554 i 3 [t Sn ^,r„x,r„ LIBRARY fl » SCIENTIFIC & a §> §3 i 3 §3 & i 3 & g UNITED STATES PATENT OFFICE i 3 & i 3 « « fr- ig « « - c: Hi u ADVERTISEMENT. The Committee appointed by tlie Royal Society to direct the publication of the Philosophical Transactions, take this opportunity to acquaint the Public, that it fully appears, as well from the council-books and journals of the Society, as from repeated de- clarations which have been made in several former Transactions , that the printing of them was always, from time to time, the single act of the respective Secretaries, till the Forty-seventh Volume : the Society, as a Body, never interesting themselves any further in their publication, than by occasionally recom- mending the revival of them to some of their Secretaries, when, from the particular circumstances of their affairs, the Transactions had happened for any length of time to be intermitted. And this seems principally to have been done with a view to satisfy the Public, that their usual meetings were then continued, for the improvement of knowledge, and benefit of mankind, the great ends of their first institution by the Royal Charters, and which they have ever since steadily pursued. But the Society being of late years greatly enlarged, and their communications more numerous, it was thought advisable that a Committee of their members should be appointed, to reconsider the papers read before them, and select out of them such as they should judge most proper for publication in the future Transac- tions; which was accordingly done upon the 26th of March, 1 752. And the grounds of their choice are, and will continue to C iv 3 be, the importance and singularity of the subjects, or the advan- tageous manner of treating them ; without pretending to answer for the certainty of the facts, or propriety of the reasonings, contained in the several papers so published, which must still rest on the credit or judgment of their respective authors. It is likewise necessary on this occasion to remark, that it is an established rule of the Society, to which they will always adhere, never to give their opinion, as a Body, upon any sub- ject, either of Nature or Art, that comes before them. And therefore the thanks, which are frequently proposed from the Chair to be given to the authors of such papers as are read at their accustomed meetings, or to the persons through whose hands they receive them, are to be considered in no other light than as a matter of civility, in return for the respect shewn to the Society by those communications. The like also is to be said with regard to the several projects, inventions, and curiosi- ties, of various kinds, which are often exhibited to the Society; the authors whereof, or those who exhibit them, frequently take the liberty to report, and even to certify in the public news-papers, that they have met with the highest applause and approbation. And therefore it is hoped, that no regard will hereafter be paid to such reports, and public notices ; which in some instances have been too lightly credited, to the disho- nour of the Society. CONTENTS. I. On the fire-damp of coal mines , and on methods of lighting the mines so as to prevent its explosion. By Sir H. Davy, LL. D. F. R. S. V. P. R. I. p. i II. An account of an invention for giving light in explosive mix- tures of fire-damp in coal mines, by consuming the fire-damp. , By Sir Humphry Davy, LL. D. F. R. S. V.P.R. I. p. 23 III. On the developement of exponential functions ; together with several new theorems relating to finite differences. By John Frederick W. Herschel, Esq. F. R. S. p- 25 IV. On new properties of heat, as exhibited in its propagation along plates of glass. By David Brewster, LL. D. F. R. S. Loud, and Edin. In a Letter addressed to the Right Hon. Sir Joseph Banks, Bart. G. C. B. P.R. S, p.- 4^ V. Farther experiments on the combustion of explosive mixtures confined by wire-gauze, with some observations on flame. By Sir H. Davy, LL. D. F. R. S. V. P. R. I. p. 1 15 VI. Some observations and experiments made on the Torpedo of the Cape of Good Hope in the year 1812. By John T. Todd, late surgeon of His Majesty's ship Lion. Communicated by Sir Everard Home, Bart. V.P.R.S. p. 120- VII. Direct and expeditious methods of calculating the excentric from the mean anojnaly of a planet. By the Reverend Abram Robertson, D. D . F. R. S. Savilian Professor of Astronomy in the University of Oxford, and Radcliffian Observer. Commu- nicated by the Right Hon. Sir Joseph Banks, Bart. G. C. B. P.R. S. p. 127 C Vi ] VIII. Demonstrations of the late Dr. Maskelyne’s formulcefor finding the longitude and latitude of a celestial object from its right ascension and declination ; and j or finding its right ascen- sion and declination from its longitude and latitude , the obli- quity of the ecliptic being given in both cases. By the Rev , Abram Robertson, D.D. F.R.S. Savilian Professor of Astronomy in the University of Oxford , and Radclijfian Ob- server. Communicated by the Right Honourable Sir Joseph Banks, Bart. G.C.B. P.R.S. p. 138 IX. Some account of the feet of those animals whose progressive motion can be earned on in opposition to gravity. By Sir Everard Home, Bart . V. P. R. S. p. 149 X. On the communication of the structure of doubly refracting crystals to glass , muriate of soda , fluor spar , and other sub- stances, by mechanical compression and dilatation. By David Brewster, LL.D. F.R.S. Bond, and Fdin. In a letter addressed to the Right Hon. Sir Joseph Banks, Bart. G.C.B. P-R^S . p, 15(5 APPENDIX. Meteorological Journal kept at the Apartments of the Royal Society, by Order of the President and Council . The President and Council of the Royal Society ad- judged the Medal on Sir Godfrey Copley’s Donation, for the year 1815 , to David Brewster, LL.D,, for his Paper on the Polarisation of Light by Reflection, printed in the Philosophical Transactions ; And the Gold and Silver Medals on Count Rum- ford’s Donation, to William Charles Wells, M. D. for his Essay on Dew, published in the course of the preceding year. \ \ /v ' \ \; \ % PHILOSOPHICAL TRANSACTIONS. I. On the fire-’ damp of coal mines, and on methods of lighting the mines so as to prevent its explosion. By Sir H. Davy, LL. D. F. R. S. V. P. R. I. Read November 9, 1815. The accidents arising from the explosion of the fire-damp or inflammable gas of coal mines, mixed with atmospherical air, are annually becoming more frequent and more destruc- tive in the collieries in the North of England. A committee has been for some time formed at Sunderland for the benevolent purpose of investigating the causes of these accidents, and of searching for means of preventing them. In consequence of an invitation from the Rev. Dr. Gray, one of the most active members of this committee, I was induced to turn my attention to the subject. I went to the North of England, and visited some of the principal col- lieries in the neighbourhood of Newcastle, for the purpose of ascertaining the condition of the workings, and the state of their ventilation. I found the greatest desire to assist my enquiries in the gentlemen acquainted with the northern col- lieries, as well as in the inspectors or viewers of the mines ; mdcccxvi, B 2 Sir Humphry Davy on the fire-damp of coal mines , and on and I have particular obligations on this point to the Rev. Dr. Gray, Cuthbert Ellison, Esq. M. P., the Rev. John Hodgson, Mr. Buddle, and Mr. Dunn. Dr. Fenwick, Dr. Clanny, and Mr. Fenwick, likewise kindly offered me their assistance. From the information which I collected on the spot, in- creased by the perusal of a report of Mr. Buddle on the state of the mines, I was convinced that, as far as ventilation was concerned, the resources of modern science had been fully employed ; and that a mode of preventing accidents was only to be sought for, in a method of lighting the mines free from danger, and which, by indicating the state of the air in the part of the mine where inflammable air was disen- gaged, so as to render the atmosphere explosive, should oblige the miners to retire till the workings were properly cleared. An account of an ingenious apparatus for burning a candle supplied with atmospherical air by a bellows through water, has been published in the Philosophical Transactions, by Dr. Clanny ; but I believe this apparatus has not yet been used in any of the collieries. The common means employed for lighting those parts of the mine where danger is apprehended from the fire-damp, is by a steel wheel, which, being made to revolve in contact with flint, affords a succession of sparks : but this apparatus always requires a person to work it; and, though much less liable to explode the fire-damp than a common candle, yet it is said to be not entirely free from danger. Mr. Buddle having obligingly shown to me the degree of light required for working the collieries, I made several ex- methods of lighting the mines without producing its explosion. 3 periments, with the hope of producing such a degree of light, without active inflammation; I tried Kunckel’s, Canton’s, and Baldwin’s phosphorus, and likewise the electrical light in close vessels, but without success ; and even had these degrees of light been sufficient, the processes for obtaining them, I found, would be too complicated and difficult for the miners. The fire-damp has been shown by Dr. Henry, in a very ingenious paper published in the nineteenth volume of Nicholson’s Journal, to be light carburetted hydrogene gas, and Dr. Thomson has made some experiments upon it; but the degree of its combustibility, as compared with that of other inflammable gases, has not, I believe, been examined, nor have many different specimens of it been analysed; and it appeared to me, that some minute chemical experiments on its properties ought to be the preliminary steps to enquiries respecting methods of preventing its explosion. I therefore procured various specimens of the fire-damp in its purest state, and made a number of experiments upon it. And in examining its relations to combustion I was so fortunate as to discover some properties belonging to it, which appear to lead to very simple methods of lighting the mines, with- out danger to the miners, and which, I hope, will supply the desideratum so long anxiously required by humanity. I shall in the following pages have the honour of describing these properties, and the methods founded upon them, to the Royal Society, and I shall conclude with some general observations. The fire-damp is produced in small quantities in coal mines, during the common process of working. 4 Sir Humphry Davy on the fire-damp of coal mines , and on The Rev. Mr. Hodgson informed me, that on pounding some common Newcastle coal fresh from the mine in a cask furnished with a small aperture, the gas from the aperture was inflammable. And on breaking some large lumps of coal under water, I ascertained that they gave off inflammable gas.* Gas is likewise disengaged from bituminous shist, when it is worked. The great sources of the fire-damp in mines are, however, what are called blowers, or fissures in the broken strata, near dykes, from which currents of fire-damp issue in con- siderable quantity, and sometimes for a long course of years.-f When old workings are broken into, likewise, they are often found filled with fire-damp ; and the deeper the mine the more common in general is this substance. * This is probably owing to the coal strata having been formed under a pressure greater than that of the atmosphere, so that they give off elastic fluid when they are exposed' to the free atmosphere : and probably coals containing animal remains, evolve not only the fire-damp, but likewise azote and carbonic acid, as in the instance of the gas sent by Dr. Clan n y. In the Apennines, near Pietra Mala, I examined a fire produced by gaseous matter, constantly disengaged from a shist stratum : and from the results of the combustion, I have no doubt but that it was pure fire-damp. Mr. M. Faraday, who accompanied me, and assisted me in my chemical experiments, in my journey, collected some gas from a cavity in the earth about a mile from Pietra Mala, then filled with water, and which, from the quantity of gas disengaged, is called Aqua Buja. I analysed it in the Grand Duke’s laboratory at Florence, and found that it was pure light hydro-car- bonate, requiring two volumes of oxygene for its combustion, and producing a volume of carbonic acid gas. It is very probable, that these gases are disengaged from coal strata beneath the surface, or from bituminous shist above coal ; and at some future period new sources of riches may be opened to Tuscany from this invaluable mineral treasure, the use of which in this country has supplied such extraordinary resources to industry. f Sir James Lowther found a uniform current produced in one of his mines for. two years and nine months. Phil. Trans. Vol. XXXVIII. p. 112. methods of lighting the mines without producing its explosion . 5 I have analysed several specimens of the fire-damp in the laboratory of the Royal Institution ; the pure inflammable part was the same in all of them, but it was sometimes mixed with small quantities of atmospherical air, and in some instances with azote and carbonic acid. Of 6 specimens collected by Mr. Dunn from a blower in the Hepburn Colliery, by emptying bottles of water close to it, the purest contained only of atmospherical air, with no other contamination, and the most impure contained of atmospherical air ; so that this air was probably derived from the circumambient air of the mine. The weight of the purest specimen was for 100 cubical inches 19.5 grains. One measure of it required for its complete combustion by the electric spark nearly 2 measures of oxygene, and they formed nearly 1 measure of carbonic acid. Sulphur heated strongly, and repeatedly sublimed in a por- tion of it freed from oxygene by phosphorus, produced a con- siderable enlargement of its volume, sulphuretted hydrogene was formed, and charcoal precipitated; and it was found that the volume of the sulphuretted hydrogene produced, when it was absorbed by solution of potassa, was exactly double that of the fire-damp decomposed. It did not act upon chlorine in the cold ; but, when an elec- tric spark was passed through a mixture of 1 part of it with 2 of chlorine, there was an explosion, with a diminution to less than and much charcoal was deposited. The analysis of specimens of gas sent to my friend John George Children, Esq. by Dr. Clanny, afforded me similar results; but they contained variable quantities of carbonic acid gas and azote. 6 Sir Humphry Davy on the fire-damp of coal mines , and on Different specimens of these gases were tried by the test of exposure to chlorine both in darkness and light: they exhibited no marks of the presence of olefiant gas or hydro- gene; and the residuum produced by detonation with chlorine showed them to be free from carbonic oxide. It is evident, then, that the opinion formed by other chemists respecting the fire damp is perfectly correct ; and that it is the same substance as the inflammable gas of marshes, the exact chemical nature of which was first demonstrated by Mr. Dalton; and that it consists, according to my view of definite proportions, of 4 proportions of hydrogene in weight 4, and 1 proportion of charcoal in weight 11.5. I made several experiments on the combustibility and ex- plosive nature of the fire-damp. When 1 part of fire-damp was mixed with 1 of air, they burnt by the approach of a lighted taper, but did not explode ; 2 of air and 3 of air to 1 of gas produced similar results. When 4 of air and 1 of gas were exposed to a lighted candle, the mixture being in the quantity of 6 or 7 cubical inches in a narrow necked bottle, a flame descended through the mixture, but there was no noise : 1 part of gas inflamed with 6 parts of air in a similar bottle, produced a slight whistling sound : 1 part of gas with 8 parts of air, rather a louder sound : 1 part with 10, 11, 12, 13 and 14 parts, still inflamed, but the violence of combustion diminished. In 1 part of gas and 15 parts of air, the candle burnt without explosion with a greatly enlarged flame ; and the effect of enlarging the flame, but in a gradually dimi- nishing ratio, was produced as far as 30 parts of air to 1 of gas. The mixture which seemed to possess the greatest explo- ) methods of lighting the mines without producing its explosion . 7 sive power, was that of 7 or 8 parts of air to 1 of gas; but the report produced by 50 cubical inches of this mixture was less than that produced by T L of the quantity of a mixture of 2 parts of atmospherical air and 1 of hydrogene. It was very important to ascertain the degree of heat required to explode the fire-damp mixed w ; ith its proper proportion of air. I found that a common electrical spark would not explode 5 parts of air and 1 of fire-damp, though it exploded 6 parts of air and 1 of damp : but very strong sparks from the discharge of a Leyden jar, seemed to have the same power of exploding different mixtures of the gas as the flame of the taper. Well burned charcoal, ignited to the strongest red heat, did not explode any mixture of air and of the fire-damp ; and a fire made of well burned charcoal, i. e. charcoal that burned without flame, was blown up to whiteness by an explo- sive mixture containing the fire-damp, without producing its inflammation. An iron rod at the highest degree of red heat, and at the common degree of white heat, did not inflame ex- plosive mixtures of the fire-damp ; but, when in brilliant com- bustion, it produced the effect. The flame of gaseous oxide of carbon as well as of olefiant gas exploded the mixtures of the fire-damp. In respect of combustibility, then, the fire-damp differs most materially from the other common inflammable gases. Olefiant gas, which I have found explodes mixed in the same proportion with air, is fired by both charcoal and iron heated to dull redness. Gaseous oxide of carbon, which explodes when mixed with 2 parts of air, is likewise inflammable by red hot iron and charcoal. And hydrogene, which explodes when mixed with j- of its volume of air, takes fire at the lowest \ 8 Sir Humphry Davy on the fire-damp of coal mines, and on visible heat of iron and charcoal ; and the case is the same with sulphuretted hydrogene. I endeavoured to ascertain the degree of expansion of mixtures of fire-damp and air during their explosion, and likewise their power of communicating flame through apertures to other explosive mixtures. I found that when 6 of air and 1 of fire-damp were exploded over water by a strong electrical spark, the explo- sion was not very strong, and, at the moment of the greatest expansion, the volume of the gas did not appear to be in- creased more than In exploding a mixture of 1 part of gas from the distilla- tion of coal, and 8 parts of air in a tube of a quarter of an inch in diameter and a foot long, more than a second was required before the flame reached from one end of the tube to the other; and I could not make any mixture explode in a glass tube -j of an inch in diameter : and this gas was more inflammable than the fire-damp, as it consisted of carburetted hydrogene gas mixed with some olefiant gas. In exploding mixtures of fire-damp and air in a jar con- nected with the atmosphere by an aperture of half an inch, and connected with a bladder by a stopcock, having an aper- ture of about i of an inch,* I found that the flame passed into the atmosphere, but did not communicate through the stop- cock, so as to inflame the mixture in the bladder : and in com- paring the power of tubes of metal and those of glass, it appeared that the flame passed more readily through glass tubes of the same diameter; and that explosions were stopped * Since these experiments were made. Dr. Wollaston has informed me, that he and Mr. Tennant had observed some time ago, that mixtures of the gas from th§ distillation of coal and air, would not explode in very small tubes. methods of lighting the mines without producing its explosion, g by metallic tubes of j of an inch,* when they were l^inch long; and this phenomenon probably depends upon the heat lost during the explosion in contact with so great a cooling surface, which brings the temperature of the first portions exploded below that required for the firing of the other por- tions. Metal is a better conductor of heat than glass : and it has been already shown that the fire-damp requires a very strong heat for its inflammation. Mixture of the gas with air I found, likewise, would not explode in metallic canals or troughs, when their diameter was less than the \ 0 f an inch, and their depth considerable in proportion to their diameter ; nor could explosions be made to pass through such canals. Explosions likewise I found would not pass through very fine wire sieves or wire gauze. I mixed azote and carbonic acid in different quantities with explosive mixtures of fire-damp, and I found that even in very small proportions they diminished the velocity of the inflam- mation. Azote, when mixed in the proportion of 1 to 6 of an explosive mixture, containing 12 of air and 1 of fire-damp, deprived it of its power of explosion ; when 1 part of azote was mixed with 7 of an explosive mixture, only a feeble blue flame slowly passed through the mixture. 1 part of carbonic acid to 7 of an explosive mixture de- prived it of the power of exploding; so that its effects are more remarkable than those of azote ; probably, in conse- quence of its greater capacity for heat, and probably, likewise, * I do not give this result as perfectly exact, as the bore of the metallic tube had not the same polish as that of the tube of glass. c MDCCCXVI. io Sir Humphry Davy on the fire-damp of coal mines , and on of a higher conducting power connected with its greater density. The consideration of these various facts, led me to adopt a form of a lamp, in which the flame, by being supplied with only a limited quantity of air, should produce such a quantity of azote and carbonic acid, as to prevent the explosion of the fire-damp, and which, by the nature of its apertures for giving admittance and exit to the air, should be rendered incapable of communicating any explosion to the external air. If in a close lantern, supplied with a small aperture below and another above, a lighted lamp having a very small wick be placed, the natural flame gradually diminishes, till it arrives at a point at which the supply of air is sufficient for the combustion of a certain small quantity of oil ; if a lighted taper be introduced into the lantern through a small door in the side, which is instantly closed, both lights will burn for a few seconds, and be extinguished together. A similar phenomenon occurs, if, in a close lantern, supplied with a quantity of air merely sufficient to support a certain flame, a mixture of fire-damp and air is gradually admitted, the first effect of the fire-damp is to produce a larger flame round that of the lamp, and this flame, consuming the oxy- gene which ought to be supplied to the flame of the lamp, and the standard of the power of the air to support flame being lowered by the admixture of fire-damp and by its rarefaction, both the flame of the fire-damp and that of the taper are extin- guished together; and as the air contained a certain quantity of azote and carbonic acid before the admission of the fire- damp, their effect, by mixing with it, is such as to prevent an explosion in any part of the lantern. methods of lighting the mines without producing its explosion. 