t»^'^ "^^1^ :^ -^'- >e- ##■ ,^^ r 1^ 1 r/ :^ ^*J THE physical nature of the sun's body, whether it be solid* gaseous, or both, is a matter of doubt to philosophers. The peculiar appearance of the spots and the changes they un- dergo, lead to the supposition that a gaseous envelope surrounds whatever may be the interior ; and Arago's determination, that the sun's direct light is not polarized, renders it probable that the envelope is flame. I have lately made some photographic experiments, which may tend further to the establishment of this opinion. It has been long known that the light proceeding from the centre of the sun is more intense than that from the edge. I have taken several pictures of the sun in a camera obscura, by means of a photographic process, exposing the prepared surface of the plate to be acted on for different periods of time. For instance, the Camera being set, and the prepared plate in focus, I have allowed the picture of the sun to fall on it for as short a time as it was pos- sible to uncover and cover again the aperture. I then opened the apei-turc again for a somewhat longer period, having first moved the plate so that another part of it would be acted on. I caused the picture then to fall on another portion of the plate for a longer time, and so on, taking on the same prepared surface iix or eight pictures, each the result of a different length of ex- * There is no rotatory teudency in the plane of oscillation, excepting iki so far as this is produced as a result of the earth's constraint on the point of suspension, in other words, the rotatory effect is due to the earth. In this sense it is the eaith's rotation made visible though the angular mo- tion is slower tlian that of the earth ; and the case may be compared to the motion of the box containing? the main-spring of a watch, as evidenced by tbc motions of the hands. ' ) t Commupicated by the Author. ^ Dr. Woods on the probable Nature of the Sun's Body. 25 posure. The examination of these pictures showed that they were of different sizes, the sraallest being produced by the shortest exposure ; and that they increased in extent with the length of time the aperture was open up to a certain size. The centre of the picture was apparently intensely acted on_, as it had the appearance of being what photographers called "burnt/' And this deep spot was surrounded by a ring of light not so darkly marked. The " burnt'^ centre increased in size, not in depth of intensity, with increased length of exposure ; the ring about it also increased, but not in proportion to the enlargement of the centre. A piece of red glass placed before the aperture of the camera renders the sun's action less powerful, and allows the pictures to be taken less rapidly. These experiments are a fur- ther proof that the light from the centre of the sun acts more energetically than that from the edges ; the latter requiring a longer time to produce as much effect as the former on a photo- graphic surface. I thought that these experiments might furnish a ground for obtaining evidence of the probable nature of the sun's envelope. I determined to try whether ^ame would affect a sensitive plate after a manner similar to the sun ; and if so, whether a solid body producing light would differ in its action. I therefore exposed a prepared surface in a camera in the focus of a lighted candle, and also of a gas-jet. In both cases the action was ex- actly similar to that of the sun, but more marked, as to variety of extent, in the size of the pictures produced, because the light was not so powerful, thereby allowing more leisure in the mani- pulation. The picture of the flames in one second made a slight impression, in two seconds the impression increased in size and apparent depth of action, and so on, up to 15 seconds, when the picture produced was about three times the size of that taken in one second in the case of the gas-jet. In numerous experiments I have made with flames, caused to burn steadily lest the waver- ing might influence the result, I have always found that their action on the plate was similar to that of the rays from the sun's disc, viz. an increased extent of picture for an increased period of exposure. It now remained to try what effect a solid body giving out light — not reflecting it — would produce. It was not easy to find a means of heating a solid body sufficiently high to get a light capable of acting on a sensitive plate. I tried iron heated to whiteness, and platina in the flame of a gas-jet, but neither affected the plate in a camera. The lime-light, however, acted well. A piece of lime acted on by the oxy-hydrogen blowpipe was rendered luminous, and a picture of it thrown on the pre- pared surface by the camera. In one second a deeply-m?irked 26 Dr. Woods on the- probable Nature of the Sun's Body, image was produced ; and the size of the picture of the solid was not influenced by the length of time of exposure. I at first thought a very shght difference of size was apparent in pictures produced by hirgely different lengths of time the plate was acted on, but I found on examination that the appearance was produced by the gases employed to heat the lime. I mention the circum- stance in order to guard others from the mistake. Taking into consideration all the experiments I have made, I have no doubt that the light from the centre of flame acts more energetically than that from the edge on a surface capable of receiving its impression ; and that light from a luminous solid body acts equally powerfully from its centre or its edges ; and therefore conclude that, as the sun affects a sensitive plate simi- larly with flame, it is probable its light-producing portion is of a similar nature. In the experiment I have just spoken of, I used a sensitive surface prepared according to a formula which I am anxious to publish, as I believe it will be found more sensitive, and perhaps more easily manageable than any other hitherto known. I have by means of it taken a very good picture of a building, on a bright day, in as short a time as it was possible to uncover and cover again tbe aperture of the camera with the hand. The length of the focus of the lens was 6 inches, its aperture f ths of an inch in diameter. The process differs from the usual collodion one in substituting a mixture of iodide and chloride of iron for iodide of potassium, and using collodion having in solution some common salt. In 1844 I first introduced the iodide of iron as a photographic agent. I found it at that time the most sensi- tive I could procure, and since then, whether in processes on paper, or in albumen or collodion on glass plates, I have always succeeded with it better than w ith any other, both as to rapidity and facility of use. Mr. Fox Talbot has found it sufficiently sensitive when employed with Mr. Hunt's discovery of sulphate of iron, to produce instantaneous results. The details of the process are as follow : — Take of Sulphate of iron 40 grains. Iodide of potassium ... 24 grains. Common salt 6 grains. Spirits of wine or alcohol . 2 oz. Mthev 2 drachms. Strong water of ammonia . 3 drops. Powder the salts and mix them well together, add the alcohol and aether, and finally the ammonia. Allow the precipitate to subside. For preparing the plate, mix one part of the clear solution ^iik three parts of collodion, to which has been added On new Theorems relating to the Moon's Orbit. 27 a saturated solution of common salt in the proportion of one fluid drachm of the salt solution to four ounces of collodion. Spread on the glass plate in the usual way and immerse it for one mi- mute to one minute and a half in a neutral solution of nitrate of silver, 30 grains to the ounce. Develope the picture with a solution of sulphate of iron one scruple to the ounce of water ; and finally fix with the hyposulphite of soda. A very beautiful picture may also be obtained by using the developing solution of sulphate of iron, of the strength of 20 or 30 grains to 4 ounces of water, and adding to the hyposulphite wash strong water of ammonia, in the proportion of 20 drops of the latter to 6 or 8 ounces of the f(Jpmer. The iron solution should be well washed off previously to putting the plate in the ammonia and hyposul- phite. By this process I have obtained most exquisite pictures in very short spaces of time. In many cases the light parts of the pictures are pure silver, forming a good mirror. Alkaline reaction in the bath or the collodion causes cloudi- ness, which may, however, be remedied by a corresponding amount of nitric acid. If a bottle of strong ammonia be left open in the room where the plate is prepared, cloudiness will be produced. I brought for a few minutes a dish containing a solution of hyposulphite of soda, to which had been added a small portion of hydrosulphuret of ammonia, into the room in which I prepared a plate, and for some hours after I could not get a picture without cloudiness. By thoroughly ventilating the room I got rid of the annoyance. It would therefore be better if the ammonia be added to the hyposulphite solution, as recommended above, to keep it at a safe distance from the other materials. I have also found that filtering the caustic solution through the red-coloured blotting-paper is sufficient to produce alkaline reaction and cloudiness. Parsonstown, June, 1864. v.. On Professor Challis's new Theorems relating to the Moon's Orbit. By J. C. Adams, Esq., FM.S., Fellow of Pembroke; College, Cambridge. To the Editors of the Philosophical Magazine and Journal, GeNTLEMExY, IN the June Number of your valuable Journal, Professor Challis calls attention to some circumstances connected with his withdrawal of a paper, relating to the moon's motion, which he had communicated to the Cambridge Philosophical Society, and of the principal results of which he had given an account in your Number for April (p. 278). Professor Challis mentions that one of the reporters, whqse 08 Mr. J. C. Adams on Professor Challis's new Theoi'ems unfavourable judgement led to this withdrawal, had of his own accord communicated to him some of the reasons on which this judgement was based. Professor Challis, however, thinks these reasons to be very unsatisfactory, and consequently invites the reporter to discuss with him the questions on which , they are at issue, in the pages of the Philosophical Magazine. ,..,., .,^ As I am the reporter thus referred to, I beg that you will allow me to state some reasons which appear to me sufficient to prove, beyond a doubt, that the principal conclusions of Professor Challis's paper are erroneous, in order that he may have the opportunity, which he desires, of replying publicly to my object tions*. At the same time, 1 must decline to enter into any pro- longed controversy on the subject, submitting with confidence what I have now to say to those who are competent to form a judgement respecting it. The principal results of Professor Challis's paper are embodied in two theorems, which, as already stated, form the subject of an article in the Philosophical Magazine for April last. As my main objections to the paper relate to these theorems, I shall confine my observations almost entirely to the article in question. It will be convenient, however, to make a few preliminary remarks on the nature of the process usually followed in the lunar theory. Professor Challis objects to the logic of this pro- cess, on the ground that the introduction of the quantities usually denoted by c and g into the first approximation to the moon's motion is only suggested by observation. He therefore considers the results of the ordinary process to be hypothetical, until they are confirmed by observation. But surely the sufficient and the only test of the correctness of any solution is, that it should satisfy the differential equations of motion at the same time that it contains the proper num^lpi,^^ of arbitrary constants to fulfill any given initial conditions, cj-vfj^ Any process which does this, no matter how it may be 5if^- gested to us, must be logical ; and if the results obtained by it should not agree with observation, the conclusion would be that the law of gravitation, which was assumed in forming the ori- ginal differential equations, is not really the law of nature. If we begin with the supposition that the moon's orbit is an immoveable ellipse, the differential equations cannot be satisfied, without adding, to the fii-st approximate expressions for the moon's coordinates, quantities which are capable of indefinite increase ; and this proves, as is stated by Professor Challis, that an immoveable ellipse is not, or rather does not continue to be, an approximation to the real orbit. * It may be proper to mention that the opinion of the other reporter on the paper perfectly agreed \^ith my own. m^-mKV vu ^,eia^in^ to the Moon's Orbit, '^ ^ -^'^ 29 "But if we introduce the quantities usually denoted by c and^, having assigned values slightly differing from unity, which amounts to supposing the apse and node to have certain mean motions, we find that the differential equations are satisfied by adding to the first approximate expressions for the moon's coor- dinates, terms, which always remain small ; and we thus know that our first approximation was a good one, and that the true and the only true solution of the differential equations has been obtained. On the other hand, no solution can be a true one, which does not contain the proper number of arbitrary constants ; and any person who asserts that one of the constants usually considered arbitrary is not so, is bound to show by what other really arbi- trary constant the former is replaced. I will now proceed to consider Professor Challis's two theo- rems, which are thus enunciated by him. Theorem I. All small quantities of the second order being taken into account, the relation between the radius-vector and the time in the moon's orbit is the same as that in an orbit described by a body acted upon by a force tending to a fixed centre. Theorem II. The eccentricity of the moon's orbit is a function of the ratio of her periodic time to the earth's periodic time, and the first approximation to its value is that ratio divided by the square root of 2. '''^^ I will endeavour, in the first place, to show that these theorems cannot possibly be true ; and secondly, to point out the fallacies in the argument by which Professor Challis attempts to establish them. ^^ The problem will be simplified by supposing the moon to iKbve in the plane of the ecliptic, and the earth's orbit to be a circle. On these suppositions, Professor Challis's fundamental equations become •: ... , ,. 5 = _ ^ + ^, + 1»^ eos [e-^^hT-^) t "■ wS ffp -f ' dt^ r^ 2a'^ 2>a'^^ ^ ' -•■^'- yv M Multiply these equations by y and x respectively, and subtract the results ; and again multiply by x and y, and add the results together ; thus we obtain, after expressing x and y by means of polar coordinates, *^ ^ >t*iMi d ( dO\ Sm'r^ ' ^** .-^o - 3idi:j/ 5 6 =:nt + € + 2e sin {cnt -\- €—v) -h-T^e'^ sin 2 (cw/ + e— to-) 11 + -g- m^sin (2nt + €—2n't + ^) 15 , -\- -j-mesixi(2nt -i- €^2n't + ^ — cnt -^ €—'a)f where 2 1^ ,0 m' rl i 3 ^ AT fl'^ w ' 4 ' and fl, €, e, and w are the four arbitrary constants required by the complete solution. The fact that the differential equations are satisfied by these expressions for r and Q, whatever be the value of e, is quite suf- ficient to show that Professor Challis is mistaken in restricting e to one particular value. The terms of the second order in the value of r, which depend on the arguments 271/4-6— 2w7H-e and 2w^H-€— 2»7 + 6'--C7i^ + €— w, and which constitute the well-known inequalities called the '' variation '^ and the " evection," prove the incorrectness of Pro- fessor Challis's Theorem I. ; since in an orbit described by a body acted on by a force tending to a fixed centre, and varying, as Professor Challis supposes, as some function of the distance, the expression for the radius-vector in terms of the time cannot possibly contain any terms dependent on the sun's longitude, I now come to consider the reasoning by which Professor Challis arrives at his theorems. All this reasoning is based on bis equation U; +;^ ~ 2?5 + ^-0, •••(C) the truth of which, he says, cannot be contested. In speaking of the truth of this equation, Professor Challis cannot mean that it is anything more than an approximation to the truth, since in forming it he avowedly neglects all quantities of orders superior to the second. Now what I assert is, first, that the degree of approximation attained by the equation (C) is not sufficient to justify Professor relating to the Moon's Orbit. ■ '^ ' --■' 31 Challis in inferring Theorem I. from it ; and secondly, that Theorem II. does not follow from that equation at all. To prove the first of these assertions^ I remark that the equa- (dr\^ -^ I in terms of r, but that it does not profess to include terms of the third order. dr Now -J- is itself a quantity of the first order, and consequently at /'dr\^ an error of the third order in ( -^ j leads to one of the second order in -r, and therefore to one of the same order in the value of r expressed in terms of t. Hence Professor Challis is not entitled to infer that the relation between the radius-vector and the time in the moon^s orbit is the same, to quantities of the second order, as that which would be given by the equation (C), We may test the degree of accuracy to be attained by the use of this equation in the following manner. By differentiation, the constant C disappears, and the result- dr ing equation becomes divisible by -j-; dividing out, we obtain d^r ^^ .H' ^'^ __n dF'^'i^'^^''2^ This is a strict deduction from Professor Challis's equation ; we will now obtain directly from the equations of motion given above, an expression to be compared with it. Integrating equation (1), and putting, with Professor Challis, nt-\-6 for 6, and a for r in the term of the second order, we find c,d6 , 3 m' fl^ ,^ ^-j ,^ r^-Tr = h+--i^—cos(2nt-i-e'-'2n't + €'), dt 4«'^ n ^ ' The value of the constant A, expressed in terms of the system of constants before used, is Hence r^(^y==;i2^ |^a4 cos (25^7+7-2^7+?), (ddy h^ 3 m' ^\'5^/'^^'^2^^^^^(^^^"+"^""^"'^ + ^')' putting, as before, a for r in the small term. Substituting this value of r( -^ j in equation (2), we find <^r h^ , fJL wir „ m' ,~ ^-7 — -^^ ^ S2 Mr. J. C. Adams on Professor Challis's new Theorems The equation above deduced from Professor Challis's differs from this by the omission of the last term, which gives rise to the variation inequahty. In order to find the evection, which is also an inequality of the second order, it would be necessary tQ carry the approximation one step still further than we have he|?g done. This shows how unfitted equation (C) is for giving any acq^^ rate information respecting the moon's orbit. (^ As a matter of fact, it may be observed that this equation would make the moon's apsidal distances to be constant. A simple inspection of the calculated values of the moon's hori- zontal parallax, given in the Nautical Almanac, is sufficient iii show how far this is from the truth. - r .r ,v';~ -\\ I now proceed to make good my second assertion, viz. that Professor Challis's Theorem II. cannot be inferred from his equa- tion (C). The process by which he attempts so to infer it is of the following nature, lijf first finds that a method, apparently legitimate, of treating the equation (C) leads to a difficulty. To get rid of this difficulty, he makes the strange supposition that the equation (C) contains the disturbing force as a factor, and then tries to show that, in order that this condition may be satisfied, the arbitral^ constants h and C must have a certain relation to each other, fi*om which it would immediately follow that the eccentricity must have the value assigned to it in Theorem II. Now it is remarkable that every one of the steps of this pro- cess is unwarranted. The difficulty to which Professor Challis is led is purely imaginary; the supposition that the equation (C) contains the disturbing force as a factor is wholly unsupported by any proof ; and even if that supposition were well founded, it would not follow that the constants h and C must have the relation assigned to them by Professor Challis. The supposed difficulty is founded on the inference at the bottom of p. 280 of Professor Challis's paper, " Hence we must conclude that the mean distance and mean periodic time in this approximation to the moon's orbit are the same as those in an elliptic orbit described by the action of the central force ^." But this is not a correct conclusion : if A and C be supposed to have the same values in equation (C) and in that obtained from it by putting a for r in the small term, the values of the mean distances in the two cases would not be the same, but would differ by a quantity of the second order. This may be readily shown in the following manner, ii ii&i^i dr At the apsides ^=0, and therefore the equation (C) gives the 5^*«^^ lit^iv relaivng to the Mobie^ OrlM^ -^ "^ -^ 33 following equation for finding tlie kpsidal distances, 'P:^/^^^. • Wo'(?^2:?M the mean distance, and e the eccentricity, the apsidal 3istarices'are a[\-\-e) and «(1— e). Substituting these values for r in the above equation, and de- veloping the small term to quantities of the fourth order, we obtain A h^^2fJM{l + e) -h Ca%l 4- 2^ + e^) - £^ a\l -f 4e + 6e^) = 0 ^ - -riQfi g^xioofiT j')di 'to muln/ b-; whence it follows that . MroRgsfe^ iu ai Ji ^^ai^-.2/>tfl + C«2(l + e2) _ ^a4(i^gg2)^0 ^ ^^ These equations give the relations between the arbitrary con- stants h and C, and the new constants a and e by which the former may be replaced. ^ From the second of them, we find '^ 'C'lq aim to , 3 . ri <( jf wov^A siUmiO m&t>n. . ■ a= y^+^7t; - :.. ^r 4 ^^^^ (0) itoiimfp^}M L a L , ^^^ ^5 or, putting for a in the small term its first approximate value ^, which agrees with Professor Challis^s expression in p. 281. ' ' Now apply a similar process to the equation -i'^i^M^ which diifers from the equation (C) in having a put for r in the smalj term. In this case, we find and ^ « , m' ^ | from the latter of which equations it follows that v - * C 2«'^ G^ PAi/. ilfa^. S. 4. Vol. 8. No. 49. July 1854. D 84 Mr. J. C. Adams on Professor Challis's new Theorems or fi m' fi? to the same degree of approximation as before. Hence we see that the values of a, in the two cases supposed, differ by a quantity of the second order. Consequently the dif- ficulty into which Professor Challis is led by the conclusion that these values are the same, disappears, and the solution of the difficulty with it. But even if we were to suppose, with Professor Challis, that the equation (C) contains the disturbing force as a factor (of which, as already remarked, no proof whatever is given), it would not follow, as is inferred by him, that h^Q> must be equal to /x^. On the contrary, it is evident that the required condition would be satisfied if /t^C differed from yu,^ by any quantity involving the disturbing force as a factor ; whence it would follow that e must be some function, indeed, of the disturbing force, but it could not be decided what function. Professor Challis attempts to find the relation between r and t by direct integration of the equation (dr\^ -jr) is a small quantity of the second order which vanishes twice in each revolution, and that /dr\^ the difference between the complete value of i-rf and the ap- proximate value which is used instead of it in the above equation, is a periodic quantity of the third order. Hence it follows that the quantity _p_A2 2^ f^2 may vanish for values of r different from those which make \lf) ^^^^^^f ^^^ ^^^* ^^ '^^y ^v®^ become negative for actual values of r, which f ^J itself can never do. Therefore the coefficient of dr in the above differential equation may become infinite, or even imaginary, within the limits of in- relating to the Moo'n/s Orbit. 85 tegration, so that it is not surprising* that Professor Challis should have met with such difficulties in performing the inte- gration. The relations between r, 6, and t, given in page 281 (which profess to include all small quantities of the second order),, are said to be derived from the equations (B) and (C). It is easy to seCj however, that they do not satisfy the first of those equa- tions, since the term of the second order in the right-hand member of that equation involves the longi- tude of the sun, which does not occur at all in the relations in question. The contradiction to Professor Challis's theory, which is pre- sented by the eccentricity of the orbit of Titan, is supposed by him to be occasioned by the large inclination of that orbit to the plane of the orbit of Saturn. But in page 280 it is remarked that the inclination of the orbit is taken into account ; and even if this were not the case, no proof is ofi'ered that the taking it into account would tend to reconcile the discrepancy. At the bottom of page 282, Professor Challis attempts to show, a priori, that the eccentricity of the moon^s orbit must be a function of the disturbing force in the following manner. If there were no disturbing force, the value of the radius vector drawn from the earth's centre in a given direction, would be constantly the same in different revolutions. But if a disturbing force act in such a manner as to cause the apsidal line to make complete revolutions, the value of the above-mentioned radius- vector would fluctuate in different revolutions, between the two apsidal distances. Hence it is argued that, since if there were no disturbing force there would be no such fluctuation of distance, therefore the total amount of such fluctuation, and consequently the eccentricity, must be a function of the disturbing force. But, on consideration, it will appear that this argument is fallacious. No doubt it may be inferred that some of the cir- cumstances of this fluctuation of distance will depend on the disturbing force which causes it, but it cannot be asserted, without investigation, that the total amount of such fluctuation must necessarily depend on the disturbing force. As a simple example, we will suppose the principal force to vary inversely as the square of the distance, and a central disturbing force to be introduced which varies inversely as the cube of that distance. In this case we know, by Newton's 9th section, that the motion would be accurately represented by supposing it to take place in a revolving ellipse, the angular D2 M l)r. Stenliouse^w the Action of Bromine velocity of the orbit being always proportional to that of the body at the same instant; and the eccentricity of the orbit might be any whatever, and would not at all depend on the dis- turbing force. Now, since the orbit would be fixed, were it not for the dis- turbing force, it might be argued in exactly the same manner as is done by Professor Challis in the passage above referred to, that the eccentricity of the orbit tnust be a function of the force which causes the orbit to revolve, but this we know to be a false conclusion. WTiat would depend on the disturbing force in this case, would be, not the total amount of the fluctuation of distance in different revolutions, but the number of revolutions of the body in which such fluctuation would take place, or the time of revolution of the apse. If the disturbing force were increased, the total fluctua- tion in the value of the radius-vector in question would be the same as before, but the change from one of the extreme values to the other would occupy a shorter time. The objection mentioned by Professor Challis at the top of page 283, is alone quite fatal to the supposition that the eccen- tricity of the moon's orbit must have a particular value. Where is the proof that the eccentricity would settle down to such a value, as Professor Challis imagines, if it were initially different ? In fact, it is easy to show, by the method of variation of elements, that there would be no such settlement, but that the non-periodic part of the eccentricity would remain constant. I have the honour to be. Gentlemen, Your obedient Servant, Pembroke College, Cambridge, J. C. Adams. June 20, 1854. VI. On the Action of Bromine on Nitropicric Acid, !) Bij John Stenhouse, LL.D., F.R.S."^ M IT is stated, on the authority of Marchand, at p. 683 in the 5th volume of Gmelin's Handbook of Chemistry, that bro- mine has no action on nitropicric acid. As this assertion appeared to me highly improbable on several grounds, I was induced to undertake the following series of experiments. The nitropicric acid on which I operated was made by treating the resin of the Xanthorrhoea hastilis (the yellow gum-resin of Australia) with nitric acid. The resin, which costs only from fourpence to sixpence per pound, yields nearly half its weight of * Commimicated by the Author. ''^^''^^' MNitropicric Aciit!^^''^^ * 37 nitropicric acid, and is therefore by far its most oeconomical source. A quantity of nitropicric acid was digested with water and bromine in a retort, so connected with a condensing apparatus that the bromine and acid vapours, on cooling, flowed back into the mixture. As cork was rapidly attacked and destroyed by the bromine vapours, the different parts of the apparatus were connected by means of plaster of Paris. The mixture of bro- mine and nitropicric acid was digested for several hours ; and when the greater portion of the bromine had disappeared, new quantities of it were added from time to time, and the digestion continued. Bromopicrine and bromanil were, with the exception of hydrobromic acid, almost the sole products. Permanent gases were evolved only in comparatively small quantity, their amount increasing towards the close of the digestion. No carbonic acid was evolved, and the gases consisted chiefly of nitrogen and its oxides, especially the binoxide. The production of these gases appears to arise from the decomposition of bromopicrine. It seems, therefore, that nitropicric acid, when it is digested with bromine, is resolved into bromanil and bromopicrine, probably as follows : — 2(Ci2 H3 (N04)3 02) + 28Br=Ci2Br4 04 + 6(02 61-3 (NO^)) + 6HBr. '^p Bromopicrine, C^Br^NO"^. — When the products obtained by the preceding operation are rectified, bromopicrine of a deep yellow colour, from containing excess of bromine, distils over, and forms an oily fluid under the aqueous solution which has come over with it. It was washed with water containing a little carbonate of soda, and then agitated with mercury to remove any adhering bromine. Although the boiling-point of bromo- picrine is much higher than 212° F., it came over chiefly with the first portions of the water, and was perfectly colourless when the excess of bromine had been previously removed. But when bromopicrine had been rendered anhydrous by contact with fused chloride of calcium, though it might be heated to nearly its boiling-point without alteration, yet when it began to boil it was partially decomposed, with the evolution of brownish-red vapours, even though the operation was conducted in an atmosphere of carbonic acid gas. As it was plain therefore that anhydrous bromopicrine could not be purified by distillation, it was sepa- rated from the chloride of calcium by filtration, none of the chloride of calcium being retained in solution. The bromo- picrine prepared in the way just described, when subjected to analysis, gave 85*1, 85-2, and 85*6 per cent, of bromine. The formula of bromopicrine (C'^Br^NO'^) requires only 80*54 per cent. 3S Dr. Stenhouse on the Action of Bromine of bromine. It is clear from the results of the above analyses, therefore, that the bromopicrine prepared in the manner just de- scribed is impure, and contains a quantity of a substance which is richer in bromine, most probably the carburet of bromine (C^Br*), which maybe readilyproduced by the long- continued actionof bro- mine on bromopicrine. It is necessary, therefore, to prepare bromopicrine by some other process where such a decomposition is not likely to be produced. Nitropicric acid was consequently digested with excess of hypobromite of lime, in a manner pre- cisely similar to that by which I many years ago prepared chloropicrine. The bromopicrine obtained was washed with solution of carbonate of soda, agitated with mercury, and ren- dered anhydrous by chloride of calcium. When analysed — , I. 0-6645 grm., when ignited with quick lime, gave 1*2495 grm. of bromide of silver. II. 0*5225 grm., when ignited with quick lime, gave 0*9825 grm. of bromide of silver. Theory. Found. ^ * , <—• ■■ ' ^ I. II. C? = 12 403 Br* =240 80-54 80*01 8002 N0*= 46 15-43 298 10000 Bromopicrine is a colourless liquid, which is heavier than water; its jodour very closely resembles that of chloropicrine, and its vapour attacks the eyes very strongly. It is very slightly soluble in water^ but readily dissolves in alcohol and aether. Its alcoholic solution is not immediately precipitated by nitrate of silver ; but on standing for some time, even in the cold, and im- mediately on the application of heat, bromide of silver precipitates. When bromopicrine is strongly heated, it is decomposed with a slight explosion. Bromopicrine is therefore a much less stable compound than chloropicrine, which in most other respects it 80 closely resembles. Broinanil, C^^Br'^0'*. — The residual matters remaining in the retort after the distillation of the bromopicrine produced by the digestion of bromine with nitropicric acid, were found to consist chiefly of bromanil and some un decomposed nitropicric acid. The excess of nitropicric acid was removed by repeated digestion with hot water, when a quantity of impure bromanil remained as yellowish-red crystalline scales. These scales contained a small quantity of a reddish resinous substance, which was readily removed from the bromanil by taking advantage of its greater solubility in alcohol and aether. When the bromanil had been twice crystallized out of alcohol, it formed beautiful crystalr on Nitropicric Acid* 39 line scales of a golden lustre, very closely resembling chlor- anile or iodide of lead. When heated, it melted, forming a brownish liquid, and readily sublimed, yielding sulphur-yellow crystals. It is nearly insoluble in water, slightly soluble in cold, but tolerably soluble in hot alcohol and in sether. Bromanil crystallized out of alcohol, when analysed, gave the following results : — 0-3695 grm., burnt with chromate of lead, gave 0*2325 grm. of carbonic acid. [The small quantity of water found was equal to 0*19 per cent, of hydrogen.] 0*3925 grm., burnt with caustic lime, gave 0*6985 grm. of bromide of silver. Theory. Found. Ci2=^72 16*98 17-16 Br4=320 75*47 75*73 0* = 32 7-55 7*11 424 100-00 . 100*00 Bromhydranil, C^^ Br'* H^ 0*. — When sulphurous acid gas is passed through hot spirits of wine containing an excess of brom- anil, the bromanil gradually dissolves, and a colourless solution is produced. When this solution is sufficiently concentrated, bromhydranil is deposited in colourless crystals, which have a mother-of-pearl lustre. When bromanil is boiled with an aqueous solution of sulphurous acid, bromhydranil is also pro- duced, but extremely slowly, because bromanil and bromhydranil are both nearly insoluble in water. Bromhydranil is very soluble in alcohol and in sether, but it is nearly insoluble in water, and is therefore precipitated as a white crystalline powder from its concentrated alcoholic solutions on the addition of water. When heated, it melts and readily sublimes, forming soft colourless scales. 0*9412 grm. of bromhydranil, crystallized out of spirits of wine, when burned with chromate of lead, gave 0*5915 grm. of carbonic acid, and 0*0485 grm. of water. Found. 17-14 0-55 426 100*00 Bromanilic Acid, C^^ Br^ H^ O^. — When bromanil is thrown into hot potash lye, it immediately dissolves, forming ^ deep Theory. C'2=: 72 16*90 Br4= 320 75*12 H2 = 2 0*47 0^ = 32 7*51 to Dr. Stenhotise m the Action of Bromine pui-ple solution, out of which dark brownish-red needles of a potash salt are speedily deposited, as they are insoluble in the alkaline liquid. This potash salt readily dissolves in water, but it is nearly insoluble in alcohol. Its crystals, after being washed with alcohol, were dried in vacuo over sulphuric acid, and sub- jected to analysis. 0*325 grm. gave 0-143 grm. of sulphate of potash. 0*2575 grm. gave 0*2475 grm. of bromide of silver. According to these determinations, therefore, this salt contains (like the corresponding chloranilate of potash analysed by Erd- mann) 2 equivs. of water, as is shown by the following results : — Theory. Found. C^«="72 18*35 Br2 = 160 40-77 40*87 t- H2= 2 0*51 ^ K'^= 78*4 19*98 ^^'^^r-i h.ioirn,.^'' 0^0= 80 20*39 ^ ^"^ ^^'^''^' ' 392*4 10000 The aqueous solution of bromanilate of potash very closely resembles, in its reactions on metallic solutions, those of the chloranilate of potash. It forms with solutions of the greater number of the heavy metals and with that of baryta, difficultly soluble precipitates, whose colours very much resemble those produced by the chloranilate of potash. If sulphuric or hydro- chloric acids are added to an aqueous solution of bromanilate of potash, or to a solution of bromanil in hoi potash lye, the purple colour of the solution immediately disappears, and bromanilic acid is gradually deposited in beautiful, shining, crystalline scales of a reddish colour, which when dried are of a bronze colour. /li^Sromanilic acid is not precipitated by acetic acid. ' '0*2735 grm. of the crystals, when ignited with caustic lime, gave 0*3465 grm. of bromide of silver. Found. 53*91 298 10000 The solutions of bromanilic acid in alcohol and water are of a deep purple colour. Its solution in aether is yellowish, but Theory. 0' = 72 24*16 Br2 = 160 53-69 H2 = 2 0*69 08 = 64 21-46 5Msm>'«?L on NiU'opid'ic Acid, ^iM t(} 4J becomes purple on the addition of alcohol. Long-continued digestion of bromanil with water appears slowly to produce a small quantity of bromanilic acid ; at any rate, water, when long boiled with bromanil, gradually becomes of a purple colour. Bromanilamide (C^^ N^ Br^ H'* O'*) is prepared by passing dry ammoniacal gas into a hot solution of bromanil in alcohol con- taining some bromanil in suspension. Bromanilamide is also prepared when a mixture of bromanil and alcohol is heated along with concentrated liquor ammonise. A smaller quantity of brom- anilamide is obtained by this process than when all the sub- stances employed are anhydrous, as a larger amount of the brom- anilamate of ammonia, which dissolves in the spirit, is produced. Bromanilamide forms a brownish red crystalline powder, which is nearly insoluble in water, alcohol and aether. It sub- limes, under partial decomposition, in brown-coloured crystals. That portion of the bromanilamide subjected to analysis had been previously dissolved in a weak alcoholic solution of potash, and precipitated by acetic acid. 0-2555 grm. gave 0-3255 grm. of bromide of silver. Theory. Found. ^d? '\o sac?fft 19)89113 dd.1 -^Mooirf Br2=160 54-06 54-21 '''' Bromanilamic Acid. — Bromanil, in its reactions with aqueous ammonia, appears closely to resemble chloranil. The brownish- red solution of bromanil in strong aqueous ammonia, deposited deep brownish-red needles of a salt which appears to be brom- anilamate of ammonia. When sulphuric acid is cautiously added to an aqueous solution of this salt, bromanilamic acid pre- cipitates in nearly black-coloured needles. If, while neutralizing the solution of this salt, any considerable elevation of tempera- ture is not carefully avoided, the solution becomes colourless, and crystals are deposited which appear to be bromanilic acid. St. Bartholomew's Hospital, June 22, 1854. 00-00 f lr..te . ■ ( — - r€i^= 72 24-32 N2=z 28 9-46 Br2=160 54-06 H4 = 4 1-35 0^ = 32 1 \n fT< >• 10-81 296 100-00 [ 42 J VII. On certain recent Investigations in the Theory of Light, By Professor Stokes. To the Editors vf the Philosophical Magazine and Journal. Gentlemen, IN the recently published Part of the Philosophical Transac- tions occurs a paper by my friend the Rev. Joseph Power, entitled "Theory of the Reciprocal Action between the Solar Rays and the different Media by which they are reflected, refracted, or absorbed; in the course of which various optical laws and phsenomcna are elucidated and explained,^' for a copy of which I am indebted to the kindness of the author. The results arrived at in this paper are of a remarkably novel and therefore attractive character, but the investigations appear to me to lie open to the gravest objections. I am at present engaged in discussing the matter privately with Mr. Power, and I am unwilling to trouble the public and fill your pages with the details of the con- troversy. If, as I hope and expect, Mr. Power and I come ulti- mately to agree, our views can be laid before the public with much more brevity. My only object in mentioning the subject at present is to show that the question has been taken up. I am. Gentlemen, Your faithful Servant, Pembroke College, Cambridge, G. G. Stokes. June 20, 1854. VIII. On the Mathematical Theory of Electricity in Equilibrium, By William Thomson, B.A., Fellow of St. Peter^s College. [Extracted from the "Cambridge and Dublin Mathematical Journal," Nov. 1845. Notes and additions of the present date, March 1854, are enclosed in brackets.] I. On the Elementary Laws of Statical Electricity^. 1. nnHE elementary laws which regulate the distribution of A electricity on conducting bodies have been determined by means of direct experiments, by Coulomb, and in the form he has given them, which is independent of any hypothesis f, they have long been considered as rigorously established. The problem of the distribution of electricity in equilibrium on a conductor of any form was thus brought within the province of mathematical analysis; but the solution, even in the simplest cases, presented so much difficulty that Coulomb, after having * This paper is a translation by the author (with considerable additions) of one which appeared in Liouville's Journal de Mathhiatique, vol. x. p. 209. t See the first Note at the end of this paper. On the Mathematical Theory of Electricity in Equilibrium, 43 investigated it experimentally for bodies of various forms, could only compare his measurements with the results of his theory by very rude processes of approximation. Without however giving rigorous solutions in particular cases, he examined the general problem with great care, and left nothing indefinite in the conditions to be satisfied, so that it was entirely by analytical difficulties that he was stopped. As an example of the success of his theoretical investigations, we may refer to the well-known demonstration of the theorem (usually attributed to Laplace) relative to the repulsion exercised by a charged conductor on a point near its surface*. The memoirs of Poisson, on the mathematical theory, contain the analytical determination of the distribution of electricity on two conducting spheres placed near one another, the solution being worked out in numbers in the case of two equal spheres in contact, which had been investigated experimentally by Coulomb (as well as in another case, not examined by Coulomb, which is given as a specimen of the numerical results that may be deduced from the formulae). The calculated ratios of the in- tensities at different points of the surface he is therefore enabled to compare with Coulomb^s measurements, and he finds an agreement which is quite as close as could be expected, when we consider the excessively difficult and precarious nature of quan- titative experiments in electricity. But the most remarkable confirmation of the theory from these researches is the entire agreement of the principal features, even in some very singular phsenomena, of the experimental results with the theoretical deductions. For a complete account of the experiments, we must refer to Coulomb^s fifth memoir {Histoire de V Academic, 1787), and for the mathematical investigations to the first and second memoirs of Poisson [Memoires de VInstitut, 1811), or to the treatise on Electricity lu the "Encyclopaedia Metropolitana," where the substance of Poisson^s first memoir is given. The mathematical theory received by far the most complete development which it has hitherto obtained in Greenes '^^ Essay on the Application of Mathematical Analysis to the Theories of Electricity and Magnetism f/^ in which a series of general theorems were demonstrated, and many interesting applications made to actual problemsj. Of late years some distinguished experimentalists have begun to doubt the truth of the laws established by Coulomb, and have made extensive researches with a view to discover the laws of certain phsenomena which they considered incompatible with his theory. The most remarkable works of this kind have been * See Note II. f Nottingham, 1828. % See Note III. 44 Prof. Thomson on the Mathematical Theory of undertaken by Mr. Snow Harris and Mr. Faraday, and in their memoirs, published in the Philosophical Transactions, we find detailed accounts of their researches. All the experiments, however, which they have made, having direct reference to the distribution of electricity in equilibrium, are, I think, in full accordance with the laws of Coulomb, and must therefore, instead of objections to his theory, be considered as confirming it. As however many have believed Coulomb's theory to be overturned by these investigations, and as others have at least been led to entertain doubts as to its certainty or accuracy, the following attempt to explain the apparent difficulties is made the subject of the first of a series of papers in which various parts of the mathematical theory of electricity, and corresponding problems in the theories of magnetism and heat, will be coft^ sidered. ^'^ 2. We may commence by examining some experimental re- sults published in Mr. Harris's first memoir " On the Element- ary Laws of Electricity*.'' After describing the instruments employed in his researches, Mr. Harris gives the details of some experiments with reference to the attraction exercised by an insulated electrified body on an uninsulated conductor placed in its neighbourhood. The first result which he announces is that, when other circumstances remain the same, the attraction varies as the square of the quantity of electricity with which the insu- lated body is charged. It is readily seen, as was first remarked by Dr. Whewell in his " Report on the Theories of Electricity, &c.t/' that this is a rigorous deduction from the mathematical theory, following from the fact that the quantity of electricity induced upon the uninsulated body is proportional to the charge on the electrified body by which it is attracted. The remaining results have reference to the force of attraction at different distances, and with bodies of different forms opposed. As these are generally very irregular (such as " plane circular areas backed by small cones"), we should not, according to Coulomb's theory, expect any very simple laws, such as Mr. Harris discovers, to be rigorously true. Accordingly, though they are announced by him without restriction, we must examine whether the experiments from which they have been deduced are of a sufficiently comprehensive character to lead to any general conclusions with respect to electrical action. Now in the first place, we find that in all of them the attraction is "independent of the form of the unopposed parts" of the bodies, which will be the case only when the intensity of the induced electricity on the unopposed parts of the uninsulated * Philosophical Transactions, 1834. t British Association Report for 1837. '•. ^,r Etectricity in Equilibrium, ^^^ ■'^"*''- 45 body is insensible. According to the mathematical theory, and according to Mr. Faraday's researches " on induction in curved lines/^ which will be referred to below, the intensity never absolutely vanishes at any point of the uninsulated body : but it is readily seen that in the case of Mr. Harris's experiments, it will be so slight on the unopposed portions that it could not be perceived without experiments of a very refined nature, such as might be made by the proof plane of Coulomb, which is in fact, with a slight modification, the instrument employed by Mr. Faraday in the investigation. Now to the degree of approxi* mation to which the intensity on the unopposed parts may be neglected, the laws observed by Mr. Harris when the opposed surfaces are plane may be readily deduced from the mathema-' tical theory. Thus let v be the potential in the interior of the charged body, A a quantity which will depend solely on the state of the interior coating of the battery with which in Mr. Harris's experiments A is connected, and will therefore be sensibly constant for different positions of A relative to the uninsulated opposed body B. Let a be the distance between the plane opposed faces of A and B, and let S be the area of the opposed parts of these faces, which will in general be the area of the smaller, if they be unequal. When the distance a is so small that we may entirely neglect the intensity on all the unopposed parts of the bodies, it is readily shown from the mathematical theory that (since the difference of the potentials at the surfaces of A and B is v) the intensity of the electricity produced by induction at any point of the portion of the surface of B which is opposed to A, is j — , the intensity at any point which is not so situated being insensible. Hence the attraction on any small element o), of the portion S of the surface of B, will be in a direction perpendicular to the plane and equal to 27r ( 1 — I *. Hence the whole attraction on B is gr>a"5B V47rfl!/ : .;} •^M Sird This formula expresses all the laws stated by Mr. Harris as results of his experiments in the case when the opposed surfaces are plane. 3. When the opposed surfaces are curved, for instance, when A and B are equal spheres, we can make no approximation analogous to that which has led us to so simple an expression in the case of opposed planes; and we find accordingly that no such simple law for the attraction in this case has been * See Mathematical Journal, vol. iii. p. 275, 46 Prof. Thomson on the Mathematical Theory of announced by Mr. Harris. He has, however, found that it is expressed with tolerable accuracy by the formula c(c-2ay where c is the distance between the centres of the spheres, a the radius of each, k a constant, which will depend on a and on the charge of the battery with which A is in communication. Though however this formula may give results which do not differ very much from observation within a limited range of distances, it cannot, according to any theory, be considered as expressing the physical law of the phsenomenon. For, according to it, when the balls are very distant, F ultimately varies as -g. Now it is clear that the law of force must ultimately become the inverse cube of the distance, since the quantity of electricity induced upon B will be ultimately in the inverse ratio of the distance, and the attraction between the balls as the product of the quantities of electricity directly, and as the square of the distance inversely, and hence the formula given by Mr. Harris cannot express the law of force when the balls are very distant. In the experiments by which his formula is tested, the force of attraction is measured by means of an ordinary balance and weights : the only comparison of results which he publishes is transcribed in the following table. Distance of centres. Measured force in grains. Values of '^'^•^^•-^l ri = 2-3 ea=2-5 03=2-8 e4=30 15 8-25+ 4-6 + 3-5 - 15 8-28 4'62 3-46 From this table we see that the formula is verified in three cases to the extent of accuracy of the experiments. Comparisons extended to a much wider range of distances would be required to establish it, and it would be necessary to take precautions to prevent the experimental results from being influenced by dis- turbing causes. In the experiments made by Mr. Harris we find that no precautions have been taken to avoid the disturbing influence of extraneous conductors, which, according to the descriptions and drawings he gives of his instruments, seem to exist very abundantly in the neighbourhood of the bodies operated upon, being partly metal in connexion with the insu- lated system with which the body A communicates, and partly uninsulated metal, in the fixed parts of the electrometer, and in the moveable parts by which B is supported. The general effect Electricity in Equilibrium. 4i7 produced by the presence of such bodies in disturbing the observed law of force, must be to make it diminish less rapidly with the distance when A and B are separated by a considerable interval : and it is probably owing, at least in part, to such dis- turbing causes that Mr. Harris's results nearly agree, as far as they go, with a formula which would ultimately give for the law of force the inverse square of the distance between A and B, instead of the inverse cube. 4. The determination by the mathematical theory of the at- traction or repulsion between two electrified conducting spheres has not hitherto, so far as I am aware, been attempted, and would present considerable difficulty by means of the formulse ordinarily given for such problems. It may, however, very readily be effected by means of a general theorem on the attrac- tion between electrified conductors, which will be given in a subsequent paper*. Thus, if F (c) be the force of attraction, corresponding to the distance c between the centres, in the par- ticular case when the two spheres are equal (the radius of each being unity), and the potential in the interior of one of them is nothing (as will be the case when the body is uninsulated), the potential in the interior of the other being v, I have found the following formulae which express F (c) by a converging series. where ^w=''^.; ' ciifj See Murphy's " Electricity," p. 41, or Pratt's " Mechanics," Art. 154. ' tCavendish demonstrates mathematically that if the law of force be any other than the inverse square of the distance, electricity could not rest in equilibrium on the surface of a conductor. But experiment has shown, that electricity does rest at the surface of a conductor. Hence the law of force must be the inverse square of the distance. Cavendish considered the second proposition as highly probable, but had not experimental evidence to support this opinion, in his published work (An attempt to explain the phrenomena of Electricity by means of an Elastic Fluid). Since his time, the most perfect experimental evidence has been obtained that electricity resides at the surface of a conductor ; in such facts, for instance, as the perfect equivalence in all electro-statical relations of a hollow metallic con- ductor of ever so thin substance, or of a gilt non-conductor (possessing a conducting film of not more than ^^oWjt of ^"^ i^^ch thick) and a solid conductor of the same external form and dimensions j the minor premise of his syllogism is thus demonstrated, and the conclusion is therefore established.] Phil Mag. S. 4. Vol. 8. No. 49. July 1854. E 50 Prof. Thomson on the Mathematical Theory of distance, and at all smaller distances there is attraction between the bodies. These results are, with all their peculiarities, in full accordance with the theory of Coulomb, which indicates that, if the quan- tities of electricity be equal, and the bodies equal and similar, there will be repulsion in every position : but if there be any difference, however small, between the charges, the repulsion will necessarily cease, and attraction commence, before contact takes place, when one body is made to approach the other. Un- less, however, the difference of the charges be sufficiently consi- derable, a spark may pass between the bodies, and render the charges equal, before attraction commences. In Mr. Harris's experiments, in which the bodies seem to have been nearly oblate spheroids, the attraction is generally sensible before the distance is small enough to allow a spark to pass, if the charge on one be double of that on the other. Mr. Harris next proceeds to investigate the theory of the proof plane, and to examine whether it can be considered as indicating with certainty the intensity of electricity at any part of a charged body, and, principally from an experiment made on a charged non-conductor (a hollow sphere of glass), comes to a negative conclusion. It should be remembered, however, that, the proof plane having never been applied to determine the in- tensity at points of the surface of a charged non-conductor, such conclusions in no way interfere with adopted ideas. Since there can be no manner of doubt as to the theory of this valuable instrument, as we find it explained by M. Pouillet*, nor as to the experimental use of it made by Coulomb, it is unnecessary to enter more at length on the subject here. 7. Mr. Faraday's researches on electro-statical induction, which are published in a memoir forming the eleventh series of his " Experimental Researches in Electricity,'' were undertaken with a view to test an idea which he had long posstessed, that the forces of attraction and repulsion exercised by free electri- city are not the resultant of actions exercised at a distance, but are propagated by means of molecular action among the conti- guous particles of the insulating medium surrounding the electrified bodies, which he therefore calls the dielectric. By this idea he has been led to some very remarkable views upon induction, or in fact upon electrical action in general. As it is impossible that the phsenomena observed by Faraday can be incompatible with the results of experiment which constitute Coulomb's theory, it is to be expected that the difference of his ideas from those of Coulomb must arise solely from a different method of stating, and interpreting physically, the same laws : • See Note IV. V; Electricity in Equilibrium. ;::'^^ |>1 and further, it may I think be shown that either method, of viewing the subject, when carried sufficiently far, may be made the foundation of a mathematical theory which would lead to the elementary principles of the other as consequences. This theory would accordingly be the expression of the ultimate law of the phsenomena, independently of any physical hypothesis we might, from other circumstances, be led to adopt. That there are necessarily two distinct elementary ways of viewing the theory of electricity, may be seen from the following considera- tions, founded on the principles developed in a previous paper in this Journal*. Corresponding to every problem relative to the distribution of electricity on conductors, or to forces of attraction and re- pulsion exercised by electrified bodies, there is a problem in the uniform motion of heat which presents the same analytical conditions, and which, therefore, considered mathematically, is the same problem. Thus, let a conductor A, charged with a given quantity of electricity, be insulated in a hollow conducting shell, B, which we may suppose to be uninsulated. According to the mathematical theory, an equal quantity of electricity of the contrary kind will be attracted to the interior surface of B (or the surface of B, as we may call it to avoid circumlocution), and the distribution of this charge, and of the charge on A, will take place so that the resultant attraction at any point of each surface may be in the direction of the normal. This condition being satisfied, it will follow that there is no attraction on any point within A, or without the surface of B, that is, on any point within either of the conducting bodies. The most conve- nient mathematical expression for the condition of equilibrium, is that the potential at any point Pf must have a constant value when P is on the surface of A, and the value nothing when P is on the surface of B ; and it will follow from this that the potential will have the same constant value for any point within A, and will be equal to nothing for any point without the sur- face of B. If A be subject to the influence of any uninsulated conductors, we must consider such bodies as belonging to the shell in which A is contained, and their surfaces as forming part of the surface of B : in such cases this surface will generally be the interior surface of the walls of the room in which A is contained, and of all uninsulated conductors in the room. If, however, we * On the Uniform Motion of Heat, and its Connexion with the Mathe- matical Theory of Electricity, vol. iii. p. 73 [Phil. Mag. S. 4. vol. vii. p. 502]. t The term used by Green for the sum of the quotients obtained by dividing the product of each element of the surfaces of A and B, and its electrical intensity, by its distance from P. E2 62 Prof. Thomson on the Mathematical Theoi^ of have to consider the case iu which A is subject to no external influence, we must suppose every part of the surface of B to be very far from A. The most general problem we can contemplate in electricity (exclusively of the case in which the insulating medium is heterogeneous, and exercises a special action, which will be alluded to below), is to determine the potential at any point when A, instead of being a single conductor, is a group of separate insulated conductors charged to different degrees, and when there are non-conductors electrified in a given manner, placed in the insulating medium, in the neighbourhood. The conditions of equilibrium will still be that the potential at each surface due to all the free electricity must be constant, and the theorems stated above will still be true : thus the attraction will be nothing in the interior of each portion of A, and without the surface of B ; and the whole quantity of induced electricity on the latter surface will be the algebraic sum of the charges of all the interior bodies with its sign changed. When the potential due to such a system is determined for every point, the compo- nent of the resultant force at any point P, in any direction PL, may be found by differentiation, being the limit of the differ- ence between the values of the potential at P, and at a point Q, in PL, divided by PQ, when P moves up towards and ultimately coincides with P, and the direction of the force, on a negative particle, being that in which the potential increases. By Cou- lomb's theorem, the intensity at any point in one of the con- ducting surfaces is equal to the attraction (on a negative unit), at that point, divided by 47r. Now if we wish to consider the corresponding problem in the theory of heat, we must suppose the space between A and B, instead of being filled with a dielectric medium (that is, a non- conductor for electricity), to be occupied by any homogeneous solid body, and sources of heat or cold to be so distributed over the terminating surfaces, or the interior surface of B and the surface of A, that the permanent temperature at the first surface may be zero, and at the second shall have a certain constant value, the same as that of the potential in the case of electricity. If A consist of different isolated portions, the temperature at the surface of each will have a constant value, which is not neces- sarily the same for the different portions. The problem of distributing sources of heat, according to tliese conditions, is mathematically identical with the problem of distributing elec- tricity in equilibrium on the surfaces of A and B. In the case of heat, the permanent temperature at any point replaces the potential at the coiTcsponding point in the electrical system, and consequently the resultant flux of heat replaces the resultant attraction of the electrified bodies, in direction and magnitude. ' Electricity in Equilibrium. ' *^>*'^ 63 The problem in each case is determinate, and we may therefore employ the elementary principles of one theory, as theorems, relative to the other. Thus, in the paper in which these consi- derations are developed, CoulomVs fundamental theorem relative to electricity is applied to the theory of heat ; and self-evident propositions in the latter theory are made the foundation of Green's theorems in electricity*. Now the laws of motion for heat which Fourier lays down in his Theorie Analytique de la Chaleurj are of that simple elementary kind which constitute a mathematical theory properly so called ; and therefore, when we find corresponding laws to be true for the phsenomena pre- sented by electrified bodies, we may make them the foundation of the mathematical theory of electricity : and this may be done if we consider them merely as actual truths, without adopting any physical hypothesis, although the idea they naturally sug- gest is that of the propagation of some efi^ect by means of the mutual action of contiguous particles; just as Coulomb, although his laws naturally suggest the idea of material particles attract- ing or repelling one another at a distance, most carefully avoids making this a physical hypothesis, and confines himself to the consideration of the mechanical efi'ects which he observes and their necessary consequences f. All the views which Faraday has brought forward, and illus- trated or demonstrated by experiment, lead to this method of establishing the mathematical theory, and, as far as the analysis is concerned, it would, in most general propositions, be even more simple, if possible, than that of Coulomb. (Of course the analysis of particular problems would be identical in the two methods.) It is thus that Faraday arrives at a knowledge of some of the most important of the general theorems, which, from their nature, seemed destined never to be perceived except as mathematical truths. Thus, in his theory, the following proposition is an elementary principle. Let any portion a of the surface of A be projected on B, by means of lines (which will be in general curved) possessing the property that the resultant electrical force at any point of each of them is in the direction of the tangent : the quantity of electricity produced by induction on this projection is equal to the quantity of the opposite kind of electricity on a J. The lines thus defined are what Faraday calls the " curved lines of inductive action.^' For ■ * It was not until some time after that paper was published, that I was able to add the dh-ect analytical demonstrations of the theorems, which are given in the papers on " General Propositions in the Theory of Attrac- tion," Math. Journ. vol. iii. pp. 189, 201, and which I have since found, are the same as those originally given by Green, t See Note I. + See Note IV. ^ 5if Prof. Thomson on the Mathematical Theory of a detailed account of the experiments by which these phenomena are investigated, reference must be made to Mr. Faraday's own memoirs, published in the Philosophical Transactions, and in a separate form in his " Experimental Researches." 8. The hypothesis adopted by Faraday, of the propagation of inductive action, naturally led him to the idea that its effects may be in some degree dependent upon the nature of the insu- lating medium or dielectric, by which, according to this view, it is transmitted. In the second part of his memoir he describes a series of researches instituted to put this to the test of experi- ment, and arrives at the following conclusions. If the dielectric be air, the inductive action is quite inde- pendent of its density or temperature (which, as Mr. Faraday remarks, agrees perfectly with previous results obtained by Mr. Harris) ; and in general, if the dielectric be any gas or vapour capable of insulating a charge, the inductive action is invariable. Hence he concludes that " all gases have the same power of or capacity for, sustaining induction through them (which might have been expected when it was found that no variation of density or pressure produced any effect.) '^ When the dielectric is solid, the induction is greater than through air, and varies according to the nature of the substance. Numbers which measure the ** specific inductive capacities" of the dielectrics employed (sulphur, shell-lac, glass, &c.), are de- duced from the experiments. To express these results in the language of the mathematical theory, let us recur to the supposition of a body, A, charged with a given quantity of electricity, and insulated in the interior of a closed conducting shell, B. The potential of the system at the interior surface of B, and at every point without this surface, will be nothing ; at the surface and in the interior of A it will have a constant value, which will depend on the form, magni- tude, and relative position of the surfaces A and B, on the quantity of electricity on A, and, according to Faraday's dis- covery, on the dielectric power of the insulating medium which fills the space between A and B. If this be gaseous, neither its nature, nor its state as to temperature, pressure, or density, will "affect the value of the potential in A ; but if it be a solid sub- stance, such as sulphur or shell-lac, the value of the potential will be less than when the space is occupied by air, and will vary with the nature of the insulating solid. The result in the case of a gaseous dielectric is what would follow from Coulomb's theory, if we consider gases to be quite impermeable to electricity, and to be entirely unaffected by electrical influence. The phsenomena observed with solid dielec- trics, which agree with the circumstance observed by Nicholson, Electricity in Equilibrium, 56 that the dissimulating power of a Leyden phial depends on the nature of the glass of which it is made, as well as on its thick- ness, have been by some attributed to a slight degree of con- ducting power, or of penetrability, possessed by solid insulators. This explanation, however, seems to be very insufficient ; and besides, Faraday has estimated the nature of the effects of imper- fect insulation, by independent experiments, and has established, in what seems to be a very satisfactory manner, the existence of a peculiar action in the interior of solid insulators when subjected to electrical influence. As far as can be gathered from the experiments which have yet been made, it seems probable that a dielectric, subjected to electrical influence, becomes excited in such a manner that every portion of it, however small, possesses polarity exactly analogous to the magnetic polarity induced in the substance of a piece of soft iron under the influence of a magnet. By means of a certain hypothesis regarding the nature of magnetic action*, Poisson has investigated the mathematical" laws of the distribution of magnetism and of magnetic attrac- tions and repulsions. These laws seem to represent in the most general manner the state of a body polarized by influence, and therefore, without adopting any particular mechanical hypothesis, we may make use of them to form a mathematical theory of electrical influence in dielectrics, the truth of which can only be established by a rigorous comparison of its results with experi- ment. Let us therefore consider what would be the effect, according to this theory, which would be produced by the presence of a solid dielectric, C, placed in the space between A and B, the rest of which is occupied by air. The action of C, when excited by the influence of the electricities on A and B, may (as Poisson has shown for magnetism) be represented, whether on points within or without C, by a certain distribution of positive electricity on one portion of the surface of C, and of an equal quantity of negative electricity on the remainder. The condition necessary * Faraday adopts the corresponding hypothesis to explain the action of a sohd dielectric, which he states thus : — " If the space round a charged globe were filled with a mixture of an insulating dielectric, as oil of tur- pentine or air, and small globular conductors, as shot, the latter being at a little distance from .each other, so as to be insulated, then these in their condition and action exactly resemble what I consider to be the condition * and action of the particles of the insulating dielectric itself. If the globe were charged, these little conductors would all be polar ; if the globe were discharged, they would all return to their normal state, to be polarized again upon the recharging of the globe." — (Experimental Researches, § 1679.) The results of the mathematical analysis of such an action are given in the text. It may be added that the value of the coefficient k will diflfer sensibly from unity if the volume occupied by the small conducting balls bear a finite ratio to that occupied by the insulating medium. 6^- Prof. Thomson on the Mathematical Theonj of and sufficient for determining this distribution may (as can be shown from Poisson's analysis) be expressed as follows. Let R be the resultant force on a point P without C, and R' on a point P' within C, due to the electrified surfaces A and B, and to the imagined distribution on C. If P and P' be taken infinitely near one another, and consequently each infinitely near the surface of C, the component of 11' in the direction of the normal must bear to the component of R in the same direction a constant ratio \~r) depending on the capacity for dielectric induction of the matter of C*. The components of R and R' in the tangent plane will of course be equal and in the same direction, and, if p be the intensity of the imagined distribution on the surface of C, in the neighbourhood of P and P', the difference of the normal components will be Airp, as is evident from Coulomb's theorem, referred to above. Let us now suppose C to be a shell surrounding A, and let S and S', its interior and exterior surfaces, be surfaces of equili- brium in the system of forces due to the action of A and B, and of the polarity of C. It may be shown that the same surfaces S, S' would necessarily be surfaces of equilibrium, if C were removed and the whole space were filled with air ; and conse- quently, that the whole series of surfaces of equilibrium, com- mencing with A and ending with B, will be the same in the two cases. Hence the resultant force due to the excitation of the dielectric C, or to the imagined distributions of electricity on S and S' which produce it, on points within S or without S', must be such as not to alter the distributions on A and B when the quantity on A is given, and is therefore nothing. Accordingly, let Q be the total force on a point indefinitely near S, and within it ; Q' the total force on a point without S', but indefinitely near it. Since the forces on points without S and within S' indefi^it * From this it follows, that, in the case of heat, C must be replaced by a body whose conducting power is k times as great as that of the matter occupying the remainder of the space between A and B. . - ['fhe same demonstration, of course, is applicable to the influence of a piece of soft iron, or other " paramagnetic" (i.e. substance of ferro-magnetic mductive capacity), or to the reverse influence of a diamagnetic on the magnetic force in any locality near a magnet in which it can be placed, and shows that the lines of magnetic force will be altered by it precisely as the lines of motion of heat in corresponding thermal circumstances would be altered by introducing a body of greater or of less conducting power for heat. Hence we see now strict is the foundation for an analogy on which the amducting power of a maynetic medium for lines offeree may be spoken of, and we have a perfect explanation of the condensing action of a para- magnetic, and the repiilsive effect of a diamagnetic, upon the lines of force of a magnetic field, wiiich have been described by Faradav. — (Exp. He- searches, §§ 280/, 2808).] rii8«:io W n* Electricity in Equilibrium, -^^^'i'^ '^^^ ^ 57 nitely near the former points are, according to the law stated Q 01 above, y- and -r, it follows that the intensities of the imagined distributions on S and S', in the nieghbourhood of the points considered, are Hence, if U, U' be the potentials at S, S', due to A and B alone, and V the potential at any point P, it follows* that the potential at P. due to the polarity of the dielectric, is -('-i)-('-.>. or M .A 'nfyiiftiU ^(l^j\+ (}-l)vy that is 0, according as P is within S, within S' and without S, or without S'. Hence the total potential will be, according to the position ofP, „_(l-|)(U-U'), or V. -^<7./^i ■f>-my^[tf$nhD': Hence the sole effect of the dielectric C, on thfe state of A and B, is to diminish the potential in the interior of the former by the quantity (l_l)(U-U'). If the whole space between A and B be occupied by the solid dielectric, the surfaces S and A will coincide, as also S' and B, and therefore U=:V, U'=0. Hence the potential in the inte- rior of A will be V ■J. k ' f b^'r}-: or the fraction y of the potential, with the same charge on A, and with a gaseous dielectric. From this it follows that, when * See Green's Essay, art. 12; or Math. Journal, vol. iii. p. 75. - 68 Prof, Thomson in this equa- tion, and then resolve for k. Thus we find p-a If only one of the apparatus be originally charged, according as it is the first or the second, we shall have or If the substance examined (the dielectric of the first appa- ratus) be any gas, or air in a different state as to pressure or temperature from the air of the second apparatus, Faraday always finds the intensity after contact to be half the original intensity, and hence for every gaseous body k = l. If the dielectric of the first apparatus be solid, the intensity after contact is found to 1)3 greater than half the original inten- sity when the first, and less than half when the second is the apparatus originally charged. Hence for a solid dielectric ^> 1. For sulphur Faraday finds the value to be rather more than 2'2; for shell-lac, about 2; and for flint-glass, greater than 1*76. The commonly received ideas of attraction and repulsion eiercised at a distance, independently of any intervening me- dium, are quite consistent with all the phsenomena of electrical action which have been here adduced. Thus we may consider the particles of air in the neighbourhood of electrified bodies to be entirely uninfluenced, and therefore to produce no effect in the resultant action on any point : but the particles of a solid non-conductor must be considered as assuming a polarized state when under the influence of free electricity, so as to exercise attractions or repulsions on points at a distance, which, with the 69 Prof. Thomson on the Mathematical Theory of action due to the charged surfaces, produce the resultant force at any point. It is no doubt possible that such forces at a distance may be discovered to be produced entirely by the action of contiguous particles of some intervening medium, and we have an analogy for this in the case of heat, where certain effects which follow the same laws are undoubtedly propagated from particle to particle. It might also be found that magnetic forces are propagated by means of a second medium, and the force of gravitation by means of a third. We know nothing, however, of the molecular action by which such effects could be produced, and in the present state of physical science it is necessary to admit the known facts in each theory as the foundation of the ultimate laws of action at a distance. St. Peter's College, Nov. 22, 1845. -'^ NOTES. Note I. Coulomb has expressed his theory in such a manner that it can only be attacked in the way of proving his experimental results to be iaaccurate. This is shown in the following remarkable passage in his sixth memoir, which follows a short discussion of some of the physical ideas then com- monly held with reference to electricity. " Je previens pour mettre la th^orie qui va suivre a Vahri de toute dispute syst^matique, que dans la supposition des deux fiuides electriques, je n*ai d'autre intention que de prisenter avec le moins d'eMmens possible, les resultats du calcul et de I'exp&ience, et non d'indiquer les v^tables causes de V4lectr%cit^. Je renverrai, h la Jin de mon travail sur I* electricity, Vexamen des principaux systhnes auxqiiels les ph^iomenes Electriques out donnE naissance." — H«*- toire de VAcademie, 1788, p. 673. Note II. This theorem may be stated as follows. Let A be a closed surface of any form, and let matter, attracting inversely as the square of the distance, be so distributed over it that the resultant attraction on an interior point is nothing : the resultant attraction on an exterior point, indefinitely near any part of the surface, will be perpendicular to the surface and equal to 47r/), if pa) be the quantity of matter on an element to of the surface in the neighbourhood of the point. Coulomb's demonstration of this theorem may be found in a preceding paper in the Mathematical Journal, vol. iii. p. 74. He gives it himself, in his sixth memoir on Electricity {Histoire de VAcad^mie, 1788, p. 677)j in connexion with an investigation of the theory of the proof plane in which, by an error that is readily rectified, he arrives at the result that a small insulated conducting disc, put in contact with an electrified conductor at any point, and then removed, carries with it as much electricity as lies on an element of the conductor at that point equal in area to the two faces of the disc ; the quantity actually removed being only half of this. This result, however, does not at all afiVict the experimental use which he makes of the proof plane, which is merely to find the ratios of the intensities at difi'erent points of a charged conductor. As the complete theory of this valuable instrument has not, so far as I am aware, been given in any English work, I annex the following remarkably \yt ivic^^ Electricity in Equilibrium, &i clear account of it, vfrhich is extracted from Pouillet's Traits de Physique : — " Quand le plan d'epreuve est tangent a une surface, il se confond avec 1' Element qu'il touche, il prend en quelque sorte sa place relativement h. I'^lectricite, ou plutot il devient lui-meme Telement sur lequel la fluide se repand ; ainsi, quand on retire ce plan, on fait la meme chose que si I'on avait decoupe sur la surface un element de meme epaisseur et de meme etendue que lui, et qu'on I'eAt enleve pour le porter dans la balance sans qu'il perdit rien de I'electricite qui le couvre ; une fois separe de la surface, cet element n'aurait plus dans ses differents points qu'une epaisseur €lectrique moiti^ moindre, puisque la fluide devrait se repandre pour en couvrir les deux faces. Ce principe pose, I'experience n'exige plus que de rhabitude et de la dexterite : apres avoir touche un point de la surface avec le plan d'epreuve, on I'apporte dans la balance, oti il partage son electricite avec le disque de I'aiguille qui lui est egale, et I'on observe la force de torsion a une distance connue. On repete la meme experience en touchant un autre point, et le rapport des forces de torsion est le rapport des repulsions electriques; on en prend la racine carree pour avoir le rapport des epaisseurs. Ainsi le genie de Coulomb a donne en meme temps aux mathematiciens la loi fondamentale suivant laquelle la matiere electrique s'attire et se repousse ; et aux physiciens une balance nouvelle, et des principes d' experience au moyen desquels ils peuvent en quelque sorte sonder Tepaisseur de I'electricite sur tous les corps, et determiner les pressions qu'elle exerce sur les obstacles qui I'arretent." To this explanation it should be added, that, when the proof plane is still very near the body to which it has been applied, the effect of mutual influ- ence is such as to make the intensity be insensible at every point of the disc on the side next the conductor, and at each point of the conductor which is under the disc. It is only when the disc is removed to a consi- derable distance that the electricity spreads itself symmetrically on its two faces, and that the intensity at the point of the conductor to which it was applied, recovers its original value. It was the omission of this considera- ^on that qaused Coulomb to fall into the error alluded to above. Note III. This memoir of Green's has been unfortunately very little known, either in this country or on the continent. Some of the principal theorems in it have been re-discovered within the last few years, and published in the following works : — Comptes Rendus for Feb. 11 th, 1839, where part of the series of theorems is announced without demonstration, by Chasles. Gauss's memoir on " General Theorems relating to Attractive and Re- pulsive Forces, varying inversely as the square of the distance," in the Result ate aus den Beohachtungen des magnetischen Vereins imJahre, 1839, Leipsic, 1840. (Translations of this paper have been published in Taylor's Scientific Memoirs for April 1842, and in the Numbers of Liouville's Journal for July and August, 1842.) Mathematical Journal, vol. iii. Feb. 1842, in a paper " On the Uniform Motion of Heat, &c." Additions to the Connaissance des Terns for 1845 (published June 1842), where Chasles supplies demonstrations of the theorems which he had pre- viously announced. I should add that it was not till the beginning of the present year (1845) that I succeeded in meeting with Green's Essay. The allusion made to his name with reference to the word " potential" (Mathematical Journal, vol, iii. p. 190), was taken from a memoir of Murphy's, " On Definite 63 Hoyal Society. Integral! with Physical Applications," in the Cambridge Transactions, where a miitaken definition of that term, as used by Green, is given. Note IV. This theorem may be proved as follows :— Let S be any closed surface, containing no part of the electrified bodies within it, which we may conceive to be described between A and B ; let P be the component in the direction of the normal, of the resultant force at any point of the surface S, and let ds be an element of the surface at the same point. Then it may be easily proved (see Math. Joum.vol. iii. p. 204), that JJpds^o, (fl) the integrations being extended over the entire surface. Now let S be supposed to consist of three parts ; the portion a, of the surface of A ; its projection /S, on the interior surface of B ; and the surface generated by the curved lines of projection. The value of P at each point of the latter portion of S will be nothing, since the tangent at any point of a line of projection is the direction of the force. Hence, if iJjFds]^ and ( ffFds) denote the values of /yPrfs, for the portions a and ^ of 8, the equation (a) becomes l//?ds-] + {//Pds)^0, But if p be the intensity of the distribution on the surface A or B, at any point, we have, by Coulomb's theorem, P Hence lffpds]^-{ffpds)^0, which is the theorem quoted in the text. IX. Proceedings of Learned Societies. ROYAL SOCIETY. [Continued from vol. vii. p. 626.] May 4, 1854.