esq., M. B. 31, York-street. * Hudson, Henry, Esq., M. B. 24, Stephen’s-green, North. * Hume, Arthur, Esq. 63, Dawson-street. * Hutton, Robert, Esq., F.G.S. Putney Park, Surrey, and 15, Manchester Buildings, London. * Hutton, Thomas, Esq., F.G.S. V. P. Geological Society of Dublin, Treasurer of the Royal Zoological Society of Ireland. Elm-Park, and 116, Summer-hill. * Hutton, Henry, Esq. 18, Gardiner’ s-place. Hamilton, Charles William, Esq., F.G.S. See. Geological Society of Dublin. 13, Meuntjoy-square, East. ix Hamilton, John, Esq. 13, Nassau-street. Hardy, Simeon, Esq. 15, Fitzwilliam-square, North. Hardy, Philip Dixon, Esq. Greenfield Lodge, Stillorgan, and 3, Cectlia-street. Hart, John, Esq., M. D. V. P. Royal Zoological Society of Ireland. 3, Ely-place. Hemans, G. W., Esq., C. E. 22, Marlborough-st. Hill, William, Esq. Donnybrook, Doneraile, Cork. Hodder, Thomas, Esq., R. M. Kildare-street. Hogan, William, Esq. A.M. Fitzwilliam-place. Homan, Rev. John, A. M. Seapoint House, Black Rock. b Horgan, Rev. Matthew. Blarney, Cork. Hudson, William E. Esq. 39, Upper Fitzwilliam-street. Hughes, William John, Esq. 49, Westland-row. Hutton, Edward, Esq., M.D. 29, Gardiner’s-place. * Jessop, Frederick Thomas, Esq. Doory Hall, Longford. * Johnson, Hon. Justice, LL.D. 45, Harcourt-street. * Jones, Lieut.-Col. Harry D., M.I.C.E. Hora Villa, Donnybrook, and Custom-house. Jacob, Arthur, M. D. V. P. Geological Society of Dublin. Professor of Anatomy, Royal College of Surgeons. 23, Ely-place. James, Sir John Kingston, Bart. 9, Cavendish-row. Jellett, J. H., Esq., Fellow of Trinity College. College. Jennings, Francis M., Esq. Cork. Jones, Robert, Esq. Fortland, Dromore, West. Joy, Henry Holmes, Esq., A. M. Treasurer of the Geo- logical Society of Dublin. 17, Mountjoy-square, East. . : ¥: * Kelly, Dennis Henry, Esq. Castle Kelly, Mount Talbot, Roscommon. * Kiernan, George, Esq. London. x * Knox, Rev. Thomas. River Glebe, Toomavara, Nenagh. * Knox, George J., Esq. 1,-Maddoa-street, London. * Knox, Rey. H. Barry. Deanery House, Hadleigh, Suffolk. * Kyle, William Cotter, LL.D. 8, Clare-street. Kane, Robert, M.D. Professor of Natural Philosophy, Royal Dublin Society.—Secrerary or CovunciL. Black Rock. Kelly, Thomas F., LL. D. 88, Lower Mount-street. Kennedy, George A., M.D. President of the King and Queen’s College of Physicians. 25, Talbot-street. Kent, William T., Esq. 37, College-green. King, Hon. James. Mitchelstown Castle, Mitchelstown. Kingsley, Jeffries, Esq. 11, Westmoreland-street. Knox, Rey. Robert. See House, Limerick. * Lareom, Thomas A., Captain, R.E. Ordnance Survey Office, Phenix Park. * Lardner, Rev. Dionysius, LL. D. F. R. S. L. and E., B.ayAs Ss * La Touche, David Charles, Esq., Bank, Castle-street. * La Touche, William Digges, Esq. 3, Fitzwilliam-square, East. Leader, Nicholas P., Esq. Dromagh Castle, Castle Mills, Cork. * Leitrim, Rt. Hon. Nathaniel Earl of. Killadoon, Celbridge. * Lenigan, James, Esq. Castle Fogarty, Thurles. * Litton, Samuel, M. D. Professor of Botany, Royal Dublin Society. 