1 1 I tried several experiments on the burning of a flame in atmospheres containing fire-damp. I inclosed a taper in a little close lantern, having a small aperture below and a larger one above, of such size that the taper burnt with a flame a little below its natural size. I placed this lantern, the taper being lighted, on a stand under a large glass receiver standing in water, having a curved tube containing a little water, adapted to its top to confine the air, and which was of such a capacity as to enable the candle to burn for some minutes; I then rapidly threw a quantity of fire-damp into the receiver from a bladder, so as to make the atmosphere in it explosive. As the fire-damp mixed with the air, the flame of the taper gradually enlarged, till it half filled the lantern ; it then rapidly diminished, and was suddenly extinguished without the slightest explosion. I examined the air of the receiver after the experiment, and found it highly explo- sive. • * I tried similar experiments, throwing in mixtures of air and fire-damp, some containing the maximum, and others the minimum of fire-damp necessary for explosion, and always with the same satisfactory results. The flame considerably increased, and was soon extinguished. I introduced a lighted lantern to w T hich air was supplied by two glass tubes of To °f an inch in diameter and half an inch long, into a large jar containing an explosive mixture of 1 part of fire-damp and 10 parts of air; the taper burnt at first with a feeble light, the flame soon became enlarged, and was then extinguished. I repeated these experiments several times, and with a perfect constancy of result It is evident, then, that to prevent explosions in coal mines, C 2 12 Sir Humphry Davy on the fire-damp of coal mines, and on it is only necessary to use air-tight lanterns, supplied with air from tubes or canals of small diameter, or from apertures covered with wire gauze placed below the flame, through which explosions cannot be communicated, and having a chimney at the upper part, on a similar system for carrying off the foul air ; and common lanterns may be easily adapted to the purpose, by being made air-tight in the door and sides, by being furnished with the chimney, and the system of safety apertures below and above. The principle being known, it is easy to adopt, and multi- ply practical applications of it. The first safe lantern that I had constructed, was made of tin-plate, and the light emitted through four glass plates in the sides. The air was admitted round the bottom of the flame from a number of metallic tubes of of an inch in diameter, and an inch and £ long. The chimney was composed of two open cones, having a common base perforated with many small apertures, and fastened to the top of the lantern, which was made tight in a pneumatic rim containing a little oil; the upper and lower apertures in the chimney were about ~ of an inch : the lamp, which was fed with oil, gave a steady flame of about an inch high and half an inch in diameter. When the lantern was slowly moved, the lamp continued to burn, but more feebly, and when it was rapidly moved, it went out. To obviate this circumstance, I surrounded the bottom of the lantern with a perforated rim; and this ar- rangement perfectly answered the end proposed. I had another chimney fitted to this lantern, furnished with a number of safety tin-plate tubes of the sixth of an inch in diameter and two inches long : but they diminished consi- methods of lighting the mines without producing its explosion . 1 3 derably the size of the flame, and rendered it more liable to go out by motion ; and the following experiments appear to show, that if the diameter of the upper orifice of the chimney be not very large, it is scarcely possible that any explosion produced by the flame can reach it. I threw into the safe lantern with the common chimney, a mixture of 15 parts of air and 1 of fire-damp : the flame was immediately greatly enlarged, and the flame of the wick seemed to be lost in the larger flame of the fire-damp. I placed a lighted taper above the orifice of the chimney-: it was immediately extinguished, but without the slightest pre- vious increase of its flame, and even the wick instantly lost its fire by being plunged into the chimney. I introduced a lighted taper into a close vessel containing 15 parts of air and 1 of gas from the distillation of coal, suf- fered it to burn out in the vessel, and then analyzed the gas. After the carbonic acid was separated, it appeared by the test of nitrous gas to contain nearly j of of its original quantity of oxygene ; but detonation with a mixture of equal parts of hydrogene and oxygene proved that it contained no sensible quantity of carburetted hydrogene gas. It is evident, then, that when in the safe lantern j the air gradually becomes contaminated with fire-damp, this fire- damp will be consumed in the body of the lantern ; and that the air passing through the chimney, cannot contain any in- flammable mixture. I made a direct experiment on this point. I gradually threw an explosive mixture of fire-damp and air into the safe lantern from a bladder furnished with a tube which opened by a large aperture above the flame ; the flame became enlarged, and 1 4 Sir Humphry Davy on the jire-damp of coal mines , and on by a rapid jet of gas I produced an explosion in the body of the lantern ; there was not even a current of air through the safety tubes at the moment, and the flame did not appear to reach above the lower aperture of the chimney ; and the ex- plosion merely threw out from it a gust of foul air. The second safety lantern that I have had made is upon the same principle as the first, except that instead of tubes, safety canals are used, which consist of close concentric hollow me- tallic cylinders of different diameters, and placed together so as to form circular canals of the diameter of from - 1 - to — of Ha 4-0 an inch, and an inch and long, by which air is admitted in much larger quantities than by the small tubes. In this ar- rangement there is so free a circulation of air, that the chim- ney likewise may be furnished with safety canals. I have had lamps made for this kind of lantern which stand on the outside, and which may be supplied with oil and cotton without any necessity of opening the lantern; and in this case the chimney is soldered to the top, and the lamp is screwed into the bottom, and the wick rises above the air canals. I have likewise had glass lamps with a single wick, and argand lamps made on the same principle, the chimney being of glass covered with a metallic top containing the safety canals, and the air entering close to the flame through the circular canals. The third kind of safe lamp or lantern, and which is by far the most simple, is a close lamp or lantern into which the air is admitted, and from which it passes, through apertures covered with brass wire gau%e of ~o an i nc h thickness, the apertures of which should not be more than of an methods of lighting the mines without producing its explosion. 1 5 1 1 inch; this stops explosions as well as long tubes or canals, and yet admits of a free draught of air. Having succeeded in the construction of safe lanterns and lamps, equally portable with common lanterns and lamps, which afforded sufficient light, and which bore motion per- fectly well, I submitted them individually to practical tests, by throwing into them explosive atmospheres of fire-damp and air. By the natural action of the flame drawing air through the air canals, from the explosive atmosphere, the light was uniformly extinguished; and when an explosive mixture was forcibly pressed into the body of the lamp, the explosion was always stopped by the safety apertures, which may be said figuratively to act as a sort of chemical fire sieves in separating flame from air. But I was not contented with these trials, and I submitted the safe canals, tubes, and wire gauze fire sieves, to much more severe tests : I made them the medium of communication between a large glass vessel filled with the strongest explosive mixture of carburetted hydro- gene and air, and a bladder ~ or ■§■ full of the same mixture, both insulated from the atmosphere. By means of wires passing near the stop-cock of the glass vessel, I fired the explosive mixture in it by the discharge of a Leyden jar. The bladder always expanded at the moment the explosion was made ; a contraction as rapidly took place; and a lambent flame played round the mouths of the safety apertures, open in the glass vessel ; but the mixture in the bladder did not explode : and by pressing some of it into the glass vessel, so as to make it replace the foul air, and subjecting it to the electric spark, repeated explosions were produced, proving the perfect security of the safety apertures ; even when acted 1 6 Sir Humphry Davy on the fire-damp of coal mines , and on on by a much more powerful explosion than could possibly occur from the introduction of air from the mines. These experiments held good whatever was the propor- tions of the explosive mixture and whatever was the size of the glass vessel, (no one was ever used containing more than a quart) provided as many as 12 metallic tubes were used of y of an inch in diameter, and 2|- inches long ; or provided the circular metallic canals, were ~ of an inch in diameter, i.i of an inch deep, and at least 2 inches in circumference ; or pro- vided the wire gauze had apertures of only-j-^-yof an inch. When 12 metallic tubes were employed as the medium of commu- nication, ~ of an inch in diameter and an inch long, the ex- plosion was communicated by them into the bladder. Four glass tubes of the of an inch in diameter and 2 inches long, did not communicate the explosion ; but one of this diameter and length produced the effect. The explosion was stopped by a single tube of an inch in diameter, when it was 3 inches long, but not when it was 2 inches long. The explosion was stopped by the metallic gauze of when it was placed between the exploding vessel and the bladder, though it did not present a surface of more than half a square inch, and the explosive mixture in the bladder in passing through it to supply the vacuum produced in the glass vessel, burnt on the surface exposed to the glass vessel for some seconds, producing a murmuring noise. A circular canal ~ of an inch in diameter, an inch and a * These results appear at first view contradictory to those mentioned page 9. But it must be kept in view that the first set of experiments were made in tubes open in the air, and the last in tubes exposed to the whole force of air explosion, and con- nected only with close vessels filled with explosive mixtures. methods of lighting the mines without producing its explosion. 17 half in circumference, and i t 7 y+I + K whose complete integral is x,y K =C./ C T . x,y y ^ y—i x — |— • • • • . ( 1 ) ,x 1 . 2 , 7 ^* C x Cy— 0 1 C y being an arbitrary function of y, to determine which we have only to consider that x is always, necessarily, unity ; and consequently (_!)'+' C,.. VL — ,= I X I 1 V ' 1.2 ... . {x— i) Now, we know that (*— l)* X X — X .. ■f- &c. 1.2 .... x developement of exponential functions, &c. Q 9 that is, — . . x x - l - 1 m 2 • • • X I« 2 • ^ M I whence it is plain that and of course that X (*- -0 J I) • I I 1 . 2 ... • •y f- ).»■;■■- (O referring the D to the functional characteristic/*, and the A to the o and its powers.— Or, we may throw it into the fol- lowing form, |m i ) A + D^ i) A * + ^ai> A q 0 * Upon this, we have to observe — first, that the addition of the term/ (l) at the beginning of the series within the brackets makes no difference in the result ; adding only to it the term /(i)xo , which vanishes of itself: and, in the next place, that we are at liberty to suppose the series continued to infinity ; as every term beyond y A * ° vanishes, owing go Mr . Herschel on the to the well-known property of the functions A x + l o x > A x+z o x , &c., each of which is equal to zero. Our series then becomes {/(i) +2X1 i2a+&c. } o * = f ( i+a)o* and we have therefore /(/)=/( 1 )+ 4 */ ( 1 + A ) 0 + rr / ( 1 + A ) 0 " 4 - &c * • — ( 2 ) In applying this series to any particular case we have only to develope/^i-j-A) in powers of A: then striking out the first term, as well as all those where the exponent of A is higher than that of t, to apply each of the remaining ones imme- diately before the annexed power of o, and the developement is then in a form adapted to numerical computation. This formula may be also farther compressed into /(/) ” /( X + A) /' ; .(3) by simply writing it as follows : /(/)=/(!+ a){i+t+tt+ & <4 I shall notice one more form in which the same Result may be exhibited. If we continue the series ( 1 ), as before, to infinity, and add the term 1 at its commencement, it becomes { a+ AS + A£!+ &c,} «*/(>)■ f A V./( 1) whence, we obtain y(/)==/(i) +7 ./ ,D o./(i) + — • ^ AD ° 2 */( 1 ) + & c - or, attending carefully to the application of the symbols /(«)=f iD { 1 +r + £ rr+ &c - 1 =/ • D+ “-y(i) ; (4) We will now proceed to apply these results to the actual 1 / developement of exponential functions , &c. 3 1 developement of equation ( a ). And, first, in the case where n is a positive integer, we have /(/)=(/-!)”; /(*.) = consequently, f ( l+A)=( 1 -j-A — l) = A wherefore the equation (2) becomes f t t .71 . t* t 3 A n X I o (f - 1 ) =y- a °+— - a 0 + 7 x^ a ° 3 + &c -; (5)- of which the first n — 1 vanish of themselves. Let us next consider the formula (/ — 1 — n being a negative integer. As this function, when developed, must evidently contain the negative powers of t, as far as t— n , we first throw it into the form , ° r its equal t~ n ** j” supposing then/(/) = { I we sha11 bave b y a PPty in g the equation (2) {i^]”=»+fd i H ±A T 0+ ri- 1M— }”»‘ + &c.; ( 6 ). All that now remains to be done is, to develope the func- tion in powers of A. When n = 1, the deve- lopement is well known to be J. £ 4. £.* _ & c 1 I 2*3 3 ' Hence, if we suppose t £ ‘ — I we shall have * B log. (I+A) 0* X A JA'i. I * 3 + ± Z+iS’ ( 7 )- 3 s Mr. Herschel on the and in general, if = + .2.'+ &c. we shall have B | lQ g- ( )\ n A }V; (8). The coefficient of A* in the function j A) j n f deve- loped in powers of A, is evidently d x + n. ( log. t) n 1.2 ( x + n ). dt x + n t being made = l after the differentiations Now we easily find, that the expression ^i 0 g ,t) n 77*- h* ’ After executing the operations indicated must take the form A -j - 1 A .log. £-f n *A . (log. t) XX X t x + n n— i and the equations which determine A , &c. are X ‘ A *+i — — (*+») - n ~'K n— i n — 2 A,, , = -(*+«) ,"-*A x +{n~i ).»-> a X & x+1 = ~ (*+n). A^-f i, The integration of these equations is attended with no diffi- culty, and gives for the value of A^ (the only one wanted) as follow#: ( l )* i .2 (x -\-n — l). 2 — 1 2 — l — 2 2 1 x-t-n x+n X -\- n where there are (n—i ) signs of integration ; a constant being included under each. If now we suppose f + T+ It}’ i^ + r 3 + r 3 + = 8 ■ 1 s’— 1 A considerable simplification of the latter case takes place owing to this circumstance : the alternate values of 2 B^ being MDCCCXVI, F 34 Mr. Herschel on the susceptible of an expression by means of those of *B : In fact, the odd values of B^ vanishing (except B ), we have = + + B 2 + &c .)Y and, comparing the coefficients of t 2X+1 in the two members of this equation, we obtain “ “ ( 2X + 1 )- B 2 .r * Hence this remarkable theorem, ( 10 ) which may also be regarded as affording another general ex- pression for the numbers of Bernouilli. Laplace has shown that the developement of the function may be derived from that of and that, if the coeffi- cient of t" in the developement of the latter be represented by a , it will be — in that of the former. Now, by the application of our equation (2), we find that <»>. Making then n=i, we find for the value of a x — 1 _ j z -^- 2 A - 2^-3 a * + ....... ± A *- 1 | 0 &X—1 1 . 2 . ..... ( X 1 ). 2 X and consequently the coefficient of t* in will be | A -** -3 A a + ± A * -1 } o*~ l 1.2 . . . z*. (2*— x) Dr. Brinkley has arrived at the same result. (12) The computation of the functions n l S j —■ J > n j & c . is attended with very little difficulty ; for, if we multiply toge- ther successively the terms 1+ it, 2 + %, 3 4 " & c * an< ^ ca ^ developement of exponential functions , &c. 35 the co-efficient of z*—P in the product &S (i),we shall have wanted, the principal part of the work consists in calculating the first n terms of the successive products, which, (being derived from one another) except n is considerable, is attended with very little trouble. The remarkable form of our equation (2) enables us to ex- hibit a variety of properties of the functions comprehended under the expression A n o x , some of the principal of which I shall now proceed to notice. Suppose//') == a 0 + 0, . t -j- a 2 t* + &c. Then, as we have shown. from which we find /(l + A)o* = i.2 x.a x . (14) If then the developement of f (s') be given, we are enabled to assign the value off (1 + A )o* in functions of x, and the con- verse. It is scarcely necessary, however, to remark, that the extent of these equations is not limited to cases in which the actual developement off (1 -f- A) in powers of A is practicable , or in which the form of/ is known, or even dependent on analytical relations. > Let us suppose a function F(f), and any two others//) and f ! /), so related that and, as every value of n 1 S j ~ l , from x—n up to x= 00 is Let also F (0 =/(*)•/'(*) F /) = A o + Aj . t + A 2 1 * + &c. F 2 Mr. Herschel on the a similar notation being used, for f(t) and/'(/), changing only A into a and a '. It is evident then, that A X a . a' -* 1 “ ci . a! -I- ..... <2 . a! . O X * I X — 1 ■ X 0 In this equation, substituting for A^ &c., their values drawn from (13), we find F( 1 + ak=/(i 4 a y.f( 1 + A y+ 1 + Ay.f(i + a y-i 4 &C. This equation may be abbreviated, upon the principles we have all along adopted, by a very simple and convenient arti- fice of notation, viz. by applying an accent to one of the A and also to the corresponding 0 ; these accents not altering the meaning of the symbols, but solely pointing out those which are to be applied to one another. The second number of this equation then becomes /(l+A)o°./'(x+A')o'* +y/(x+A)o./' (l+A')o' x-I +&c. in which the symbols of operation may now, without confu- sion, be separated from those of quantity, when it will take the form / ( 1 + A ) »/ # ( 1 + A' ) [ o' x + “ • o '*— 1 4 & c - } And our equation becomes F (l+A>'=/(l+A) ./' (x+a')[H-o'}' ; (15) We must here notice, that the second member of this equation is precisely what the first would become, if, instead of F(i-}-a) we had written /( 1 4* A) .j* (1 4 A), its equivalent , and in- stead of 0 the symbolic expression 040 which is equal to it in quantity, and then applied the former A to the former 0, and the latter to the latter, by the method of accentuation 37 developement of exponential functions, &c. above explained. Pursuing this idea, let us suppose F(£) to be decomposable into any number of factors/ (£), f’(t) } f" (t), &c., and by executing the same mechanical process on the expression F ( l -f- A )o x , we resolve it into /( 1 + a)./'(i -j- A'). &c. |o + o'+o" + &c.p. A moment's attention to the method by which (15) was ori- ginally derived, will convince us that (attending to the proper application of the symbols) we are at liberty to develope the expression | 0 -4- o' 0" &c. j*, and thus we have the equation F(i + A)o*=/( 1 + A)/'(l+A') &c. j o+o'+&c. p (16) Should any one of the functions / ( 1 -f- A), &c., be of the form ( 1 -j- A any term multiplied by o l in the developement of j 0 -j- o' -f- &c. j* will acquire the coefficient ( 1 -f- A ) k o\ which, being, by (14), the coefficient of V in the dovelope^ ment of (1 + £ — 1 ) k , or multiplied into 1.2.3 is evi- dently equal to k. Now it is the same thing whether we write k ! for (i-|-A)*o* after the developement, or at once strike out (1 + A ) k , and for 0 write k previously to it. Hence we conclude that ( i+A)*.F{i+a )o^==/( 1 a )f\ 1 -J-A'j.&c. | &+o-f.o'-|-&c. | ; (17) where, as before, F(£.) =/(£) .f (t). &c. The expression /( 1 -|-a)o* is susceptible of a somewhat varied form, deducible from the identical equation 1 /(/)=/{(/)”} The coefficient of V in the second member of this is equal to that of t* in/ { (£)*} multiplied by that is, by (13), to Mr. Herschel on the SB i / jj (1 + and thus we obtain H x * 1.2 ..... x / {( 1 + A)“}o* = «*/(! + A )o'; (18) From this equation it is easy to derive the two following 0 = {/C 1 + A ) +/(i^)j° 2 *“ I; (i9j o= {/(i + a) — (so) Let/(/) be a rational, integral, finite function of and suppose it to contain the powers of t , t p , t r , &c. ; it is evi- dent then that we shall have, by (14) /( 1 + A)o* = o; (21) in every case except where x is equal to either of the num- bers p } q , r, &c. The following forms off satisfy this condition /(O = ( lo g- 0" /(0=*L(i) + *L|f} /(0=’ ! L(x + i) + (-i)': ”L| 1 + -L]. /(0 = ”C(i) -(-!)» »c{-i} or, lastly, the sums, powers, or products of any of these forms, any how combined.* The excepted values of x, are— for the first of these forms, x = n — for the second, x = 2, and for the third and fourth, x = n,orn — 2, n — 4, &c. Also from the general theorems delivered by Mr. Spence, we find for the value of/(i A )o»— ** (which comprehends all the excepted cases) in the third and fourth of the above forms re- spectively zx Jj ( 2 ) and z *+ I C(i). It may not be uninteresting to descend to a few more par- ticular applications of these general theorems. If we suppose • Logarithmic transcendents, pages 45, 69. dev elopement of exponential junctions, &c.. 39 f (£)=(log. t) n , n being a positive integer, we have and consequently, by equation (14), | log. ( 1 -J-A ) 0* = 0 . (22). in every case but where oc=m, when it becomes 1. 2 .... n. If n~i, this becomes °=~ r + ±— ( 2 3)- in every case but where w=i If we take f (£) = -*- , or/* ( /)=f— *, we find in the same way l=A*o* — A x ~ l o*+ ..... ,+Ao* (24). Again, let f{t) = then will/(/) = sec =J, and as the coefficient of 9 2x in sec. 9 is (as Euler has shown )* v 2x + i ' ^ 0 )> that of F* in sec. - ~ t — will be V—i f_ , 1*,** + * 2X+1 -^rr+i c (l ). / 7T * which, compared with the expression /( * + a) o 2A , gj ves I»2* • • • 2r X r — 2# “f * I o *** 1 ¥ 1 f c(i) S =H)-.kL i±L- 0 2x . (Qt) which seems the most compendious form in which this com- plicated function is capable of being exhibited in finite terms, as well as the most easy of computation in any insulated case. If /(0 => ~T=--^ZT > we have / ( f ')= tan -L~, and a 1 _2 Q 2X—1 1.2 ..... ( 2* 1 ) * I-f (X+A ) a Cale. differentialis. 