— Colonel Sabine, R.A.,Treas. and V.P.. in the Chair. THE following papers were read : — 1. " Account of Researches in Thermo-electricity." By Professor W. Thomson of Glasgow, F.R.S, § I. On the Thermal Effects of Electric Currents in Unequally Heated Conductors. Theoretical considerations (communicated in December 1851 to the Royal Society of Edinburgh), founded on observations which had been made regarding the law of thermo-electric force in an un- equally heated circuit of two metals, led me to the conclusion that an electric current must exercise a convective effect on heat in a homogeneous metallic conductor of which different parts are kept at different temperatures. A special application of the reasoning to the case of a compound circuit of copper and iron was made, and it 18 repeated here because of the illustration it affords of the mecha- nical principles on which the general reasoning is founded. Royal Society, 63 Becquerel discovered that if one junction of copper and iron, in a circuit of the two metals, be kept at an ordinary atmospheric tem- perature, while the other is raised gradually to a red or white heat, a current first sets from copper to iron through the hot junction, in- creasing in strength only as long as the temperature is below about 300° Cent. ; and becoming feebler with farther elevations of tempera- ture until it ceases, and a current actually sets in the contrary direc- tion when a high red heat is attained. Many experimenters have professed themselves unable to verify this extraordinary discovery, but the description which M. Becquerel gives of his experiments leaves no room for the doubts which some have thrown upon his conclusion, and establishes the thermo-electric inversion between iron and copper, not as a singular case (extraordinary and Unex- pected as it appeared), but as a phsenomenon to be looked for be- tween any two metals, when tried through a sufficient range of tem- perature, especially any two which lie near one another in the thermo-electric series for ordinary temperatures. M. Regnault has verified M. Becquerel's conclusion so far, in finding that the strength of the current in a circuit of copper and iron wire did not increase sensibly for elevations of temperature above 240° Cent., and began to diminish when the temperature considerably exceeded this limit; but the actual inversion observed by M. Becquerel is required to. show that the diminution of strength in the current is due to a real falling oflF in the electromotive force, and not to the increased resist- ance known to be produced by an elevation of temperature. From Becquerel's discovery it follows that, for temperatures be- low a certain limit, which, for particular specimens of copper and iron wire, I have ascertained, by a mode of experimenting described below, to be 280° Cent., copper is on the negative side of iron in the thermo-electric series, and on the positive side for higher tempera- tures ; and at the limiting temperature copper and iron are thermo- electrically neutral to one another. It follows, according to the general mechanical theory of thermo-electric currents referred to above, that electricity passing from copper to iron causes the absorp- tion or the evolution of heat according as the temperature of the metals is below or above the neutral point ; but neither evolution nor absorption of heat, if the temperature be precisely that of neu- trality (a conclusion which I have already partially verified by experiment). Hence, if in a circuit of copper and iron, one junction be kept about 280°, that is, at the neutral temperature, and the other at any lower temperature, a thermo-electric current will set from copper to iron through the hot, and from iron to copper through the cold junction ; causing the evolution of heat at the latter, and the raising of weights too if it be employed to work an electro-mag- netic engine, but not causing the absorption of any heat at the hot junction. Hence there must be an absorption of heat at some part or parts of the circuit consisting solely of one metal or of the other, to an amount equivalent to the heat evolved at the cold junction, to- gether with the thermal value of any mechanical effects produced in other parts of the circuit. The locality of this absorption can only 64 Boyal Society, be where the temperatures of the single metals are non-uniform, since the thermal effect of a current in any homogeneous uniformly- heated conductor is always an evolution of heat. Hence there must be on the whole an absorption of heat, caused by the current in passing from cold to hot in copper, and from hot to cold in iron. When a current is forced through the circuit against the thermo- electric force, the same reasoning establishes an evolution of heat to an amount equivalent to the sum of the heat that would be then taken in at the cold junction, and the value in heat of the energy spent by the agency (chemical or of any other kind) by which the electromotive force is applied. The aggregate reversible thermal effect, thus demonstrated to exist in the unequally heated portions of the two metals, might be produced in one of the metals alone, or (as appears more natural to suppose) it may be the sum or difference of effects experienced by the two. Adopting as a matter of form the latter supposition, without excluding the former possibility, we may assert that either there is absorption of heat by the current passing from hot to cold in the copper, and evolution, to a less extent, in the iron of the same circuit; or there is absorption of heat produced by the current from hot to cold in the iron, and evolution of heat to a less amount in the copper ; or there must be absorption of heat in each metal, with the reverse effect in each case when the current is reversed. The reversible effect in a single metal of non-uniform temperature may be called a convection of heat ; and to avoid cir- cumlocution, I shall express it, that the vitreous electricity carries heat with it, or that the specific heat of vitreous electricity is positive, when this convection is in the nominal " direction of the current," and I shall apply the same expressions to " resinous electricity '* when the convection is against the nominal direction of the current. It is established then that one or other of the following three hypo- theses must be true : — Vitreous electricity carries heat with it in an unequally heated conductor whether of copper or iron ; but more in copper than in iron. Or Resinous electricity carries heat witii it in an unequally heated conductor whether of copper or iron; but more in iron than in copper. Or Vitreous electricity carries heat with it in an unequally heated conductor of copper, and Resinous electricity carries heat with it in an unequally heated conductor of iron. Immediately after communicating this theory to the Royal Society of Edinburgh, I commenced trying to ascertain by experiment which of the three hypotheses is the truth, as Theory with only thermo- electric data could not decide between them. I had a slight bias in favour of the first rather than the second, in consequence of the positiveness which, after Franklin, we habitually attribute to the vitreous electricity, and a very strong feeling of the improbability of the third. With the able and persevering exertions of my assistant, Mr. M*^Farlane, applied to the construction of various forms of ap- paratus and to assist me in conducting experiments, the research has been carried on, with little intermission, for more than two years. Mr. Robert Davidson, Mr. Charles A. Smith, and other friends have also given much valuable assistance during the greater part of this time, in the different experimental investigations of which results are now laid before the Royal Society. Only nu- gatory results were obtained until recently from multiplied and varied experiments both on copper and iron conductors; but the theoretical anticipation was of such a nature that no want of expe- rimental evidence could influence my conviction of its truth. About four months ago, by means of a new form of apparatus. I ascertained that resinous electricity carries heat with it in an unequally heated iron conductor. A similar equally sensitive arrangement showed no re- sult for copper. The second hypothesis might then have been ex- pected to hold ; but to ascertain the truth with certainty I have continued ever since, getting an experiment on copper nearly every week with more and more sensitive arrangements, and at last, in two experiments, I have made out with certainty, that vitreous elec- tricity carries heat tvith it in an unequally heated copper conductor. The third hypothesis is thus established : a most unexpected con- clusion I am M'illing to confess. I intend to continue the research, and I hope not only to ascer- tain the nature of the thermal effects in other metals, but to deter- mine its amount in absolute measure in the most important cases, and to find how it varies, if at all, with the temperature ; that is, to determine the character (positive or negative) and the value of the specific heat, varying or not with the temperature, of the unit of current electricity in various metals. '*t' ■AM, § II. On the Law of Thermo-electric Force in an unequally heated '^^ circuit of tivo Metals. ::• A general relation between the specific heats of electricity in two diflferent metals, and the law of thermo-electric force, in a circuit composed of them according to the temperatures of their junctions, was established in the communication to the Royal Society of Edin- burgh referred to above, and was expressed by an equation* which may now be simplified by the thermometric assumption (jx denoting Carnot's function, J Joule's equivalent, and t the tempe- rature measured from an absolute zero, about 273^° Cent, below the freezing-point,) since this assumption defines a system of thermometry in absolute measure, which the experimental researches recently made by Mr. Joule and myself establish as not differing sensibly from the scale of the air- thermometer between ordinary limits. The equ^,*] tion, when so modified, takes the following form : — ^^'l F=j{|(s-T)+j;;.(i-i)*}. "^ where ^ denotes the excess of the specific heat of electricity in the * See Proceedings R.S.E. Dec. 1851, or Philosophical Magazine, 1852. -• «»rt PhiL Mag, S. 4. Vol. 8. No. 49. July 1854. F 66 Royal Society, metal through which the current goes from cold to hot above the specific heat of the same electricity in the other metal, at the tem- perature t ; F the thermo-electric force in the circuit when the two junctions are kept at tlie temperatures S and T respectively, of which the former is the higher ; and 9g the amount of heat absorbed per unit of electricity crossing the hot junction. The following relation (similarly simplified in form) was also established : — ^ Q de These relations show how important it is towards the special ob- ject of determining the 8j)ecific heats of electricity in metals, to in- vestigate the law of electronjotive force in various cases, and to de- termine the thermal effect of electricity in passing from one metal to another at various temperatures. Both of these objects of research are therefore included in the general investigation of the subject. The only progress I have as yet made in the last-mentioned branch of the inquiry, has been to demonstrate experimentally that there is a cooling or heating effect produced by a current between copper and iron at an ordinary atmospheric temperature according as it passes from copper to iron or from iron to copper, in verifica- tion of a theoretical conclusion mentioned above : but I intend shortly to extend the verification of theory to a demonstration that reverse effects take place between those metals at a temperature above their neutral point of about 280° Cent. ; and I hope also to be able to make determinations in absolute measure of the amount of the Peltier eflfect for a given strength of current between various pairs of metals. With reference to laws of electromotive force in various cases, I have commenced by determining the order of several specimens of metals in the thermo-electric series, and have ascertained some very curious facts regarding varieties in this series which exist at different temperatures. In this I have only followed Becquerel's remarkable discovery, from which I had been led to the reasoning and experimental investigation regarding copper and iron described above. My way of experimenting has been to raise the temperature first of one junction as far as the circumstances admit, keeping the other cold, and then to raise the temperature of the other gradually, and watch the indications of a galvanometer during the whole process. When an inversion of the current is noticed, the changing temperature is brought back till the galvanometer shows no current ; and then (by a process quite analogous to that followed by Mr. Joule and Dr. Lyon Playfair in ascertaining the temperature at which water is of maximum density) the temperatures of the two junctions are ap- proximated, the galvanometer always being kept as near zero as possible. When the difference between any two temperatures on each side of the neutral })oint which give no current is not very great, their arithmetical mean will be the neutral temperature. A regular deviation of the mean temperature from the true neutral tempera- ture is to be looked for with wide ranges, and a determination of it Royal Society. BT would show the law according to which the difference of the spe- cific heat of electricity in the two metals varies with the tempera- tures ; but I have not even as yet ascertained with certainty the ex- istence of such a deviation in any particular case. The following is a summary of the principal results I have already obtained in this department of the subject. The metals tried being, — three platinum wires (P^ the thickest, Pg the thinnest, and Pg one of intermediate thickness), brass wires (B), a lead wire (L'), shps of sheet lead (L), copper wires (C), and iron wire (I), I find that the specimens experimented on stand thermo-electrically at different temperatures in the order shown in the following Table, and explained in the heading by reference to bismuth and antimony, or to the terms " negative " and " positive " as often used : — Temp. Cent. Bismuth " Negative. Antimony * Positive." -20 0 37 64 130 140 280 300 ...P, ..R...r .Pi. .Pi. ...P3 6...{L'PJ C.Pi I. ...P3. ...P3. ...P3. ...P3. ...Ps. .Pa... h...V {CPi} I P^ {BP.}...L... C I .P2 rTPx...{BL} C ...I .P2 Pi.^ b... {CI} ...... .Pa Pi b,...,.l C It must be added, by way of explanation, that the bracket en- closing the symbols of any two of the metallic specimens indicates that they are neutral to one another at the corresponding temperature, and the arrow-head below one of them shows the direction in which it is changing its place with reference to the other, in the series, as the temperature is raised. When there is any doubt as to a posi- tion as shown in the Table, the symbol of the metal is a small letter instead of a capital. The rapidity with which copper changes its place among some of the other metals (the platinums and iron) is very remarkable. Brass also changes its place in the same direction possibly no less rapidly than copper ; and lead changes its place also in the same direction but certainly less rapidly than brass, which after passing the thick platinum wire (PJ at 130° Cent, passes the lead at 140°, the lead itself having probably passed the thick platinum at some tempera- ture a little below 130°*. * I have since found that it does pass the thick platinum, at the temperature 118°. [May 16, 1854.] F2 ^8 Royal Society. The conclusion ns regards specific heats of electricity in the dif- ferent metals, from the equation expressing thermo-electric force given above, is that the specific heat of vitreous electricity is greater in each metal passing another from left to right in the series as the temperature rises than in the metal it passes : thus in particular, — The specific heat of vitreous electricity is greater in copper than in platinum or in iron ; greater in brass than in platinum or in lead ; and greater in lead than in platinum. It is probable enough from the results regarding iron and copper mentioned above, that the specific heat of vitreous electricity is positive in brass ; very small positive, or else negative, in platinum, perhaps of about the same value as in iron. It will not be difficult to test these speculations either by direct experiment on the convective effects of electric currents in the different metals, or by comparative measurements of thermo-electric forces for various temperatures in circuits of the metals, and I trust to be able to do so before long. § III. On Thermo-electricity in crystalline metals, and in metals in a state of mechanical strain. Having recently been occupied with an extension of the mechani- cal theory to the phaenomena of thermo-electricity in crystalline metals, I have been led to experimental investigation on this branch of the subject. The difficulty of obtaining actual metallic crystals of considerable dimensions made it desirable to imitate crystalline structure in various ways. The analogies of the crystalline optical properties which have been observed in transparent solids, in a state of strain, and of the crystalline structure as regards magnetic induc- tion which Dr. Tyndall's remarkable experiments show to be pro- duced not only in bismuth but in wax, thick paste of flour, and " the pith of fresh rolls," by pressure, made it almost certain that press- ure or tension on a mass of metal would give it the thermo-electric properties of a crystal. The only case which I have as yet had time to try, verifies this anticipation. I have found that copper wire stretched by a weight bears to similar copper wire unstretched, ex- actly the thermo-electric relation which Svanberg discovered in a bar cut equatorially from a crystal of bismuth or antimony compared ■with a bar cut axially from a crystal of the same metal. Thus I found that : — If part of a circuit of copper w ire be stretched by a considerable force and the remainder left in its natural condition, or stretched by a less force, and if either extremity of the stretched part be heated, a current sets from the stretched to the unstretched part through the hot junction : and if the wire be stretched and unstretched on the two sides of the heated part alternately, the current is reversed (as far as I have been able yet to test, instantaneously) with each change of the tension. I intend to make similar experiments on other metallic wires ; also to try the effect of transverse as well as of longitudinal tension on slips of sheet metal with their ends at different temperatures^ when placed longitudinally in an electric circuit ; and the effects of oblique tension on slips of metal similarly placed in a circuit, but kept with Eoyal Society. £j$ their ends at the same temperature and their lateral edges unequally heated. I have no doubt of being able so to verify every thermo- electric characteristic of crystalline structure, in metals in a state of strain. Glasgow College, March 30, 1854. P.S. April 19, 1854. — T have today found by experiment that iron wire when stretched by a considerable 'force bears a thermo-electric relation to unstretched iron wire, the opposite of that which I had previously discovered in the case of copper wire ; and I have ascer- tained that when the wire is alternately stretched and unstretched on the two sides of a heated part the current is reversed along with the change of tension, always passing from the unstretched to the stretched part, through the hot locality. I hope before the end of the present Session to have a complete account of all the experiments of which the results are stated above, ready to communicate to the Royal Society. 2. "An Introductory Memoir upon Quan tics." By Arthur Cayley, Esq., F.R.S. The subject of Quantics is defined as the entire subject of rational and integral functions, and of the equations and loci to which these give rise, but the memoir relates principally to the functions called quantics ; a quantic being in fact a rational and integral function, homogeneous in regard to a set of facients (j?, y. .), or more gene- rally homogeneous in regard to each of several such sets separately. A quantic of the degrees m, m' .. in the sets {x, y . .) {x\ y'. .) &c. is represented by a notation such as (*)(^,y..)V.y--)"'..). where the mark # is considered as indicative of the absolute gene- rality of the quantic. The coefficients of the different terms of the quantic may be either mere numerical multiples of single letters or elements, such as a, ^>, c, or else functions (in general rational and integral functions) of such elements ; this explains the meaning of the expression the elements of a quantic. The theory leads to the discussion of the derivatives called covariants. Of these covariants a very general definition is given as follows, viz. considering the quantic (#) (a;, y..)"^(y,y'.. )""'..), and selecting any two facients of the same set, e. g. the facients x, y, it is remarked tliat there is always an operation upon the elements tantamount as regards the quantic to the operation xdy, viz. if we differentiate with respect to each element, multiply by proper functions of the elements and add, the result will be that obtained by differentiating with dy and multi- plying by X. And if the operation upon the elements tantamount to xd is represented by {xd^}, then writing down the series of ope- rations {xdy)— xdy, . .{x'd'y}—x'dy', . .&c., where x, y are considered as being successively replaced by every permutation of two different facients of the set {x,y..), x',y' by every permutation of two different facients of the set ix',y' ..) &c., ^0 Royal Society, then it is clear that the quantic is reduced to zero by each of the ope- rations of the entire system, but this property is not by any means confined to the quantic ; and any function having the property in question, i. e. every function which is reduced to zero by each ope- ration of the entire system, is said to be a co variant of the quantic. The definition is afterwards still further generalized, and its connec- tion explained with the methods given, in the memoir ' On Linear Transformations,* Camb. and Dub. Math. Journal, Old Series, t. iv., and New Series, t. i., and the ' Memoire sur les Hyperd<§terminants,' Crelle, t. xxx., and some other theorems given in relation to the subject. The latter part of the memoir relates to the theory of the quantic (*)(j:', y)"*, and to the number of and relations between the CO variants, and as part of such theory to the beautiful law of reciprocity of MM. Sylvester and Hermite. May 1 1 . — The Earl of Rosse, President, in the Chair. The following paper was read : — " On the relation of the Angular Aperture of the Object-Glasses of Compound Microscopes to their penetrating power and to Oblique Light." By J. W. Griffith, M.D., F.L.S. The explanation given by Dr. Goring and others of the advantage of increased angular aperture in microscopic objective- glasses ap- pears to the author to be correct, as applied to the case of opake ob- jects, and accordingly his remarks in the present communication have reference to transparent objects only. It is known that delicate markings on a transparent object, such as the valve of a Gyrosigma, may be rendered more distinctly visible by using an object-glass of large aperture, by bringing the mirror to one side, and by placing a central stop jn the object-glass or the con- denser or in both ; the increased distinctness produced in these seve- ral ways being due to the illumination of the object by oblique light. Experiment also shows that the degree of obliquity of the light re- quisite varies with the delicacy or fineness of the markings, being greater as these are more delicate ; so that the finest markings re- quire tbe most oblique light which can possibly be obtained to ren- der them evident, and the angular aperture of the object-glass must necessarily be proportionately large, otherwise none of these oblique rays could enter it. If the parts of an object which refract the light are large in pro- portion to the power of the object-glass and of irregular form, they will refract a certain number of rays, so that these cannot enter the object-glass; hence certain parts will become dark, and will map out, as it were, in the image formed of the object, the structural peculiarities of the same. But if the parts are minute, of a curved form and ap- proximatively symmetrical, they will act upon the light transmitted through them in the manner of lenses, and their luminous or dark appearance will vary according to the relation of the foci of these to that of the object-glass. Thus the parts of an object may appear dark and defined, from the refraction of the light out of the field of the microscope ; alsO) from the concentration or dispersion of por- Royal Society, f\ tions of the light by these parts, all the rays being admitted by the object-glass, or entering the field. Another condition affecting distinctness consists in the relation which the luminousness or darkness of an object bears to that of the field or back ground upon which it is apparently situated. The refraction of the light out of the field of the microscope or beyond the angle of aperture of the object-glass is the ordinary cause of the outlines of objects becoming visible ; and in these cases, an increase of the angular aperture of the object-glass will impair their distinctness, because it will allow of the admission of those rays which would otherwise have been refracted from the field, and the margins will become more luminous and less contrasted with the luminous field. The cause of the distinctness of an object by refraction when all or nearly all the rays enter the field of the microscope, may be investigated in a drop of oil immersed in water, or in a drop of milk, as illuminated by light reflected from an ordinary mirror. The refractive power of the globules is so great and their form such, that each acts as a minute spherical lens; and the parts within the margin will appear light or dark according to the relation of the focus of the little lens to that of the object-glass. Under an object-glass of small aperture and moderate power the outline will appear black, because the marginal rays do not enter the object-glass. If the object-glass be of sufficient aperture to admit these marginal rays, the black margin will disappear, and the little lens will only be distinguishable by the above focal relation. Its appearance under oblique light (thrown from all sides, as when the condenser and a central stop are used) will vary ; but taking the case of extreme obliquity of the rays, the lens will only be visible by a luminous mar- gin from reflexion, giving it a very beautiful annular appearance. Hence it is more distinct by direct, or slightly oblique, than by very oblique light. But in certain objects, the irregularities of structure are of such extreme minuteness, or the difference of the refractive power of the various portions of the structure is so slight, that the course of the rays is but little altered by refraction on passing through them, and, under ordinary illumination, all the rays will enter the object-glass ; neither are the rays accumulated into little cones or parcels, of suffi- cient intensity to map out the little light or dark spots in the field of the microscope, according to the relation of their foci with that of the object-glass. Let us take the instance of an object with minute depressions on the surface, as the valve of a Gyrosigma. These are so minute, that when the light reflected from the ordinary mirror is used, the rays passing through the depressed and the undepressed portions, are not sufficiently refracted to cause either set to be excluded from the object-glass, consequently both sets will enter it. The slightly oblique and converging rays passing through a portion of the valve become separated into two sets, one passing through the thinner depressed portions, the other through the thicker and unde- 7fi Rayal Society. pressed portions : still both sets enter the object-glass. But on trans- mitting oblique light through the object, one set of the rays will be refracted so as not to enter the object-glass, whilst the other set will gain admission ; thus the two parts, which have diiFerently refracted the rays, will become distinct. If the markings were more delicate, or if the difference between the refractive power of the two portions of the valve were less, both sets would enter the object-glass. But on rendering the light still more oblique, one set would be again excluded by being refracted out of the field. Hence it is evident why the angular aperture of the object-glass must be larger as the markings are finer, or the difference between the refractive power of the two portions of tissue is less ; because the obliquity of the light requisite will be very great to cause the exclusion of one set of the rays, and the other set will be too oblique to enter the object-glass unless it be of correspondingly large aperture. This is the explanation of the advantage of oblique light. It has no peculiar power of rendering objects distinct, as has sometimes been believed, and the following experiment, supposed to show such peculiar power, is really to be explained on different grounds. A piece of net, or some similar texture, is placed behind a hole made in a window- shutter, and when thus viewed, the fibres are not well seen ; but when the texture is moved on one side, they become very distinctly visible, and this has been erroneously attributed to the illumination by oblique light ; whereas the increased distinctness in the lateral position is owing principally to the circumstance that the object is then viewed on a dark instead of a white ground as in the first instance ; although it is also true that in this position the oblique rays, being reflected in large numbers from the fibres into the eye, contribute to the distinct vision of the object when viewed as it then is upon a dark ground . The most difficult point has been to explain, how an object-- glass of large angular aperture will render markings evident;' which were not visible under an object-glass of smaller aperture ; be- cause it would naturally be imagined that the larger aperture would admit both sets of rays, one of which was excluded by the ob- ject-glass of smaller aperture. The difiiculty vanishes when it is re-l- collected that the additional rays admitted by the object-glass of largel*'-^ aperture are more oblique; hence one set of these rays will be re- fracted from the field of the microscope, whilst the other set will enter the object-glass and will illuminate the more highly refractive parts of the object ; thus the two kinds of differently refractive struc- ture become distinctly separated, one appearing dark, the other lumi-- nous ; in fact, by means of the additional rays admitted by the larger aperture we illuminate more highly one part of the object whilst the illumination of the other is not increased. In short, the object is illuminated, first, by rays corresponding to those admitted by an object-glass of small aperture ; and, secondly, by the additional rays admitted by the object-glass of larger aperture. The first set not being sufficiently oblique, no part of them is refracted beyond the angular aperture of the object-glaes ; the second, being more oblique* Royal Society. 73 are refracted out of the field by certain parts of the object and not by others, and thus contribute to render its different parts distin- guishable by contrast of darkness and illumination. The first set of rays, by illuminating all parts of the object, tend to diminish this contrast, and consequently do not add to but impair the discrimina- tive power of the object-glass for the fine markings of transparent objects, and accordingly these are rendered more distinctly visible by intercepting the less oblique rays by means of a central stop. It has been here assumed that the obUque light requisite for the display of the markings upon objects is separated into two sets of rays by refraction ; but the author observes that it might be ques- tioned whether they are not separated by reflexion. There can be no doubt that the latter is not generally the case ; perhaps the most important reason which may be assigned for this is, the considerable comparative breadth of the luminous portions of the valve of the Gyrosigma for instance. On transmitting unilateral light obliquely through the valve of an Isthmia, in which the depressions are large, in such manner that part of it is reflected by portions of them, it is easily seen how small the amount of reflected light is ; and this because the surface of the depressions is curved, and thus the por- tions inclined at the requisite angle for reflexion are also very small. As the amount of light reflected is so small in this case, it would be inappreciable in that of the Gyrosigma, in which the depressions are so exceedingly minute. In fact, attention to this point affords a ready means of distinguishing whether an object is illuminated by reflexion or refraction. The author next considers the relation of the penetrating power of an object-glass to its defining power. Penetrating power depends upon angular aperture, and consequently on oblique light. The question whether there be any essential difference between pene- trating and defining power is best answered by experiment. If we take a fragment of the valve of an Isthmia and examine it under a high power of small aperture, all the parts are very distinctly seen by the ordinary light of the mirror ; and the various depths of shadow of the different parts of the depressions and the undepressed por- tions render these also clearly distinguishable ; and when an object- glass of very large aperture is used, the distinctness is rather im- paired than improved. But if we examine a fragment of the valve of a Gyrosigma, and this requires an object- glass of large aperture to render the markings visible, no distinction of the various parts of the depressions and the undepressed portions is visible ; all we see is, that the depressions as a whole are dark and the undepressed por- tions are luminous. Hence the Isthmia requires defining power, whilst the Gyrosigma requires penetrating power or large angle of aperture to exhibit the markings ; yet the structures differ only in size. And there can be no doubt that if we could examine the valve of the Gyrosigma under a power as high relatively to the size of the depressions, as that under which we can examine the Isthmia, the same relations being preserved between the angle of aperture of the object-glass and the angular inclination of the refracted rays, the 74 Royal Institution, various parts of the depressed and undepressed portions would be equally recognizable in both cases. This is also true of fine lines scratched or etched on glass ; for although the coarser lines upon glass micrometers are well seen with an object-glass of small aperture with good defining power and direct light, yet the finest lines upon Nobert's test-slide require penetrating power in the object-glass, and oblique light. Large an- gular aperture or penetrating power is but a very imperfect substitute for defining power — an important point which the author believes has not hitherto been noticed, and to which he would invite the earnest attention of object-glass makers. The author concludes by observing that his remarks have been principally confined to one class of objects requiring penetrating power, viz. the valves of the Diatomacese. This has been done ad- visedly, because the scales of insects, which may be regarded as form- ing the type of the other class, involve considerations of a mixed kind, which would have tended to confuse the subject. The longi- tudinal ridges upon the scales of insects, in their relation to pene- tration, may be viewed as representing the undepressed portions of the valves of the Diatomaceae ; and the same explanation will apply to the visibility of both under various conditions. The transverse lines seen upon the scales are not indications of true structure ; but their origin, as also that of the lines seen upon the valves of the Diatomaceae, from circular or angular depressions, does not come within the conditions involved in the principle which it has been the object here to elucidate. It will suffice to say that the true struc- tures producing the appearance of transverse markings upon the scales of insects are best resolved by small angular aperture and good definition. It has been assumed also, that the markij:igs upon the valves of the Diatomaceae arise from depressions. This can be proved to be the case in the larger ones {Isthmia, &c.); and there is sufficient evidence to render it at least highly probable in the remainder. But this is an unessential point as regards the principle, and therefore it has not been dwelt upon. ROYAL INSTITUTION OF GREAT BRITAIN. May 19, 1854. — " On some Phaenomena connected with the Motion of Liquids." By J. Tyndall, Esq., Ph.D., F.R.S., Pro- fessor of Natural Philosophy in the Royal Institution. The lecturer commenced by referring to certain phaenomena ex- hibited by liquids, and at variance with our commonly received notions as to their non-cohesive character. According to Donny, when the air has been as far as possible expelled from water by per- sistent boiling, such water possesses an extraordinary cohesive power, sufficient indeed to permit of its being heated to a tempera- ture of 275° Fahr. without boiling. The adhesion of water thus prepared to the surface of a glass tube was shown experimentally ; the force being sufficient to sustain a column of water of conside- rable height. The contractile force of a soap-bubble was referred to; and the lecturer passed on to the exhibition of the phaenomena Hoyal Institution, 75 resulting from the shock of two opposing liquid veins. In this case, though the forces are in opposite directions, motion is not annihi- lated ; but the liquid, as first shown by Savart, spreads out so as to form a thin transparent film, the plane of which is at right angles to the direction of the jets. By varying the pressure on one side or the other, or by making the jets of different diameters, the plane film could be converted into a curved one, and sometimes actually caused to close, so as to form a pellucid sack. A cistern, situated at the top of the house and communicating by pipes with the lecture table, placed a considerable pressure at the disposal of the lecturer, and enabled him to exhibit in a striking manner the various phseno' mena described by Savart in his researches on the motion of liquids. A vein was caused to fall vertically upon a brass disc upwards of 3 inches in diameter : the liquid spread laterally on all sides and. formed an umbrella- shaped pellicle of great size and beauty. With a disc of an inch in diameter, a pellicle of at least equal magnitude was formed. When a candle was placed underneath the curved sheet of water a singular effect was produced. The film above the candle was instantly dissipated ; and on moving the candle, its motion was followed by a corresponding change of the aqueous surface. Ou turning a suitable cock so as to lessen the pressure, the curvature of the film became increased, until finally the molecular action of the water caused it to form a curve returning upon itself, and exhibit- ing the appearance of a large flask, When the film completely embraced the vertical stem which supported the brass disc, a change in the form of the liquid flask was observed, the latter became elon- gated, and was sometimes divided into two portions, one of which glided down the vertical stem and was broken at its base. When the jet was projected vertically upwards, large sheets were also obtained. The jet was also suffered to fall into small hollow cones of various apertures, and the shape of the liquid sheet received thereby some] beautiful modifications. The enclosed sides of the hollow cone gave the liquid an ascending motion, which, combined with the action of gravity, caused the film to bend and constitute a vase-shaped surface of great beauty. The lecturer next referred to the constitution of a liquid vein ; he had pointed out, some years ago, a simple mode of observing this constitution by means of the electric spark ; this method corroborated the result before arrived at by Savart, that the lower portion of a liquid vein owes its turbidity to the fact of the mass being there reduced to drops, although the quickness with which they succeed each other gives the eye the im- pression of continuty. Savart's last experiments on this subject were repeated : a tube about 5 feet long and 2 inches wide had a perforated brass disc fixed at its lower extremity ; the tube was filled with water, which, after it had become motionless, was permitted to issue from an orifice pierced in the centre of the disc. As the liquid escaped it gave birth to a succession of musical notes of sufficient intensity to be distinctly heard throughout the theatre. That these notes were not due to the motion imparted to the air by the descend- ing drops of the liquid vein was proved, first, by intercepting the vein in its continuous portion, and secondly, by permitting it tp 76 Intelligence and Miscellaneous Articles. discharge iteelf into a vessel containing water, the orifice being caused to dip beneath the surface of the latter. In this case the mass of liquid was continuous, but the notes were nevertheless pro- duced ; thus showing that the vibrations which produce them must take place in the glass cylinder itself; — and corroborating the con- clusions arrived at by Savart from his earliest experiments on this subject. The pitch of the note depends upon the height of the liquid column which produces it ; and by attaching a tube of an inch in diameter, furnished with a perforated bottom, to a cylindrical vessel about IS inches wide, and filling the whole with water, a note of long duration and of sensibly constant pitch was obtained. The lecturer concluded with an experimental illustration of the total reflexion of light at the common surface of two media of dif- ferent refractive indices. The tube communicating with the reservoir before referred to was fitted into the top of a small box, into one of the sides of which was fitted a glass tube ^ of an inch wide and 5 inches long. The side of the box opposite to that through which the glass tube was introduced was of glass. Behind the box was placed a camera, by means of which the electric light could be condensed and caused to pass, first through the glass back of the box, and then through the tube in front, so as to form a white disc upon a screen held in the direct path of the light. When, however, the cock was turned so as to permit water to spout from the tube, the light on reaching the limiting surface of air and water was totally reflected, and seemed to be washed downward by the de- scending liquid, the latter being thereby caused to present a beautiful illuminated appearance. X. Intelligence and Miscellaneous Articles. ON THE PRINCIPLES WHICH GOVERN THE DISENGAGEMENT OF ELECTRICITY IN CHEMICAL ACTIONS. BY M. BECQUEREL, ALL the questions relating to the evolution of electricity are ex- ceedingly interesting in the physico-chemical sciences and their application to the arts and manufactures, seeing that they are of the same order as those which aflfect the production of heat during combustion . The amount of electricity associated with the molecules of bodies is so great as to startle the imagination, as I showed in 1846. Un- fortunately only an excessively small portion of this electricity can be collected, in consequence of the recomposition which takes place on the contact of tlie bodies. The eff^orts of physicists must be directed to the discovery of the means of preventing this recomposi- tion, if they wish to furnish society with a motive power which may contend successfully with steam, producing much more varied eflfects, as it acts not only as a mechanical force, but also physically in the production of heat and light, and chemically in the. decomposition of bodies and in efi^ecting the combination of their elements. Such was the end which I proposed to myself in 1823, when I pro- duced my researches on the disengagement of electricity in chemical reactiooB, researches which enabled me to establish the principles Intelligence and Miscellaneous Articles, 77 which govern this evolution, and by means of which I have succeeded in reproducing a certain number of mineral substances, and in re- covering lead and silver from their respective ores, without any other employment of heat, except what is required for simple roasting, and even without the intervention of this amount of heat. This last in- vestigation, which has taken several years of constant research, is now terminated, and I propose to lay its results before the Academy very shortly. The experiments have been made upon more than 30,000 kilogrammes of ores, not only from Mexico, but from various parts of the globe, and upon a sufficiently large scale to show whether the process is or is not practically applicable. My account of the principles which govern the disengagement of electricity in chemical reactions has been generally adopted, but as my experiments have now been published some thirty years, I have thought it advisable, after so long a period, to go over these re- searches again. The apparatus employed was the depolarizing ap- paratus, which I have lately presented to the Academy, and of which I have given a description in this memoir. I first attended to the electrical effects produced in the reaction of acid, alkaline or neutral solutions upon water, and upon one an- other, avoiding especially the effects of polarization resulting from products deposited upon the platinum plates intended for the trans- mission of the currents. I arrived at this result, that water is ne- gative in relation to all acids and to saturated solutions of neutral salts and positive in relation to the alkalies ; that in the reaction of acids upon each other, the most oxidizing acids are the most positive, and that the acids, in combination, transmit to their compounds their electro-positive properties, so that when mixed or combined, solutions of nitrates are positive in relation to sulphates, and sul- phates in relation to chlorides. Hence we see why the intervention of nitromuriatic and nitric acids in galvanic batteries produces a greater evolution of electricity than the other acids, as was pointed out by me in 1827, when I described the pile in which each pair was formed of nitric acid, potash and platinum. My experiments with the depolarizing apparatus have led me to this general fact : when water and several other neutral, acid or alka- line solutions are in contact (two and two) so as only to combine or mix very slowly, the electrical effect produced is the sum of the individual electrical effects produced at each surface of contact. This is in opposition to the principle advanced by Volta, namely, that when several solid or fluid substances are in contact one after the other, the electrical effects produced are the same as if the two ex- treme substances were immediately in contact. The principle which 1 have just indicated leads to this result, that electrical circuits may be formed with liquids alone, as in fact I had shown to be possible in a memoir laid before the Academy in 1847. Similar circuits must also exist in living organized bodies, and hence we may conceive the possibility of the production of electro-chemical effects in organic tissues. In my memoir I have given two examples of currents of this nature, in the stems of vegetables during the movement of the sap, and in the tubers of the potato. 78 Intelligence and Miscellaneous Articles. I have also shown how, with fluids and platinum or charcoal with- out an alkaline solution, we may succeed in obtaining piles with a constant current. I conclude my memoir by showing fully the evo- lution of electricity in the combustion of gases or of charcoal. I had already taken up this question in 1824, by means of the con- densing electrometer and plates of platinum ; a year afterwards M. Pouillet analysed these effects, especially those produced by the combustion of charcoal. Having already proved that during the contact of the flames with the plates of platinum thermo- electrical effects were produced, I again went over all my experiments in 1849, no longer with the electrometer, as I had found that flames were conductors of electricity of very low tension, as well as glass when heated even considerably below redness. It was on this occasion that my son Edmond made a series of experiments to show that hot air, and all gases heated to a suitable temperature, were conductors of electricity. It is extremely probable that all non-conducting bodies, when sufiiciently heated, become conductors of electricity, just as they do when in a state of extreme tenuity. I have been led to the discovery of a new property of platinum of ■which no idea has ever been entertained, — that of presenting differ- ent thermo-electrical properties at different temperatures. With these new means of action I have been able tojshow exactly that platinum, either in plate or wire, ought never to be employed in collecting the electricity of flames, seeing that it only produces thermo-electrical effects. With the same means of action, different from those hitherto employed, I have examined the evolution of electricity during com- bustion, and have been led to the same result as M. Pouillet ; except that it is much more distinct, and its intensity may be augmented by assisting the combustion with nitre. From the facts detailed in this memoir the following consequences may be deduced : — 1. In all chemical reactions electricity is disenrT-aged. 2. In the reactions of acids or acid solutions with metals or alka- line solutions, the acids and acid solutions always take an excess of positive electricity, the metals and alkaline solutions a correspond- ing excess of negative electricity. 3. The disengagement of electricity during combustion ii governed by the same principle, that is to say the combustible body disengages negative, the burning body positive electricity. 4. Decompositions produce inverse electrical effects. 5. There is no disengagement of electricity unless the two bodies are conductors of electricity ; thus in the combination of a metal with dry oxygen, iodine or bromine, there is no production of electricity. 6. In the mixture of acids with water, or in their combination with that fluid, the water acts as a base, whilst it acts as an acid in relation to alkaline solutions. 7. Concentrated solutions of neutral salts act towards water in regard to the electrical effects produced in the same manner as acid« with bases. 8. Acids when combining or mixing with each other behave so that Meteorological Observations, 79 the most oxidizing acids are the most electro-positive; in combination with bases they appear to retain the same property, so that in the reac- tion or mixture of saturated solutions of two neutral salts, the nitrate is positive in relation to the sulphate, the sulphate to the phosphate, &c. 9. When several acid, neutral, or alkaline solutions are placed side by side so as to mix slowly, the electrical effects produced are the sum of the individual effects which take place at each surface of contact. 10. Contrary toVolta's opinion, an electric circuit, or rather a closed circuit, may be formed entirely with liquids in which a current of elec- tricity circulates, and from which phsenomena of decomposition and recomposition are produced, if there exist in this circuit corpuscles which are conductors of electricity. Living organized bodies present numerous examples of circuits of this kind, capable of giving rise to electro- chemical effects which have not yet been studied. — Comptes Rendus, April 24, 1854, p. 757. METEOROLOGICAL OBSERVATIONS FOR MAY 1854. Chiswick. — May 1. Rain. 2. Rain: low white clouds. 3. Cloudy. 4. Very fine. 5. Foggy : very fine. 6. Cloudy : uniformly overcast : slight frost at night. 7. Fine : rain. 8. Heavy rain. 9. Showery : thunder, with heavy showers. 10, 11. Cloudy. 12» Foggy : very fine : boisterous at night. 13. Fine. 14, 15. Very fine. 16. White clouds : partially overcast : very clear : frosty. 17. Uniform haze : clear, with very dry air : overcast. 18. Uniformly overcast : clear at night : frosty. 19. Clear and fine. 20. Cloudless: very fine : clear. 21. Cloudy and fine : rain. 22. Densely clouded : rain. 23. Rain : fine : very clear. 24. Heavy showers : clear at night : frosty. 25. Fine : showers, partly hail : clear. 26. Heavy clouds : very fine : heavy rain at night. 27. Heavy rain : hail-storm, with thunder and lightning quarter to five p.m. : clear at night. 28. Fine : cloudy : showery: heavy rain. 29. Rain. 30. Overcast: rain: cloudy. 31. Very fine throughout. Mean temperature of the month 50°-07 Mean temperature of May 1853 51 '27 Mean temperature of May for the last twenty-eight years . 53 '85 Average amount of rain in May 1*77 inch. Boston. — May 1. Cloudy : rain a.m. 2. Cloudy : rain a.m. and p.m. 3. Cloudy : rain P.M. 4. Fine. 5. Cloudy: rain p.m. 6. Fine. 7. Cloudy: rain, with thunder and lightning a.m. and p.m. 8. Cloudy. 9. Cloudy : rain, with thunder and lightning a.m. and p.m. 10. Cloudy. 11. Cloudy: rain a.m. 12. Fine, 13. Cloudy. 14, 15. Fine. 16. Cloudy. 17. Fine. 18. Cloudy : rain a.m. 19, 20. Fine. 21. Cloudy. 22. Cloudy: rain a.m. 23. Rain a.m. and p.m. 24. Cloudy : rain a.m. 25. Fine. 26. Cloudy : rain a.m. 27. Cloudy : rain a.m. and P.M. 28. Fine. 29. Cloudy : rain a.m. 30. Cloudy : rain a.m. and p.m. 31. Cloudy. Sandwick Manse, Orkney. — May 1. Clear a.m. : drops p.m. 2. Clear, fine a.m. : clear p.m. 3 — 5. Clear and fine a.m. and p.m. 6. Clear a.m. : rain p.m. 7. Clear and fine a.m. and p.m. 8. Clear, fine a.m. : cloudy p.m. 9, 10. Bright a.m. : showers P.M. 11. Bright a.m. : cloudy p.m. 12. Cloudy a.m. and p.m. 13. Bright a.m. : showers p.m. 14. Cloudy a.m. : drizzle, showers p.m. 15. Clear A.M. and P.M. 16. Drops a.m. : damp p.m. 17. Showers a.m. and p.m. 18. Clear a.m. and p.m. 19. Cloudy a.m. and p.m. 20, 21. Showers a.m. : cloudy p.m. 22. Cloudy a.m. : drops p.m. 23. Clear a.m. and p.m. 24. Bright a.m. : clear p.m. 25. Cloudy a.m. : rain p.m. 26 — 30. Cloudy a.m. and p.m. 31. Damp a.m. : drizzle p.m. Mean temperature of May for twenty-seven previous years . 47°*98 Mean temperature of this month 48*39 Mean temperature of May 1853 49 '07 Average quantity of rain in May for thirteen previous years . 1 68 inch. ■1 •^IS^ ?.8 :no -": .^?S?8 S' t* o to : V? i ON p ^ •u. ; On w rl e*> p : S^« N p ;? 1 : * ' * rt •^atiinqo rpS \t r^r S^2^&,2?2^2 3..^?: to , o V*- ' ii^^iiiii^t^^^i^jjUiiiiii^i^^ia •ucniOQ i « !i 1 i 1* 1 1 ^ « « « i ^' « s ^- s « d &:• « « « i i i 1 ^ i ^ •Old I 1 1 i i E «'- i « s ^ « 1 s « s § s s -» - i 1 i i 1 E - - ^ E 1 it a S ?3??:?|^^5.5S.5i%'5$?^^5^?'51^^^5^^s.s.^';5- 1 •uojsoa rt +T*-0 b r^»^« O\00 f< K^O'* fOONOvw M ton o »/^M tou^ u-^\D •4- t^vO ro M i f« M t^ t^oo t.oo m vp o ^P S S t--0 O w^tnOMiOO OOOVO r^t-. t-^vo M 0\V0 tJ-m t^h t1 « ro^cjNflOOiOH w-»vO NO VO O NOVO NOVO «0 NOVO NO VO NO VO NO novo t^VO NO NO NO VO NO «ONO »ONO t> 00 NO ' 1 a a C<^00 HI 00 M On tJ- NO »O00 O T^^^t^^'^^O00 t^ONr^OvNOOvNO OSNO C< NO On V t>. p rj- NOVO •I _(S Ti- ONVO C^0O OO On jH O O J-" _OvVO no N .»0 t-s t>, _t^ vO t^OO ON O ©0 On On On ON On On On On ON b\ Ov ON bv b O O O Ov On Os 'on 'on *Ov On Os *On 'o\ 'o\ 'ov O NO H ONVO "H tOOO Ov Ov NOVO m •+ to OvOO «^ to --I t}- On rj- tOOO t^ t^ O H NOOO O « t^oo c» NOVO ro 1-1 c< VO On t^oo oooowMOvi-ii-it^NOTj- rovo 00 oo r^vo r^ On O do c» bv On bv bv bv bv bN bN bv bv bN bN b b bv b b bv bN bN bv bN bv bN bN 'on bN bN b rtHNMHcrN«otoc«cotoHrtr«t. NO t^vo t^ t->.oo r^vo oor^T*-"^ w to^^-r* H tot< tovr do do bv bv bv bv bN bN bN bN bN bN on bN bN bv bN bN bN bN bv bv bN bN bN bv bv bN bv bv b N On 1 00 t-^t^ONO NOflOONO r» OnOO to tl t-^ NO t< O On OvvO rJ ■«4- Ov O 00 On rj-vo »O00 H NO CO tJ-nO O '-' •«4-t^0Nto>-«00 fi ONtl t*VTt- OnOO O Ov-inovo Nocoto t^vO tJ M 11 Th NOVO NO NO •>rJ tOrJ-MOOOO 1-1 On novo O OnOnO toO Ovrt •*« -^ Q ti m tJ-OOO OvOO ONVO 00 NO Ov Ov ON NOVO ro J^OO "i to N tONO tJ- N vO 00 OO vovo O O m ,J. f< «ri f» M 5^ rt-vp vp ,NO ,No _NOOO p O « _•-« "-I w w M w H " 00 y^^ r^OO t^ t^ t^NO 00 "i On bv bv bN bN bN bN bN On b b b b b b b b b b b bvbNbvbNbNbNbv'oN'oN'oN b rt«Hf ' ' Pny and if new information be given which changes the probabilities of some of them, suppose of hm+i and all that follow, without having otherwise any reference to the rest, then the pro- babilities of these latter have the same ratio to one another, after the new information, that they had before ; that is, P^l'p'9"'P'm=Pl'P2"'Pfn> where the accented letters denote the values after the new infor- mation has been acquired.'^ I am not at present going to dis- cuss this principle, but I adduce it as an instance of the general position maintained, viz. that the ordinary doctrines and prin- ciples of the theory of probabilities do run up into some more general ones, the truth of which, when they are once stated, the mind can hardly refuse to acknowledge, and which seem to be involved in the very nature of expectation and of thought. I go on to observe, that such principles, if truly axiomatic, lead in every pure science, and therefore in the theory of probabilities, to a developed system of truth, or of methods for the attainment of truth, which possess certain invariable characteristics never found unimpaired where error has been permitted to enter. These are, mutual consistcrry, the property of verification wherever verifi- cation is possible, continuity, and perhaps some other qualities to which I cannot refer. Now I propose to show, before I have done, that the theory of probabilities does actually admit of this on the Theory of Chances. 89 kind of statement, progression and results. At present I merely ojQfer these observations as preliminary to the question which I am called upon now to consider. Mr. Wilbraham's remarks chiefly apply to two solutions of the following problem respectively published in this Journal by Mr. Cayley and myself. " The probabilities of two events Aj, Ag are Cj and c^ respectively. The probability that if A, present itself another event E will accompany it i^p^, and the probabiUty that if Ag present itself E will accompany it is p^. The event E cannot happen in the absence of Aj and A^, but of the connexion of the latter events nothing is known. Required the probability of E.^^ (See also Laws of Thought, p. 321.) Representing Aj, Ag, and E by x, y, z respectively, the data of this problem are Prob . x—c^ Prob . y^c^ Prob . xz^c^p^ Prob . yz = Cc^p,^ Prob. 5'(l-^)(l-2/) = 0. Mr. Wilbraham shows that both Mr. Cayley's solution and my own introduce two equations. To this I remark in passing, that there can be no objection so long as the equations in ques- tion are consequences of the laws of thought and expectation as applied to the actual data. Respecting the equations involved in my own solution, Mr. Wilbraham remarks : — " The second of these two assumed equations, though perfectly arbitrary, is per- haps not an unreasonable one I do not, however, see that it is a more reasonable or probable hypothesis than others that might be framed; for instance, than those assumed by Mr. Cay- ley in his memoir in this Magazine. But the first of these equa- tions appears to me not only arbitrary but eminently anoma- lous.^' After this he deduces the equations which represent in a similar manner Mr. Cayley's hypotheses. I should be reluctant to enter into any comparison of Mr.^ Cayley's solution and my own if the above remarks did not render it necessary to the interests of truth. It cannot be doubted that Mr. Cayley's solution is erroneous. Granting for a moment that both solutions involve hypotheses, there is this diiFerence between, them (a difference passed over in silence by Mr. Wil- braham), that Mr. Cayley's hypotheses lead to results absolutely inconsistent with the data — that my own hypotheses do not. One case easily tested is when we havejOj = l, and at the same timej02=0. Another and more general case is when the con- stants are so related that we have either CiPi + Cc,{l-p^) = \, or I would refer on these points to a paper " On the conditions by 90 Prof. Boole on the Theory of Chances. which the Solutions of Questions in the Theory of Probabilities are limited," which I forward for publication with this letter. On the other hand, there are no cases whatever in which the problem is solvable by other methods, which do not furnish a verification to the solution I have given. Now I cannot but think that a cautious inquirer after truth, seeing that two hypo- theses (still adopting Mr. Wilbraham's language), one of which appears to him " eminently anomalous," conduct to a solution which cannot by any known test be proved erroneous, while two other hypotheses, which appear to him "perhaps not unreason- able " (for this, Mr. Wilbraham's language already quoted implies with reference to Mr. Cayley's hypotheses), conduct to a solution which will not bear the test of examination, would be led to sus- pect that he had been judging of the reasonableness and of the anomalous character of hypotheses by some false standard. Of course if a solution is eiToneous, it need not to be argued that there must be error in the hypotheses by which it was obtained. But it is easy to show this directly. If we apply the second of the equations representing Mr. Cayley's hypotheses to the par- ticular case in which p^ = l, p^=Oj a case perfectly consistent with the character of the original data, it will be found to lead to the equation c^c^=0, an equation not implied by those data in the particular case contemplated. On the other hand, I afiirm without hesitation that there is no case in which the equa- tions deduced by Mr. Wilbraham from my method of solution can be proved to be erroneous. They do not, indeed, represent "hjrpotheses,^* but they are legitimate deductions from the general principles upon which that method is founded, and it is to those principles directly that attention ought to be directed. I would request your readers to observe that I do not offer the above remarks as affording any proof that the principles upon which my method is established are true, but only as con- clusive that Mr. Wilbraham^s objections against them, drawn from what to him appears to be the anomalous character of an equation to which they lead, are of no value whatever. Nor is it difficult to see what is the source of the erroneous judgements, for erroneous I cannot but term them, which Mr. Wilbraham has been led to form. It is in a principle, the influence of which appears to me to tinge the whole course of his speculations, that those events which in the language of the data appear as simple events, are the ultimate elements of consideration in the problem. These are the elements in terms of which he expresses his equa- tions, overlooking the fact that it is by mere convention that such elements are presented as simple, and that the problem might have been expressed quite otherwise. It cannot be too often repeated that the distinction of simple and compound is wholly On the Solutions of Questions in the Theory of Probabilities, 91 relative — ^that there ia not and cannot be any kind of pre-emi- nence among events founded merely upon the mode of their expression. The neglect of this consideration makes truth to be not merely the creature of language, but the creature of the merest accidents of language. The paper which I forward on the Conditions by which the Solutions of Questions in the Theory of Probabilities are limited, will be followed, should circumstances permit, by two others ; one containing a statement of the principles upon which my method is founded, the other an analysis of its results considered especially with reference to the question of the conditions of limi- tation. It was my design to publish all these researches in a single memoir. I have now determined to send them forth at once, in the hope that when I shall have calmly stated my views, I may with propriety leave the further discussion of them to others. I am. Gentlemen, Your most obedient Servant, Lincoln, July 5, 1854. George Boole. XIII. On the Conditions by which the Solutions of Questions in the Theory of Probabilities are limited. By George Boole, LL.D,, Professor of Mathematics in Queen^s College, Cork^, SUPPOSE the following question in the theory of probabili- ties to be given : " The probability that it rains on a given day is p, the probability that it both rains and hails is q ; required the probability w that it neither rains nor hails/^ We know that the data of this problem cannot represent a possible experience unless p is equal to or greater than q. The absolute probability of an event " rain," cannot be less than the probability of the joint occurrence of that event and of another event 'Hiail." Again, we know that the probability w which we have to seek cannot exceed 1 —p. The probability that it neither rains nor hails cannot exceed the probability that it does not rain. Hence the data of the problem are limited by the condition and the probability sought, viz. w, by the condition w^l —p. If the former condition is not satisfied in the data, the problem is not a real one. If the latter is not satisfied in the solution, that solution may at once be pronounced to be incorrect. Con- ditions of this nature are involved in almost every problem on * Communicated by the Author. 92 Prof. Boole on the conditions by which the Solutions of chances in which the data are not the probabilities of simple in- dependent events. I propose in this paper to develope an easy and general method of determining such conditions. This object has been attempted in Chapter XIX. of my treatise on the ^ Laws of Thought.' But the method there developed is somewhat dif- ficult of application, and I am not sure that it is equally general with the one which I am now about to explain. I premise the following proposition. Proposition, — To eliminate any symbol of quantity a? from any system of inequations in the expression of which it is involved. The general method will be best explained by an example. Suppose it required to eliminate x from the inequations 3y—x—z^0 x-2y-hz = 0. Reducing each of these inequations to a form in which the first member shall be x, we have a^^z—y x^Sy—z x = 2y''Z. From these equations it appears that x has for a superior limit Sy—z, and for inferior limits z—y and 2y—z. As the superior limit must in general exceed each of the inferior limits, we have Sy-z = z-y, 3y-z=2y-z, whence And these are the only conditions which are independent of x. The general rule would therefore be to seek from the sevei-al inequations the superior and inferior limits of x, and then to express by new inequations the conditions that each superior limit shall be equal to, or greater than, eveiy inferior limit. If it is a condition that a? is a positive quantity, then must each superior limit be made J 0 j or we might add to the system of inequations the inequation x^O, and apply the general rule. When several quantities, as x, y, &c., are to be eliminated, we can proceed by first eliminating x, then from all the inequations which either result or remain eliminating y, and so on. - It is obvious that the number of inequations obtained by the elimination of a symbol may greatly exceed that of the inequa- tions from which the elimination has been effected. Questions in the Theory of Probabilities are limited. 93 General proposition. — The probabilities of any events whose logical expression is known being represented hj p, q, r , . re- spectively^ required the conditions to which those quantities are subject. Here also it may be well to commence with a particular case. I will take the problem already discussed in this Journal (Oct. 1853, Jan. 1854) by Mr. Cayley and myself. The elements of that problem may be thus expressed, w being the element sought in that discussion. Prob. x=Ci Prob. y = C2 Prob. xz=:c^p^ Prob. y^f^c^p^ Prob. ^=m; Prob. ^(1 -a?) (1-2/)= 0. . (1) Here, according to the notation of the calculus of logic, Prob. xsf denotes the probability of the occurrence of the events x and z together. Prob. 2{l—£c){l—y) denotes the probability of the occurrence of z conjointly with the absence of x and ?/, &c. The events whose probabilities are given may all be resolved by logical development into disjunctive combinations of events, which do not admit of further resolution with reference to the same elements of distinction x, y, z. Thus xz — xzy -f xzi^ — y) x-=.xyz -{■ xy[l-' z) -{■ x[].—y)z -\- {\—x){\. — y){Y— z). And hence we have Vvoh. xz=^Vvoh. xyz+'?voh, x[\—y)zy , . (2) and so on. Now assume V Yoh. xyz-=X Prob. ^y(l — 2*) =/Lfc Vxoh. x[\—y)z — v Prob. <2?(1— 2/)(l— 2')=p Prob. {\'-'x)yz=.o- Prob. (1-%(1-^) = T Prob. (1 - ^) (1-2/) (l-^) = t;. These represent all the possible combinations of x, y and z, ex- cept z[\^x){\—y)y which by the data is excluded. The equation (2) gives, by virtue of (1), and forming all similar equations furnished by the data, we have \ + IM + V + p = C^ X + v =Cii?i )') ' ' ' • • (^) X + O- =^2i^2 ' X + v + o- =^w J to which we may add the necessary condition X + //- + v + p + cr-f T + f = 1. ... (4) 94 Prof. Boole on the conditions by which the Solutions of Now the quantities X, fi, v, &c. are individually J 0. More- over, they are subject to no other relations than the above. Our object, then, is to seek the relations among w, Cj, Cg, CjjOj, Cj/?^^ which are necessary in order that the above conditions may be satisfied. For this purpose we must, and the rule is of general applica- tion, determine as many of the quantities X, /a, v, &c. as we can in terms of «;, Cj, c^, &c., and make their expressions J 0. These ■will furnish a part of the conditions sought. We must substitute the above expressions in the equations of the system (3) (4) which remain, and, supposing those residual equations to be n in num- ber, find from them the expressions of n more of the quantities X, /x, V in terms of the quantities which remain, and of the known quantities Wy Cj, c^ &c. We must make these expressions also ^0, and from the inequations thus formed eliminate by the previous proposition such of the positive quantities X, fi, v as are still left. This will furnish the remaining conditions among the constants Wy c„ Cg, &c. In the steps of this process we shall have successively introduced all the conditions X J 0, /x J 0 . . . i; J 0, and shall therefore have obtained all the equations con- necting the elements w, c„ Cg, c^p^ and c^jOg- Thus, from the third, fourth, and fifth equations of (3), we find , + C2J92— w, furnishing the conditions w— CjjOi^O «^— CgjOg^O Cip^—c^p^—w^O. (5) Substituting the values of o-, v, and X in the remaining equa- tions of (3) and (4), we find on transposition, fl + T^CciO—p^) fl+p-\-T-\-V=il—W. Hence, selecting p, t, and v as the quantities to be determined, we have p=Ci(l-;?i)-/A v=l^w-Ci{l'-py)-c^{l-p^)-hfi; whence, therefore, \-w^c^{\-p^)-c^[\-p^-\-ti = 0. Or, in order to eliminate fi, , Questions in the Theory of Probabilities are limited, 95 And hence ^2(1 -P^) > ^1 (1 -Pi) + OciO- -Pi) - 1 + w; ; or w w = l-Ci(l-i?i)J From the conditions (5) and (6), we spe that w has for its lower limits, the expressions ^1/^1 and C2P2, (7) and for its upper limits, the expressions CiPct + c^P2> 1—Ci(l—J0j) and 1 — ^2(1— jOg). . . (8) These are the conditions assigned in my treatise on the Laws of Thought, p. 325. They show, that if it is our object to deter- mine Prob. z or w, the solution, to he a correct one, must lead us to a value of that quantity which shall exceed each of the values assigned in (7), and fall short of each of those assigned in (8). They show also that the data of the problem will only represent a possible experience when each of the values in (7) shall fall short of, or not exceed each of those in (8). There is a class of problems characterized by the circumstance that the quantities X, //., v . . are fewer in number than the equa- tions in which they enter, which treated by this method lead to equations as well as inequations connecting the data with each other and with the probability sought. Whenever, too, the pro- bability sought can be expressed as a linear function of the pro- babilities which are given, its actual expression will be deter- mined by the above method, and it will agree with the result which would be assigned by the general method in probabilities (Laws of Thought, Chap. XVIL). To exemplify this, let us take the following problem (Ibid. p. 279). Given Prob. a?=jo, Prob. y=q, Prob.(a?(l--y) +2^(1 — a?)) =:r, to find the limits of Prob. ocy or w. Assume Prob. a??/=\ Prob. a?(l— 2/)=/Lt Prob. (l~-a7)y=:v Prob. (l-a?)(l-2/)=p. Then we liave as the conditions furnished by the data, \+fi=p X + v=q ^ fj, + v:=r j>. (9) \ = w 96 Prof. Boole on the conditions by which the Solutions of From the three first equations and the last we find ^—p—q — r furnishing the conditions p-^q^r, p + r = q, q + r^p, p-{-q + r~2. There still remains the fourth equation of the system (9), in the first member of which, substituting for \ its value, we find p + q—r the value of Prob. xy sought (Laws of Thought, p. 280). There is a peculiarity in these " determinate '^ solutions to which I desire to advert. It is, that if in any series of observa- tions the events referred to in the data occur with a frequency exactly proportional to their assigned probability, the event whose probability is sought will occur in the same series with a frequency exactly proportionate to its determined probability. For instance, in the problem just solved, if in n observations the events a?, y, and x{l — y) -\-y(l—a:) occur exactly np, nq, and nr times respectively, the event xy will in the course of the same T) ~f~ O ~~- 7' . observations occur exactly n- — ^ times. This is easily shown by substituting throughout the demonstration contained in Prop. 2, 'Ncc for Prob. x, Ny for Prob. y, N applied to the ex- pression of any class denoting the number of individuals con- tained in that class; and generally substituting numbers for probabilities. This change will not afiect the truth of the equa- tions. For instance, if we have Na?=a ^xy=b, we shall have Na? — Na?^ = « — 6, or Na?(l— y) = a— Z», and so on. I remark that this is a. peculiarity of the above de- terminate solutions. If the probabilities of two independent events x and y are p and q respectively, the probability of their concurrence is pq ; but we are not permitted to affirm, that if in n observations n occurs np times, and y occurs nq times, their concurrence will be observed exactly npq times. « When by the method of this chapter we have found the con- ditions of limitation of the solution of a question in the theory of probabilities, we can at once ascertain from those conditions Questions in the Theory of Probabilities are limited, 97 in what cases the problem becomes determinate in the sense above explained. Thus in the particular problem discussed in Pro- position 2, since we have it follows that whenever one of the upper limits of w becomes equal to one of the lower_, the other conditions remaining satisfied, the problem becomes determinate. Thus^ if we have 7?2 = 0, we find from the above^ Now as lu cannot at the same time be both greater and less than Cip^f it must be equal to c^p^; the other conditions simply redu- cing to 1 — ^2 > ^\Pv ^^^ solution, therefore, is w=zc^p^, the data being necessarily connected by the condition Let us apply to this case the solutions of the general question in probabilities respectively given by Mr. Cayley and myself. Mr. Cayley's solution is expressed by the quadratic equation (\-c,(l-p,)-w')(\-c^{\-p^)-w) = {\-c,)(\-c^)[\-w).