10, Lower Gloucester-street. * Lloyd, Rev. Humphrey, D. D., F.R.S., Fellow of Trinity College, Prof. Nat. Phil. Vice-PresipENT AND SE- CRETARY OF FoREIGN CORRESPONDENCE. 35, College. * Luby, Rev. Thomas, D. D., Fellow of Trinity College. 15, College. La Touche, George Digges, Esq. 91, Baggot-street. Law, Robert, M.D. _ 34, Granby-row. * x1 Lee, Rey. William, A.M., Fellow of Trinity College. College. Levinge, Godfrey, Esq. Cullion, Mullingar. Lindsay, Henry, Esq. Armagh. Lloyd, William T., Esq. 10, Crescent, Upper Mount-st. Logan, Rev. H. F. C., D. D. Oscott, Birmingham. Longfield, Mountifort, LL.D. Professor of Feudal and English Law, University of Dublin. 6, Fitzwilliam- square, West. Longfield, William, Esq. 19, Harcourt-street. Lyle, Acheson, Esq., A. M. Treasurer of the Geological Society of Dublin. 17, Gardiner’s-place. Lynch, J. F., Esq. 19, Belvidere-place. * Mac Carthy, Viscount de. Toulouse. * Mac Cullagh, James, LL. D., F. R.S., Fellow of Trinity College, Prof. Math.—Secrerary oF THE ACADEMY. College. * Mac Donnell, John, M.D. 4, Gardiner’s-row. * Mac Donnell, Rev. Richard, D.D. Senior Fellow of Trinity College. College. * Mackay, James Townsend, Esq. 5, Haddington Ter- race. * M‘Kay, Rev. Maurice, LL.D. Drogheda. * M‘Neece, Rev. Thomas, A. M., Fellow of Trinity College. College. * Macniell, John, Esq., F.R.S. F.R.A.S., Professor of the Practice of Engineering, University of Dublin. 9, Whitehall-place, London. * Magrath, Sir George, K.H. M.D. F.R.S. F.L.S. F.G.S. Plymouth. * Mahony, Pierce, Esq. 23, William-street. * Marsh, Sir Henry, Bart. M.D. V.P. Royal Zoological Society of Ireland. 24, Molesworth-street. * Martin, Rey. John C., D.D. Killesandra. xii * Mason, Henry Joseph Monck, LL.D. Queen's Inns, Henrietta-street. * Mayne, Rev. Charles, Killaloe. * Miller, Rev. George, D.D. Armagh. Mae Cullagh, W. Torrens, Esq. 8, Upper Gloueester-st. Mae Dowell, George, Esq. Fellow of Trinity College. 26, College. Magee, James, Esq. 39, Leeson-street. Mallet, Robert, Esq. 8, Ryder’s Row, Capel-street. M<‘Mullen, John, Esq. William-street. Marks, Rev. Edward, D.D. Molyneux Asylum, Peter- street. Mollan, John, M.D. 32, Gloucester-street. Monsell, William, Esq. Tervoe, Limerick. Montgomery, William F., M.D. 18, Molesworth-street. Morrison, Sir Richard. 49, Upper Mount-street. Mulvany, W. T., Esq. Dovehouse, Black Rock. Murphy, Patrick M., Esq. 33, Lower Baggot-street. Murray, William, Esq., 72, Lower Gardiner-street. * Napier, Joseph, Esq. 17, Mountjoy-square, South. * Nicholson, John A., Esq., M. B. Clontarf. Nelson, Joseph, Esq. 7, Gardiner’s-place. Newenham, Thomas, Esq. Sandford Cottage, Cullens- wood, * Odell, Edward, Esq. Carriglea, Dungarvan. * O’Ferrall, Joseph M., Esq. 38, Rutland-square, West. * O'Reilly, Miles John, Esq. * Orpen, Thomas Herbert, M.D. 13, South Frederich-street. * Orpen, John Herbert, LL. D. 13, South Frederich-street. * Owen, John Underhill, M. D. O’Brien, Sir Lucius, Bart. Dromoland, Newmarket-on- Fergus, Clare. O’Conor, Matthew, Esq. 5, Mountjoy-square, South. 