2X +* C(i) is used to denote the series — -d— + — ! — — &c. 2JT+I j 5 4° Mr. Herschel on the But the coefficient of t 2 x 1 in tan. is (-i) x ( z %x — l). I. 2 ...... ( 2.z) ^ 2X— I where B here denotes the x th in order of the numbers of ZX — I Bernouilli. Equating these two values, we find B =- ( —I ) x . zx ZX-l it C®); We will now proceed to consider the developement of any function of the form u —f{t\ i i", &c.) t , t t" , See. being any number of independent variables. The coefficient of t x . t'K t" x . Sec. being denoted by A have j^+3'4- &c - M , we A Tj y> z > i. 2 ,rx i.. . .y X &c. x dA dl! y . Sec . Now, regarding w as a function of /, we have £i=/(i+A, &c.) o" Again, considering this as a function of we obtain _ f( l+A, 1+A', £ '", &c.) o*. cfl. dt*. dt 'y J v (the accents over the A, and o, indicating, as before, the application of the symbols) — and so on. Thus we find d x +y+z+Scc. u _ i-UA', Sec.) o". o'y. o"\ Sec. it*. di'y. dt"*. Sec. J K (®7-) di and of course, A /(* + A , 1 + Ah I + A", &c.) o*. p'r o Sec. x,y,z, Sec.~~~ i .... x X i .... y X I &c. Laplace has shown,* that, in any function u x x ^ &Cm of x, y, See. if x be made to vary by a,y by (3, See. simultaneously, the following equation, analogous to ( a ) will hold good : * Theorie Analytique des Probabilites, p. 70. developement of exponential functions , &c. 41 n A u r a. — 4- & c * 'x, y, z, 8cc. L ~ ^ 1 x, y, z, &c, * * * * * ^0 Hence the function to be developed is p. V'. ill Sec. } n n being a positive or negative integer In the former case, the coefficient of t*. t' y . Sec. is |(i + a). (i + a'). &c. — x o*. o'y. &C. 1.2. ...XX 1.2 . ... y X &C. that is, developing the numerator | ( 1 + A )". (i + A') n . &c. — ~( I + A ) n T 1 &C.+ &c. | 0 *. o'K 8 c C. 1.2 JT X I • 2 . . . X &C* Now, ( i-f-A) w o* = ra*, (i+a')* o ly —n y , Sec. and thus the numerator of this expression becomes, n x+y + 8c ^_n^n— 1 ) X+y+8£C ‘-J r &C. — , A w &c ’ and the coefficient of t*. V y . See. therefore becomes ,*+>+ &c. A (28). : — n) A" o'" i . 2 . . . .x x i . 2 . . . . ;y x &c. x, y. See. In the latter case, where the exponent is negative (: the function to be developed is {*■+'+ &c the coefficient of t x . t ,y . Sec. in the latter part of this expres- sion, is flog. { (I + A )• ( I + A' ). &C. "I ] n 1 i L i o* o fy Sec |(I + A)(X + A / ).&C.-I j 3. 2 ..... AT X I. 2. ...,^X See. Now, let us for an instant suppose the expression flog. |(I + A)(I + A'). &c. } n y • • • • . ^ ^ ^ . < p(i + A)(i + A')- &c. — i G MDCCCXVI. 42 Mr . Herschel on the •Vr ' developed in a series of powers of (i-{-a)( i+A'). &c. con» tinued both ways to infinity, (which is evidently possible) and letK(i+A) i . (i-j-A')h & c. be any term of the deve- lopement. The corresponding term in the above coefficient will be K( i-J-a)''0*. ("i+a)*. o y . &c. -that is, K. i*. i y . &c. or K. **+:v+ &c - g ut * s p] a j n the performance of the Sec. same operations on | Iog ‘ — | n o x + y ~ r ^ would have led to the same result : and we may therefore conclude that the numerator of ( is n B x-\-y + Sec. A ^ rtf ;W. x, y, See. 1 xxi y x &c. 5 • • • • • (*9-) and’ the same reasoning may be applied to any function of J ' J " See. whatever. £• £ • £' Analogous theorems to those we have deduced respecting functions of one variable may easily be deduced from the value of A „ given in (27). Thus, since x,y> Sec. f{e n ‘ n't' >.£ &C. J =/ { (/)”,(/ f, &C- } we ought to have “ F /{(i + A)",(l+A')' ,, ) &c. }o*.o' y . &c. ihisldo oyy j f 1 1 -f- A, i-}-A / , & c. | 0 x . 0 y . &c. ...... . (30) which, by assigning particular values to n, n', Sic. affords an infinite number of theorems analogous to ( 19) and 20). Similar theorems respecting the product of two or more functions of /, &c. may be derived. For instance, if x y n .n . Sic. developement of exponential functions , & c. 43 F(MO =F(MT*/,(M') we shall have F| [ X + A ), ( 1 + A') 1 0 *. of) — =/{(l+A),(l + A')}x/''{(l+A,),(l + A/)}(o+0,)“ r -( 0 '+ 0 /y> • • •• • • • ( 3 l). This, as well as other analogous theorems, flows with such facility from the principles above laid down, that it is unne- cessary, as it would lead me beyond the limits I proposed, to enter into any detail respecting them. Let us now consider the developement of a function of the form f^ n (t), f, and ^ being functional characteristics of a given form, and denoting the result of n — 1 successive substitutions of if/(£) for t in the expression of vl/ ( t ). Let us then suppose, for brevity’s sake, t]/ (log* (l-TO) = ^ (0> an d equation (3) will give JHt) a )/'* (/) and for f writing f\ \ n 1 again for f writing/^ n ~ 2 and for t,

(A') + o'.?)(A") + — r<>( n l \t • , . . .(32) The second number of this equation, actually developed be- comes / (A) 1*0 13 -n.n . W ^ «■ - ; X I • £»»••&& I.*2 1 • » ^ G 2 44 Mr. Herschel on the S denoting that the sum of all the possible values of the expression within the brackets is to be taken ; a, (1, .... v, (whose number is n) varying through all integer values, separately, from o to co . Now the several factors which compose this expression are respectively, the coefficients of in the developements of// (£), (/£)*, (/£)/ . . . . (t Let these coefficients be represented by H a » “K#* ^K y , . . . . and we shall find /+* (0 = s { H. . . % “K, . f } ; (33) If for instance, / (t) = e t == log.— i /), we have H = /(* 4 A )o« . « 12..,. a *K, (3 1.2 .... /3 ,, &C. whence we obtain /io g .-» ( t) = (m) To take another example, let us suppose the developement of /+"(0 were required, where / (/) = e f _ i. In this case 'equation (/) becomes simply /+(0=/( A)^ and the formula in (32) gives f^ n [t) =/(A)s°- a ' + 0 '- A“ + ....o(»~0.f In this case also (33) becomes • A* ■ A g Al£ z ,1. which gives, if/ (2) = t, ,J, ■( M — .«? j A / X A g . A** o’ f , I V ' ( I....|3 x I .... V J fV (0 = 5 Now Ao 0 = 1, and if, for the sake of symmetry we write a, /3, ^ instead of j3, 7, . . . . we shall have developement of exponential functions , &c. 45 { «/3 |3 y .A u, the number of the indices a, ( 3 , {x, being ?z — 1. It seems hardly necessary, after what has been said, to notice that the developement of any function, such as & c.} in which t, V, &c. denote any number of independent vari- ables, \|/, 'p, &c., any functional characteristics, and n , n\ &c., any indices, may be accomplished by the same means — or, more conveniently, derived from (33) in the same manner as the formula (27) was obtained from our equation (2) ; and the result included in a brief and simple expression. The cases however are few, where the results afforded appear, if I may so express it, in their natural form, and it would therefore be useless at present to extend our views farther in this direction. JOHN F. W. HERSCHEL. Cambridge, Nov. 17 , 1815 . C 46 3 r ; II m z l II £{ fit. :, ■*;*■ aff'f on f- % W* q. *(•> - IV. Ora 72 m properties of heat , as exhibited in its propagation along plates of glass. By David Brewster, LL. D. F. R. S. Lond. and Edin. In a Letter addressed to the Right Hon. Sir Joseph Banks, Bart. G. C. B. P. R. S . tbn iTfd U: t 4 ,.' ' ■ > j.iil'i “:V’ t ? Read January 11 , 1816. Dear Sir, sfftpns jdqi - In two papers published in the Transactions of the Royal Society,* I have given some account of the action of heat in enabling glass to arrange a beam of light, into two oppo- sitely polarised pencils, and I have shown that unannealed glass, in the form of Prince Rupert's drops, possesses dis- tinct optical axes, and acts upon light like all regularly crystallized bodies. My attention was sometime ago recalled to this subject, in consequence of having discovered that reflection from all the metals, and total reflection from the second surfaces of trans- parent bodies, produced the same effect as crystallized plates, in separating a beam of polarised light into its complementary tints. I was thus led to believe, that the existence of two oppo- sitely polarised pencils, and the production of the complemen- tary colours, were concomitant effects, and I prepared to exa- mine the truth of this supposition in the case of heated glass. In my early experiments on this subject, I had not observed these colours, as I was not then in the possession of a mode of detecting them, when they formed the lower tints of the * See Phil. Trans. 1814, p. 436, and 1815, p. 1. Dr. Brewster on new properties of heat , &c. 47 first order of Newton's scale ( Opticks , B. II. Part II.) ; but I have since discovered a method of rendering them in every case visible, by their effects in modifying the colour of a standard plate of sulphate of lime. The results of these experiments, while they confirm the supposition which I had made, have also led to the discovery of many singular phenomena, which constitute a new branch of physics, analogous in its general character to the sciences of magnetism and electricity. The curious properties of light and heat, which are explained in the following paper, and the new views which are unfolded respecting the structure of cry- stallized bodies, will I trust, attract the notice of the chemist, the mineralogist, and the natural philosopher; while the variety and splendour of the phenomena which it embraces, will recommend it to the attention of those, who value scientific researches merely as subjects of exhibition or amusement. Sect. I. On the transient effects exhibited during the propagation of heat along plates of glass, or during its communication from glass to surrounding bodies. Proposition I. When heat is propagated along a plate of glass , its progress is marked by the communication of a crystalline structure, which changes its character with the temperature , and which vanishes when the heat is uniformly diffused over the plate . If we lay the edge of a plate of glass upon a bar of red hot iron placed horizontally, and transmit through it a ray of light polarised in a plane inclined 45 0 to the horizon, the light will be depolarised in various degrees in different parts of the glass. When the temperature is made uniform, the glass plate loses its property of depolarisation. In order to prove that an 4$ Dr, Brewster on new properties of heat, ■9 inequality of temperature is necessary to the developement of this structure, I held a small plate of glass in a pair of hot pincers with globular ends. It instantly acquired the depola- rising structure, and lost it when the diffusion o the heat be- came uniform. I then cooled the glass, and held it a second time in the same pincers, which were now much colder than before : the depolarising structure was again communicated to it as formerly. The same result was obtained wdten 12 plates of glass were placed upon a bar of red hot iron. Proposition II. JVhen a plate of glass is brought to an uniform temperature con- siderably above that of the atmosphere, the communication of its heat to the surrounding air, or to other contiguous bodies colder than itself, is marked by the production of a crystalline structure, similar to that which is described under the preceding propo- sition. I took three plates of thick mirror glass, and brought them to an uniform temperature by immersion in boiling water. In this state they exercised no action upon polarised light ; but when their edges were placed upon a mass of cold iron, the inequality of temperature, occasioned by the abstraction of their heat, produced a crystalline structure at the very edge of the plates, which polarised a bluish white tint of the first order. At a greater distance from the edges, the plates de- polarised a lower" tint in Newton's scale. When the plates * One tint is said to be higher than another, when it belongs to a higher order, or is at a greater distance from the black, or the commencement of the scale. This ex- planation is rendered necessary, in consequence of M. Biot’s having used this term in the opposite sense. as exhibited in its propagation along plates of glass. 49 are held in the air, the same effect is produced, but in a less degree. See Prop. XIV. Proposition III. When heat is propagated along a plate of glass , its particles as- sume such an arrangement that it exhibits distinct neutral and depolarising axes , like all doubly refracting crystals , the neutral axes being parallel and perpendicular to the direction in which the heat is propagated. When a ray of light polarised in a plane inclined 45 0 to the horizon, is transmitted through a glass plate DCEF Fig. 1. (Pl. II.) placed upon a piece of hot iron AB, lying hori- zontally, it is completely depolarised ; but when the plane of primitive polarisation is parallel or perpendicular to the hori- zon, no change is produced upon the polarised ray, an inter- mediate effect being exhibited in intermediate positions, as in regularly crystallized bodies. Hence DE is the neutral axis, and DF the depolarising axis of the plate. Proposition IV. When the depolarising structure is communicated to glass by heat in the manner already described , the glass acquires the property of arranging polarised light into its complementary colours. The apparatus being arranged as in Prop, III, let the light transmitted through the glass DCEF be analysed by a prism of calcareous spar, or by reflection at the polarising angle from a plate of black glass, having a motion of rotation round the polarised ray. When the plane of reflection from the black glass is perpendicular to the plane of primitive polarisation, the whole surface of the glass plate will be covered with beautiful and highly coloured fringes parallel to CD* as MDCCCXVI. H » 50 Dr. Brewster on new properties of heal, represented in Fig. 2. (PI. II .) ; and when the plane of reflection is moved round 90° from this position, the surface of the glass will be covered with the complementary fringes, the colours gradually passing from the one state into the other during the rotatory motion of the black glass, in the same manner as in crystallized bodies. The nature and intensity of the tints are represented by the following formulas, which are the same as those which M. Biot found for crystallized bodies.* p = O -j- E cos. 2 2 a. n = E sin. 2 2 a. In these formulae P represents the ordinary pencil, and n the extraordinary pencil : O is the coloured tint which preserves its primitive polarisation, and is not acted upon by the crys- tallized glass : E is the complementary tint which has lost its primitive polarisation by the action of the glass being polarised in an angle equal to 2 a: and a is the azimuthal angle which the axis of the plate forms with the plane of primitive pola- risation. Proposition V. The coloured fringes mentioned in the preceding Proposition, and represented in Fig . 2. consist of six different sets, two exterior, two interior, and two tei'minal sets. The exterior sets occupy the edges , the interior sets the middle, and the terminal sets the extremities of the glass plate , and each set is separated from its adjacent set by a deep black fringe . These different sets of fringes are represented in Fig. 2. (Pl. II.) where CDEF is the glass plate, and CD the edge of it which rests upon the hot iron. The first exterior or lateral * See Biot’s Rechcrches sur la polarisation dc la lumiere, p. 21. as exhibited in its propagation along plates of glass . 51 set, is comprehended between CD the edge of the plate and the black fringe MN, and the 2d exterior or lateral set between the opposite edge of the plate FE and another black fringe OP. The first interior or central set lies between MN and a b, a line equidistant from the two black fringes, and the 2d interior or central set between OP and the same line a b. The first exterior set contains a greater number of fringes than the se- cond exterior set, but in the latter they have a greater breadth ; and in both these sets the fringes diminish in breadth, as they recede from the black spaces MN, OP. The terminal fringes appear at the extremities MO, NP of the plate.* They are separated from the central fringes by a faint black space, which becomes lighter as the tints increase ; and from the lateral fringes by a diagonal black space bisecting the angles E, C, D, F. As the tints increase in number, the terminal fringes suffer particular changes, which will be described in the second part of this paper. When the glass plate extends far beyond the heated iron, the terminal fringes are not produced. Proposition VI. To explain the successive developement and subsequent extinction, of the fringes during the propagation of the heat along the glass plate . When the plate of glass CDEF, Fig. 2. (PI. II.) is set upon the hot iron, a fringe or wave of a pale white colour instantly appears along the line CD, and gradually advances upon the * The terminal fringes are not shown in this figure ; but they are represented in Hgs. 3 , 4, 8, (PI. II.) 20 and 21. (PI. III.) H* 52 Dr. Brewster on new properties of heat, glass, driving as it were before it a dark and undefined wave. Nearly at the same instant a similar but fainter white wave advances from the upper edge EF, driving before it a similar undefined dark wave ; and at no perceptible interval of time, another white fringe appears in a very diluted state about the centre a h, advancing towards the edges CD and EF. The waves of white light, which have their origin at the edges of the plate, and those which advance to meet them from the middle, have the effect of condensing the undefined dark waves into two black fringes MN, OP. A faint yellow wave next appears at CD, encroaching gradually upon the white one, and is followed by orange and red tints, completing the first order of colours in Newton’s scale. The colours of the second order next advance in succession, and the same thing happens with all the superior orders, so that three, four, and sometimes even nine or ten orders of colours are distinctly seen between MN and CD. When the green colour of the second order ap- pears at CD, a wave of yellow of the first order is seen at FE advancing upon the plate, and is followed by tints of orange, red, purple, &c. till several orders are distinctly visible be- tween FE and OP; and nearly at the same time another yellow wave developes itself at a h, and gradually encroaches on both sides upon the white fringe, but never reaches MN or OP. The yellow at a b next becomes orange, pink, purple, blue, green, &c. Each of these colours advances towards MN and OP, but never covers entirely the preceding colour, so that new fringes, sometimes to the number of six or eight, are thus formed between the black spaces. The terminal fringes are developed at the same time, and nearly in a similar manner. as exhibited in its propagation along plates of glass. 53 As the heat of the iron becomes more uniformly diffused •s over the plate of glass, the fringes between MN and CD di- minish rapidly in number, and pass off at CD, those which remain always increasing in magnitude. The same effect takes place at EF, but more slowly, so that there is a particular time when the fringes between EF and OP are equally numerous as those between CD and MN. The two interior sets diminish and disappear in a similar manner, the part AB re-exhibiting all its former colours in an inverse order. Nothing is now seen but the white and black fringes, which gradually die away, and at last disappear when the temperature of the glass becomes uniform. Proposition VII. The colours of the fringes in all the six sets ascend in Newton’s scale as they recede from the black spaces MN, OP, the fringes adjacent to these spaces being composed of the colours of the first order. The truth contained in this proposition might have been safely deduced from a comparison of the tints with those in Newton’s scale, or with the table of colours which I have found in the rings exhibited by topaz when exposed to a polarised ray.* In order, however, to obtain a more convincing proof, I took a plate of sulphate of lime, which polarised a bright blue of the second order, and combined it with the plate of glass CDEF. When the axis of the sulphate of lime was parallel to the axis CD, the blue of the second fringe below MN was con- verted into black, a tint due to the difference of their ac- tions ; but when its axis was at right angles to CD, the same * See Phil. Trans, 1814, p. 204. 54 Dr. Brewster on new properties of heat , blue fringe was converted into a yellowish green , a tint due to the sum of their actions. Hence it follows, that the blue in the second fringe below MN is a blue of the second order. Similar results were obtained by combining the sulphate of lime with the parts of the glass which produced the other sets of fringes. Another proof of the proposition was obtained in the fol- lowing manner. I took two plates of thick glass, and having placed them on a hot iron, as before, I waited till all the fringes had disappeared except the white of the first order. When one of the plates was lifted vertically, so that the portion of the glass CDNM was opposite to a b , the two white fringes produced a black tint. When the same plate was depressed till a b of the one plate was opposite to CD of the other, the white fringe above CD was also converted into black. This black, however, w r as not so deep as before, as the white in the exterior fringe is brighter than in the interior one. In the first case, this superiority was compensated by the cooling of the glass at CD, in consequence of its being lifted from the hot iron, whereas in the second case, the cooling had not affected the interior part a b. When, on the contrary, the one plate was held in such a position that its fringes were at right angles to those of the other, as shown in Fig. 3, (PI. II.) the white of the exterior fringes of the one plate combined with the white of the exterior fringes of the other, produced black. Ihe white of the interior fringes of the one plate, when combined witli those of the other plate, produced black, and the white of the interior fringes of the one plate, when combined with the white of the exterior fringes of the other, produced a brighter white. as exhibited in its propagation along plates of glass. 55 The result of these combinations is the production of a dark cross, as represented in Fig. 3. (PL II.) This cross is extremely regular and beautiful when the two plates have the same breadth, polarise the same tints, and have their exterior fringes of the same magnitude at both edges. When some of these circum- stances are varied, the cross changes its form in a manner which can easily be ascertained from a previous examination of the separate fringes ; but, when the one plate polarises higher tints than the other, the cross is no longer produced. The fringes of the plate which polarises the highest tint, are bent from their rectilineal direction, as represented in Fig. 4. (PI. II.) As the figures exhibited at the intersection of two plates can always be determined, a priori, from a knowledge of the fringes which each plate produces separately, so the nature of the separate fringes, and the rate at which the tints change, may be easily predicted from the figures which are exhibited at the place of intersection. When the tints polarised by the two plates are numerous and brilliant, the intersection al figures are singularly beautiful. 