{n) If we make jt?2=0, it becomes (1 -Cj(l -p^) -m;)(1 -Cg-w) = (1 -cy) (1 -Cg) (1 -m;), and this equation is not satisfied when we make w=:c^Py. The solution which I have given is contained in the quadratic equation {w-^c^p^)[w-Cc^p^)[l-w) = (\-c^{\-p^)-w) (}-Cc,[l-p^-w)[c,p^-\-Cc,pc,-w)', . . (12) and this equation, on making jOg— ^^ i^ satisfied by the value w=-c^Pi. The reader may examine for himself, and with exactly similar results, the class of cases in which the data happen to be connected by the relation CiPx + c^{l-p^=:\, or by the relation C2^2 + c,(l-i^i) = l. But there is another and more remarkable distinction to which I would advert. I have shown (Laws of Thought, p. 324), that in all cases in which the data of the abx)ve general problem are , possible, the quadratic equation (12) furnishes one root, and only one, falling within the limits assigned by the method of this chapter. It is needless to remark that Mr. Cayley's equation Phil. Mag, S. 4. Vol. 8. No. 50. Aug, 1854. H 98 Prof. Challis on certain Questions does not "possess this characteristic. It may readily be shown that that equation will always furnish a single root satisfying the two conditions m;= 1— Ci(l— j9,) w^l — Cgfl—Pi) ; but that the remaining three conditions assigned in (10) will not be satisfied by it unless certain other conditions, distinct from the conditions of possible experience, obtain. And this leads me to notice, in the last place, a remarkable distinction, a posteriori, between unwarranted hypotheses in the solution of questions in the theory of probabilities, and axiomatic principles flowing out of the very idea and definition of proba- bility, or sanctioned by the laws of thought. It is that the latter never impose, either upon the data or upon the solution, any limitations but those under which alone experience is possible, while the former do in general (always, I think, when the equa- tion of a solution rises above the first degree) impose such limi- tations. But these considerations only conduct us again to that general view of the theory of probabilities which is contained in my reply to the strictures of Mr. Wilbraham. They confirm, so far as they go, the doctrine already advanced, that its claim to rank among the pure sciences must rest upon the degree in which it satisfies the following conditions : — 1st. That the principles upon which its methods are founded should be of an axiomatic nature. 2nd. That they should lead to results capable of exact verifi- cation, wherever verification is possible. 3rd. That they should be capable of a systematic development consistent in all its parts and processes, and neither acknow- ledging nor imposing any limitations but those which exist in the nature of things. Lincoln, July 6, 1864. XIV. On certain Questions relating to the Moon's Orbit, in reply to the objections of Mr, Adams. By Professor Challis. To the Editors of the Philosophical Magazine and Journal, Gentlemen, BEFORE replying to the contents of the letter addressed to you by Mr. Adams on my new theorems relating to the moon's orbit, I think it right to state, in explanation of the origin of the discussion, that Mr. Adams came to the decision that the paper containing those theorems which I submitted to the Cambridge Philosophical Society was without merit, and relating to the Moon's Orbit, 99 that the publication of it by an order of the Council of that body would bring credit neither to myself nor to the Society. If that opinion of the paper can be maintained, I shall admit that Mr. Adams had good reason for advising the Council not to print it. But I am well persuaded that the decision was rash_, and made on mistaken grounds, and that my paper contained important additions to the lunar theory. I am therefore glad, as well for the sake of the interests of science as on my own account, that Mr. Adams has consented to publish his objections in the Philosophical Magazine. The article in the July Number gives me the opportunity I desired of vindicating my views. I shall discuss the objections seriatim, and in the order in which they occur, after premising some general remarks on the ques- tions at issue. It is well known that the theoretical determination of the motion of the moon^s apse has been attended with difficulties. Newton gave, in the ninth section of the First Book of the Prin- cipia, methods of determining apsidal motion when the force is wholly central, but left nothing applicable to the circumstances of the moon's motion. The successors of Newton, who applied analysis to the lunar theory, finding that the process of approxi- mation failed on starting from a fixed ellipse, altered the hypo- thesis of the approximation by assuming the apse to have a mean motion. This was done by " introducing " (to use Mr. Adams's expression) the quantity usually denoted by c. Laplace intro- duces this factor hypothetically, and refers to a subsequent veri- fication. (Theorie de la Lune, vol. vii. sect. 4.) Plana, on the contrary, is led to it by the method of the variation of parame- ters. {Theorie de Mouvement de la Lune, Chap. II. § 3.) On the principle of the latter method I shall say a few words in the sequel, at present I am concerned with the introducing process. Now I think I may assert that mathematicians have felt that there is something unsatisfactory in this process ; that it is a pis alter, to which recourse was had because no better method was discovered. Though it is undoubtedly legitimate and leads to true results, a method which would conduct directly to the form of the expression for the radius-vector to the first order of small quantities would seem to be more logical and more complete. I long since directed my attention to the discovery of such a method; and having at length remarked that the approximate solution of the problem of the moon's motion, as usually treated, rests on two distinct hypotheses, viz. a mean motion of the radius-vector and a mean motion of the apse, it occurred to me to attempt the investigation on the single hypothesis of a mean motion of the radius-vector. On doing so in the manner indi- cated in my communication to the April Number of the Philo- H2 loo Pi'of. Cballis on certain Questions sophical Magazine, I arrived at an equation which will be very frequently referred to in the course of this discussion, viz. 5? + ;5---2^3+C-0 (C) I saw at once that this equation, which, as I believe, had not been previously noticed by any writer on the lunar theory, might be employed in obtaining directly the true form of an approxi- mate value of the radius-vector. The process for this purpose will be considered in the course of the discussion. I have a few remarks to make on statements contained in page 28 of Mr. Adams's letter, which refer to views expressed in the introductory part of my paper. My objections to the logic of the process usually followed in the lunar theory are there stated in these words : — "As it is certain that the mean motions of the apse and node are consequences of the sun's disturbing force, there must be some direct means of deducing them from the dynamical equations of the motion. In fact, the method of calculating the motion of the moon's node in the third book of Newton's Principia shows, step by step, that the motion results from the dynamical conditions of the problem, and in this respect is logically more exact than the analytical method, which only shows, on the hypothesis of such motion as Newton deduced, that the dynamical equations are satisfied. There must be some hiatus in the analytical method which requires to be filled up in order that the logic of the lunar theory may be free from reproach." My paper supplied this defect in the case of the mean motion of the node as well as in that of the apse, and by processes analogous to each other, as I shall take occasion to show hereafter. Again, with reference to the principle of introducing the quan- tities c and ff, I said that they were introduced hypothetically j the apse and node being thereby supposed to have certain mean motions; and that these hypotheses, suggested probably by observation, are the real basis of the approximation in the usual treatment of the lunar theory. The symbolical ^oXwiiow obtained on these suppositions is, as Mr. Adams urges, proved to be cor- rect by its satisfying the differential equations of motion ; but its applicability to a particular instance (as that of the moon's motion) is not proved till the hypotheses on which the solution was based are shown, by direct or indirect comparison with obseiTation, to hold good in that instance. This is the confir- mation by observation that I spoke of. The solution which I have proposed, being based on the single supposition that there is a mean motion in longitude, requires :only that we establish by observation that the moon's motion satisfies this condition. I relating to the Moon^s Orbit. ^ 101 said, moreover, that while my solution leads necessarily to the same numerical results as former methods, it adds something to our knowledge of the moon's orbit. It will be proper to state here, also, my ideas respecting the constants introduced by integration, when the solution of the differential equations is only approximate. When an exact solu- tion can be effected, I quite agree with Mr. Adams that, provided the proper number of constants be obtained, it matters not what is the process of integration and how it is suggested, simply for the reason that there is but one such solution, and its form is unique. Also the constants are arbitrary, and therefore entirely independent of each other. From an exact integral obtained in any manner, integrals applying to particular cases may be de- rived by assigning particular values to the arbitrary constants, or subjecting them to certain conditions. But when, as in the instance of the lunar theory, an exact solution is not attainable, that process is no longer possible, and recourse must be had to approximate sohitions based on certain hypotheses. Now the form of an approximate solution entirely depends on the hypo- thesis on which the approximation proceeds, and may be different for every different hypothesis. Also each hypothesis requires a particular process of approximation which it is very important to discover. The constants introduced by the integration, if they should be the same in number as those of the exact solu- tion, are not generally in the same degree arbitrary and inde- pendent of each other, because an integration performed on a certain hypothesis is equivalent to a particular case of the general integral. These constants may therefore have certain relations to each other, for the same reason that, in the common elliptic theory, the arbitrary constants of the general integral satisfy cer- tain conditions in the particular cases of motion in a circle and a parabola. The process of approximation, if conducted strictly according to rule, will itself determine those relations between the constants which are appropriate to the circumstances defined by the hypothesis of the approximation. I am persuaded, from long consideration of the subject, that these principles are true, although they do not coincide with those laid down by Mr. Adams. I proceed now to a particular discussion of Mr. Adams's objections. The first in order is that which begins at the top of page 30, to which an immediate answer may be given on the principles I have just explained. The fallacy of the argument consists in assuming that the constants a, e, e, and -cr are neces- sarily arbitrary and independent of each other, because the values of r and 6 containing them satisfy the di^erential equations (1) and (2) at the bottom of page 29. Such reasoning is valid only in the case of the complete solution of exact equations. Also 102 Prof. Challis on certain Questions the approximative process of integration made use of to obtain the values of r and 6, does not decide whether or not the con- stants are mutually related, because it is conducted in an irregular manner. After assuming that there is a mean motion of the radius-vector, it makes the additional assumption of a mean motion of the apse ; whereas my method of integrating the equa- tions (1) and (^) to the first approximation deduces the mean motion of the apse from an assumed mean motion of the radius- vector ; and in the course of making this deduction, a certain relation between the constants h and C (which may replace a and e) is found which gives for e a special value. The reasoning which leads to this result will be defended in a subsequent part of the discussion. The assertions in the next paragraph (p. 30) respecting the " variation '^ and " evection,^' are simply not true, the previous values of r and 6 belonging to my method of integration for the same reason that they belong to the ordinary method. After obtaining the value of r to the first order of small quantities by the process given in my communication to the April Number (p. 281), I may use it in conjunction with the equations (1) and (2) to obtain the values of r and 6 to the second order of small quantities precisely according to the usual method, the only dif- ference being, that having deduced instead of assuming the form of the first value of r, I am entitled to ascribe to e a special value. In the latter part of the same paragraph Mr. Adams has fallen into a misconception respecting Theorem I., which may have arisen from the terms in which the theorem is enunciated. In my article in the April Number (p. 280), after obtaining the equa- tion (C), I say, " this equation proves Theorem I.'^ I could not, therefore, mean any other relation between the radius-vector and the time than that expressed by the equation (C). Mr. Adams's objection to the correctness of the theorem will be met by enun- ciating it with more precision as follows : — " All small quantities of the second order being taken into account, the relation between the radius-vector and the time in the moon's orbit, as expressed by a differential equation of the first order, is the same as that in an orbit described by a body acted upon by a force tending to a fixed centre." Mr. Adams then goes on to consider the reasoning by which Theorems I. and II. are arrived at, and makes this remark : " All this reasoning is based on the equation (C), the truth of which, he (Prof. Challis) says, cannot be contested." The rea- soning to establish Theorem II. is certainly based on that equa- tion, but Theorem I. is merely a verbal statement of what the equation indicates. Again, I said (Phil. Mag. for June, p. 430) that the proof of the equation cannot be contested; and if I said relating to the Moon's Orbit, 108 this untruly, why does not Mr. Adams contest it, or even allude to it ? One sound argument against the reasoning employed to deduce the equation would suffice to settle the whole question. I can assure Mr. Adams, that while he has been unable to con- test that reasoning, I have had no difficult task in discovering the fallacy or irrelevancy of every one of his attempts to nullify the equation. The argument in the first paragraph of page 31 shows that the integral of the equation (C) gives the value of r only to the first order of small quantities. As this result perfectly accords with my views, I have no remark to make upon it. Neither in my paper nor in the Philosophical Magazine had I occasion to take into consideration the value of r to the second order of small quantities. I come now to an argument which, among others, Mr. Adams communicated to me to justify his advising the Council of the Cambridge Philosophical Society to reject my paper. The argu- ment then appeared to him to prove beyond a doubt that the equation (C) was erroneous : now he proposes it as a " test of the degree of accuracy to be attained by the use of that equa- dr Hon J' By differentiating the equation (C) and dividing by -j. there results dt^ ^3 -+-^2 2«'3 ^^ But the equations (1) and (2) already referred to, give d'^r W- fjb mJr 3m'a ^-^3 + ^-3^3- ^co8(3n< + 6-2»'< + ^)=0, (E) which equation is certainly true to small quantities of the second order. Since, therefore, the equation (D) is not true, it was argued that the equation (C) from which it was deduced could not be true. If Mr. Adams had known the days of the Cam- bridge school exercises for mathematical honours, he would have got credit by propounding such an argument as this. As oppo- nent he might have put the syllogism thus : if (C) be true, (D) is true, being '^ a strict deduction from (C).^^ But (D) is not true, because (E) is true. Therefore (C) is not true. Ergo, cadit qucestio. A clever respondent would, however, have imme- diately answered, nego major em; that is, he would not have admitted (D) to be a strict deduction from (C) by a retrograde step, unless (C) is deducible from the premises of the question through (D). But (D) is the antecedent of (C) only in case the force is wholly central and th§ integration is emctf which are not 104 Prof. Challis on certain Questions the premises of the question. jBh/o, vaiet consequentia. It astonishes me that Mr. Adams did not perceive, that as the force is not wholly central, and the integration is approximate, the equation (E) is the legitimate antecedent of (C). ]3y multiplying the former by ^, integrating, and omitting the quantity of the third order which the last term gives rise to, the equation (C) is immediately obtained. In this method it is assumed that the dr value of -1- contains a factor of the first order of small quantities, or, in other words, that the radius -vector oscillates in value to a small extent about a mean value, which might easily be shown to be a consequence of the supposition of a mean motion of the ► radius-vector in longitude. My method of proving the equa- tion (C) rests only on this latter supposition." From this argument Mr. Adams does not, as before, conclude that the equation (C) is positively false, but that it is " unfitted for giving accurate information respecting the moon's orbit.'' I must be permitted to express my great surprise that Mr. Adams could have written so unscientific a sentence as this. What has a mathematician to consider but the truth of his equations ? If they are false, they give no information ; if true, they necessarily give accurate information when rightly interrogated. There is no intermediate species of equations. My equation being proved to be true, must form an essential part of the lunar theory. True results may be obtained without it by pis aller processes, but without it all that is true of the moon's orbit cannot be known. It is clear to me that Mr. Adams is involved in a dilemma by having committed himself to the opinion that there was no merit whatever in my paper. He cannot now admit that it contained an important equation which remained un- discovered from the days of Newton, and being unable to resist the evidence for the truth of the equation, he has recourse to the strange expedient of endeavouring to throw discredit upon the information it gives. The arguments relating to Theorem I. conclude with the assertion that the equation (C) "would make the moon's apsidal distances to be constant,'^ and a needless appeal to the Nautical Almanac ; to which I reply, that the apsidal distances are not made constant by deducing the value of the radius-vector to the first order of small quantities from the equation (C), any more than they are made constant by assiming this same value. We have now come to Theorem II. (p. 32). And here I can- not understand why Mr. Adams is solicitous to remove a diffi- culty which I found in extracting information from the equa- tion (C), since he is of opinion that this equation is unfitted to relating to the Moon^s Orbit. 105 give accurate information. I should have thought that he would have concluded the difficulty to be a confirmation of that opinion^ and not regarded it as ^' purely imaginary/' 1, who have no doubt of the truth of my equation, may well believe that the difficulty is only apparent, and admits of explanation. Mr. Adams even volunteers to give an explanation, but, as might be ex- pected, is not successful. He is equally unsuccessful in stating the difficulty. In the quotation from my article, inserted towards the bottom of page 32, the reference to the mean distance might have been omitted without detriment to the conclusion, as may be thus shown. Put a for r in the small term of equation (C), and we have dr^ h^ 2fA> 7n'a'^ .n-n Now this equation informs us that the orbit is a fixed ellipse, and the force is wholly central and equal to -^^ The difficulty consists in its giving this information, although the effect of the disturbing force to small quantities of the second order has been taken into account. Also there are other ways in which the difficulty presents itself. By putting the equation under the form ,, —rdr at= — Fa' m'r* \/-Cr^-h'-^2f.r + '^, 2ft'3 substituting a for r in the small term, and integrating, I find a relation between r and t, which, combined with the differential equation between r and 6, leads to apsidal motion, the amount of which is entirely false. Again, if in the small term a-^r — a be put for r and be expanded to the first power of r—a, the result is an apsidal motion equal in amount to the know^n first approximation, but contrary in sign. These absurd and con- tradictory results plainly indicate that the equation (C), though it contains the disturbing force explicitly when a is put for r in the small term, contains it so as to give no information respect- ing the orbit. The only inference from this fact is, that the equation contains the disturbing force as a factor. Analysis supplies no other language by which the fact may be expressed. Mr. Adams asserts that this inference is "unwarranted," and "wholly unsupported by any proof." But here, as in other parts of the discussion, his assertions are stronger than his argu- ments. For if we now turn to the explanation he offers of the " supposed difficulty," we shall find that he leads us unwittingly to the very same conclusion respecting the existence of a factor. 106 Prof. Challis on certain Questions Irinnp dt dv After deducing from the equation (C), by making -t; =0, the equation for finding the apsidal distances, viz. A«-2Mr + Cr»- ^^/'=0, . . . . (P) Mr. -Adams goes on to obtain values of the apsidal distances by an approximate solution of this equation . The process he adopts, though conducted in an unusual manner, is nothing more than the ordinary Newtonian method, applied to approximate to two roots of an equation of /owr dimensions. On the reason for this process he is quite silent. The roots being put under the form a(l ± e) the resulting value of a is C "^ '^^' which is known from independent considerations to be true. Mr. Adams might have added the resulting^ value of e^, which is equally true, viz. ■ .--? -^; This very remarkable result was first obtained in my paper, and ought alone to have saved it from unqualified condemnation. Now, as to the rationale of the above process, it is known from the theory of equations, that since the term of highest dimen- sions contains a very small coefficient, the process would be quite illusory unless that coefficient be a factor of the equation. But it is a factor of the equation in case ^^— 2ftr + Cr^ be a com- plete square, that is, if h^C=fi^. For then the equation takes the form 7^ = 0, i'-ff- 2a'^ and, putting —■ +/8 for r, may be transformed into Hence the required condition is satisfied if the unknown quan- m tity / be such that /* = ^-^. All that remains to complete this reasoning is to show that no result applicable to the moon^s orbit can be derived from the equation (F), unless it be treated as an equation of four dimensions. Here, again, Mr. Adams comes to my assistance. For he has shown, that if the equation be put under the form A«-Vr+(c-^)r'=0, relating to the Moon's Orbit. 107 and be solved as a quadratic, the resulting value of a is which is not true. If, without altering the form of (F), a be put for r in the small term, and the equation be solved as a quadratic, the value of a is found to be '^. These contradictory and false results show that the apsidal distances can be obtained only by solving (F) as a biquadratic, and consequently that the equation contains the disturbing force as a factor. Mr. Adams is not happy in the inference he draws (in the first paragraph of page 34) respecting the different values of a given by his two processes. Plainly he had not bestowed on the subject all the consideration it demands. In reply to the argument in the next paragraph, that " the required condition would be satisfied if h^C differed from fi^ by any quantity involving the disturbing force as a factor,^^ it is enough to say that the equation h^C = fju^ is sufficient , and that it would be a violation of the principles of analytical reasoning to introduce gratuitously a quantity to determine which there are no conditions. It is true that on carrying the approximation to small quantities of a higher order,- it will be found that h^C~-fju^= a quantity containing the disturbing force as a factor, but at the same time the approximation itself determines the form and value of this quantity. The next attack on the equation (C) is made on the principle, that an approximate equation, formed so as to include all quan- tities of the second order, may be proved to be false by reference to quantities of the third order which have been neglected in deducing it. No one, I think, ever heard of such a principle before. To state this argument is to refute it. In the first paragraph of page 35 it is contended that the relations between r, 6 and t, in page 281 of my article in the April Number, do not satisfy the equations (B) and (C) from which they are derived. They satisfy these equations by taking account of a term involving the sun^s longitude, which by the integration rises to the third order, and which on that account was omitted. Surely there was no necessity to bring forward such an argument as this. The three differential equations which are the basis of the whole of the analytical reasoning, were formed on the supposition that the ordinate z is small compared to the radius-vector r. In Titan^s orbit, z may be very nearly the half of r, for which reason the theory does not apply to that body. In fact, it can- »ot be tested by reference to a system of satellites, the mutual lOd Prof. Challis on certain Questions disturbances of which may countervail the disturbing force of the sun. I conic now to an argument in which I admit that Mr. Adams has taken a right view. I attempted by reasoning conducted verbally, to confirm the results of an analysis which stood in need of no such confirmation. If that reasoning had been good, it would have shown that the eccentricity is proportional to the square of the ratio of the periodic times, and not, as stated in Theorem II., simply proportional to that ratio. I am therefore thankful to Mr. Adams for proving that this verbal reasoning was in fault. The assertion in page 36, that " if the disturbing force were increased the total fluctuation in the value of the radius-vector would be the same as before," begs the question at issue. So also does the " fatal objection " which follows it. To determine generally the orbit described under given initial circumstances, it would be necessary to commence the approximation on the single supposition that the ratio of the moon's radius-vector to that of the sun is small, a problem which has never been attempted. To this supposition is always added that of a mean motion of the radius-vector differing little from the true motion. I have shown that this latter supposition conducts to a special value of the eccentricity depending on the ratio of the mean motions of the moon and sun, and have thus given at least a negative proof that no part of the eccentricity would be constant if that particular relation did not exist. To prove the same thing positively would require the solution of the general problem above mentioned. It would be waste of time to say more in defence of what I only stated to be a probability. As Mr. Adams appeals to the method of the variation of para- meters in support of the last argument, I shall take the occasion to say a few words on the principle of this method. In the first place, I remark that it has been applied in the lunar theory only on the hypothesis of a mean motion of the radius-vector, and has decided on that hypothesis that the non-periodic part of the eccentricity is constant; but not having been applied to the more general problem, it has not decided that there would be a constant part of the eccentricity under all initial circum- stances. Again, the method of the variation of parameters is simply a process of integration applicable to differential equa- tions of a cei-tain form, and requiring the same rules of treat- ment whether the differential equations be approximate or exact. Consequently in the former case as well as in the other, the con- stants introduced by the integration necessarily present them- selves as independent of each other and arbitrary in value ; but in the case of an approximate solution, they are not thus proved relating to the Moon*s Orbit. iO& to be arbitrary and independent. For considerations quite sepa- rate from the process of integration by the variation of parame* ters, and arising out of the hypothesis of the approximation, may show that those constants may have certain analytical expressions or values, and certain relations to each other. Thus the process of integration by the method in question proves that there is a constant part of the radius-vector ; the process of approximation (m^ e^\ 1 — -^ + -^ ) . So by the variation of parameters the eccentricity is proved to have a con- stant part ; but that process is incapable of arriving at such an equation as e^ = 1 ^ + ^s^ns' much less of deciding whether h and C have a relation to each other. All that is proved by the method of the variation of parameters must be true ; but other results not inconsistent with its indications, and not deducible by it, may also be true. I contend, therefore, that it affords no handle for an argument against my views. I have now met, I think successfully, the whole congeries of Mr. Adams's arguments, the number of which does not make up for their want of force. By attacking an equation, the evidence for which is irresistible, Mr. Adams took up a false position which it was impossible to maintain. Nothing is now wanting to establish fully the solution of the lunar problem, of which I have indicated the initial steps, than to show, by carrying the approximation further, that it explains the variation and evec- tion, and gives more approximate values of the eccentricity and the mean motion of the apse. I have not yet had time to do this, but I feel confident that the solution, if rightly conducted, will bear this test. In concluding this long letter, I propose to give the method of determining, by a direct process to the first approximation, the mean motion of the moon^s node, which, as before intimated, was contained in my paper. The differential equations of the motion are, d'^z fjLZ m'z _ The last term in the third equation is a small quantity of the third order on account of the small ratio of z to r. If, therefore, we neglect this term, and suppose, as Newton does, the orbit to be a circle, we have for determining the period of the moon's 110 On certain Questions relating to the Moon's Orbit. oscillations in latitude the equation 27ra* The time of an oscillation is therefore —;=-. Also the known VfJb approximation to the moon's periodic time, as derived from the first two equations, is 2'7ra^/ m'(^ As this period is longer than the period of oscillation in latitude, the node regresses, and the amount of regression in one lunation is the arc which the moon describes in the difference of the periods ; that is, putting p and P for the periodic times of the moon and sun, the regression is 27r x -^ nearly. This, however, as is well known, is a false result, and it is necessary, therefore, to retrace our steps. The last term of the third equa- tion ought not to have been omitted, if that equation contains a small quantity of the first order as a factor, which will be found to be the case. For, putting a for r in the third equation, and integrating inclusively of the last term, we have r=:Acos(N^ + B), which shows that the small factor of the equation is A, the maxi- mum value of z. The period of the moon's oscillation in lati- tude is nearly which is less than the moon's period by Hence in one revolution of the moon the node regresses through the arc 27r x ^^> which is the known first approximation. Con- sequently, the result it was required to obtain. This investigation presents several points of analogy with that for finding the mean motion of the apse. I am. Gentlemen, Your obedient Servant, Cambridge Observatory, J. Challis. July 18, 1854. [ 111 ] XV. Further researches on the Methods of Preserving the Sensi- tiveness of Collodion Plates. By John Spiller and William Crookes*. THE object of our former paper in the Philosophical Maga- zine for May, was to draw attention to the principle of preserving the collodion surface moist by taking advantage of the deliquescent character of certain bodies ; and we preferred that method of communicating our discovery, as, although theo- retically correct, it was not sufficiently developed to warrant our laying it before practical photographers, but required further experiments by which the comparative merits of the different substances at our disposal could be determined. Having decided against the use of nitrate of zinc, we tried other substances, and among the rest the acetate of potash ; but although by its use we succeeded in obtaining very good results, yet the sparing solubility of acetate of silver necessitates so many precautions, that we determined if possible to find an equally efficacious salt among the nitrates. On giving the nitrate of magnesia a further trial, under cir- cumstances which later experience had shown to be necessary, our former difficulties vanished, and we are now enabled to com- municate to the Society the following process, which, in our opinion, scarcely admits of an improvement. The plate coated with collodion in the usual manner is to be rendered sensitive in a 30-grain nitrate of silver bath, in which it should remain rather longer than is generally considered ne- cessary (about five minutes), it must then be slightly drained and immersed in a second bath, consisting of — Nitrate of magnesia . . 4 ounces. Nitrate of silver ... 12 grains. Glacial acetic acid ... 1 drachm. Water .13 ounces. and there left for about five minutes, then removed and placed in a vertical position on blotting-paper, until all the surface- moisture has drained off and been absorbed ; this generally takes about half an hour, and they may then be packed away in any convenient box until required for use. Not only is the sensitiveness unimpaired by this treatment, but we think, on the contrary, that it is slightly increased; instantaneous negatives have been taken on plates which had been prepared some days previously. We are not yet in a posi- tion to give the length of time that may elapse between the pre- paration of the plate and development of the picture ; such expe- * From the Journal of the Photographic Society, July 21, 1854. 112 Methods of preserving the Sensitiveness of Collodion PlateS* riments necessarily require a more lengthened period than we Lave at present been able to give, but as long as they have yet been kept (upwards of three weeks), there has been no appear- ance of deterioration. Before the development, we find it advisable to moisten the Collodion film by immersion in the silver-bath for about half a minute, as otherwise the pyrogaTlie acid or iron solution would not flow evenly over the plate. The fixing, &c. is of course con- ducted as usual. It will be as well to draw attention to a few points which, although not absolutely essential, may possibly be found useful in practice. The glass plates should be cleaned with more care than is necessary when they are to be used immediately; we have found strong nitric acid applied with a tooth-brush most convenient. With regard to the collodion, we have tried very many different samples, and with tolerably uniform success. The greater number of our experiments have been made with a tolerably thick collodion, the alcohol and aether of which were in the proportion of 1 : 2, made sensitive with four grains of iodide and half a grain of bromide of ammonium to the fluid ounce. We have also employed a collodion containing iodide and bro- mide of cadmium with good success. Of the 30-grain silver solution for exciting the plate we have only to recommend the use of acetic instead of nitric acid, to give the bath that faintly acid reaction which is by some opera- tors considered desii'able. There are one or two circumstances to be attended to in the preparation of the magnesia-bath. Commercial fused nitrate of magnesia is very liable to contain chlorine, and also to have an alkaline reaction on account of the fusion being carried too far. Of course the quantities of acetic acid and nitrate of silver given in the formula for the bath arc on the supposition that the nitrate of magnesia is pure ; if this be not the case, it should be rendered perfectly neutral with acetic acid, the chlorine exactly precipitated with nitrate of silver, and then the proper amounts of acid and silver added. However, if the impurities are very considerable, it will be safer to reject the salt at once. This bath will keep in good order for a long time ; the only point to be attended to is to drain the plates slightly after coming from the silver-bath, and, if necessary, to remove the liquid from the back with blotting-paper, so as to introduce as little silver as possible into the nitrate of magnesia. A solution of one grain of silver to the ounce is quite sufficient to keep the plates sen- sitive ; and when the strength rises, as it will in time, to above a certain limit, the slight evaporation that always takes place will render the silver solution sufficiently strong to dissolve off Prof. Gerling^s Description of two Letter-scales. 113 the iodide in small holes. If this occur the bath can be restored by nearly, but not quite, precipitating the silver with a solution of chloride of magnesium, and then filtering. One of the most important things to be attended to is the necessity of preserving the plates where they are perfectly free from any light. It will be evident to all, that anything short of absolute darkness, when the sensitive surface is exposed' to its action for day after day, and perhaps week after week, must be fatal to its subsequent cleanliness. The necessity for protecting the plates from any deleterious gases, ammonia, for instance, is too obvious to require comment. XVI. Description of two Letter-scales. By Prof. Gerling of Marburg^. [With a Plate.] THE introduction of postage- stamps renders it desirable that private individuals should possess the means of weighing letters with accuracy and facility. It will perhaps be permitted me, in addition to the letter-scales already in use, to describe two others which a yearns practice has proved correct, and which on account of their simplicity are comparatively cheap. A side view of the first instrument is given in Plate I. fig. 1. It consists of the unmoveable slab of wood A, and the four small wooden pillars B, which latter are united by the thin steel axes C. The moveable portions consist, in the first place, of four equal bent levers D, C, E of sheet metal. Through the ends of these levers pass the four axes DD and EE. These axes carry the two strips of sheet metal DD, a piece of metallic gauze being spread across from one strip to the other to form the table on which the letter is placed. Below are two similar strips of metal, EE, which serve as a counter- weight to the letter placed above. The strips EE which remain horizontal, move more or less to the right according as the weight placed above is greater or less. The wire ^ is a fixed index, and the divisions which answer to a quarter of an ounce, half an ounce, an ounce, and so forth, are first determined empirically and marked along the strip EE. The second balance, fig. 2, consists simply of a glass tube filled with water, into which another smaller tube passes and sinks to a certain depth ; the latter tube is furnished with a little plat- form on the top, on which the letter is weighed. The internal tube sinks when a weight is placed above, and the depth to which it sinks for certain weights is first empirically determined ; these depths are marked upon the surface of the tube, and are the in- dices by which the weight of the letter placed above is given. * Communicated by the Author. Phil Mag, S. 4. Vol. 8. No, 50. Aug. 1854. I [ 114 ] XVII. On the Law of Prime Numbers, By Charles James Hargreave, Esq,, LL.D., F.R.S.* IN a paper written by me in the year 1849, and published in the rhilosophical Magazine, vol. xxxv. p. 36, I attempted, by means of certain principles there laid down, to apply the pro- cesses of analytical investigation to the theory of numbers ; and I thereby arrived at certain conclusions relative to the occurrence of prime numbers in the ordinal series which were expressed in the following proposition : — " The average distance between two successive prime numbers at the point x in the ordinal series is . log X ; and the average number of primes which may be expected to occur between x and x' is the logarithm-integral of x between those limits, or \\x'—\ix." The nature and exact purport of this theorem will be readily understood by any person who takes the trouble of counting the number of primes between various limits, when he will discover that, by taking ranges of sufficient magnitude, the rate at which the primes occur appears to follow a very regular and uniform law, though nothing can be apparently more irregular than the particular places at which the individual primes are to be found. In the paper above alluded to, the law was verified for various numbers under one million ; and it was found that the formula always produced the proper number of primes within very mode- rate limits of error. I propose in the present paper, first, to make a further inves- tigation as to the exact nature of the formula, and of the demon- stration upon which it rests ; and secondly, to point out a prac- ticable method by which the number of primes can be counted to a point in the ordinal series far beyond the limits of the exist- ing tables of primes, a method which will of course enable us to apply a more satisfactory test to the formula itself. Discussion of the Formula \ix. For the process by which this formula was orginally obtained I must refer the reader to the paper above mentioned. It will suffice for the present purpose to state, that the power of analy- tically investigating such a question was made to depend upon the substitution of an analytical equivalent for a quantity which was necessarily from the nature of the problem indeterminate, hut susceptible only of certain specified values. The equivalent thus substituted was, as may be anticipated, the arithmetical mean of the possible values. Since the publication of that paper, my attention has been directed by my esteemed friend Mr. Sylvester to an investigation * Ck)mmunicated by the Author. Mr, C. J. Hargreave on the Law of Prime Numbers. 115 of a similar problem, by Professor Tchebycheff of the University of St. Petersburgh, which appeared in the Transactions of the Academy of Sciences of St. Petersburgh, having been read before that learned body in the month of May, 1848 *. In that memoir the same formula, lice, was arrived at by a process with which the paper in the Philosophical Magazine has nothing in common; and the formula was considered as denoting the limiting value of the number of primes up to cc, as x increases without limit, rather than as being a mode of determining the average number of primes between given limits. The results given in that paper, (to which, as being a novel and highly ingenious mode of applying analysis to a question in the theory of numbers, the attention of the reader is particularly called), may be thus stated. The author first demonstrates that if <^^ be used to denote the exact number of primes between 0 and OS, then the expression (the summation with respect to x extending from the commence- ment of the ordinal series 2 to £c= Qc) approximates to a finite limit as p approximates to zero ; from which, it is readily inferred that there are an infinite number of values of a? for which (j)X lies between \ix+ ■T^ — -^3 however small a be taken, and however - (loga?)"^ large n be taken. The author then shows that any function of x which differs from lia? by a quantity of the order of magnitude denoted by X -T- (log xY, is incapable of approximating to (j>x within quan- tities of the order of ^ -f- (log x)"^ ; so that, for example, the con- jectural formula given by Legendre would ultimately give results at variance from the truth by quantities of the order denoted by X -T- (log x)"^ ; though it will not begin permanently to deviate from the truth until x has reached a magnitude of about a mil- lion and a quarter. The ultimate result is, that lia? expresses (jba? as accurately as it can be expressed by means of x and its logarithmic and expo- nential functions ; and the expression approximates to truth as X increases without limit. The following new investigation of the formulae relating to the occurrence of prime numbers has been suggested, partly by a perusal of M. Tchebycheff's memoir, and partly by the theo- * " Sur la fonction qui determine la totalite des Nombres Premiers infe- rieurs a une limite donnee," par M. le Prof. Tchebycheff. Lu le 24 Mai, 1848. 12 116 Mr. C. J. Hargreave on the Law of Prime Numbers. terns given in the latter part of my former paper. In that paper the term average is applied in its ordinary sense, which is well understood as meaning the rate at which primes occur at and about any particular points of the ordinal series. It is easy, however, to suggest other and more algebraical meanings of the term average as applied to this subject. Let Pn denote the wth actual prime number ; and let us compare the expression 2<^(j9„)from ;?„=2 to ;;„= oc with another expression S<^(P„) between the same limits, where P„ represents one of a series of terms P,, Pg, P3 . . . vvhich are connected with each other by the law Pn+i = P„ + V^(Pn). Then if 2„), or differs therefrom only by quantities of an order lower than 2^(j9„),we may say that the two series pY,p^,p^,;V^,V2,l^s'** run pari passu with each other, though there may be no such thing as an absolute equality between any term of one series and the corresponding term of the other. The law of formation, which is strictly true with regard to the latter series, may be regarded as possessing a species of average truth with reference to the former series. Lemma. The expression \p , where V = H- 2TT; + 3rrp + 4rrp + • • • c^d infinitum approximates to 7, or '57712 ... as /o diminishes without limit. For r tp ^'\^dt=\ tp{6-^ + e-''^-\-6-^^+...)dt=T(p-\-l)\p. Jo ^""^ Jo But, since • 1 1 1 j_,_2._f_ LJl l-€-'~ t'^2'^12 30[4]^43[6] '"' we have £t<'j^,dt=Tp+lT{p+i)+hr{p+z)-±r(p-\-3)+...; whence and From this it follows, that as p diminishes, the logarithm of \p approximates to — log /3 4- 7/3. Now, by referring to my former paper, it will be seen that Mr. C. J. Hargrcave on the Law of Prime Numbers. 117 \og{\p) = -hs^l-^^')-hs(l-~)-log(l-^-... 21+P ^ 31+P ^ 51+p ^ 71+p ^ + certain quantities which have a finite limit. We may therefore conclude that the series 21+P 31 +p 51+P 7'+p differs from the logarithm of p-^ by a quantity, which, as p di- minishes without limit, approximates to a certain finite constant. It will also be readily perceived, by integrating the function Xp with respect to p, that the expression 111 + TT—TT^TTTT-. + ^T—ii^rTT:; + •••; or --/\pdp + p, (log2)2^+p ' (log 3)3' +p ' (log4)4i+p approximates to —logp-{-{l—ry)p+ a constant: from which we infer that {log n)n^+p* where n has every value from 2 to oc , differs only by a constant from S — fip, where fi has the value of every prime number from 2 upwards, and p is supposed to be as small as we please ; so that, when p = 0, these two expressions, which are infinite and of the order —• log p, differ only by a finite constant. Or fjL n log n But S -T is in reality the sum of the reciprocals of a series n log n '' of numbers, each of which is equal to the one before it increased by its logarithm (see Phil. Mag. vol. xxxv. p. 49) ; and we thus see that the sum of the reciprocals of the prime numbers differs only by a constant from the sum of the reciprocals of a series of numbers which follow the law P„+i = P^ + logP„, the magnitude of the constant being dependent on the point at which the latter series is made to commence. If we call the series which obeys the law P^+ logP^ = l\+i the series of theoretical primes, and assign a proper value to the first term of the series, we may then assert that the infinite sum of the reciprocals of the real primes is equal to the infinite sum of the reciprocals of the theoretical primes ; and we may, in the sense before indicated, assert that the average distance between two primes at the point x in the ordinal series is log x. 118 Mr. C. J. Hargreave on the Law of Prime Numbers. A practical Method of ascertaining the exact number of Primes up to an advanced point in the Ordinal Series. In the paper above referred to, I verified the formula \ix by computing it for various values of a? up to a million ; and com- pared the results with those derived from actually counting the primes up to that point from Burckhardt's and Chernac's tables. The number of primes up to a million, as counted, appeared to be 78,493, the formula giving 78,626. Since that period, I ascertained, by counting, the number of primes between two millions and three millions to be 67,751, the formula giving 67,916. I now propose to point out a method of ascertaining the num- ber of primes up to a point considerably beyond the limits of any tables ; and to apply it to the number 10,000,000 and in- ferior numbers. Let us denote by Pa? the exact number of primes inferior to x, (X\ sc — j the number — when integer, and the next whole number below - when it is not integer. If we take at random P a set of prime numbers jo,, jSg, jOg . , .pm the number of numbers between 0 and x which are not divisible by any of the set /?„ p^ . . .pny is .-x{»(^^)}..{»r|)}-x{»(i)}.... ±n( ^— ); the 2 being intended to cover every combination of one, of two, of three, &c., as the case m^y be, taken'out of the setpi,j9j,.,j9„. For example, the number of numbers up to 1 0,000 not contain- ing either 2, 3, 5, 7 or 11, will be 10,000 - (5000 + 3333 + 2000 -f 1428 + 909) + (1666+1000+714+454+666+476+303+285 + 181 + 129) -(333 + 238 + 151 + 142 + 90 + 64+95 + 60 + 43 + 25) + (47 + 30 + 21 + 12 + 8) -4. This proposition is obvious from the considerations developed at pages 38 and 39 of the former paper, and its truth will im- mediately suggest itself on consideration*. * The theorem may be generalized as follows. Denote by An the sum Mr. C. J. Hargreave on the Law of Prime Numbers. 119 The proposition is, however, useless when the number of primes to be eliminated is considerable ; for the number being n, the number of terms to be found by actual division would be 2"+ ^, if it were not that some of them vanish. It may be observed, however, that when the number x is large, the result will not differ materially from '0-,^)('-i)-(-i). which can be formed at once. If the number be of the form A ( jOj xp^ . . . xjo«), the result is simply A.[p-^ — \){p^—\) . . . (jo^ — l). Thus the number of numbers up to 2 . 3 . 5 . 7 . 11 . 13 . 17 . 19, or 9,699,690, not divisible by either 2, 3, 5, 7, 11, 13, 17 or 19, is simply 2 X 4 X 6 X 10 X 12 X 16 X 18, or 1,658,880. It should be observed, that the result is exclusive of the primes Pu P2, &c. themselves, but inclusive of 1. It is scarcely neces- sary to say that the process is of the easiest possible character^ though tedious from the number of divisions to be effected. I have ascertained by it that the number of ordinals up to ten millions not divisible by either 2, 3, 5, 7, 11, 13, 17, 19 or 23, is 1,635,877 j and the corresponding result up to five millions is 817,944. If we suppose this process performed for all the primes up to the square root of Xy the result would lead us at once to the accurate value of Vx ; but, for the reason above stated, the process is not practically applicable except for the purpose of of the integer quotients obtained by dividing a given number A^ by every possible combination of a set of primes, m in number, taken n and n together -, and let the series be called ^t. Then (!) will express the number of ordinals not exceeding A^ which do not contain any one of the m primes. Similarly, — ^'(1) will express the number of ordinals which contain one, and no more, of the set of m primes ; — <^"(1) the number of ordinals which contain two, and no more, 1 of these primes ; and generally + -i — 00 0*^^''(1) will express the num- ber of ordinals, each of which contains p distinct individuals of the set of primes, and no more. Thus up to 10,000, the number of terms not containing 2, 3, 5, 7 or 11, is 2077 ; the number containing only one of this set is 4193 ; the number containing two* distinct members of this set, and no more, is 2819; the number containing exactly three is 809 ; the number containing exactly four is 98 ; and the number of terms containing all the five is 4. 120 Mr. C. J. Hargrcave on the Law of Prime Numbers. eliminating those numbers whicli contain the iirst 10 or 11, or at the utmost 12 primes. I therefore pass to another pro- cess. If we take any number, say 10,000, and divide it successively by the prime numbers less than its square root, and if we count the number of primes between each divisor and its quotient (both included when prime), the aggregate of these results is obviously the number of numbers up to 10,000 which are com- posite of two primes, or double numbers. For each prime from nn Pi to — has a corresponding double number, of which p^ is one Pi factor and the prime in question is the other ; so that this pro- cess exactly exhausts all the double numbers including squares. If now we take each quotient obtained in the last process, down to that quotient which was obtained by dividing by the prime next below the cube root of w, and deal with it in exactly the same manner as we before dealt with the number itself, that is, divide it by every prime up to its square root, and count the primes from the divisor to the quotient, the aggregate of the results will exactly exhaust all the composites of three primes or treble numbers including cubes. The repetition of the operation upon each of the quotients in the last part of the process, or rather upon such of them as admit of the operation, gives us all the quadruple numbers ; and so on, as far as the magnitude of the number enables us to carry the process. The number of prime divisors diminishes as we proceed, but the number of dividends to be operated upon increases rapidly ; so much so, that this process is utterly impracticable for those small prime divisors which occur early in the series, such as 2, 3, 5, &c. We have, therefore, two processes ; the first of which enables us to expel that large mass of composite numbers which con- tain the small primes, such as from 2 to 19 or 23, or if need be, to 29 or even 31, but is scarcely practicable beyond this point ; and the second of which processes enables us to ascertain the number of composite numbers which include only the larger primes, such as those lying between 19 or 23 and the square root of the number, but which would be quite unavailing for the determination of the number of terms involving the small primes 2, 3, 5, &c. By using both processes, however, we bring the problem within the province of reasonable industry. As the second process may not be veiy clear without an ex- ample, I will apply the two processes to the determination of the number of primtb under one million, for which we shall not have occasion to use any table of primes beyond 35,000. Using the first process for the primes from 2 to 23, we find Mr. C. J. Hargreave on the Law of Prime Numbers. Sn(-) =1,498,954 121 ^N w =1,000,000 (~) = 901,506 SN^^-^) = 53,597 \pppp / 0, />0, ff^O; .... (55) while k may still receive any value from 0 to n, and h still varies in the summations between these latter limits: and thus the number of equations, supplied by the formula (54), between the constants {fyh), is reduced, as was lately stated, to (n-}'l)n^; while the number of those constants themselves had been seen to be reduced to {n + l)n^, by the same supposition Cq = 1. [9.] Additional reductions are obtained by introducing the law of conjugation (32), or by supposing K . Lft,g=Lg(,f, with the consequences already deduced from that law or equation in [5.]. Using S' to denote a summation relatively to h from 1 to n, and taking separately the two cases where A: = 0 and where A;> 0, we have, for the first case, by (54), ^\efh){gh)^%<{fgh){eh); (56) and for the second case, (ef){gQk)-{fg){eOk)=X<{(efh)(ghk) + [fgh){ehk)}. (57) No new conditions would be obtained by interchanging e and g ; but if we cyclically change efg to fge, each of the two sums (56) is seen to be equal to another of the same form; and two new equations are obtained from (5 7), by adding which thereto we find, 0=l,<{{efh){shk) + {fgh){ehk) + {geh)(fhk)}; . (58) and therefore, {fg){eOk)-{ef){gOk) = -^'{geh)ifhk) (59) When e=/, the equations (56) and (59) become, respectively, 0^1'{fh){fgh), (60) and {fg){fOk)-(f){ffOk)=l.'{gfh){fhk); . . (61) which are identically satisfied, if we suppose also f=g ; the pro- perties [5.] of the symbols (fgh) being throughout attended to : while, by the earlier properties [2.], the symbol (eO^) or {Oek) is 128 Sir W. R. Hamilton on some equal to 0 or to 1, according as e and k are unequal or equal to each other. And no equations distinct from these are obtained by supposing e=/7, or f=ff, in (56) and (59). The associative conditions for which k = 0 arc, therefore, in number, w(7i— 1) of the form (60), and Jw(w— 1) (n — 2) of the form (56) ; or -^(n^ — w) in all. And the other associative conditions, for which A: > 0, are, in number, 7i*(7i— 1) of the form (61), and ^n^(/i~l)(n— 2) of the form (59), or ^(w'*— n^) in all. It will, however, be found that this last number admits of being diminished by ^(n^— w), namely by one for each of the symbols of the form {fff) ; and that if, before or after this reduction, the associative equations for which X; > 0 be satisfied, then those other ^{n^—n) conditions lately mentioned, for which ^=0, arc satisfied also, as a neces- sary consequence. The total number of the equations of associa- tion, included in the formula (54), will thus come to be reduced to |(n4_n3)_^(n2-n), or to l7i(w-l)(w«-l) ; but it may seem unlikely that even so large a number of condi- tions as this can be satisfied generally , by the ^w(n^ + 1) constants of multiplication [5.]. Yet I have found, not only for the case 71 = 2, in which we have thus 5 constants and 3 equations, but also for the cases w = 3 and w = 4, for the former of which we have 15 constants and 24 equations, while for the latter we have 34 constants and 90 equations, that all these associative condi- tions can be satisfied : and even in such a manner as to leave some degree of indetermination in the results, or some constants of nmltiplication disposable. [1 0.] Without expressly introducing the symbols [fyh)^ results essentially equivalent to the foregoing may be deduced in the following way, with the help of the characteristics [3.] of opera- tion, S, V, K. The formula of association (51) may first be written thus* : tStV' + tV^V'=Sa'.^" + Vtt'.t"; . . . (62) in which the symbols Stt' and Vtt' are used to denote concisely, without a point interposed, the scalar and vector parts of the product u, but a point is inserted, after those symbols, and before l", in the second member, as a mark of multiplication : so that, in this abridged notation, Stt' . t" and Yli! . t" denote the products which might be more fully expressed as (S . id) x t"and (V . u') X l" ; while it has been thought unnecessary to write any point in the first member, where the factor t occurs at the left hand. Operating on (62) by S and V, we find the two following equations of association, which are respectively of the scalar and * There is here a shght departure from the notation of the Lectures on Quaternions, by the suppression of certain points, which circumstance in the present connexion cannot produce ambiguity. Extensions of Quaternions. 129 vector kinds : S(AVtV'-t"Va') = 0; (63) V(^Vi'^" + i'^VuO = ^"Sw'-tStV'; . . (64) because the law (32) of conjugation, iIt = Ku', gives, by (41), For the same reason, no essential change is made in either of the two equations, (63), (64), by interchanging o and l" ; but if we cyclically permute the three vector-units, 1 1' c", then (63) gives S(fcV6V') = S(t'Vt"0 = S(^"Vit'); • . . (65) and there arise three equations of the form (64), which give, by addition, Y(LYcU^' + o'Yi"L+L"yLi')=0; .... {66) and therefore conduct to three other equations, of the form* Y(tVL'o") = i"Scc'-c'SL"i (67) Equating t" to t, the two equations (65) reduce themselves to the single equation, S{lVu') = 0', (68) and the formula (67) becomes V(iya') = tV-^Su': (69) both which results become identities, when we further equate o^ to L. And no equations of condition, distinct from these, are obtained by supposing l^ — i!, or l' = l, in (65) and (67). The number of the symbols l being still supposed =^, and therefore by [5.] the number of the constants which enter into the expressions of their n^ binary products (including squares) being =l(n^ + 7i), these constants are thus (if possible) to be made to satisfy ^(n^—n) associative and scalar equations of con- dition, obtained through (63), from the comparison of the scalar parts of the two ternary products, i . iJJ' and i v' . a" ; namely, n(n—l) scalar equations of the form (68), and ^n(n--l)(n—2) such equations, of the forms (65). And the same constants of multiplication must also (if the associative law is to be fulfilled) be so chosen as to satisfy ^(n^—n^) vector equations, equivalent each to n scalar equations, or in all to ^(n'^—n^) scalar condi- tions, obtained through (64) from the comparison of the vector parts of the same two ternary products (51) ; namely, n{n — l) vector equations of the form (69), and ^n(n—l)(n—2) other vector equations, included in the formula (64). This new ana- lysis therefore confirms completely the conclusion of the fore- going paragraph respecting the general existence of i(n'*— w^) * This formula is one continually required in calculating with quater- nions (compare page li of the Contents, prefixed to the author's Lectures). Phil. Mag. S. 4. Vol. 8. No. 50. Aug. 1854. K 130 Sir W. R. Hamilton on some + y(w^— 7i) associative and scalar equations of condition, between the A(n^H-7i) disposable constants of multiplication, when the ge- neral conception of the polynomial expression P of [1 .] is modified by the suppositions, Iq=1 in [2.], and iU=Ki? in [5.]. At least the analysis of the present paragraph [10.] confirms what has been lately proved in [9.], that the number of the conditions of association can be reduced so far; but the same analysis will also admit of being soon applied, so as to assist in proving the existence of those additional and general reductions which have been lately mentioned without proof, and which depress the number of conditions to be satisfied to ^{n'^ — n^) —^{n^—n)» Meanwhile it may be useful to exemplify briefly the foregoing general reasonings for the cases ri=2, /i=3, that is, for trinomial and quadrinomial polynomes. [11.] For the case w=2, the two distinct symbols of the form I may be denoted simply by i and i/ ; and the equations of asso- ciation to be satisfied are all included in these two, t.a'=AV, c',L'c=c'h; .... (70) which give, when we operate on them by S and V, two scalar equations of the form (68), and two vector equations of the form (69), equivalent on the whole to six scalar equations of condition, between the five constants of multiplication, (1) (2) (12) (121) (122), if we write, on the plan of preceding articles, .^=(1), .'^=(2), Sa'=(12),n From (68), or from (60), or in so easy a case by more direct and less general considerations, we find that the comparison of the scalar parts of the products (70) conducts to the two equations, 0= (121)(1) + (122) (12) = (122) (2) + (121) (12). . (72) From (69), or (61), we find that the comparison of the vector parts of the same products (70) gives immediately four scalar equations, which however are seen to reduce themselves to the three following : (121)(123)=-(12); (122)5= (1); (131)«=(2); . (73) the fii'st of these occurring twice. And it is clear that the equa- tions (72) are satisfied, as soon as we assign to (1) (2) and (12) the values given by (73). If then we write, for conciseness, (121) = «, (122) = 5, (74) we shall have, for the present case (n = 2), the values, (1)=6», (2) = a«, (12) = -fl6. . . (75) Extensions of Quaternions. 131 And hence (writing k instead of J), we see that the trinome^, T = z + ix-\-Ky, ...... {76) where xyz are ordinary variables, will possess all the properties of those polynomial expressions which have been hitherto con- sidered in this paper, and especially the associative property, if we establish the formula of multiplication, {tx + icy) {ix' + Ky') = {bx — ay) {bx' — ay') -{■{aL-{-bK){xyf-yx'); .... (77) wherein a and b are any two constants of the ordinary and alge- braical kind. In this trinomial system, s'l + 1^1 _j_ Ky" =(2 + Lx + fcy) [z' + 1<2/ + Ky'), . (78) if x" =zx' + z'x + a {xy' —yx'), -^ y" = zy^+z'y + b{xy'-yx'), I . . . . (79) z" = zz' + {bx '— ay) {bx' — ay') ; J we have therefore the two modular relations, z" + bx"-ay"={z-{-bx-ay){z'-{-bx'-ay'), \ zti _ ba;'f + ay" = {z-bx + ay) {z' - bx' + ay') ; J ' ^ ^ that is to say, the functions z+ {bx — ay) are tuw linear moduli of the system. A general theory with which this result is con- nected will be mentioned a little further on. Geometrical inter- pretations (of no great interest) might easily be proposed, but they would not suit the plan of this communication. [12.] For the case n = S, or for the quadrinome r =XQ-f- L^X^-\- 12^2' ^3'^3) .... \y^) we may assume 8*2%= ^1, 8*3*1 = 62, 8*1*2=^3, J and 7*2*3= — V%*2= hh + *2^3 + *3^2J ^ 763^1 = — 7*1*3= *2/2 + *3?Wi 4- *iW3, i* . . . . (B3) V*i*2 = — • V*2*i = *3/3 + *iW22 + ^2^1 '> J and then the ^{n'^—n^)=27 scalar equations of condition, in- cluded in the vector form, V(*.*VO=V(**'.*"), (84) are found on trial to reduce f themselves to 24 ; which, after elimi- * I am not aware that this trinomial expression (76), with the formula of multiplication {77), coincides with any of the triplet-forms of Professor De Morgan, or of Messrs. John and Charles Graves : but it is given here merely by way of illustration. t The reason of this reduction is exhibited by the general analysis in [14.]. K2 132 Sir W. R. Hamilton on some nation of the 6 constants of the forms here denoted by a and b, or previously by (/) and {fy)j furnish 18 equations of condition between the 9 other constants, of the forms here marked /, m, n, or previously (fyh) ; and these 18 equations may be thus arranged* : 0=/9(»i-»»i)=4K-m2) = /i(n3-m8), I . . . . (85) 0=/3(ni-mO = /i(/i2-m2) = /2(n3-w?3) ;J 0=(n2 + Wl2)(Wi— 7Wi) = (/l3+7W3)(W2 — W2) = K+'Wl)('*3 — '«3)> 0=(w3 + W8)(Wi-m,) = (n, + m,)(n2-?W2) = K + W2)(w3-m3);J they are therefore satisfied, without any restriction on l^j^^^ by our supposing w,=wii, 712=^2, ^3=7713; . . . (87) but if we do not adopt this supposition^ they require us to admit this other system of equations, 0 = /i=/2=^8=Wi + %='*2 + ^2='*3 + %- • • (88) Whichever of these two suppositions, (87), (88), we adopt, there results a corresponding system of values of the six recently eli- minated constants, of the forms a and h, or (/) and {fg) ; and it is found t that these values satisfy, without any new supposition being required, the ^(/i^ — 7i)=8 scalar equations, included in the general form S(t.tVO = S(tt'.^'0, .... (89) which are required for the associative property. [13.] In this manner I have been led to the two following systems of associative quadrinomials, which may be called systems (A) and (B) ; both possessing all those general properties of the polynomial expression P, which have been considered in the pre- sent paper ; and one of them including the quaternions. For the system (A), the quadrinomial being still of the form (81), or of the following equivalent form, Q=w + tx + Ky-\-7\^j (90) where wxyz are what were called in [1.] the constituents, the * For it is found that each of the three constants {eff)-\-{eg g) must give a null product, when it is multiphed by any one of the constants {e'fg'), or by any one of these other constants, {e"f'f")—{e"g"g") ; if each of the three systems, efg, e'fg', e"f"g"y represent, in some order or other, but not necessarily in one common order, the system of the three unequal indices, 1, 2, 3. t This fact of calculation is explained by the general analysis of [15.]. The values of a and b may be deduced from the formulae, ai=mi^— /j/a, 6,=/iwij— msng, with others cycUcally formed from these. Extensions of Quaternions. 133 laws of the vector-units ikX are all included in this formula of multiplication for any two vectors, such as p=.ix-{-Ky-\-\Zy p' = LCc'-{-Ky' + 7^ : . . (91) (A) . . pp'=z [m-^ — Iji^oca^ + (/jmi — mg^g) {y:^ + zy^) + (m/ — 4/1)^2/' + {l^m^—m^mi) {za/ + xs^) 4- (^3^ — ^1 /a) -2'2^' + (/3W3 — ^1^2) (^y + yx') + (i/i + Km^ + Xm^ {y^ — zy) + (/c/g + Xmi + im^ [zx^ — xz') -{-{\I^-\-tm^-j-Km{){xy' — yx')', .... (92) and it is clear that Quaternions^ are simply that particular case of such QuADRiNOMEs (A), for which the six arbitrary constants /j . . w?3 and the three vector-units c k\ receive the following values : 1^ = 1^ = 1^=1^ mi = m2=»?3=0, L = ij K=j, \=Jc. . (93) For the other associative quadrinomial system (B), which we may call for distinction Tetrads, if we retain the expressions (90) (91), we must replace the formula of vector-multiplication {92) by one of the following form : (B) . . pp'= [Ix + my-\- nz) [W + m^i/ + nz^) + {/cn—\m) (yz'—zy') + {\l—m){zx'—xz') + {cm—Kl) (xy'—yx') ; (94) involving thus only three arbitrary constants, Imn, besides the three vector-units, o /c\; and apparently having no connexion with the quaternions, beyond the circumstance that one common analysis [12.] conducts to both the quadrinomes (A), and the tetrads (B). As regards certain modular properties of these two quadri- nomial systems, we shall shortly derive them as consequences of the general theory of polynomes of the form P, founded on the principles of the foregoing articles. [14.] In general, the formula (59) gives, by [2.], the two following equations, which may in their turn replace it, and are, like it, derived from the comparison of the vector parts of the general associative formula, or from the supposition that A; > 0 in (54) : (fy)=X{ffeh){fhe),iie%ff; .... (95) 0 =l^{geh){fhk),ifk%e,k%ff; , . (96) the summation extending in each from ^=1 to h=:n. Inter- changing/and g in (95), we have {gf)=^{feh)(ghe),iie%f; .... (97) * See the author's Lectures, or the Philosophical Magazine for July, 1844, in which the first printed account of the quaternions was given. 184 Sir W. R. Hamilton on some and making ^=/, in either (95) or (97), we obtain the equation, (f) = -S.(feh)(fhe),\ie%f. (98) For each of the n symbols (/), there are n—\ distinct expres- sions of this last form, obtained by assigning different values to e ; and when these expressions are equated ,to each other, there result 7i(7i— 2) equations between the symbols of the form (fgh). For each of the ^n(n — 1) symbols of the form {fg), where /and g are unequal, there are w — 1 expressions (95), and n — \ other expressions of the form (97), because, by (33) and (36), (^/) = [fg) ; and thus it might seem that there should arise, by equating these 2n—2 expressions for each symbol {fg), as many as 2n—Z equations from each, or ^n[n — 1) (2/i— 3) equations in all between the symbols {fgh) . i3ut if we observe that the sums of the n — \ expressions (95) for {fg)j and of the n — \ expressions (97) for {gf)> ai'e, respectively, [n-\){fg) = l.,Mgeh)(flie), "1 (n-\)(gf)=^,-%,{feh)(ghe);i where the summations may all be extended from 1 to w, because- {ffh) and (ggh) are each =0, by (35), since /i >0; and that these two double sums (99) are equal; we shall see that the formula {9f) = {f9), (100) though true, gives no information respecting the symbols (fgh) : or is not to be counted as a new and distinct equation," in com- bination with the n — \ equations (95), and the ti— 1 equations (97). In other words, the comparison of the sums (99) shows that we may confine ourselves to equating separately to each other, for each pair of unequal indices /and g, the n — \ expres- sions (95) for the symbol {fg), and the n—V other expressions (97) for the symbol {gf), without proceeding afterwards to equate an expression of the one set to an expression of the other set. We may therefore suppress, as unnecessary, an equation of the form (100), for each of the ^n{n — \) symbols of the form {fg), or for each pair of unequal indices / and g, as was stated by anticipation towards the close of paragraph [9.]. There remain, however, 2(n— 2) equations of condition, between the symbols {fgh), derived from each of those ^n{n—\) pairs; or as many as n{n — \){n^2) equations in all, obtained in this manner from (95) and (97), regarded as separate formulae. Thus, with- out yet having used the formula (96), we obtain, with the help of (98), by elimination of the symbols (/), {fg), {gf), through the comparison of ti— 1 expressions for each of those n^ symbols, rP{n — 2) equations of condition, homogeneous and of the second Extensions of Quaternions, 1^ dimension, between the symbols of the form {fgh). And with- out any such elimination, the formula (96) gives immediately ^n^[n — \)[n—2) other equations of the same kind between the same set of symbols ; because after choosing any pair of unequal indices e and g, we may combine this pair with any one of the n values of the index/, and with any one of the n — % values of k, which are unequal both to e and to g. There are therefore, altogether, ^n^[n + l)(7i— 2) homogeneous equations of the second dimension, obtained by comparison of the vector parts of the general formula of association, to be satisfied by the ^n\n — \) symbols of the form {fgh) . [15.] To prove now, generally, that when the vector parts of the associative formula are thus equal, the scalar parts of the same formula are necessarily equal also, or that the system of conditions (56) in [9.] is included in the system (57) or (59) ; we may conveniently employ the notations S and V, and pursue the analysis of paragraph [10.], so as to show that the system of equations (65), including (68), results from the system [Q7), including (69) ; or that if the formula (84) be satisfied for every set of three unequal or equal vector-units, i t! t", then, for every such set, the formula (89) is satisfied also. For this purpose, I remark that the formula of vector -association (67),. when com- bined with the distributive principle of multiplication [1.], and of operation with S and V [5.], gives generally, as in quater- nions, the transformation V^Vo-T=TSpo— o-S/dt; ..... (101) where p, <7, t may denote any three vectors , and the symbol V/oVcrr is used to signify concisely the vector part of the product p X V(' = /o'S/9ts- + cr'Scr'nr + T'ST«r, . . (107) and consequently S|0/o'=Scr(7' = STT': (108) but this is precisely by (103) the formula of scalar-association 186 On some Extensions of Quaternions, (65), stated in its most general form. The general dependence of (65) on (67), or of (56) on (57), is therefore proved to exist; and -the y(»^— w) associative conditions, for which A; = 0 in (54), are seen to be consequences of the J(w'*— w^) other conditions for which k^O; or even of those conditions diminished in num- ber by ^(n*— w), according to what was stated by anticipation in [9.] , and has been proved by the analysis of [14.] . This result is the more satisfactory, because otherwise the conditions of association would essentially involve a system of homogeneous equations of the thi7'd dimension relatively to the symbols {fyh), obtained by substituting in (56) the expressions (95) or (97) for the symbols of the form (J^), including the values (98) of the symbols (/). But we see now (as above stated) that the total number of distinct conditions may be reduced to ^{n'^ — n^) — ^{n^—n), between the total number ^{n^ + n) of constants of multiphcation ; or finally, after the elimination of the ^(n^ + n) symbols of the forms (/) and {fff), to a system of homogeneous equations of the second dimension, namely those determined in [14.], of which the number amounts (as in that paragraph) to ^{n^-n^)^n''=^n%n + l){n-2), . . (109) between the symbols of the form {fyh), whereof the number is i{n^ + n)-i{n^ + n)=in%n-l). . . (110) [16.] For example, when n=2, the two constants (121) and (122) have been seen in [11.] to be unrestricted by any con- dition. When w=3, we have 9 constants, lately denoted by /j 4 4 ^1 wig m^ n^ 7^2 Wg, wherewith to satisfy 18 homogeneous equations of the second dimension, namely those marked (85) and (86) in [12.] ; which it has been seen to be possible to do, in two distinct ways (A) and (B), and even so as to leave some of the constants arbitrary, in each of the two resulting systems, of associative quadrinomes and tetrads, A similar result has been found by me to hold good for the case 7i = 4, or for the case of associative quines, such as P = M; + w: + iey + X^ + /AW, .... (Ill) involving four vector-units lkX/j., which obey the laws of con- jugation (32), and of association (51). For although there are in this case only 24= Jw^(n— 1) constants of the form (fyh), to satisfy 80 = J7i^(/i -|- 1) (n — 2) homogeneous equations of the second dimension, yet I have found that the forms* of these equations * The subject may be illustrated by the very simple remark, that although the four equations tx=:0, ty=iO, Ma?=0, My=0, are such that no three of them include th^ fourth, since we might (for example) satisfy the three first alone by supposing ^=0, x=0, yet they can all four be satisfied together by Dr. Day^s Mineralogical Notices, 137 are such as to allow this to be done in various ways, and even without entirely determining the constants. And it appears not impossible that similar results may be obtained for higher values oi n; or that associative^ polynomes of higher orders than quines may be discovered. Observatory of Trinity College, DubUn, July 4, 1854. [To be continued.] XX. Mineralogical Notices. By Dr. Alfred Day. To the Editors of the Philosophical Magazine and Journal. Gentlemen, THE following notices of British species and their localities, which have not as yet found their way into our standard works on mineralogy, may be interesting to a portion of your readers. Ankerite. — For some years past I have noticed on the boards of the mineral dealers at Clifton ornamental specimens of iron ore, which have been sold as the produce of the neighbourhood, but which after considerable inquiry I find are brought from Whitehaven to the ports of South Wales. They consist of sili- ceous ironstone covered with hsematite, then coated with spe- cular iron, often of highly iridescent hues, with quartz almost dodecahedral, or in which the prism planes are much reduced, with a great variety of forms of carbonate of lime and what appears to be brown spar. The latter, which has the curvilinear faces common in this species, is sometimes dark brown and at others of a nankeen-yellow with a wax-like surface. On analysis I generally find that this last consists roughly of about one -half supposing either x=0, y—0, or t=.0, m=0. Compare the equations (85) or (86), which are of the forms to=iO, ty=Q, tz=-b, ux=0, uy=^0, uz=zO, vx=^0, vy=0, vz=.0. In the theory of quines, however, the forms are not quite so simple. * The octaves, or octonomial expressions, which Mr. Cayley published in the Philosophical Magazine for March 1845, and which had been previously but privately communicated to me by Mr. J. T. Graves about the end of 1843, after my communication to him of the quaternions, are not associa- tive polynomes. Thus in Mr. Cayley's notation, the four following of his seven types, (123) (624) (176) (734), give i^. 1^1^ = iite= — 17, but ij tg . 