3 | O'Grady, Michael Martin, M.D. La Mancha, Swords. O'Grady, James, Esq., LL.D. 25, Denzille-street. Ogilby, Robert L., Esq. Dungiven. O’ Halloran, Major-General Sir Joseph, K.C. B. 51, Up- per Seymour-street, Portman-square, London. Orpen, Charles Edward Herbert, M.D. Woodside, Liver- pool. Osborne, Jonathan, M.D. 26, Harcourt-street. Otway, Cesar G., Esq., A. B. Owen, Jacob, Esq. 2, Mountjoy-square, West. * Parker, Alexander, Esq. Rathmines. * Petrie, George, Esq., R.H. A. 21, Great Charles-street. * Phibbs, William, Esq. Seajield, Sligo. * Pim, George, Esq. Brennanstown, and 15, Usher's Island. * Porter, Rev. Thomas H., D.D. Ballymully Glebe, Dun- gannon. * Portlock, Joseph Ellison, Esq., R.E. F. R.S. F.G. S. V. P. Geglogical Society of Dublin. V.P. Royal Zoo- logical Society of Ireland. 50, Upper Sackville-street. * Prior, Rev. Thomas, D.D. Senior Fellow of Trinity College. College. * Prior, James, Esq. 14, Oxford Terrace, Hyde Park, London. Packenham, Hon.and Very Rev. Henry, Dean of St. Pa- trick’s. 19, Merrion-square, N., and Deanery-house. Palmer, Abraham, Esq., M.B. 38, York-street. Patten, James, A. M., M.D. Belfast. Pim, James, Jun., Esq.—Treasurer. Monkstown Castle, and 35, College-green. Ponsonby, The Hon. Frederick. 36, Kildare-street. * Radcliffe, Right Hon. John, LL. D. Judge of the Court of Prerogative. 14, Hume-street. xiv * Renny, H. L., Esq. Assistant Professor of the Practice of Engineering, University of Dublin. Sec. Geologi- cal Society of Dublin. Royal Hospital. * Rhodes, Thomas, Esq. Shannon Commission. * Roberts, Rev. John Cramer. * Robinson, Rev. Thomas Romney, D. D. Observatory, Armagh. * Rosse, Right Hon. The Earl of. Birr Castle, Parsons- town. * Rowan, Rev. Arthur B., A.M. Bellmount, Tralee. Richards, Goddard, Esq. Ardamine, Co. Wexford. Reid, Rev. James. Clontarf. Reid, Robert, M.D. 16, Belvidere-place. Roberts, William, Esq., Fellow of Trinity College. College. * Sadleir, Rev. Franc, D.D. Provost of Trinity College.— Provost's House, College. * Sadleir, Rev. William Digby, A.M. Fellow of Trinity College. 4, College. * Singer, Rev. Joseph Henderson, D. D., Senior Fellow of Trinity College——Vicz-Presipent. 4, College. * Smith, Rev. George Sidney, D. 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James Henthorn, D.D., Fellow of Trinity Col- lege.—Vice-Presipent. 35, College. * Traill, Rev. Robert, D.D. Westskull Rectory, Shib- bereen. * Trimlestown, John Thomas Lord. Trimlestown Castle. * Turner, William, Esq. Tighe, Robert, Esq. 14, Fitzwilliam-square, North. Toleken, John, Esq., M.D., Fellow of Trinity College. College. * Vandeleur, Crofton Moore, Esq. Kilrush, county of Clare. Vignoles, Rev. Charles, D.D. Dublin Castle. Vignoles, Charles, Esq., F.R.A.S. Trafalgar-square, London. * Wall, Rev. Charles William, D.D. Senior Fellow of Trinity College. 