5 $ Dr. Brewster on new properties oj heat , Proposition VIII. The parts of the plate of glass which exhibit the two exterior sets of fringes, have the same structure as that class of doubly refract- ing crystals , including sulphate of lime, quartz, &c. in which the extraordinary ray is attracted to the axis , while the parts of the glass, which exhibit the two interior and the terminal sets, have the same structure as the other class of doubly refracting crystals, including calcareous spar, beryl, &c. in which the de- viation of the extraordinary ray from the axis, is produced by a : repulsive force.* The portions between these which produce the black spaces, have an intermediate structure, like those por- tions of muriate of soda, fluor spar, and the diamond, which are destitute of the property of double refraction. In order to establish this singular result, I combined a standard plate of sulphate of lime which polarised a bright blue of the second order, with the different parts of the glass which produced the six sets of fringes. When the axis of the plate of sulphate of lime was parallel to the fringes, or to CD, the blue of the second fringe in the first exterior set below MN, and the blue of the second exterior fringe above OP, were converted into black, but when the axis of the sulphate of lime was perpendicular to CD, the blue of the same fringes was converted into yellowish green. On the contrary, when the axis of the plate of sulphate of lime was perpendicular to CD, the blue of the second fringe of the first interior set above MN, and the blue of the second fringe of the second interior • See Laplace’s valuable Memoir, Sur la lot de la refraction extraordinaire dans les cristaux diapbanes, Mem. de L’lnstitut. 1809. / as exhibited in its propagation along plates of glass. 57 set below OP, were converted into black; but when the axis of the sulphate of lime was parallel to CD, the blue of the same fringes was converted into a yellowish green. Hence it follows, that the axis of the parts of the glass which form the exterior sets of fringes, is at right angles to the axis of the parts which form the interior sets. The same result is deducible from the second experiment in Prop. VII. Since, therefore, the same effects as those which we have described, are pro- duced by combining crystallized plates taken from the two classes of doubly refracting crystals, as has been ably proved by M. Biot,* we may consider the truths stated in the Pro- position as completely established. Cor. It follows from this Proposition, that a single plate of glass, crystallized by the propagation of heat, and exposed to a polarised ray, exhibits the same variety of phenomena as all the crystals in the mineral kingdom. We have already seen, that it possesses the structure of all the three classes of doubly refracting crystals. But the individual crystals which compose these classes, are distinguished from each other by the magnitude of their polarising forces, and the same variety is exhibited in the polarising forces of the glass, the parts which are adjacent to CD, ab, and FE, having the structure which gives the greatest polarising force, and the parts adja- cent to OP, MN, the structure which gives the least polarising force. * See M. Biot’s Memoire sur la decouverte d’une propriete nouvelle dont jouissenf les forces polar isantes de certains cristaux. Mem. de 1’Institut, 1814. I MDCCCXVI, 4 58 Dr. Brewster on new properties of heat , Proposition IX. When the temperature of the source of heat remains the same , the thicknesses of the glass , whether one or more plates are used , which polarise any particular colour , under a perpendicular incidence, are proportional to the thicknesses of thin uncry- stallized plates, which would reflect the same colour in the phenomenon of coloured rings. M. Biot has shown with much ingenuity, that the thicknesses of sulphate of lime, rock crystal, and calcareous spar, which polarise any particular colour, are proportional to the thick- nesses of the uncrystallized plates which reflect that colour :* and there was reason to believe that the same law would regu- late the phenomena exhibited by heated glass. I took several plates of glass of various thicknesses, from the thinnest German crown glass, about ~th of an inch thick, to plate glass J of an inch thick, and, having placed them all upon a piece of red hot iron, I found that the number of orders of colours which were developed, was nearly related to the thickness of the glass. As these plates, however, had not the same chemical composition, I employed several pieces of thick mirror glass cut out of the same plate. I placed one of these by itself on the hot iron, and marked the particular tint which it polarised in the first order of Newton’s scale. All the rest of the plates having been placed on the hot iron at the same time with the first, I took each of them in succession, and joined it to the first plate ; the tints which were thus produced, ascended in the order of colours as the * See Biot’s Recherches sur la polarisation de la lumiere, p. 53. as exhibited in its propagation along plates of glass. 59 number of plates was increased, and were always such as belonged to a thickness taken in proportion to the number in the third column of Newton's scale. When one plate, for example, polarised at ab, a yellow of the first order, two plates gave an indigo of the second order, three a red of the second order, four a green of the third order, five a bluish red of the third order, and six a yellowish green of the fourth order. Now the numbers representing these tints in Newtons scale, are nearly 4, 8, is, 16, so, 24, and the corresponding thicknesses are 1, 2, 3, 4, 5, 6. A variety of other experiments were made with the same result. Proposition X. If a number of glass plates of the same form and of the same chemi- cal composition, but of various thicknesses, are placed upon a hot iron , then if two or more of them are combined symmetrically , that is with their edges CD coincident , the colour polarised in any part will be the same as that which would have been polarised by a single plate having a thickness equal to the sum of the thicknesses of the plates ; but if the plates are placed transversely , or with their edges CD at right angles to each other, the colour polarised at those parts of the glass, which are similarly situated with regard to the black spaces , is the same as that which would have been polarised by a single plate, whose thickness is equal to the difference of the thicknesses of the two transverse plates or systems of plates • I took two plates of mirror glass that had different thick- nesses, but nearly the same colour, and having cut them into equal rectangular pieces, I foUnd that three of the one had the same thickness as five of the other. I 2 6o Dr. Brewster on new properties of heat , These two parcels of plates were then placed upon the hot iron, and the one parcel exhibited the same tints as the other, both in the exterior and interior fringes. In order to prove the second part of the proposition, I took three parcels, one of two plates, another of four plates, and a third of six plates, all of them having been cut out of the same mirror. I then placed the different parcels upon the hot iron, and when the colours were perfectly developed, I held the system of four plates in a position transverse to the system of six plates as shown in Fig. 3. (Pl. II. ) A broad fringe of blue light of the second order appeared at the intersection of the central lines a b, a'b'. The very same colour was polarised by the system of two plates, whose united thickness was equal to the difference of the thickness of the transverse parcels. See Prop. XV. Proposition XI. The number and form of the plates of glass remaining the same , the tints which are polarised at the central line a b, and at the edges CD, FE, Fig . 2, (PL II. ) ascend in Newton’s scale as the temperature of the source of heat is increased. I took a thick plate of mirror glass 6,9 inches long, 2,27 inches high, and 0,163 thick, and having placed it upon a heated iron, which just appeared red hot in the dark, I found that it polarised the green of the second order in x\\q first ex- terior set of fringes, and the greater part of the white 01 the first order in the second exterior set of fringes. When the heat was more intense, the same plate polarised th egteen of the third order in the first exterior set of fringes. When 15 plates of mirror glass were placed upon the top A- as exhibited in its propagation along plates of glass. 6 1 of a tin vessel enclosing water at a temperature of igo°, they polarised a green of the second order. The united thickness of these plates was 1.7 of an inch. When the heat of my hand was communicated to 11 plates of crown glass, they polarised the blue of the first order, and exhibited distinctly the two black spaces. The temperature of the room during these experiments was 64®. Even one plate of crown glass about 0.28 of an inch thick, exhibits the black spaces and the bluish white fringes by the heat of the hand. The preceding results are neither sufficiently numerous nor accurate to enable me to determine the relation between the thickness corresponding to the highest tint, and the tem- perature of the source of heat. An apparatus, however, is pre- paring for me, by which this point will be easily ascertained by obtaining various temperatures from heated oil or mercury. See Sect. II. Proposition XII. The number and form of the plates of glass, and the temperature of the source of heat remaining the same, the magnitude of the fringes of the first exterior set depend upon the law of the decrease of temperaiure in that part of the glass which produces them. The highest order of colours is always developed where the tem- perature is a maximum, and the tints descend in the scale as the temperature diminishes. Let CDEF, Fig. 5. (PI. II.) be a plate of glass, MN one of the black spaces, and the portion CDNM, that which produces the first exterior set of fringes. The temperatures at the points B, K, G may be represented by the ordinates BD, GH, KL, of the curve TLHD. The 62 Dr. Brewster on new properties of heat , highest tint is polarised at B where the temperature BD is greatest. A lower tint in the scale appears at G, depending on the temperature GH, and a still lower tint at K where the temperature is reduced to KL. As the temperature of the iron RS diminishes, and the diffusion of the heat over the glass be- comes more uniform, the temperature at B will be changed to B d, the temperature at G to G h , and the temperature at K to K l. So that the curve will now have the form mlh d. When this happens, the fringes grow broader and diminish in number* When the diffusion of the heat is uniform, the temperatures and consequently the ordinates will every where be equal, and the curve will change into a straight line, in which case, the fringes completely disappear. When the plate CDEF is lifted from the iron, it begins to cool at CD. The fringes pass off at the edge CD, exhibiting a broad fringe of the same tint. The differences of the temperatures now vary less rapidly, and the line TLHD, becomes a curve of contrary flexure, such as TLHVW or TLHX, when the cooling has made greater progress. I have not been able to ascertain exactly the relation be- tween the thickness corresponding to the polarised tints at different distances from the source of heat, and the tempera- ture of the glass at the same points ; but by assuming the most probable law of the decrease of temperature, and com- paring it with the magnitude of the fringes, there is reason to believe, that the thicknesses are nearly proportional to the temperature. The tints polarised at different parts of the glass plate (a sec- tion of which is shown in Fig. 6. (PI. II.) by ACB) will be as exhibited in its propagation along plates of glass. 63 represented by the ordinates of some curve m n op q, cutting the axis at the neutrai points n p. They reach their maximum at m and q, where they have the same character, and also at o, where they have an opposite character ; and they vanish at. n,p, the points which correspond to the black spaces. Pkoposition XIII. The upper edge of the plate which polarises the highest tint in the second exterior set of fringes, has received no sensible accession of heat, and the central parts of the plate, which form the two interior sets of fringes, exhibit no variation of temperature con- nected with the colours which they polarise. JVhen the number and form of the plates of glass, and the temperature of the source of heat remain the same, the magnitude of these three sets of fringes depends upon the law of the decrease of temperature at that part of the glass which produces the first exterior set. It will be seen from experiments given under a subsequent Proposition, that the depolarising structure is communicated to the upper edge of the plate of glass, even when it is 2, 4, 5, 6 , and 7 inches high. In some of these cases, the edge of the glass has the same temperature as the circumambient air, although the heat necessary to produce the same fringe at the lower edge of the plate, is much greater than that of boiling water. By spreading over the surface of the plate a thin film of oil of mace, which melts with a slight degree of heat, I was enabled to ascertain that there was no particular variation of tempe- rature connected with the tints which were polarised by the three sets of fringes mentioned in the Proposition. I 64 Dr. Brewster on new properties of heat, In every case the number of fringes in these sets increased and diminished with the number in the first exterior set. Their breadth also varied with the breadth of the fringes of the first exterior set, and consequently depended on the law of the decrease of temperature in that part of the glass. Scholium. The truth contained in the preceding Proposition, will, I have no doubt, be regarded by philosophers, as one of the most extraordinary in physics. The production of a crystalline structure in the part of the glass adjacent to the heated iron, though a curious property of radiant heat, is in no respect hostile to our established notions. But the communication of the same structure to the remote edge of the glass, where there is no sensible heat, and where the corpuscular forces, by which the particles cohere, are not weakened by any ap- proximation to fluidity, and the existence of an opposite struc- ture in the middle of the glass, developing itself on both sides from a central line, are results to which we can find nothing analogous, but in the perplexing phenomena of magnetica! and electrical polarity. 1 ( . .... ; I . as exhibited in its propagation along plates of glass. Proposition XIV. When a plate of glass heated uniformly , and having a temperature considerably above that of the atmosphere , receives a crystalline structure in cooling , as described in Prop. IL the parts which produce the four sets of fringes have each a structure opposite to that which they had when the plate was crystallized by the in- troduction of heat from without. That is, the parts of the glass which afford the two exterior sets of fringes, have the same structure as the class of doubly refracting crystals , in which the extraordinary ray is repelled from the axis, and the parts which form the tzvo interior sets of fringes, have the same structure as the class in which the extraordinary ray is attracted to the axis. I took 12 plates of mirror glass, and brought them to an uniform heat by laying them successively on their sides and edges upon a bar of hot iron. Having ascertained, by expos- ing them to a polarised ray, that they had no action upon light, I placed them with their edges upon a cold iron, so as to exhibit distinctly the white fringes of the four different sets. When the axis of a plate of a sulphate of lime, which pola- rised a blue of the second order, was placed at right angles to the direction of the fringes, the white of the two exterior sets was converted into a brozvnish red, and the white of the two interior sets into a light green. The converse of this hap- pened, when the axis of the sulphate of lime was coincident with the direction of the fringes. When the four white fringes are produced by placing the glass upon a hot iron, all these phenomena are reversed, the green tint being now produced MBCCCXVI. K 66 Dr. Brewster on new properties of heat, instead of the brownish red, and the brownish red instead of the green . The same result was obtained by combining glass plates crystallized in these tw r o different w'ays. In order to obtain a still more uniform temperature, I took a parcel of 15 crown glass plates, and suspended them in a vessel of boiling water, at some distance from the bottom- As soon as they had acquired the temperature of the water, I lifted them out, and placed them with their edges on a cold iron. The black spaces and fringes immediately appeared, and a yellow tint was visible in the middle of the interior fringes. The interior fringes had the same properties as the exterior fringes described in Prop. VIII. and vice versa. This experiment was frequently repeated with the same result. The fringes produced in this manner, we shall call the unusual series of fringes, in opposition to the usual series, or those produced by placing cold glass upon a hot iron. I was now anxious to observe the phenomena that would be presented by inducing the unusual series of fringes upon a parcel of plates that already possessed the usual series. In order to effect this, I placed the parcel of 1 5 plates of glass, already mentioned, with their edges on the bottom of a vessel filled with boiling water. The bottom of the vessel being very hot, communicated to the parcel of plates the usual series of fringes, just like a plate of hot iron. When the parcel was taken out and placed upon a cold iron, the usual series of fringes was distinctly seen ; but after the lapse of some seconds, it gradually disappeared, and was displaced by the unusual series advancing from the edges, and occasioned by the cooling of the plates. The as exhibited in its propagation along plates of glass. 67 struggle between the advancing and retiring fringes, had a curious appearance. Before the usual series of fringes vanished, the external fringes became broader, while the middle one gra- dually diminished. The two black spaces met in the middle of the plate, forming a broad undefined dark space, and the new or unusual series were seen advancing from the edges of the glass. At this instant there were two white spaces in the middle of the plate, and two external ones, but one of the middle white spaces quickly died away, and the unusual series was speedily developed. If plates of glass that exhibit the usual fringes are taken from the hot iron and allowed to cool in the open air, the fringes will gradually pass away as described in Prop. VI. but, as soon as they disappear, or a little before their disap- pearance, the opposite sets begin to advance upon the plate in the manner already described. Proposition XV. When similar fringes of the usual and unusual series are combined symmetrically , the polarised tint is that which is due to the dif- ference of the thicknesses , but when they are combined trans- versely . , the tint is that which is due to the sum of the thick- nesses of the plates. When dissimilar fringes of the tzvo series are combined symmetrically , the polarised tint is that which is due to the sum of the thicknesses , but when they are combined transversely , the polarised tint is that which is due to the diffe- rence of the thicknesses of the plates that produce them. The preceding truth was established by combining the fringes produced by 15 plates of crown glass cooled from the heat of boiling water, |with those produced by a plate of glass Ke 68 Dr. Brewster on new properties of heat, placed on a hot iron. The effects produced by the transverse combination will be understood from Fig. 7. (PI. II. ) in which C, C, &c. represent the similar fringes where the combined effect is produced, and DD, &c. the dissimilar portions where the difference of the effect is produced. The portions C, C, &c. will therefore polarise tints higher up the scale than any that are polarised by the plates singly, whereas the portion DD, &c. will polarise tints much lower on the scale than any of those polarised by the single plates. When the tints of the usual series are of the same intensity with those of the unusual series , the effect of crossing is very beautiful, and is represented in Fig. 8. (PL II.) where the portions corresponding to C, C, &c. are obviously affected with high tints in the scale, while those corresponding to DD, &c. are almost entirely black. The tint polarised in the central fringes of the plates, when separate, was the commencement of yellow. The combined tint, in the figure of a round cir- cular spot, was a beautiful indigo , which appeared at the centre of the square of intersection ABCD. This gradually shaded off through all the lower tints, and terminated in a dark cir- cular fringe. Beyond this fringe, towards the angles A,B,C,D, an opposite set of fringes were seen ; but towards the sides nothing but a dark shade was visible. All these phenomena are the necessary results of the principles already laid down. a.* Scholium. The phenomena described in the Proposition are the same as those which are exhibited by crossing plates of the two classes of doubly refracting crystals. The former, are how- ever, far more beautiful than the latter. as exhibited in its propagation along plates of glass. 6g Proposition XVI. To explain the effects produced upon the fringes by varying the height of the glass plates. In order to observe the changes occasioned by increasing the height of the plates, I employed pieces of glass whose height varied from 0.18 of an inch to 8 inches. When the height is very small, and not above 2 inches, the black spaces occupy nearly the position as shown in Fig. 2. (PL II.) The fringes are therefore very small, as they must always dimi- nish with the height, but they are remarkably brilliant, and exhibit much beauty in their developement. When the plates exceed two inches in height, the distances NP, PE, Fig. 2. ( PI. II. ) increase much faster than ND ; a smaller number of fringes is developed beyond OP, and their brightness is much impaired. (This effect is shown in Fig. 9. PI. II.) When the plates are 8 inches high, the whole fringe is faintly seen above OP. The colours of the two interior fringes are developed from a line much nearer MM than OP, and the black fringe OP is extremely indistinct. As high plates almost always burst in pieces when the maxi- mum tint is nearly produced, I was obliged to use plates of common window glass, but, on account of its dark green colour, I could not examine the phenomena with much satis- faction ; in using parcels of these large plates, much caution is necessary, as there is almost a certainty of some of them bursting with violence during every experiment. 