14=^3 t4=z-\-iy; or with Mr. Graves's symbols, the triads ijk, ion,jln, klo, give i.jl=.inz=z — 0, but ij.l=kl=-^o. See note to page (61) of the Preface to my Lectures. It was my perceiving this latter property of Mr. Graves's symbols in 1844, which chiefly discouraged me from pursuing the study of those octaves, as a species of extension of the quaternions, which Mr. Graves as well as Mr. Cayley had designed them to be, and which in one sense no doubt they are. 188 Dr. Day's Mineralogical Notices, carbonate of lime, while the remaining portion is composed of the cai'bonates of iron, magnesia, and manganese in varying pro- portions. In various pieces which I have tried I have found upwards of 20 per cent, of carbonate of magnesia, and never, I believe, less than 10; while the reaction for manganese with soda on platinum-foil, though interfered with by the tendency of the mineral to grow dark under the blowpipe flame, is still very evident. I do not pretend to the last degree of accuracy in these examinations, and when the acknowledged difficulties of the quantitative determination of magnesia are considered, this will be excused. The analysis of carbonate of magnesia varies much in different hands, as may be seen by reference to Brande ; and I do not feel certain whether, in the combination with lime and iron, the water should be regarded as an essential constituent. On the principle of carbonate of magnesia entering as an iso- morphic element into the union in question, I should think not. By a reference to the analyses of foreign ankerite, it will be noticed that while the carbonate of lime appears to be of nearly uniform amount, agreeing almost exactly with my determination, the quantities of carbonate of iron, magnesia and manganese, which enter as isomorphic elements, are quite capricious, and all my trials give results within the same limits. There cannot, therefore, be any doubt of the close agreement of the species. The quartz is sometimes singularly distorted by the unusual enlargement of some of its planes, so as to create a momentary difficulty in recognizing the form, and in other cases forms thin plates cut at all angles to the axis. In one instance it forms a thin hexagonal table, in which all the edges are bevelled, corre- sponding to the situation of the twelve pyramidal planes, and all the prism planes are reduced to thin lines of light when held so as to catch the reflexion. Topaz. — Some time back a friend placed in my hands portions of the rocks of Lundy Island ; and on looking at a small speci- men composed of quartz crystals, I found three topazes among the group, which I recognized by their crystalline form. They can be traced quite through the body of the quartz crystals nearly three-fourths of an inch long, but so that the latter have inter- fered with their perfect development, indicating that they have penetrated while the material of each was soft. Since this another friend has brought from the island a detached crystal, which he picked up there, exhibiting a curious fracture where it has been torn from its matrix, which on examination with the lens exhibits numerous small crystalline prominences, apparently smaller individuals; This may, in fact, prove that it is not a fracture proper, but such a termination as is often seen in tour- malines, and which is thought to be connected with their electric Royal Society, 139 properties. The considerable size of these topazes renders them interesting as English specimens, those of Cornwall and the Mourne Mountains, Ireland, being generally very minute, I believe. Silex.—YYom the table of a mineral dealer on Clifton Downs I lately obtained a portion of a large ironstone nodule, coated internally with quartz, which is concealed under an accumulation of siliceous matter, whose form is unknown to me, but possesses a characteristic structure, having much the appearance of antho- phyllite in this respect, a kind of indistinct radiating texture, composed of extremely fine laminae in groups, and of a pinkish hue. It is composed almost wholly of pure silex, with traces of iron and lime, and possibly alumina, which I have not attempted to separate from the iron, the former however so much in excess as to render it probable that their presence is either accidental or a mechanical admixture. The large nodule in which this is contained is said to have been brought from the summit of Broadfield Down, Somersetshire, where trap rocks make their appearance at no great distance. The quartz is so concealed by it, that it looks as though the former had been changed into it, or its crystallization suspended by some alteration of heat or pressure, or other cause, so that the elements have arranged themselves in a new form. Celestine. — The beautiful and unique variety of this mineral, found at Pyle Hill, near Bristol, presenting fine crystals of the primitive rhombic prism with single replacements on the alter- nate solid angles, so well investigated and described by Mr. William Sanders, of Bristol, some years back, has not as yet, that I know of, been noticed in any of the manuals. Some of the smaller crystals, though retaining the general rhombic form, show minute replacements in addition to the principal one on the alternate solid angle, whose symbol it would be interesting to determine, and of which I have preserved specimens. XXI. Proceedings of Learned Societies, ROYAL SOCIETY. [Continued from p. 74.] May 18, 1854.— The Earl of Rosse, President, in the Chair. HE following paper was read : — " On some conclusions derived T from the observations of the Magnetic Declination at the Ob- servatory of St. Helena. By Colonel Edward Sabine, R.A., V.P.R.S. The author commences with the following preliminary remarks : — •* The part taken by the Royal Society in promoting, by its influence with Government, the establishment of the Colonial Magnetic Ob- servatories, and in drawing up instructions for the guidance of those 140 Royal Society. who were employed in them, makes it the duty of the person charged with their superintendence, to spare no pains to place before the Fellows, on suitable occasions, the results of researches designed to obtain a foundation of facts, on which a correct theory of the mag- netic variations might be framed, and an insight be gained into the nature of the physical agency by which they are produced. " In this first stage of scientific inquiry, when we have only the phsenomena themselves to guide us in their classification, or to indi- cate by apparent correspondences the existence of some causal con- nexion of which we have no other knowledge than that which the observations themselves may afford, the first difficulty to be met consists, in disentangling from the complication in which the mag- netic variations proceeding from different causes first present them- selves, the effects which may appear to be due to certain amongst them ; and in presenting these in some methodical order or arrange- ment, which may best assist the physicist or the mathematician in his conception of the problem or problems, to the solution of which he may desire to apply himself. " The first and most obvious separation of the magnetic variations is into those which are presented at one time at diflferent parts of the earth's surface, and have special reference therefore to space ; and those which present themselves at different times at one and the same place, and have special reference therefore to time. It is the object of magnetic surveys to collect the facts of the first, and of magnetic observatories the facts of the second, of these primary divi- sions. The present communication belongs to the second, and re- gards the variations depending upon time at a single station (St. Helena). " Still, however, the phsenomena even at a single station are too complicated for ready comprehension, and stand in need of further subdivision. This is most satisfactorily effected by the customary separation into three classes, or elements as they are frequently termed, the Declination, the Inclination, and the Intensity of the Directive Force. The discussion is limited on the present occasion to a single element, the Declination, and to a portion only of the results obtained by the observations of that element at St. Helena." After premising a description of the instrument with which the observations were made, and of the mode of observing and of record- ing the observations, which is omitted here because it may be found in the Introduction to the fiirst volume of the ' St. Helena Magnetical Observations,' the author proceeds to the conclusions which he de- sires to notice, and to the manner in which these have been obtained, which we follow, by adopting, as nearly as may be convenient, his own words. "Before we attempt to examine those periodical variations, or fluctuations about a mean value, which, from their having for periods, for example, the solar year or the solar day, we naturally refer to causes depending in some way upon the earth's place in its orbit re- latively to the sun, or to the earth's revolution round its axis, it is desirable to examine, and if practicable, to eliminate the effects of a variation which we have reason to believe belongs intrinsically to the Royal Society. 141 magnetism of the earth Itself. The geographical aspect, if we may so express it, of the terrestrial magnetism, or the different measure in which the magnetic force exists at different parts of the earth's surface, and the different directions which a magnet assumes in dif- ferent places by virtue of this force, so far from being permanent, are found to be subject to a continual change, which differs from all other magnetic variations with which we are acquainted, inasmuch as it does not present to us the character of an oscillation of the phaenomena around a mean value in periods of greater or less dura- tion, but appears, especially when viewed generally in its operation over the whole globe, as a continuously progressive change ; it has for this reason received the appropriate name of * secular change.' It is possible indeed that the magnetism of the earth may have its periods, — that the phsenomena existing at one and the same epoch over the whole surface of the globe may be identically reproduced at a subsequent epoch, — and that what has been called the secular change of each of the magnetic elements, which we perceive to be in progress at any particular point of the surface, St. Helena for ex- ample, may be part of a succession of changes which operate in a cycle, of which the duration, vast as it may be, may hereafter be found to be calculable. But as far as our knowledge has yet gone, it is insufficient to justify the assumption of even approximate pe- riodical laws of this variation of the terrestrial magnetism ; and we must continue to regard it therefore for the present as a secular change, of which the period, if there be one, or the periods, if there be more than one, are as yet unknown. But although the secular change has no intrinsic relation, as far as we have been able to dis- cover, to any of the periods of time determined by other phsenomena, either of our own planet or of any other of the heavenly bodies, it is obvious that we may assign the average rate at which the change is taking place, in any of the magnetic elements and at any particular station (the declination for example at St. Helena), corresponding to any definite measure of time in usage amongst us (say for example a month, or the twelfth part of a solar year), by taking the successive differences between the monthly means of all the hourly observations in the first and second months of their continuance, then between the second and third months, then between the third and fourth, and so on. By thus proceeding in the case of the Declination at St. He- lena, we have sixty differences thus accruing in the five years of hourly observation, by which we find that the monthly increase of West Declination during these five years amounted on the average to 0'-657, or to an annual increase of 7'" 88. " It is not however necessary for this investigation that the system of observation should be hourly : a much less onerous system is suf- ficient, provided that the observations be distributed equably through the year, and that the intervals between the observations of each day be, approximately at least, equidistant. Before the commence- ment of the hourly series there had been fifteen months of two- hourly observations, and after its close the observations were con- tinued for twenty-one months more at five hours of each day, the hours being such as to give by their combination a true mean value 142 Royal Society. for each day. We are thus enabled to take in a more extended period, amounting to ninety- six consecutive months, or eight years, from which to derive the average rate of secular change at St. Helena. Proceeding as before, we find for this period an average rate of 0'* 661 for the increase of West Declination in a month, or an annual in- crease of 7'*93 in a solar year. During these eight years the hori- zontal magnetic direction at St. Helena had consequently changed altogether rather more than one degree. «. " When the number of years are few from which an annual average rate of secular change is derived, it is necessary to be particular in regard to the regular distribution of the observations as to months and hours, because observations made at one time of the year or at one hour of the day, are not strictly comparable with those made at other times of the year or at other hours of the day, unless indeed corrections based on a long series of observations at the same spot or in its vicinity are applied for the annual and diurnal variations. But when the periods of comparison include intervals of consider- able length, the comparative influence of the annual and diurnal variations is greatly diminished, and, if the comparison extend over a great number of years, it may practically be disregarded. Now, St. Helena being a naval station, and frequently visited by navigators of our own and other countries, who have had the requisite knowledge and have been at the pains to take the necessary precautions to make trustworthy observations, we are able to collect from the nar- ratives of their voyages a succession of determinations of the Decli- nation, all made at the same spot, namely, at the one anchorage at St. Helena, which extend over a period of 236 years, or from 1610 to 1846. The following Table contains eleven such determinations, all from authorities of high repute, which are fortunately so far equably distributed in respect to the years when they were made, as to throw light not only upon the average amount of the secular change of declination during that long period, but also in a consider- able degree upon the regularity, or uniformity with which the change has taken place. By treating these eleven determinations according to well-known methods, we obtain 11° 48' as the west declination corresponding to the middle epoch, the year 1763, and 8''05 as the most probable rate of the annual increase during the 236 years. Declinations observed at the Anchorage at St. Helena. 1610. Davis - 7 13 Calculated- 8 44 Obs.-Calcul.+? 31 1677. Halley - 0 40 1691. Ilalley + 1 00 1724. Mathews + 7 30 1775. Wales -|-12 18 1789. Hunter -f 15 3^ 1796. Macdonald -|-15 48 1806. Krusenstern -(-17 18 1839. Du Petit-Thouars ... -f-22 17 1840. Ross -j-22 53 1846. Berard -|-23 11 Mean Epoch 1763 Mean Declination -t-ll° 48^ Annual Increase of West Declination 8'-05 + 0 16 -0 56 -h 2 08 -1 08 4- 6 34 +0 56 -f 13 25 -1 07 + 15 18 +0 12 -1-16 14 -0 26 -1-17 34 -0 16 +22 00 +0 17 +22 08 +0 45 +22 57 +0 14 Royal Society. 143 " We have here then a striking example of the magnitude and character of the changes wrought at a particular station by this very remarkable feature of the earth's magnetic force. In less than two centuries and a half, the horizontal direction which a magnet takes at St. Helena by virtue of the terrestrial magnetic force has been found to have changed more than 30°, or more than a twelfth part of the whole circle : and when we further examine the facts more closely, we find reason to conclude that this great change has taken place by a steady, equable and uniform progression throughout the whole period. The rate of annual change derived from the eight years during which the observations were maintained by the detachment of the Royal Artillery stationed at the Observatory (7'*93) differs so slightly from that derived from the observations made at the anchor- age from the earliest period at which observations are recorded (i, e. 8'*05), that we may practically regard them as the same. To examine whether this has been a uniform rate throughout the 236 years, or otherwise, the same calculation which gives 8'*05 as the most probable average rate of change between 1610 and 1846, will give also for each of the years in which the Declination was observed the most probable values of the Declination corresponding to the same rate of change supposed uniform. These calculated values are placed in the Table opposite to the years to which each belongs, and adjoining the observed values. The differences are shown in the next column. On inspecting these, we perceive that not one of the differences exceeds the limits, which, with a due consideration of the irregularities to which magnetic observations made on board ship are liable, may be ascribed to accidents of observation ; and, what is still more important, that they fall indiscriminately to the east and to the west of the values calculated on the supposition of a uniform rate, and without the slightest appearance of any systematic character which might indicate that the rate had been otherwise than regular. We have reason to conclude, therefore, that, from the earliest date to which we can refer, the progression of secular change at St. Helena has gone on from year to year, as nearly as may be, in one uniform annual rate. "The instruction to be derived from the St. Helena observations does not however stop here. By a suitable arrangement of the observations of the eight years, they may be made to show that, when allowance is made for comparatively very small irregularities superimposed upon the regular march of the phsenomenon by dis- turbing causes which will be treated of in the sequel, the average annual change takes place by equal aliquot portions in each month of the year. The eight years of observation commenced with June 1^41 : if we take a mean of the eight monthly means in the eight Junes from ] 841 to 1848, we shall have a better assured mean value of the Declination corresponding to the month of June, than if we had confined ourselves to a single year. If we then do the same with the eight Julys, and with each of the other months in succes- sion, we shall have twelve monthly values for a year commencing with June and ending with May, which will represent in a simple 144 Royal Society, and condensed form the means of the whole eight years. These are exhibited in the next table, and we perceive at the first view that the increase of west declination is progressive in each month of the year without a single exception. If we desire to examine further the degree of approximation which these values present to a progres- sion absolutely uniform, we may apply an aliquot portion of the an- nual value (7'-93) to each of the monthly means corresponding to the difference in time from the mean epoch (December 1) . These ali- Months. Mean Declina< tion. Correction for secular change to Dec. 1. Mean Declina- tion in the year. Differences (^/'-^/'0. June July August ... September October ... November December January ... February... March April May 23-42 24-45 24-91 25-30 26-32 27-07 27-73 28-29 29-23 29-76 30-21 +3-64 +2-97 +2-31 + 1-65 -^0-99 +0-33 -0-a3 -0-99 -1-65 -2-31 -2-97 -3-64 23 27-06 = 23 27-42 = 23 27-22= 23 26 95 = 23 27-31 = 23 27-40= 23 27 40= 23 27-30 = 23 27-58 = 23 27-45 = 23 27-24 = 23 2705 = +0-22 -0-14 +006 +033 -0-03 -012 -0-12 -0 02 -0-30 -017 +0-04 +0-23 Mean, corresponding to Dec. 1 23 27-28 23 27-2S = ^ quot portions are sho^ni in the second column, and it will be seen by the third column, containing the mean declinations of the year deduced severally from the observation-values in the different months, with the correction for secular change assumed uniform applied, how very nearly the results derived from the several months approximate to one and the same value. The small differences which are shown in the last column are for the most part such as would probably dis- appear by a longer continuance of the observations ; but we may notice, by the character of the signs, that there is also visible amongst them the indication of a comparatively very small semi-annual affec- tion, depending on the sun's position on either side of the equator, which will be reverted to when treating of superimposed effects. *' The same features of regularity and uniformity are manifested if the examination be further pursued into shorter periods, by comparing with each other the twenty-six fortnightly means in the year; but enough has been already stated to show the magnitude, the regula- rity, and the systematic character of the changes called secular, which are thus produced by forces in constant operation at the sur- face of our planet. In our entire inability to connect these changes with any other of the phaenomena of nature, either cosmical or ter- restrial, we appear to have no other alternative than to view them as a constituent feature of the terrestrial magnetic force itself, and as one of its most remarkable characteristics, not to be overlooked by those who would seek to explain the phaenomena of that force by Royal Society, 145 means of a physical theory. I'he attempts which have sometimes been made to explain them by a supposed connexion of the ter- restrial magnetic phaenomena with the distribution of land and sea at the surface of the globe, or with the distribution of heat on that surface, or by electrical currents excited by the rotation of the earth on its axis, contain no provision to meet a systematic variation of this nature ; and break down altogether when the facts of the secu- lar change are duly apprehended. From the phaenomena of a single element at a single station, as here presented, we may assure ourselves that effects proceeding with so much order and regularity, which we cannot ascribe to any other cause than that of the ter- restrial magnetism itself, and cannot therefore separate from its other manifestations, must find a place in any physical theory which pro- fesses to explain the phaenomena of the earth's magnetism. To learn the changes in this and in the other magnetic elements which are simultaneously in progress in other parts of the globe, and to appre- hend their mutual connexion and the general system of secular change which they indicate, it is necessary that the facts should be collected in the same manner as at St. Helena, at a great number of stations distributed over the earth's surface, and that they should be studied both separately and together. This may indeed appear a work of labour ; but it is the most certain, if not the only certain mode of arriving at a correct knowledge of phsenomenal laws, when the laws of their causation are wholly unknown. In this, as in simi- lar studies, however complex the phaenomena may appear at the first aspect, — and it is fully admitted that those of the secular magnetic change do appear extremely complex at the first view, — the mind soon begins to recognize order amidst apparent irregularity, and system amidst incessant variation. The order and regularity with which we are impressed at a single station are soon perceived to cha- racterize, in an equally remarkable manner, a general systematic change taking place connectedly over the whole surface of the globe, and which can everywhere be traced to have been continuously in operation since the earliest epoch of magnetic observation. To those who find pleasure in tracing phaenomena of great apparent com- plexity to laws of comparative simplicity which appear to embrace them all, this study affords its own repayment; and it is indis- pensable towards the acquisition of a knowledge of the laws of terrestrial magnetism. By a comparison of the isogenic lines cor- responding to different epochs (lines of equal Magnetic Declina- tion employed by Halley and since found so useful in generali- sation in this branch of the magnetic phaenomena), we perceive that a secular change of the Declination, almost identical with that at St. Helena, has prevailed at the same time over the greater part of the southern Atlantic ; and that from the /orm of the isogonic lines in that quarter of the globe (which has undergone very little variation in the last 200 years), the regularity of the progression, and its persistence in the same direction, is in accordance with that general progressive motion from east to west, which magneticians have long since recognized as distinguishing the general systematic Phil Mag, S. 4. Vol. 8. No. 50. Aug, 1854. L 146 Royal Society. change in the southern hemisphere from that in the northern, which takes place in the opposite direction ; whilst from the form of the isogenic lines in that quarter, we may further anticipate that, at St. Helena, the secular change of the Declination will continue to take place in the same direction as at present, until the line drawn through the conical summits of the isogonic curves shall in its western pro- gress pass the geographical meridian of that station." The author then proceeds to the Variations which are found to take place in periods corresponding to a solar year and a solar day ; a correspondence which, he remarks, " enables us to recognize a phy- sical connexion, although we are still uncertain as to the mode of operation between cause and effect. A correct knowledge of the phsenomena themselves is the surest guide to a correct judgement amongst the many theories which have been propounded in anticipa- tion of that knowledge ; and I have therefore taken this opportunity of bringing before the Society a careful analysis of the primary an- nual and diurnal variations at St. Helena attributable to solar influ- ence, in the belief that they will be found to place in a very distinct light some {)oints which are important to be kept in view in framing or in judging of such theories." For this purpose diagrams were exhibited, representing on a large scale the mean diurnal variation of the Declination at St. Helena in the different months of the year, and the annual variation at each of the twenty-four hours, both de- rived from the mean of five years of hourly observation ; the secular change having been previously eliminated, these diagrams were re- garded by the author as exhibiting what might be considered as typical views of the annual and diurnal variations, correct in their relations to the mean Declination in the year, or to the arithmetical mean of all the hourly observations in the year, taken as zero. As on the first aspect the diurnal phsenomena in the several months are seen to separate themselves into two groups, having the equinoxes as at least approximate epochs of separation, the months in which the sun is north of the equator were coloured red, and those in which he is south of the equator were coloured blue. Having in these diagrams the conjoint representation of two distinct classes of phaenomena, a diurnal variation in each of the months, and an annual variation at each of the hours, the author proceeded to treat of each of these variations separately, commencing with the annual, which he illustrated by taking the hour of 7 a.m. as an example, and (referring to the diagram) showing the order and succession of the several months in the annual cycle at that hour, which are as follows : — in April the mean declination is about half a minute east of the mean declination in the year ; in May about 2' east; in June about 2'^ east; in July and August, when the sequence is slightly irregular, respectively 2'*1 and 2'' 6 east ; in Sep- tember the declination is again approaching the mean line, being less than 1'^ east of it ; in October it has passed the mean line, being about l'^ west of it; November, December, January and FebruEiry are congregated near the western extremity of the annual range, whilst in March we perceive that the declination is again approach- Royal Society, 147 ing the mean line, and in April it has passed to the east of the mean line. '* We have here, then," the author proceeds, " in the success- ive changes of the declination in the course of the year, the general fact of the existence of an annual variation, of which, at the solar hour of 7 A.M., selected as an example, or when the sun is five hours east of the meridian, the phsenomena are such as have been thus cursorily- described. Were there no annual variation at that hour the different months would all have the same mean declination, and the extended figure, which in the diagram represents the annual cycle, would be concentrated into one point. The annual variation difl^ers con- siderably at the different hours ; but it is a general feature amongst them that the months on either side of the one solstice are either congregated together towards one extremity of the annual range at the hour, w.hilst the months on either side of the opposite sol- stice are similarly congregated at the opposite extremity, or the months of both solstices are contemporaneously in pretty rapid transition from the one extremity to the other. It is this annual variation which has been overlooked in the supposition entertained by a very eminent authority, that in the vicinity of the equator the magnetic direction would be found to be constant at all hours of the day and night. If we group together the monthly means of each period of six months separated by the equinoxes, we have two semiannual mean lines, each differing comparatively very slightly from any one of the months of which it is composed, but the two differing very greatly from each other, and both differing very considerably from the mean diurnal march in the year. If the latter line, viz. the mean diurnal march in the year, be projected as a straight line, as is done in the zero-line of fig. 1 in the annexed woodcut, the semiannual groups take respectively the forms exhibited in that figure, the continuous line being the semiannual march in the half year when the sun is north of the equator, and the dotted line the semiannual march when the sun is south of the equator. It is in this form that the phsenomena of the annual variation in different parts of the globe may be most advantageously compared with each other. Fig. 2 represents the analogous phaenomena at Toronto in 43° north, and fig. 3 those at Hobarton in 43° south latitude. The semiannual groups at Toronto and Hobarton have been obtained* in precisely the same manner as those at St. Helena ; the scale is the same in the three figures, i. e. '5 of an inch to 1''0 of Declination, the dotted and continuous lines refer respectively to the same periods of the year, and the zero line is in each figure the mean diurnal variation in the year at the station. " In viewing these three figures, it is scarcely possible to doubt that they represent substantially the same phsenomenon. The magni- tude and inflexions of the curves are not indeed identical, but they approach so near to it that we may well suppose the small differ- ences to be very minor modifications which will some day receive their explanation. It will be remarked that during the hours when the sun is above the horizon and the effects are greatest, the corre- spondence of the phsenomena at the three stations is most striking, L2 ILLUSTRATIONS OF THE ANNUAL VARIATION OF THE MAGNETIC DECLINATION. Black /i»^.— Mean Semiannual Diurnal Variation, March 22 to September 20. Dotted line.— Mean Semiannual Diurnal Variation, September 22 to March 20. Fig. 1.— St. Helena. t h k h h h h k 12 13 14 IS 16 17 18 19 h h h h hh h h h h h hhhh h IT 20 31 22 23 0 1 2 3 4 5 6 7 8 9 10 11 12 a-0 /^ 1-0 r \ /-■ — x 0-0 \# *'•• •••*"♦ *""^> A y^ ^■^— -.^ ^ 10 /^^ V- .-' 2*0 Fig. 2.-Toroiito. Fig. 3.— Hobarton. 2-0 I'D / / \. \. O'O 1*0 2-0 12 13 14 IS l6 17 18 19 20 21 22 23 0 1 2 3 * ^ ^ '^ ^ ^ ^^ " j|. oiTAmJoaa t ^o mn^tiir jtdii^y^t. Am Royal Society. 149 and that there is no inversion of the phanomena in the opposite hemi^ spheres ; in both (as well as at St. Helena, in the tropics), the De- clination is easterly of the mean in the forenoon and westerly in the afternoon when the sun is north of the equator, and the reverse when the sun is south of the equator. The effects are the same at the three stations, though in the one hemisphere the sun being north of the equator corresponds to summer, and in the other hemi- sphere to winter ; whilst in the tropics this distinction of seasons almost ceases to be sensible, and the epochs of maximum and mini- mum of temperature do not correspond with either of those of the extra-tropical stations. The pha^nomena thus represented embrace above 86° of latitude, presenting not only almost extreme contem- poraneous diversities of climate, but also not less remarkable diver- sities of absolute dip, declination and magnetic force. ** No doubt can, I apprehend, be entertained that the annual variation which is here represented, is attributable, primarily, to the earth's revolution round the sun in a period of the same duration and in an orbit inclined to the equator. But in what way, it may be asked, does the sun superimpose upon the earth's magnetism this comparatively small but systematic magnetic variation ? The simi- larity of effect, amounting almost indeed to identity at the hours when the sun is above the horizon of the station, taking place at stations where both the climatic and the terrestrial magnetic con- ditions are so dissimilar, seems to remove it altogether from those l^hysical connexions, which have so often and in so many various ways been referred to as affording possible explanations of the mag- netic variations. In this difficulty some assistance may perhaps be afforded by examining more closely, by means of the St. Helena observations, theepochs when the phaenomena of one of the semi- annual groups passes into the very dissimilar phsenomena of the other semiannual group. This has been stated to take place approximately at the equinoxes. The approximation, particularly at the September equinox, is very distinctly and definitely marked. The day of the equinox is the 21st of September; if a mean be taken of the diurnal march in the three weeks from the ist to the 21st of September, the line which represents it scarcely differs sensibly at any hour of the twenty-four from the mean line of the pre- ceding half-year, taken from the 22nd of March to the 20th of Sep- tember ; thus showing that the phaenomena of that semiannual group are unchanged up to the time of the equinox. If in the same way a mean be taken of the diurnal march in the three weeks following the 21st of September, the line which represents them shows that the passage from the phsenomena of one semiannual group to those of the other has not only commenced, but that in half ths period of three weeks, i. e. within eleven days of the equinox, the change has already advanced very far towards its completion ; and by the middle of Oc- ? tober it is found to be quite complete, the mean ni October retaining no trace of those semiannual characters which had undergone no '.. modification ten days before the equinox." The facts thus stated ,| were illustrated by diagrams. h'i 150 Royal Society, "At the March equinox the commencement of the change is equally definite : no trace of change can be discovered in the mean from the Ist to the 20th of March, when compared with the mean of the six months from the 22nd of September to the 20th of March ; the change then commences, but from some cause not yet apparent, the conversion from the phaenomena of the one half-year to those of the other is effected less rapidly at this than at the September equinox. The mean of the month of April retain* the distinct traces of the group which it has quitted, and is in fact a month of transition between the two groups, but in May the conversion is quite com- plete ; the phaenomena of that month have no characteristic distin- guishable from those of June, July and August. •• From what has been stated in the preceding paragraphs, it will be evident that the epochs of the sun's passage of the equator have a very marked influence on the phaenomena under consideration, and that the influence is the same and produces similar effects whether the station itself be north or south of the equator, and however di- verse may be its climatic or magnetic conditions. The semiannual characteristics continue unchanged up to the days of the respective equinoxes ; these form the epochs when the transition from the cha- racters of the one semiannual group to those of the other commences, the transition being completed a very few days after the September equinox, but somewhat less rapidly after the March equinox. Like the changes in the induced magnetism of ships, which follow immediately the changes in the terrestrial magnetism corresponding to the ship's altered geographical position, but complete the change only after in- tervals of time of greater or less duration, so the changes which we are here considering appear to commence at the equinoxial epochs, but to require a greater or less interval of time for their completion." The divergence of the semiannual groups at the different hours from a mean march in the year has been shown in figs. 1, 2 and 3 by their comparison with the latter projected as straight lines, because the accordance of the divergence at the three stations is seen thereby in its simplest form. In another diagram the lines thus projected as straight lines were exhibited in their true Declination values, and com- pared with a Zero-line representing at each station the mean Decli- nation in the year. " In the previous comparison of the annual varia- tions at the three stations with each other, it was shown that there is no inversion, or contrariety, between the phaenomena at Toronto and Hobkrton as representativesof opposite hemispheres, the same semi- annual group diverging (during the hours of the day when the cha- racters are most marked) in the same direction at the same hours at both stations. But markedly opposite characteristics are shown when we compare the divergences of the mean diurnal variation in the year from the zero-line at different stations ; these divergences, so far from according with each- other at the two stations, present a strong contrast throughout; the divergence at Toronto being to the east at the hours when at Hobarton it is to the west, and vice versd. St. Helena, moreover, which agrees with both the other stations in the divergences of the semiannual groups, differs from both in those Royal Society, 151 of the mean of the whole year. The phsenomena of the solar annual variation superimposed upon those of the solar diurnal variation, — and those of the solar diurnal variation itself, — are in this respect contradistinguished by important differences. '' To have completed the view of the solar variations of the Decli- nation at St. Helena would have required a notice of the so-called irregular disturbances of that element, which are now known to have a periodical character dependent on solar hours ; and also of the re- markable cycle which is found to pervade all the magnetic variations depending upon the sun, corresponding in its period and epochs with those of the phaenomena of the solar spots ; but as both these subjects have been recently brought before the Society in separate memoirs, the author does not think it necessary to do more than merely advert to them on the present occasion." June 15. — The Earl of Rosse, President, in the Chair. The following paper was read : — " On Osmotic Force." By Prof. Graham, V.P.R.S. (The Bakerian Lecture.) This name was applied to the power by which liquids are im- pelled through moist membrane and other porous septa in experi- ments of endosmose and exosmose. It was shown that with a solu- tion of salt on one side of the porous septum and pure water on the other side (the condition of the osmometer of Dutrochet when filled with a saline solution and immersed in water), the passage of the salt outward is entirely by diffusion, and that a thin membrane does not sensibly impede that molecular process. The movement is con- fined to the liquid salt particles, and does not influence the water holding them in solution, which is entirely passive : it requires no further explanation. The flow of water inwards, on the other hand, affects sensible masses of fluid, and is the only one of the movements which can be correctly described as a current. It is osmose, and the work of the osmotic force to be discussed. As diffusion is always a double movement — while salt diffuses out, a certain quantity of water necessarily diffusing in at the same time in exchange — diffusibility might be imagined to be the osmotic force. But the water introduced into the osmometer in this way has always a definite relation to the quantity of salt which escapes, and can scarcely rise in any case above four or six times the weight of salt, while the water entering the osmometer often exceeds the salt leaving it, at least one hundred times. Diffusion is therefore quite insufficient to account for the water current. The theory which refers osmose to capillarity appears to have no better foundation. The great inequality of ascension assumed among aqueous fluids is found not to exist, when their capillarity is cor- rectly observed : and many of the saline solutions which give rise to the greatest osmose are undistinguishable in ascension from pure water itself. Two series of experiments on osmose were described, the first series made with the use of porous mineral septa, and the second series with animal membrane. The earthenware osmometer con- 152 Royal Society. sisted of the porous cylinder employed in voltaic batteries, about 5 inches in depth, surmounted by an open glass tube 06 inch in dia- meter, attached to the mouth of the cylinder by means of a cap of gutta percha. In conducting an experiment the cylinder was filled with any saline solution to the base of the glass tube, and immediately placed in a large jar of distilled water ; and as the fluid within the instrument rose in the tube, during the experiment, water was added to the jar so as to prevent inequality of hydrostatic pressure. The rise (or fall) of liquid in the tube was highly uniform, as observed from hour to hour, and the experiment was generally terminated in five hours. From experiments made on solutions of every variety of soluble substance, it appeared that the rise or osmose is quite insig- nificant with neutral organic substances in general, such as sugar, alcohol, urea, tannin, &c. ; so also with neutral salts of the earths and ordinary metals, and with chlorides of sodium and potassium, nitrates of potash and soda and chloride of mercury. A more sen- sible but still very moderate osmose is exhibited by hydrochloric, nitric, acetic, sulphurous, citric and tartaric acids. These are sur- passed by the stronger mineral acids, such as sulphuric and phos- phoric acid and sulphate of potash, which are again exceeded by salts of potash and soda possessing either a decided acid or alkaline reaction, such as binoxalate of potash, phosphate of soda and car- bonates of potash and soda. The highly osmotic substances were also found to act with most advantage in small proportions, pro- ducing in general the largest osmose in the proportion of one-quarter per cent, of salt dissolved. Osmose is eminently the phsenomenon of weak solutions. The same substances are likewise always che- mically active bodies, and possess affinities which enable them to act upon the material of the earthenware septum. Lime and alu- mina were accordingly always found in solution after osmose, and the corrosion of the septum appeared to be a necessary condition of the flow. Septa of other materials, such as pure carbonate of lime, gypsum, compressed charcoal and tanned sole-leather, although not deficient in porosity, gave no osmose, apparently because they are not acted upon chemically by the saline solutions. Capillarity alone was manifestly insufficient to produce the liquid movement, while the vis motrix appeared to be chemical action. The electrical endosmose of Porrett, which has lately been defined with great clearness by Wiedemann, was believed to indicate the possession of a peculiar chemical constitution by water, while liquid, or at least the capacity to assume that constitution when polarized and acting chemically upon other substances. A large but variable number of atoms of water are associated together to form a liquid molecule of water, of which an individual atom of oxygen stands apart forming a negative or chlorous radical, while the whole remain- ing atoms together are constituted into a positive or basylous radical, . which last will contain an unbalanced equivalent of hydrogen giving I the molecule bnpicity, as in the great proportion of organic radicals. i Now it is this voiun»inous basylous radical that travels in the elec- -j trical decomposition of pure water, and resolves itself into hydrogen Royal Socieiy, 153 gas and water at the negative pole, causing the accumulation of water observed there, while the oxygen alone proceeds in the opposite direc- tion to the positive pole. Attention was also called to the fact that acids, and alkalies, when in solution, are chemically combined with much water of hydration, sulphuric acid for instance evolving heat when the fiftieth equivalent of water is added to it. In the combi- nation of such bodies, the disposal of the water is generally over- looked. Osmose was considered as depending upon such secondary- results of combination, that is, upon the large number or volumi- nous proportions of the water molecules involved in such combina- tions. The porous septum is the means of bringing out and render- ing visible, both in electrical and ordinary osmose, this liquid move- ment attending chemical combinations and decompositions. Although the nature and modus operandi of chemical action pro- ducing osmose remains still very obscure, considerable light is thrown upon it in the application of septa of animal membrane. Ox-bladder was found to acquire greatly increased activity, and also to act with much greater regularity when first divested of its outer muscular coat. Cotton calico also impregnated with liquid albumen and afterwards exposed to heat so as to coagulate that substance, was sufficiently impervious, and formed an excellent septum, resembling membrane in every respect. The osmometer was of the usual bulb- form, but the membrane was supported by a plate of perforated zinc, and the instrument provided with a tube of considerable diameter. The diameter of the tube being one- tenth of that of the mouth of the bulb or the disc of membrane exposed to the fluids, a rise of liquid in the tube, amounting to 100 millimeters, indicated that as much water had permeated the membrane and entered the osmometer, as would cover the whole surface of the membrane to a depth of one millimeter, or one twenty-fifth part of an inch. Such millimeter divisions of the tube become degrees of osmose, which are of the same value in all instruments. Osmose in membrane presented many points of similarity to that in earthenw*are. The membrane is constantly undergoing decompo- sition and its osmotic action is exhaustible. Salts and other sub- stances, also capable of determining a large osmose, are all chemi- cally active substances, while the great mass of neutral organic sub- stances and perfectly neutral monobasic salts of the metals, such as chloride of sodium, possess only a low degree of action or are wholly inert. The active substances are also relatively most efficient in small proportions. When a solution of the proper kind is used, the osmose or passage of fluid proceeds with a velocity wholly unprece- dented in such experiments. The rise of liquid in the tube with a solution containing one-tenth of a per cent, carbonate of potash in the osmometer, was 167 degrees, and with 1 per cent, of the same salt 206 degrees, in five hours. With another membrane and stronger solution, the rise was 863 millimeters, or upwards of 38 inches, in the same time, and as much water was therefore impelled through the membrane as would cover its whole surface to a depth of 8' 6 millimeters or one-third of an inch. The chemical action must be 154 Royal Society, different on the substance of the membrane, at its inner and outer surfaces, to induce osmose ; and according to the hypothetic view which accords best with the phaenomena, the action on the two sides is not unequal in degi'ee only, but also different in kind. It appears as an alkaline action on the albuminous substance of the membrane, at the inner surface, and as an acid action on the albumen at the outer surface. The most general empirical conclusion that can be drawn is, that the water always accumulates on the alkaline or basic side of the membrane. Hence, with an alkaline salt, such as car- bonate or phosphate of soda in the osmometer, and water outside, the flow is inwards. With an acid in the osmometer, on the con- trary, the flow is outwards, or there is negative osmose, the liquid then falling in the tube. In the last case the water outside is basic when compared with the acid within, and the flow is therefore still towards the base. The chloride of sodium, chloride of barium, chlo- ride of magnesium, and similar neutral salts, are wholly indifferent, or appear only to act in a subordinate manner to some other active acid or basic substance, which last may be present in the solution or membrane only in the most minute quantity. Salts which admit of dividing into a basic subsalt and free acid exhibit an osmotic activity of the highest order. Such are the acetate and various other salts of alumina, iron and chromium, the protochloride of copper and tin, cliloride of copper, nitrate of lead, &c. The acid travels outwards by diffusion, superinducing a basic condition of the inner surface of the membrane and an acid condition of the outer surface, the favour- able condition for a high positive osmose. The bibasic salts of pot- ash and soda, again, although strictly neutral in properties, such as the sulphate and tartrate of potash, begin to exhibit a positive osmose, in consequence, it may be presumed, of their possible resolution into an acid supersalt and free alkaline base. The following Table exhibits the osmose of substances of all classes : — Osmose of 1 per cent, solutions in Membrane. Degrees. Oxalic acid -148 Hydrochloric acid (O'l perc.) - 92 Terchloride of gold — 54 Bichloride of tin — 46 Bichloride of platinum... — 30 Chloride of magnesium... — 3 Chloride of sodium -f 2 Chloride of potassium ... 18 Nitrate of soda 2 Nitrate of silver 34 Sulphate of potash 21 to 60 Sulphate of magnesia ... 14 Chloride of calcium 20 Chloride of barium 21 Chloride of strontium ... 26 Chloride of cobalt 26 Chloride of manganese ... 34 Degrees. Chloride of zinc 54 Chloride of nickel 88 Nitrate of lead 125 to 211 Nitrate of cadmium 137 Nitrate of uranium 234 to 458 Nitrate of copper 204 Chloride of copper 351 Protochloride of tin 289 Protochloride of iron 435 Chloride of mercury 121 Protonitrate of mercury... 356 Pernitrate of mercury 476 Acetate of sesquioxide of iron 194 Acetate of alumina 280 to 393 Chloride of aluminium ... 540 Phosphate of soda 311 Carbonate of potash 439 Royal Society, 155 The osmotic action of carbonate of potash and other alkaline salts is interfered with in an extraordinary manner by the presence of chloride of sodium, being reduced almost to nothing by an equal proportion of that salt. The moderate positive osmose of sulphate of potash is converted into a very sensible negative osmose by the presence of the merest trace of a strong acid, while the positive osmose of the first-mentioned salt is singularly promoted by a small proportion of an alkaline carbonate. The last statement is illustrated by the following observations : — Osmose in same membrane. Degrees. 1 per cent, sulphate of potash 21 Same 4-0*1 per c. carb. potash . , 254 Same + Same 264 0*1 per cent, carbonate of potash alone 92 Same 95 It may appear to some that the chemical character which has been assigned to osmose takes away from the physiological interest of the subject, in so far as the decomposition of the membrane may appear to them to be incompatible with vital conditions, and that osmotic movement must therefore be confined to dead matter. But such apprehensions are, it is believed, groundless, or at all events pre- mature. All parts of living structures are allowed to be in a state of incessant change, of decomposition and renewal. The decompo- sition occurring in a living membrane, while effecting osmotic pro- pulsion, may possibly therefore be of a reparable kind. In other re- spects chemical osmose appears to be an agency particularly adapted to take part in the animal oeconomy. It is seen that osmose is pecu- liarly excited by dilute saline solutions, such as the animal juices really are, and that the alkaline or acid property which these juices always possess is another most favourable condition for their action on membrane. The natural excitation of osmose in the substance of the membranes or cell- walls dividing such solutions seems there- fore almost inevitable. In osmose there is further a remarkably direct substitution of one of the great forces of nature by its equivalent in another force — the conversion, as it may be said, of chemical affinity into mechanical power. Now what is more wanted in the theory of animal functions than a mechanism for obtaining motive power from chemical decom- position as it occurs in the tissues ? In minute microscopic cells, the osmotic movements should attain the highest velocity, being entirely dependent upon extent of surface. May it not be hoped, therefore, to find in the osmotic injection of fluids the deficient link, which certainly intervenes between muscular movement and chemical de- composition ? [ 156 ] XXII. Intelligence and Miscellaneous Articles, ON THE OCCURRENCE OF ZINC IN THE VEGETABLE ORGANISM. BY A. BRAUN. IT is well known that the calamine hills of Rhenish Prussia and the neighbouring parts of Belgium possess a peculiar flora ; visi- tors to these regions are particularly surprised by a species of violet allied to Viola tricolor, which unfolds its beautiful yellow flowers in uninterrupted profusion from spring until the end of autumn, and is known in the neighbourhood of Aix as the Calamine violet, or in the dialect of the district " Kelmesveilchen." This plant has been described by Lejeune in his " Revue de la Flore de Spaa " as a distinct species under the name of Viola calaminaria, but he has since characterized it (Comp. Fierce Belgica) as Viola lutea. Smith. Koch and other authors have also rightly considered it as a variety of V. lutea, Smith {grandiflora, Huds.), a species principally distin- guished from V. tricolor by its filiform subterraneous i-unners, by means of which it survives the winter. In its habits it is remarkably distinct from the ordinary Viola lutea of the Alps, as well as from the form of this plant occurring on the higher Vosges on granitic and syenitic soils (described by Spach as Viola elegans) ; its stem being more procumbent and repeatedly branched at the base, and the flowers being generally smaller. I will not, however, express any further opinion as to whether this violet may or may not be a distinct species, for the violets of the same group as V. tricolor pre- sent so many diflficulties to systematic botanists in consequence of their extraordinary variability, that it is diflScult to find the middle course between the union of them all under one name, and the establishment of a multitude of species. Many other plants grow in company with the Viola calaminaria, which, although in this district peculiar to the calamine hills, nevertheless grow in other localities in soil free from calamine. The colour of the flowers of the Viola lutea of the Alps and Vosges varies from the darkest violet to the purest yellow, whilst the flowers of V. calaminaria, at least in the neighbourhood of Aix, are almost always yellow. On the borders of the calamine district specimens are met with here and there with pale violet, or bluish, or mixed blue and yellow flowers, which have been regarded by Kalten- bach as hybrids between this plant and the V. tricolor, which cer- tainly occur on cultivated land in the neighbourhood. But I have also seen a specimen of the true V, calaminaria from the calamine region of Westphalia which is of a dark violet colour. The plant when cultivated in gardens is said to change and become like the common V. tricolor. The connexion between the occurrence of the V. calaminaria and the presence of calamine in the soil, which is so constant that even mining experiments have been undertaken with good results from the indications furnished by this plant, induced me, when in Aix, to urge M. Victor Monheim of that place, to examine the plant especially with reference to its containing zinc. He afterwards Intelligence and Miscellaneous Articles. 157 sent me the following account of a chemical investigation of the plant, performed in his laboratory and under his eye, by M. F. Bel- lingrodt, which I give in the latter gentleman's own words : — "The plants, some of which were still in flower, were collected in the month of October on the Altenberg and in the immediate neighbourhood of its large zinc works. To get rid of adhering earth completely, the fresh, uncut herbage with the roots was washed with water, until, when macerated for sixteen or eighteen hours with water containing muriatic acid, it gave no inorganic matter to the dilute acid. The whole was then finely chopped and digested on the vapour-bath for twelve hours with water and mu- riatic acid ; the vegetable matter was separated from the extract, and this treated with chlorate of potash. The addition of an excess of ammonia to the decolorized extract, now produced a precipitation of alumina, organic substances, and partially of the iron. " The precipitate produced in the filtrate by sulphuret of ammo- nium was dissolved in muriatic acid, oxidized by nitric acid, and the iron then completely separated by ammonia. A portion of the filtered fluid was boiled with solution of potash, when traces of man- ganese were precipitated. Solution of sulphuretted hydrogen then rendered the presence of zinc in the filtrate quite evident. " Another portion of the fluid filtered from the iron precipitate was precipitated at once by sulphuret of ammonium, the dried pre- cipitate calcined in a platinum crucible, moistened with nitric acid, again calcined, and then treated with dilute acetic acid ; the zinc was precipitated from the solution in acetic acid by solution of sulphuretted hydrogen. " From another portion of the herb, freed from external impurities, the juice was expressed, and the presence of zinc in this was also distinctly proved by the above process." This metal must therefore be added to the eighteen elements hitherto known to occur in the vegetable organism. — Poggendorff's Annalen, vol. xcii. p. 175. ON THE COMPOSITION OF TANNIC ACID. BY A. STRECKER. It appears from my experiments, that tannic acid and the tannins in general are much more complex bodies than is generally supposed. In fact, by the action of mineral acids, of alkalies, or of ferments, they are resolved into glucose and a new acid by fixing the elements of water. This resolution, which I announced two years ago, has served me as a starting-point in the determination of the molecule of tannic acid. According to the analyses of Pelouze, Liebig and Berzelius, the molecule of tannic acid is expressed by the formula C'^ H^ O'^, and it is supposed that in its neutral salts 3 equivs. of water of this for- mula are replaced by 3 equivs. of metallic oxide. There is never- theless only one tannate (that of lead) which appears from analysis to contain the carbon and metal in the proportion of 18 : 3 equivs. Perceiving from the splitting of tannic acid into glucose (C'^H^'^O'^) and gallic acid (C^^H^O'^) that the above formula could not express 158 Intelligence and Miscellaneous Articles, the molecule of acid, I undertook a series of experiments to deter- mine the true formula of tannic acid ; of these I now lay the results before the Academy. To obtain tannic acid in a pure state, I purified the acid prepared by the method of M. Pelouze, in two ways ; one portion was dis- solved in pure aether and the solution precipitated by water, the other portion was dissolved in water and precipitated by aether. Under these conditions two or three distinct strata are obtained, of which the heaviest consists of tannic acid, dissolved in the setherial fluid. This syrupous liquid was dissolved in water and then evapo- rated in vacuo ; the residue was analysed after being dried at 248° F. Ten analyses made with oxide of copper in a current of oxygen gas upon substances obtained at seven different preparations, gave results leading to the formula C^* H^^ O^*. I. II. III. IV. V. VI. VII. VIII. IX. X. Calculated. C 62-5 52-2 52-2 522 52-2 52-3 52- 1 52-2 52-3 523 54 = 52-4 H 3-8 3-8 37 37 36 39 3-8 36 37 35 22= 3-6 0 34=440 According to this formula, the resolution of tannic acid into gallic acid and glucose may be represented by the following equation : — C54H2«03^ + 8HOi=3(C'*H6 0>o)-|-Ci^^H»oo>o. This equation is confirmed by the quantities of the two compounds obtained by the decomposition of tannic acid. The former was found to be 87 per cent, (maximum) by Wetherill ; of glucose I have obtained as much as 22 per cent. The quantity of water which may be displaced by metallic oxide in the molecule C^* W^ O^* I have determined directly by digesting tannic acid with oxide of lead, and the analysis of the neutral and basic salts. By the former method I found that the acid loses 4*4 per cent., or 3 equivs. of water, which is confirmed by the analysis of the salts of lead prepared by precipitation, in which the compo- Bition of the anhydrous acid is represented by the formula C^^* H»» O'l, differing by 3 equivs, of water from the formula C** H'^ O^*. The precipitates obtained by tannic acid and acetate of lead contain from 3 to 10 equivs. of oxide of lead, in proportion to C**. The analyses of tannates made by Pelouze, Liebig, Berzelius, Mulder and Biichner, agree with the new formula of tannic acid, if we suppose that some salts do not lose all their water at 212° F., or that they were not completely dried. According to Berzelius, tannic acid combines with sulphuric or muriatic acid, when these acids are added to a solution of tannic acid in water. In these cases precipitates are obtained which are dissolved at the commencement, until the fluid contains an excess of sulphuric or muriatic acid. These compounds are distinguished from the conjugate acids, as the mineral acid can be separated there- from by salts of baryta or silver. The analysis of these precipitates shows that they are nothing but tannic acid imbued with the acid liquor in which they are deposited. In fact, this sulphuric tannin only contains from 2 to 4 per cent, of sulphuric acid ; and the mu- riatic tannin, when placed in vacuo over quicksilver, loses its muriatic Meteorological Observations, 159 acid completely. Moreover, these precipitates diflFer in no respects from tannic acid, which has been acidulated with a mineral acid. The formation of a precipitate by a mineral acid in a solution of tannin is therefore perfectly conformable to the precipitation of the same solution by chloride of sodium and other alkaline salts, and even by aether, and must be explained by a diminution of the solu- bility of the tannin in consequence of the change in the solvent. Gallic acid, which, according to some chemists, contains in the formula C'^H^O^o 4 or 2 equivs. of water, is, from my analyses, a tribasic acid ; and the yellow lead salt, regarded by Liebig and Biichner as a neutral salt, and represented by the formula 4PbO.C«^H2 06, is a basic salt, which, when dried at 248° F., has a composition re- presented by the formula 4PbO . C'4 H3 07, or 3PbO . C'^ W Q? + PbO. In fact, five analyses performed with materials prepared at different times gave 75*9 to 76*1 per cent PbO ; numbers which approach much more closely to the latter formula than to that of Liebig and Biichner. — Comptes Rendus, July 3, 1854, p. 49. METEOROLOGICAL OBSERVATIONS FOR JUNE 1854. Chiswick. — June 1. Fine : cloudy. 2. Rain. 3. Cloudy : clear. 4. Cloudy : clear and cold at night. 5. Uniformly overcast : fine. 6. Cloudy and cold. 7, 8. Cloudy. 9. Overcast. 10. Fine. 11. Fine : overcast. 12. Densely clouded : slight shower : very clear at night. 13. Rain: clear. 14. Cloudy: very fine. 15. Hazy and drizzly. 16. Hazy : rain. 17. Uniformly overcast : very fine : clear. 18. Clear and very fine. 19. Very fine : cold at night. 20. Slight haze : cloudy : fine : clear. 21. Fine : cloudy : rain. 22. Very fine. 23. Uniformly overcast : very fine : clear. 24,25. Cloudy and fine. 26. Fine. 27. Fine: rain at night. 28. Showery : very clear. 29. Cloudy : clear. 30. Very fine : rain at night. Mean temperature of the month 56°*93 Mean temperature of June 1853 59 '16 Mean temperature of June for the last twenty-eight years . 60 -51 Average amount of rain in June 1*90 inch. Boston. — June 1. Cloudy. 2. Rain a.m. 3 — 11. Cloudy. 12. Cloudy: rain A.M. 13—15. Cloudy. 16. Cloudy : rain p.m. 17, 18. Cloudy. 19—22. Fine. 23. Fine : thermometer 83° half-past 2 p.m. 24. Fine : thermometer 80° half- past 2 P.M. 25. Fine: thermometer 87°: rain p.m. 26. Cloudy: rain a.m. 27. Cloudy. 28. Cloudy : rain a.m. and p.m. 29. Cloudy. 30. Cloudy : rain p.m. Sandwick Manse, Orkney. — June 1. Drizzle a.m. and p.m. 2. Cloudy a.m. and p.m. 3. Bright a.m. : cloudy p.m. 4. Cloudy a.m. and p.m. 5. Damp a.m. and p.m. 6. Cloudy a.m. and p.m. 7. Cloudy a.m. : drizzle p.m. 8. Damp a.m. : cloudy, fine p.m. 9. Drops a.m. : small rain p.m. 10. Cloudy a.m. : drops p.m. 11. Clear a.m.: rain p.m. 12. Clear a.m.: clear, fine p.m. 13. Clear a.m.: drops P.M. 14. Cloudy a.m. : showers, cloudy p.m. 15. Cloudy a.m. : clear p.m. 16. Bright A.M. : cloudy P.M. 17. Clear a.m. : cloudy p.m. 18. Damp a.m. : cloudy p.m. 19. Rain a.m. : fog p.m. 20. Clear a.m. and p.m. 21. Clear, fine a.m. and p.m. 22. Bright a.m. : cloudy p.m. 23. Drizzle a.m. : cloudy, fine p.m. 24. Rain a.m. : clear, fine pm. 25. Clear, fine a.m. : cloudy, fine p.m. 26. Showers a.m. : damp p.m. 27. Showers a.m. : cloudy p.m. 28. Clear, fine a.m. : cloudy P.M. 29. Clear, fine a.m. : drizzle p.m. 30. Drizzle a.m. : drizzle, showers p.m. Mean temperature of June for twenty-seven previous years . 52°'81 Mean temperature of June 1853 55 '21 Mean temperature of this month 52*86 Average quantity of rain in June for thirteen previous years . 2-24 inches. •ao^sofl •:pi4inti3 ^0*8 5.^ '5.*: t^^ : ^ •^u&ptns •u(n«og H d I s I «• I i ^ i 1 1 i s s ^ ^ ^ s.- 1 1^ ^>- « i « » ^ i •in-d I •ipmnqa a fl ii-d o§ S sn o> •tu-« f8 •U0?80a 00 O T^vO ■^tJ-H r^M t>^iH O OnN «OvO W-, o> On O eovo »^0\m rt-OvO O c*» in vr> «0 u-> »r» u-> ui u^vo w^vo NO «OVO VO VO VO 10 u-ivo VO vO VO VO r^ t-^vO VO VO SO »0'^.^m'»i-.t<-i«Orl-Ti-rOTj-rh»Oto w->vO •<1- "4- ^ rj- »0 t>.t^O e< N ONh^iO T^^O vr» t-s uivo O O t^OvOVO t^c« t^t^MOo uioo m O SO i/^sO VO VO w-i vovo VOVOVOVOVOVOVOVOVO t^vO vO vO t^ r>. t^OO VO VO VO t» t-^ t<^M r>.r< ^OvO^O r* r^OO rJ-^t^O ^»OtJ-m O rooo »^ 0\ t^vo m 10 u-> lo rr'rr'r^rr*?^ r^^ p r* .'^ r*^ ^ ^ p^ r^oo oo o© o o© t^ ^j-vo oo oo oo b O O O O O O Ov ON ON Os *ON ON ON "ctn Ov *0\ On OS Ov On On b Os Ov On On b\ ON ON 00 ONrhOvM M m-tl-Tt-Ovi-i OnH t^rloo r^vo O M t^*-" inu-iON»on ^on»o P P r r fr^r*??* V 7^ "^ rofo O O O O O O O b On ON On 'o ON "on bv ON On On On b\ b\ On On b\ ON On bs On bN 'o\ •aojsoa •* r^ t- t^ t-^vo 10 >o M 00 >o O On lovo 00 O coO Onw Tj-mtoO H rt ONrot^vOOO t^ rooo t<^ 11 to M O vO CO t^ t-^ t« "i 0>nO oovot^oOOOON ONOo vo »o u-»vo VO VO »o r^ onoo o O •-' O 00 vo r-»vo vovo On on on b b b b ON ON on on on on On 'o\ On On On On On b O b b On On On *On On On HH«focototo«0«*N'- litharge, and metallic lead, gave 6*759 grains carbonic acid and •975 grains water. III. 6*85 grains substance, heated with carbonate of potash^ gave 6-707 grains iodide of silver. Calculation. Carbon . . . No. 1. , . 25-750 No. 2. 25-25 25-19 CIO 60 Hydrogen . . . ... 1-48 1-26 H^ 3 Oxygen . , ... 20-17 0^ 48 Iodine . . . . . 52-909 ... 53-38 1 127-1 100-000 100-00 100-00 2381 ( These results correspond exactly with the formula C^^H^IO^ + H0. lodopyromeconic acid is monobasic, and forms salts, of which I have minutely examined only those of baryta and lead. It does not appear to form an ammonia salt. lodopyromeconate of baryta is readily prepared by mixing together alcoholic solutions of acetate of baryta, and of the acid made slightly alkaline with ammonia. After a short time it deposits a fine network of delicate crystals, of little solubility either in cold or hot water or alcohol. It is alkaline to litmus paper, and at 212° it suffers no loss of weight. The following result was obtained on igniting the salt with sulphuric acid: — 4-49 grains substance gave 1*63 grains of sulphate of baryta, which corresponds to the formula BaO^ (jiog2jQ5_j.jjQ^ as shown by the following calculation : — Carbon . , Hydrogen Oxygen . Iodine . Baryta . Experiment. 23-84 100-00 \y\ r ' "^ 19-068 CIO 60 •954 w 3 15-255 06 48 40-394 I 127-10 24-329 BaO 76-55 100-000 314-65 lodopyromeconate of lead is readily obtained as a fine colour- less amorphous precipitate, on mixing alcoholic solutions of the acid and acetate of lead, with the addition of a small quantity of 206 Mr. J. F. Brown on a General Method of Substituting ammonia. As thus prepared, it is apt to carry down an excess of oxide of lead, which is easily removed by warm acetic acid. It is of sparing solubility in alcohol or water, and becomes highly electrical when rubbed. This salt, contrary to expecta- tion, evolves free iodine, like the acid itself, when burned with chromate of lead ; but the phsenomenon is probably owing to the decomposition of the salt taking place at a temperature much lower than that sufficient to enable the iodine to combine with lead. For this reason I contented myself with a determination of its oxide of lead, which was effected by igniting the salt, after the addition of a few drops of concentrated sulphuric acid : — 6*15 grains substance, dried in the air, gave 2-76 grains sul- phate of lead, corresponding to the formula PbO, C^^ H* 10^ as shown by the subjoined calculation : — Experiment Calculation. Carbon . . . . 17-612 CIO 60 Hydrogen . . Oxygen . . . Iodine . . . . ... •587 11-743 37-309 H2 05 I 2 40 127-1 Oxide of lead . 3303 32-749 PbO 111-56 100-00 100-000 340-66 I have already mentioned, that when the quantity of chloride of iodine employed, is larger than is requisite for the production of iodopyromeconic acid, the fluid acquires a yellow colour, due to the presence of another compound, of very remarkable cha- racters, produced by a further decomposition of pyromeconic acid, and to which I give the name of iodomecone. When potash is gradually added to the fluid, after separation of the iodopyromeconic acid, a blackish precipitate immediately falls, which rapidly dissolves on agitation of the fluid, while a peculiar odour is evolved. After the addition of the potash has been continued for some time, a point is reached at which the pre- cipitate assumes a lighter colour, is no longer dissolved, and is not increased by further addition of the alkali. The precipitate is then filtered from the alkaline fluid, washed with cold water, and purified by repeated crystallization from boiling alcohol. By subsequent experiments, I ascertained that it was easy to convert pyromeconic acid entirely into this compound, by adding a large quantity of chloride of iodine, when the crystals of iodo- pyromeconic acid at first formed rapidly disappeared, and car- bonic acid was evolved. Exactly similar effects are produced by bromide of iodine. Iodomecone is obtained in large hexagonal plates of a bright Iodine for Hydrogen in Organic Compounds, 207 yellow colour and brilliant lustre, and having an odour re- sembling that of saffron. It is insoluble in water, soluble in alcohol, especially on boiling, and in aether. It is insoluble in hydrochloric acid, and may be boiled with that reagent without suffering decomposition. Strong nitric acid attacks it with great violence, but does not effect a complete oxidation of all the iodine. It is unacted on in the cold by strong sulphuric acid, but if heated, it is decomposed with the liberation of iodine. Caustic potash when long boiled with it, removes a very small quantity of iodine. It does not affect litmus paper, and seems to possess neither acid nor basic properties. It sublimes un- altered at a temperature greatly below that of boiling water. These characters closely approximate to those of iodoform, and I at first considered it to be that substance. The analysis, how- ever, made with every care, and on specimens prepared at dif- ferent times, gave results which cannot be made to agree with the formula of that substance. The analyses are as follows : — I. 7-141 grains substance, air-dry, gave 0-913 grains carbonic acid and 0*913 grains water. II. 4-365 grains substance, air-dry, gave 4*365 grains car- bonic acid and 0*164 grains water. III. 8*153 grains substance, air-dry, gave 0*958 grains car- bonic acid and 0*346 grains water. I. 5*697 grains substance, air-dry, gave 9-706 grains iodide of silver. II. 3*611 grains substance, air-dry, gave 6*140 grains iodide of silver. No. 1. Carbon .... 3*48 Hydrogen ... Oxygen Iodine No. 2. No. 3. lost. 3-204 0*417 0*471 . . . 4*440 12*060 91*885 100*000 100*000 100000 Calculation. Carbon . . Mean. . 3-337 3*258 C^ 36^ Hydrogen . . 0-444 0*364 H4 4 Oxygen . . . 4*247 4-344 0^' 48 Iodine . . . 91-972 92034 P 1016-8 100000 100-000 1104*8 The formula is therefore C^ H^ I^ 0^. The decomposition by which iodomecone is produced from 208 On substituting Iodine for Hydrogen in Organic Compounds* pyromeconic acid, now becomes obvious. It is represented by the following equation :— * CIO H4 06+8ICl+8H0=C«H'» P 06H-4COH8HCI. This being the mode of its formation, it seemed probable that meconic and comenic acids, which differ from pyromeconic acid only by the elements of carbonic acid, would yield the same sub- stance when acted on by chloride of iodine. Accordingly, I have found that it is immediately produced with all its charac- teristic properties from these acids, by the same process. The Telations of this substance to meconic and pyromeconic acids, are of a very remarkable character, and cannot at present be di- stinctly brought out. It obviously belongs to the same class as the very curious product obtained by Cahours, by the action of bromine on citric acid, and which he has called bromoxaform. According to this chemist, when bromine is added to citrate of potash, effervescence takes place from the evolution of carbonic acid, and on the addition of potash, an oily matter is thrown down, which consists of three substances, one bromoform, the other a crystalline solid, bromoxaform, and the third apparently an accidental product, for it is obtained in too small quantities to admit of examination. It can scarcely be doubted that brom- oxaform would be the only ! product, if the action could be properly moderated, and that the bromoform is a secondary pro- duct of the former substance, from which indeed it is readily obtained by treatment with caustic potash. If this be the case, the decomposition of citrate of potash would be quite analogous to that of pyromeconic acid, as represented in the equation — QX1 H5 K3 O" + 2H0 + Br" = C« HBr* O^ + 600^ + 3K Br + 6HBr. Citrate of potash . Bromoxaform . The relation which these curious substances bear to their parent acids is very obscure, and cannot be elucidated without further experiments. In regard to iodomecone, the small quan- tity in which I was able to obtain it, has prevented my following out its decompositions as I could have wished, but I propose ex- tending this investigation to some of the stronger acids, by which means some light may probably be thrown upon the con- stitution of these bodies. It was my desire to have extended my examination of the iodine substitution products obtained by chloride of iodine to some other substances. As yet, however, I have only tried codeine; but the instability of the compound produced has occasioned such difficulties, that I have hitherto been unable to On the presence of Pyridine in Naphtha^ /^ 9^ arrive at satisfactory results. When chloride of iodine is added to a concentrated solution of hydrochlorate of codeine, a fine yellow crystalline precipitate makes its appearance. It is inso- luble in water, but readily soluble in boiling alcohol. If this solution is carefully effected, and too much of the substance be not added, it crystallizes on cooling in stellar groups of a fine red colour, but if a large quantity is dissolved, it is deposited as a perfectly amorphous mass. Unfortunately, the iodine is retained with a very feeble affinity, and I have found that at every crystallization, a small quantity is separated and remains in the fluid, so that results of a satisfactory character could not be obtained on its analysis. It is soluble in hydrochloric acid, and if the solution be made hot, it deposits at first an oily sub- stance, which afterwards concretes to a flocky mass. Both am- monia and potash precipitate it from its solution in hydrochloric acid, the former giving a slightly coloured substance. With chloride of platinum it yields a bright yellow precipitate, one de- termination of the platinum in which gave 12"20 per cent.; 11-95 corresponds to the formula C^^ H'^ F NO^ HCl PtCF 4- HO, which represents the hydrated salt of a base, which may be called di-iodocodeine, as being derived from codeine by the substitution of two atoms of iodine for two of hydrogen. These experiments were conducted in the laboratory of Pro- fessor Anderson, to whom I am mwch indebted for assistance during their prosecution. XXIX. On the presence of Pyridine among the volatile Bases in the Naphtha from the Bituminous Shale of Dorsetshire, and on the fractional Crystallisation of Platinum-salts. By C. Gre- viLLE Williams*. IN 1846 we were made acquainted with a new organic base which occurred, together with aniline and leucoline, in coal-tar ; subsequently to this, the same substance was found to exist in the Oleum animate Dippellii, as procured from bones by distillation : the interesting discovery was also made by Anderson, that this base, to which he gave the name of picoline, was one of a series of nitryle bases having the general formula (C"* H"~^) N, of which the first term was pyridine, C^^ H^ N. In an examination which I made of the basic part of the Dorsetshire shale naphtha t, I ascertained the presence of this series of bases from picoline upwards, as far as the one recently discovered, consisting of C^^* H^^ N. I also showed the presence of a new base still higher in the series, and consisting of C^^ H '^ N. * Communicated by the Author. t Quarterly Journal of the Chem. Soc. July 1854. Phil, Mag, S. 4. Vol. 8. No. 51. Sept, 1854. P 816 Mr. C. 6. Williams on the presence of Pyridine in The alkaloids were chiefly separated from each other by frac- tional distillation, but the more volatile of them were present in too small a quantity to render this method applicable ; I there- fore availed myself of the platinum-salts as a means of purifica- tion, and on adding a strong aqueous solution of chloride of platinum to a solution of the first fraction in hydrochloric acid, a preci})itate was obtained, which on combustion gave exactly the composition of picoline. But the fraction from which this re- sult was obtained, distilled below and at 210° Fahr., while the boiling-point of picoline, according to Anderson, is 272°; I there- fore suspected the presence of a more volatile base, but was pre- vented by deficiency of material from pursuing the investigation further. Having since that time obtained another small quantity of liquid from the same source and boiling at the same temperature, I availed myself of the opportunity of studying the separation of bases by fractional crystallization of platinum-salts. The basic oil, amounting to about three-fourths of a drachm, was supersaturated with hydrochloric acid, an aqueous solution of chloride of platinum added, and the whole diluted until the pre- cipitate at first formed was redissolved; the liquid was then allowed to crystallize spontaneously, and at the end of three days yielded a considerable crop. On examination these were found to consist of two sorts, a and b ; the former had assumed the shape of sword-blades of a pale yellow colour, and more than half an inch long; b, on the other hand, formed small flattened four-sided prisms, very thick in pro- portion to their length, and of a deep ruby-red. It was, of course, supposed that the salts of two bases had crystallized in the same liquid, but on careful ignition the following numbers were obtained : — J fa. 4-707 grs. gave 1*482 platinum. \b. 6022 grs. gave 1-910 platinum. Per cent. a. b. Theory {lutidine). 31-48 31-70 31-51 We therefore see that both salts had the same composition, but the anomaly in the^. boiling-point, and the difi*erence in the appearance of the ci-ystals, renders the opinion probable that two bases are present, bearing the same relation to each other that picoline does to aniline. Recent researches having shown the constitution of platinum- salts to be remarkably modified by the action of heat upon their solutions, the evaporations in these experiments were made by exposing them to a surface of sulphuric acid until a crop was obtained, which was then removed and the operation repeated. the Naphtha from the Bituminous Shale of Dorsetshire. Sll It is absolutely necessary before igniting the salts to pulverize the crystals and wash them with a mixture of alcohol and aether ; the appearance of the powder becomes much altered by this operation, as it removes a resinous impurity which causes the particles to hang together, while after washing with the mixture indicated, and subsequent drying, the powder becomes as mobile as fine dry sand*. Moreover, it is inadmissible to dry the cry- stals by heat, a temperature of even 212° having the power to cause a slow evolution of the base, and also appearing to alter the constitution of the salt j it was always dried, therefore, over sul- phuric acid until it ceased to lose weight. The second crop of crystals consisted of large thick prisms. - II. 3-505 grs. gave 1-115 gr. platinum. Per. cent. Theory (lutidine). 