20, College. * Wall, Rev. Richard, D.D. 6, Hume-street. * Walshe, Francis Weldon, Esq. Upper Glentworth-street, Limerick. * Weaver, Thomas, Esq., F. R.S. F.G.S. London. * Webb, William, Esq. Mount-street, Lower. * Weld, Isaac, Esq., F.G.S. See. Royal Dublin Society, Ravenswell, Bray. * Westenra, Hon. H. R. * Williams, Thomas, Esq. Drumcondra Castle, and 38, Dame-street. ’ XVi * Williams, Richard Palmer, Esq. 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F.R.S. &e. Manchester. Daubeny, Charles Giles Bridle, M.D. F.R.S. F.L.S. F.G.S. Professor of Chemistry and of Botany, Oxford. Ozford. Donop, Baron. Saxe Meiningin. Dumas, Jean Baptiste. Paris. Dupin, Charles, Baron. Paris. Edgeworth, Miss Maria, Edgeworthstown. Ellis, Sir Henry, K.H. F.R.S. Sec. S.A. Librarian of the British Museum. Forshall, Rev. Josiah, M. A. F.R.S. F.S.A. British Mu- ~ seum. Gauss, Karl Friedrich. Gottingen. Graberg, Count. Florence. Graham, Robert, M.D. F.R.S.E. Professor of Botany, Edinburgh. Edinburgh. Greville, R.K. LL.D. Halliwell, James Orchard, Esq., F.R.S. F.S.A. Selip, Or- Sordshire. Hamilton, Francis, M.D. F.R.A.S. Harcourt, Rev. William V. Vernon, M.A. F.R.S. F.G.S. York. Haughton, Sir Graves Chamney. K.H. M.A. F.R.S. &e. 14, Grafton-street, Bond-street, London. Herschel, Sir John Frederick William, Bart. D.C.L. F.R.S.L. & E. F.G.S. F.R.A.S., &e. Collingwood, near Hawk- hurst, Kent. Herschel, Miss Caroline. Hobhouse, Right Hon. Henry. Hooker, Sir William Jackson, K.H. LL.D. F.R.S. F.S. A. F.L.S. F.G.S. &e. Kew. Hope, Thomas Charles, M.D. F.R.S. V.P.R.S.E. &c. Edinburgh. Jameson, Robert, Esq. F.R.S.L. & E. F.L.S. F.G.S. &e. Regius Professor of Natural History, Edinburgh. Zdin- burgh. Museum. _ Lagasca, Doctor. Madrid. og Liebig, Justus. Giessen. a _M‘Laughlin, David, M.D. Paris. Macedo, Sinor, Jacquine Jose da Costa. Sec. Royal Acade- ___- my of Sciences of Lisbon. Lisbon. Madden, Sir Frederick, K.H. F.R.S. F.S.A. British Museum. _ Murchison, Roderick Impey, Esq. F.R.S. Pres. G.S. 16, Belgrave-square, London. Pi Northampton, Spencer Joshua Alvyne, Marquess of, Pres. R.S. F.G.S. &e. 145, Piccadilly, and Castle Ashby, ® Northampton. Norwich, Right Rev. Edward Stanley, Lord Bishop of, D.D. ~—«*«#BL.S. F.G.S. F.Z.S. 38, Brook-street, London, and + Norwich. _ Parry, Sir William Edward, Knt. D.C.L. Captain R.N. F.R.S. F.R. AS. &ce. 2, New-street, Spring Gardens, London. - Phillipart, Sir John. _ Prichard, James Cowles, M.D. F.R.S. &e. Bristol. ’ Quetelet, Adolphe Jacques, Director of the Observatory of Brussels. Brussels. _ Rafn, C. C. Sec. Royal Society of Northern Antiquaries of 4 Copenhagen. Copenhagen. a Rennie, George, Esq., V.P.R.S. 21, Whitehall Place, London. Rosellini, Professor. Florence. oh Schumacher, Heinrich Christian. Altona. i sedgwick, Rev. Adam, M.A. F.R.S. F.G.S. F.R.A.S. % -Woodwardian Lecturer, Cambridge. | Cambridge. Smyth, William Henry, Esq., Captain R.N. D.C.L. For. “Sec. R.A.S. F.R.S. F.S.A., &e. Chelsea, London. Konig, Charles, Esq. K.H. F.R.S. F.L.S. &e. British ‘ 4 xx Somerville, Mrs. Mary. — Chelsea. South, Sir