7o Dr. Brewster on new properties of heat. Proposition XVII. To explain the effect produced upon the fringes by varying the shape of the glass plates . When the breadth of the plates is very small compared with their height, the black spaces have the form shown in Fig. 10, 11. (PI. II.) the breadth AB of the former being 0.8 of an inch, and that of the latter 2.25 inches. In Fig. 10. (PI. II.) the upper black space ABCD was indistinct about CD, and was scarcely separated from the lower black space Eg F. Coloured fringes appear at 1, 2, 3, and a white space between AB, CD extending pretty high, and grow- ing gradually fainter, the parts 1, 2, have the same tint, and the parts 3, 4, the opposite tint With a piece of glass whose height AC was 4^ inches, its breadth AB 4 inches, and its thickness f— of an inch, I obtained an effect similar to what is represented in Fig. 11. (PI. II.) The lowest part of the black fringe above 2 was \\ inch above CD, and the space at 4, all the way to the edge AB, was a pale bluish white. There were numerous fringes between C and D. In Fig, 11. (PL II.) the black spaces AB CD, and EF were separated by a whitish space 2. The portions 1, 2, 3, had the same tint, and the portions 4, 5, the opposite tint. See Prop. XXXVI. The form of the black spaces and the fringes varies in general with the outline of the plates. When the lower edge CD, Fig. 12. (PI. II.) had a waving form, and was placed upon a hot iron, the adjacent black space had likewise a wav- ing form, and the parts M, N, though the most distant from the source of heat, polarised tints higher in the scale than th§ parts O, P. as exhibited in its propagation along plates of glass. 71 In a piece of glass shaped as in Fig. 13. (PI. II.J when CD was heated, part of the upper black space had the form a be, and the other part e f terminated at/. Proposition XVIII. To explain the effects produced upon the fringes by an interruption in the continuity of the glass. If the second exterior and the two interior sets of fringes were caused by the actual communication of heat to the parts of the glass which produce them, there was reason to believe, that they would not be affected by any breach of continuity in the glass, which did not obstruct the progress of the heat. In order to determine this, I broke a plate of glass ABCD, Fig. 14. (PL III.) through the middle mn, and having ob- tained a very clean fracture, I placed the upper fragment CD, upon the lower one. This compound plate was set upon the hot iron RS; but no effect was produced on the upper plate, the fringes developing themselves in AB, just as if CB had been removed. When the heat was almost uniformly dif- fused over AB, CD began to exhibit faint traces of the white fringes, AB now serving as a new source of heat. The very same result was obtained when the two plates were joined by the interposition of zuater , Canada balsam , or rosin. I now took a piece of glass ABCD, Fig. 15. (PI. III.) in- terrupted by a fissure, or crack m n extending a short way into the plate. When the heat was communicated to its lower edge, the fringes were seen above mn, as if the crack had not existed, and the depolarised white light appeared con- densed at n, like a fluid rushing round the point. The crack, however, suddenly extended to 0; the upper piece of glass 7 s Dr. Brewster on new properties of heat , flew off with violence from the lower one, and a black fringe instantly sprung up below the new edge mp, just as if the upper part of the glass had never been in contact with the lower part. In another experiment, attended with the same result, the crystalline structure above m n instantly vanished when the crack reached o , although the two pieces of glass still cohered with some force. When the fissure m n was placed vertically, as in Fig. 16. (PI. III.) the same effect took place as if the two pieces had been separate, and no change was observed by cementing them with Canada balsam. Instead of fissures, I now substituted deep grooves cut across the glass. A thick plate which had a horizontal groove cut half through it, and extending from edge to edge, was laid upon the hot iron. The white fringes appeared imperfectly above the groove, and an undefined dark wave below it, as if some fluid had been obstructed in its passage through a nar- row channel. It is not improbable that this dark wave was occasioned by the combination of two white fringes of different sets. For if BC, DE, Fig. 17. (PI. III.) be a vertical section of the plate, and AFG the groove, the parts GF omE may be considered as acting like a separate plate, and will there- fore have op, rn n for its black spaces, while the other part, DBCAF 0 m, will also act as a separate plate, and have tu,r s, for its black spaces. But the white of the exterior fringe of the first of these plates between FG and op will thus be oppo- site to the white of one of the interior sets in the other plate, and as these are produced by opposite crystallizations, a black tint will be the result of their union. The bursting of the plate in the direction of the groove, prevented any farther examination of the phenomena. as exhibited in its propagation along plates of glass . 73 I next took a plate of glass that had a diamond cut across the middle, where the interior white fringes appeared. Having broken it in- two, a black fringe instantly arose between the cut mn % Fig. 14. (PL III.) and the plate displayed all the interior sets of fringes without receiving an additional supply of heat. I now attempted to bring the two separated surfaces into close contact by grinding them upon each other ; but I could not succeed in making them act upon light like a single plate; The following method, however, enabled me to surmount the difficulty, and to obtain some new results. I took a piece of annealed crown glass of the size repre- sented in Fig. 52. (PL V.) about 0.42 inches thick, and 0.5 broad, and having made a notch with a file at the point B, I applied to it a heated iron, which instantly produced a fissure Bb c d, and intercepted all the incident light by the total reflection which was produced. After standing an hour, this fissure began to disappear, and in the course of a day, it was as completely closed up as if it had never been made. The fissure was frequently reproduced by a hot iron ; and it regularly closed, unless when the expansive effect of the heat was capable of separating the surfaces to too great a distance. Sometimes it closed in a few seconds, and at other times a little mechanical pressure was requisite to effect the reunion. When the fissure was open, I laid the glass upon a hot iron, and it quickly pro- duced the fringes shown in Fig. 53. ( PL V.) where the pheno- mena are exactly the same as if the two pieces AB, BD, had been completely separated. But when the fissure was closed, and the glass laid upon the hot iron, it exhibited the different sets of fringes as shown in Fig. 54. (PL V.) just as if it had been one continuous mass* MDCCCXVI. L 74 Dr. Brewster on new properties of heat , Now it is manifest, that the two pieces AB, BD, though they touch one another optically, are not in physical contact, or in the same state in which they were before the fissure was formed. If we were to make several other notches in the glass with a file, it would always break at the place of the fissure ; which proves that the force of cohesion has there been weakened, and that the surfaces, though optically in contact, are physically at a distance. The crystallization of the solid AD, as if it were continuous, forms a fine analogy with the curious fact in magnetism, that two bars of steel pressed together at their extremities, may be magnetised as if they had formed only a single bar, and will exhibit a neutral point at the place of junction. Proposition XIX. When heat is propagated from the centre of a plate of glass in radial lines , all the fringes and the black spaces form concen- tric circles , and four black radial spaces , at right angles to each other , diverge from the centre in directions parallel and perpen- dicular to the plane of primitive polarisation . I took a large plate of glass, and applied to its centre a ball of red hot iron. The four black radial lines were distinctly seen diverging from each other at right angles, but the two concentric dark spaces were indistinctly developed. I next in- tended to grind a hole in the centre of the plate, and to place in it a red hot ball, but having discovered a much better method of generating the circular fringes, which will be ex- plained in the next section, I proceeded no farther in the experimental illustration of the Proposition. If we suppose ABCDEFGH, Fig. 18, (PI. Ill,) to be eight as exhibited in its propagation along plates of glass. 75 equal plates of glass placed upon the faces of octagonal bars of hot iron, the black spaces and fringes will have likewise an octagonal form, abstracting the effects which take place at the extremities of the plates. Now if light polarised in a plane inclined 45 0 to the horizon, is transmitted through this system of plates, the fringes will be distinctly seen in the four plates A, C, E, G, because their depolarising axes are all coincident with the plane of primitive polarisation, but no fringes will be seen in the plates B, D,F, H, as their depo- larising axes are inclined 45 0 to the plane of polarisation. If this system of plates be now turned round the centre O, each of them will exhibit its fringes when it comes into the positions A, C, E, G. These fringes will gradually disappear during the motion of the plates into the positions B, D, F, H, where they will cease to be visible. Let us now suppose, that the hot iron is applied to the centre of a circular plate of glass ABCDEFGH Fig. 19. (PI. 111 .) the black spaces will obviously have a circular form abed efg h and ABCDEFGH; and as the neutral axis of each elementary plate, into which we may suppose the circle of glass to be divided, is directed to the axis O, the dark positions will still be B, D, F, H, and consequently there will be a black cross B bf F, D d h H, having its arms in- clined 45 0 to the horizon. This cross will continue in the same position during the rotation of the plate about its centre O, every elementary plate losing its depolarising power when it comes into the lines B bf F, D d h H. L 2 7 6 -Dr. Brewster on new properties of heat, Proposition XX. When heat is propagated from Izvo different sources , in contact with the opposite edges of a plate of glass , the different Sets of fringes preserve the same character , the only effect of the addi- tional heat being to polarise higher tints in the different sets of fringes. I placed 12 plates of window glass upon a hot iron, and when the different sets of fringes were distinctly visible, I held another bar of hot iron in contact with their upper edges, and observed higher tints polarised in all the four sets of fringes. Many of the plates, however, burst with great violence, so that I could not perceive the phenomena that took place when the diffusion of the heat became more uniform. Proposition XXI. TVhen heat is propagated through calcareous spar , rock crystal , topaz , beryl , the agate and other minerals that have the pro- perty of double refraction, no optical change is produced in their structure. The greatest heat which I could conveniently apply to dou- bly refracting crystals, produced no change whatever in their action upon light, whether the heat was propagated in the direction of their neutral, or of their depolarising axes. These crystals appear to be in the state of steel bars saturated with magnetism, which cannot acquire any additional impregnation. Being already in a state of perfect crystallization, they are not capable of receiving from heat any addition to their crystalline structure. as exhibited in its propagation along plates of glass. 77 Proposition XXII. When heat is propagated through muriate of soda,fluor spar , obsi- dian, semi-opal , and other minerals that have not the property of double refraction , they exhibit the same phenome?ia as heated glass . A mass of muriate of soda, when laid upon a hot iron, exhi- bited a yellow of the first order, both in the external and internal fringes. Fluor spar was very slightly affected. Semi- opal suffered a greater change; and Obsidian displayed the fringes as readily as glass. A piece of Obsidian of consider- able transparency, and about ~ of an inch thick, possessed naturally the fringes produced by heat. It must therefore have been formed by igneous fusion. This specimen, for which I was indebted to Mr. Sivwright, was cut out of a round mass, and preserved its original outline. It probably was of the first variety discovered by Sir George Mackenzie.* Rosin , gum copal, horn , amber, tortoise shell, the indurated ligament of the chama gigantea,f and various other sub- ’* Sir George Mackenzie has observed, that there are two very distinct varieties of obsidian. One of these transmits light when cut into thin plates, which, however, seldom appear of an uniform degree of transparency. This variety, at a temperature much under that which can be excited in a common fire place by a pair of bellows, swells, and is converted into pumice by the extrication of a gaseous fluid, which Sir George Mackenzie and Dr. John Davy attempted without success to collect. During the experiment, the smell of nitrous acid was very perceptible. The other variety is denser, of the deepest black colour, and is scarcely translucent at the edges of thin fragments. It does not swell on the application of heat, much more intense than what converts the other variety into pumice. Should this note meet the eye of a skilful analyst, he would do a service to mineralogy by examining both varieties, and by comparing the analysis of pumice with that of the pumice formed from the first variety. f I have been indebted to Dr. Francis Buchanan, F. R. S. for this curious substance. It is as hard and transparent, and has as rich a colour a? amber. 78 Dr. Brewster on new properties of heat , stances, both of animal and vegetable origin, receive a new • structure during the propagation of heat. Sect. II. On the permanent effects produced upon glass by the com- munication of its heat to surrounding bodies. The phenomena described in the preceding Section are of the most transitory nature. Every fringe is in a state of per- petual change : one colour quickly succeeds another, and after heat has rapidly developed all the various tints due to its intensity, they repass through the same hues which they exhibited in their formation, and they finally disappear after a slow and gradual decline. In this respect, only, do the phe- nomena of crystallized glass differ from those of the regularly organised bodies that compose the three kingdoms of nature. The fine display of colours which characterises the action of crystalline laminae upon polarised light, are in every respect permanent. The same mineral possesses an invariable struc- ture, and patience only is necessary to detect the phenomena which it presents, and to obtain an accurate knowledge of the character and intensity of its action. The coloured fringes of heated glass, on the contrary, are not susceptible of correct mensuration. Where every thing is in a state of change, no fixed character can be seized, and, instead of measuring, it is often difficult to observe their variations. From this perplexity, however, I have been fortunately relieved by the discovery of a method of fixing glass in a crystalline state, and giving it a character as permanent as that of the most perfect minerals. An account of this method, and of the results which it has enabled me to obtain, will form the subject of the present Section. as exhibited in its propagation along plates of glass. 79 Proposition XXIII. When a plate of glass brought to a red heat is cooled in the open air , or is placed with one of its edges upon a bar of cold iron , the different sets of fringes described in Section I. are developed during its cooling , and they have the same character with those which are produced by placing cold glass upon a hot iron. When the cooling is completed, the structure which affords the f ringes, becomes permanent, and the colours, when thus fixed, possess the same brilliancy which they displayed during their formation. When the red hot plate is exposed to a polarised ray, it exhibits at first no action upon light ; the tints advance slowly from the edges, and, after the lapse of 12 or 15 minutes, the glass is cooled, and the crystallization complete. In this way I have formed various plates of glass which possess a permanent structure, and exhibit the phenomena described in the Proposition, but not havipg obtained a com- plete series of different heights and thicknesses, I have not yet taken any exact measurements of the fringes. The following results with four different plates of glass, will convey some idea of the nature of the tints which are deve- loped. All the plates were brought to a red heat so as not to lose their shape, and were cooled by placing their lower edges upon iron of the same temperature as the surrounding air. Thickness of the plates. Maximum tint at the lower edge. Tint in the middle. Numbers in New- ton’s Table corre- sponding to the maximum tint. No. 1. 2. 3 - 4 - c.1125 inch 0.2000 0.2833 °-4375 | Beginningof blue ( of the 2d. order t Green of the 3d l order. $ Green of the 4th { order. f Nearly end of the < red of the 5th [ order. Blue of the 1st. 7 order, 3 Beginningofblue 7 of the 2d. order, j Beginningofpur- \ pleoftheist. order ) Pink of the 2d. 7 order. j 8.7 16.2 22.7 35-5 &o Dr. Brewster on new properties of heat , By comparing the numbers in the 5th column, which are mil- lionth parts of an inch, with those in the second column, it will be found that the constant factor, by which we must mul- tiply the thickness of any plate of glass, in order to obtain the thickness of the plate which would afford by reflection a tint similar to its maximum tint, is nearly tttso* It is a curious circumstance, that the permanent fringes have precisely the same character as the transient fringes which are produced by placing glass plates upon a hot iron, while the transient fringes, developed during the cooling of glass plates, have an opposite character. The limiting temperature at which the former are changed into the latter, is probably that, at which the permanent struc- ture is communicated. When the glass plates are cooled more at one edge than at another, the fringes are less distinct, and the tints lower at the edge that is least rapidly cooled. This difference becomes more perceptible as the height of the plates is increased. When the plates of glass are thick, and exposed to a con- siderable heat, they often lose their polish, and exhibit on their surface a delicate fibrous texture when examined by a micro- scope. This texture sometimes consists of grooves which exhibit by reflection the coloured images produced by mother 'Of pearl. It also communicates the same property to wax. as exhibited in its propagation along plates of glass. 81 Proposition XXIV. When a plate of glass, crystallized in the manner described in the preceding Proposition , is inclined to the polarised ray in a plane perpendicular to the direction of the fringes, the central tints ascend in the scale of colours , as if the plate had increased in thickness ; but , when it is inclined in a plane parallel to the direction of the fringes, the central tint descends in the scale , as if the plate had become thinner. When the plane of inclina- tion forms an angle 0/ 45 0 with these planes, no change is pro- duced in the tints. I took a plate of crystallized glass which polarised in the line a b , Fig. 2. (PL II.) a broad but very faint tinge of yellow; when it was inclined in a plane perpendicular to the direction of the fringes, the tint which it polarised became a dark orange yellow — but, when it was inclined in a plane at right angles to the former, the tint became a pale bluish white. A similar result was obtained, when the colours belonged to higher orders in the scale. The effect of inclination may be seen more advantageously when two plates that polarise the very same tint, are placed transversely, so as to exhibit the cross represented in Fig. 3. (PI. II.) By inclining one of the plates, the other is necessa- rily inclined in an opposite plane, so that the tints of the one ascend, while those of the other descend in the scale of colours. The consequence of this is a separation in the middle of the cross, producing two curved black fringes, having the same appearance that is afforded by crossing two plates that pola- rise different tints. MDCCCXVI. M 8 s Dr. Brewster on new properties of heat, I 6 Cl ^ .iy ■' ; (J *• <** -tf. V' ' ? •• : • ■■ ' X J ' '■■ ' . \ \ f Ti£ ' J Proposition XXV. If a plate of crystallized glass is cut in two pieces by a diamond along the line a b, Fig. 2 o. (PI. III. ) each of the separate plates will exhibit the properties of a whole crystallized plate. The portion r sop of the separate plate which had formerly the struc- ture of the attractive class of doubly refracting crystals , has now the structure of the repulsive class ; another portion op which had the attractive structure , has now an intermediate structure , similar to that of muriate of soda, &c* and so on with the other parts of the crystal. If a plate of crystallized glass ABCD, Fig. 20. ( PL III . ) is cut with a diamond along the line a b, through the central white fringe, the portion a b DC has the same structure as the whole plate, as is represented at rsGH, Fig. 21. (PI. III.) a dark space having started up at op, while the other dark space MN has descended to«»; the portion r sp 0, m n GH, have now the structure of the repulsive class, and the intermediate portion op n m-, that of the attractive class of crystals. The same change takes place in the upper plate A B ba. Fig. 20. (Pi. III.) which has the appearance shown at EF sr Fig. 21. (PI. III.) In one case I found that the fringes in the upper plate were exactly the reverse of those in the under plate. When the plate is cut perpendicularly to the fringes, an analogous effect is produced. Terminal fringes instantly ap- * See the Transactions of the Royal Society of Edinburgh, Vol. VIII. Part I. where the properties of this intermediate class of crystals are described. as exhibited in its propagation along plates of glass. 