31-81 31-51 The third ; long thin square prisms. III. 3-507 grs. gave 1-130 gr. platinum. Per. cent. Theory {picoline). 32-22 32-94 The fourth crop ; very hard short prisms of a deep red colour. IV. 4-520 grs. gave 1*478 gr. platinum. Per, cent. Theory (picoline). 32-69 32-94 The fifth crop ; groups of deep orange radiated needles. V. 5-t52 grs. gave 1-823 gr. platinum. Per. cent. Theory (pyridine). 34-71 34-60 The first and second crops are seen therefore to be alike, also the third and fourth ; the first two consisting of lutidine, the next two of picoline, and the fifth of pyridine; the reason of the latter base appearing only in the last crop is in consequence of the smallness of the quantity present. It is interesting to ob- serve the steadiness of the rise of platinum in the fractions until we read the last, when it suddenly springs from 32*7 to 34-7. The assertion in my former memoir that the fractional crystal- lization of platinum salts affords a far readier mode of purification of homologous volatile bases than distillation, appears, therefore, to be borne out by this result, for it is certain that even with many times the quantity of material, a separation like this could not have been effected by the other method. It is difficult to explain how a liquid containing a considerable quantity of picoline which boils at 272°, a somewhat less amount of lutidine (boiling-point 310°), and a little pyridine boiling at 240°, should distil below 210° (especially as it was ascertained * It is beheved that Hofmann first indicated the importance of this pro- cedure in his researches on the volatile organic bases. P2 212 On the presence of Pyiidine in Naphtha. that no other bases having diflferent per-centages of platinum in their salts were present), unless by supposing thereal boiling-points to be much lower than those indicated by their discoverer, and, in fact, I have since ascertained that he does not by any means insist upon their accuracy. If the suggestion thrown out, of the presence of two bases of the composition of lutidine, be correct, we can easily imagine that to be the cause of the discrepancy; but I have obtained in the ciystallization of the platinum-salts of sethylamine, crops forming together, and yet having no resem- blance in colour or form, some being thin lemon-coloured plates, and others solid deep red prisms, both, however, giving the same results on analysis. It is somewhat singular that the so-called quinoline, submitted to fractional distillation, yields a base having a constitution ap- parently closely allied to the pyridine series ; in fact one of the fractions converted into platinum salt yielded exactly the quantity of carbon, hydrogen, and platinum in the base between lutidine and parvoline ; this result, and some others, has induced me to undertake a rigid examination of quinoline. It was, unfortunately, impossible to obtain enough platinum- salt of pyridine from the shale products at my disposal for a combustion ; but when we consider that in the bases from the same source I have demonstrated the existence of all the other members of the series, and that the fifth fraction gives exactly the theoretical quantity of platinum, we have no reason to doubt the presence of pyridine ; the more especially, that although the powerfully-odorous picoline is present, it is unable entirely to conceal the overpowering smell peculiar to the former base. The difficulties in the way of separating several basic liquids of analogous constitution by fractional distillation is so great, that it would appear quite hopeless to obtain any one product absolutely pure, even where the quantity of material at command is very considerable ; but by first fractionating the liquid by di- stillation and then converting the fractions into platinum- salts and repeatedly crystallizing until the product gives exactly the theoretical quantity of platinum, we may, by distillation with potash, obtain the base in a state fit for examination of its pro- perties. To show the connexion between the two series, I append the following table from my former memoir. Unknown C^oH^N Pyridine CJOH^N Aniline C12H7N Picoline C^^H^N Toluidine CHH9N Lutidine C14H9N Xylidine CiSHiiN New base CieppiN Cumidine C18H13N Parvoline CIS HIS N [ 213 ] - XXX. On Sensitive Collodion. By Thomas Woods,, M.D. To the Editors of the Philosophical Magazine and Journal. Gentlemen, Parsonstown, August 1854. TO answer some inquiries which have been addressed to me with respect to the photographic process pubHshed in the July Number of this Magazine, I beg to make the following addenda. The mixture of iodide and muriate of iron acts better when it is a few days old ; these salts of iron being formed by the double decomposition which occurs between the iodide of potassium and muriate of soda on the one hand, and the sulphate of iron on the other, and the last-named salt being with difficulty dissolved in the alcohol, the action requires some time before the full effect is produced. The picture developed by the sulphate of iron as an exciting agent is a positive one, and if rapidly taken, not deep enough to print from. The usual pyrogallic acid solution (3 grains to the ounce of water, with half a drachm of glacial acetic acid) brings out the picture much more deeply marked. With the pyrogallic acid developing solution I have taken a likeness in about 1|- second which could be printed from very fairly. I have found from late experiments that the intensity of the picture may be considerably increased by using collodion without the salt recommended in the paper published last July, but substituting for it one drop of chloroform to the mixture when about to be poured on the glass plate; that is, mixing together 1 part of the solution of iodide of iron, 3 parts of col- lodion, and 1 drop of chloroform to each drachm of this com- pound fluid when about to be poured on the plate. The first effect of the chloroform on the collodion is to precipitate the gun-cotton which comes in contact v/ith it, but it soon redissolves by giving a shake or two to the vessel. I am, &c., Thomas Woods, XXXI. F^'oceedings of Learned Societies. ROYAL SOCIETY. [Continued from p. 155.] June 15, 1854. — The Earl of Rosse, President, in the Chair. THE following papers were read : — " Examination of the Cerebro-spinal Fluid." By William Turner, Esq., Scholar of St. Bartholomew's Hospital. In the Bulletin de TAcademie de Medecine for December 1852, a paper is published by M. Bussy, containing an analysis by M. Des- 214 Royal Society, champs of a fluid, which flowed from the ear of a man who had sustained a fracture of the base of the cranium. From a comparison between the composition of this fluid and that given by M. Lassaigne as the composition of the cerebro- spinal fluid, M. Bussy arrived at the conclusion that they were identical in their origin. In addition, how- ever, to the albumen and ordinary saline constituents, M. Deschamps found that the fluid obtained from the fractured cranium contained a certain constituent which possessed the peculiar property of re- ducing the blue protoxide of copper to the state of the yellow sub- oxide. As this power of reducing the oxide of copper is possessed also by grape-sugar, M. Bussy arrived at the conclusion that this fluid con- tained a small portion of grape-sugar, and as additional evidence in support of this conclusion he quotes the experiments of M. Bernard, who, by irritating the base of the encephalon and the origin of the vagus nerve, produced an excess of sugar in the secretions. He supposes that in the present instance the fracture through the base of the cranium may have produced some irritation at the origin of the pneumogastric, and thus have excited the formation of sugar. Such a supposition would have received additional confirmation if at the same time an analysis could have been made of the blood, urine, or other secretions, so as to determine if sugar was present in those fluids — no such analysis however is given. The property of re- ducing the oxide of copper was also found by M. Bussy to reside in the cerebro-spinal fluid of the Horse and Dog. In none of these experiments was he able to induce fermentation. As this reducing power is not peculiar to grape-sugar, but is possessed by other orga- nic substances, such as lactine and lactucine, this test alone should not be relied on as aff^ording any positive indications of its presence ; recourse should therefore be had to other confirmatory experiments. With a view to determine this point, Mr. Paget, in the early part of March last, gave me for examination three separate portions of the cerebro-spinal fluid, obtained by puncturing a spina bifida in a child, several days intervening between the removal of each portion. Those removed on the first two occasions were perfectly clear and pellucid, giving an alkaline reaction to test-paper, their spec. grav. being r006, no spontaneous coagulation taking place after standing for some time ; that removed on the third occasion had a slightly yellow tinge, and a distinct coagulum formed in it on standing. The presence of fibrine in this instance was owing doubtless to some slight inflammation having been set up, caused by the successive puncturings. The three specimens corresponded in the following characters : — 1 St. No precipitate on applying heat, merely an opalescence being produced ; on the addition of a few drops of nitric acid a white flaky precipitate subsided. Nitric acid alone, without heat, also caused a precipitate. The non-precipitation of the albumen, until the addition of the acid, was owing to the alkalinity of the fluid. Royal Society, 216 2nd, Boiled with liquor potassse a very faint pinkish tint was pro# duced ; a few white flakes also fell down. 3rd. Heated in a water-bath with the blue oxide of copper, in a few minutes the yellowish red powdery suboxide precipitated. This reaction took place both in the original albuminous liquid and after the coagulation of the albumen by heat and nitric acid. 4th. A piece of flannel, saturated with the chloride of tin, was well moistened with the fluid, and then heated over a red-hot coal ; no brown colour of the flannel was produced, such as occurs when grape-sugar is present. (Maumene's test.) 5 th. A portion mixed in a test-tube with some German yeast was placed for several hours in a warm cupboard, but there was no deve- lopment of gas. From these experiments it appears that of the various tests em- ployed, only one gave any indication of the presence of grape-sugar, that test also being the one which is most liable to deception. The lowness of the specific gravity, in which respect this fluid and that analysed by M. Deschamps closely corresponded, would, cl priori y almost lead to the assumption that no grape-sugar was present. The presence of the reducing agent could not in this case depend upon any irritation of the origin of the vagus, for the irritation, if any, produced by a spina bifida is at the end of the cerebro- spinal axis furthest removed from the origin of that nerve. That the ma- terial however which eflfects this reduction is of a very changeable nature, was shown by allowing a portion of the fluid to stand for several days until putrefaction had commenced. The fluid was then filtered so as to separate the insoluble albuminous flakes, and the clear liquid heated in a water-bath with the blue oxide of copper ; when, instead of the suboxide being produced, the black anhydrous oxide was formed, just as is the case when the blue oxide is heated merely with water, thus satisfactorily showing that the reducing substance had been destroyed. The recent investigations of Virchow* and Buskf have shown that substances of a non-nitrogenous nature exist both in the brain and spinal cord, but they hold somewhat difi^erent opinions respect- ing their exact characters ; for whilst the former considers them to be cellulose, the latter regards them both in their "structural, che- mical and optical properties " to resemble starch. In conformity with these views, it was interesting to determine if any indications of the presence of either of these substances could be found in the cere])ro-spinal fluid ; accordingly a portion of the fluid was evapo- rated nearly to dryness and then divided into two portions ; to one was added an alcoholic solution of iodine and concentrated sulphuric acid, when a violet tint was produced, which after a few minutes dis- appeared ; but it was also found that this same appearance was pro- duced when the acid and iodine solution were mixed together alone, the violet colour being evidently owing to the volatilization of a part of the iodine and the evolution of its characteristic violet tint ; to the other a solution of iodide of potassium and then nitric acid was * Quarterly Journal of Microscopical Science, January 1854. f Ibid. 216 Roijal Society. added, when a brown colour was i)roduced, owing to the liberation of the iodine. In neither portion could it be said that any evidence of the presence of starch or cellulose was detected. A comparative trial was also made between the effects produced upon the blue oxide of copper by the cerebro-spinal fluid, solutions of grape-sugar, cane-sugar, starch, cellulose, and mannite, an unfer- mentizable sugar. These various substances were heated in a water- bath for the same length of time, when it was found that whilst the grape-sugar eiFected a reduction immediately, and the cerebro-spinal fluid only after the lapse of several minutes, neither the starch, cellu- lose, cane-sugar nor mannite effected any reduction at all. The power of reducing the blue oxide of copper is not confined to non-nitrogenous substances, for I found that if a solution of leucine* be heated along with it in the usual manner, the reduction is effected in about the same length of time, and in the same way as by the cerebro-spinal fluid. This single experiment is not of itself sufficient evidence that the reducing power in both cases depends upon the presence of the same substance. Such an assertion could only of course be proved by obtaining from the cerebro-spinal fluid leucine in the crystallized form. A proper quantity of the fluid was not, however, left to investigate this point. From the above experiments I think it may be safely asserted that the power possessed by the cerebro-spinal fluid of reducing the oxide of copper, is not owing to the presence either of grape-sugar or any of the allied substances : whether it may depend upon the presence of leucine or other modifications of albumen of a somewhat similar nature, or whether it may be due to the presence of a substance be- longing to another series, is a point that has yet to be determined. Note hy Mr. Paget. — The patient from whom the fluid analysed by Mr. Turner was obtained, was a girl born of healthy parents. An infant cousin had lately died from the same congenital defect as she presented. The upper part of the body was well formed, but the pelvis and lower limbs were small and nearly powerless. The sac containing the fluid was seated over the last lumbar vertebra, pro- jecting (as the examination after death showed) through an opening between its unclosed arches. It enlarged quickly after birth, but did not evidently affect the child's health, unless it were connected with a very frequent spasmodic action of the muscles closing the glottis, which, almost from the time of birth, had produced the peculiar '* crowing inspiration," or laryngismus stridulus. The fluid was first withdrawn when the child was three months old. Neither on this, nor on any subsequent occasion, did its removal produce any mani- fest effect, although the flaccidity of the emptied sac indicated that the pressure upon the spinal cord was greatly diminished. After every evacuation the sac very quickly filled again, notwithstanding pressure exercised upon it. * Leucine C'^NH'^O^, a weak base, belonging to the same series as glycocine and alanine, is generally obtained by the decomposition of albuminous substances. It has been obtained by Scherer from the spleen, and, according to Gregory, has been detected as a natural product in the liver of the Calf. Royal Society. '^17 The examination after death showed that the fluid was collected in the expanded tissue of the pia mater, or subarachnoid spaces, about the cauda equina. The pia mater presented appearances of inflammation long past, as well as of that which had probably been the cause of death. The canal in the axis of the spinal cord was distinct in its whole length. Commencing, below a large fourth ventricle, with a diameter of about one-fourth of a line, it gradually- widened, till, at the lumbar part of the cord, it had a diameter of a line and a half. Its termination at the end of the cord could not be traced in the confusion of parts caused by the distension and inflam- mation of the membranes. " On the Oxidation of Ammonia in the Human Body." By H. Bence Jones, M.D., F.R.S. In the last edition of Professor Lehraann's Animal Chemistry, vol. ii. p. 363, a very decided opinion is expressed against the con- clusion to which I arrived in consequence of some experiments pub- lished in the Philosophical Transactions for 1851. I considered it proved that ammonia was partly at least converted into nitrous acid in its passage through the body. In opposition to this Professor Lehmann states, — 1st. That the method which I employed must of necessity give a reaction resembling that given by nitrous acid ; his words are, " Es ware nun leicht einzusehen dass schweflige Saure, durch welche be- kanntlich lodwasserstofF zersetzt wird, in die Vorlage iibergeht und so jene vermeintliche salpetersaure Reaction bedingt." 2ndly. That when nitric acid was added to urine and it was di- stilled with phosphoric acid instead of sulphuric acid, no trace of blue colour with starch and iodide of potassium could be obtained. " Das nach Anwendung von Phosphorsaure erlialtene Destillat giebt aber auch jene vermeintliche salpetersaure Reaction nicht, ja selbst dann nicht, wenn dem Harn vorher absichtlich einige Tropfen Salpetersaure zugesetzt worden waren." It appeared to me undesirable merely to reply to Professor Leh- mann, that I had expressly stated that the indigo and protosulphate of iron tests were used, and gave as decided proof of the presence of nitrous acid in the urine as Price's test gave ; and that sulphurous acid could not have produced the same effect as nitrous acid in these tests. It seemed more desirable to repeat the experiments which had been made in Professor Lehmann's laboratory on the action of sulphurous acid, and on the effect of using phosphoric instead of sulphuric acid in the distillation of the urine. I was fortunate enough to obtain the assistance of Mr. Malone to carry on the experiments continuously from day to day, and through the kindness of Dr. Hofmann this was done in the College of Che- mistry. 1st. On the action of sulphurous acid on starch and iodide of potassium and very dilute hydrochloric acid. In England it is by no means well known that sulphurous acid decomposes hydriodic acid. On the contrary, theoretically it should not liberate iodine, and experimentally not only does it not liberate 218 Royal Society, iodine, but it hinders the liberation of iodine und stops the formation of the blue colour when Price's test is used and nitrous acid is pre- sent ; and if sulphurous acid be added after the blue colour is formed it makes it disappear. Pure sulphurous acid was prepared, some nitre was fused, and a dilute solution was made, and it was tested by Price's test (starch, iodide of potassium and very dilute hydrochloric acid), then the di- lute nitre solution immediately gave the deep blue iodide of starch ; but when much or little sulphurous acid was added previously to the nitre solution, no blue colour at all was produced ; and when, instead of the nitre solution, much or little sulphurous acid alone was added, contrary to the statement of Lehmann, no decomposition of the hydriodic acid could be obtained. If instead of pure iodide of potassium it was mixed with iodate of potassa, an immediate blue colour was of course observed. I can only suppose that in this way Professor Lehmann obtained the re- action which he has attributed wrongly to the action of sulphurous acid on hydriodic acid, unless indeed no sulphurous acid at all was present and the acidity of the distillate was unneutralized. Dr. Leh- mann is however right as well as wrong, in saying that Price's test for nitric acid fails when sulphurous acid is present. The test fails, not, as he says, because sulphurous acid has the same action as ni- trous acid in liberating iodine, but because it has exactly the oppo- site property of hindering the iodide from being set free even when nitrous acid in small quantity is present. It is possible that in distilling the urine with sulphuric acid, the distillation, if carried too far, may give rise to sulphurous acid, and that thus Price's test may fail to detect nitrous acid in the urine. Moreover, portions of the distillate may be projected against the sides of the hot retort, by which the sulphuric acid acting on the organic matter may be decomposed, and minute quantities of sul- phurous acid may be liberated. This sulphurous acid, instead of de- composing hydriodic acid, causes the reformation of hydriodic acid when nitrous acid liberates iodine in Price's test. 2ndly. Lehmann states that experiments were made by distilling urine to which a few drops of nitric acid were added with phosphoric acid, and that then the distillate gave no reaction with Price's test. - The following experiments were made with every precaution. Anhydrous phosphoric acid was prepared, and it was found to be free from nitrous acid. Some healthy urine was taken and some pure nitrate of potassa, in the proportion of two grains of salt to an ounce of fluid, and distilled with phosphoric acid (ten ounces of urine, twenty grains of nitre, and one ounce of anhydrous phosphoric acid). On concentrating, the neutralized dilute nitrous acid was detected by all the tests, namely, the indigo test, the protosulphate of iron and Price's test. In a second experiment, five ounces of urine with five grains of nitre and half an ounce of anhydrous phosphoric acid, gave nitrous acid by all the tests. The distillation was continued until the con- tents of the retort were viscid. Royal Society. %\% In a third experiment, three ounces of urine with a grain and a half of nitre were distilled with three drachms of glacial phosphoric acid ; the distillate neutralized and evaporated gave no trace of nitrous acid; the same urine with the same quantity of nitre and three drachms of sulphuric acid, when distilled, gave a distillate, which when neutralized and evaporated gave decided evidence of nitrous acid. In my former paper I showed that by distilling with sulphuric acid when only one-tenth of a grain of nitre was added to each ounce of urine, nitrous acid could be detected. From these experiments it appears that distillation with sulphuric acid is to be preferred to distillation with phosphoric acid ; but even with this last acid, when a grain of nitre is added to an ounce of urine, the nitrous acid can be detected. I then endeavoured, by using phosphoric instead of sulphuric acid in distilling urine passed after a salt of ammonia had been taken into the stomach, to detect nitrous acid in the urine. Two drachms of muriate of ammonia were taken in seven ounces of distilled water. The urine was collected for six hours afterwards. Twelve ounces of this urine were distilled with one ounce of phos- phoric acid (anhydrous). The distillate, when concentrated, did not give any evidence of nitrous acid by Price's test. The same experiment was repeated with no better result. In another experiment, sulphuric acid, six drachms to twelve ounces of urine, was used instead of phosphoric acid. The distillate as soon as it was obtained gave the slightest precipitate with chloride of barium insoluble in nitric acid, showing that a trace of sulphuric acid was carried over into the receiver. The distillate was made alkaline with pure carbonate of soda, evaporated, and nitrous acid was immediately detected by the indigo and iron test, as well as by Price's test. A portion of the distillate left exposed to the air, on the following day had lost the power of liberating iodine. This arose from the nitrous acid passing into nitric acid. Pure nitre gives no colour with starch, iodide of potassium and dilute hydrochloric acid, b';t when fused it produces the liberation of iodine immediately. If the solution of fused nitre is exposed to the air it loses this property, but regains it when the solution is evaporated to dryness and refused and again dissolved. In another experiment six ounces of urine passed before the mu- riate of ammonia was taken were distilled with half an ounce of sul- phuric acid, the distillate was highly acid, and gave a slight preci- pitate with chloride of barium ; it was made slightly alkaline, eva- porated to a smr.'l residue, and then gave no evidence of nitrous acid. Then two drachms of muriate of ammonia were taken in seven ounces of distilled water, eight ounces of urine passed four hours afterwards were distilled with half an ounce of sulphuric acid. The distillate was fractional ; the first portion gave no colour with starch test ; it contained a minute trace of sulphurous acid. The second portion was highly acid ; it was made slightly alkaline, evaporated nearly to dryness, and then gave most positive evidence of nitrous 220 Royal Society, acid by Price's test, and also by decolorizing a deep solution of indigo. Thus before the salt of ammonia was taken no nitrous acid could be detected in the urine, whilst after the ammonia nitrous acid was proved to be present, not only by Price's test, l)ut by the indigo test also. In conclusion, it results from these experiments, — 1st, That in Price's test sulphurous acid produces exactly the opposite effect to nitrous acid, and even hinders nitrous acid from liberating iodine from hydriodic acid. 2ndly. That phosphoric acid, when mixed with urine containing nitre and distilled very low, does liberate nitrous acid ; though when used instead of sulphuric acid, it does not enable the nitrous acid to be detected so readily as when the latter acid is employed. Hence the experiments performed in Professor Lehmann's labo- ratory by Herr JafFe*, do not invalidate Price's test for nitrous acid in the way Professor Lehmann supposes ; and by again repeating some of my former experiments, I still arrive at the conclusion that when ammonia is taken into the body nitric acid may be detected in the urine, but that the quantity which can be made to appear is so small that the most delicate method is required for its detection. This however is no proof that a much larger quantity may not be lost in the process for obtaining it from the urine. " On the Disintegration of Urinary Calculi by the Lateral Dis- ruptive Force of the Electrical Discharge." By George Robinson, M.D., Licentiate of the Royal College of Physicians of London, and Lecturer on Medicine in the Newcastle-upon-Tyne College of Prac- tical Science. The great and diversified powers of electricity have long suggested the possibility of its being employed as a means of effecting the de- struction of calculi in the human bladder, and thus obviating the necessity for the painful and dangerous operation of lithotomy. But the attempts hitherto made in this direction have contemplated the solution of the stone through electrolytic action rather than its disintegration by the mechanical force of the electrical discharge. A moment's reflection will however suffice to convince us that the force which shatters a steeple or cleaves an oak, is also capable of reducing to fragments the largest urinary concretion. Nor can I imagine any other than the following sources of objection to the prac- ticability of employing this force for the purpose of breaking down vesical calculi in situ, namely, 1 . the danger to the living structures from the necessity of using a powerful discharge ; 2. the difficulty of conveying the force to the required spot, or in other words, causing the discharge to pass through the calculus. The first objection is in a great measure met by the fact of our being enabled to regulate with the utmost precision the degree of intensity of the discharge, and it would be almost entirely removed were it possible to apply the dis- ruptive force of electricity without any portion of the body being included within the circuit traversed by the electrical current. The * Erdmann's Journal, vol. lix. p. 238, 1853. Royal Society, 22L second objection rests upon the mechanical difficulty of bringing the calculus within the direct route of the electrical discharge, but would scarcely apply were it demonstrated that the disruptive effects of electricity can be obtained without any such direct transmission of the current. My own attention was some years since directed to the subject by reading an account of the following experiment first performed by Mr. Crosse. " Two platinum wires one-thirtieth of an inch in diameter were secured to a slip of window glass half an inch wide and four inches long, so that they rested upon the flat surface of the glass, leaving an interval between their points of one-twentieth of an inch. The wires were connected, one with the negative con- ductor of a powerful machine, the other with a ball to receive sparks from the prime conductor. On placing the glass in a flat dish filled with water and turning the machine, the glass between the points soon became fractured, and after 100 revolutions the fracture enlarged and two small cracks appeared. After 200 revolutions an excavation was formed, but on the side opposite to that on which the wires were tied. After 250 revolutions the glass was completely perforated. Many variations of this experiment were made, in all of which the same kind of mechanical effect was obtained. Even quartz was excavated*." It being thus shown that a lateral disruptive action takes place within a certain distance of the seat of discharge, the idea at once suggested itself to me, that by using two parallel wires separated at their extremities like those in Mr. Crosse's experiment, and similarly connected with an electrical machine or Leyden jar, bringing their ends in contact with the surface of a calculus, and then allowing a series of moderate discharges to take place between the extremities of the wires, a disintegrating effect would be produced upon urinary calculi of the same nature as that witnessed in glass and quartz. And short of the actual disintegration of a calculus in the bladder of a living person, the following experiments will, I trust, be deemed conclusive on this point. Two copper wires, one-twentieth of an inch in diameter, were connected, one with the external, the other with the internal surface of a Leyden jar, having about 400 square inches of internal metallic coating. These copper wires were soldered to platinum wires half an inch long and one -thirtieth of an inch in diameter. Each wire was drawn through a fine gutta percha tube, and the tubes, having first been placed perfectly parallel, were warmed and gently pressed together so as to assume somewhat of the appearance of a flexible bougie ; the platinum wires projecting beyond the gutta percha to the extent of one-eighth of an inch, and their free extremities being slightly everted and separated from each other by an interval of one- tenth of an inch. In experimenting, the united gutta percha tubes were grasped and the projecting platinum points pressed against the surface of the calculus : the jar was then discharged by another * Described by Mr. Walker in Lardner's Cabinet Cyclopaedia, vol. ii. pages 218-220. S!22 Ro7jal Society. person, and a series of such discharges thus passed between the free extremities of the parallel platinum wires while resting upon the surface of the stone. With this simple arrangement, fragments a quarter of an inch long were broken off flints immersed in water, and the same force was applied to urinary calculi with the following results : — Exp. 1. June 7th. — A piece of a large lithic acid calculus was placed in a bladder, nearly filled with water, into which the gutta percha bougie containing the wires was then introduced and the neck of the bladder tied round the instrument. The bladder with its contents being placed on a wet board, the projecting platinum wires were then kept in contact with the surface of the calculus and the jar discharged. On opening the bladder and examining the stone, it was found to be broken into numerous fragments by the single discharge. Exp. 2. — A small phosphatic calculus, very smooth and hard, was experimented upon in a similar manner. The first five discharges produced no perceptible effect, but the sixth split it into at least twenty fragments, and many of these, on being slightly pressed between the finger and thumb, readily broke down. Exp. 3. — A very large oxalate of lime or mulberry calculus with projecting tubercles was similarly tested, and the first discharge pro- duced a small cavity in the surface to which the wires were applied, separating a considerable quantity of fine sand ; but subsequent dis- charges did not act so eflficiently on this very large stone. Exp. 4. — On the following day, June 8th, the experiment was repeated in the presence of Messrs. Potter, Rayne and Furness, sur- geons in Newcastle, and a small calculus, removed a few months since by the gentleman last mentioned from a young boy, was, after a few trials, split through the centre, one-half being reduced to frag- ments, and the other exhibiting in its interior a dark-coloured nucleus of lithic acid. These experiments appear to demonstrate the practicability of applying the lateral disruptive force of the electrical discharge to the disintegration of calculi in the bladder. There can be no diflSculty in bringing the end of a gutta percha catheter, conveying two cop- per wires, in contact with the surface of a stone in the bladder, and a very simple mechanical contrivance will enable the extremities of the platinum wires to be protruded when the end of the catheter touches the calculus. By employing two wires, one connected with the positive, the other with the negative, portion of the jar or ma- chine, not only is the intensity of the discharge increased, but the body is also prevented from forming any j)art of the circuit, and the risk of injury thereby materially diminished. The bladder used in the above-mentioned experiments was not at all injured, and on re- taining a portion of it between the platinum wires so that the dis- charge passed through it, no perforation or other destructive effect took place. The gutta percha tubes, having the projecting platinum wires, were placed in the mouth without being in contact with the lips, and a discharge sent through the wires, but there was no per- Royal Society. ^§8 ceptible shock. When, however, the bladder containing the stone rested upon the hand, during the act of disintegration a smart im- pulse was felt. On the whole, I am of opinion that the electrical force applied in the manner indicated, will be found quite as efficient for the disin- tegration of calculi in the bladder as the more formidable analogous operation of lithotrity, occasionally practised. And, as regards sim- plicity and security, the electrical apparatus certainly appears pre- ferable to the instruments used for crushing the stone by ordinary mechanical force. " The Attraction of Ellipsoids considered generally." By Mathew Collins, Esq., B.A. The author commences by stating, that the attraction of an ellip- soid ^on a point on its surface or within it, in a direction perpendi- cular to one of its principal planes, is proportional to the distance of the attracted point from that plane. This general proposition, which is an extension to ellipsoids of those already given for spheroids in Airy's Tract ** On the Figure of the Earth," Prop. 8 and 10, and in MacLaurin's 4th Lemma, " De causa physica Fluxus et Refluxus Maris," he demonstrates — 1 . In the case when the attracted point is on the surface of the ellipsoid. The demonstration of this is much like those given by the above- named authors for the less general case of spheroids, and its final step is effected by Cor. 1 to Prop. 87 of the first book of the Prin- cipia. 2. When the attracted point is within the ellipsoid. The demonstration in this case is effected by showing that an ellipsoidal shell, bounded by two similar and similarly placed ellip- soidal surfaces, exerts no attraction on a point situated anywhere within it or upon its interior surface. The foregoing proposition shows that the attraction of an ellip- soid on any point on its surface, or within it, can be got at once from the attraction of the same ellipsoid on a point placed at the extre- mity of an axis, and the author proceeds to show how the latter attraction can be found and reduced to elliptic functions. He then gives this proposition : Let a, h, c be the semiaxes of a homogeneous fluid ellipsoid, and A, B, C the forces acting on points at the extremities of a, b, c, caused partly by the ellipsoid's own attractions on its parts, and partly by centrifugal forces of revolution about an axis (2c), or by the action of an extraneous force directed towards its centre, and varying as the distance from the centre, then the ellipsoid will pre- serve its form if Aa=Bb = Cc. The last proposition stated in the paper is thus given : let R and r be the radii of two homogeneous concentric spheres ; A and a the attractions of each on a point on the surface of the other, then A a -— =— , whatever be the law of attraction as a function of the di- stance. 224 Royal Society. The demonstration given of the first of tliese two theorems is very concise, and of the second is direct and elementary. ** Researches on the Impregnation of the Ovum in the Am- phibia; and on the Early Stages of Development of the Embryo." (Third Series.) From the MS. papers of the late George Newport, F.R.S., F.L.S. &c. Selected and arranged by George Viner Ellis, Esq., Professor of Anatomy in University College, I^ondon. In this paper the author has given the result of further inquiries into the manner by which the frog's egg is impregnated, and has supplied in addition some very interesting facts respecting the de- velopment of the embryo during the earlier stages of its growth. In consequence of the difficulties that arose in the course of the inquiry, and of the doubts that might be suggested by others from the difficulty of manipulating with the egg of the Amphibia unless certain precautions are taken, the author first describes the apparatus used and the mode of proceeding he has employed ; and his results show that he has successfully surmounted the obstacles to micro- scopic investigation caused by the opacity, the great size, and the tendency to movement inherent in the egg. The fact of the impregnation of the ovum through the entrance of the spermatozoon into the yelk by its own movement was com- municated to the Royal Society in a preceding paper*, and the ori- ginal experiments there referred to as serving to establish the fact, are now detailed. In. addition, the circumstances aflfecting the pas- sage of the sperm-body through the thick investing envelopes are considered, and thence it is concluded, that " when there is any de- ficiency in the usual power, arising from an unhealthy condition of the fertilising body, or an increase in the resistance of the yelk mem- branes, the spermatozoon is unable to pass through the membranes into the yelk and the egg remains unfertilized." The two small rounded bodies that appear on the surface of the yelk in the interval or chamber between it and the investing mem- brane, have been traced from their origin, through their changes, till their disappearance after the equatorial division of the yelk. The investigations as to the true import of these bodies have not been further carried out, in consequence of the untimely death of the author ; but his observations have induced him to put forth the fol- lowing statement regarding them, viz. " that they are usually, and perhaps invariably, at that part of the yelk at which the head of the embryo is afterwards found." By following the changes in the segmenting yelk, evidence has been obtained of the derivation of different parts of the future being from definite segments of the yelk. Thus it has been found, that the half of the yelk on one side of the second or crucial cleft begins its subdivisions sooner than the opposite, and that the trunk and tail of the embryo are derived from this first subdividing part, whilst the head is produced from the other half. Having ascertained so much respecting the foundation of different parts of the embryo, the author next determined that the axis or * Philosophical Transactions for 1853, p. 271. Royal Society. 225 spine will primarily lie in a line with the first cleft of the yelk, though it may afterwards deviate somewhat from that line during the growth of the embryo. Lastly, it has been sought to discover what influence the artificial application of the spermatozoon to only one side of the eg^ would have upon the direction of the primary cleft of the yelk. The result of this inquiry seems, very curiously, to be, that the first cleft of the yelk will lie, under the circumstances stated, in a line with the point of the g^^ that has been touched with the impregnating fluid. ** Contributions to the Anatomy of the Brachiopoda." By Thomas H. Huxley, F.R.S. In the course of the dissection of certain Brachiopoda with which I have recently been engaged, I have met with so many peculiarities which are unnoticed in the extant and received accounts of their anatomy, that although the pressure of other duties prevents me from attempting to work out the subject with any degree of completeness for the present, I yet gladly avail myselC of the opportunity of com- municating a few of the more important results at which I have arrived, in the hope that they may find a place in the Proceedings of the Royal Society. My investigations were principally made upon Rhynchonella psit- tacea, for specimens of which I am indebted to Prof. Edward Forbes, while Dr. Gray obligingly enabled me to compare them with Wald- heimia flavescens and with Lingnla. 1 . The Alimentary Canal ofTerehratulida. — Professor Owen, in both his earlier and his later memoirs on the anatomy of the Terebratulidae, describes at length the manner in which the intestine, as he states, terminates on the right side between the lobes of the mantle. On the other hand, Mr. Hancock has declared himself unable to observe at this point any such anal aperture, and concludes from his own oliservations that the latter is situated on the ventral surface of the animal in the middle line, just behind the insertion of the great adductor muscle. M. Gratiolet, in a late communication to the Academic des Sciences, takes the same view. To get rid of the ob- vious difficulty, that this spot is covered by the shell, and therefore that if the anus existed here, there would be no road of escape for the fseces, Mr. Hancock and Mr. Woodward appear to be inclined to suppose that some cloacal aperture must exist in the neighbour- hood of the pedicle. The existence of any such aperture, however, has recently been denied with great justice by Professor Owen. The result of my own repeated examinations of Rhynchonella psit- tacea and of Waldheimia flavescens is — 1. that the intestine does not terminate on the right side of the mantle as Professor Owen describes it, but in the middle line, as Mr. Hancock describes it in Waldheimia^ while in Rhynchonella it inclines, after curving upwards, to the left side; and 2. that there is no anus at all, the intestine terminating in a rounded csecal extremity, which is straight and conical in Wald- heimia, curved to the left side and enlarged in Rhynchonella. I confess that this result, so exceptional in its character, caused Phil Mag. S. 4. Vol. 8. No. 51. Sept. 1854. Q 226 Royal Society. me no small surprise, and I have taken very great pains to satisfy myself of the accuracy of my conclusion ; but notwithstanding the strong prejudice to the contrary, to which the known relations of the anal aperture in Lingula gave rise, repeated observation has inva- riably confirmed it. Professor Owen's statement is, that in Rhynchonella {Terebratula) psittacea " the intestine inclines to the right side and makes a slight bend forwards before perforating the circumscribing membrane in order to terminate between the mantle lobes on that side." — On the Anatomy of the Brachiopoda, p. 152. 1 find, on the contrary (figs. 1 and 2), that the intestine passes Fig. 1. Fig. 1. Rhynchonella psittacea, viewed in profile; the lobes of the mantle and the pedicle being omitted. Fig. 2. The same viewed from behind, the pedicle having been cut away. The left half of the body and the liver are omitted. a. mouth ; b. oesophagus ; c. stomach and liver ; d. intestine ; e. imperforate rectum ; /. mesentery ; g. gastro-parietal bands ; h. ilio-parietal bands ; i. superior ' heart ' ; k. inferior ' heart ' ; /. genital bands ; m. openings of pallial sinuses ; ». pyriform vesicle ; o. sac at the base of the arm ; p. ganglion ; q. adductors. Royal Society. 227 at first straight downwards in the middle line, as in Waldheimia, but instead of terminating in a rounded tapering extremity as in that genus, it bends upwards and then curves round to the left side, forming a sort of free caecum in the visceral cavity. My reasons for believing that it is a free caecum are these : — in the first place, no anal aperture can be detected in the mantle cavity, either on the right or left sides, although the small size of the animal allows of its being readily examined uninjured, with considerable magnifying powers. Secondly. If the shell be removed without injuring the animal and the visceral cavity be opened from behind by cutting through its walls close to the bulb of the pedicle, it is easy not only to see that the disposition of the extremity of the intestine is such as I have de- scribed it to be, but by gentle manipulation with a needle to convince oneself that it is perfectly unattached. And in connexion with this evidence I may remark, that the tissues of the Brachiopods in general are anything but delicate ; it would be quite impossible for instance to break away the end of the intestine of Lingula from its attach- ments without considerable violence. Fig. 2. Thirdly. If the extremity of the intestine, either in Rhynchonella or m Waldheimia, be cut off and transferred to a glass plate, it may Q2 228 Koyal Society, readily be examined microscopically with high powers, and it is then easily observable that its fibrous investment is a completely shut sac. In Rhynchonella the enlarged caecum is often full of diatoma- ceous shells, but it is impossible to force them out at its end, while if any aperture existed they would of course be readily so extruded. However anomalous, physiologically, then, this caecal termination of the intestine in a molluscous genus may be, I see no way of escaping from the conclusion that in the Terebratulidce (at any rate in these two species) it really obtains. There are other peculiarities about the arrangement of the alimentary canal, however, of which I can find either no account at all or a very imperfect notice. The intestinal canal (figs. 1 and 2 h, d, e) has an inner, epithelial, and an outer fibrous coat ; the latter expands in the middle line into a sort of mesentery, which extends from the anterior face of the intestine between the adductors, to the anterior wall of the visceral chamber, and from the upper face of the intestine to the roof of the visceral chamber ; while posteriorly it extends beyond the intestine as a more or less extensive free edge. I will call this the mesentery (/). From each side of the intestinal canal, again, the fibrous coat gives off two ' bands,' an upper (^), which stretches from the parietes of the stomach to the upper part of the walls of the visceral chamber, forming a sort of little sheath for the base of the posterior division of the adductor muscle, which 1 will call the gastro-parietal band ; and a lower, which passes from the middle of the intestine to the parietes, supporting the so-called ' auricle.' I will call this the ilio- parietal band {h). The ilio-parietal and gastro-parietal bands are united by certain other ridges upon the fibrous coat of the intestine, from whose point of union in the middle line of the stomach posteriorly, a pyriform vesicle (w) depends. The mesentery divides the liver into two lateral lobes, while the gastro-parietal bands give rise to the appearance that these are again divided into two lobules, one above the other. I am inclined to think that these bands are what have been described as * hepatic arteries,' at least there is nothing else that could possibly be confounded with an arterial ramification upon the liver. This description applies more especially to Rhynchonella and Waldheimia, but the arrangement in Lingula is not essentially dif- ferent. 2. The Circulatory System of TerebraiulidcB. — Considerable differ- ences of opinion have prevailed among comparative anatomists as to the nature and arrangement of the vascular system in the Brachio- I)oda. A pair of organs, one on each side of the body, have been re- cognized as Hearts since the time of Cuvier, who declared these hearts in Lingula to be aortic, receiving the blood from the mantle and pouring it into the body, the principal arterial trunks being dis- tributed into that glandular mass which Cuvier called ovary, but which is now known to be the genital gland of either sex. Professor Owen in his first memoir follows Cuvier's interpretation, stating that in Orbicula the pallia 1 veins terminate in the hearts. Royal Society, 229 from which arterial branches proceed to the liver and ovary. Pro- fessor Owen further adds for the Brachiopoda in general, — " Each heart, for example, in the Brachiopoda is as simple as in Ascidia, consisting of a single elongated cavity, and not composed of a distinct auricle and ventricle as in the ordinary Bivalves," and he compares the hearts of Brachiopoda to the auricles of Area, &c. (Trans. Zoological Society, vol. i. p. 159). In 1843, however, M. Vogt's elaborate memoir on Lingula ap- peared, in which the true complex structure of the * heart ' in this genus was first explained and the plaited ' auricle ' discriminated from the ' ventricle; ' and in 1845, Professor Owen, having apparently been thus led to re-examine the circulatory organs of Brachiopoda, published his ' Lettre sur I'appareil de la Circulation chez les Mol- lusques de la Classe des Brachiopodes,' in which he felicitates M. Milne-Edwards on the important confirmation of the views which the latter entertains with respect to the lacunar nature of the circu- lation in the MoUusca, aflTorded by the Brachiopoda, and describes each heart of the Terebratulidse as consisting of a ventricle and a plaited auricle, the pallial veins not terminating in the latter but in the general visceral cavity. As the Professor does not recal the view which he had already taken of the circulation in Orhicula, I presume that he considers two opposite types of the circulatory organs to ob- tain in the Brachiopoda, the direction of the current being from the mantle through the heart towards the body in Orbicula, and from the mantle through the body towards the heart in Terebratula. The possibilities of nature are so various that I would not venture, without having carefully dissected Orbicula, — no opportunity of doing which has yet presented itself, — to call this view in question, but I think it seems somewhat improbable. Indeed the structural rela- tions which I have observed and which are described below, do not appear to me to square with any of the received doctrines of Bra- chiopod circulation, but I offer them simply as facts, not being prepared at present to present any safe theory on the subject. In Waldheitnia flavescens there are two * hearts,' situated as Pro- fessor Owen describes them, but so far as I have been able to ob- serve, the ventricle cannot be described as an ' oval ' cavity, inas- much as it is an elongated cavity bent sharply upon itself. Hastily- examined of course this may appear oval. I have been similarly unable to discover * the delicate membrane of the venous sinuses,' which is said by Professor Owen to " communicate with and close the basal apertures of the auricles," or to perceive that tlie auricular cavity can be " correctly described as a closed one, consisting at the half next the ventricle, of a beautifully plicated muscular coat in addition to the membranous one, but at the other half next the venous sinus of venous membrane only ; the latter might be termed the auricular sinus, the former the auricle proper." I presume that ' this delicate membrane of the venous sinuses ' is what I have called the ilio-parietal band, in which the base of the auricle is -as it were set, like a landing-net in its hoop, but this does not close the base of the auricle, the latter opening widely into the visceral chamber. 230 Eoyal Society, I have equally failed in detecting any arteries continued from the apices of the* ventricles ; and I have the less hesitation in supposing I have not overlooked them, as Mr. Albany Hancock, whose works are sufficient evidence of the value of his testimony, permits me to say that he long since arrived at the conclusion that no such arte- ries exist. What has given rise to the notion of the existence of these arteries appears to me to be this. A narrow band resembling those I have already described, is attached in Waldheimia along the base of the * ventricle' and the contiguous outer parietes of the auricle: inferiorly it passes outwards to the sinuses, and running along their inner wall, forms a sort of ridge or axis* from which the genitalia, whether ovaria or testes, are developed, stretching through their whole length and following the ramifications of the sinuses. It is the base of these ridges seen through the walls of the sinuses, where they extend beyond the genitalia, which have been described as arteries. The upper end of the band passes into the sinuses of the upper lobe of the mantle, and comes into the same relation with the genitalia which they enclose. The walls of the auricle in Waldheimia are curiously plaited, but I have been unable, in either auricle or ventricle, to detect any such arrangement of muscular fibres as that which has been described. The epithelial investment of the auricle, on the other hand, is well developed, and in the ventricle the corresponding inner coat is raised up into rounded villous eminences. The ventricle lies in the thickness of the parietes, while the auricle floats in the visceral cavity, supported only by the ilio-parietal band. The former is at first directed downwards, but then bends sharply round and passes upwards to terminate by a truncated extremity close to the suboesophageal ganglion and bases of the arms. Mr. Hancock informs me, that in his dissections he repeatedly found an aperture by which the apex of the 'ventricle' communi- cated with the pallial cavity ; and that, taking this fact in combina- tion with the absence of any arteries leading from this part, he had been tempted to doubt the cardiac nature of these organs altogether, and to regard them rather as connected with the efferent genital system, had not the difficulty of determining whether these aper- tures were artificial or natural prevented his coming to any definite conclusion at all. Before becoming acquainted with Mr. Hancock's investigations, I had repeatedly observed these apertures in Rhynchonella, but preoc- cupied with the received views on the subject, I at once interpreted them as artificial. A knowledge of Mr. Hancock's views, however, led me to reconsider the question, and I have now so repeatedly observed these apertures both in Waldheimia and in Rhynchonella, that I am strongly inclined to think they may after all be natural. If these organs be hearts, in fact, Rhynchonella is the most remark- able of living MoUusks, for it possesses /oMr of them. Two of these occupy the same position as in Waldheimia, close to the origins of the calcareous cms (k), while the other two are placed above these, and * This arrangement is, I find, particularly described by M. Gratiolet. ' " ;_^ Royal Society. 231 above the mouth, one on each side of the liver (i). It is these latter which Professor Owen describes, while he has apparently overlooked the other two, at least he says (speaking as I presume of Rhyncho- nella) (/. p. p. 148) that the venous sinuses " enter the two hearts or dilated sinuses which are situated exterior to the liver, and in T. Chilensis and T. Sowerbii just within the origins of the internal calcareous loop." The fact is, that while the ilio-parietal bands support two ' hearts' as usual, the gastro-parietal bands are in relation with two others. The base of the 'auricle' of the latter opens into the re-entering angle formed by the gastro-parietal band with the parietes, while its apex is directed backwards to join the ventricle, which passes downwards and backwards along the posterior edge of the posterior division of the adductor muscle. The auricles in Rhynchonella are far smaller, both actually and proportionally, than in Waldheimia. They exhibit only a few longi- tudinal folds, and not only present the same deficiency of muscular fibres as those of Waldheimia, but are so tied by the bands which support them that it is difficult to conceive how muscular fibres, even if they existed, could act. The 'ventricles' in like manner lie ob- liquely in the parietes of the body, and simply present villous emi- nences on their inner surface, which has a yellowish colour. All these ' hearts' exhibit the same curious relation with the geni- talia in Rhynchonella as in Waldheimia ; that is to say, a ' genital band ' (/) proceeds from the base of the ' ventricle ' and becomes the axis of the curiously reticulated genital organ. But in Rhynchonella the genital bands of the upper genitalia come from their own ' hearts.' The arrangement of the genitalia in Rhynchonella is very remark- able. The sinuses have the same arrangement in each lobe of the mantle. The single trunk formed by the union of the principal branches in each lobe opens into the inner and anterior angle of a large semilunar sinus which surrounds the bases of the adductors, and opens into the visceral cavity. The floor of this great sinus is marked out into meshes by the reticulated genital band, and from the centre of each mesh a flat partition passes, uniting the two walls of the sinus, and breaking it up into irregular partial channels. There are the same anastomosing bands uniting the gastro-pa- rietal and ilio-parietal bands on the stomach in Rhynchonella as in Waldheimia, and a pyriform vesicle of the same nature, but I did not observe in Rhynchonella those accessory vesicles upon the origins of genital bands, which I observed once or twice in Waldheimia. I could find no trace of arteries terminating the elongated, ovoid and nearly straight ' ventricles' of Rhynchonella ; their ends appeared truncated, and as I have already said, repeatedly presented a distinct external aperture. Such appear to me to be the facts respecting the structure of the so-called hearts in the Terebratulida ; what I believe to be an import- ant part of their peripheral circulatory system, has not hitherto, so far as I am aware, received any notice. Royal Society. In Waldheimia the membranous walls of the body, the parieto-in- testinal bands and the mantle, present a very peculiar structure ; they consist of an outer and an inner epithelial layer, of two corre- Etponding fibrous layers, and between them of a reticulated tissue, which makes up the principal thickness of the layer, and in which the nerves and great sinuses are imbedded. The trabeculse of this reticulated tissue contain granules and cell- like bodies, and I imagined them at first to represent a fibro-cellular network, the interspaces of which I conceived were very probably sinuses. Sheaths of this tissue were particularly conspicuous along the nerves. On examining the arms, however, I found that the oblique markings, which have given rise to the supposition that they are surrounded by muscular bands, proceeded from trabeculae of a simi- lar structure, which took a curved course from a canal which lies at the base of the cirri (not the great canal of the arms, of course) round the outer convexity of the arm, and terminated by breaking up into a network. These trabeculae, however, were not solid but hollow, and the interspaces between them were solid. The network into which they broke up was formed by distinct canals, and then, after uniting with two or three straight narrow canals which ran along the outer convexity of the arm close to its junction with the interbrachial fold, appeared to become connected with a similar system of reticulated canals which occupied the thickness of that fold. It was the examination of the interbrachial fold, in fact, which first convinced me that these reticulated trabeculae were canals ; for it is perfectly clear that vessels or channels of some kind must sup- ply the proportionally enormous mass of the united arms with their nutritive material, and it is so easy to make thin sections of this part, that I can say quite definitely that no other system of canals than these exists in this locality. The facts, then, with regard to the real or supposed circulatory organs of the TerebratuUdte, are simply these : — 1. There are two or four organs (hearts), composed each of a free funnel-shaped portion with plaited walls, opening widely into the visceral cavity at one end, and at the other connected by a constricted neck, with narrower, oval or bent, flattened cavities, engaged in the substance of the parietes. The existence of muscular fibres in either of these is very doubtful. It is certain that no arteries are derived from the apex of the so-called ventricle, but whether this naturally opens externally or not is a point yet to be decided. 2. There is a system of ramified peripheral vessels. 3. There are one or more pyriform vesicles. 4. There are the large ' sinuses ' of the mantle, and the ' visceral cavity' into which they open. To determine in what way these parts are connected and what functions should be ascribed to each, it appears to me that much further research is required. Nervous System of Terebratulida. — Professor Owen describes and figures the central part of this system as a ring surrounding the oral Royal Society. 233 aperture, its inferior portion being constituted by a mere commis- sural band. M. Gratiolet, however, states with justice that the inferior side of this collar is the thicker, and I find both in Rhynchonella and in Waldheimia that it constitutes, in fact, a distinct oblong ganglion, of a brownish colour by reflected light. From its extremities com- missural branches pass round the mouth, while other cords are distributed to the arms, to the superior and inferior pallial lobes, and to the so-called hearts. The nerves are marked by fine and distinct longitudinal striations, and can be traced to the margins of the pallial lobes, where they become lost among the muscular fibres of the free edges of the mantle. Structure of the Arms. — I have not been able to convince myself of the existence of that spiral arrangement of the muscular fibres of the arms which has been described in Rhynchonella and Waldheimia. I have found the wall of the hollow cylinder of the arm to be con- stituted (1) externally, by an epithelium, within which lie (2) the reticulated canals, which have been already described ; (3) by a de- licate layer of longitudinal or more oblique and transverse fibres, which are probably muscular, and (4) internally by a granular epithelial layer. In Rhynchonella the bases of the arms are terminated by two con- siderable sacs, which project upwards into the visceral cavity. Have these the function of distending and so straightening the spirally coiled, very flexible arms of this species ? Affinities of the Brachiopoda. — All that I have seen of the struc- ture of these animals leads me to appreciate more and more highly the value of Mr. Hancock's suggestion, that the aflfinities of the Brachiopoda are with the Polyzoa. As in the Polyzoa, the flexure of the intestine is neural, and they take a very natural position among the neural mollusks between the Polyzoa on the one hand, and the Lamellibranchs and Pteropoda on the other. The arms of the Brachiopoda may be compared with those of the Lophophore Polyzoa, and if it turns out that the so-called hearts are not such organs, one difference will be removed. In conclusion, I may repeat what I have elsewhere adverted to, that though the difference between the cell of a Polyzoon and the shell of a Terebratula appears wide enough, yet the resemblance be- tween the latter with its muscles and the Avicularium of a Polyzoon, is exceedingly close and striking. " On the frequent occurrence of Indigo in Human Urine." By Arthur Hill Hassall, M.D. From the present communication it appears that the occurrence of indigo in human urine is more common than the author was led to anticipate from his first inquiries. The author furnishes additional proofs of the blue colouring matter in question being really indigo, by converting it into isatine and aniline. Contrasting its chemical and physiological relations with hsema- tine and urine pigment, he shows that indigo is closely allied in its- 234 Cambridge Philosophical Society. nature and origin to those substances, and he considers that when indigo is met with in urine in considerable amount, it forms a vehicle for the elimination of any excess of carbon contained in the system. This view is borne out by the important fact, that the greater number of cases in which indigo has been observed to be developed in the urine in large amount have been cases of extensive tubercular disease of the lungs, and in which the decarbonizing functions of those organs are greatly impaired. CAMBRIDGE PHILOSOPHICAL SOCIETY. [Continued from vol. vii. p. 458.] May 1, 1854. — A paper was read by Professor De Morgan on the Convergency of Maclaurin's Series, being an Appendix to a paper on some Points in the theory of differential equations. See the abstract of the former paper, Phil. Mag. vol. vii. p. 450. Mr. Kingsley made an oral communication on the Chemical Nature of Photographic Processes. May 15. — A paper was read by Mr. Warburton on Self- repeating Series. In computing Bernoulli numbers by the formula of Laplace*, the author of this paper was led to notice, that in the fraction whose development isa series of the form i2«+i_2'^'*'^V + 3^""^^ . f^-kc, the numerator of that fraction is a recurrent function of t. This led him to investigate the question, what are the conditions which the denominator of the generating fraction, and the terms of the series generated, must satisfy, in order that the numerator of such a frac- tion may be a recurrent function of t. The paper contains the result of that investigation. The author calls those series " self -repeating" which, when ex- tended without limit in opposite directions, admit of separation into two similar arms, each arm beginning with a finite term of the same magnitude. Between this pair of finite terms, either no zero-term, or one or more zero-terms, may intervene. One arm repeats, and contains arranged in reverse order, the terms of the other arm, either all, or none, of the terms having their signs changed. The different positive integer powers of the natural numbers, of the odd numbers, and of the figurate numbers of the several orders, present familiar examples of self- repeating recurring series. The author demonstrates the following three theorems respecting self- repeating recurring series : — I. If the series arising from the development of a proper fraction is the right arm of a self-repeating recurring series, and if the deno- minator of such a fraction is a recurrent function of t, then the nu- merator also is a recurrent function of t. II, Other things remaining the same, if the numerator of the fraction is a recurrent function of /, then the denominator also is a recurrent function of /. ♦ Sec Memoirs of the Academy of Sciences, 1777- Cambridge Philosophical Society, 2S5 III. If the numerator and the denominator of a proper fraction are each a recurrent function of t, then the series, arising from the deve- lopment of the fraction according to the positive integer powers of t, will be the right arm of a self- repeating recurring series. By way of example, the author applies his first theorem to the summation of the infinite series 1'' — 2' + 3^ — &c., and compares his. process with the corresponding processes of Laplace and of Sir John Herschel. The sum in question is given by Sir John Herschel (see Jameson's Journal, January 1820) in terms of the differences of the powers of 0, extending from A'O^ to A^O''. In the author's process, the requisite differences extend from A'O^ only to A^O^, and the nu- merical coefficients of these are of diminished magnitude, and of very easy determination. The author makes other applications of his theorems; but on these we forbear to enter. A paper was read by Professor Challis on the Determination of the Longitude of the Cambridge Observatory by Galvanic Signals. The experiment of which this paper contains the details, was made at the suggestion of the Astronomer Royal, and conducted according to a scheme arranged by him for giving and receiving the signals. A galvanic connexion having been established between the Greenwich Observatory and the Cambridge Telegraph Office, by means of the London central station of the Electric Telegraph Company, signals were sent on the nights of May 17 and 18, 1853, between 11^ and 12^ mean time. The signals were made by causing two needles, one at Greenwich, the other at Cam- bridge, to start by completing the galvanic circuit at either place of observation. The times of starting were noted at both places, and reduced to the sidereal times of the respective observatories, to serve by comparison for determinations of the difference of their longi- tudes. On each night the signals were made alternately for a quarter of an hour at one station, in batches containing an arbitrary number of signals not exceeding nine, and then for a quarter of an hour at the other station in a similar manner. On the first night the total number of signals was 151, and on the second night 139. The two observers, Mr. Dunkin of the Greenwich Observatory, and Mr. Todd of the Cambridge Observatory, changed places in the interval between the two nights' observations ; Mr. Todd observing at Greenwich, and Mr. Dunkin at Cambridge, en the second night. Also it was arranged that the two observers should observe identical stars on the two nights, as well as the stars ordinarily used for clock errors, and that the same apparent right ascensions of the stars should be employed for reducing the signal-times at both observatories. The Cambridge Observatory time was conveyed with the greatest care to the Tele- graph Office at the Cambridge Railway Station by the transfer of three chronometers. By a first calculation, the longitude of the Cambridge Observatory was found to be 23®'03 east of Greenwich. Professor Challis subsequently made another calculation, taking into account the effect on the times of meridian transits of stars produced by the forms of the transit-pivots, according to a method 236 Intelligence and Miscellaneous Articles. which he has described in the Memoirs of the Royal Astronomical Society (vol. xix. p. 103). The errors arising from the deviation of the pivots from the cylindrical form being eliminated, the longitude is found to be 22''70 east of Greenwich, which is less by 0"*84 than the value hitherto adopted. May 29. — A paper was read by Professor Fisher, entitled " Ad- ditional Observations on the Development of the Vertebral System." XXXII. Intelligence and Miscellaneous Articles. ON THE ARTIFICIAL PRODUCTION OF TAURINE. BY A. STRECKER. rr^HE properties of taurine convinced me that we should one day •*• succeed in preparing it artificially. M. Redtenbacher has already attempted to produce taurine by means of aldehyde and bisulphite of ammonia, but he only obtained an isomerous body with different properties. With the same view I undertook the following experiments. Sulphate of methyle, C^H^ O . SO^, furnishes with ammonia, sul- phomethylane and wood-spirit, according to the formula 2(C^ H30 . S03) + NH^=C5^ H^ NS^ O^ -f C^ H^ O^. With sulphate of sethyle we might therefore hope to obtain tau- rine if the decomposition were analogous, — 2(C4 H^O . S03) +NH3 = C^ H7 NS^ Qe + C^ H^ O^ Sulphate of athyle. Taurine, but I found that sulphate of oethyle behaves in a different manner tc sulphate of methyle ; a conjugate acid is formed, described by me some years ago under the name of sulphsethamic acid. Substituting methylamine for ammonia, sulphate of methyle might, from analogy, furnish taurine ; thus — 2(C2H30.S03) + C2H^M = C-*H7N06S*-i-C«H^02. Sulphate of Methylamine. Taurine, methyle. I did not try this mode of formation, as I was convinced by expe- riment that taurine does not give a trace of methylamine on its decomposition with potash. Nitrite of aethyle, C-^ H^O . NO^, placed by M. Gerhardt amongst p4 TT3 1 the nitryle compounds j^q^ \ , would produce taurine (or its iso- mer) by the action of bisulphite of ammonia, if it behaved like nitro-naphthaline. According to M. Piria, with nitro-naphthaline and bisulphite of ammonia we have — C^o H7 NO^ + 6S0« 4- 2H0 = C20 H9 NS« 0« + 4S0\ Nitro-naphthahne. Naphthionic acid. By analogy we should get with nitrous aether, — C*H'>NO*-|-6SO«-|-2HO=C^H7NS2 0« + 4SOs. Nitrous aether. Taurine. Intelligence and Miscellaneous Articles. 237 Experiment proves that nitrite of sethyle does not act like nitro- naphtliaiine with bisulphite of ammonia ; nitrogen is evolved, and a formation of sulphuric and aethylosulphuric acids takes place. IsEethionic acid, prepared according to M. Regnault, by means of anhydrous sulphuric acid and defiant gas, when in combination with ammonia only differs from taurine in composition by two equivs. of water, — NH^O . C^H^O . 2S03=C^H7N06 S^ + HO. Issethionate of ammonia. Taurine. This salt fuses at 248° F. without disengaging ammonia, and it might be hoped that at a still higher temperature it would lose water. I first ascertained that taurine might be heated to 464° F. without decomposition or fusion. Issethionate of ammonia heated to 392° F. began to lose weight ; I heated it to 446° F., and kept it at this tem- perature until it had lost 1 1 per cent, of its weight. The mass was dissolved in water ; on the addition of alcohol it is precipitated in crystals ; this precipitate, dissolved in water, furnished by sponta- neous evaporation large crystals exactly identical with the crystals of taurine prepared from bile. Like taurine, they bear exposure to a temperature of 464° F. without fusing or acquiring colour; they evolve no ammonia with a solution of potash ; they do not pre- cipitate the salts of baryta when boiled with nitric acid or nitro- muriatic acid. When fused with potash and nitrate of potash, they evolve ammonia, and the mass contains sulphuric acid. All these properties being the same as those of taurine, and its mode of forma- tion proving that its composition is similar, this product is identical with the taurine of the bile. — Comptes Rendus, July 3, 1854, p. 61. ON THE ELECTRO- CHEMICAL DECOMPOSITION OF WATER. BY F. LEBLANC. With the hope of obtaining a gas much charged with ozone by the electrolysis of water, I arranged a voltameter so as to keep it in action in a freezing mixture. In this way, water containing at least one-tenth of its volume of concentrated sulphuric acid was decom* posed at a low temperature by means of four ordinary Bunsen's ele- ments. Although the electrodes were formed of simple platinum wires, the volume of oxygen collected was much less than half the volume of the hydrogen disengaged in the same time at the negative pole. The oxygen was strongly ozonized, but the proportion of ozone absorbable by spongy silver did not warrant the attribution of the diminution in the volume of gas collected at the positive pole, to any difference in volume between ozone and ordinary oxygen. I observed that the liquid in the voltameter had acquired new pro- perties— energetic oxidizing action ; it whitened sulphuret of lead, and superoxidized hydrated oxides like oxygenated water. I continued these researches, and ascertained the existence of some peculiar phaenomena of oxidation, by employing spongy platinum at the positive pole, and placing oxidizable substances in the cold vol- 238 Intelligence and Miscellaneous Articles, tameter ; such as acetate of potash, which was rapidly converted into the formiate, &c. — Comptes Rendus, March 6, 1854, p. 444, ON SOME COMBINATIONS OF HYDRARGYROMETHYLE AND HY- DRARGYRiSTHYLE. BY A. STRECKER. Frankland found a short time since, that when iodide of methyle and iodide of amyle in contact with mercury are exposed to the influence of the solar rays, crystals are formed of which the composi- tion is expressed by the formulae C*H3 Hg^I and C'oH" Hg^I, and to which he gave the names of iodide of hydrargyroroethyle and iodide of hydrargyramyle. He did not succeed in producing an ana- logous compound with iodide of aethyle, although the existence of this combination might be presumed. Before I was acquainted with Frankland's experiments, I had already obtained the iodide of hydrargyraethyle, which may easily be produced from a mixture of iodide of aethyle and mercury under the influence of diffused light. After some time crystals are formed, of which the quantity increases until the whole of the liquid sets into a mass. The crystals dissolve in boiling aether and alcohol, from which they separate in thin, colourless, shining laminae. They sublime at 212° F., but only fuse at a higher temperature. They do not dissolve in water, but are soluble in ammonia and in solution of potash, from which they crystallize again without decomposition. On analysis I found their composition to be C^ H'' Hg^I. With nitrate of silver they furnish iodide of silver and nitrate of hydrargyraethyle, C* H^ Hg^O . NO^, which crystallizes on evaporation in colourless prisms. Chloride of sodium precipitates chloride of hydrargyraethyle, C^ H^ Hg^ CI, from the watery solution of the nitrate ; it cannot be distinguished from the iodide by its characters. These aethyle com- pounds are decomposed by sun-light, and this is the reason why Mr. Frankland did not obtain them. I have also prepared the nitrate of hydrargyromethyle ; its composition is C^ H^ Hg^ O . NO^ + H0. — Comptes Rendus, July 3, 1854, p. 57. ON THE ARTIFICIAL PRODUCTION OF CINNAMON OIL. BY A. STRECKER. I pointed out some years since, that styrone, which is obtained by treating styracine with a concentrated or alcoholic solution of potash, is the alcohol of cinnamic acid, as it exhibits the same relation with regard to this acid as alcohol to acetic acid. By experiments made at my suggestion, M. Wolff has proved that styrone, under the influ- ence of energetic oxidizing agents, becomes converted into cinnamic acid. I have found that styrone, in the same conditions in which alcohol is converted into aldehyde, furnishes the aldehyde of cinnamic acid, or cinnamon oil. For this purpose it is suflicient to moisten platinum black with Meteorological Observations. 239 liquid st3rrone, and leave the mixture exposed to the air. In a few days the greater part of the styrone is converted into cinnamic alde- hyde, v^rhich is separated from the unaltered styrone by the excellent process of M. Bertagnini. With a concentrated solution of bisul- phite of potash, crystals are obtained, which are washed with aether to free them from the styrone. The crystals are purified by the addition of sulphuric acid diluted with pure cinnamic aldehyde . The crystals dissolve in nitric acid, and in a few moments crystals are formed of the nitrate of the hydruret of cinnamyle. The conversion of styrone into hydruret of cinnamyle by the oxygen of the air is explained by the equation — CIS H'o 02 + 20=Ci« H8 02+ 2H0. Styrone. Hydruret of cinnamyle. — Ibid. p. 61. METEOROLOGICAL OBSERVATIONS FOR JULY 1854. ChiswicJc. — July 1. Heavy rain : overcast. 2. Very fine : slight rain. 3. Slight rain : fine. 4. Densely clouded. 5. Showery. 6. Very fine : heavy showers. 7. Overcast : heavy showers. 8. Rain : very fine : clear. 9. Very fine : cloudy. 10. Showery : heavy rain at night. 11. Cloudy. 12. Drizzly : densely overcast. 