James, Knt. F.R.S.L. & E. F.L.S. F.R.A.S. &e. Observatory, Camden Hill, Kensington. Sussex, His Royal Highness Augustus Frederick Duke of, K.G. F.R.S. F.S.A. &e. Kensington Palace, London. Sykes, Lieut-Colonel William Henry, F.R.S. F.L.S. F.G.S., &e. 47, Albion-street, Hyde-park, London. Taylor, Thomas, M.D. Cork. Thomson, Thomas, M.D. F.R.S.L. & E. F.L.S. F.G.S. Regius Professor of Chemistry, Glasgow. Glasgow. Turner, Dawson, Esq. F.R.S. F.S.A. F.L.S. &e. Yar- mouth. Walsh, Rev. Robert, LL.D. 53, Summer Hill. Wallace, Professor. Edinburgh. Wheatstone, Charles, Esq., F.R.S., Professor of Experimen- tal Philosophy, King’s College. London. Whewell, Rev. William, D.D. F.R.S. F.S. A. F.G.S. F. R. A. S., Master of Trinity College, Cambridge. Cambridge. of Copper and Tin. Order Relation to Cast of _ |Characteristi ies, in Worki _|Iron, in Presence acid aracteristic Properties, in Working, &c of a Sdivent,4. ©. lity. Sea Water. 5 Well known. Aleces e= us 4 a §'o 3 Several of these | fa 2 Similar &c., are malleable at|; £2. ‘és 1 high temperatures. || 2 Seg 5 0 Seas N 9 | Bath Metal. Sere E Dutch Brass. | ae SB ss 7 | Rolled Sheet Brass. aé = 2, 6 British Brass. | TS = 6 | German Brass. <3 5 6 be Brass, Watchmakers. is _ 5 | Very Brittle, A Hast $ 5 Very Brittle, | Too hard to file or 3 uss z, 5 Very Brittle, | turn, lustre nearly Sec a 5 | Brittle, equal to Speculum || $ $5 n 5 | Brittle, Metal. 2s Be Pe 5 | Very Brittle, CONE 58 5 | Barely malleable. Sega 8 4 | Brittle. Ze ie a 3 | White Button Metal. £53 q | Brittle. =o5 1 Brittle, well known. js ee 16 Well known. 15 Gun Metal, &c. 14 Gun Metal, &c. 13 Gun Metal and Bronze. 12 Hard Mill Brasses, &c. 11 | Brittle, All these alloys i 10 | Brittle, found occasionally Crumbles, in bells, with mix- Crumbles, tures, of Zn. and Brittle, Pb. Small bells, Brittle. 8 Brittle. TABLE II.—Copper and Tin. mum increase is due to tin. Speculum Metal of authors. - Files, tough. ” Files, soft and tough. Well known. Every alloy of Cu. + Sn. increases the corrosive action of sea water on cast iron, in their presence; the maxi- a mr tor OD TOO Abbr E. Earthy. Pe Fibrous, C. Conchoidal, V.C. Vitreo-Conchoidal, V. Vitreous, e before disrupVen are those which each prism just sustained for a few seconds by oxidatiop™ Wall. They were alloyed in a peculiar apparatus, to avoid loss Zn, asis d fusible metal, generally Cu. 4- Zn. + Pb.; or Cu. -4{- Sn. + {Procerepines R. I. A., vol. ii. p, 95. TABLES Nos. I. anp Tle Showing the Chemical and Physical Properties of the Atomic Alloys of Copper and Zine, and of Copper and Tin. 7 8 9 10 11 12 5 Ci ition by Weight] A | 4 3 E | =o : Set igs omposition e), omic Be oc | | oe Chemical Constitution. P per eee ene Woght, eee Bid r Ore cs . | Order | Order | Relation to Cast Ze Gave: Colour. ae 2 g 5 Dake aes eran, wee Characteristic Properties, in Working, &¢,|!ron, in Presence rs] aS EF = Si H=1 u : sac et . << Gia @O°. GS. Gear €G0 € ats da Pas as rate ac a «€ cweaee ! « (ra ek a a < ; & ra (Amen @ < « €4E* ¢ SS c a <<