83 pear at the new extremities. A similar, though a more unex- pected result, was obtained by breaking in pieces a large plate, in which the crystallization was extremely irregular, polarising here and there a portion of white light. The plate had a small crack in it, and when broken in three pieces, principally along a line nearly parallel to its edge, each piece was regularly crystallized, having the two black spaces with their accompanying fringes of white light. The same effects are produced when the plate is cut in pieces by a slitting wheel, or has its shape altered by grinding. The preceding experiments are not easily made, as it is very difficult to cut this kind of glass with a diamond. It generally flies into many pieces as soon as it is scratched, and, when this does not happen, the pieces separate of their own accord, some time after the diamond has been applied. Scholium. The truth contained in the preceding Proposition is analo- gous to the celebrated experiment in magnetism, where the smallest portion detached from the extremity of a magnet, becomes itself a complete magnet, possessing distinct north and south poles. The exhibition of the same phenomena in glass transiently crystallized during the propagation of heat, as described in Prop. XIII., might have been supposed to arise from some new property of heat, which enabled it to act on the remote edge of the glass without any sensible indication of its presence. This opinion, however, is to a certain extent excluded by the results obtained with glass permanently crys~ tallized and having an uniform temperature. Any portion of the glass passes with the utmost facility from one crystalline M 2 84 Dr * Brewster on new properties of heat, structure to the opposite structure, and from one degree of crystallization to another, according to its position with regard to the edge of the plate ; and there cannot be an equilibrium among the forces, by which this change is produced, unless the plate exhibits the different sets of fringes which have al- ready been described. This optical polarity is produced by heat, just as electrical polarity is developed in the tourmaline, and other minerals by the same agent ; and there is as much reason to ascribe the production of the optical phenomena to the action of a peculiar fluid, as there is to explain the phenomena of elec- tricity and magnetism by the operation of magnetical and elec- trical fluids. The optical fluid, as we may call it, may be supposed to reside in all bodies whatever in its natural state, consisting of two fluids in a state of combination, and capable of being decomposed, and fixed in particular parts of a body by the agency of various causes. It would be a waste of time to point out the numerous and striking analogies, which exist between many of the results contained in this Proposition and some of the most interesting phenomena of electricity and magnetism. Some of them will be noticed in the demonstra- tion of a subsequent Proposition. as exhibited in its propagation along plates of glass. 85 / ■ -ns im atfsoqqo adt ol STi4oinJ?'. Proposition XXVI. When a rectangular plate of glass is brought to a red heat, and cooled as already described, it will acquire such a permanent structure as to exhibit the coloured fringes when polarised light is transmitted through any of the parallel faces by which it is bounded; every rectangular plate being considered as a solid contained by six parallel planes. The depolarising axes are distinctly developed in all these directions, and form angles of 45 0 with the common sections of the planes. The fringes described in the Proposition are extremely minute, in plates of glass of an ordinary thickness. They consist of the same number of sets, having the same cha- racter and properties as those seen through the broad sur- faces of the plates, and their maximum tint is generally lower, though sometimes higher, than the maximum tint of the large fringes produced by the broad surfaces. They are in general perfectly regular, even when there is a great degree of irregiu larity in the form of the large fringes. In a plate of glass which had various breadths, and which polarised a faint yellow of the first order in its central fringes, and a bright blue of the second order in its exterior fringes, the central tints seen through its edges varied with the breadth of the plate, from a faint yellow of the first order, to a deep blue of the second order. In order to examine with more accuracy the fringes formed by transmitting polarised light through the different faces of a plate of glass, I crystallized a rough parallelopiped of crown glass, which was about three inches long, and half an inch 4 8(> Dr. Brewster on new properties of heat , thick, and when it was properly cut, and polished on a lapi- dary's wheel, it had the dimensions shown in Figs. 22, 23, and 24, (PI. III.) The fringes seen through its two broadest surfaces are represented in Fig. 22. (PI. Ill,) The maximum tint of the central fringes is the commencement of the green of the second order, and that of the exterior fringes a green of the third order. In the fringes seen through the edges of the plate, which are shown in Fig. 23. (PI. III.) the maxi- mum tint of the interior set is a yellow of the second order, and that of the exterior set is a green of the third order. The fringes seen through the ends of the glass plate are very curious, and are represented in Fig. 24. (PI. III.) where A shows their form when the line AB is inclined 45 0 to the plane of primitive polarisation, and B their form when the line AB is parallel, or perpendicular to that plane. I have another parallelopiped of flint glass, about 4.3 inches, by 1 broad, and 1 inch deep, which was crystallized when in the form of a cylinder, and afterwards ground into the shape of a paralle- lopiped. It exhibited the same phenomena as the preceding, and equalled it in the fine display of numerous orders of colours. The beautiful figures produced by crossing these two pieces, surpass in splendour every optical phenomenon that I have seen. In these and several other specimens of very thick crystal- lized glass, the maximum tint was always diminished by the operations of grinding and polishing. The following descriptions of four specimens of crystal- lized glass will point out the effects which are produced by changing the form of the plate. as exhibited in its propagation along plates of glass. 87 No. 1 . One of the most curious specimens of crystallized glass which I have obtained, is a parallelopiped. about 0.38 of an inch broad and deep, and 1.11 inch long. It depolarises a faint yellow of the first order in the central fringe* when polarised light is transmitted through the faces of the paral- lelopiped. But when the light is transmitted along the axis of the parallelopiped, and when the lines AC, AB are parallel or perpendicular to the plane of primitive polarisation, the two images formed by calcareous spar exhibit the forms repre- sented in Figs. 25, 2 6. (PL III.) The first of these consists of a black cross surrounded with beautiful fringes of contrary flexure, and has bright green spots of the third order with a little yellow of the same order; their centre at the four angles, A, B, C,D. Figure 25. (PL III.) exhibits a form exactly com- plementary to Fig. 2 6 . (PL III.) and remarkable like it for the symmetry of its form. The coloured spots at the angles are now a brilliant pink, with a spot of blue in the middle of them. When the lines AB, AC are inclined 45 0 to the plane of primitive polarisation, the two images exhibit the forms represented in Figs. 27, and 28, (PL IV.) No. 2. Is another piece of glass of a square form, and 0.3 of an inch thick, it produced the central cross, and exhibited at the angles all the tints up to the blue of the second order arranged in circles, having the blue or maximum tint in the centre. See Figs. 29 and 30. (PL IV.) No. 3. A third plate 0.4 of an inch thick produced the same effect, the angular tints rising in this case to the yellow of the second order. No. 4. A fourth plate, 1.2 inch thick, produced fringes of contrary flexure like those of No. 1, but rising to the pink of the fourth order. 88 Dr. Brewster on new properties of heat, The terminal and lateral fringes are produced by No. 2, 3, 4, when they are turned round 45V Their complementary fringes are extremely beautiful. When No. 2 is combined with No. 3, they produce fringes of contrary flexure like No. 1. The nature and origin of ail these fringes are explained in a subsequent Proposition. Proposition XXVII. If a rectangular plate of crystallized glass which exhibits the fringes through its edges is inclined to the polarised ray in a plane perpendicular to the direction of the fringes, the central tint will descend in the scale as if the plate had increased in depth ; but when it is inclined in a plane parallel to the direc- tion of the fringes, the tint will ascend in the scale as if the plate had diminished in depth . The result contained in this Proposition was established by the same experiments which are described in Prop. XXIV., the fringes seen through the edges of the plate being used instead of those seen through its broad surfaces. The effects of inclination in these two cases are directly opposite. Proposition XXVIII, The regularity in the crystallization of a plate of glass according to one of its dimensions, is not disturbed by any irregularity of its crystallization in another direction. If a plate of glass is crystallized from a centre, as in Prop. XIX., or if a confused crystallization is induced by cooling it at different places, so that no distinct fringes can be seen when polarised light is transmitted through the broad surfaces of the plate, the fringes seen through its edges will be perfectly as exhibited in its propagation along plates of glass. 89 developed, and will possess the same properties as if the whole plate had been regularly crystallized. . Proposition XXIX. At the extremities A, B of every plate of crystallized glass, there are four portions N, S, N' S', at the boundary between the terminal and the lateral fringes , which possess a structure diffe- rent from the rest of the plate. These portions have their axes inclined to axes of the other parts of the glass. The portions N, N have their axes in the same direction, and S, S’ in a direction opposite to those of N, N'. When a plate of crystallized glass is exposed to a polarised ray, so that its length in the direction of the lateral and cen- tral fringes is parallel or perpendicular to the plane of primi- tive polarisation, it will exhibit the appearance shown in Fig. 31. (Pi. IV.) where all the lateral, central, and terminal fringes have vanished. Four luminous spots, however, N, S, N', S', will be seen at the extremities A, B, exhibiting tints which, in general, vary from the white of the first order to the pink of the second order, and sometimes exceed, and some- times fall below, the maximum tint of the central fringes. In order to examine the nature of these tints, I took a plate of glass, which when held in the position already mentioned, polarised at the points N, S, N', S', a blue of the second order. I then combined with it a plate of sulphate of lime which pola- rised the same tint, and which had its axis inclined 45°to the plane of primitive polarisation. The resulting tints at the angles N, N', were black, or that which was due to the difference of their actions, while the resulting tint at S, S', MDCCCXVI. N go Dr. Brewster on new properties of heat, was green, or that which was due to the sum of their actions. The same result was obtained when I combined with the above plate the central part of another crystallized plate which had the direction of its fringes inclined 45 0 to the plane of primitive polarisation. When the axis of the plate of sulphate of lime was turned round go 0 , or when the blue tint was taken from the lateral fringes of a plate of crystallized glass, having the direction of its fringes inclined 45 0 to the plane of primitive polarisation, an opposite effect was produced, that is, the resulting tint of the portions S, S', was black, and that of the portions N, N', green. In two crystallized plates of a square form which afforded the lateral sets of fringes C, D, and the terminal sets A, B, but no central sets, as shown in Fig. 32. (PI. IV.) the por- tions N, N', S, S', had the structure described in the Propo- sition. When the plate was held with the line A, B, parallel or perpendicular to the plane of primitive polarisation, it exhi» bited the phenomenon shown in Fig. 33. (PL IV. ) When any plate of crystallized glass, as AB, Fig. 31 . (PI. IV.) is cut through at CD, either by a diamond or upon a lapidary's slitting wheel, new fringes, n, n' , s, s' similar to N, N' S, S' start up at the new extremities of the plate. The fringes described in this Proposition may be called the diagonal fringes . as exhibited in its propagation along plates of glass. 91 Proposition XXX. In all the phenomena which have hitherto been described, the results are precisely the same, whether the anterior or the posterior face of the glass plate is exposed to the polarised ray; but, in the portions N, N' S, S' the tints change their character, according as one or other of the faces first receives the polarised light. If the plate a b, Fig. 34. (PI. IV.) has its lower surface ex™ posed to the polarised light, the portions n, n' exhibit, when combined with sulphate of lime, a tint due to the difference of their action ; and 5, 5' a tint due to the sum of their action ; but when the upper surface is exposed, as in Fig. 35. (PL IV. ) the portions .9, s' exhibit, in combination with sul- phate of lime, a tint due to the difference of their action, and the portions n, n' , a tint due to their sum. This curious phenomenon arises from the axes of the elementary crystals suffering an angular change of position, amounting to 90°, by turning the other side of the plate to the polarised ray, as shall be more particularly explained in a subsequent Pro- position. N 2 92 Dr. Brewster on new properties of heat , Proposition XXXI. If a crystallized plate a b, Fig. 34. (P/. IV. ) is placed symmetri- cally above A B, Fig. 31 . (P/. IV . ) either with the two anterior or the two posterior faces coincident , or with the anterior face of the one coincident with the posterior face of the other , or with the end a above A or b above B, or with b above A or a above B, in all these positions the tints polarised by the portions N, N' S, S' will ascend in the scale of colours , and be that which is due to the sum of the thicknesses of the plates. If the extremity a or b is placed above B or above A 6 so that the lines AB, a , b,form a continuous straight line , the tint polarised by the combination , will descend in the scale , and be that which is due to the difference of the thicknesses of the plates. The truth contained in this Proposition, has been established by direct experiment, although it might have been deduced from the Propositions which precede it. Proposition XXXII. When the neutral axes of a plate of crystallized glass are parallel or perpendicular to the plane of primitive polarisation, both the exterior and interior sets of fringes vanish , if the polarised ray is incident perpendicularly upon the plate ; but , if the plate is inclined to the incident ray, four sets of fringes are developed. They are separated from each other by three black spaces, and the fringes on each side of the central black line have the same character. When the lateral and the central fringes have vanished, the four diagonal fringes A, B, C, D, Fig. 3 6. (PL IV.) alone 93 as exhibited in its propagation along plates of glass. appear at a vertical incidence, but, upon inclining the plate to the incident ray, in the direction of its length OP, three black spaces mn , OP, qr, are gradually developed. One of them OP passes through the centre of the plate ; and between the black spaces are four sets of fringes 1,1; 1,1 ; 2,2; 2,2; By examining these fringes with a standard plate of sulphate of lime, and with plates of crystallized glass, I found that the fringes 1, 1, 1,1, had the same character as the diagonal fringes A, D, while the fringes 2,2, 2,2, had the same character as the other two diagonal fringes C, B. In; one plate, where the maximum tint of the interior fringe was a faint yellow of the first order, the fringes 1 , 1, 2, 2, consisted of a blue of the first order, and in another plate where the maximum tint of the interior fringe was a faint yellow of the second order, the fringes between m n and q r consisted of a green of the second order. Proposition XXXIII. When a plate of crystallized glass is placed on a red hot iron , the number of its fringes is increased. These additional fringes are the same that would have been produced by combining with the crystallized plate an uncrystallized plate of the same form and thickness , and subjected to the same temperature as the cry- stallized plate. They disappear when the glass cools, but the permanent fringes are not altered unless the heat be very intense , in which case , they suffer a small diminution. The results described in the Proposition were obtained by placing crystallized plates upon bars of iron of different tem- peratures. The plate was held out of the heat of the red hot iron, when its effect was combined with that of an uncrystal- 94 2 >. Brewster on nezv properties of heat, lized plate. The state of the crystallized plate is analogous to that of a bar of steel not saturated with magnetism. It is capable of receiving from heat a much higher degree of crys- tallization. See Prop. XXL Proposition XXXiV. When a plate of permanently crystallized glass is brought to an uniform temperature in boiling water , or boiling oil , and is then cooled in the open air , the tints descend in the scale , in propo?'- tion to the temperature employed , but , they again resume their former intensity when the plate acquires the temperature of the surrounding air. This diminution of the tints, arises from the production of the transient and unusual series of fringes described in Prop. XIV., which, being of an opposite character from the perma- nent fringes, necessarily causes them to descend in the scale. The effect is here precisely the same, as if the permanently crystallized plate had been combined, when cold, with a hot plate of the same thickness, oppositely and transiently crystal- lized by cooling. Proposition XXXV. When the centre of a plate of glass brought to a red heat is laid upon the summit of a small cylinder of iron standing vertically , it acquires in cooling a permanent structure . which exhibits black spaces , and fringes of a circular form, and the black cross exhi- bited in Fig. 19. (FI. III . ) In a specimen of plate glass crystallized in this manner, the dark spaces and the black cross are very distinctly developed, a yellow tint of the first order appearing between the dark as exhibited in its propagation along plates of glass. 95 spaces. When polarised light is reflected from this plate at the polarising angle, the preceding phenomena are very finely displayed. The minute fringes mentioned in Prop. XXVI. are also seen by looking through the edges of the plate, and are not affected by the circular crystallization. Proposition XXXVI. When a cylinder of glass is brought to a red heat, and cooled in the open air, it acquires a permanent crystallization, in which the principal sections of all the elementary crystals are directed to the axis of the cylinder. The phenomena exhibited by transmitting polarised light along a cylinder of this kind, about 9 ,~ inches long, and of an inch in diameter, are. shown in Figs. 37 and 38. (PI. IV.) where A B CD, Fig. 37. (PI. IV.) is the principal image, and abed , Fig. 38. (PI. IV.) the complementary image. The dark cross AC, BD, instead of having its arms inclined 45 0 to the horizon, as in Fig. 19. (PI. III.), has them parallel and perpendicular to the horizon, as the light transmitted through the cylinder happened to be polarised in the plane of the horizon. The luminous spaces between the arms of the cross contain about 10 beautiful rings of coloured light. The com- plementary image abed is marked with four dark spots, cor- responding to the four luminous portions round the central part of the cross, and the outer part has four dark sectors A, B, C, D, corresponding with the light ones in the other image, and formed of small concentric arches of a dark hue, fringed with tints of different colours. In ord r to see this phenomenon in all its beauty, it is necessary th.t the polarised ray beexactly parallel to the axis of the cylinder, as the slight- est deviation completely destroys the regularity of the figure. 9 6 Dr. Brewster on new properties of heat , The crystalline structure which exhibits the dark rectan- gular cross may be imitated, by forming a circle with various sectors of calcareous spar, having the principal sections of each directed to a common axis. Having had occasion to grind a part of a glass tube into the shape shown in Fig. 39. (PL IV.) I was surprised to observe, upon transmitting polarised light along its axis, and analysing it with calcareous spar, that it was depolarised in eight places, H 2, 3, 4, 5, 6, 7, 8, Fig. 40. (PI. IV.) When the line AS was parallel or perpendicular to the plane of primitive polari- sation, the tints were of the first order of Newton’s scale. The other image formed by the spar, had the appearance shown in Fig. 41. (PI. IV.) where the dark spots correspond to the white ones in Fig. 40. ( PL IV. ) . In order to discover the origin of these depolarising aper- tures, I cut another piece out of the same tube and polished the ends of the small cylinder, without grinding off any of the cylindrical circumference. When it w r as exposed to pola- rised light, it exhibited the appearance shown in Fig. 42. (PL IV.) where ACBD is a dark cross, separating four luminous sectors, and MNOP a dark circular space increasing in darkness towards the points M, N, O, P. If we now suppose the portions C a h, D c d to be cut off, something like eight luminous apertures will be left, as in Fig. 40. (Pl. IV.) This however is not the cause of the phenomenon. The four aper- tures on each side of the centre C, are the four diagonal fringes of the square pieces AC, BC, which act as if they were separated at C, the communication being nearly cut off. In this case, the cylindrical crystallization was converted into a rectangular crystallization by changing the shape of the glass. See Prop, XXV. as exhibited in its propagation along plates of glass. gy When polarised light was transmitted through the flat sides of the glass ABCD, Fig. 39. (PL IV.) four white spots were depolarised as shown at 1,2, 3, 4. All these spots have the same bluish white tint, but those marked i, 2, have their axis at right angles to that of the spots 3, 4.* The preceding phenomena as explained by the reasoning in Proposition XIX. furnish us with a complete explanation of the appearances exhibited by oil of mace , and described in a former paper.-f The dark and luminous sectors are obvi- ously produced by circular groups of crystals, having their axes directed to the same centre, and the halo, or nebulous image must be caused by the crystals having a form approach- ing to that of a sphere. This species of circular grouping is actually seen in a particular kind of adipocire , which I have noticed in the Paper already quoted. The axes of the crystals of adipocire, however, are not directed to the same centre, and therefore do not exhibit the same phenomena as oil of mace, Schoijum. The results contained in the Proposition, afford the most satisfactory explanation of the optical properties of Prince Rupert's drops described in a former Paper. (See Phil. Trans. 1815? p. 1.) The cleavages which they exhibit in lines con- verging to the axis of the drop, and in lines concentric with the outer surface, are necessary consequences of the radial crystallization explained in the Proposition, and may be re- garded as an ocular demonstration of its truth. * These spots are the diagonal fringes described in Prop. XXIX. f See Phil . Trans. 