13. Very fine. 14. Overcast : clear. 15. Densely clouded : very fine. 16. Very fine. 17. Rain: very fine. 18 — 21. Very fine : air very dry. 22. Quite cloud- less. 23. Clear and calm. 24. Sultry : lightning at night. 25. Very hot : light- ning at night. 26. Slight haze : cloudy : rain. 27. Easterly haze : rain. 28. Clear and fine. 29. SUght fog : cloudy. 30. Very fine : thunder-storm 2 to 5 p.m. 31. Uniformly overcast : heavy thunder clouds. Mean temperature of the month 61°-59 Mean temperature of July 1853 61 '94 Mean temperature of July for the last twenty-eight years ... 63 '17 Average amount of rain in July 2*42 inches. Boston. — July 1. Cloudy : rain a.m. 2. Cloudy. 3. Cloudy : rain p.m. 4. Fine : rain p.m. 5. Fine. 6, 7. Cloudy. 8. Cloudy : rain a.m. 9. Cloudy. 10. Cloudy: rain a.m. and p.m. 11. Cloudy. 12. Rain a.m. and p.m. 13. Cloudy. 14,15. Cloudy : rain a.m. and p.m. 16 Fine. 17. Cloudy : rain a.m. and P.M. 18. Cloudy : rain a.m. 19, 20. Cloudy. 21. Fine : thermometer 84° 5 P.M. 22—24. Fine. 25—29. Cloudy. 30. Fine. 31. Cloudy : rain a.m. and P.M. Sandwich Manse, Orkney. — July 1. Cloudy a.m. and p.m. 2. Cloudy a.m. : showers p.m. 3. Cloudy a.m. : rain p.m. 4. Rain a.m. : fog p.m. 5. Cloudy a.m. : hazy p.m. 6. Bright a.m. : rain p.m. 7. Clear a.m. : clear, fine p.m. 8. Bright, fine A.M. : cloudy p.m. 9. Drizzle a.m. : cloudy p.m. 10. Bright a.m.: cloudy P.M. 11. Cloudy A.M. and p.m. 12. Drizzle a.m. and p.m. 13. Rain a.m. : damp P.M. 14. Damp a.m. and p.m. 15. Rain a.m. : clear, fine p.m. 16. Cloudy A.M. : cloudy, fine p.m. 17. Damp a.m. : clear, fine p.m. 18. Clear, fine a.m. : fine, fog P.M. 19. Hazy a.m. : cloudy p.m. 20, 21. Clear, fine a.m. and p.m. 22. Showers a.m. : clear p.m. 23, 24. Cloudy a.m. and p.m. 25. Drizzle a.m. : cloudy P.M. 26. Showers a.m. : clear, fine p.m. 27. Clear a.m. : cloudy, fine p.m. 28. Clear, fine a.m. and p.m. 29. Clear, fine a.m. : cloudy, fine p.m. 30. Cloudy A.M. : fog P.M. 31. Fog a.m. and p.m. Mean temperature of July for twenty-seven previous years ... 55°-08 Mean temperature of this month 55 '25 Mean temperature of July 1853 58 -15 Average quantity of rain in July for fourteen previous years . 2*40 mches. •ao)8oa •:pi4ii«l3 ^ ^ POPOOOMOO^OM I 'i(3iMptras 1 8 ^ i « g' » « a ^ i II' i;| i| g i i ill ti ^ i d i i i » ■ao)8og ^«^i?^^^^lBEflC^^«^'l«l|.^l23i5J«Sl^^ fe • !t . ^ S rt 2 1^ ■ II O •mdi 'uo)8og 4) &H 1?^ g « Si o I OO t^ T^- Ti->0 t^ ON ON p p ,000 vp *0 OO OO pNOO 1^-. On OS ON O O N fJ C< j-" On r>. t-^ O\0nOn0n0nOnO\0n0 O OnO\OnCT\OnOnOnOnO\0\OnOnO O O O O O 0\OnO\ •tn*B f8 *UO)BOS OOvO OVO N ^n ri M r<^M rhO tJ-OnOn'-i vocTnOvO c^OO H m O H 00 f^ trvvo t- 1-^ n u-^vo ONN N pjvovo ONt-v tJ-vo 00 vo r^vo NO >o ^ u-t ii-1 ^ u-i r^oo •<+ w o-i oe 00 vo "1^ vo t>« t^ r^oo oo t-^t~-t^r^o\ONONONO m hi q q O O o "-i ooovo OO 0\»^0 t< t^coO coONW^M tJ- t1-vO NOO r^ O Tl-ro-■* ^ O N O H Tj-u-itv^o O iJ^w^rJ ONf< lowoooo t^O '^O K-iO »^OOOvo O On pNOO vo t^ r^ r>. r^ JC-~ On OnOO 00 On O HI p p ^On P « (N H. M p .-I M jN hi _OnOO On ON On On ON ON On ON On ON ON On ON ON b b b b Ov b O O O O O O O O O On ON 2^ 2^ CO 9 4* »^vO t^OO On c3 to ^ ^NO t^OO ON c5 « tJ t^ ^ lONO r^oo On 6 MHIHIHIMMMM(4C4C)HNr«r)C)t4rO 1^ THE LONDON, EDINBURGH and DUBLIN PHILOSOPHICAL MAGAZINE AND JOURNAL OF SOIENOE. [FOURTH SERIES.] OCTOBER 1854. XXXIII. On the douhh Refraction temporarily produced in Iso* tropic Bodies. J5?/ M. G. Wertheim*. [With a Plate.] Description of the Apparatus and manner of operation. IN a homogeneous body submitted to compression in one direction only, the molecules are caused to approach each other in this direction, and they are forced asunder in the two perpendicular directions : the reverse takes place when we sub- stitute traction for compression. The relations between simul- taneous dilatations and compressions, have been actually ascer-* tained to a degree of exactitude equal to that of which experi- mental questions are usually susceptible. This mechanical effect is accompanied by an optical one, which we can observe in trans- parent bodies, and which is explained by the diminution of the elasticity of the sether in the direction of the mechanical com- pression, and its augmentation in the direction of dilatation. It is proposed to discover the relations subsisting between the force applied to a body of known dimensions and the two species of effects produced, whatever may be the mechanical or optical elasticities of the bodies operated on, provided that they are con- stant in all directions. In other words, the two surfaces of elas- ticity being spheres in the natural state of the body, it is pro- posed to determine the form and position of the two surfaces after the application of an external force, which, by pressure or by traction, acts in a uniform manner upon the whole body ill one of its dimensions. * Extracted from a separate Pamphlet published by Mallet-Bachelier. Paris, 1854. Phil Mag, S. 4. Vol. 8. No. 52. Oct, 1854. R 242 M. G. Wertheim on the double Refraction The apparatus (Plate II. figs. 1 and 2) which I have used to produce the mechanical eflfect is composed of two pieces for com- pression A, and A^, of one piece for traction B, and two electro- magnetic spirals, which form part of the apparatus of M. Ruhm- korff, and which carry, one the polarizing Nichol C, and the other the doubly refracting prism D. All these pieces are fixed upon a support of oak, furnished with notches so as to give pass- age to the hooks destined to bear the weights, and with grooves q in which slide the prolongations of the cores of the spirals. It is easy to undeffetand the dispositions of the presses which we shall name weight presses, fig. A; each of them is com- posed of a vertical stirrup a, fastened down to the bench, and of the two horizontal plates b, parallel to each other and to the horizontal portion of the stirrup. This latter is pierced with two apertures, in which slide with gentle friction two cylindrical stems c, which connect the two moveable plates, the upper one of which is placed on the piece p submitted to compression, while the lower one is furnished with a ring d for the application of the charge. The whole press is in bronze, 2 centimetres thick and 3 centimetres wide, and hence sufficiently solid to prevent any of its parts from suffering a sensible flexure under the action of the charge, which never exceeded 600 kilogrammes. The parallelopiped ^ is placed on the horizontal portion of the stir- rup, so that its centre is in the prolongation of the axes of the prisms; the two horizontal sui'faces of this piece, those that receive the pressure, are furnished each with a plate of vulcanized india-rubber, and several doubles of thin pasteboard. In this manner the pressure distributes itself in a uniform manner over the whole parallelopiped, since the upper plate cannot deviate from the horizontal line; and if, notwithstanding these pre- cautions, some defect of parallelism should exhibit itself, it can always be remedied by means of the screws r. One of these weight presses Aj is destined for the employment of heavy charges, which are placed in the -chest E furnished with a support at its base ; it is only necessary to lower this support to cause the entire charge to be carried by the bar e, which is suspended from the ring d. The other press A^, the use of which we shall explain imme- diately, is destined to receive comparatively light charges only ; it therefore carries only a square bar/, furnished with cross-bars at its two extremities, which reach over the bench, and receive each one-half of the charge. The apparatus for extension, fig. B, is composed of a support of cast iron g, larger and more elevated than the stirrups of the presses, and of the two truncated bronze cones, the superior one of which carries a strong vice i, while the inferior one k is fur- temporarily produced in Isotropic Bodies, 243 nished with a ring /, destined to carry the hook m and the weight-chest E. The piece/?, which is submitted to extension, is fixed with red mastic to the bases of these two cones, which has the double inconvenience of rendering the experiment deli- cate, since the mastic is detached by the least transverse shook, and of limiting its extent. This mastic scarcely supports, for the square centimetre, a traction of 50 kilogrammes. However, this mode of fixation is the only one admissible ; for the vice, or any other mechanical appliance, necessarily exerts unequal pressures in different directions, which give rise to the exhibition of colours of the same nature as those we would observe, but so irregularly distributed as completely to conceal the principal phsenoiaaenon. The vice i of the superior cone is maintained vertical by means of the traverse n, and its screw o serves to place the centre of the piece p in the axis of the apparatus. These three supports are usually fixed on the bench ; how- ever, when it is desired to bring into simultaneous action both mechanical and magnetical forces, two of the supports are raised so as to leave only the piece A or the piece B, according as we operate by pressure or by traction. In causing the spirals to glide in their grooves q, they are made to approach as nearly as possible to the piece to be sub- mitted to their action ; they are fixed in this position by means of the screws F, and against their bases the two pieces of soft iron s are applied so that their cores constitute a single electro- magnet. It is doubtless unnecessary to remark that an interval ought always to exist between the piece jo and the poles, suffi- ciently large to prevent the poles from moving towards each other when the current is excited, and clasping the piece between them, which would introduce a mechanical compression in the direction of the axis of the piece. The same motive has caused me to reject the iron and steel presses which I had first employed. In the prolongation of the optic axis of the apparatus is placed a plate of white Sevres porcelain Gr, strongly illuminated by white light, by the light of the salt-lamp, or else by a Carcel lamp, the rays of which, before arriving at the Nichol, have tra- versed glasses or liquids sensibly monochromatic. It would doubtless be better to operate with direct white light, and with coloured rays well defined by their vicinity to a line of the spec- trum ; but this has not been possible, owing to the situation of my laboratory and the long duration of each experiment. Supposing now, to fix the ideas, that a cube of a transparent substance, colourless and isotropic, is placed in the press, that the principal sections of the Nichol and of the doubly refracting prism are parallel to each other, and enclose an angle of 45° with the vertical, and that white light is made use of. As long as R2 244 M, G. Wertheim on the double Re/faction the weight-chest reposes on its support, two images of the aper- ture of the diaphragm placed behind the Nichol, a white or ordi- nary image, and a black or extraordinary one, are seen. When the cube is of glass, a gray tint is perceived on the latter image ; but this effect, due to a residue of temper, may usually be neglected in the case of well- annealed glasses, as we shall see further on. As the pressure augments, the two images become successively coloured with all the colours of thin plates ; the ordinaiy image always taking the colours of transmitted light, and the extraor- dinary image presenting the complementary tints, or the colours of the^ings in reflected light. Tlie two images exhibit flat tints, if the experiment is well made, when the pressure is exerted in a uniform manner, and the substance is very homogeneous ; but if the least irregularity exists, it is discovered by the experiment itself, and this, I think, renders this method preferable to any purely mechanical means. Thus, when the upper plane b deviates in a slight degree from the horizontal line, and when consequently the charge is thrown more upon one of the edges of the parallelopiped, we see at the same side, in each image, a colour more elevated in the scale than on the side opposite. This irregularity usually indicates that the piece is not exactly in the middle of the press, at least that the two horizontal faces of the piece possess some slight defect of parallelism. When the piece, at the same time that it is compressed, takes a transverse flexure, — which is often the ease, notwithstanding their small height, — however small this flexure may be, coloured bands make their appearance similar to those obtained by means of the press of Fresnel : these bands sometimes vanish by a slight displacement, or by the turning of the piece j but in many cases it is necessary to cut the faces anew, or to reject the piece altogether. Finally, diflerent colours are sometimes ob- served in the two images which are quite irregularly distributed, and which are a certain indication that some defect of homoge- neity exists in the substance. Method employed to measure the artificial double Refraction. We have already said that the colours follow the scries of tints in coloured rings. Newton having measured the thickness of the plate of air which transmits and reflects each of these comple- mentary colours, it is natural to attempt to make use of these measurements to express numerically each tint obtained either by compression or by traction. The following table contains some of these determinations; the thickness of the plate of air e is expressed in millionths of the English inch, and the temporarily produced in Isotropic Bodies. M5 charge P in kilogrammes. This latter acts as a pressure, and the weight of the chest E, of the hook e and the press A, are comprised in the charges stated in the table. Colour of the image E. Crown glass. Elate glass. Crown glass of Clichy, P. Flint glass. Alum. Very black Black Bluish Blue White Yellow Orange ... Red Violet Indigo Blue Green Yellow Orange Bright red Deep red . . . Purple Indigo Blue Green Yellow Orange Bluish-red 1 2 2| 5i 7i 8 9 14 15i 162 19| 21 23f 25^ 27f 29 32 15 32 40 72 100 130 140 155 170 190 212 240 260 287 290 300 310 325 370 395 430 465 150 16-0 16-6 13-7 141 16-3 15-5 13-9 13-2 13-6 140 14-7 151 15-7 14-7 14-3 140 13-9 14-7 14-6 14-8 14-5 40 90 100 210 300 370 420 480 520 560 400 45-0 41-7 400 42-2 46 46-7 42-9 40-5 400 10 25 32 66 90 110 138 144 150 184 205 242 251 280 295 310 320 334 370 391 423 466 100 12-5 13-3 12-6 12-7 13-8 15-3 12-9 11-7 13-1 13-6 14-9 14-6 15-3 150 14-8 14-5 14-3 14-7 14-4 14-6 14-6 30 58 80 145 175 230 257 295 320 360 420 475 515 550 300 290 33-3 27-6 24-6 28-8 28-6 26-4 250 25-7 27-8 291 29-9 3001 30 60 80 150 225 248 300 352 410 450 492 300 300 33-3 28-6 31-6 31-0 33-3 31-5 320 321 32-5 It is evident that the differences of the paths of the two rays are sensibly proportional to the charges, still the variations which P subsist for the same piece in the values of the ratio — suffi- ciently indicate that the procedure is not capable of furnishing very exact results. In point of fact, each of the colours exhibits a gr§at number of degradations, and however careful we may be to choose the most decided tint, and that which accords best with the desig- nation of Newton, it is hardly reasonable to hope that we shall 346 M. G. Wertheim on the double Refraction alight on the exact tint to which his measurement of the thick- ness of the plates refers. To operate with more exactitude, I have had recourse to the homogeneous light emitted by salt and alcohol, which light, according to Mr. Miller, contains almost solely orange rays in the vicinity of the line D of Fraiinhofer, and the wave-length of which is consequently 589 millionths of a millimetre. We shall hence have extinction of the extraordinary image whenever the difference of the paths is an even multiple of ^ or of 294*5 ; and extinction of the ordinary image whenever the difference of path amounts to an odd multiple of the same quantity ; we shall also know the amount of the charges which produce this differ- ence of path. It must, however, be remarked, that besides the orange rays, the flame of alcohol and salt contains a certain quantity of violet light ; hence in these experiments the black colour, which would be the result of a complete extinction, is replaced by a violet coloration, which is very distinct in one of the two images, when all the orange rays have disappeared ; this, however, does not interfere in the slightest degree with the ex- actitude of the experiments, for it is easy to seize the moment when this colour presents itself in the greatest purity and with the least intensity. In this manner we obtain a certain number of fixed points in the chromatic scale, which it is our purpose to construct, and others are found with equal certainty by operating with white light. M. Biot* assigns the arc of 24 degrees to the rotation impressed upon the mean yellow rays by a plate of rock-crystal of the thickness of one millimetre ; combining this determina- tion with the rotations which refer to the lines of the spec- trum, the length of whose undulations are known, we find for these rays the length 550*6, and consequently we have ~ =275*3 ; but we also know the limiting tints of the reflected and trans- mitted rings ; they are those in which the mean yellow ray is destroyed. We can therefore determine the charges which give these teintes de passage, sufficiently sombre in the first rings at least, and characterized with sufficient clearness to serve as points of reference. Among these colours the teinte sensible distin- guishes itself, which, according to M. Biotf, is reflected by a plate of air of about 21 millionths of an English inch, or of * " Memoire sur les phenomenes rotatoires op^res dans le cristal de roche" (M^. de VAcad. vol. xx. p. 284). t *• Memoire sur la polarisation lamellaire " {Mim. de VAcad. vol. xviii. p. 644). temporarily produced in Isotropic Bodies, 347 533*4 millionths of a millimetre, which thickness is very nearly equal to 2 7^. "" To construct the following table, I have chosen a piece of very pure Clichy crown glass (borosilicate of zinc of the manufacture of MM. Maes and Clemandot), which could be compressed in • the press A, until it gave a difference of path of 7 ^ ; beyond this limit the colours are too much mixed with white light, and are consequently too pale to serve as measures. The charges ! which it was found necessary to employ are as follows : — \ 2* 2^. 2 3 t 4- i 5^. 2 ^ 2 i 1- i With white light ... With the flame of! salt and alcohol, j 68 74 142 163 74 79 216 233 74 80 290 313 74 80 365 394 75 81 440 475 75 81 515 75 These figures are the means of a great number of concordant measures ; they may be considered exact to about 1 kilogramme for the experiments with the white light, and to 2 kilogrammes for the experiments with the homogeneous orange light. The charge which produces the difference of path ^ is consi- derably less than all which follow ; this same inequality is pre- sented by all isotropic bodies, and we shall have to take it into account ; but at present it is enough to prove that it ia sufficiently small, and that the augmentation of the charge is sufficiently regular, to permit of our finding by interpolation the difference of path corresponding to any charge, and consequently to any tint whatever. We have chosen in each ring a certain number of tints well characterized and easy to reproduce, and have determined the charges necessary to be applied to the same piece of crown glass to produce them. Let "P^ be one of the charges, and suppose that it stands between P^ which gives the double refraction measured by n -^, and Pj which corresponds to («-f 1) ~; we have for this charge the difference of path This formula has served for the construction of the following table, in which the second column d contains the difference be- tween the paths traversed by the ordinary and extraordinary rays, expressed in millionths of a millimetre. In the third column e, are inscribed the thicknesses of the plates of air which transmit and reflect the colours inscribed in M. G. Wertheim on the d^ubk IRefraction the fifth and sixth cohimns. These thicknesses arc calculated in millionths of the English inch, so that they may be immedi- ately compared with the measures of Newton. Finally, we shall see that the designations of the colours, which I have sought to render as faithful as possible, agree most usually with those recently published by M. Briicke*. No. d in milHonths of a millimetre. e in millionths of an English inch. P charge. Colour of the O image. Colour of the E image. r ^ mm 0 0 0 White. Black. 2 40 0-78 10 White. Iron-gray. 3 97 1-91 24 Yellowish-white- Lavender-gray. 4 158 311 39 Brownish- white. Blue-gray. 5 218 4-29 54 Yellow-brown. A clearer gray. 6 234 4-61 58 Brown. •< White with a slight tint of green. 7 259 510 64 Clear red. White, almost pure. 8 267 5-25 66 Carmine-red. Yellowish-white. 9 275 5-41 68 { Brown-red very deep,almostblack. •Pale yellow. rio 281 5-53 70 Deep violet. Pale yellow. 11 306 602 77 Indigo. Clear yellow. 12 332 6-53 84 Blue. Brilliant yellow. \ 13 430 8-46 110 Greenish-blue. Yellow-orange. 14 505 9-84 130 Bluish-green. Reddish, orange. 15 536 10-55 138 Pale green. Warm red. 1 16 551 10-84 142 Yellowish-green. Deeper red. h; 565 1112 146 Green, clearer. Purple. 18 575 11-32 149 Greenish-yellow. Violet. 19 589 11-59 153 Vivid yellow. Indigo. -^20 664 1307 183 Orange. Blue. 21 728 14-33 200 Brownish-orange. Greenish-blue. 22 747 14-70 205 Carmine-red, clear. Green. L23 826 16-26 216 Purple. Clearer green. r24 843 16-59 221 Violet-purple. Yellowish-green. 25 866 1705 228 Violet. Greenish-yellow. J 26 910 17-91 240 Indigo. Pure yellow. 127 948 18-66 250 Deep blue. Orange. 28 998 19-64 263 Greenish-blue. Reddish-orange, vivid. [29 1101 21-67 290 Green. Violet-red, deep. 30 1128 22 20 298 j Yellowish-green. • Bluish-violet, clear, teinte de passage. J 31 1151 2266 • 305 Impure green. Indigo. 132 1258 24-76 334 Flesh-colour. Blue, greenish tint. 33 1334 26-26 354 Moderate red. Bluish-green (water- I34 1376 27-0'J 365 Violet. Brilliant green, [green). r35 1426 28-07 380 Violet-blue,grayish. Greenish-yellow. 36 1495 29-43 400 Greenish-blue. Rose-red. ^37 1534 30-20 410 Fine green. Carmme-red. 38 1621 31-91 432 Clear green. Purple-carmine. 39 1652 32-52 440 Yellowish-green. Violet-gray. r40 1682 33-11 449 Greenish-yellow. ! Gray-blue. 41 1711 33-68 468 Gray-yellow. j Greenish-blue, clear. 42 1744 34-33 468 Mallow. Bluish-green. 143 1811 35-65 486 Carmine. Fine clear green. 44 1927 37-93 615 Gray-red. Clear gray-green. L45 2007 3951 535 Gray-blue. Gray, almost white. * PoggendorflTs Annalen, vol. Ixxiv, pp. 461, 582, temporarily produced in Isotropic Bodies. 249 This table has served for all the experiments with white light ; the most sensible tints have been preferred, those which are found on the limits of the rings. But it is not always possible to push the experiments to so great a difference of path, partly because of the two great di- mensions of the piece, and partly because the substance will not support a notable compression without being bruised, cloven, or at least without being optically changed. This last alteration is observed in several crystallized bodies, and among others in rock-salt. It consists in a separation of the laminse of the cry- stal, which, though invisible to the eye, manifests itself in polar- ized light by permanent chromatic phsenomena, of such an inten- sity that they often predominate over the temporary effect of the charge*. In the experiments by means of traction, we are equally obliged to stop at small charges on account of the fragility of the mastic ; it was therefore indispensable to be able to measure small differences of path with a precision greater than that which appertains to the determinations made by means of the pale and not very sensible tints which are found at the commencement of the first ring. This object has been attained by the simultaneous employ- ment of two pressures, or of one pressure and one traction. We place under the press Aj, either the piece of crown glass which we have just employed, or another piece for which the charges producing the colours inscribed in our table have been pre- viously determined, and compress it until the teinte sensible appears. We then place the piece to be examined either in the press A^, or in the apparatus of extension B, and apply to it the feeble charge which it can carry without inconvenience. Look- ing now across the two pieces, we see that the teinte sensible has disappeared, and that it is replaced by a colour, more elevated, if the second piece be compressed, and by a colour inferior in the order of tints if the piece be elongated. In order to produce the teinte sensible, it is necessary, in the first case, to remove from the press A J a charge equivalent to that which has been applied to A^, and, in the second case, to add a charge equivalent to that which acts on B. We see that the press Aj then acts as a veri- table compensator, the sensibility of which may be regulated at pleasure by placing in it parallelopipeds which require charges more or less considerable. We may operate in a different manner by comparing the traction with the pressure; first, we apply the traction, and afterwards seek the charge which it is necessary to apply to Aj in order to reduce the difference of the paths to zero. This * Comptes Rendus, vol, xxxiii. p. 577. 260 M. G, Wertheim on the double Refraction method is more direct than the preceding one; but it often leaves more uncertainty, because of the invariably incomplete extinction of the image E. Suppose, in the first place, that two compressions had been combined. Let P„ be the charge which it is necessary to apply to the compensating piece placed on Aj, so that the double Pj and P, two equivalent weights, the first of which has been removed from the press Aj, and the second placed upon the press A^; Pj the weight sought, which produces in the piece placed on Ag the double refraction measured by ~ ; then we have . P P4= p-I*a. This formula applies equally to the traction ; only if we ope- rate according to the second method, which is that of the com- plete compensation of two double refractions. Pa represents the charge which produces, by pressure, the difference of path -^, These compensations also furnish us with a means of verifying the exactitude of an hypothesis which we have implicitly ad- mitted in the construction of our table. After having demon- strated that the differences of path which correspond to all charges may be found by means of intei'polations between the fixed points -^, ~, 2-^, 2-^ .... y we have afterwards made the same interpolations between 0 and ^ ; but this latter we were 2 not authorized to do, and the accuracy of the procedure has not thus far been verified, save by the coincidence of our determina- tions with the measurements of Newton. We can now fill this gap ; for this purpose we place in the two presses two pieces, for which the values P« and P/, have been previously determined by direct experiment. We compress the former up to the teinte sensible, and we determine afterwards the equivalent charges P, and Pg which correspond to the different double refractions comprised between 0 and -^ ; if between these two limits the optic compressibility is subject to any notable temporarily produced in Isotropic Bodies. 251 variation ; if, for example, it be greater between 0 and - than it \ X . . is between -: and rr, this variation will manifest itself in the successive values of P& which are found by means of our formula. If, on the contrary, the proportionality exists between these two limits, we shall obtain, by calculation, the same value of P^ that has been found by direct compression. The following table contains some of these determinations : — By direct measure- ment. Pa. P*. Equivalent weights. Calculated. P,. Pft. Two compressions, flint and crown.. , Two compressions, plate glass and crown Two compressions, crown and alum Compression and traction, crown and plate glass ... Compression and traction, crown and flint 140 r292 r 75 r 68 68 185 27 210 155 58 90 120 50 80 120 14 34 71 120 12 19 16 24 33 44 52 15-0 28-0 450 600 310 500 87-0 50 12-5 250 45-0 35-0 55-0 35-0 550 75-0 950 1150 650 67-0 700 700 1810 1820 187-0 26-8 27-6 26-4 281 1.98-0 197-0 1490 1560 1560 1470 1500 These examples are sufficient to enable us to form a judgement as to the exactitude of the procedure ; they show us at the same time the little variations of compressibility and extensibility which occur within the limits of the first half ring, and which we are to take into account in the construction of the curve which represents the route of the compressions and elongations. After the details into which I have just entered, I can in the subsequent portion of this memoir dispense with describing for each piece the whole series of operations to which it has been submitted, and confine myself to stating the charges which, by traction or pressure, have successively produced difiierences equal to ^, or to the length of a semi-undulation of the mean yellow ray. For example, I will designate by Tg - and Pg - the weights which it is necessary to add, so that the difference of path which was ^ may be equal to 2 jr, and so of the rest ; consequently the total charge will always be equal to the stum of the successive values of T and P. 252 M. G, Werthcim on the double Refraction a § 00 1 I ^2 m 32396 34714 26978 29923 •32593 25917 50932 Mean for each sub- stance. 1 ? fe § § QO 00 ^'"2 X . . . . » 00 CO 00 00 00 Oi « 3J © ©« © »0 .-N -"(J" OS QO >J» CO ^ d) 9» ^» CO ^« <>» t^ CO ob 00 © • Ji) ,^ U4 ^ *^ • M « - . - . _ :::::::: :^ ::::: : : • : t : : .«o . . . ; -^ • J • :::::;:;©b»cooo;;;: ; .M . . . «0 . . . . 2; i1< » t* to :^ : : : i" j«ioeow5eo»«oso»>». © b* (N (M C5 !>. «0 «>• O © »0 »>» CO 05 0» loosciocj u 00 U5 ©I 00 © -Tj* >*}< eo rp ©

»©*>.© (N ©© W5 ©© *>»00 «>»irs 05 CO CO eoco W5 «o © •Si ii '^ :©» :co'^«i«o*>»oo :oj© :•-• : ©i CO '«!< U5 «0 b» Y ■ "^ , . y ', 1 . 1 i • j o o -^ o ^ : v^ I'l sill c '3 o c j 3d It. temporarily produced m Isotropic Bodies, 253 3 -to s C6 Coeffi- cient of ticity. 57332 52031 55605 15197 38483 Mean for each sub- stance. to m ^ CO Cf3 -^ CO rf CO OS l->» I—I I-* > A A Jl. ?o^'«i-Ht>'icic>9'*«M«po5ep'7tcp05 '^coeo(N(N'^iH'^'«jco ^'" , i" •^TiJilJziitiJiilSi'*''* i'" ^ i i : :S : : : : i i : : -^^ : : : : i 'il« p^ •^ i i : :^ i : : ! H = : :^^ 1 i i = : i'- . . . 1 -^ i igS^ :::!:::• \%'^ : : : : : j pT ooooo oo »>» 00 «>. 1-^ ?0 . 90 0< pT 0000000000©0©©»0©00©©9> i '. I ', I I I ', I '. '. I I I ', '» ' \ ' I '• i i'" f ^ ©»>»W5l>»C0'*'«l« Ttf(NeO©©'-<-^-^»«(NCf)OS'^M S,-H,-(rH fH ri i-^ rl ■-( i-l i-t r-l(M fH i-i ^ %i ©(M t^ rf» rj* kC N '^ CO © -* f-H Cq ITS CO «3 CO 05 CO O irj »>» CO t>» CO CO (M U5 © QO u^ ->!# CO 00 QO «N »p CO 11 V V V 1 iili 1 IM = ill J 1&« 1 !si.2 g Us 1 1 1 1 E , Jl ^ -jBds-Jonij J '^IBS-JIDOH 264 M. G. Wertheim on the double Refraction All these substances are colourless, with the exception of the heavy flints and some of the fluorides of lime, and among these latter there are some possessing a tint so clear that the light, after having traversed a considerable distance of them, might still be regarded as sensibly white ; we have sought to neutralize the tinting of the others by glasses coloured with the comple- mentary tint. Another process consists in employing in the first instance the substance itself as a coloured glass, and deter- mining by the compression of a colourless glass the lengths of the undulations of the light which it transmits. We shall see immediately, that when once this length is known, it is easy to calculate the weight which it would have been necessary to em- ploy with white light. 1 have called inactive alum an alum procured from a manufac- tory at Muirancourt (Aisne), respecting the method of preparation of which I have been unable to obtain any information ; very limpid, not tarnishing in moist air, and preserving for years the polish imparted to its surfaces, natural or artificial ; this aluin possesses also the precious quality of being completely exempt from laminar polarization, notwithstanding the notable quantity of ammonia which enters into its composition. Even when a piece of this alum is pressed to crushing, the fragments exert no action on polarized light ; it also distinguishes itself from ordinary alum by its conchoidal fracture. The numbers which refer to rock-salt do not merit the same degree of confidence as the other numbers contained in the pre- ceding table ; notwithstanding all the care which I have taken to neutralize the pre-existent laminar polarization, and the per- manent tinting which exhibits itself on the application of the mechanical force itself, this cause of error, combined with the imperfect transparency of the substance, has necessarily rendered the determinations less sure and precise. I have cited in the foregoing table, among the crystals which belong to the regular system, only the species and the individual (if I may use the expression) which under the action of mecha- nical forces behave as homogeneous or isotropic bodies*. Experimental Laws, 1. The weight [necessary to be applied to produce a certain double refraction) is independent of the height of the parallelopiped. This proposition, evident of itself, is confirmed by all the experiments; to cite only one example, the value of P x is 2 the same for the two specimens of fluor-spar 21 (first experi- * See my notes on the artificial double refraction produced in crystals of the regular system (Coiwp^es Henrftw, vol. xxxiii.p.57/,and vol.xxxv.p.276). temporarily produced in Isotropic Bodies. 255 ment) and 22, although their heights are in the proportion of 1 to 2. 2. The weight is independent of the length of the piece. This law is demonstrated by the equality of weights applied to the pieces 1 and 2, 21 and 23, 31 and 32, &c., and it is con- firmed by the direct experiment of verification which follows. After having deterniined for the piece 10 the value of P, I cut the piece in two by a saw perpendicular to its length ; two pieces were thus obtained of the same transverse dimensions as the entire piece, but the lengths of which were 10*5 millims. and 22 millims. j each of these two parts, tested in both directions, required, to give the same tint as the entire piece of 35 millims., the application of the same charge as we have found for the latter. 3. For the same substance , the charges are proportional to this width of the pieces. We have verified this law by means of the charge P ^ x , which 2 has been determined for all the pieces ; in fact, the fifteenth column of our table contains the values of the ratio -— 1-, and these values are constant for the same substance, excepting such dif- ferences as may be attributed to slight variations in their density or structure. But the pieces 10 and 11 present a remarkable anomaly; both of them require greater charges when the smallest of their trans- verse horizontal dimensions is placed in the sense which we denominate as width. They furnish, therefore, for the ratio, values which differ among themselves, according to the direction in which the pressure has been applied. It must be remarked that these two parallelopipeds, as alsd the piece 12, have been obtained by a process csWedirefoulementj and which consists in compressing the glass while it is still in the condition of a paste, so as to make it take the form of the heated mould. The annealing is not always sufficient to cause the traces of this operation to disappear; hence it is that this glass, perfectly homogeneous in appearance, and which in polarized light shows only the gray cross which is attributed to its temper, is already, and in a permanent manner, compressed in one direction and dilated in the two others. Knowing the direction in which the pasty mass has been compressed, I have been able to convince myself, by these expe- riments and by others not included in the table, that the great- est charge always corresponds to the pressure apphed in the 266 M. G. Wertheim on the double Refraction direction of refoulement, that is to say, in the direction in which the molecules had been previously approximated. It might be supposed that this difference ought not to be ob- served except at the commencement of the experiment, and that a slight traction applied in the direction of refoulementj or a slight pressure in the directions perpendicular to the latter, would be sufficient to restore the equilibrium, and to bring the glass to the state of homogeneity which constitutes the true zero of the expe- riment. But, far from this, the difference exists under the greatest pressures, which proves that there is an alteration in the homogeneity of the matter, which does not manifest itself by any optic phsenomenon, as long as the body is not subjected anew to the action of mechanical forces. This fact appears to me to be very important, not only because it is in opposition to the opinion generally admitted, according to which all defects of homogeneity are indicated by an action on polarized light, but also because the same anomaly is often met with in crystals, and can furnish us with indications regarding the molecular pressures which such a crystal must have experi- enced at the moment of its formation. 4. The double refraction, or the difference of path between the two rays, is proportional to the mechanical lengthening or shorten^ ing, but these are not rigoroushj proportional to the charges. Taking for abscisses the weights, and for ordinates the shortenings and lengthenings which these weights produce, we obtain for the pressures a curve concave to the abscisses, and for the tractions a curve convex to the abscissa; these curves become less as the charges increase, and finally confound themselves ivith the same straight line, ivhich corresponds to the coefficient of elasticity gene- Tally adopted. Our last table shows the comparative route of the double refractions and the charges ; the value of P;^ is always the most T feeble, the charges augment afterwards up to Pa or P^x., and 2 2 from this point forward seem to rest stationary. The inverse takes place with the tractions ; the greatest values are those of Tx ; they diminish afterwards ; and although the experiments have not been pursued as far as those of compression, they suf- fice to show that the two curves approximate to one and the same straight line. Before going further, it will be necessary for us to resolve the following question : — Is there an absence of proportionality be- tween the double refraction and the purely mechanical effect, or between the mechanical effect and the charge ? temporarily produced in Isotropic Bodies. 'WSi I have attributed to the latter the cause of the observed dif- ferences ; these are my reasons : Mechanical force acts directly only upon ponderable matter ; the differences in the tension of the aether are only a secondary consequence of the differences of the molecular or mechanical tensions. The double refraction is necessarily a function of the temporary linear changes, and, for the same substance, the optic axes depend for magnitude and position on the principal mechanical axes. It is therefore neces- sary that the form of this function should change according to the intensity of the mechanical forces applied externally, and that it should change not only with the amount of the charges, but also with their mode of action ; since the double refractions differ among themselves according as the substance is compressed or elongated by the same weight, provided the latter does not exceed a certain limit. In the first case, we produce artifi- cially a body possessing negative double refraction, in which the extraordinary ray is propagated with greater velocity than the ordinary ; in the second case we obtain a positive body, in which ^ it is the ordinary ray which moves quickest. If, now, with double refractions of different magnitudes in the two cases, the mecha- nical shortenings and lengthenings were still equal to each other, it would follow that the ratio of the indices of refraction of the two rays would vary according as the one or the other moves quickest ; which conclusion is hardly admissible. It might be objected, it is true, that the double refraction does not depend upon the linear change which takes place in the direction of the force, but upon the difference between this latter and the changes of length which occur in the two directions perpendicular to that of the force, and that this difference, or what amounts to the same thing, that the law of change of volume might vary with the magnitude and the sign of the force applied ; but this would be a purely gratuitous hypothesis, without any fact to support it. On the contrary, we find a decisive proof in favour of the ex- planation which we have given, in the results of the direct mea- • surements of the elongations and compressions. It has often been observed, that the first elongations, which require the most feeble charges, are too small as compared with the subsequent elastic elongations. This remark has been made by M. Poncelet* with reference to the experiments of M. Ardant ; the same thing reproduces itself in my experiments and in those of Mr. Hodg- kinson. On the contrary, the first compressions obtained by the same author are generally too great; only, inasmuch as they refer to differences so small as not to be capable of mea- * Mecanique Industrielle, p. 347. PhiL Mac;. S. 4. Vol. 8. No. 52. Oct. 1854. S 268 M. G. Wertheim on the double Refraction surement with certainty, being of the same order in point of magnitude as the possible errors, no conclusion can be drawn from them. Our method causes all these uncertainties to disappear; we have already remarked, that with our parallelopipeds, which pos- sess on an average a section of 500 square millimetres perpen- dicular to the direction of the force, a difference of 1 kilogramme in the force translates itself into a sensible difference of tint. Let us say, for the sake of more certainty, 2 kilogrammes; supposing the coefficient of elasticity of the substance to be only 5000, the result is that a difference in the charge of 4 grms. per square millimetre, and a shortening or elongation of less than a millionth of the height, are sensible and measurable, while such quantities completely escape the direct modes of ex- periment. We can even double or triple the sensibility of our process by doubling or trebling the length of the pieces ; for with the same charge the tint remains the same, while the mechanical linear change will be only one-half or one-third of what it was. At the same time, we have the advantage of operating, not with bars several metres in length, but with small cubes, which enables us to avoid numerous causes of error. Dividing the values of P and of T by the length La, I have re- duced them to what they would be for a parallelopiped I millimetre in length, or what is the same thing (according to 1 and 2), to what they would be for a cube 1 millimetre the side ; the weights have been plotted on the axis of the abscissae, each division of which re- presents a kilogramme. The double refractions corresponding are represented by the ordinates, each division of which corresponds to a difference of path of ^^^th of a millimetre in the air. It is to these curves which we must have recourse whenever we wish to determine with precision the lengthening or shortening which corresponds to a feeble charge ; but we observe at the same time how little this curve deviates from the straight line which repre- sents the ordinary coefficient of elasticity. I have calculated, for all the pieces contained in the table, the ratios of the successive values of P and T. Assuming each value of P,\^ equal to 10 ; here follow the means of these quo- 2 tients*, which for the same difference of path differ very little from^each other : * I have not comprised in this mean the tractions which refer to the pieces 10 and 12, and which show that, in the sense in which the pressures become too small, the tractions, on the contrary, augment in an extraordi- narv manner. temporarily produced in Isotropic Bodies. 259 /^^x' V \' ^2^' ^3A_' ^4\' ^s\^' ^«x^' ^?\ 2222 2 22 22 10-64 10-85 10 10-34 10*42 10'75 11-01 10-88 11-02. The latter compressions deduced from a small number of ex- periments are probably too great ; we may assume that the first pressure PjX^ is to the definite values of P and T as 1 is to 1*08; 2 consequently, starting from the point where the double refrac- tions become proportional to the charges, we will multiply by this coefficient the numbers inscribed in the sixth column in order to find the constant augmentation of the charge. We give the name of coefficient of mechanical elasticity E to the ratio between the charge applied to the unit of surface, and the elongation or compression which it has produced in the unit of length. In a similar manner we will give the name of coefficient of optical elasticity C to the ratio between the charge applied to the unit of surface and the double refractions which it produces, taking for the unit of double refraction a diff*erence of path in the air equal to the unit of length. Let P be one of the mean values inscribed in the sixth column, we shall have for the coefficient of optic elasticity the following expression, C = P x 1*08 x - — ^^r^^s^ — ■ ; the different values of C have been carried into the seventeenth column. We might have represented by a formula of interpolation the route of the pressures and tractions ; but it might have been demanded whether the proportionality really exists beyond a certain limit, whether the curve becomes confounded with a straight line in all the rest of its course, and whether this takes place even when permanent changes of length add themselves to the temporary changes. The actual observations are still too limited to enable us to respond to these questions in an absolute manner ; however, I believe that I have elsewhere demonstrated that the coefficient of mechanical elasticity increases and diminishes with the density of the substance. Now, according to the law of changes of volume, the compression augments the density, while the trac- tion diminishes it ; the curve thus appears to prolong itself at both sides to the two points of rupture, by tearing and by crushing. The results which we have just obtained are of no practical importance in constructions ; these differences are too small to be taken into account in the employment of materials, and our S2 260 On the double Refraction produced in Isotropic Bodies, experiments prove that we might safely continue to make use of the s.une coefficient of elasticity in calculating the effects of trac- tions and of compressions. But the results acquire a great importance when they are regarded from the point of view of the theory of molecular forces, or those of mechanical oscillations, or of sonorous vibrations ; I believe that they will furnish the solution of a certain number of questions which have hitherto rested in suspense, and to which I propose to return on another occasion. 5. The difference d 0/ the path passed over is independent of the length of the undulation \; hence the dispersion of the double refraction is insensible. The charges P are proportional to the differences of path between the limits which we have defined ; hence, if our propo- sition be true, we ought to have the equation in which X and V are the lengths of the undulations of two simple rays, and P, P' the chai'ges which must be applied to the same parallelopiped to obtain extinctions of the same order in the one or the other image. This equation is already in part demonstrated by the deter- mination of the fixed points which we have made use of in the construction of our table ; to verify it between the widest limits, I thought it necessary to make some observations with the red and violet rays. I have employed successively red glasses of two descriptions ; experiment itself showed me that neither of the two was rigour- ously monochromatic ; but in placing them one above the other, I have obtained a deep red colour without any trace of other rays. The violet light was obtained by the passage of white light through a solution of the ammoniacal sulphate of copper; the light transmitted still contained some yellow rays. We shall now make use of our experiments to determine the colours of the spectrum, assuming for point of comparison the mean yellow ray Xy=550. On some Extensions of Quaternions. ' fSS m ■■ Weights applied with the light. Ratios. Substances. No. Violet. White. Salt and alco- hol. Red. V 0 y r s' ^\- 52 68 74 78 0-765 1-088 M47 56 74 79 87 0-757 1-068 1176 Crown of Clichy. 8- 2 V 58 74 80 89 0-784 1081 1-203 i V ... 74 81 88 1-095 1-189 ■V 2 128 155 ... ... 0-826 Flint 1'1< 2 107 140 145 182 0-764 1036 1-300 120 146 155 190 0822 1-062 1-301 2 120 145 167 189 0-828 1-152 1-303 2 ... 185 ... 222 1-200 Flint 13. 2 V 2 ... 190 233 1-226 Mean ... ... ... 0-792 1-083 1-227 Consequently we have \ „=4 36: K=t )96: X, = 6 75, These numbers show that the solution of the sulphate of cop- per transmits rays of the line G, which is found at the limits of the indigo and violet; that the light of saline alcohol corre- sponds sensibly to the line D ; and finally, that the two super- posed red glasses transmit rays which are found in the spectrum far beyond the extreme red of Fresnel, without attaining, how- ever, the extreme red of Fraunhofer. [To be continued.] XXXIV. On some Extensions of Quaternions, By Sir William Rowan Hamilton, LL.D., M.R.I.A., F.R.A.S., Correspond- ing Member of the French Institute, Hon. or Corr. Member of several other Scientific Societies in British and Foreign Coun- tries, Andrews* Professor of Astronomy in the University of Dublin, and Royal Astronomer of Ireland, [Continued from p. 137.] [17.] '^T^HE following remarks may be useful, as serving to A illustrate and develope the general analysis con- 262 Sir W. R. Hamilton on some tained in some of the preceding paragraphs, especially in [14.], and as adapted to give some assistance towards any future study of associative polynomes, such as quines, of an order higher than quadrinomes, but subject like them to the law of conjugation (32). The expression (98) may be thus more fully written : (f) = {f^ef + (feg){fye)+S{feh)(fke); . . (112) where efgh are all supposed to be unequal ; the summation ^ being performed relatively to h, for all those w — 3 values of the latter, which are distinct from each of the three former indices. Interchanging e and ^, and subtracting, we eliminate the symbol (/), and obtain the following formula : I- (feeY-(fggf=T{(fymhg)-(feh){fhe)}; (113) which type I. includes generally n[n—2) distinct and homo- geneous equations, of the second dimension, with 2(w— 2) terms in each, between the ^n^{n—\) symbols of the form (fgh). Thus, for the case of quadrinomials (w=3), by writing, in agreement with (82) and (83), «, = (!), ^ = (23), /i = (231), ;/z, = (313), 7.j = (122), (114) and suppressing the sum S\ we have by (112) the two expres- sions (compare a note to [12.]) : a^-=m^—lj,^=n^^ — ljt^; .... (115) together with four others formed from these, by cyclical permu- tation of the indices 1, 2, 3 ; and we are thus conducted, by elimination of the three symbols «,, a^, a^, to three equations of the form n^^=m^'^; that is, to the 3 equations on the first line of (86), involving each 2 terms. For quines {n=4), if we make also, with the same permitted permutations, «, = (4), c, = (14), j».= (334), \ r, = (141), *, = (142), <,=(143), «, = (144),J the index h receives one value under each sign of summation S\ and the resulting formulae may be thus written : (a^■\-lJ^-j-p^t^-s^p^=:^)n^^^ip^t^ = m^^s^P3=u^^-^lsIc,; (H^) where the line (117) is equivalent to three lines of the same form : so that the elimination of Oi . . a^ conducts here to 8 equa- tions, of 4 terms each, between the 24 symbols of the form {fyh), or 1 1 . . Wg, as by the general theory it ought to do. For poly- nomes of higher orders (n > 4), we have the analogous equations, (/) - iMifff") -(M) ifkg) - {fke) ifek) = (/««)' - ( /y*) (#y) + S ' (M)iM = (fgg?-(fkc)(fek)^-X\fgh){fkj) =(fkkf-{fcg)(fge)^X\fkh)(fhk); . (119) Extensions of Quaternions. 263 where h, under S'\ receives only «— 4 values, being distinct from each of the four unequal indices, efgk. [18.] By changing e to f'm (95), and attending to the pro- perties of the symbols {fgh), we obtain the expression (fg)='Z{fgh){hff); ..... (120) where / and g are unequal, and the summation 2 extends from h-=\ to h=n. The term for which A =/ vanishes, and the for- mula (1 20) may be thus more fully written : {f9)-{f9eWf) = {f9g){sff] + S(fgh){hff); . (131) where the letters efg denote again some three unequal indices, and the summation 2^ is performed as in the foregoing para- graph. But also, by (97) and (100), {fy)''iM{eff) = (fee){gee)-^T{feh){ghe); . (122) subtracting, therefore, (122) from (121), we eliminate the sym- bol {fg)f and obtain the type II. (fee) {gee) - (fgg){gff)=X { (fgh) [Jiff) -(/eh)(ghe) }; (123) which represents in general a system oi n(n — l)(n—2) distinct and homogeneous equations of the second dimension, containing each 2{n—2) terms, and derived by eliminations of the kind last mentioned, from the formulee (95), (97), (100), in a manner agreeable to the analysis of paragraph [14.]. Indeed, it was shown in that paragraph, that the equation {fff)={fg), (100), though known from earlier and simpler principles to be true, might be regarded as included in (95) and (97) ; but this need not prevent us from ming that equation in combination with the others, whenever it may seem advantageous to do so : and other combinations of them may with its help be formed, which are occasionally convenient, or even sometimes necessary, although all the general results of the elimination of the symbols {fg) are sufficiently represented by the recent type II., or by the for- mula (123). For example, a subordinate type, including only ^n{n—l){n—2) distinct equations, of 2(7* -—2) terms each, be- tween the symbols {fgh), may thus be formed, by subtracting (95) from (97), under the condition that efg shall still denote some three unequal indices ; namely, 0='S.{ifeh){ghe)-{geh){fhe)}; . . . (124) or more fully, but at the same time with the suppression of a few parentheses, which do not appear to be at this stage essen- tial to clearness, {fge)(eff+egg) = X(geh.flie-feh.ghe): . (125) this last formula admitting also of being obtained from (122), 264 SirW. H. llamilroii on some by interchanging / and e);S where e under the sign 2' is distinct from each of the two indices y* and ^; but, under the double sign 2S, both e and /* may each receive any one of the values from 1 to n. The two double sums are equal, as in [14.], and therefore we must have, identically/, [M + ^'[M = [fffi +-^'l<)fe] : . ■ (132) the equation (100) being at the same time seen again to be a Extensions of Quaternions. 266 consequence, by simple additions, of the form ulse (95) and (97). Thus, after assigning any two unequal values to the indices/ and ff, we see that the two symbols, {fy), [gf) ; the two others, r^], [gf] ; the n—2 symbols, [fge] ; and the n — 2 symbols, Igfe], are indeed all equal to each other: but that the 2n—l equations between these 2n equal symbols are connected by a relation, such that any 2n — 2 of them, which are distinct among themselves, include the remaining one; and that therefore, after the elimination of [fg) and {gf), there remain only 2(n— 2) distinct equations of condition, as was otherwise shown in [14.] . But, in that paragraph, we proposed to form those resulting con- ditions on a plan which may now be represented by the formulae U9] = U9e'\, [^/] = [^M; • • • 033) whereas we now prefer, for the sake of the convenience gained by the disappearance of certain terms in the subtractions, to employ that other mode of combination, which conducted in [18.] to the formula (123), and may now be denoted as follows : U9l = lgM, [9n = if9e'\. ■ ■ ■ (134) Summing these last with respect to e, we find («-2)[/^]=2'[^/«]> {»-2)[^/]=2'[^«]; . (135) and therefore, by the identity (132), ('»-3)[<;/] = (»-3)[/^] (136) If, then, n^S, we are entitled to infer, from (123) or (134), the following formula, which is equivalent to (126), Q?/] = M; (137) and therefcre also by (134) this other type, equivalent to (124)> LM^lfffil (138) which includes n—2 equations, when/ and ^ are given, and conducts, reciprocally, by (132), to (137). In general, therefore, if we adopt the type (134), we need not retain also either of these two latter types, (137), (138). But in the particular case where n=S, that is, in the case of quadrinomes, the identity (132) reduces the two equations (134) to one, after/ and ^ have been selected ; and with this one we must then combine either of the two equations (137) or (138), which in this case become iden- tical with each other. [20.] In particular, for this case of qudrinomials (^^ = 3), we have with the notations (114) (128), the four following values for (23), or for ^j (compare again a note to [12.]) : (139) 266 Sir W. R. Hamilton on some [23] =231 . 122 + 233 . ^22^l^n^-n^m^', [231] =211. 311+231. 313= --?W2"3 + A^u [32]=321.133 + 322.233 = /,m,-?n3W2; [32]]=311. 211 + 321. 212=-WgW2 + /i/i,;. but, whether we equate the first to the fourth, or the second to the third of these expressions for Z>j, in conformity with the type (134), we obtain only one common equation of condition, WjWig = W37W2, equivalent indeed by cyclical permutation to three, namely to the following, 0 = WgWg — n^m^ = WgWi, — n^m^ = n^m^ — n^^ ; . (140) which evidently agree with certain simple combinations of the six equations on the two last Hnes of (86) . If however we com- pare either the first value (139) with the third, or the second of those values with the fourth, according to the type (137) or (138), we find by each comparison the common condition l^n-^=^l^m^, and thus recover the three equations of the first line of (85). In this way then we may obtain the required number of six distinct equations, with two terms each, between the nine symbols [fgh), or /, . . . Tig, for the case of quadrinomes, by elimination of the three symbols [fg), or of ^j, Z>2, b^. [21.] For the case of quines (w=4), the general theory requires that the corresponding elimination of the 6 -^n[n — \) symbols of this form [fg), or b^ ., » Cg, should conduct to 24=n(7i~l) (w — 2) distinct equations of condition, with 4=2(w — 2) terms each, between the ^n^(/i~l) = 24 symbols of the form (fgh), or /, . . . Wg, each equation thus obtained being homogeneous, and of the second dimension ; and that all these 24 conditions should be included in the formula (134), or in the single type (123). And in fact we thus obtain, by comparison of the six expressions for ij, of which one is Z,, = (23) = [23]=2;(23A. A22) = /i7ii-W2mg-j3ir2, (141) the four following equations of condition, included in that type or formula : 0= [23] - [321] = [32] - [231] H 0= [23] -[324] = [32] -[234]; J * * ^ ^ that is, with the notations /j . . t/g, n^m^ + WgWg =J03*3 + llm^ = l^n^ —p4*t Part I. — On the Elastic Forces of Vapours at Saturation in vacuo. I shall not stop to describe the processes which I have em- ployed in determining the elastic forces of saturated vapours in vacuo. These processes are similar to those applied by me to the vapour of water, which are described in detail in vol. xxi. of the Memoir es de VAcademie. Nor do the limits assigned to this note allow of my giving the immediate results of my determinations, which are very nume- rous. I shall merely give the elastic forces at every 10° C. of the following liquids, which I have studied between the most ex- tended limits. These are alcohol, sether, sulphuret of carbon, chloroform, and essence of turpentine. Tensions of the Tensions of the Sulphuret of Chloroform by Essence of tur- vapour of alcohol. vapour of sether. carbon. tension in vacuo. pentine. o mm mm „ mm mm mm - 21 312 - 20 69-2 - 16 58-8 + 10 1304 0 2-1 - 20 3-34 -10 113-2 - 10 79-0 20 190-2 10 2-3 - 10 6-50 0 182-3 0 127-3 30 276-1 20 4-3 0 12-73 10 286-5 10 199-3 36 3422 30 70 10 24-08 20 434-8 20 298-2 40 11-2 20 44-0 30 637-0 30 434-6 By the method 50 17-2 30 78-4 40 913-6 40 617-5 of ebullition. 60 26-9 40 134-10 50 12680 50 852-7 70 41-9 50 220-3 60 1730-3 60 1 162-6 ... 80 61-2 60 3500 70 2309-5 70 15490 36 313-4 90 91-0 70 539-2 80 2947-2 80 2030-5 40 3640 100 134-9 80 812-8 90 3b99-0 90 2623-1 50 524-3 110 187-3 90 1190 4 100 4920-4 100 3321-3 60 738-0 120 257-0 100 1685-0 110 6249-0 110 4136-3 70 976-2 130 3470 110 2351-8 116 7076-2 120 5121-6 80 1367-8 140 462-3 120 3207-8 lao Q2m-Q 90 1811-5 150 604-5 130 4331-2 ... 136 7029-2 100 2354-6 160 777-2 140 5637-7 110 3020-4 170 989-0 150 7257-8 ... 120 38180 180 1225-0 152 761 7-3 ... ... 130 47210 190 200 210 220 222 1514-7 1865-6 2251-2 2690-3 2778-5 These results have been obtained, either by the determination of the elastic forces in vacuo, or by determining the temperature of the vapour of a boiling liquid under the pressure of an 272 M. V. Regnault on the Elastid Forces of Vapours artificial atmosphere. The former method has been followed for the low temperatures; the second has been exclusively employed in the high temperatures. In all cases they are arranged in such a manner that the curves of the clastic forces given by the two methods should present a common part by which we may judge of their coincidence. I have already shown, in my memoir on the elastic force of water vapour, that this coincidence is exact in the case of water, the two methods giving perfectly identical results. I have ascertained that the same is the case with other volatile liquids, provided they are in a state of perfect purity. When a liquid contains even an ex- tremely small portion of another volatile substance, the two methods give different values for the elastic force of its vapour at the same temperature ; so that this furnishes an extremely delicate means of judging of the homogeneity of a volatile body. Sulphuret of carbon is easily obtained in a state of purity, but the same cannot be said of alcohol and aether. As to chlo- roform, whatever care may be taken in its preparation, it always contains several intermixed substances, which it is impossible to separate by fractional distillation even when operating upon large masses. The vapour has a different elastic force and a sensibly different density, according as the first or the last products of distillation are operated with. Chloroform has also constantly given different values for its elastic force at the same temperature, according to the method by which it was determined. This cir- cumstance is easily seen from the preceding table, in which 1 have only given a single series of the experiments which I have made upon chloroform. Some liquids become modified in their molecular constitution when boiled for a long time under high pressures. It thus often happens that at the end of a series of experiments the liquid is found not to have the same boiling-point under the ordinary pressure of the atmosphere as at the commencement. Essence of turpentine offers a remarkable example of this. Thus, a con- siderable quantity of the essence (30 or 40 litres) having been boiled for several hours under a pressure of 7 to 8 atmospheres, became almost completely converted into a liquid which boiled at a temperature above 230° C. under the ordinary atmospheric pressure. I put this modified liquid aside in order to deter- mine its nature, but it has since been thrown away by mistake. Other liquids appeared to undergo molecular modifications, rendered sensible by the tension of their vapours, when left by themselves for a longtime in hermetically closed tubes. iEther has presented me with a curious example of this. I shall return to this subject on another occasion. I may remark, in conclusion, that the method of ebullition in . in vsicvio and in Gases, nic^il / }/i 273 artificial atmospheres, the thermometers being immersed in the vapour, necessarily gives accurate results for homogeneous liquids when the actual pressure is exactly determined ; for it is by this method that the boiling-point of thermometers is fixed. But vv^hen solutions of fixed substances in volatile fluids, or mixtures of several unequally volatile matters are in question, the tension of the vapour may be very difi'erent according as it is determined in the static condition, if I may use the expression, — the vapour and the volatile liquid being both immersed in a medium of invariable temperature, — or in a dynamic state^ under the influ- ence of a current of heat which traverses the apparatus, the liquid receiving the heat which produces the vaporization, whilst the vapour is subjected to refrigerating agencies which produce its partial condensation. The limits which I am compelled to observe in this note prevent me from giving further development to these considerations. Part II. — On the Boiling-points of Saline solutions. Everyone knows that saline solutions require a higher tempera- ture to boil them than pure water under the same pressure. For a given salt the excess of temperature increases in proportion to the quantity of matter dissolved. All soluble substances do not possess in the same degree the faculty of retarding the boiling- point of the water in which equal weights of them are dissolved. This faculty does not depend only upon their solubility; it appears to result principally from a special affinity of the substance for water. Rudberg has made the very curious observation, that when concentrated saline solutions are kept boiling at temperatures much above 100° C. under the ordinary pressure of the atmo- sphere, the vapours which they emit nevertheless only possess the temperature which they would present if they were disen- gaged from pure water in ebullition under the same pressure. Rudberg has made a great number of experiments on the most various solutions, and with very exact instruments. The con- clusion which he has drawn from them is as follows : — Whatever temperature a solution must attain before boiling, the vapour never presents a higher temperature than that which it would have had if it had been disengaged from pure water ; in other words, it presents the temperature at which the tension of this vapour, at saturation in vacuo, is in equilibrium tvith the pressure under which the ebul- lition takes place. This conclusion must of course refer, not only to the saline solutions experimented upon by Rudberg, but also to all solutions in a volatile liquid of substances which are fixed at the temperature of its ebullition. It is not difficult to account for this circumstance, that a saline PML Mag. S. 4. Vol. 8. No. 52. Oct. 1854. T 274 M. V. Regnault on the Elastic Forces of Vapours solution must boil at higher temperatures than the volatile liquid alone. Thus it may be conceived, that when the pure volatile liquid is submitted to the action of heat, its molecules, in order to assume the state of vapour, have only to overcome the external pressure to which they are subjected, and the adhesion or special affinity which they possess for the similar molecules which retain the liquid form. In the case of a saline solution, on the other hand, the molecules which assume the form of vapour have also to overcome the attraction exerted upon them by the particles of the dissolved substance, an attraction which is generally greater than that arising from similar particles. It is consequently necessary for the development of vapour that the fluid medium should assume a higher temperature than if it consisted solely of the volatile substance. But I do not so clearly perceive how the vapour, at the moment of its disengagement from the liquid, should possess a much lower temperature than that of the last strata of liquid which it has just traversed. I admit that the vapour, at the moment of its formation in the midst of the solution, possesses an elastic force greater than that which gives an equilibrium to the external pressure, since it must also overcome the attractive force of the saline particles. But as soon as this vapour has collected in a bubble rising through the liquid, it must expand, and only pre- serve the elastic force which is necessary to place it in equili- brium with the hydrostatic pressure which it experiences in the stratum of liquid in which it is at the moment, and with the capillary action of the liquid walls of the bubble, an action which diminishes in proportion as the bubble acquires greater develop- ment. I admit that, in consequence of this successive expansion, the temperature of the vapour must be lowered ; but as the bubble is surrounded by a hotter liquid, this ought constantly to furnish the heat which is lost by expansion ; and the bubble, on issuing from the liquid, ought to present an equilibrium of tem- perature with this. To explain Rudberg^s law, it is necessary to assume that the vapour, as long as it remains in the midst of the boiling liquid, possesses, in consequence of the attraction of the saline particles, a greater density than corresponds under the same temperature with the hydrostatic pressure exerted upon it ; and that it only assumes its normal density at the moment when, escaping from the liquid, it is relieved from this action. The vapour would then experience a sudden dilatation, which would cause the excess of heat to become latent, and bring it exactly to the tem- perature at which its elastic force is in equilibrium with the atmospheric pressure. But, on the one hand, it is necessary to admit that this excess in vacuo and in Gases. 275 of density continues, whatever volume the bubble may acquire in rising through the liquid ; for I have ascertained that the tem- perature of the vapour is the same, whether the solution boil quickly or slowly, and that it is also the same when the liquid rises to a great height above the heated bottom, although in this latter case the bubbles often acquire a very considerable volume before bursting at the surface of the liquid. On the other hand, in order to explain the great diminution of temperature undergone by the vapour at the moment of its escape from a boiling solution strongly impregnated with certain salts, admitting the results which I have obtained as to the quantity of heat which becomes latent by the expansion of elastic fluids, we must suppose that the bubble of vapour whilst still in the midst of the fluid, experiences a very considerable excess of compression, much greater, indeed, than can reasonably be admitted. I have, however, instituted some experiments with a view to ascertain whether the fact proved by Eudberg arises from a general law, such as that enunciated by him, or whether it must be attributed simply to the circumstances under which his expe- riments were made. I first of all wished to ascertain whether this phsenomenon is presented with the same constancy when saline solutions are boiled under pressures very different from the ordinary atmo- spheric pressure, for all Rudberg's experiments were made under the latter. I made use of the small copper boiler in which I made my former determinations of the elastic force of the vapour of water {Mem. de VAcad. vol. xxi. p. 515). The lid of this boiler is traversed by four tubes hermetically closed at their lower extremities ; two of these tubes descend into the boiling fluid, and the other two reach no further than the vapour. These tubes contain a small quantity of mercury, in which the reser- voirs of the thermometers are immersed, so that these are thus protected from the internal pressure. The disengaging tube of the boiler communicates with a refrigerator, which serves to condense the vapour ; and this refrigerator itself communicates with a large reservoir of air, of which the pressure may be varied at will. Into the boiler I put concentrated solutions of chloride of cal- cium, which I caused to boil under pressures sometimes weaker, sometimes stronger than the ordinary pressure of the atmo- sphere, and noted the temperatures indicated simultaneously by the thermometers immersed in the vapour and those which de- scended into the liquid. The results obtained are given in the two following tables, of which the second refers to a solution containing a larger quantity of salt. T2 276 M. V. Regnault on the Elastic Forces of Vapours Table I. Pressure) under Temperature of whicl) the tem- peratures are atuined. Temperature of \ Temperature of the liquid. i the vapour. 1 the vapour of distilled water under the same pressure. mm O 1 o 82-52 52-0 I 47-88 47-84 136-61 61-58 : 58-20 5816 21944 71-80 ' 68-73 68-61 286-43 1 74-94 74-84 43419 87-54 85 09 85-07 75722 i 99-88 99-90 180715 129-86 ' 126-63 126-16 2182-35 136-30 1 132-92 132-42 2702 13 ' 142-79 1 140 35 13981 3123-69 14791 145-57 145-00 Table IT. 57-83 41-15 41-00 58-45 41-25 41-17 5909 4141 41-37 13307 57-78 57 63 198-25 .::.■:: 66-46 66-31 198-41 78-45 66-50 66-35 282-92 79-1 74-65 74-17 283-68 7472 74-59 362-49 85-i" 80-65 80-56 479-17 91-1 87-68 87-59 754-71 1022 100-00 99-81 The inspection of these tables shows that the thermonuiter immersed in the vapour constantly indicates a temperature a little higher than that of the vapour of pure water under the same pressure ; but the difference is small, and may perhaps be attri- buted to the radiation of the hot liquid and the drops of fluid which are thrown up in abundance by saline solutions during ebullition. As to the thermometers which descend into the boiling liquid, their course is extremely irregular, presenting rapid variations which often rise to several degrees. It is im- possible to deduce anything certain from the indications which they furnish. It may consequently be admitted that the phaenomenon ob- served by Rudberg with regard to saline solutions in ebullition under the ordinary pressure of the atmosphere, is also presented when they are boiled under pressures greater or less than this. To observe more readily the circumstances under which the phenomenon occurs, I made some experiments in a glass balloon with a wide mouth, upon mixtures of water and sulphuric acid in in vacuo and in Gases. 277 variable proportions, taking care never to add sufficient sulphuric acid to allow any portion ofthat substance to pass by distillation. Into the neck of the balloon I fitted two wide copper tubes, placed one within the other like the tube of a telescope. The upper tube carried towards its summit two lateral tubulures, affording an exit for the vapour ; its upper orifice was closed by a cork, through which the stem of a very sensitive thermometer was passed. By this arrangement it was easy to place the bulb of the thermometer in any region of the balloon, still keeping the entire mercurial column in the vapour. Operating in this manner, it is soon seen to be impossible to find any position in the balloon, where the bulb of the ther- mometer does not constantly get covered with water, which falls back, drop by drop, into the boiling liquid. Now every one will understand that if the instrument be constantly moistened with condensed vapour, it can never indicate a higher tempera- ture than that at which the pure liquid boils under the same pressure. It is therefore evident that no experiment in which the thermometer becomes wet can prove anything in favour of Rudberg's law ; and there can be no doubt that this has taken place in the experiments of that physicist. The greater part of the water which runs down the thermome- ter is produced by condensation on the upper part of the stem. In order to prevent this water from reaching the reservoir, I attached to the stem immediately above the reservoir a very thin metallic disc, which collected it ; a second similar disc, attached to the former by means of thin wires hung below the reservoir, so as to protect this at once from the radiation of the super- heated liquid and from the drops of the solution which are always projected in abundance by boiling liquids. The bulb of the thermometer was not more than 8 millimeters in diameter. Even with this arrangement it is very difficult to place the thermometer in such a manner as that the bulb shall not be- come wetted. As long as the bulb is at a distance of more than 3 or 4 centimeters from the boiling solution it always becomes wet, and then it can never indicate any other temperature than that of the ebullition of pure water. But when it is lowered so as to go nearer the liquid, the temperature rises, the reservoir at the same time becoming dry. The temperature thus continues to rise until the bulb touches the liquid. The region of the balloon in which the thermometer indicates a temperature above that of pure boiling water, may usually be recognized even by sight ; it is that in which the inner walls of the balloon remain dry, whilst the upper portions of its walls are always moistened by condensed drops. The height of the stratum of super-heated vapour depends upon the temperature 278 M. V. Regnault on the Elastic Forces of Vapours of the boiling liquid, and especially upon the briskness of the ebullition. The observations which 1 have just described confirm the fact announced by Rudberg, but it appears to me that they also show its cause ; for whenever the thermometer only indicates the temperature under which pure watery vapour is in equilibrium with the external pressure, we find that the reservoir is wet. On the other hand, the instrument shows a higher temperature when its reservoir is dry, a condition which I have only been able to realize in the strata of vapour immediately above the super-heated liquid. I think, therefore, that the vapour, originating in boiling saline solutions, is equal in temperature to them, and does not possess an elastic force much superior to the hydrostatic pressure which they exert upon it. If the temperature of this vapour be suddenly lowered to the degree which corresponds with its satu- ration under this pressure, this arises from the circumstance that in consequence of the small capacity for heat possessed by vapours in comparison to their volume, the excess of heat is rapidly absorbed by external refrigerating causes, and especially by the vaporization which acts upon the infinity of minute liquid globules, which are constantly projected into the atmosphere of vapour, at the moment when the bubbles burst at the surface of the boiling liquid. I have determined, with several aqueous solutions, the tempe- rature to which they must be raised in a manometric apparatus, in order that the vapour, thus produced in vacuo, should be in equi- librium with a pressure of 760 millimeters. The excess of this temperature over that of 100° C. which would give water vapour this tension of 760 millimeters, if it were in presence of pure water, may seem, as M. Pliicker has lately pointed out, to mea- sure the excess of afiinity possessed by watery vapour for the saline substance, in comparison with that which it presents for the similar particles of water. But in order that this afiinity, thus measured, may constitute a specific character of the sub- stances, it is necessary that it should vary in proportion to the quantity of the same salt in the solution. Now I have found that this is not the case ; the variation follows a more complex law, which appears to depend upon the nature of the salt. I attach particular interest to the comparison of the tempe- rature at which the vapour given off^ in vacuo by a saline solution is under a pressure of 760 miUimeters in equilibrium, with the temperature presented by the same solution when boiling under the same pressure. Unfortunately, it is nearly impossible to determine, with any degree of precision, the boiling-point of a concentrated saline solution. The ebullition is always irregular ; in vacuo and in Gases, -^^^^u ^.fvr. 279 it proceeds by jerks and starts, and the thermometer indicates sudden variations, which sometimes exceed 10° C. We know besides that the temperature of ebullition varies according to the nature of the vessel and the form of its walls. The ebullition of a liquid is a very complicated phsenomenon, especially when the liquid is not homogeneous. Molecular forces, of which the nature is still but little known, play an important part in it. It is impossible to get rid of these complex actions, and only take into consideration, in the study of this phsenome- non, the pressure of the external atmosphere and the temperature of the boiling liquid. But if it be nearly impossible to deduce any certain results from the determination of the temperature of ebullition of saline , solutions, it is very different with the elastic forces of the va- pours given off by these solutions in vacuo. These may be de- termined with great precision, and I have no doubt that the study of them will hereafter furnish a most valuable means of ascertaining the chemical phsenomena which take place in solu- tions. I have convinced myself, in fact, that as soon as a phse- nomenon of this nature takes place with dissolved substances, it betrays itself by a singular point in the curve of the elastic force of the vapour furnished by the solution. I shall give a few examples of the phsenomena which may be studied by this method. It is well known that certain salts crystallize from their aqueous solutions with different amounts of water, according to the tem- perature at which crystallization takes place. We may inquire whether this water combines with the salt in the midst of the liquid, or whether the combination only takes place at the mo- ment of crystallization. The sulphates of soda, iron, copper, manganese, &c. present very curious examples of these modifica- tions. It will be interesting to compare the variations undergone by the elastic force of the vapour furnished by a saline solution at different temperatures, with the variations in the solubility of the salt under the same circumstances. Lastly, when we shall have ascertained the law by which we may calculate the elastic force of the vapour furnished by the mixture, in known proportions of two solutions which exert no chemical action upon one another, from the elastic forces of the vapours given off by the separate solutions, we shall be able to ascertain whether double decompositions take place in the solu- tions themselves, or only at the moment of precipitation. These examples, which I might readily multiply, will suf- fice to show that the study of the elastic forces of the vapours given off by solutions, will furnish a most valuable mode of in- 280 Sir J. W. Lubbock on a Graphical Method of vestigation in the study of a multitude of phsenomena in mole- cular chemistry ; the results to be anticipated from which may be as important as those which M. Biot has deduced from the study of rotatory polarization. This method, besides, will pos- sess the advantage of a more extended application. In regard to these subjects, I have only been able to make a series of observations upon the sulphates mentioned above. Notwithstanding the lively interest which I attach to re- searches of this nature, I have been compelled to abandon them for the present, as they would have led me too far from the principal object towards which my efforts must be directed. [To be continued.] XXXVI. Note on a Graphical Method of clearing a Lunar Distance. By Sir J. W. Lubbock, Bart., F.R.S. ^c* BY the principles of the Gnomonic projection, to delineate an arc of any given number of degrees beginning from any given point S and in any given direction SR, the following construction obtains. Let CPV be drawn per- pendicular to the line PR through C the centre of the picture, and make VP in CP produced = V~WT~CW, D = CB being the distance of the picture. D is"a constant quantity, and is to be taken of any convenient length. At V make RVS equal to the given angle. RS is the re- quired delineation. In order to find graphically the angles A B Cof a spherical triangle, of which the sides a, b, c are given, we have — 1st. To delineate the triangle correctly by the rules of per- spective. 2nd. To ascertain the values of the original angles by means of their delineations in the picture. Suppose, for example, we have the apparent zenith distances or altitudes of two stars Sj, Sg, and their apparent angular distance ; if we place Z the zenith at C the centre of the picture, the following construction obtains for the accurate delineation of the spherical triangle SjCSg : — * Communicated by the Author. clearing a Lunar Distance. 281 Take CS, representing the apparent zenith distance ^"1 of Sj, CS. & and with radius CSg describe a circular arc EF. CSj and CSg are the natural tangents of fj, and fg to radius D. From ^1 draw any Une S^P, and lay down upon it SjK repre- senting the angular distance Sj Sg by the first rule. In this way one point is obtained of the conic section which represents the small circle described about Sg, whose intersection with the circle EF described with radius ZSg determines the place of Sg. In the same manner any number of points in the conic section may be found ; but as it is easy to see very nearly where Sg is situated, it will generally be sufficient to find two points on the conic section in the presumed vicinity of 85, and the intersection of a straight line joining them with the circle will give the place of 83 very nearly. The locus of the point P is a circle described with radius |S|C, and the locus of the point Y is a circle de- scribed with radius S,V, SiV^zrSiC^ + D^. If R is near the true place of 83, Sg will be found nearly by the intersection of a cir- cular arc described with radius SjU and the circular arc EF. SjCSg is the accurate delineation in perspective of the spherical triangle SjZSg. To measure the angle ZSjSg, produce SjC to Q, making SiQ = 90°, by making S^BQ aright angle, and CB perpendicular to CQ=D. Draw QT perpendicular to S^Q, and in SjQ take QV= ^D2 + CQ^=BQ. Produce SjSg cutting QT in the point T and join VT, the original angle ZSjS^ is equal to QVT. 282 Dr. Barry oti the Mode of Origin of the Cell-membrane, As the correction in the distance for S, is approximately equal to the correction in altitude of Sj rnultij)lied by the cosine of the angle QVT, on VT take from scale the correction of S, in alti- tude = VM, draw NM parallel to QT, then VN is the correction in distance on the same scale approximately. In the same way the angle ZSjSj may be measured, and the correction of the distance due to the error of altitude of Sg may be found. When the point Z is placed at C the centre of the picture, the angle on the picture S,ZS2 is equal to the original angle SjZSg. The point Z may be placed anywhere in the picture, and the proper construction may be inferred from what precedes ; but then the circle described with radius ZSg will be replaced by a conic section, and the angle SjZS^ will not be equal to the original angle SiZSj. XXXVII. — I. An Attempt to show the Mode of Origin of the Cell- Membrane, and the Nature of tJie Earliest Pores. II. Remarks on the Article " Ovum " in the Cyclopedia of Physiology. By Martin Barry, M.D., F.R.S.* [With a Plate.] THE discoveries of Keber on the porosity of bodies have re- minded me of some drawings of mine from nature, which lie buried in two rows of figures at the foot of a Plate in the Phil. Trans, for 1841 f; — drawings which, from some remarks I made at the same time, it will be seen that I then believed to illustrate the mode of origin of the membrane of the cell J. Further, there being among those drawings one which has long seemed to me to present the earliest pores, I will reproduce a few of them on this occasion. There is first seen a large mother-cell. The nucleus of this divides into many parts — each part being itself a nucleus. From their origin in a mother-cell, these nuclei, after their liberation, are found in groups. They form cells, which are elliptical at first, become more spherical, and are often seen to be tapered at one end. (What the cells in question are, will be stated further on.) Plate II.* fig. A represents one of the nuclei now mentioned as arising from division of the nucleus of a mother-cell. It has a nu- cleolus. At B such a nucleus has become segmented, and that * Communicated by the Author, t Plate 25, figs. 164 to 173. X Phil. Trans. 1841, p. 243. § 193. See also in the same volume the description of figs. 1/0 and 171, in the explanation of the plates. and the Nature of the Earliest Pores. 283 which in A was a nucleolus has in B passed into the state of nucleus. The segments in B are nucleolated nuclei. Fig. C represents a stage somewhat more advanced ; the nucleus is vesicular (its nucleolus parietal). In D such segments as those at B and C have divided into groups of nucleolated nuclei, g. In fig. E some of these groups remain ; others have broken up into single nucleolated nuclei. The latter are arranged so as to lay the foundation of a membrane, h. This membrane is the primary membiane of a cell. (Its elements usually appear first as mere globules, in which no nucleolus can be discerned, and which are too minute for examination.) At a later period I noticed the state fig. F. In F were nuclei such as those at h in E, and the nucleoli were most regularly equidistant. Up to this period the formation of the membrane is incomplete, and it continues incomplete until fibre forms. The nucleolated nuclei A of E and F are the elements of fibre. From these drawings it will be seen that, according to my observations, the cell-membrane does not form around the nucleus, but is the outer part of the nucleus in an altered state. The nucleus, in fact, passes into the condition of a cell. In order to this it becomes segmented. The segments are usually globules or granules, too minute for examination. These coalesce and thus lay the foundation of a membrane. But there is one nucleus — that in fig. A — the segments of which are of sufiicient size to show distinctly that they are nuclei themselves, each of these having its nucleolus, fig. B. The great size of the seg- ments of this nucleus, no doubt, has reference to the functions which the cell it passes into is destined to perform, as well as to the enormous magnitude which it attains. That cell is my ovisac. It remains to add, that, having discerned traces of a like process in the formation even of the most transitory cells, I be- lieve that the membrane of every cell has the same mode of origin as the membrane of the ovisac. When at Giessen in 1852 I had the pleasure of reading the work of Baron Liebig, entitled " Untersuchungen iiber einige Ursachen der Saftebewegung im thierischen Organismus,'1848/^ and pointed out to that justly celebrated man the nucleoli in my drawing now reproduced in fig. F, stating to him my belief that it represented pores. I am still of the opinion that in the half-formed state of membrane fig. F, nucleoli are the only pores. And in proof that such is the case, have only to refer to what I have been maintaining since the year 1840, when, in the Phil. Trans, for that year I showed a suctorial power to be manifested by the protrusion of the parietal uncovered hyaline nucleolus of the germ spot, to take up the equivalent, corresponding, or counterpart from the spermatozoon ; and to drawings I gave in 284 Dr. Barry's Remarks on the Article " Ovum" the following year representing cells, the membranes of which, like that of the germ vesicle, presented in the situation of the nucleolus an orifice^, I lately wrote, " In mere nuclei, too, it is often seen that at the very part where the nucleolus lies the nucleal investment ceases t-^' My belief, indeed, is, that at some period every nucleus has in its nucleolus a pore. I am anxious to poiut out a connexion between nucleoli and pores, because of what I have for years been endeavouring to prove, — that in absorption, assimilation, reproduction and secre- tion, the nucleolus is the prime mover. But other pores exist, as pointed out by Keber — spaces between the filaments and scales, far more capacious than nucleoli ; which larger pores I do not suppose to represent more than passages. II. Remarks on the Article " Ovum " in the Cyclopedia of Physiology. I am glad to see from what has just been published^ of this luminous and comprehensive article, that the observations of its excellent author enable him to confirm my own, published sixteen years before (in the Phil. Trans, for 1838), that the germ vesicle is the part which first arrives at full formation, and that my ovisac is formed around it J. Still more gratifying would it have been to find that Prof. Allen Thomson was aware of some observations I published three years afterwards — Phil. Trans. 1841 ; for, besides establishing the two facts just mentioned, as published in 1838, my later ones enabled me to record the first with far more minuteness, as well as to make known several others. Of the drawings I gave in 1841, the Professor was evidently not aware, or he would have seen that they represent Nature even more accurately than his own. They not only show the order of formation of the parts in question, but also that what he terms granules are nucleolated nuclei. They further show that these nuclei lay the foundation of the membrane of the ovi- sac. I have only to add, that, buried as my said drawings of 1841 have been with a host of others, in a memoir, the title of which did not denote connexion with the ovum, I am not sur- prised at the oversight. I have exhumed a few of the said drawings ; and it is these that I reproduce in Plate II. {figs. A to F). Once more referring to these drawings, I have now more fully to explain them. In figs. C to E, c is the germ vesicle with its ♦ Phil. Trans. 1841. t Monthly Journal of Medical Science, July, 1854. X The ovisac acquires a vascular covering, and there is thus formed a "Graafian follicle." M. Barrv, Phil. Trans. 1838. in the Cyclopcedia of Physiology. 285 originally single spot. (Thus the germ vesicle is formed out of what in A was a nucleolus, and in B had become a nucleus.) In figs. E and F, h is the ovisac, or rather the foundation of its membrane. In fig. E, g represents the granular contents of a future cell — the ovisac. They are part of the nucleus, fig. A. Out of these granular contents [g, fig. E) are formed the albu- nienous contents of the ovisac, including von Baer^s membrana granulosa and my retinacula, as well as the yelk and vitelline membrane*. From my observations then it appears that the ovisac and all within it are formed out of a nucleus — fig. A ; that the ovisac is the cell, and that the germ vesicle is what was once a nucleolus. This nucleolus (young germ vesicle) often divides into two or more parts, and then the ovisac comes to include a plurality of ova; for a yelk forms around each part of the divided nucleolus. Besides what has now been mentioned, the said article ''Ovum^' in the Cyclopaedia of Physiology adds yet another proof to many in my experience, that it is often unfortunate for an observer to have the exploring of new ground. His observations may remain so long disregarded or denied, that when at length, after the lapse of no small fraction of a century, they come to be confirmed, he has the pain of exhuming them, all remem- brance thereof being gone. I have had large experience of this, and am now compelled to endure the pain of more. Thus Prof. Allen Thomson was certainly not aware of what I had recorded in 1 839, or he would not have considered altogether " novel '' some views published in Germany in 1852. H. Meckel, 1852 — as j-eported in the article " Ovum,'^ 1834. *' Many physiologists have felt the incongruity of the comparison gene- rally made between the minute and simple ovum of the mammifer, and the large and more complex yolk of the bird, and most are disposed to acknowledge the necessity of making some more markeddistinctionbetween the granular and the cellular yolk substance in the two great groups to which these ova respectively belong. It has before been stated, that von Baer, on his discovery of the mamraiferous ovum, regarded it as corresponding, not to the whole Martin Barry, Phil. Trans. 1839. After showing that cleavage, so called, takes place in the ovum of the highest class, Mammalia, I re- marked : " In Fishes the divisions in question do not include the whole yelk-ball, but are confined to a pro- jection on one side. In the Frog those divisions include the whole of the yelk-ball, but they begin and proceed more vigorously on one side. In Mammalia also, as we have seen, the divisions include the w hole of the so-called 'yelk-ball.' This comparison may perhaps assist us in determining what portion it is of the * The said drawings A to E represent the young ovum and ovisac of a Bird — the Wryneck, Yunx torquilla. In ¥ is part of a young ovisac of the Canary, Vringilla Canaria. 286 Dr. Barry's Remarks on the Article " Ovum.^ ovum of birds, but to the vesicle of Purkinje. The discovery, in 1834, of the germinal vesicle in the mam- miferous ovum, of the existence of which von Baer had no distinct knowledge, induced Valentin and others to maintain that the essential parts of the ovum are the same in the bird and the mammifer. But it may be doubted whether physiolo- gists may not have proceeded further than they were wai-ranted by obser- vation in regarding the vitelline membrane and large corpuscles of the yellow yolk of birds as essentially eoiTcsponding parts with the zona pellucida and the smaller granular yolk of the mammifer." " The minutely granular yolk [of the Bird], in which the cicatricula originates, and the germinal vesicle together are the true representatives of the small ovum of the mammifer.'* In conclusion it is remarked : " This substance by itself constitutes the whole yolk of mammalia; but in birds it probably remains as a part, if not the whole, of the proligerous disc (afterwards cicatricula)*." ova of the animals just mentioned which corresponds to the ' yelk-ball ' in Mammalia. Is not the * discus vitellinus ' in the ovarian ovum of the Bird the seat of similar divisions? If so, it will perhaps appear that the so-called * yelk-ball ' in the marami- ferous ovum coiTcsponds more par- ticularly to the ' discus vitellinus * (with its germinal vesicle) in the ovum of the Bird .... If the con- tents of the ovarian vesicle of Baer correspond to no more than the * discus vitellinus ' in the ovarian ovum of Birds and other animals, the former will not appear to be relatively so minute as hitherto sup- posed. As to the difference in form of these two objects, perhaps a globular form of the substance com • posing the ' discus vitellinus ' would have been incompatible with its position under the vitellary mem- brane and with the presence around it — in the ovum of the Bird for instance — of a large quantity of true yelk, provided for a future purpose ; while no such provision being re- quired in the ovum of the mammal, the substance corresponding, as I suppose, to the * discus vitellinus ' of other animals fills the vitellary membrane (/), and is therefore glo- bular in formf." " In the theoretical deductions '' made from his observations, Prof. Allen Thomson remarks that the German author " has not been equally successful/' The paper of Dr. H. Meckel I have not seen, and became aware of its existence through the article '* Ovum '' published in June of the present year : but, judging from the following, quoted by Prof. A. T. from the said paper, I too am of the opinion that in theoretical deductions its author * Article " Ovum," I. c. pp. 76 and 79- t Researches in Embryology, Second Series, Phil. Trans. 1839, {»p. 369, 370. I added at the same time in a note (p. 370) : " If the ana- ogy in question really exists, the * discus vitellinus ' is obviously a nucleus destined to undergo changes like those occurring in the so-called ' yelk-ball * of the Mammalia. The round white spot called the * cicatricula ' in the Bird's laid egg may possibly con-espond to my layer of ' cells,' plate 6. figs. 1 1 1-1 13, lining the vitellary membrane (/) in the uterine ovum of the IVlammal ; while my * mulberr}'-like object,' in the same figures, may perhaps be represented in the Bird's laid egg by the stmcture which lies under the * cicatricula,' and has been denominated Keimhiigel, cumulus proligerus," &c. Keber on the Porosity of Bodies. 287 is not free from error. " I believe, therefore/' says H. Meckel, " that that alone ought to be regarded as the true egg which exists in Man, Mammalia, Naked Amphibia and Osseous Fishes ; and that in the remaining Vertebrata the ovum consists only of the so-called vesicle of Purkinje, and that all the other parts are accessory, superimposed and unessential. In particular that the yellow yolk of the bird and scaly reptile is analogous to the corpus luteum of the human ovary '' [!], &c. Prof. Allen Thomson seems to think, with H. Meckel, that the zona pellucida in Birds disappears, that the "yellow yolk'' is then added, and that around the yellow yolk a membrane is afterwards formed, which is the vitelline membrane of the Bird's laid e^^. I have entered upon no renewed inquiries with the microscope upon this subject, but must say that I did not observe any such disappearance of the original zona in the ova- rian ovum of the Bird, and have always considered the vitellary membrane of its laid e^^ to be the original one in a distended state, it having imbibed the material for the superadded true yellow yolk. XXXVIII. Some account of the Discoveries of Keber on the Porosity of Bodies ; with Confirmations. By Martin Barry, M.D., F.RS.^ AFTER reading the work of Keber on the porosity of bodies, a copy of which the author was so good as to send me immediately after its publication, I felt that English physiologists would be glad to see an account of the same, and thus be afforded an opportunity of testing the observations it records. I therefore wrote to Dr. Keber, stating, that if he were inclined to send me a short abstract of the work, I would, my health permitting, translate and send it to one of our journals. The following is the result — in communicating which t have the satisfaction of knowing it to be the opinion of the illustrious Owen, that the said work has " peculiar value," from its indefatigable author having devoted his skill " to a depart- ment of research of prime influence at the actual phase of the physiology of tissues." Microscopic Researches on the Porosity of Bodies. By F. Keber. " Under this title I have recently published a paperf contain- ing the results of microscopic researches continued for months. * Communicated by the Author. t F. Keber, Microscopische Untersuchungen iiber die Torositdi der Korper. Nehst einer Abhandlung uber den Eintritt der Samenzellen in das Ei. Mit Zusatzen von M. Barry. Konigsberg, 1854. 288 Dr. Barry's Account of the Discoveries of Keber After the numerous proofs furnished by experiment as well as through logical conclusions, all acquainted with physics and physiology had long considered the porosity of solid bodies as an established fact. My object was to give optical demonstra- tion of the same. Of the methods I pursued, and the results thereby obtained — which to physiology and the practice of medi- cine may not be unimportant — the present communication is intended to give a short outline. That porosity is a universal quality of bodies, i. e. that bodies do not entirely fill the space they take up, but enclose interstices between their particles, is properly adopted in physics as an established fact. Any compendium of physics may be referred to in proof of this. To cite merely one of the most striking examples, I remember an experiment instituted by the Acade- micians of Florence in 1661. A hollow sphere of gold having been filled with water, was exposed to strong pressure, when its whole surface became covered with minute drops, like those of dew. Since then the experiment has often been repeated with different metals, and always with the same result. Now, gold being one of the densest bodies, still less can the finely porous structure of others be filled up. Thus it is known that stones which have lain for a long time at the bottom of rivers or the sea, are in their interior more or less moist. The porosity of all animal and vegetable textures follows from their name ; for as every texture consists of a network of vari- ously twisted threads or filaments, the organic parts of textures must consequently have interstices. That such is really the case, daily experience shows. Thus wood steeped in water increases in weight and volume; while, on the contrary, wood lying in the air, with dry weather dries up, and with wet weather swells. Further, by means of atmospheric pressure, mercury may be pressed through dense woods, &c. What especially concerns animal membranes, — the membrane of the cell, the epidermis, the mucus and vascular membranes, — is the penetrability of the same for gases and liquids ; which, since the application by Dutrochet to the process discovered by Parrot and Fisher of the expressions Endosmose and Exosmose, has been an established and universally adopted axiom. Whether by these expressions is to be understood, as by most natural pnilosophers, merely imbibition and diffusion, the effect of capillary attraction, or whether peculiar properties are to be vindicated for them, which it has lately been attempted to de- duce from the chemical nature and the mechanical constitution of the membranes themselves*, is for our purpose a matter of * Justus Liebig, Untarsuchungen uber einiye Ursachen der S'dftebeweyuvy im thierischen Organismus, 1848, pp. 68, 59. on tJie Porosity of Bodies. 289 indifiference. This much is certain, modern physiology so far adopts a porosity of the organic membranes, as to admit that these are permeable for liquids and gases, but not to allow the passage through them of any solid substance. Thus, with re- ference to the latter, the following enunciation has been given by Johannes Miiller : — '^ The appearance of globules in secre- tions, presupposes formation of the same at the moment of separation. They cannot pass out of the blood through the capillaries*.^' Further, it is said by Henle in his treatise on ' Eiterinfection,' " I regard the vascular wall as a hermetically closed membrane, which keeps at a distance from the blood the exciters to putrefaction — microscopic organisms t.^' The full validity of these enunciations has, however, recently been called in question, through various physiological and patho- logical facts, which deserve the greatest attention, although no one has hitherto been able to find for them sufficient explanation. To these belongs, in the first place, the penetration of the fat globules into the lacteals and blood-vessels, concerning which it has with tolerable certainty been shown, that they as such get through the intestinal walls without previous chemical change J. Further, may be mentioned what experience shows to take place, the penetration, in the form of minute globules, of the mercury contained in blue ointment through the skin into the humours, whereof salivation and other symptoms aff^ord proof to every physician. The powerfully healing effects of the rubbing in of lard and other fatty ointments, do not well admit of being otherwise explained. Now, after the passage of metallic mer- cury into the blood of animals — partly rubbed into uninjured parts of the skin, and partly given them in food — had been microscopically shown, which was first done by Osterlen§, who arrived at the same result in his experiments with carbon, these observations were most fully confirmed by Eberhardt||, Mensonides^, and Donders**, and extended to the penetration of particles of sulphur and starch-granules. So that consequently the possibility of the penetration of finely-divided substances * Handbuch der Physiologie des Menschen, 4th edit., vol. i. p. 202. t Handbuch der rationellen Pathologie, vol. i. 1847, p. 7(^7- X F. Bidder and C. Schmidt, Die Verdauungss'dfte und der Stoffwechsel, 1852, p. 250. § Archiv fur physiol. Heilkunde, 1843, p. 536 j and Zeitschrift fur rationelle Medizin, vol. v. p. 434. II Henle's and Pfeufer's Zeitschrift fur rat. Medizin, New Series, vol. i. 1851, p. 406. % Aldus Mensonides, De absorptione molecularum solidarum nonnuUa. Traj. 1848. ** Nederlandsch Lancet, vol. iv. ; and Zeitschrift fur rat. Medizin, 1851, p. 415. PhiL Mag. S. 4. Vol. 8. No. 52. Oct. 1854. U fi90 Dr. Barry's Account of tlie Discoveries of Keber into the humours can be no longer seriously doubted. Lastly, the circumstance that, after its application as blue ointment, mercury in the metallic form has been found, not only in many parts of the body, but even in the saliva*, is evidence of a very general porosity of the animal formations. To meet these inexorable postulates of logic and experimental proof, science in its present position gives us on this exceedingly important subject no satisfactory disclosure. In vain do we seek in €ompendiums of physics for definite specifications of the size, form, and condition in other respects, of the pores of gold through which, in the experiment above mentioned, water is pressed out, or of the pores of granite through which the latter in water becomes saturated. Still less is modern physiology in a condition to mark with certainty the ways in which those sub- stances get from the surface of the skin into the blood. While, through the united efibrts of the greatest physiologists of the age, we have at length advanced so far as to see laid aside the vice clandestinaf of former days, through which it was sought to explain the passage into the urine of substances introduced into the stomach, suspicion from another side shows itself anew, that the animal membranes, and especially the capillary walls, notwithstanding their undoubtedly closed state, may either everywhere, or at certain parts, possess apertures which have defied the methods of examination hitherto employed, and by which minutely divided solid substances are let through. But the permeability of organic membranes for gases and fluid substances also, has nothing in modern science to support it besides the grounds of induction, it having hitherto with certainty been optically demonstrated by none. In proof of the correctness of these assertions, I refer to what has been enunciated by some of the greatest authorities now living ; for instance, by a Johannes MiillerJ, Valentin§, R. Wagner||, Henle^, Liebig**, and others, from whose accordant evidence it follows, that the permeability of animal membranes for gases, liquids, and even under particular circumstances for finely divided solid bodies, is in physiology an established fact, yet * In the saliva of a child in scarlatina, treated with blue mercurial ointment on accoimt of swelling of glands of the neck, single globules of mercury, having a diameter of ^xyW"> were, as moderate sahvation ap- peared, also noticed by myself. t See J. MiiUer, Handb. der Physiol, des Mencken, vol. i. 1844, p. 1.97. j Handbach der Physiologie des Menschen, vol. i. 1844, pp. 193, 194. § Lehrbuch der Physiologie des Menschen, vol. i. 1844, p. 63. II Lehrbuch der Speciellen Physiologie, '2nd edit., 1843, p. 206, § 171, note 2. If Rationelle Pathologic, vol. ii. 1847, p. 145. •* Untersuchungen iiber einige Ursachen der SUftebewegung, 1848, p. 4. on the Porosity of Bodies. 291 morphologically requires further clearing up, inasmuch as the apertures in the substance of the textures necessarily assumed, from the occurrences above mentioned, could not until now be demonstrated. After many fruitless attempts, I have been so fortunate as to discover in the substance of all organic bodies already formed, microscopic spaces from yoVo'" ^^ i;oVo'" (Paris line) in dia- meter, and generally in all the bodies which I have examined, to recognize signs of an optically demonstrable and measurable microscopic porosity. Referring, then, to my more ample re- presentation given in the above-mentioned paper, and to the delineations which accompany it, I beg leave here to offer a short description of the simple methods followed by me in my researches, and of the results. While reflecting on the difficulties which, notwithstanding the perfection of modern microscopes, opposed themselves to the attainment of the long-striven-for end in question, I feared most of all that, with our present means, the objects to be examined could not be finely enough divided to make the spaces between their particles plain. Manifold as had been the searches after pores, there was nothing to make it probable that their perfora- tions were in a perpendicular direction. It seemed much more likely that they ran in directions the most varied, of the sloping and oblique, perhaps even zigzag, for it had been suggested by Henle*, that the pores of the epidermis " might perforate the skin obliquely," and on this account be imperceptible. Further, it was clear that even a thin animal membrane, but which con- sisted of several layers of different fibres, forming a texture far more perfect than the artificial ones wrought by the hand and machines of man, must indeed have spaces between its fibres ; but that so long as the different layers of that texture ran over and through one another, it would be difficult with certainty to discern those spaces. So that, although having at command even the best illumination, and with a microscope of the first order, he who might attempt to search out the pores of an animal membrane, would find himself going astray just as much as one who endeavours to see through a board ; for both con- sist of variously twisted fibres covering one another, the spaces between which nothing but very minute division can bring into view. But further, as all bodies by no means possess a fibrous structure, and as even organic fibres, so far as they undergo change of material and through moisture swell and are filled out, must likewise themselves be porous, it was evident that through perception of the spaces between the fibres the porosity * Allgemeine Anatomic, 1841, p. 237. U2 292 Dr. Barry's Account of the Discoveries of Keber of bodies in general would not be shown, and consequently the problem before us would be far from being solved. As I further meditated thereupon, in what way I might succeed in dividing the subjects of observation to a degree of minuteness that should answer the requirements above mentioned, I con- cluded to select Nature herself as a guide, and first to consider more intimately such objects as always present themselves in a minutely divided state without artificial aid. Among the first to be considered are undoubtedly the delicate particles of dust, which, in consequence of the gradual weathering of solid bodies, come to hover in the air, and are deposited upon all bodies and everywhere in our dwellings. Now Nature being, as the micro- scope daily shows us, often greatest in the most minute things, and solid bodies being gradually weathered into dust, the said par- ticles of dust appeared to be just a product of the most minute divi- sion of Nature's own preparing, in delicacy such as could scarcely be exceeded, or even reached by art. I therefore devoted myself to the examination of glass, which, after lying from twelve to fourteen hours uncovered, had become slightly dusty. This I did without adding watery and without a covering of glass, under the aplanatic eye-piece of my large microscope by Schick, with 200 and 300 times linear magnifying power. The addition of water I omitted, in order not to produce a swelling of the delicate dust particles, and a change in the volume of their pores. The larger dust particles, whose form and compass were most manifold and irregular, it is true, appeared to me almost entirely untransparent, and only at their borders, here and there, diaphanous. On the contrary, in many of the most minute, which likewise presented varied forms, I perceived, on close examination, exceedingly minute spaces and clefts, having a diameter of about the T2V0'" *^ ^^^ TJjn'" (P^^is line), the colour of which, however, principally with bright illumination, mostly exhibited a reddish or greenish tinge. With long examination, I noticed that the borders also of the dust-particles, as well as their finer indentations and inlets, frequently presented exactly the same reddish and greenish edges, and hence concluded that the colouring of those spaces might be owing to interference and flexion of the light, the modifying influence of which on illu- mination was known to microscopic observers long since. This accordance in the colouring of the borders, with that of the apparent spaces in the substance of the dust-particles (which, especially with strong illumination, was often observable also when the microscope was placed at a very considerable distance from the window), could not in my opinion do otherwise than serve as a confirmation of my belief that I here had before me real spaces and minute orifices, even had I upon other grounds on the Porosity of Bodies, u .^n 293 been able to mistrust the aplanatic eye-piece of my microscope. A real doubt as to the objective nature of those spaces, more- over, after long and repeated occupation with the same object, could not last longer, as with alternate elevation and lowering of the minute objects, and with alternately increased and dimi- nished illumination, I distinctly saw the light flash through them ; and even in examining the larger dust-particles, could follow the spaces in all gradations j from complete opacity through the different degrees of the diaphanous to entire transparency. Although, therefore, I was at first much inclined to take what I saw for an optical illusion, long examination compelled me, entirely to abandon such a thought, — ever convincing me anew that porosity is a constant formation common to all dust-particles without exception, and that the pores in the larger of them are either wholly or in part covered, through the lying one upon another of several lamellae and scales. This discovery prompted me to examine other organic and inorganic bodies also in a like manner, i. e. without the addition of watery and in as minutely divided a condition as possible. I took, for example, a morsel of dried bladder of the hog, and holding the same over a clean glass, freed from all dust, scraped most gently on it with a sharp knife, so that extremely small portions, scarcely visible with the naked eye, fell therefrom upon the glass ; covered these with glass, likewise cleansed from all dust, in order to avoid any confounding with other particles, and then under the microscope sought out the smallest of the said scrapings. The porosity of these appeared with a distinct- ness just the same as in the minutest dust-particles, in casses where the scrapings had been made with sufficient minuteness, and where of these again only the minutest were selected for examination. In the larger scrapings also, where their too great thickness did not render them opake, I was at any time able with certainty to recognize the higher or lower degree of the diaphanous, as well as a loose, richly spaced structure, in their whole extent ; consequently distinct traces of porosity. Since then 1 have with perfect certainty recognized, as well individual microscopic pores, as also generally a highly porous structure, not only in all the organic, but also in all inorganic bodies, access to which was possible, even granite and the metals, and, as will be more amply stated further on, have with the mi- crometer measured the pores. The methods therein followed I now put together in a few words. [To be continued.] [ 294 ] XXXIX. On the bearing of the Barometrical and Hygrometrical ObservatioTis at Hobarton and the Cape of Good Hope on the general theory of the Variations of Atmospherical Phanomena. By Professor Dove of Berlin'^. I HAD hoped to have prefaced this volume with a discussion of the meteorological observations made hourly at Hobarton from January 1841 to September 1848 (of which the abstracts were published in 1850 in the first volume of the Hobarton Observations), from the pen of Professor Dove, who had kindly undertaken, at the magnctical and meteorological conference at Cambridge in 1845, to participate to that extent in the reduc- tion and application to theoretical conclusions, of the results of the Observations at the British Colonial Observatories; but M. Dove's appointment, on the death of Professor Mahlmann in November 1848, to the charge of the meteorological obser- vatories in the Prussian states has materially abridged the time at that gentleman's disposal, and he has found himself unable to complete the discussion he had undertaken for the present volume without occasioning an inconvenient delay in its publi- cation ; the discussion will therefore be prefixed to the fourth volume ; but in the meantime Professor Dove has kindly fur- nished for this volume the subjoined remarks (written in German) upon the bearing which the barometrical and hygrometrical observations, at the Colonial Observatories at Hobarton and the Cape of Good Hope, have had on the general theory which pro- fesses to explain the physical causes of the variations which we observe in the atmospherical phsenomena of the globe. The testimony borne by so eminent a meteorologist to the import- ance and value of this portion of the observations made at the British Colonial Observatories, cannot fail to be highly accept- able to the Government which instituted it, and to the public who have paid for these establishments, as it must be most satis- factory to the officers and to their assistants, by whose patient and unremitting labour facts of which the importance is thus recognized have been added to the foundations of meteorological science. The generalization in which M. Dove has applied them is remarkable alike for its extent and its simplicity, and I am glad of the opportunity of enriching this volume with so inter- esting a document. Woolwich, March 17, 1853. Edward Sabine. * From " Observations made at the Magnetical and Meteorological Ob- Tatory at Hobarton, in Van Dicnien Island," vol. iii. Introduction. gcrvatory On the theory of the Variations of Atmospherical Phcenomena. 295 The establishment of meteorological stations in distant parts of the globe had, generally speaking, for its immediate object, so to complete the partial knowledge we already possessed of the phsenomena over a considerable portion of its surface, as to enable us to take a general view of their course over the whole globe ; the result of those endeavours has even exceeded what was hoped for, as besides the information obtained respecting regions where our knowledge was most defective, fresh light has been thrown on those with which we had supposed ourselves already completely acquainted. Meteorology commenced with us by the study of European phsenomena, and its next principal extension was to phsenomena observed in the tropical parts of America. If what is true of Europe were equally true of the temperate and cold zones of the earth in all longitudes, and if tropical America in like manner afforded a perfect example of the tropical zone generally, it would be of little consequence where the science of meteorology had been first cultivated ; but this is not the case, and a too hasty generalization has led to the neglect of important problems, while others less important have been regarded as essential and placed in the foremost rank. It was necessary that the science should be freed from these youthful trammels, and this needful enfranchisement has been effected by the Russian and by the English system of observations. Russia has done her part in freeing the meteorology of the temperate and cold zones from impressions derived exclusively from the limited European type ; and England, which by its Indian stations had undertaken for the torrid zone the same task of enlarging and rectifying the views previously entertained, has besides, by its African and Australian stations (Cape of Good Hope and Hofearton), opened to us the southern hemisphere, and first rendered it possible to treat of the atmosphere as a whole. I will now endeavour to show the importance of being enabled to take such general views, selecting as an example the annual variation of the barometer. The study of the annual barometric variation had long been singularly neglected, while the diurnal barometric variation had had devoted to it an attention quite disproportioned to its subor- dinate interest in reference to the general movements of the atmosphere. This otherwise incomprehensible mistake is excused by the localities where nature had been first interrogated. As the diurnal variation had manifested itself with great distinctness and regularity in tropical America, it naturally presented itself as an object of interest in Europe also. The annual variation, on the other hand, is inconsiderable, both in Europe and the tropical parts of America ; and thus, while atmospheric phseno- mena were treated simply as facts of which the periodicity alone 296 M. Dove on the theory of the Variations was to be investigated, without seeking for physical causes, it was natural that a phaenomenon, in which opposite effects result- ing from two different causes counterbalance each other, should altogether escape notice. It is, perhaps, more remarkable that no surprise should have been excited when the atmospheric pres- sui'e was not found to diminish from winter to summer, with increasing heat When, by the labours of Prinsep more particularly, the phae- nomena of the tropical atmosphere in Hindostan became more known, there was seen to be a great difference between the baro- metric variation there and in tropical America ; inasmuch as the Indian observations showed a decidedly well-marked annual variation. A new en-or was now fallen into, and it was supposed that the phsenomenon did not extend beyond the torrid zone, and that it was an immediate consequence of the periodical change of wind, i. e. of the monsoons. This erroneous view was completely refuted when the barometric relations at the Siberian stations became known ; for it was then found, that north of the Himalaya (which in the supposed hypothesis must have formed the limit of the ph?enomenon), the annual barometric variation was exhibited on a large scale, and over a region so extensive, that the shores of the Icy Sea itself could hardly be assumed as its boundary. A greatly diminished atmospheric pressure taking place in summer over the whole continent of Asia must produce an influx from all surrounding parts ; and thus we have west winds in Europe, north winds in the Icy Sea, east winds on the east coasts of Asia, and south winds in India. The monsoon itself becomes, as we see, in this point of view only a secondary or subordinate phsenomenon. I have endeavoured to establish the reality of the above phse- nomenon and its climatological bearings in several memoirs ; and I must refer for the numerical values to Poggendorff's Annalen, vol. Iviii. p. 177; vol. Ixxvii. p. 309; and to the Berichte oi the Berlin Academy, 1852, p. 285. I will here embody the results in distinct pro])ositions, in order to show, in connexion there- with, the importance of the bearing of the Hobarton observations. 1. At all stations of observation in the torrid and temperate zones the elasticity of the aqueous vapour contained in the atmo- sphere increases with increasing temperature. In the region of the monsoons this increase from the colder to the warmer months is greatest near their northern limit. Hindostan and China pre- sent in this respect the most excessive climate. No differences of similar magnitude are found in the southern hemisphere. The form of the curve of elasticity of the aqueous vapour shows, however, a less decidedly convex summit in the region of the monsoons than beyond it, having in that i*egion rather the cha- of Atmospherical Phenomena. '^'( 297 racter of a flattened summit or table-land, the elasticity con- tinuing nearly the same throughout the period of the rainy mon- soon. Near the equator the convex curve of the northern hemi- sphere becomes, first flattened, and then gradually transformed into the concave curve of the southern hemisphere. In the Atlantic this transition takes place in a rather more northerly parallel. In regard to the magnitude of the annual variation, the following rule appears generally applicable in the torrid zone : the annual variation is considerable at all places where equatorial currents prevail when the sun^s altitude is greatest, and polar currents when the sun's altitude is least; and inconsiderable wherever the direction of the wind is either comparatively constant throughout the year, or where it changes in the contrary sense to that above described. At the last-named class of places the rate of decrease in the mean annual tension of the aqueous vapour with increasing distance from the equator is more rapid than in the first class. 2. At all stations in Europe and Asia the pressure of the dry air decreases from the colder to the warmer months, and every- where in the temperate zone has its minimum in the warmest month. 3. If we compare the annual variation of the pressure of the dry air in northern Asia and Hindostan with the variation in Australia and the Indian Ocean, we shall be satisfied that some- thing more takes place than a simple periodical exchange of the same mass of air in the direction of the meridian, between the northern and southern hemispheres. From the magnitude of the variation in the northern hemisphere, and the extent of the region over which it prevails, we must infer that at the time of diminished pressure a lateral overflow probably takes place ; that it actually does so may be considered as proved for the northern part of the region, by the fact that at Sitka, on the north-west coast of America, the pressure of the dry air mcreases from winter to summer. It is not probable that the overflow takes place exclusively to the east, it probably occurs also to the west ; and on this supposition the small amount of the diminution of the pressure of the dry air from winter to summer in Europe would be caused, not solely by the moderate amount of the difference of temperature in the hotter and colder seasons, but also by the lateral afflux of air in the upper regions of the atmosphere tend- ing to compensate the pressure lost by thermic expansion. As at the northern limit of the monsoon, at Chusan and Pekin, the annual variation of the pressure of the dry air is most consider- able, while at the northern limit of the trade wind in the Atlantic Ocean, i. e. at Madeira and the Azores, it is very small, it is pro- bable that there is in the torrid zone also a lateral overflow in the 39% M. Dove on tJie theory of the Variations upper strata of the atmosphere from the region of the monsoons to that of the trades. 4. From the combined action of the variations of the aqueous vapour and of the dry air we now derive immediately the perio- dical variations of the whole atmospheric pressure. As the dry air and the aqueous vapour mixed with it press in common on the barometer, so that the upborne column of mercury consists of two parts, one borne by the dry air, the other by the aqueous vapour, we may well understand that as with increasing tempe- rature the air expands, and by reason of its augmented volume rises higher and at its upper portion overflows laterally, — while at the same time the increased temperature causes increasing evaporation, and thus augments the quantity of aqueous vapour in the atmosphere, — so it naturally follows that the composite result in the periodical variations of the barometric pressure should not everywhere bear a simple and immediately obvious relation to the periodical changes of temperature. It is only when we know the relative proportions of the two variations which take place in opposite directions that we can determine whether their joint effect will be an increase or a decrease with increasing temperature, — whether in part of the period the one variation may preponderate and in other parts the other variation. The following are the results which we are enabled to derive from observation. 5. Throughout Asia, the increase in the elasticity of the aqueous vapour with increasing heat is never sufficient to com- pensate the diminished pressure of the dry air, and the annual variation of barometric pressure is therefore everywhere repre- sented, in accordance with the variation of the pressure of the dry air, by a simple concave curve having its lowest part or minimum in July. The observations in Taimyr Land, at lakousk, Udskoi and Aiansk, show that this is true up to the Icy Sea on the north, and to the sea of Ochotsk on the east. On the west a tendency towards these conditions begins to be perceived in European Russia in the meridian of St. Petersburg, and becomes more marked as the range of the Ural is approached. On the Caspian and in the Caucasus the phsenomenon is already vei-y distinctly marked ; its limit runs south from the western shore of the Black Sea, so that Syria, Egypt, and Abyssinia fall within the region over which it prevails. Towards the confines of Europe there is almost everywhere a maximum in September or October, the barometric pressure increasing rapidly from July to the autumn. This maximum is followed towards the latter part of the autumn by a slighter inflexion or secondary minimum ; it is only beyond the Ural that the curves become uniformly con- cave, with a single summer minimum and winter maximum, of Atmospherical Phanomena, ■ - 299 which character they retain throughout the rest of the Asiatic continent, even to its eastern coast. In winter the absolute height of the barometer at the northern limit of the monsoon is very great. The still considerable amount of the annual varia- tion at Nangasaki, and the little difference between the curve of Manilla and that of Madras, show that the region in question extends beyond the eastern coast of Asia into the Pacific Ocean ; in higher latitudes, however, its limits appear to be reached in Kamschatka. As the annual variation, which is greater at Madras than at Manilla, is found greater at Aden than at Madras, the western limit of the region would appear to extend far on the African side. 6. In middle and western Europe the barometric pressure appears to decrease everywhere from the month of January to the spring, usually attaining a minimum in April ; it then rises slowly but steadily to September, and sinks rapidly to November, when it usually reaches a second minimum. In summer, there- fore, the whole atmospheric pressure gains more by increased evaporation than it loses by expansion. This over-compensation is probably, as we have seen above, to be explained by the lateral overflow received in the upper regions from Asia. In Sitka the whole annual curve is convex, a result only found in Europe at considerable mountain elevations, where it is a consequence of the expansion, and extension upwards, of the whole mass of the atmosphere in summer. 7. The region of great annual barometric variation, on the Asiatic side of the globe where monsoons prevail, extends much further to the north in the northern hemisphere, than it does to the south in the southern hemisphere ; for the variation reaches its maximum at Pekin, while at Hobarton, in nearly a corre- sponding latitude, it has already become inconsiderable ; and it is generally greater in the northern than in the corresponding southern latitudes. The exact contrary is the case on the Atlantic side and in the region of the Trades ; for here the annual variation, though nowhere very considerable, is decidedly greater in the southern than in the northern hemisphere, as is shown by the results of observation at the Cape, Ascension, St. Helena, Rio Janeiro, and Pernambuco, compared with the "West Indian Islands and the southern parts of the United States. Hence it follows, that if we compare places in the same latitude, we find but little difference between the annual variation in the southern Atlantic and southern Indian oceans, while in the northern hemisphere we have in the same latitude the very large annual variation in the north part of the Indian and in the Chinese seas, and the almost entire absence of annual variation in the Atlantic (compare Chusan with the Azores and Madeira). 300 On the theory of the Variations of Atmospherical Pluenoinena. The explauation of the last-uamed phsenomenon, i. e. that of the northern hemisphere, by a lateral overflow in the upper parts of the atmosphere, seems so direct, that I think we may pronounce the irregular form of the annual barometric curve in the West Indies to be a secondary phaenomenon, the primary causes of which must be looked for on the east. 8. It is known that in the eruption of the Coseguina on the 20th of January, 1835, when the isthmus of Central America was shaken by an earthquake, not only were volcanic ashes car- ried to Kingston in Jamaica, a distance of 800 English miles ni the opposite direction to the trade wind, but some of the same ashes also fell 700 miles to the westward, on board the Conway, in the Pacific Ocean. We infer, therefore, that in the higher regions of the atmosphere in the tropics the air is not always flowing regularly from S.W. to N.E., but that this usual and regular direction is sometimes interrupted by currents from east to west. I think I have indicated the probable cause of such anomalous currents in the above described barometric relations of the region of the monsoons compared with that of the trades. If we suppose the upper portions of the air ascending over Asia and Africa to flow off" laterally, and if this takes place suddenly, it will check the course of the upper or counter current above the trade wind, and force it to break into the lower current. An east wind coming into a S.W. current must necessarily occasion a rotatory movement, turning in the opposite direction to the hands of a watch. A rotatory storm moving from S.E. to N.W. in the lower current or trade, would in this view be the result of the encounter" of two masses of air impelled towards each other at many places in succession, the further course of the rotation (originating primarily in this manner) being that described by me in detail in a memoir " On the Law of Storms,^' translated in the Scientific Memoirs, vol. iii. art. 7. Thus it happens that the West India hurricanes and the Chinese typhoons occur near the lateral confines on either side of the great region of atmo- spheric expansion, the typhoons being probably occasioned by the direct pressure of the air from the region of the trade winds over the Pacific into the more expanded air of the monsoon region, and being distinct from the storms appropriately called by the Portuguese " Temporales,^' which accompany the out- burst of the monsoon when the direction of the wind is reversed. The fact of the rotatory storms being of much more rare occur- rence in the South Atlantic Ocean arises from the more equal distribution of the periodically diminished atmospheric pressure in the southera as compared with the northern hemisphere. Here, therefore, the rotatory storms take place principally in the mon- soon itself. .mm^i Prof. Sedgwick on the May Hill Sandstone. 301 9. It is evident that the unsymmetrical distribution of land and sea, which gives rise to the abnormal variations in the forms of the isothermal lines, is at the same time the principal cause of the movements of the atmosphere. Thus the monsoon is but a modification of the trade wind, of which the cause is to be sought in part beyond the tropic. The region of great thermic expan- sion of the air in summer in the interior of the continent of the Old World presents all the characteristic marks of the region of calms, being a centre towards which all adjacent masses of air are drawn. Hence there is no complete sub-tropical zone, in the sense of a zone encompassing the globe. The region over which the heated air ascends does not therefore move up and down, or north and south, parallel with the sun's change of declination, but has rather a kind of oscillatory movement, in which the West Indies represent the fixed point, and the greatest ampli- tude of oscillation is on the side of India. The northern excur- sion is much greater in the northern hemisphere than is the southern excursion on the side of the southern hemisphere. The European atmospheric relations, especially in summer, are therefore essentially of a secondary nature ; and we must regard the little alteration in the atmospheric pressure in the course of the year in Europe as a secondary result, of which the explana- tion would not have been possible without the observations from Asia and Australia. Berlin, January 5, 1853. XL. On the May Hill Sandstone, and the Paleozoic System of England. By the Rev. Prof. Adam Sedgwick, F.R.S., F.G.S. To the Editors of the Philosophical Magazine and Journal. Gentlemen, THE following paper was drawn up for the Geological Society of London during last October, in the hope of its being read at their first Meeting after the summer recess. I was, however, too late in my application ; and in consequence of a long protracted illness, I was never able to attend a single meet- ing of the Society during the past winter or during the spring of this year. The paper was consequently postponed, and at length read, in my absence, at one of the concluding spring Meetings of the Geological Society. The Council are ready to print the paper — suppressing the discussions on classification and nomenclature — in their Quarterly Journal. I believe that any such suppression would destroy the value of the paper ; and I oiFer it to you as it was originally drawn up, with the following exceptions. One of the diagrams (fig. 4) has been corrected — Prof. Sedgwick on the May Hill SandstonCy the " Tabular view '* of the Devonian, Carboniferous, and Per- mian series has been slightly expanded, and a few short expla- natory notes have been added. In other respects, it is, with the mere exception of verbal corrections, word for word as it was submitted to the Geological Society. I have the honour to be. Gentlemen, Your faithful Servant, A. Sedgwick. Cambridge, August 20, 1854. This paper is a continuation of one which was read before the Geological Society (Nov. 3rd, 1852), and was afterwards pub- lished in their Journal, vol. ix. p. 215. The results stated by Prof. M'Coy and myself in that paper were as follows : — 1st. The May Hill sandstone contains a group of fossils es- sentially distinct from those which are found in the sections of Horderley and Caer Caradoc. Its fossils are of a true Wenlock type ; and it must consequently be cut off from the Caradoc sandstone, and arranged as the base of the Wenlock group. 2ndly. In the great series of beds on the south-western flank of the Malvern Hills, more than 2000 feet of strata, which had been called Caradoc sandstcme, were separated into two distinct groups ; — the lower (Hollybush sandstone and Black shale) being provisionally called Caradoc sandstone and shale; the upper group being the exact equivalent of what we called the May Hill sandstone. Adopting the same nomenclature, we found in the more northern sections, on the west flank of the Malverns, no traces of the Caradoc (or Hollybush) sandstone. It was further stated [loc. cit. p. 228), that during a former visit to the Horderley section (made in 1842) I had found beds of shale, with Trinucleus, Caractaci, &c., immediately above Stret- ford Bridge. Now, if this were true, the well known Pentamerus or Hollies limestone must be overlaid by a true Caradoc shale ; and the ascending order of succession must be (as stated in the paper referred to) — " (1) Caradoc sandstone, ending with the Pentamerus or Hollies limestone ; (2) Caradoc shale ; (3) Wen- lock shale ; (4) Wenlock limestone,^^ &c. This conclusion was strenuously opposed by Professor M^Coy ; but we had no oppor- tunity, in 1852, of bringing it to the test. It was derived from an old note-book; and as it made against myself , I thought myself bound to state it. Were the conclusion true, it would only prove, that on the banks of the Onny (as in several sections east of the Berwyn chain) the Wenlock shale is brought by an unconformable overlap, into immediate contact with the true Caradoc group, and without the intervention of the May Hill and the Palceozoic System of England. 303 sandstone *. I may further state, that during two short visits to the Onny section, made by my friend John Ruthven and myself, in the summers of 1846 and 1851, for the sole purpose of collecting fossils, we did not find a single characteristic Cara- doc species over the Hollies limestone. The state of the river had on both occasions been very unfavourable to our examination of the shales near Stretford Bridge ; but my friend Mr. Duppa, of Cheney Longville, promised (in 1851) to make excavations among them, in places where they were out of the reach of the waters. He has since then amply performed his promise, and his excavations have not laid bare any characteristic Caradoc species in the shales immediately above the bridge. I therefore now accept a suggestion (more than once made by Mr. Salter and Prof. M^Coy), that, in my note-book of 1842, 1 had mistaken Stretford Bridge for another bridge further up the Onny ; and in this way the section of the Onny is no longer (as it will ap- pear in the sequel) in any real antagonism with the sections of May Hill and the Malverns. These preliminary remarks will sufficiently explain the pur- pose of our short visit, made near the end of August (1853), to the frontiers of Wales and Siluria. My first intention was to re-examine (during the early part of last summer) the grits, conglomerates, and shelly sandstones which range from Conway to the neighbourhood of Corwen, and form the base of the Denbigh flagstone : and I may remark, by the way, that these important beds had been carefully laid down in 1843 by Mr. Salter and myself, and were at that time con- sidered and coloured as Upper Silurian. After having effected this first purpose, I hoped to follow the same grits and sand- stone in their range along the Berwyn chain ; and lastly to fol- low them, as they are laid down (I doubt not with great accu- racy) in the Government Map, until they finally thin out and disappear. I believe that, with very limited exceptions, the whole '^ Middle Silurian " group of the Government Map is the exact equivalent of the "May Hill sandstone.'^ The conglomerates, grits, and sandstones above mentioned are unconformable to the Cambrian rocks on which they rest, in their range from Conway to Corwen, and, in that part of their range, are the undoubted equivalents of the May Hill sandstone. That they are unconformable to the Cambrian rocks on which they rest, in a part of the Berwyn range, is also, I think, evident ; for they appear as the highest beds of a trough, on both sides of which there is an outcrop of * I stated this hypothetical conclusion in a letter to my friend Mr. Salter before he commenced his re-examination of the Horderley and Wenlock sections in 1853. 304 Prof. Sedgwick on the May Hill Sa/idstone, the Bala limestone ; and if we make sections from these highest beds to the limestones on the two sides of the trough, we find a discrepancy in thickness which can be readily explained by the discordant position of the overlying mass, and cannot, I think, be explained any other way. I state this fact from my remem- brance of the sections made by Mr. Salter and myself in 1843. Lastly, it is 1 think clear, from a glance over the map of the Government Survey, that their so-called ''Middle Silurian '^ group is generally unconformable to the older Cambrian rocks on which it rests. It must, therefore, be obvious, that the task I had proposed to myself was immediately connected with the facts and conclusions of my preceding paper (read Nov. 3rd, 1852) ; but the bad state of my health compelled me, very reluctantly, to abandon the greater part of it. There remained, however, a second and shorter task in which Professor M'Coy had promised to join me, so soon as he had completed his work in the Cambridge Museum. We proposed to examine in detail the section of Mathyrafal, near Meifod, the sections of the Pentamerus limestone on the flanks of the Longmynd, the sections of the Onny and of Caer Caradoc, and lastly, the sections of Builth, Llandovery, and Llandielo *. I thought that the facts exhibited in these sections must have a direct bearing on the conclusions we had drawn in the preceding year. A very vexatious accident detained us full three weeks beyond the time we had fixed on for the commencement of our task. It was in consequence left incomplete, and our examina- tion of the following sections was confined within the limits of a single week, during more than half of which I was unable to take the field, or to give any help to my fellow -labourer. I. Mathyrafal Section. This section is seen on the north side of the valley, a few miles above Meifod, and its upper beds are now cut through by the new road (from Meifod to Llanfair) which did not exist (in 1843) when the section was examined by Mr. Salter and myself. I will not enter on details which have been already published in the Journal of the Geological Society, but I wish to recall to memory the fact, that there are at least two calcareous bands in the lower part of this section ; and that the upper band, which is concretionary and discontinuous, is associated with a coarse conglomerate and with a hard sandstone, which appears in a nearly vertical position by the side of the new road. These ver- tical beds are overlaid by highly fossiliferous shales and flag- stones of a considerable thickness, which gradually lose their * All the above are critical sections, at the junction of the groups I call Cambrian, with the overlying groups which are undoubtedly Silurian. and the Palceozoic St/stem of England. 3p5 great inclination and pass under the regular terrace of thCiWeji^- lock shale. j, ; An important negative fact is presented by this section. It gives no trace of the May Hill sandstone; and there is no pass- age between the soft earthy beds of the Mathyrafal group and the beds of Wenlock shale which rest upon them, the upper formation having been brought over the lower by an unconform- able overlap. If, in any single section near the cuttings of the new road, there be the appearance of such a passage, it is, I believe, deceptive. The same remark I would now apply without hesitation to the mistaken appearance of a passage between the Cambrian rocks of Glyn Ceiriog and the overlying beds of Wenlock shale, as seen a few miles to the south of Llangollen, where, in like man- ner, the May Hill beds are entirely wanting. I may further remark, that when two unconformable deposits are composed of soft yielding materials (like those just alluded to), it is often impossible, on the evidence of one section, to conclude that they are the conformable portions of a regular and uninterrupted sequence. The lower soft and yielding beds, when pressed down by the superincumbent mass, may give a false appearance of conformity, which may become still more deceptive in cases where both the upper and lower masses have been afterwards subjected to common movements of contortion. On the con- trary, where the lower beds are hard and inflexible, a discordancy of position becomes at once palpable and obvious. Thus, in the neighbourhood of Welch Pool, we have, between the hard and highly inclined Cambrian rocks (which have, I now think erro- neously, been called Caradoc sandstone), and the overlying flag- stones of the Wenlock age, very obvious cases of unconformity. In the hope of making these conclusions clear, I subjoin three ideal vertical sections, two of which (figs. 2 and 3) show the actual sequence of deposits to the east of the Berwyn chain {e. g, at Mathyrafal and Glyn Ceiriog), while the other (fig. 1) shows a similar sequence, among rocks of nearly the same age, on the west side of the Berwyn chain on the line of the Holyhead road. Of these sections, fig. 1 gives a fine exhibition of the May Hill sandstone overlaid by the Denbigh flags, Wenlock and Ludlow, and underlaid discordantly by a part of the great Bala group. Fig, 2 represents a case like that of Mathyrafal, where the May Hill sandstones and conglomerates disappear, and the Wenlock groups rest, with a slight discordancy of position, upon the Cam- brian rocks, which here belong to a high part of the Bala group. Fig. 3 represents the case of Glyn Ceiriog, where there is no apparent discordancy of position, but where the May Hill group is entirely wanting. In one respect all these sections are imper- FUl. Mag, S. 4. Vol. 8. No. 52. Oct, 1854. X 306 Prof. Sedgwick on the May Hill Sandstone, feet, inasmuch as not one of them shows a perfect and continuous sequence of all the deposits within the limits of the section, and I have never seen any such perfect section in North Wales*. Fig. 1. Denbigh flag (Wenlockand Ludlow). May HiU sandstone, &c. Conglomerate. Fig. 2. a 4» m> SZ^-^ ^^^ ^^i^^ ^ Fig. 3. Earthy slates. Calcareous beds and con- glom«rate. Limestone of Meifod. Slates, &c. not exposed in the section. ""• III .__! Paste-rock. Upper lime- stone. Lower lime- stone. Slates and porphyries, &c. alterna- ting. Three sections representing the junction of Cambrian and Silurian rocks in North Wales. Fig. 1. From the neighbourhood of Cemiogie on the Holyhead road, where the May Hill group (No. 2) is largely developed, and rests uncon- formably upon a part of the Upper Bala group (No. 1), and is surmounted conformably by the Denbigh flag (Wenlock, &c.) (No. 3). Fig. 2. From Mathyrafsd. Here the Upner Bala group (No. 1) has an unusual mineral type, and is overlapped. with a slight discordancy of posi- tion by the Wenlock series (No. 3). The May Hill series (No. 2) is entirely wanting. Fig. 3. From Glyn Ceiriog, south of Llangollen. Here a portion of the Upper Bala group (No. 1) is overlaid, without any apparent discordancy of position, by the Denbigh flag (No. 3) j but the May Hill group (No. 2) is entirely wanting. * I believe, however, that some rather soft earthy slates (seen at Glyn and the Palaozoic System of England. 307 II. Pentamerus beds of Norbury and Linley^, The extension of these beds along the southern edge of the Longmynd chain, upon which they rest unconformably, has been well known to geologists since the publication of the ^ Silurian System/ In Siluria they were discovered, and there they have their best, and perhaps their only unequivocal type. Their thickness is not great, and at Linley and Norbury the thickness might, on a superficial view, be easily overrated, inasmuch as the beds dip very nearly with the inclination of the ground, and therefore are spread over a considerable surface. It would be idle for me to attempt any detailed description of these well- known beds; but I may just remark, — (1) That some of the lowest beds are very irregular, coarse, and of mechanical struc- ture, and with very few traces of fossils. (2) That over the above are five or six feet of a bluish-gray ragstone : the beds with very uneven upper and lower surfaces, separated by semi- indurated wayboards, marked by many ferruginous stains, and with a few casts of fossils. (3) That higher in the section are five or six feet of gray and yellowish-gray beds, slightly ferrugi- nous, and with many cellular streaks marking the presence of fossil casts ; also bands of ferruginous " rotten-stone," with in- numerable casts of fossils. As usual, the calcareous matter had quite disappeared from the "rotten-stone" bands. (4) That over the above comes the well-known and beautiful Pentamerus (or Norbury) limestone.' This limestone is, in the Norbury quarries, extensively worked for the neighbouring hme-kilns. The beds are very irregularly deposited, but their average thick- ness is about five or six feet. The preceding group plunges under the soil, and no higher beds were seen ; but there seems to be no doubt that it is almost immediately overlaid (as repre- sented in our best maps) by the Wenlock shale. These facts would not be worth noticing, did they not serve to give a con- nected meaning to the following account of the fossils we found in the quarries of Linley and Norbury. Ceiriog, and also in several sections near the road from Llangollen to Ruthin), which I have often called the paste-rock, are very nearly at the crown of the whole Cambrian series. They were in 1843 sometimes regarded as " beds of passage " by my friend Mr. Salter and myself. They were not, however, true beds of passage in the places where we saw them, as they were overlaid by the Wenlock shales, without the intervention of the May Hill sandstone. * This small group is an important member of the palaeozoic system, and it deserves a geographical name. It may (from its best locality) be con- veniently called Norbury limestone. " Pentamerus limestone " is a bad name for this small group ; for a Pentamerus (though of a different species) is also characteristic of another limestone — the Aymestry. X2 308 Prof. Sedgwick on the May Hill Sandstone, Fossils of the Pentamerus limestone and May Hill sandstone of Linley and Norbury, First of all, we may remark that we have, especially in some of the upper beds, the Pentamerus oblongus and the Pentamerus lavis in infinite abundance. Here, indeed (as I believe also at the Hollies and other well-known localities), they seem to have in a great measure supplied the calcareous matter of the lime- stone. But in addition to these two abundant fossils, and after rejecting many specimens which were too imperfect to give secure results. Prof. M'Coy determined the following species, the list of which is here given in his own words : — '* Ptylodictya lanceolata (as at Dudley). Palaopora interstincta (common to Cambrian and Silurian rocks). Favosites multiporatus (do.). Petraia bina (as in Wenlock limestone and May Hill sandstone). P. bina, an unnamed species (same as at May Hill). Encrinurus punetatus (common to Cambrian and Silurian rocks). Lepttjena transversalis (as in the Wenlock limestone of Wool- hope, Dudley, and in the May Hill sandstone). Leptana euglypha (Wenlock limestone and Dudley limestone). Orthis elegantula (common to Cambrian and Silurian rocks). O. pecten (do.). O. Davidsoni (Wenlock limestone of Walsall and May Hill sandstone). Spirigerina reticularis (Cambrian, Silurian and Devonian). Littorina Octavia (same as in Wenlock limestone) .^^ Upon this list I may remark, that out of fifteen carefully de- termined species, eight have not yet, so far as I have heard, been found except in the Wenlock group or its equivalents ; and that, of the remaining seven species, one ranges up to the Devonian rocks inclusive. The remaining six belong to species which were already known to be common both to Cambrian and Silurian rocks. And lastly, that all those very abundant types, which have hitherto been found exclusively in the Bala and other un- doubted Cambrian groups, are here entirely wanting. We found no other examples of species common to Cambrian and Silurian rocks. But we wepe by no means surprised to find several well known common species in a deposit which is at the base of the Wenlock shale. It is the exact locality where we should have expected to find such species. By itself, this evidence might not be considered sufficient to prove that the Norbury group is to be cut off from the Caradoc sandstone, and arranged with the May Hill sandstone. But and the Palaozoic System of EnglamA. 309 this evidence cannot be taken by itself. It it be called doubtful, there is other evidence in reserve which is not doubtful, andwhich, I think, proves that this Norbury group is an integral part of the May Hill sandstone; that it is unconformable to the Cam- brian rocks where the sections are most complete ; and that it does form a portion of those important arenaceous and shelly deposits which are, both physically and palseontologically, the true base of all the overlying Silurian groups*. III. Sections of Horderley and the Onny. We were well aware of the importance of some sections at the northern end of the Longmynd range, and it was part of our plan to visit them. But my health gave way, and Prof. M^Coy was unwilling to leave me ; we therefore removed to the neigh- bourhood of the Onny, and he proceeded to examine the sections above Stretford Bridge. Comparatively little could have been made of them during a period of great inundation, had not our friend Mr. Duppa previously made his promised excavations in one or two places above the water-level, and con- ducted Prof. M'Coy to them. The evidence was as follows : — About 200 yards above Stretford Bridge, in an excavation made where I had supposed (from my Notes of 1842) that the Caradoc shale extended, they found many Wenlock fossils un- mixed with any older types. Prof. M^Coy^s notes are as follows : — "1. In this excavation was an ahundance of the following species : — Graptolites Ludensis. Calymene tuberculosa, Odontochile longicaudata. Cardiola interrupta. 2. " Between this locality and that which follows, is a change of surface ; and no rock, as stated to me by Mr. Duppa, is di- stinctly seen for some hundred yards. This is the place where we might expect to see the May Hill sandstone and the Penta- merus (or Norbury) limestone ; but they are lost in the obscurity of the section. 3. " About 200 or 300 yards above Longville Bridge the following fossils are abundant, without any intermixture of the above-named Wenlock species : — Orthis calligramma. Leptcena sericea. elegantula (var. a). quinquecostata, parva. (All the above are Cambrian.) Spirigerina reticularis (Caradoc to Devonian inclusive). 4. " About thirty yards higher up the river an excavation had * The reader will observe that all the groups below the May Hill sandr stone are in this paper considered as Cambrian. 