1815, p. 38, and 49. MDCCCXVI, o 98 Dr. Brewster on new properties of heat , Proposition XXXVII. When a piece of glass is regularly crystallized, every set of lateral fringes which it exhibits is accompanied with another set of an opposite kind , and the forces by which these fringes are produced, are not in equilibrio, unless when two sets of fringes of one character are opposed to two sets of fringes of the opposite character. The truth of this Proposition is demonstrated by all the preceding experiments. Some apparent exceptions to it will be stated in the Scholium. Scholium. The result announced in the Proposition, naturally leads us to point out the striking analogy which subsists between the phenomena of crystallized glass and those of magnetism. ' In order to avoid circuitous expressions, I shall consider the part of the glass which polarises the highest tint in one set of fringes as a north pole , and the part which polarises the highest tint in the opposite set as a south pole. 1. When heat is propagated along a plate of glass, or when glass is permanently crystallized by cooling, and exhibits the fringes shown in Fig. 2. (PI. II.), its poles will be arranged as in Fig. 43. (PI. IV.) which represents a section of the glass across the fringes. The north poles are situated at N, N', and there is a south pole in the middle at S', A, and B being the neutral points corresponding to the black spaces, where the one kind of polarity passes into the other. This arrangement of the poles is precisely the same as that of a as exhibited in its propagation along plates of glass. 99 magnetical needle, which has received its polarity by placing the north pole of a magnet upon its centre, and drawing it several times towards the one extremity without returning back again, and afterwards as many times towards the other extremity. The indefinite nature of the poles and fringes, when the plate of glass is high, as described in Prop. XVI. and XVII., and when the heat advances from one edge of the plate, is perfectly analogous to the indefinite polarity commu- nicated to a steel bar, by applying the pole of a magnet to one of its extremities. The same diffused polarity is acquired by hot glass, when one of its edges is cooled much more rapidly than the other. As two distinct poles, therefore, cannot be given to steel, by applying the magnet at one extremity, in like manner a distinct polarity cannot be communicated to glass, either by heating or cooling it solely at one edge, un- less when the height of the plate is very small. Such is the resemblance, indeed, between the two classes of phenomena, that a description of the state and progress of the poles in magnetising a steel bar, is an accurate description of the state and progress of the poles in crystallizing a plate of glass. 2. When a heated plate of glass is cooled in the open air, and produces the transient fringes described in Prop. XIV., the poles are arranged as in Fig. 44. (PI. IV.) where S, S' are south poles, and N a north pole in the middle, A and B being the two neutral points. This arrangement of the poles is exactly the reverse of the preceding, and is the same as that which takes place in a needle magnetised in the manner already described, but with the north instead of the south pole. 3. In a plate of glass of the same form and size as Fig. 45. O 2 ioo Dr. Brewster on new properties of heat , (PI. V.) the two preceding structures are combined. It has three black spaces, mn, \kv, op , the parts D and B have the same structure as that which produces the exterior sets of fringes, and the parts A,C, the same structure as that which produces the interior set in regularly crystallized plates. The poles are therefore arranged in the manner shown in Fig. 46. (PI. V.) which resembles a magnet with consecutive poles, 4. Out of nearly one hundred pieces of crystallized glass I have found but one which exhibited only two sets of fringes. The piece of glass AB, Fig. 47. (PL V.) was intersected in cooling with a crack mEn, which extended completely across the plate. The parts still cohered with such firmness, as not to separate when taken up in the hand. Upon exposing it to a polarised ray, it gave two white fringes E, F, separated by a dark space OP. The two fringes had opposite charac- ters, so that the poles were arranged as in Fig. 48. (PI. V.) which resembles that of a perfect magnet. This state of the poles, however, is in the case of glass a state of violence, for when the plate broke in two pieces at the crack mEn, the fringes vanished entirely, and it retained no mark whatever of its former crystalline state. The other portion T did not act upon polarised light either before or after the separation. The pressure of the portion T, therefore, had not allowed the other piece of glass to recover from the state of constraint in which it was held. as exhibited in its propagation along plates of glass. i o i Proposition XXXVIII. To explain the origin and form of the different sets of fringes described in the preceding Propositions. j. On the fringes produced by rectangular plates. It is i>6t easy to ascertain in what manner the various sets of opposite fringes are produced during the heating and cooling of glass, (See Prop. XXXIX.) but it is obvious from the pre- ceding experiments, that when a plate of glass is either transi- ently or permanently crystallized, all the elementary crystals of which it is composed, turn one of their neutral axes in the direction of the current of heat. The principal axes of the crystals which form the exterior fringes, are parallel to the one edge, and perpendicular to the other. Thus in Fig. 49, (PI. V. ) the axes of the exterior fringes are perpendicular to AD and BC, and the axes of the terminal fringes are perpendicular to AB and DC, while the axes of the interior fringes are parallel to AD and BC. Let us now consider, what change should take place in the position of the crystals situated at the angles A, B, C, D. An elementary crystal at E will have its neutral axes perpendi- cular to AD, as it is out of the reach of the forces which act upon the crystals at the edges AB, DC ; but, a crystal G in the diagonal AH, BH being similarly situated with respect to the edges AB, AD, will have a tendency to turn its axis both in the direction AB, and in the direction AD, and being unable to obey both these solicitations, it will turn it in the direction of the diagonal AH, forming angles of 45 0 , with the axes of all the other crystals of which the glass is composed. Any / 102 Dr. Brewster on new properties of heat , other crystal a situated out of the diagonal AH, will be acted upon by forces proportional to its distances am, an, from the edges AB, AD, and in the direction of these lines. It will therefore turn its axes in the direction a A the diagonal of the parallelogram A nam. In like manner it may be shown, that all the other crystals will turn their axes towards A in lines diverging from A as a centre. Each angular portion, there- fore, exactly resembles an inverted quadrant of the cylindrical piece of glass represented in Fig. 37, (PI. IV.) and described in Prop. XXXIV., and consequently an arm of the black cross will appear in the diagonal AH in every quarter of a revolu- tion. The diagonal portions AH will be dark when all the other fringes are visible, and the diagonal fringes will appear in their full beauty, when the rest have vanished. Since the diagonal fringes at A and C have their axes AH, CH parallel, they will exhibit tints of the same character, and opposite to those of B and D which have their axes BpI, DH at right angles to the former. The reason is therefore manifest, why each diagonal fringe changes its character by inverting the plate, for when this inversion takes place the axis of the dia- gonal portion is put into a position at right angles to its first position. These observations enable us to explain the appearances shown in Fig. 10, and 11, (PI. II.) and described in Prop. XVII. In Fig. 10, where the plate is narrow, the black spaces at C and D, bisecting the angles, interfere and nearly obliterate the interior fringes, but in Fig. 11, where the plate is consider- ably broader, the influence of the angular crystallization does not extend so far, and therefore the interior fringes are seen at 2, Fig. 11. The state of the crystallization at the angles as exhibited in its propagation along plates of glass. 103 A, B. C, D, Fig. 49, ( PL V. ) is also peculiar. The glass cools more rapidly there than at any other part, and therefore a higher tint is developed at the angles, than towards the middle of the plate. 2. On the fringes produced by square pieces of glass. If the breadth of the glass plate is equal to its length, as in Fig. 32, ( PL IV.) all the four diagonal portions nearly meet, and therefore, when the lateral and terminal fringes are developed, the central part is altogether black, as the central fringes have entirely disappeared. When the line AB is parallel or perpendicular to the plane of primitive polarisation, the diagonal fringes appear as in Fig. 33, (PL IV.) being always separated from each other by a black space in the form of a cross. This black cross is a necessary accompaniment of the diagonal fringes, for it follows, from the reasoning in Sect. I. of this pro- position, that all the crystals situated in the central lines, AB, CD, have their neutral axes in the directions AB, CD, and therefore cease to depolarise the incident light when the diagonal fringes are in full perfection. 3. On the fringes produced by cylindrical pieces of glass. As the heat radiates most copiously from the heated cy- linder, in lines perpendicular to its surface, that is, in lines directed to its axis, it follows that the axis of all the elementary crystals will be directed to the axis of the cylinder. The uni- formity of the radiation in every part of the cylinder, will produce an uniformity of structure, which will develope si- milar tints at similar distances from the axis, and thus produce fringes concentric with the cylindrical circumference. The effect of a radial crystallization combined with an angular \ • . 104 Dr. Brewster on new properties of heat , crystallization is shown in Fig. 50, (PL V.) where ABCD is a plate of glass cooled upon a cylinder of iron at its centre. See Fig. 19, (PL III.) and 29, (PL IV.) When the section of the glass is a polygon of any number of sides, the form of its fringes may be easily deduced from the principles which have already been established. When the section is a triangle, no regular figure is seen. If the triangle is equilateral, the lines which bisect the angle, and those which are perpendicular to the sides, are inclined to each other 120°. So that the axes of the crystals are not symmetrically related to the rectangular axes of the particles of light. When the glass is a sphere, the axes are all directed to its centre. Proposition XXXIX. To ascertain the probable mechanical condition of the parts of the glass that produce the different sets of fringes. 1 y a peculiar application of the compressing forces, I have even succeeded in obtaining uniform tints like those produced by plates of sulphate of .lime of equal thickness. MDCCCXVf. P io6 Dr. Brewster on new properties of heal s Proposition XL. Radiant heat is not susceptible of refraction , and is incapable of permeating glass like the luminous rays. The propagation of radiant heat along glass can be ren- dered visible to the eye by the methods described in the first section of this paper. It advances from the heated edge of the plate, crystallizing the glass during its passage, and pro- ducing changes in those parts of the plate where it does not exist in a sensible state. If the radiant heat is received upon a convex lens, the very same effect is produced. Instead of being bent, like light, at the convex surfaces, it advances, whatever be the angle of incidence, in lines perpendicular to that surface, crystallizing the glass in its progress ; and, as soon as it has reached the second surface, it is again discharged, as if from a new source of heat. This experiment I conceive to be an ocular demon- stration of the first part of the Proposition. Dr. Herschel, in his celebrated inquiry into the properties of invisible heat, has deduced the very opposite result from several experiments ; but, independently of the minuteness of the effects which he observed, it is manifest, that the thermo- meter placed in the focus of his lens, received its heat by ra- diation from the lens itself ; and it is also demonstrable, that a convex lens, radiating heat at an uniform temperature, will produce *a greater effect upon a thermometer placed in its axis, than upon another having a different position. From the form of the lens, the edges are always the coldest, giving out their heat to the metallic ring in which they are placed^ as exhibited in its propagation along plates of glass. 107 and therefore, the discharge of heat must be most copious in the direction of the axis.* The inability of radiant heat to pass through glass, may be considered as a consequence of its refusing to yield to the refractive force ; for we can scarcely conceive a particle of radiant matter freely permeating a solid body, without suffer- ing some change in its velocity and direction. The ingenious experiments of M. Prevost of Geneva, and the more recent ones of M. Delaroche, have been considered as establishing the permeability of glass to radiant heat. M. Prevost em- ployed moveable screens of glass, and renewed them con- tinually, in order that the result which he obtained might not be ascribed to the heating of the screen; but such is the rapidity with which heat is propagated through a thin plate of glass, that it is extremely difficult, if not impossible, to observe the state of the thermometer, before it has been affected by the secondary radiation from the screen. The method em- ployed by M. Delaroche of observing the difference of effect, when a blackened glass screen, and a transparent one, were made successively to intercept the radiant heat, is liable to an obvious error. \ * The circumstance of the glass cooling most rapidly at the edges, which may be proved by exposing it to a polarised ray, enables us to account for the anomalous and hitherto unexplained fact observed by the younger Euler, that the focal length of a lens is shortened when its temperature is increased. The observation having always been made when the lens was actually cooling, the density, and consequently the refractive power had increased towards the circumference of the lens, and therefore its focal length was diminished. Might not the spherical aberration of lenses be diminished, and even corrected, by giving them a variable density from their vertex ? I have three object glasses of this kind, two crystallized and one uncrystallized, and ground carefully upon the same tool ; but I have not yet been able to examine their optical properties. • P 2 loB Dr. Brewster on new properties oj heat, The radiant heat would find a quicker passage through the transparent screen, and therefore, the difference of effect was not due to the transmitted heat, but to the heat radiating from the anterior surface. The truth contained in M. Dela- roche’s fifth Proposition is almost a- demonstration of the fallacy of all those that precede it. He found that M a thick plate of glass, though as much, or more permeable to light than a thin glass of worse quality, allowed a much smaller quantity of radiant heat to pass/' If he had employed very thick plates of the purest flint glass, or thick masses of fluid that have the power of transmitting light copiously, he would have found that not a single particle of heat was capable of passing directly through transparent media. Proposition XLL To construct a chromatic thermometer for measuring differences of temperature below that of find glass, by the optical effects which they produce. Differences of temperature have hitherto been measured by the expansions and contractions which they produce in solid, fluid, or gaseous bodies, and all the various thermometrical instruments that have been constructed, differ from each other only in the' method by which these mechanical effects are rendered visible. The experiments contained in the first Section of this Paper, present us with an entirely new princi- ple for the construction of a thermometer. We. have there seen, that the tints polarised by a plate of glass, increase with the temperature by which they are produced, and therefore these tints may be used as a measure of the temperature, after as exhibited in its propagation along plates of glass. log the tints, corresponding to several points in the thermometri- cal scale, have been accurately ascertained. An instrument of this kind which I have constructed, is-re pre- sented in Fig. 51 , (PI. V. ) where ABC is a series of 20 plates of glass, whose length AB is 3.2 inches, their breadth 1.2 inches, and their united thicknesses BC 5.4 inches. A metallic vessel, DEFG, has its bottom formed of a thin layer of tin or lead, or any other suitable metal which can be poured in a fluid state upon the upper edges of the glass plates, so as to touch them in every part. This perfect contact may be obtained for higher temperatures, by grinding the bottom of the metallic vessel till it touches the edges of the glass in every point. When a heated fluid is poured into the vessel DEFG, its heat will be instantly communicated to the edges of the plates, and when exposed to a polarised ray, subsequently analysed by reflection from a transparent body, they will exhibit the coloured fringes at AB. Now every tint in the scale of colours has a corresponding numerical value, which becomes a correct measure of the temperature of the fluid. Instead of pouring the fluid into the vessel, we may remove the vessel altogether, and plunge the glass plates into the fluid. They must then be taken quickly out and suspended in a position where they are properly exposed to polarised light. The maximum tint which they develope at the centre, while cooling, is a measure of the temperature which they have acquired in the fluid. In order to obtain some idea of the nature of the scale, I made the following trials.- — The heat of my hand when applied to the edges of 20 plates of glass, produced instantly the fringes with the black spaces. With 12 plates I have 210 Dr. Brewster on new properties of heat, produced the yellow of the first order ; and when one plate only was used, the black spaces, and the bluish white fringes tvere distinctly visible. A temperature of about 8o°, that of the glass being 6o°, when applied to 20 plates, polarised in the central fringe a yellow of the first order, which corres- ponds to a tint whose value is 4 in the scale of colours. Hence, one plate would have produced a tint corresponding to = 0.20 of the scale. When one of the plates was placed upon a bar of red hot iron, just visible in daylight, it polarised in the central fringe the commencement of the green of the second order, which corresponds to 9.35 in the scale. Now the difference of temperature answering to 0.20 was 8o° — 6o° = 20°. Hence we have As 0.20 : 9.35 = 20° : 935 0 the difference of temperature of the iron and the glass. The temperature of the iron is therefore 935°+ 6o°== 995 °. If we suppose the tints to be so indefinitely marked that the eye can only observe units of the scale of colours, we shall, even in this case, have a scale of 187 to measure the temperature of 935 0 — 20° = 9i5°, which is a scale having each of its divisions equal to nearly 4 0 . 9. The tints, however, are much more definite than we have supposed, for in the second order of colours, in which the observations may always be made, the eight different tints have the follow- ing measures. exhibited in its propagation along plates of glass, Tints. Values. Violet - 7.20 Indigo - - 8.l8 Blue - - - 9.00 Green 97 1 Yellow 1040 Orange - 11.11 Bright red 11.83 Scarlet - - 12.67 Now the difference of the values for violet and scarlet is 54 7, corresponding to seven different colours. Hence, upon the supposition that the eye can distinguish merely these separate colours, the accuracy of the scale is increased in the ratio of 547 to 7, that is, from 1S7 to 239, which gives 3°.83 for the value of each unit. It is quite manifest, however, that we can distinguish at least three points in the developement of each colour; and even if this could not be accomplished by the unassisted eye, it can readily be effected, to a much greater extent, by cross- ing the fringe with a standard crystallized plate, and observing the degree of curvature which is produced in the fringes. This standard plate may be shaped like a wedge, so as to exhibit the variation of its tints to a great degree of minute- ness. In a wedge of this kind, two inches long, and ground out of a crystallized parallelepiped, so as to have an angle of 8°, the highest tint is between the blue and the white of the first order, corresponding to 2.20 of the scale, and the lowest tint is between the black and the blue, corresponding to about 0.8. We have therefore a scale of nearly 2 inches to measure a variation in the tints amounting to 2.20 — 0.80 = 140, The 112 Dr. Brewster on new properties of heat , method of using the wedge or nonius is shown in Fig. 55, (PL V.) "where AB is the wedge, exhibiting tints which vary in in- tensity from A to B. If we wish to ascertain the tints of a piece of crystallized glass CD, it must be held as in the figure, and moved from A to B. When it has the position CD, the intersectional figure is open horizontally, which shows that the tints of AB, at the point m, are higher than those of CD. In the position GH the figure is open vertically, and therefore the tints of the wedge at 0 are lower than those of the plate. But in the intermediate position EF, a dark cross is produced, which evinces the perfect equality between the tints of the wedge at n and those of the plate EF. In this manner all tints may be compared with each other, and referred to the scale of colours. By forming wedges of crystallized glass in this way, we are enabled to observe the gradations by which the tints pass into each other, and to perform many experiments on the orders of colours, which would otherwise have been imprac- ticable. The sensibility of the preceding instrument depends on several other causes. 1st. On the intensity of the polarised pencil. 2d. On the transparency of the glass. And 3d. On the removal of all internal reflections at the junction of the plates. In the instrument with 20 plates already mentioned, the glass has a green tinge, and the polarised light suffers no fewer than 40 reflections before it reaches the eye. In order to remove these evils, the light should be polarised by re- flection from several of the thinnest and most colourless plates of glass that can be procured, so that each plate may polarise and reflect the light which is transmitted through the plate as exhibited in its propagation along plates of glass, 113 immediately above it. In this way, I have obtained a light as brilliant as that which is reflected from silver. The internal reflections may be removed by interposing a film of oil be- tween each of the plates, so as to rise above that part of the plate where the tint is to be examined. If the instrument is properly constructed, with these pre- cautions, I have no hesitation in saying, that it will distinctly mark a difference of temperature equal to i° of Fahrenheit's thermometer.* I have thus endeavoured to give a brief view of the nume- rous experiments which have led to the general results un- folded in the preceding enquiry. The length to which this paper has extended, has prevented me from describing many phenomena, and detailing many experiments, which, though interesting in themselves, did not appear absolutely necessary to the establishment of general views. Had I included in the demonstration of every proposition, the various experimental proofs which I had actually obtained, this Paper would have swelled to a size which would have rendered it unfit for the consideration of the Royal Society ; I have, therefore, selected such experiments as appeared most striking, and have left the detail of the rest, and the repre- sentation of many of the phenomena, for a separate work which I propose to publish on the subject.^ * This thermometer possesses advantages peculiar to itself, in enabling us to mea- sure the intensity of the heat produced by the friction of any two substances whatever. When glass is one of the substances, the method of employing the instrument is ob- vious. When any other substance is used, it must be fixed, without cement, to the lower edge of one or more plates of glass, so that its rubbing surface may be as near as possible to the edge of the glass. f There is one practical result of the preceding experiments, which deserves parti- cular notice. All articles made of glass, whether they are intended for scientific or MDCCCXVI. O 1 14 Dr. Brewster on new properties of heat , &c. 1 cannot conclude this paper without expressing my obliga® tions to the Rev. Dr. Milner of Cambridge, for the very handsome manner in which he transmitted to me a quantity of thick plate glass, which I found it impossible to procure from any other quarter. I was thus enabled to obtain several new results, and to complete many experiments that had been left imperfect.* I have the honour to be, &c. DAVID BREWSTER. To the Right Hon. Sir Joseph Banks, Bart. G. C. B. P. R. a S. Sfc. Sfc. 8 fc. domestic purposes, should be carefully examined by polarised light before they are purchased. Any irregularity in the annealing, or any imperfections analogous to what workmen call pins in pieces of steel, will thus be rendered visible to the eye, by their action upon light. The places marked out by these imperfections, are those where the glass almost always breaks when unequally heated, or when exposed to a slight blow. Hence, glass-cutters would find it of advantage to submit the glass to this examination before it undergoes the operations of grinding and polishing. * Since the preceding letter was written and sent to Sir Joseph Banks, I have learnt that M. Seebeck has published in a German Journal for Dec. 1814, an account of some experiments similar to those contained in Sect. II. of this Paper. As there is, so far as I know, only one copy of this Journal in England, in the possession of Dr. T homson, I have not been able to obtain a sight of it, in order to compare M. See- beck’s results with mine. I understand, however, that he has discovered the fact, that a plate of red hot glass often acquires, in cooling, the depolarising structure, and that the tints depend upon the mode of cooling the glass. This result, however, has no connection whatever with the new properties of heat unfolded in the first Section of the preceding Paper, and does not anticipate the developement of the phenomena contained in the Second Section. The discovery of the new property of heat was made by me early in 1814, and an account of it was read before the Royal Society on the 39th of May, 1814. See PbiL Trans . 18:4, p. 436. nffW'fSfM/ffm Th ilos. Thins. MD CCCXVI-/?^ J. p.n4- >ajcle jo. 6 . 33 . N z' / \ \ / / i Th ilos. Trans. MI) CCC X\T.T/ate II. p.in z' / \ \ / / i z' / \ \ / / i .jCOo. 'cu/Sce jc. z' / \ \ / / i ThOos-. Tram. MD CCj CXVL Plate p. J14 . C »5 3 V. Farther experiments on the combustion of explosive mixtures confined by wire-gauze , with some observations on flame. By Sir H. Davy, LL. D. F. R. S. V.P.R. I. Read January 25, 1816?. I have pursued my enquiries respecting the limits of the size of the apertures and of the wire in the metallic gauze, which I have applied to secure the coal miners from the explo- sions of fire-damp. Gauze made of brass wire, of an inch in thickness, and containing only ten apertures to the inch, or 100 apertures in the square inch, employed in the usual way as a guard of flame, did not communicate explosion in a mixture of 1 part of coal gas and 12 parts of air, as long as it was cool, but as soon as the top became hot, an explosion took place. A quick lateral motion likewise enabled it to communicate explosion. Gauze made of the same wire, containing 14, apertures to the inch, or 196 to the square inch, did not communicate explosion till it became strongly red hot, when it was no longer safe in explosive mixtures of coal gas ; but no motion that could be given to it, by shaking it in a close jar, produced explosion. Iron ware gauze of and containing 24,0 apertures in the square inch, was safe in explosive mixtures of coal gas, till it became strongly red hot at the top. i j6 Sir Humphry Davy on the combustion of Iron wire gauze of and of 24 apertures to the inch, or of 57 6 to the square inch, appeared safe under all circum- stances in explosive mixtures of coal gas. I kept up a con- tinual flame in a cylinder of this kind, 8 inches high and 2 inches in diameter, for a quarter of an hour, varying the pro- portions of coal gas and air as far as was compatible with their inflammation ; the top of the cylinder, for some minutes, was strongly red hot, but though the mixed gas was passed rapidly through it by pressure from a gasometer and a pair of double bellows, so as to make it a species of blast furnace, yet no explosion took place. I mentioned in my last communication to the Society, that a flame confined in a cylinder of very fine wire gauze, did not explode a mixture of oxygene and hydrogene, but that the gases burnt in it with great vivacity. I have repeated this experiment in nearly a pint of the most explosive mixture of the two gases ; they burnt violently within the cylinder, but, though the upper part became nearly white hot, yet no explosion was communicated, and it was necessary to with- draw the cylinder to prevent the brass wire from being melted. These results are best explained by considering the nature of the flame of combustible bodies, which, in all cases, must be con- sidered as the combustion of an explosive mixture of inflammable gas, or vapour and air ; for it cannot be regarded as a mere combustion at the surface of contact of the inflammable matter : and the fact is proved by holding a taper or a piece of burning phosphorus within a large flame made by the combustion of alcohol, the flame of the candle or of the phosphorus will explosive mixtures confined by wire-gauze , &e. 117 appear in the centre of the other flame, proving that there is oxygene even in its interior part. The heat communicated by flame must depend upon its mass ; this is shown by the fact that the top of a slender cylinder of wire-gauze hardly ever becomes dull red in the experiment on an explosive mixture, whilst in a larger cylin- der, made of the same material, the central part of the top soon becomes bright red. A large quantity of cold air thrown upon a small flame, lowers its heat beyond the explosive point, and in extinguishing a flame by blowing upon it, the effect is probably principally produced by this cause, assisted by a dilution of the explosive mixture. If a piece of wire-gauze sieve is held over a flame of a lamp or of coal gas, it prevents the flame from passing it, and the phenomenon is precisely similar to that exhibited by the wire- gauze cylinders ; the air passing through is found very hot, for it will convert paper into charcoal ; and it is an explosive mixture, for it will inflame if a lighted taper is presented to it, but it is cooled below the explosive point by passing through wires even red hot, and by being mixed with a considerable quantity of air comparatively cold. The real temperature of visible flame is perhaps as high as any we are acquainted with. Mr. Tennant was in the habit of showing an experiment, which demonstrates the intensity of its heat. He used to fuse a small filament of platinum in the flame of a common candle; and it is proved by many facts, that a stream of air may be made to render a metallic body white hot, yet not be itself luminous. A considerable mass of heated metal is required to inflame nB Sir Humphry Davy on the combustion of even coal gas, or the contact of the same mixture with an extensive heated surface. An iron wire of of an inch and 8 inches long red hot, when held perpendicularly in a stream of coal gas, did not inflame it, nor did a short wire of one sixth of an inch produce the effect held horizontally; but wire of the same size, when six inches of it were red hot, and when it was held perpendicularly in a bottle, containing an explosive mix- ture, so that heat was successively communicated to portions of the gas, produced its explosion. A certain degree of mechanical force which rapidly throws portions of cold explosive mixture upon flame, prevents explosions at the point of contact ; thus on pressing an explo- sive mixture of coal gas from a syringe, or a gum elastic bottle, it burns only at some distance from the aperture from W'hich it is disengaged. Taking all these circumstances into account, there appears no difficulty in explaining the combustion of explosive mix- tures within and not without the cylinders ; for a current is established from below upwards, and the hottest part of the cylinder is where the results of combustion, the water, car- bonic acid, or azote, which are not inflammable, pass out. The gas which enters is not sufficiently heated on the outside of the wire, to be exploded, and as the gases are no where confined, there can be no mechanical force pressing currents of flame towards the same point. It will be needless to enter into further illustrations of the theoretical part of the subject: and I shall conclude this Paper by stating, what I am sure will be gratifying to the Society, that the cylinder lamps have been tried in two of the most explosive mixtures confined by wire-gauze , &c. ng dangerous mines near Newcastle, with perfect success ; and from the communications I have had from the collieries, there be immediately adopted in all the mines in that neighbourhood, where there is any danger from fire-damp. is every reason to believe that they will C iso 3 VI. Some observations and experiments made on the Torpedo of the Cape of Good Hope in the year 1812. By John T. Todd, late surgeon of His Majesty’s ship Lion . Communicated by Sir Everard Home, Bart. V.P.R . S. Read February 15, 181b. Wh..L 5 T the Lion was stationed at the Cape of Good Hope, the seine, as is the custom throughout the navy, was frequently employed in procuring fish for the use of the ship's company, and besides the more edible kinds, many of the Torpedo were caught. In this manner the opportunity was afforded me of making the following observations, some of the imperfections of which I must be allowed to attribute to the “ manus nuda” of my situation. The fish were generally caught early in the morning, and examined as soon after as possible. When this could not be done, they were placed in buckets of sea-water, where they sometimes remained alive for three, and in one instance for five days. The torpedo is seldom met with to the eastward of the Cape of Good Hope. Hence, whilst I rarely failed in pro- curing them in Table Bay, I never but once succeeded in doing so in Simon's Bay, although the opportunities were the same in both places. It was never caught but by the seine, although the hook and line, with bait of every variety, were as often made use of exactly in the same situations. It differs in no respect, as far as I have been able to observe, from the same fish of the northern hemisphere, except that it was never 121 on the Torpedo at the Cape of Good Hope. found so large ; being never more than eight, nor less than five inches in length, and never more than five, nor less than three inches and a half in breadth. The colour of the animal is various ; the upper surface being generally hazel grey, reddish brown, or purple ; the under surface greyish white, yellowish white, or white with black patches. The columns of the electrical organs were larger, and less numerous in proportion, than those described by Mr. Hunter, in the torpedo caught at La Rochelle. When separate and uninfluenced by external pressure, they appear to be of the form of cylinders, as is shown as nearly as possible by sus- pending them by one of their extremities. The different forms which they exhibit in a horizontal section of the whole organ, are produced by their unequal attachment to one another by the intermediate reticular substance. The electrical organs are so placed within the curvature of the semilunar cartilages of the large lateral fins, as to be entirely under the influence of the muscles, which are inserted into these cartilages. So that in any lateral motions of these cartilages towards the trunk, or in any increase of curvature of these cartilages, the electrical organs must be compressed. There appears also to be a muscular structure, which connects the anterior part of these cartilages to a process projecting from the anterior part of the cranium, the action of which must tend to increase this effect. The inferior and posterior terminations of the small lateral fins are covered with laminae of osseous matter, which are enveloped in the epidermis. A much larger proportion of nerves is supplied/to the electri- cal than to any other organs. This has appeared to others so MDCCCXVI, R ' * - AS AA AAAAtcT C A\X ite, 122 Mr. Todd's observations and experiments important an observation, that it may be repeated with pro- priety. The shocks received from the torpedos which I examined. Were never sensible above the shoulder, and seldom above the elbow-joint. The intensity of the shock bore no relation to the size of the animal (sensation being the only measure of intensity), but an evident relation to the liveliness of the animal, and vice versa. The shocks generally followed simple contact, or such irritation as pressing, pricking, or squeezing, sometimes immediately, and sometimes not until after frequent repetition. Not unfrequently, however, animals apparently perfectly vivacious suffered this irritation without discharging any shock. There appeared no regularity of interval between the shocks. Sometimes they were so fre- quent as not to be counted ; at other times, not more than one or two have been received from one animal; and, in a few instances, it has been impossible by any irritation to elicit shocks from some of them. When caught by the hand, they sometimes writhed and twisted about, endeavouring to extri- cate themselves by muscular exertion, and did not, until they found these means unavailing, discharge the shock. In many instances, however, they had recourse to their electrical power immediately. The electrical discharge was, in general, accompanied by an evident muscular action. This was marked by an apparent swelling of the superior surface of the electrical organs, par- ticularly towards the anterior part, opposite to the cranium, and by a retraction of the eyes. It was so evident, that when the animal was held in the hand of another person, I was often able to point out when he received the shock. In this. on the Torpedo at the Cape of Good Hope. 12 g however, I was also sometimes deceived ; and I think I have received shocks (particularly when the animal has been debi- litated, and the shocks weak,) without having been able to observe this muscular action. Two of these animals, as nearly alike in every circumstance as possible, being each placed in a separate bucket of sea- water, from one of them frequent shocks were elicited by irritation, viz. simple contact, or pricking, &c. ; the other was allowed to remain undisturbed. The former became languid, the in- tensity of its shocks diminished, and it soon died ; the last shocks being received in a continued succession, producing pricking sensations never extending above the hand. The latter continued vivacious, and lived until the third day. This experiment was frequently repeated with the same results ; and it might be observed, in general, where there was no di- rect comparison made, that those which parted with the shocks most freely soonest became languid, and died ; and those which parted with them most reluctantly, lived the longest. Two torpedos being placed exactly in the same circum- stances as the last- mentioned, from one shocks were elicited until it became debilitated. It was then allowed to remain until the following day. When they were both examined, it was found that the animal from which no shocks had been previously received, discharged them very freely ; but it was with the greatest difficulty that they could be procured from the other. Having made an incision on each side of the cranium and gills of a lively torpedo, I pushed aside the electrical organs, so as to expose and divide their nerves. The animal was then placed in a bucket of sea-water. On examining it in Re 124 Mr. Todd’s observations and experiments about two hours afterwards, I found it impossible to elicit shocks from it by any irritation ; but it seemed to possess as much activity and liveliness as before, and lived as long as those animals from which shocks had not been received, and which had not undergone this change. Two of these animals being procured, the nerves of the electrical organs of one of them were divided after the manner above described. They were placed each in separate buckets of sea-water, and allowed to remain undisturbed. This ^vas performed in the morning, and when examined in the evening, t was impossible to distinguish between the liveliness or activity of either. Of two of these animals, the nerves of the electrical organs of one of them were divided. Being placed each in separate buckets of sea-water, they were both irritated as nearly alike as possible. From the perfect animal, shocks were received ; after frequent repetition it became weak, and incapable of discharging the shock, and soon died. The last shocks were not perceptible above the second joint of the thumb, and so w T eak as to require much attention to observe them. From the other no shocks could be received ; it appeared as vivacious as before, and lived until the second day. This experiment was frequently repeated with nearly the same results. The nerves of one electrical organ only being divided in a lively torpedo, from which shocks had been previously received, on irritating the animal it was still found capable of communicating the shock. Whether there was any difference in the degree of intensity could not be distinctly observed. One electrical organ being altogether removed, the animal still continued capable of discharging the electrical shock. on the Torpedo at the Cape oj Good Mope, 125 Having divided one of the nerves of each electrical organ! in a torpedo, from which shocks had been previously received, I still found the animal capable, after this change, of commu- nicating the shock. Having introduced a wire through the cranium of a torpedo, which had been communicating shocks very freely, all motion immediately ceased, and no irritation could excite the electrical shock. I never received a shock from a torpedo, when held by the extremities of the lateral fins or tail. The preceding account appears to me to afford grounds for the following conclusions. 1. That the electrical discharge of this animal is in every respect a vital action, being dependent on the life of the animal, and having a relation to the degree of life and to the degree of perfection of structure of the electrical organs. 2. That the action of the electrical organs is perfectly voluntary. g. That frequent action of the electrical organs is injurious to the life of the animal ; and, if continued, deprives the animal of it. Is this only an instance of a law common to all animals, that by long continued voluntary action they are deprived of life ? Whence is the cause of the rapidity with which it takes place in this instance ? Or is it owing to the re-action of the shock on the animal ? 4. That those animals, in which the nerves of the electrical organs are intersected, lose the power of communicating the shock, but appear more vivacious, and live longer than those in which this change has not been produced, and in which this power is exerted. Is the loss of the power of commit- i Mr . Todd's observations and experiments , &c. nicating the shock to be attributed to the loss of voluntary power over the organ ? Does this fact bear any analogy to the effects produced by castration in animals ? 5- That the possession of one organ only is sufficient to produce the shock. 6. That the perfect state of all the nerves of the electrical organs, is not necessary to produce the shock. And, 7. From the whole it may be concluded, that a more intimate relation exists between the nervous system and elec- trical organs of the torpedo, both as to structure and func- tions, than between the same and any organs of any animal with which we are acquainted. And this is particularly shown* 1st, By the large proportion of nerves supplied to the electrical organs : and, 2d, By the relation of the action of the electrical organs to the life of the animal, and vice versa , v- • \ to & ■ ■ k • - \ . : t 127 1 VII. Direct and expeditious methods of calculating the excentric from the mean anomaly of a planet. By the Reverend Abram Robertson, D.D. F.R. S. Savilidn Professor of Astronomy in the University of Oxford , and Radcliffian Observer. Commu- nicated by the Right Hon. Sir Joseph Banks, Bart. G. C. B. P. R. S. Read February 15, 181b. Since the publication of Kepler's discoveries in astronomy, the attention of men of science has frequently been directed to the problem distinguished by his name, and their exertions have frequently been employed to overcome the acknowledged difficulty of its solution. A statement of the various degrees of success, with which these endeavours have been made, is foreign to the present design. An account of this kind is now also needless, as Dr. Brinkley's examination of such attempts, published in the ninth volume of the Transactions of the Royal Irish Academy, affords a satisfactory review of most of the proceedings on this subject, previous to the year 1802. After the following methods had occurred to my consider- ation, and I had fully proved their utility by actual application to examples, I was anxious to ascertain whether any author had anticipated me in the manner in which the investigations are conducted. With this view I examined such solutions as are referred to in Dr. Brinkley's very able Memoir, all those mentioned by Montucla,* of which I could procure a sight, * Histoire des Mathematiques, Tom. II. p. 343, &c. I have searched, without success, for Lorgna’s and Trembley’s publications.