810 Prof. Sedgwick on the May Hill Sandstone, been made in a bed of shale, with innumerable specimens of TVinucleus, 5. " Still further up the river followed the well-known Caradoc beds of Horderley/' In the above section the highest beds are undoubted Wenlock shale. The lower beds (groups 3, 4 and 5) are undoubted Cam- brian (one of the upper sandstones of the Bala group). The intermediate, or May Hill group, is lost. There is therefore no contradiction in the section to the views given in my previous paper of Nov. 3, 1852. We have no alter- nation of true Cambrian and true Silurian types; and I now believe that the Trinucleus shale laid bare by an excavation a little above Longville Bridge, was (by an error in my notes in 1842) placed a little above Stretford Bridge. This conclusion I should have come to sooner, had I dared to coax my notes into an agreement with my subsequent views. IV. Sections near Shineton through a part of the Caradoc terrace, a few miles to the north-west of Wenlock. What I had first thought the most important object of our excursion was to examine the whole Caradoc terrace between the Onny and the Severn, in order that we might learn whether there existed in that district any unequivocal traces of the May Hill sandstone interposed between the true Caradoc beds and the Wenlock shale. I thought it probable when my former paper was written (Nov. 1852), that here (as in the lower part of Glyn Ceiriog) the Wenlock shale might hy an overlap have been brought immediately into contact with the true Caradoc group. But before we commenced our excursion, we learnt from Mr. Salter, who had just before visited the country near Wenlock, that the previous conjecture was erroneous, and that there did exist at Shineton and other places along the Caradoc terrace, a series of beds which represented the May Hill sandstone. He gave us his best localities, and a short list of the fossils he had collected from them ; and he added his conviction, that these so-called May Hill beds at the base of the Wenlock shale were unconformable to the contiguous parts of the trite Caradoc sandstone. While I was still unable to take the field. Prof. M'Coy not only traversed the north-eastern end of the Caradoc terrace, but completely verified the previous observations of Mr. Salter ; and I will give the result of his observations in his own words. (1.) " On the road-side, close to Shineton Church, are olive- coloured shales which dip about 35° E. of south, and at about 30°. They were found to contain the following fossils : — Agnostus pisiformis (as at Llandeilo, &c.) in great abundance. and the Palaozoic System of England, 811 Olenus* ? (same species as at Hollybush, — Malvern sections of Phillips). Asaphus ?, undetermined fragments. Cytheropsis Aldensis (as at Aldens on the Stincher, N. B.). Siphonotreta micula (as at Wellsfield near Builth, and at Pentre, north of Llangynyw). All the above are Cambrian types. (2.) " Over these olive shales, and also over some black shales t, with a few traces of Fuci and Orthoceratites in Belswar- dine Brook, are several thin beds of May Hill sandstone and Pentamerus limestone. Dip about 50° E. of south, at 20°. The fossils observed were, — Hemithyris hemisphcerica . Pentamerus Icsvis. oblongus. Petraia (unnamed species, same as at May Hill and Malvern), (3.) " One mile west of Harley are olive-coloured shales, like those of Shineton, and with nearly the same dip and strike. They are overlaid (with a small degree of unconformity) by very coarse unfossiliferous May Hill conglomerates; exactly like those which appear at the base of the May Hill sandstone near the top of May Hill. They are seen in numerous openings along the road to Church Green. (4.) " Beneath the above conglomerates, in large quarries near Harnage Grange, the true Caradoc sandstone and limestone are both found, dipping 10° E. of South, at about 20°, and full of the following fossils J. Or this expansa, Orthis parva. vesper tilio. Actonice. etegantula,var.a. bilohata. All of which are exclusively Cambrian.^' Such were Prof. McCoy's notes. His excursion was made during a day of almost unrelenting rain, otherwise his fossil lists would have been more complete. The above facts, combined * This was one of the species in Mr. Salter's Ust. t In these black shales (as in those of Holly Bush described by Professor Phillips) have been several ignorant trials for coal. X Professor M'Coy does not assert (as I stated by mistake to the Geo- logical Society) that the sandstones near Harnage Grange underlie the olive- coloured Olenus shales of Shineton. He merely states facts, and leaves in doubt the exact sectional position of the shales. But he regarded them as probably forming the base of the Caradoc terrace which extends from Horderley to the Severn. The fossils of the olive-coloured shales evidently indicate their true position, and prove them to be on the same parallel with the beds at Builth and Llandeilo. I was led into the mistake above- mentioned by the shortness of Professor McCoy's notes, and by finding that Shineton was close to the Wenlock terrace on the Geological Map. 312 Prof. Sedgwick on the May Hill Sandstone, with those previously observed by Mr. Salter, were, however, sufficient for our purpose, and enabled us to draw the following conclusions : — (1.) There can now be very little doubt about the geological place of the Hollybush Olenus shales. They are where I had provisionally placed them in my last paper ; adopting without reserve the published views of Professor Phillips, who first dis- covered and described them. Near Shineton, there is nothing in the sections to indicate the protrusion of any very ancient rock ; nor any igneous rock (like the Malvern syenite) to disturb the relations of the neigh- bouring strata. Hence it appears certain that the Shineton beds (although inferior to the above-mentioned beds of Harnage Grange) must be arranged with the shales which form the base of the Horderley or Caradoc terrace ; in which case they must be subordinate to the Bala group. The note of interrogation after the word Olenus in the pre- vious list may perhaps show that Prof. M'Coy is not certain as to the genus; but, whatever it may be hereafter called, he is certain that it is identical with the Olenus of the Hollybush shales. (2.) The (supposed) typical section through Caer Caradoc, Wenlock Edge, &c., is not a truly continuous, but a broken section. The true Caradoc sandstone and Caradoc shale do not graduate into the beds which immediately surmount them ; and the conglomerates, grits, and Pentamerus limestone, &c. (which discordantly overlie the true Caradoc sandstone) must here, as at the south end of the Malvern Hills, be cut off from the Cara- doc terrace and arranged with the Wenlock group. (3.) From the above facts, and from all I have seen or learnt of the older palaeozoic rocks of North and South Wales and the neighbouring English counties, I think I may conclude, that in these great physical regions there is not so much as one con- tinuous unbroken section through which we can ascend, in the way of passage, from the Cambrian to the overlying Silurian groups. There is a physical break between them exactly on the horizon of the May Hill sandstone; and in very exact co-ordi- nation with that break (sometimes distinctly marked by a dis- cordancy in the position of the beds), there is a great change in the fossil species. If this be true, and I know nothing to oppose to it, we have at length found the true physical and palseonto- logical base of a " Silurian System.'^ The accompanying section (fig. 4) represents what is, I believe, the true sequence of the deposits in the Caradoc section. Between the Longmynd slate and the overlying slate and sand- stone, there is great interval, the filling up of which requires the interpolation of, at the least, 20,000 feet of strata, from the and the Palmzoic System of England. 313 Fig. 4. A Section representing the relations of the groups of Caer Caradoc to the overlying Siluriart rocks. Fig. 4. Fig. 5. Old red sandstone. ^v5:^Li Ludlow groups. Wenlock limestone. Wenlock shale. Conglomerates, Nor- bury beds. Sandstones, &c, (l\Iay Hill group). Shelly sandstone of Horderley and Caer Caradoc. Shales, &c. with Bala and Llandeilo fossils. Old rock of the Longmyud. Carboniferous, &c. Old red sandstone. Wenlock and Ludlow. Caradoc sandstone. Llandeilo flags. Cambrian. In the section fig. 4 (from the neighbourhood of Caer Caradoc), No. 4a is, both from its position and fossils, separated from No. 3 and grouped with No. 4 (Wenlock). In the * Silurian System ' Nos. (4a) and (3) were erroneously placed in one group— the " Caradoc sandstone." The group (4«) is here regarded as the true physical and palaeontological base of the Silurian series. This vertical section (fig. 5) represents the supposed sequence of deposits near Llandeilo as given in the 'Silurian System.' But it is erroneous; as No. 1 ought, in a true vertical section, to be above No. 2. The origin of this mistake is explained by help of the profile section, fig. 6, which represents the general position of the groups near Llandeilo, without pre- tending to give any of the intricate contortions. 314 Prof. Sedgwick on the May Hill Sandstone , sections of North Wales. Again, between No. 3 (the sandstone, &c. of Caradoc) and No. 4^ CN ■*► f .■* .**" r^ P aaii i i i a s a 00 so tr(\o 00 00 w-» o t<^ c< OOON'^l-rorlOO O O u 00 2 '^ "^ ^ii i ^ i ^^^ ^ i ^ ^ i s i i i i I i g ^ i g s ^ i ^ s; i i s ^ * ^ c a B c e ii^^iiii^i iii'^»i^iii^i^i^^^^i^^^i^i^i«^^i 51 « r« rt «^VD t^vo tJ- tJ-vo w->« f» o Ovovo w^u-»^^M f«oo 0^*•<4•^^f<^iU. w-> u-> u-i ii-» lo lovo iovnu-»vr>in»oir>«oir)vnw-iu-)ir>u^»nu-)VOvriwi >0^ w^ ir> u-> *uo)8og VO «X> VO rl ■ on on CTn on on "o 0\ b on on on On On On On O O O O O On "o «HtOdcororortf^c<«flf»c0 w-iOO O •'^ v^ ON r-- r^ moo O '-' t^vo c^ t-^oo 0> m ON r«^ t< to rooo OntJ-nnono o t<^mmONc» •-• H wi vo NO OO ON On O O Onoo r>- Onoo r^ t-^OO OO on O O on t^OO O Onm coro^tr^w <-> 1^ ro ^ Onoo O On t^ ^OO r^ ^ rt vO »0 tJ-00 OO OnvO ^ rooo vOVO*-'0000r1Ob ONOO w-ip< toil u-)(/^T^ro^r4 o cOTJ-vomrJ c^iOnN "i O Onno nO On ro fo vovO f r^^ p^ p r* p p p^^ p^ p^ p^'^ ®® p^p ."" r* p^°^ p r ^^ ^ tomrj-Tj-N n On On OS On C "o O O On On On On "on On On 'on O b O On On O O *0» "o O *0 O O O O as <^ >ONO t^oo o\d M (4 («) 4* '^vo r^oo • • • • (^) which contains our propositions 1, 2, 3 and 5. pT- and pT- are the two indices of refraction Iq and I^ ; and for d^ +1 and La=l, we have P = C, and consequently I.=I.+ §, (2) where it is necessary to take the sign — for traction, and the sign -I- for pressure. It now remains to find the values of !« and E. M. Dutirou has determined the indices of refraction of the glasses derived from the same manufactories as those which I have employed ; I might therefore have made use of his results. But notwithstanding the identity of origin, the densities of my glasses differ notably from those found by M. Dutirou. These differences indicate corresponding differences in the composition, and I have thought it necessary, wherever such differences ap- peared, to ascertain by direct experiment the refractive index of the substance. For this purpose a prism was cut from the mass from which the corresponding parallelopiped was taken, and by means of the goniometer of M. Babinet, the index for the mean yellow ray was determined; this suffices in the case before us, the difference !«— lo, which it is our object to find, being inde- pendent of the length of the undulation. Fluor-spar and rock- salt are bodies of such constant properties, that I have been able with safety to make use of the indices given by Sir David Brewster; but I have deemed it necessary to determine the index of inactive alum, on account of the peculiar properties which it exhibits. The coefficient of mechanical elasticity has been found for each substance by means of the transversal vibrations of a thin plate, sufficiently long, which we were careful to take from the 844 M. 6. Wertheim on the double Refraction side of each of the parallelopipeds. Put in vibration by means of a bow, the two ends being free, each plate gave its fundamental tone and some of its harmonics. Experiments have been recently published which tend to cast some doubt on the correctness of this method, and on the certitude of the results derived from it. But by means of experiments on strips of copper of various lengths and thicknesses, which I have caused to vibrate transversely, after having previously determined the elasticity by means of direct elongation, I have assured myself anew of its accuracy ; only it is necessary to take care not to fasten one of the ends of a short plate when transversal vibrations are required : the fastening of the end causes, as is known, errors so consider- able as to alter completely the results of the experiments. The values of E which have been obtained by this method, have been afterwards divided by the coefficient of correction! '05*, in order to find those>which would have been found by the way of elongation. I have caused a plate to be cut for each of the parallelopipeds ; I have hence three plates of rock-salt from different sources, several of fluor-spar, &c. For plates of the same kind, the co- efficients of elasticity differ so little among themselves, that I have only found it necessai*y to inscribe the means in the follow- ing table, reserving to myself to publish the numbers themselves in a special memoir on the elasticity of crystals. Substances. Den- sity. Coefficient of elasticity. E C Index of ordinary refraction. Index of extraor- dinary refraction. Mecha. nical. E. Optical. C. ^0' Authors. Double refraction. Nega- tive. Positive. Crown of MM. Maes "1 andClemandot... J Crown of M. Feil Flint Guinand 2-657 2-629 3-589 2-457 2-447 3-538 3183 2-136 4-050 4-056 4-358 1-632 5888 6397 4976 6180 6220 5323 8647 3876 5208 5017 501 7t 975 26978 2992i 25917 32396 34714 32593 55605 38483 52031 50932 57332 15197 0 2182 0-2138 0-1920 0-1908 0-1792 0-1633 01555 01007 01001 00985 00875 0 0641 1-532 1-541 1-617 l-543t 1-517 1-614 1-436 1-557 1-676 1-624 1-681 1-455 W. Dutirou. W. Wollaston. Dutirou. W. Brewster. Brewster. W. Dutirou. W. W. 1-750 1-755 1-809 1-734 1-696 1-777 1-591 1-658 1776 1-722 1-768 1-519 1-314 1-327 1-425 1-352 1-338 1-451 1-281 1-456 1-576 1-526 1-594 1-391 Plate glass Ordinary crown Flint of MM. Maes \ andClemandot... J Kock-salt Borosilicate of lead... Heavy flint of M. FeU Inactive alum * Ann. de Chim. et de Phys. 3 sir. vol. xxxi. p. 39. t The density 2*329 of the plate glass employed by M. Dutirou, differs too much from that of my glass to permit of my assuming the index found by this physicist. X Having been able to procure only a single cube of the glass, I have temporarily produced in Isotropic Bodies. 345 - E The quantity I^— !«= + ^r is the true measure of the double U J 2 refraction ; for if we take as such the quantity l^ — Iq^ or ^^y we should obtain for the same substance a different birefractive power according as it happened to be temporarily positive or negative, which is inadmissible. It might be hoped that these researches would conduct to some simple ratio between the birefractive power which may be called specific, and the other properties of the body. My first experiments, which were made with some specimens of glass only, had furnished a sensibly constant value for the birefractive power ; and if this constancy had been general, important consequences relative to the distribution of force in bodies naturally birefractive would have flowed from it. But since these first experiments, I have observed* that heavy flint has an extremely high coefficient of optical elasticity ; the ratio of the two coefficients could not therefore be the same as for the other glasses, unless the flint possessed a very high coefficient of mechanical elasticity also; this is hardly probable, when we consider the great quantity of lead which enters into its composition. Indeed, experiment ha^ demonstrated the contrary, and the results which I have since obtained on the double refraction produced in isotropic crystalline bodies are in direct contradiction with any theory of this kind. The birefractive power does not stand in any simple ratio to the density ; neither is it a function of the velocity Oo of light in isotropic bodies, as might be inferred from the results which M. Broch has obtained by calculation f- We are thus obliged to assume that the birefractive power, like the refractive, is inherent in each substance, or what is the same thing, that it depends upon a relation still unknown between the mechanical and optical elasticities of the body. Further, to be sure that there is no parallel between the two kinds of double refraction,~the natural and the artificial, it is sufficient to consider the magnitude of the forces which it would be necessary to apply to an isotropic body to cause it to produce, with equal thicknesses, a difference of path equal to that which results from the passage across a plate parallel to the axis of certain birefracting crystals. Let us compare, for example, Ice- land spar with ordinary crown glass ; the difference of the two been obliged to suppose its coeflficient of elasticity equal to that of the heavy flint preceding ; but its great density renders it probable that the coefficient is really a little more elevated, * Comptes Rendus, vol. xxxii. p. 291. t Dove, Repertoire de Physique^ vol. vii. p. 58. Phil Mag. S. 4. Vol. 8. No. 53. Nov. 1854. 2 A 846 M. G» Wertheim on the double Refraction indices of refraction is sensibly the same for the two substances. For the plate of spar we have rf=L„(I.-I„); substituting this value in the equation (1), we find P=E.Lo.La; and for the unit of surface, P==E. It would therefore be necessary to apply to the plate of crown a pressure of 6220 kilogrammes to each square millimetre of the transverse section perpendicular to the thickness ; that is to say, a pressure more than a thousand times greater than that which would crush the glass to pieces. It now remains to compare the value of the double refraction which we have just found for plate glass, with that which results from the investigations of M. Neumann. After having shown that the temporary optic axes are represented by the following expressions, — C = 0' + qu+p^+py, in which the quantity 0' differs infinitely little from the velocity Oo of light in isotropic bodies, and where a, y8, 7 represent the proportional changes of length in the directions of the three mechanical axes ; M. Neumann seeks to determme the values of/? and q. To find two equations between p and q, he employs two dif- ferent processes, but both of them based on the use of formulae generally admitted for the flexure of prismatic bodies. In the first process, we determine in the medial plane the flexure assumed by the band of curved glass, and the distances of the neutral axis from two points«which possess the same tint, corresponding to a certain thickness of air as determined by the table of Newton ; of these two points, one is above the neutral axis in the compressed portion of the band, and the other at an equal distance below the axis" in the dilated portion. Assuming that a very small parallelopiped, placed at one of these points, will sufi'er the same linear changes as if it had been compressed or dilated by a force equal to that which results from the flexure, we can find, by known formulae, the relation between the double refraction and the mechanical linear change ; we have hence the value oip—q. The second process is based on the method of displacement of fringes, as in the experiment of M. Arago. Of two rays which interfere, one has passed through the dilated, and the other temporarily produced in Isotropic Bodies, 347 through the compressed portion of the curved glass ; the two systems of fringes, extraordinary and ordinary, which are ob- served with a birefracting prism, are displaced with reference to one another, and move as a vernier on its scale. The measure of the displacement gives a second equation between p and q. But in order to deduce numerical results from these experi- ments, it is necessary to assume a determinate ratio between the changes of length which occur in the directions of the three mechanical axes. In theory, this ratio, or what is the same thing, the law of change of volume, may rest indeterminate, as asserted by MM. Lame and Maxwell* ; but not so when it is the question of an experiment, the results of which we would know and apply. M. Neumann has found himself compelled to adopt the law of Poisson, the accuracy of which had not indeed been contested when his memoir was published ; consequently we have and we find jo-9 = 0-054; jo= -0-085; g= -0-139. Introducing the new law into the formulae of M. Neumann, we see that all the numerical coefficients are simplified, and we obtain at the end of the calculation the following values : — y=+8; a=;S= + |; ;>-^=0'0505; ^=_0-3006; g= -0-3511, which difi^er notably from the old ones. If, as in the present memoir, we confine ourselves to the determination of the quan- * I profit by this occasion to protest against the inexact manner in which Mr. Maxwell has reported my experiments (Trans, of the Roy. Soc. of Edin- burgh, vol. XX. part 1, page 87). " M. Wertheim," he says, "has given the results of some experiments on caoutchouc, by means of which he finds A K=A: or 11-=. — m, and he concludes that for all substances we have K=A;." «j Here Mr. Maxwell speaks only of experiments which I expressly stated to be preliminary ones, and he passes in silence others much more exact and more varied, which I have made by means of hollow cyUnders of difi'erent substances. To demonstrate afterwards that the law of the change of volume may vary with the nature of the body, Mr. Maxwell cites cork, which has a cubical elasticity smaller, and a linear elasticity greater, than the corre- sponding elasticities of a jelly. It will certainly not be admitted without difficulty that these two substances are types of homogeneous bodies ; but even if they were, Mr. Maxwell has cited no experiment in support of his opinion. 3A2 348 M . G. Wertheim on the double Refraction tity 7T> — which corresponds, in the formulae of M. Neumann, to — , — we find it equal to 0*157 by the old formulae, and equal to 7 0*168 by the new ones; this latter differs much less from the value 0*191 which we have obtained by direct experiment. But the difference becomes still less when we take into account that M. Neumann has applied his calculation to the means of measurements taken on two bands which were not of the same description of glass : further, in their composition the glasses of Germany employed by M. Neumann differ sufficiently from those of France to prevent the values of E and of C from remaining the same. A band of Bohemian glass has given me, by means of transversal vibrations, a coefficient of mechanical elasticity of 6594, which is notably superior to that of our glasses. In general, the theory of flexure itself, and the determination of the changes of volume which occur in all the parts of the body submitted to flexure, seem to me to be based on too many hypotheses with reference to the position of the neutral axis, to serve for the calculation of experiments so delicate as the present ; by following an inverse method, it is my intention to make use of the results which, by purely direct means, 1 have obtained in this memoir, on the examination and elucidation of the theory of flexure. Simultaneous effects of a mechanical force and of Magnetism, The proximity of a powerful magnet produces in certain iso- tropic bodies a rotation of the plane of polarization. It was interesting to see how this novel action of magnetism, which has been discovered by Mr. Faraday, would be modified when the same body had ceased to be isotropic, and had acquired optic and mechanic axes of different magnitudes. MM. Bertin and Matteucci have made already some researches in this direction. It has been seen how the apparatus is disposed for these ex- periments, which have been carried out principally on substances endowed with the rotatoi*y magnetic power, such as the flints. The result has been the same for all substances ; the rotation disappears according as the axes become unequal ; a relatively feeble pressure or traction is sufficient to render the phsenomenon less defined, and aftbrwards it becomes more weakened as we augment the charge; but the moment when it disappears cannot be exactly determined, because the operations lose much of their precision when, in consequence of the newly-produced double refraction, the two images become illuminated. By making use of homogeneous rays, we may in all cases convince ourselves that the rotation has completely disappeared when the difference temporarily produced in Isotropic Bodies. 349 of path has amounted to -, for then the ordinary image is com- pletely obscure ; and if the least trace of rotation existed, it would manifest itself immediately in this image. The insensibility remains the same, whether we establish the current in one or the other direction, or interrupt it^ or even when we reverse the poles of the magnet. It is to be observed, that the glass endowed with the most energetic rotatory power is at the same time that in which the birefracting power is most feeble ; the same observation applies, among isotropic bodies, to alum and rock-salt_, and a similar analogy appears to exist in bodies naturally doubly refractive : the rotation is zero in Iceland spar, the birefractive power of which is 0*175, while it is very sensible in quartz, which pos- sesses the very feeble refractive power of 0-009. This is a point which it will be necessary to take into account in subse- quent researches ; for the present it is enough that we have de- monstrated that this apparently direct action of the magnetism upon the sether depends essentially on the constitution of the latter, and that it can be annulled by forces purely mechanical. Applications of the temporary double refraction. The formula (1) contains all the quantities which exert an influence on the phsenomenon of double refraction : thus far we have made use of it to determine the value of the indices of ex- traordinary refraction; but when those indices are once known, the same formula can serve for the determination of any one of the quantities contained in it. A. Determination of the force P; — Chromatic Dynamometer. The dynamometers designed to measure the effects of traction, have, during the last few years, been carried to a high degree of perfection by the labours of MM. Poncelet and Morin; but this is not the case with regard to the measurements of pressures exerted between two solid bodies ; no exact instrument has as yet been constructed for the purpose ; we know nothing of the useful effect of the commonest machines, such as presses, vices, systems of levers, &c. The chromatic dynamometer (Plate II. fig. 3) seems to me to supply this want ; after what has been said, it will be easy to understand its construction and application. The essential part is a plate of glass, perfectly transparent in the direction of its length, of such dimensions that it can support very considerable pressures, and blackened all round with the exception of the two faces through which the operator is to look. This plate of 860 M. G. Wertheim on the double Refraction glass a, furnished on its two parallel surfaces with parallel cards of vulcanized caoutchouc, is placed between two surfaces of cast iron well planed and sufficiently thick; the inferior of these plates b carries two tubes of brass, the interior surfaces of which are blackened. The object-tube contains a Nichol d at the ex- tremity nearest to the observer, and carries at the other end a plate of white porcelain e, which is moveable in two perpendicular directions, and which, consequently, can always be placed in a position to be well illuminated. This arrangement has the ad- vantage of permitting those rays only to arrive at the Nichol which are sensibly parallel to the axis, and to cut away the internal re- flexions, which are always prejudicial ; the other tube /carries a birefracting prism g. These two tubes are mounted stiffly in the grooves h, adapted to the inferior plate, so that by employing plates of glass of different thicknesses, we can always place their axes in the prolongation of each other, and at half the height of the glass. The upper plate of metal i is altogether free ; it is placed upon the last card, and serves simply to transmit to the glass the pressure it receives, without being able by any friction whatever to cause a loss of force. It will be further understood, that the exterior diameter of the tubes ought always to be smaller than the sum of the thicknesses of the horizontal plates. The principal sections of the Nichol and the birefracting prism are parallel to each other, and form an angle of 45 degrees with the vertical. We have now only to place this small apparatus between the two surfaces on which the pressure is to be exerted. Whatever be the nature of the force applied, whatever be the losses which it may have sustained before producing the useful effect, the measure of this effect will be always given by the simple inspec- tion of the colours which exhibit themselves in the two images, that is to say, by the value of d. We have, in fact, the equation p_? on the Porosity of Bodies, ;;?? Ml d7Sk extremely delicate spangles, which show the same porosity as the finest metallic scrapings obtained by the first-mentioned method. Now as the particles loosened by gentle tapping perfectly correspond in their minutest structure with that of the detritus procured by scraping, they serve at the same time as a proof that the porosity of the finest scrapings is by no means artificial, effected through the operation of scraping, but that it is a natural formation. Further, through the tapping method porous spangles are loosened, not only from the surface of the object, but also (if one cuts it up into points and separates the latter) from its inner parts, and throughout its whole substance, — spangles, the minutest structure of which throughout corresponds with that above de- scribed. It follows hence, that we have here to do with the natural structure of the body itself, and not with an artificial product arisen from mechanical friction and continued tapping, or through the weather. There is another advantage in the tapping method. By means of it one is able to perceive with more certainty and ease the structure of all vegetable structures, than by means of scraping ; for as the vegetable structure, generally speaking, is denser and more compact than the structure of animal formations, it is in- comparably more difficult in the former to prepare scrapings fine enough for distinct recognition of the pores. Hence it is well for us to have the method of gentle tapping to resort to. 2. Method of proceeding with Bodies that are fresh and still moist* In animal and vegetable bodies that are fresh and still satu- rated with moisture, may be recognized as well porosity in general as also individual pores. In order to this, pass the knife most gently over their surface, lay the detritus upon glass, and examine without the addition of any water and without a covering of glass. By the latter, a covering of glass, the micro- scopic pores in moist organic substances are not only more or less pressed together, which renders a recognition of them more difficult, but evaporation of the plasma which saturates the texture is retarded and prevented. Now such evaporation being' just what mainly contributes towards a recognition of porosity, the more distinctly does the latter appear the further the evapo- ration has proceeded under the eyes of the observer. In the ex- amination of dried substances these collateral effects of a glass covering are not to be apprehended, as the former sometimes no longer contain any fluids, and sometimes cannot be so easily compressed ; and its application here is usually indispensable in order, as already said, to prevent any confounding with dust- particles which may possibly fall upon the glass during the observation. . . •74 Dr. Barry's Account of the Discoveries of Keber Now this circumstance, that, in thus proceeding, porosity is perceptible in entirely fresh organic formations too, immediately meets the objection which perhaps might be taken — that this porosity is merely an artificial product, the effect of drying. I would here however bring to especial remembrance the fact, that, as experience shows, organic formations by no means lose their natural texture through mere drjdng; for dried animal and vegetable textures, through fresh moistening, reassume their former appearance and original condition *. Very conspicuous are the pores in the roots of plants when examined after proceeding in the following manner. Take fresh roots filled with their juices or after having lain in water, — remove the earth, — apply gentle scraping, and then spread out upon glass for examination, without a covering of glass, the de- tritus adhering to the knife. Then, as the fine scrapings on the glass dry up and the moisture contained in their interstices evaporates under the eyes of the observer, the pores in their substance, with intense illumination, are brought out in so distinct a manner that the whole scrapings appear composed of a network of variously twisted and overlapping filaments and scales, leaflets and granules ; and in fact everywhere present a composition like that of sponge. The addition of water having been avoided, there is besides observable in the neighbourhood of the scrapings some detritus still much finer than the rest, in which one may very well recognize the disposition of the granular materials to form minute filaments, and the interstices thereby arising between them. It requires however a good light and a trustworthy microscope to recognize these pores of the roots of plants ; yet a linear enlargement of from 200 to 300 is always sufficient, and from the greater clearness thereby eflfected, is preferable to higher magnifying powers. Having now, according to the above-mentioned methods, ex- amined with perseverance and care all the animal and vegetable formations of many classes in both kingdoms which it was pos- sible to get access to, as well as all sorts of inorganic bodies, I consider myself entitled to make the enunciation, that now-a- days porosity in all solid bodies admits of optical demonstration. Far, however, am I from maintaining that every light-reddish glimmering place in fine scrapings is always an open space; rather do I unconditionally admit that many of them are covered by other delicate lamellae. Yet in my opinion this circumstance proves nothing against the porosity of bodies generally, which is more required to be established than the perception and measurement of individual pores : though during an occupation * J, Liebig, U c. p. 2. on the Porosity of Bodies. 876 with this subject that lasted many months, I met with no scrap- ings in which unequivocal pores were entirely missed. But with respect to the objections which many will feel in- clined to aim at the correctness of my statements, they have been mentioned briefly in the foregoing, and amply treated of and met in my paper ; so that to avoid being too diffuse, I must refer thereto. As for the rest, I am convinced that practised observers, should they determine with their own eyes intimately to test the accuracy of my statements according to the above described methods, will be directly led to the firm conviction that the porous structure of the particles is not the product of mechanical division into minute parts, but a natural formation, and that the porosity perceptible in the same is no optical illusion. Among the organic and inorganic bodies examined by me according to the above methods, I would especially mention the shell and membranes of the egg, the epidermis and cutis of man and many animals of different classes ; further, horn formations, hair, the cell-membrane, the mucous and vascular membranes, the walls of capillaries, lymphatics, blood-corpuscles, serous membranes, ligaments, bones, and teeth. Further, my examina- tions have extended to all parts of plants, in the course of which I repeatedly discerned the microscopic pores most definitely in the roots. In my paper already mentioned, plate 1. figs. 6, 7, 8, represent the microscopic pores of the outer layer of a white bean, of a potato-peeling, and of cork. Lastly, of the vegetable formations examined, I have to mention charcoal, pit coal, and brown coal. Of the inorganic bodies whose microscopic pores I have found, I would make especial mention of gold, tin, silver, lead, iron, granite, many crystals, &c. My paper, in plate 1. figs. 10, 11, contains drawings of the microscopic pores of gold and of iron. The pores of granite measure yaV o'" (^' ^* Pa^'is line) in diameter, those of iron 20V0'" ^^ ToVo'" > those of steel, which however are very difiicult of demonstration, appear to be still somewhat smaller. The average size of the pores in all vegetable formations may be taken at yjW'", among which there occur individual variations of from toVu *^ 2 o^(jo'"' "^^^ pores in animal formations as to size do not widely differ from those of plants ; they appear however to be a trifle larger. In the shell of the hen^s egg they measured g Jo"' *^ 2 oVo"^ i^ *^^ membrana test^ on the average jsqq'", in the membranes of the ovum of Man and the Rabbit ygVo'" ^^ tug's'" > ^^ ^^^ human cuticle and skin the same. The pores of the epithelium and mucous membranes had the same size, while in the epithelium and all other layers of the vessels I remarked and measured pores from y^^o 0 ^^ 2 oVo'''^ ^^ individual cases however even large rifts or clefts from -^^fj'" to s^jj"'* The pores of the lym- '376 Dr. Barry's Account of the Discoveries of Keber phatics measured j-^j^js'", those of the serous did not differ from those of the mucous membranes ; the pores of the bones and teeth in cases which I examined, measured from TTniij'" *^ ttt^oo'"' In respect of all other details I once more refer to my repeatedly mentioned paper. The physiological and pathological conclusions following the above mentioned facts require, for the reader acquainted with his subject, no more than a short intimation. As from the results of my examinations the vascular membranes are not " hermetically closed," but porous quite through, — as even the walls of the capillaries arc not " structureless,'^ but consist of a network of the finest filaments and plates, between which the microscopically perceptible and measurable spaces form a system of the finest hollows and interstices, — the physiological processes of endosmosis, exosmosis, absorption, nutrition, and secretion, now appear to us as a natural consequence of this physiological and mechanical constitution of the vascular membranes. It consequently follows from the above discovery — which, proceed- ing by the methods I have given is not difficult to confirm — that in all organic textures there are present and optically de- monstrable those microscopic openings, without which the most important vital processes must always appear incomprehensible to the natural understanding. By this demonstration there falls one of the most important bounds through which the doctrine of a change of material had so much of the tottering and hypothetical, and a long and on-many-sides sought positive foundation for the understanding of most organic processes has now been shown to admit of objective demonstration. That the cell-membrane of plants is by no means structureless, but is composed of the finest filaments, has very recently been demonstrated by Agardh*, who has thereby confirmed the re- presentation given by Martin Barry in 1842. v Further, I would call to remembrance the fact, that through the objective demonstration of the microscopic pores already formed in all animal membranes, the penetration recently shown by G. Newport t of the spermatozoa into the frog's ovum seems to find its natural explanation, seeing that the spermatozoa, possessing no perforating organs at their fore-end, are incapable of boring through a poreless membrane; whereas, with the presence of preformed pores, even a yielding together of the texturC'elements and an enlargement of the natural pores through * De cellula vegetabili fihrillis tenuissimis context a, Lundse, 1862, page 8. — See Proceedings of the Royal Society of London, March 17, 1853. t Phil. Trans. 1853, p. 271, Note. — The penetration of the spermatozoa into the Rabbit's ovum had been discovered by Martin Barry ten years before. (Phil. Trans. 1843.) 'y^'^^^ on the Porosity of Bodies. ''^ -^ WT mechanical pressure may follow. Here too belong the penetra- tion of entozoa and their ova into the blood, — the penetration of molecules of mercury, fat-globules, even finely pulverized solid bodies, through the pores of the epidermis and of the mucous membranes, — the passing out of blood- globules through the loosened capillary walls in menstruation, — the pressing through of blood-corpuscles in bloody secretions, in pneumonia, &c., — the penetration of the materials of disease into the blood through the outer skin and the mucous membranes, — the finding in the blood of substances introduced, &c. With regard to vegetable physiology, and in respect of the experiments long since instituted by Stephen Hales and very recently confirmed by Liebig*, I must give utterance to the de- claration, that since my discovery of the visible and measurable microscopic pores in all vegetable formations, the currents therein may with ease be referred to the physical agencies of capil- lary attraction, evaporation, &c., without requiring with Du- trochetf to have recourse to an active mysterious vis a tergo to explain the rising of the sap. In this manner of viewing the vegetable organism, it appears to us an exquisitely constructed machine indeed, yet set in motion chiefly by means of simple physical forces, — a machine whose universally-diffused porosity permits as well the ascent of the fluids out of the earth sur- rounding the roots, as also the evaporation of the plasma satu- rating all vegetable formations, according to physical laws. I have the additional remark to make, that my paper in ques- tion, plate 1. fig. 5, contains a drawing I made, faithfully de- lineating nature, the result of numerous observations, of the Aspidogaster conchicola (Baer) living in the pericardium of Unio and Anodonta, in which may be observed the pressing through of the granular molecules out of the intestinal cavity into the substance of the body ; a process that may be not only observed, but followed through all its stages, during lifeJ^ Confirmations. In testing the accuracy of Keber^s observations, so far as my health permitted, I used a J-th-inch object-glass, very lately made for me by Smith and Beck. Of the performance of this object-glass, I need say no more than that the order for it was given by my esteemed friend J. J. Lister, — that it was submitted for his approval before the fitting on, — and that he wrote to me concerning it : — '^ I can report with much satisfaction of its quality — its correction and defining power being all I should * I. c. p. 72, &c. 't' U agent immediat du mouvement vital, 1 826, p. 90. Phil. Mag. S. 4. Vol. 8. No. 53. Nov. 1854. 3 C i^TS Dr. Barry's Account of the Discoveries of Keber expect in a glass of its focal length, with its large aperture (of from 100 to 110 degrees, according to the absence or the thick- ness of a medium covering the object)/' My microscope has a " slow motion " for fine adjustment of focus, given by a nut that has its margin divided into tenths *. Keber insists on the absolute necessity of obtaining for exa- mination particles that are exceedingly minute. He conceived the beautiful idea of first dispensing with art in getting these, and collecting such as are " weathered '' off — particles of Nature's own preparing. Not until these had been well studied did he venture to examine the detritus artificially obtained, and of this, too, he always selected the minutest. Nothing could be truer than what Keber says on this subject of minuteness. It alone would have been a boon to physiology. I tried his plan, exa- mined particles '' weathered " off, — compared these with the minutest of such as had been obtained artificially,— saw the same in both, — and am therefore enabled to confii*m his statement that the appearances described by him are not the product of arti- ficial dislocation. He points out where it is important to avoid adding water, and where to add or not to add a covering of glass. Here, too, my own experience enables me to attest the advantage of rigor- ously attending to what Keber recommends. Most aptly does he describe the fine scrapings of the roots of plants, after evaporation has proceeded for a while, as appear- ing '' compose.d of a network of variously twisted and over- lapping filaments and scales, leaflets and granules ; and in fact -as everywhere presenting a composition like that of sponge." " A system of communicating hollows, interstices, or passages," as Keber describes what he saw in the detritus of scraped, dry, organic objects, no careful observer can, I think, deny. Such a composition of scales that overlap each other, and fibres that run in all directions, cannot but resemble sponge. The scales, however, met with among the weathered-off par- ticles, as well as those found when the detritus has been ob- tained, by scraping or by tapping, in its minutest form, require an additional remark. Each of these scales I find to be a flat or discoid nucleus that has divided into many still adherent parts, which are pressed into various forms, each part being itself a nucleus, and having its single nucleolus. The round orifices of Keber, I think, must be the nucleoli now referred to. In animal and vegetable formations, look where you will, you ♦ It is known that the best performance of an object-glass of such an aperture as that in question is thus obtained hy measuring the thickness of the medium covering the object, and setting the collar of the object-glass accordingly. on the Porosity of Bodies. 879 find either fibres or scales, or both ; the scales composed oi nucleolated nuclei, and these being the elements of fibre which is sometimes seen formed within the scales. Mammiferous Red Blood-corpuscles of extreme minuteness, each bearing a Cilium {as described in the Phil. Trans, for 1841, pp. 245, 246). There was a reason why these discoveries of Keber on the porosity of bodies should have especial interest for me. Since 1840, I had been stating facts which showed the material for the elements of tissues, for nutrition, and for the formation of new parts, to be derived from the corpuscles of the blood*. I had also been endeavouring to point out the importance of nucleai self-division. How satisfactory, therefore, to find as one of the results of researches continued for many months by one of the most careful of observers, that the vascular membranes are " not ^ hermetically closed,^ but porous quite through,^' and that the capillaries are *' not ' structureless,' '' but consist of a network of the finest filaments and plates, between which the microscopically perceptible and measurable spaces form a ^'system of the finest hollows and interstices/' sufficient to admit the passage of solid bodies. Further, how satisfactory now to be able to refer to a descrip- tion I gave in the Phil. Trans, for 1841, of red blood-corpuscles of extreme minuteness, each bearing a cilium. Regarding these I gave the following particulars. They arise in parent corpuscles. Some of the parent corpuscles are of prodigious size — jq"'. They are always very pale, and sometimes even colourless. You occa- sionally see them ruptured and partially discharged of their contents. In this state they frequently appear shrivelled. When not ruptured they are filled with young corpuscles. These after liberation acquire red colouring matter. Sometimes they become * Phil. Trans. 1840, 1841, Edinburgh New Phil. Journal, Oct. 1847. After closely studying the elements of nearly all the tissues of the animal body, I was enabled in 1841 to write as follows : — " Every structure I have examined arises out of corpuscles having the same appearance as corpuscles of the blood. I may here mention, that the tissues submitted to actual observation, with the result just mentioned, will be found to include the cellular, nervous, and muscular; besides cartilage, the coats of blood-vessels, several membranes, the tables, cells, and cyhnders of the epithelium, the pigmentum nigrum, the ciliary processes, the crystalline lens itself, and even the spermatozoon and the ovum. And among the vast number of obser- vations made, 1 have not been able, with the greatest care, to detect a single fact inconsistent with the conclusion above announced. If that con- clusion— which regards the formation of the tissues — be correct, it may, I think, assist us in considering ' the mode in which the floating corpuscles of the blood conduce to nourishment' during life." — Phil. Trans. 1841, p. 217. 2C2 380 M. W. Beetz en the Magnitude of Galvanic Polarization. tinged with red before their liberation. When Hberated they present a star-like form. This form I in some instances noticed them to have while within the parent corpuscle. Before becoming star-like, they present about half-a-dozen segments; each segment sends out a cilium, and hence the star-like form. Such corpuscles are seen slowly revolving, and even performing loco- motion. They are also seen effecting changes in their form — struggling, as it were, in order to separate into parts, each part or segment bearing its cilium. After such separation the ciliated segments exhibit extremely vivid motions. But these are far from being the minutest red corpuscles met with in the same blood. Many are seen not exceeding in size the separated segments just mentioned, but star-like in their form. [May not these arise from the segments in question, which are nuclei, performing self-division ?] Lastly, there are other bodies so immeasurably small as to appear as mere points. They have precisely the same red colour as corpuscles of larger size, and exhibit most vivid motions. I believe these to be no other than separated and ciliated segments of the /a^^-mentioned generation of star-like corpuscles. Such then was the account I published at the time mentioned, of this self-division of red corpuscles of mammiferous blood. It may be asked : Where do such self-divisions end ? Who will say that exudation corpuscles and all that the blood deposits for nutrition or the formation of new parts, are not nuclei thus derived from corpuscles of the blood ? Where does the formation of cilia cease ? Who will say that spermatozoon-like blood-corpuscles, of a minuteness that no magnifying power can reach, do not escape the vessels, sculled by cilia through the pores ? XL VIII. On the Magnitude of Galvanic Polarization, By W. Beetz*. THE experiments of Lenz and Saweljew have demonstrated that the polarization of a platinum plate by means of chlo- rine is nearly equal to zero, whereas I have found that the elec- tromotive force of platinum and chlorine in a gas battery is more than half as great as the force of platinum and hydrogen, and at the same time it was manifest that the effect produced upon a charge already established, by agitating the platinum electrode covered with chlorine, was to increase the current. As the mea- surements of the Petersburg physicists are vitiated by numerous sources of error, I instituted new experiments, and thereby deter- * From Poggendorffs Annalen, vol. xc. p. 42. M. W. Beetz on the Magnitude of Galvanic Polarization, 381 mined the charge of two platinum plates between which hydro- chloric acid was decomposed. In these experiments either both electrodes consisted of platinum, in which case the polarization Pt(Cl) + Pt(H) had to be subtracted from the original force of the current, or the positive plate consisted of zinc, and was immersed in a solution of sulphate of zinc, when the polarization Pt(H) alone remained ; or lastly, the negative plate consisted of copper and was immersed in a solution of sulphate of copper, in which case the polarization was Pt(Cl). In the last two cases the force of a second battery was introduced into the circle ; that is, Pt CI H -f ZnO SO^ in the one case, and Cu SOHPt CIH in the other. These forces were measured by the compensation-method, and then introduced into the calculation with their proper signs. For the sake of convenience, all the electromotive forces which will be employed in the following experiments are collected together in the following table. According to the unit here employed, the force of a Grovels battery was found from a mean of twelve measurements to be 37'26. I. rix^ PtSO^ =40-26 PtNO^ =36-24 PtS03Aq= 32-66 PtKCl =31-97 PtNaCl =31-80 PtNaBr =30-79 PtKBr =29-50 PtClH =29-10 PtKI =21-67 CuCuO 80^=21-22 ZnZnOS03= 1-34 ZnSO^Aq = 0 These numbers are for the most part deduced immediately from measurement, and partly by employing the law of the elec- tromotive powers of bodies to the actual measurements. At first, the circuit of a battery of platinum and zinc, consisting of one or more elements, was closed by means of two platinum plates in hydrochloric acid. By measuring the force of the bat- tery alone, and its force after introducing the hydrochloric acid, the following six values were successively obtained for the — .^ II. ^ Polarization, Pt (CI) -hPt (H). 29-30 27-91 30-29 30-32 27-45 27-75 Mean . . 28-83 882 M. W. Beetz on the Magnitude of Galvanic Polarization, This force varied very little with the increasing intensity of the decomposing current. Further, platinum was used for the negative, and zinc for the positive electrode ; the former being immersed in hydrochloric acid and the latter in dilute sulphuric acid, so that both liquids were in contact with a cylinder of porous clay. The result was, — III. Polarization, Pt(H). 1908 19-23 20-26 17-36 19-48 Mean . , 19-08 . In a similar manner, by employing platinum immersed in hydrochloric acid for the positive, and copper immersed in a solution of sulphate of copper for the negative electrode, the fol- lowing numbers were obtained: — IV. Polarization, Pt{Cl). 10-46 9-79 10-34 1003 10-20 10-78 Mean . . 10-27 Hence the — Polarization by chlorine = 10-27 hydrogen =19-08. Therefore the polarization by both gases is— Calculated. Observed. 29-35 28-83 Consequently, the charges have here been added together ; hut the absolute magnitudes of these charges are the same as those which I before found for the electromotive forces of chlorine and hydrogen in a gas battery ; for the latter, when reduced to the present unit, would be 10*10 and 17*89*. That such a near coincidence should take place in the decom- position of hydrochloric acid, and not in that of dilute sulphuric * Phil. Mag. S. 3. vol. xxxvi. p. 81. M. W. Beetz on the Magnitude of Galvanic Polarisation, 383 acid, may probably be thus accounted for ; in the former case the whole electrolyte is exactly decomposed into its constituents, whilst in the latter case, besides the decomposition of water, a separation of the sulphuric acid from the water also takes place, consequently a second polarization occurs. On this account I endeavoured to obtain more of such decom- positions, and employed for this purpose the haloid salts of the alkaline metals, from which the halogens were separated at the positive platinum electrode, whilst a plate of copper, immersed in a solution of sulphate of copper, served as the negative electrode. At the commencement I convinced myself that the same polariza- tions occurred in these decompositions as in those of the hydrogen acids. The following are the results : — Polarizatio n, Pt (CI). In the decomposition of a solution of — V. VI. €hloride of sodium. Chloride of potassium 10-54 11-36 10-90 11-28 10-95 Mean from V. and VI. = 11-01, Mean from IV., V. and VI. =10-58. Polarization, Pt (Br). In the decomposition of a solution of — VII. VIII. Bromide of potassium. Bromide of sodium. 710 7-11 6-46 6-93 . 6-86 Mean from VII. and VIII. =6-89 In the decomposition of a sohition of iodide of potassium the following values were obtained : — IX. Polarization, Pt (I). 3-22 3-91 3-65 Mean . . 3*59 384 M. W. Beetz on the Magnitude of Galvanic Polarization. The following table is deduced from the above and from fonner observations : — Electromotive Polarization. force. In iodine .... 3*59 3*36 f In bromine . . . 6*89 696 ^ In chlorine . . . 10"58 1010 In hydrogen . . . 19*08 17*89 In chlorine + hydrogen 28*83 27*99 Consequently the law above expressed is true for all these substances. In a former memoir* I found that the polarization of a pla- tinum plate in dilute sulphuric acid, in comparison to the force of a Grove's battery, was as 21 : 32, hence its true value is 24-4; later measurements gave a mean value equal to 25-30, or six units greater than in hydrochloric acid. This difference may probably be explained by the separation of the ^yater. The deviation of the polarization Pt(0)( = 24'4) from the elec- tromotive force of this gas ( = 3*42) is, however, very great indeed ; it cannot certainly be explained by the concentration of the acid. I expected to find that the formation of ozone caused this deviation, inasmuch as, according to its chemical and phy- sical properties, ozone always deports itself as negative with respect to chlorine. It is true that all attempts to generate a sufficient force by converting oxygen into the allotropic condition by means of an electric discharge were unsuccessful ; nevertheless I do not relinquish the hypothesis, seeing that, according to this method, only small traces of the allotropic oxygen could arrive at the gas battery, the greatest part being consumed in the forma- tion of ozone, or becoming converted into the usual condition. The polarizing action of the allotropic oxygen, therefore, is limited to the moment of its production ; and hence the polarization of the positive electrode may sink in so quick a curve to the elec- tromotive force Pt (0)t, whilst that of the negative electrode has only to traverse the small fall Pt(H), perhaps only to the reprO' duction of the original condition of the liquid. * Pogg. Ann. vol. Ixxviii. p. 3. t Ibid. vol. Ixxix. p. 10. XLIX. On the Periodical Variations of Terrestrial Magnetism, By A. Secchi, Director of the Observatory of the CoUegio Romano^. IN all physical problems it is from the intercomparison of phse- nomena that great discoveries may be hoped for, and more especially so when the cause of the phsenomena appears very ob- scure and complicated. Such are the diurnal and annual variations of the magnetic needle, which, being manifestly connected with the sun's movements, have been attributed to that heavenly body, by supposing it to act either directly as a magnetic body, or indi- rectly through the variations which it produces in terrestrial temperature. Dr. Miiller, in two memoirs published in the Italian Ateneo (which he has kindly sent to me), has recently examined the correspondence between the magnetic variations and those of temperature, and has proposed new methods for studying it in future. In the analogy found by him, and which appears to me to have been carried too far, he has pei-haps been led astray by an imperfect graphical method, and by paucity of materials; those used by him being only the observations of Arago and Quetelet, and of these only such as are quoted by Kaemtz. It does not appear that he has attempted to discuss the gigantic works, which have been executed in recent years in so many and such well-equipped magnetic observatories scattered over the globe, and more especially those established at the ex- pense of the British Government, the observations of which have been published and discussed by Colonel Sabine in nine large volumes, published at the expense of the same Government ; for Dr. Miiller says, in p. 2 of his memoii', ^Hhat in the absence of long-continued observations and well- assured data, the results hitherto obtained are but little satisfactory.'-' I have thought it useful to supply this omission, and at the same time to complete the very imperfect information given re- specting this branch of knowledge, even in the most esteemed courses of instruction, by a brief exposition of what has been hitherto done and discovered. While thus engaged, there pre- sented itself to my apprehension a law of great simplicity, by means of which all the facts are reduced to a very simple theory. So much simplicity of law, in phsenomena apparently so irregular, encouraged me to publish this memoir, which naturally divides itself into three parts : — 1. The historical exposition of what has been done towards the study of the variations of terrestrial magnetism. 2. The systematic exposition of the consequences deduced. * From the Corrispondenza Scientijica in Romtty July 15, 1854; com- municated by Colonel Sabine. 386 M. A. Secchi on the Periodical Variations 3. The discussion of the hypotheses hitherto propounded for their explanation. I hope this memoir will not be unacceptable to my readers, as the sources to which I have fortunately access, if not all that are possible, are at least the best, and moreover are such as are not at every one's command. At the present time, when observations and inquiries of all kinds are so much multiplied, it is besides most desirable that such classical works as have already been performed should be widely known, that time and labour may not be lost by doing again what has been already well done by others. Part I. — Brief historical Exposition of what has been under- taken for the study of the Magnetic Variations. In the study of great problems in terrestrial physics such as the present, the zeal and activity of a single observer are quite insufficient, not only on account of the multitude of data required, but also because simultaneous observations in many countries are needed ; thus the aid of scientific societies, and sometimes even the active cooperation of governments, becomes indis- pensable. So long ago as 1761, the observations of Cassini in France and Gilpin in England, repeated at Rome by P. Asclepi in ] 762, had shown that the needle has a diurnal variation, and the latter had even suspected an annual variation. In 1741, Celsius in Sweden and Graham in London, by a series of con- certed corresponding observations, discovered the simultaneity of great magnetic perturbations at different points of the globe ; a discovery which was afterwards forgotten, and was remade by the observations, also simultaneous, of Arago in Paris and Kupffer at Kasan in 1825. The illustrious Baron Alexander von Humboldt undertook in 1806, at first alone and after wurds with the help of others, a series of uninterrupted observations on certain days in the year. They consisted in observing the needle every five minutes on the days of the solstices and equinoxes. The apparatuses employed by these first observers were different, — Humboldt used a mag- netic coUimator of Prony, and Arago a variation needle of Gam- bey ; but notwithstanding the anomalies which this circumstance was likely to introduce, the simultaneity of the perturbations and the parallelism of the movements of the needle were manifested at Berlin, Paris, and in the Mines of Freyberg 66 metres deep. Between 1832 and 1836, Gauss, having directed his learned re- searches to the theory of terrestrial magnetism, furnished its students with new methods and instruments of observation, and thus introduced a new sera in the science. There was then orga- nized a society of observers who undertook to make observations of Terrestrial Magnetism. 387! at the same precise instants of time, on particular days, at dif- ferent places. The magnetic observations at Gottingen became the type of all establishments of this kind, and at all, the obser- vations were made, for the sake of uniformity, in Gottingen time, and with astronomical exactness. The first conclusions thus obtained were very important. Amidst many irregularities very general laws were perceived. The simultaneity of perturbations at places considerably distant was confirmed, as well as the in- fluence of auroras or northern lights, even at a distance, and the influence of seasons and of different hours of the day. For further particulars consult the memoir published by Gauss in 1836, and translated in the second volume of Taylor^s Scientific Memoirs*. But thus far the inquiry had been comparatively restricted : the vastness of the problem required a larger field, — the whole of Europe, and still more the portion of it over which the magnetic observatories extended, being very small as compared with the entire globe. To study the problem adequately, it was- necessary to determine accurately both the magnetic constants and their variations at several distant parts of the earth^s surface : this was beyond the power of scientific associations and required the support of Governments. A first proposal of this nature had been made to the Emperor of Russia by Humboldt with the sup- port of the Petersburgh Academy in 1819, with such success that magnetic establishments were formed in different parts of the Russian Empire, and even as far as China. A still wider range was however requisite ; and the same celebrated individual, aided by the British Association for the Advancement of Science, and by the Royal Society of London, applied to the English Govern- ment as peculiarly interested in all that relates to navigation, and as having within its own dominions points of the globe which could furnish science with the desired information. The request was met with the greatest alacrity, promptness and liberality. Two complete magnetic observatories were immediately esta- blished at Dublin and Greenwich, one under the direction of Dr. Lloyd, the other under that of Mr. Airy. For the distant stations four magnetical and meteorological observatories were erected at points suggested by Humboldt, Herschel, Airy and Sabine, as the best suited to disclose the laws of the phsenomena. They were chosen so as to include great variety of magnetic in- tensity, and opposite positions in respect to the magnetic poles and to the magnetic and geographic equators. * The Scientific Memoirs referred to contain translations of several of the most important memoirs on the subject of terrestrial magnetism, with descriptions of the apparatuses and methods of Gauss and Weber. S88 M. A. Seccbi on the Periodical Variations One was established at Toronto in Canada, and another at Van Diemen's Island ; these two points were chosen as being near to the two points of maximum magnetic force, and because, being almost antipodal to each other, they were eminently suited to show the differences which the opposition of the seasons in the two hemispheres might introduce in the variations. A third obsei*vatory was placed at the Cape of Good Hope as the southern extremity of the African continent, and a point important for the large amount of secular change taking place in the magnetic elements. Lastly, the fourth was established at St. Helena as a point situated within the tropics, and at a small distance from the magnetic and geographic equators, as well as from the line of minimum force. The system of observations established at these four places was in the highest degree such as science might demand, and as should form a true monument to posterity. The instruments were all of the best dimensions and greatest precision, not only for the decli- nation, but also for the inclination and intensity of the force. They included a large declinometer, a bifilar magnetometer for the horizontal force, a dipping-needle, a differential balance mag- netometer for the vertical fBrce, and a series of smaller supple- mentary instruments, with which the magnetic constants might be determined from time to time without touching the large magnets, which experience had shown ought never to be dis- placed. All these instruments were furnished with mirrors or collimators and microscopes, and were observed from a distance with telescopes so as not to disturb their action. The observatories were erected in open situations and without iron fastenings. All were furnished with proper astronomical instruments for the exact determination of time, and with a very complete series of meteorological instruments to be observed at the same times as the magnetical ones. Precise determinations were made from time to time of the different constants required for reducing the magnetic observations, such as the torsion of the thread, the coefficient of the variations of the force of the bars corresponding to variations in their temperature, the azi- muths, meridian marks, &c. Even this rough outline of the system must surprise the reader, and it may be safely said that there was never undertaken for the study of any physical problem a larger scheme or one less restricted by considerations of cost. It was arranged that the action of the different observatories w^s to be simultaneous ; their observations were made at first every two hours, and after- wards at every hour of exact Gottingen mean solar time, besides observing at least every five minutes whenever any extraordinary perturbation was perceived either in the needle or in the atmo- of Terrestrial Magnetism, 389 sphere. That such a series of observations might be carried on with due precision, a military service was organized (under the general direction of Colonel Sabine), in which the observers suc- ceeded each other day and night. They were taken from the corps of Artillery, selecting among the most intelligent those who showed most taste for the work. The staff of each observa- tory consisted of at least four non-commissioned officers and two soldiers, under the direction of a captain fully instructed in the duties to be carried on. The series was maintained for several years ; in some cases more, in others less, but nowhere for less than five years. If the quahty of the instruments, the system of distribution of the observatories, and above all the moral character of the nation, constant and assiduous in carrying through whatever it under- takes, be considered, it will be owned that here was ground for expecting the manifestation of any discoverable laws, and that such data deserve full confidence as a basis of serious discussion. But undigested masses of figures are of small profit to science, and remain always a useless incumbrance in libraries and archives, if they are not reduced, examined, and discussed. This second part of the work, perhaps not less laborious than the first, and requiring more ability, was also confided to the care of Colonel Sabine ; and under his direction the numerous calculations of the reductions have been made, and published in nine large quarto volumes, at the expense of the British govern- ment, and which have been liberally distributed ; the last was published a few months ago, and more volumes are in course of publication. Besides the numerical calculations. Colonel Sabine has given, in the Introductions to these volumes, graphical representations of the variations at each place, and has compared the results from the different parts of the world, in order to deduce from them the most important conclusions. The whole has been executed with surprising sagacity, and at the same time with the greatest reserve as to theoretic hypotheses, a thing diffi- cult in such matters, but strictly Tcquisite where the funda- mental data of a science have to be fixed. As this work is the most extensive of those hitherto published in tabular reductions, and the most important in respect of the points of the globe occupied, so it will be our principal point of departure in the deduction of laws*. We shall not however omit putting under * The work of reduction is of the highest importance, and it is necessary that it should be executed by those who have made or superintended the observations, to avoid the multifarious doubts which arise in its course. But in such reductions it is not sufficient to give annual and monthly means ; it is also necessary to give graphical constructions, which are of ftdO M. A. Seccbi on the Periodical Variations contribution the work done in other magnetic observatories, and especially in that established at Makerstoun in Scotland, at his own expense, by Sir Th. Makdougall Brisbane, and reduced by Mr. Allan Broun, a work valuable for having been performed for the express purpose of examining whether the heavenly bodies, and especially, the moon, influenced the needle. The Russian works and publications are also very important, because made in observatories formed on the same system as thfe English, and now published regularly from 1841, under the care of M. Kupffer, Director of the Central Physical Observatory of Russia. They form a collection of many volumes, and a special one, published in 1852, contains the results of the Magnetical and Meteorological Observatories of Petersburg, Catherinenburg, Barnaoul, Nertchinsk and Sitka, besides an immense number of data registered in upwards of twenty volumes, published under the title of Annuaire Magnetique et Meteorologique du Corps des Ingenieurs des Mines, St. Petersbourg, which give all the observations made in the Russian empire and at Pekin. Adding to this the many magnetic observatories established at various points in Italy, and (more especially) in Germany, in Holland, Sweden, the United States of America, and elsewhere ; the many observations made and collected by the indefatigable and learned Quetelet, inserted in the Transactions of the Aca- demy and Observatory of Brussels ; and lastly, the long series made by Arago at Paris, — and it will perhaps be seen that there is no branch of physical science in which more laborious and copious researches have been made than in this.* A good part of the magnetic observatories which have been cited, and especially those of the British Colonies, are now out of activity ; but the fruits collected remain, and it will be difficult in future to do more, or at least more useful work, than that which has been done. Rather a wise and intelligent oeconomy requires that there should first be derived as much as possible from what has been obtained, in order to find out what direc- tion should be given to new researches, when the materials afforded by the old shall be exhausted. Until such a period shall arrive, it is sufficient for the progress of science to have here and there a few centres of observation, and at this moment several such subsist. The most imposing of these is that of Greenwich. Its system of observation by photographic registration is the immense assistance in the analysis of the phaenomena. If all the ma^etie publications had been furnished with reductions of this kind, we should have been able greatly to enrich the present memoir, but unfortunately they are rendered useless to us by the total or partial want of such a pre- limmary digest, which we have not ourselves the time or the means of supplying. of Terrestrial Magnetism, 391 only one which can faithfully and fully illuminate the labyrinth of magnetic observation. I will briefly notice in what the appa- ratus, which has been working since 1847, consists, and will describe what was registered in the volume of the Meteorological Observations of Greenwich for 1847, and which I saw in 1849 through the kindness of Messrs. Airy and Glaisher. The magnetic observatory is erected in a garden adjacent to the astronomical observatory; and the instruments, of which the march is photographically registered, are the declinometer, bifilar and balance magnetometers, and, for meteorology, the barometer, dry- and wet-bulb thermometers, &c. To speak here only of the magnetic instruments, the principle of regis- tration is the following. Each magnetic bar has attached to it a small mirror, which receives through an aperture the rays of a gas-light passed through vapour of naphtha^ to render its photographic action more efficacious. The mirror reflects these rays on a lens, which concentrates them in a bright point on a prepared photographic paper. This paper is rolled round a cylinder, which is moved by clock-work, and makes an entire turn in twelve hours, having its axis of rotation parallel to the line which the magnetic needle, reflected from the mirror^ tends to trace as it vibrates. At the slightest oscillation of the needle, the reflected ray changes its place on the paper, and makes an impression on it; and this movement of the reflected image being compounded with the movement of rotation, there is pro- duced on the paper a curve, of which the ordinates represent the amounts of the variations, and the abscissae their times. If the needles are much disturbed, the pap^r is changed every twelve hours; if not, two curves are obtained on the same sheet. In order to have fixed points, and a base from which the times and ordinates may be counted, there is a second light, which sending its rays directly on the paper through a fixed hole, traces on it a straight line, to serve as the axis of the abscissae ; slight inter- ruptions are made in the curve at intervals, by intercepting the light, so as to give points of departure for counting the times of the movements without error, and independently of the possible irregularities of the clock-movement. The sheets on which these curves are traced are fixed by known photographical processes, and carefully preserved ; and there are afterwards taken from them, by means of proper scales of reduc- tion, the numerical data. Such a collection of observations cannot be otherwise than highly profitable. Science however expects its rigorous discussion with impatience. The apparent irregularities, which are numerous, especially in the more northern observatories, will disappear by the multiplication of curves ; and although their first aspect may be discouraging, we shall see 392 M, A. Seech i on the Periodical Variations that by taking a good clue as guide, it will be found here also that all is number and measure. From the rapid sketch which I have traced of what has been already done for the study of the variations of terrestrial mag- netism, it will be clear that observations are not wanting ; and what is more, that they have been made systematically and with extraordinary perseverance, guided by experience, and with unex- ceptionable instruments ; whence we may conclude, that if there were obtained at any place results opposed to the laws deduced from so imposing a mass of data, amounting to several millions, they ought to be attributed to faults either in the instruments, the observations, or the methods of reduction ; in short, to some local or accidental cause ; but we shall see that the results are more accordant than would be believed, and it is of these that we now proceed to speak. Part II. — Principal results obtained from the study of the Magnetic Variations. Magnetic variations are of three kinds; the first ordinary and periodical ; the second extraordinary, and apparently irre- gular; and the third requiring for their completion a great and unknown series of years, and therefore termed secular. All the magnetic elements, i. e. the Declination, the Intensity of the Force, and the Inclination, are subject to these variations. We will begin with what belongs to the declination and its movements, which fall under some principal laws, which we will proceed to expose. § I . On the Diurnal and Annual Variations of the Declination, First Law. — " The diurnal variations of the magnetic needle follow local time.'' Declaration. — The first discoverers of the diurnal variations of the magnetic declination suspected that the needle followed the course of the sun, and therefore the true (or apparent) time of the place of observation ; but when it was afterwards found, by comparative observations, that there were cotemporaneous varia- tions at many different places, it was suspected that there might be simultaneity of perturbation throughout the globe. When however places of observation sufficiently distant were multiplied, it was found that the ordinaiy, or diurnal variations, followed in their march the hours of local time, and that even the extra- ordinary variations, as we shall see in the appropriate place, were not completely excluded from the operation of this law. To avoid speaking equivocally, however, the term " distance" must be understood in relation to the subject of which we are treating. The extent even of the whole of Europe, and still more distances of Terrestrial Magnetism* ' 393^ of six or seven hundred miles, are very small compared to the entire circumference of the globe. In the same manner that many meteorological vicissitudes may be simultaneous for such extents, so may also the magnetic perturbations which might be produced by them ; but as it can rarely happen that meteoro- logical causes occupy the whole surface of the earth, so simul- taneous perturbations produced by them and extending over the whole globe would be equally rare. In fact, if we inspect the magnetic curves, traced in Gottingen time, for Gottingen and Prague in Europe, and for places situated in Canada and the United States of America, we shall find that the places in each continent commonly agree very well with each other; but that agreement between the continents is seldom found, although their distance apart is not great compared to the whole globe. It is necessary however to discriminate accurately between two kinds of periodical variations ; those which strictly follow local time, and those which in their periods occur at the same moment of absolute time at different stations. We shall speak of the latter subsequently; but in respect to the former, let it be regarded as assured that local time is to be alone considered ; and that if Gottingen time was at first adopted for all the ob^ servatories in common, it was for the sake of making out the law of the extraordinary movements and facilitating their calcu- lation, rather than for the purpose of recognizing the law of the diurnal variations of which we are now speaking. It would indeed have been desirable to have adopted true or apparent local solar time, instead of mean time, in the observa- tions, or at least in the reductions. The use of mean Gottingen time, besides the inconvenience of requiring the equation of time^ to be applied, has also another, which is, that it does not often ; happen that at two distant observatories the observations fall at even hours of local time. This is one of the points (and we shall see others presently) in which the discussion of past obser- vations throws light on the system to be adopted in future. It is to be hoped that future observations will be made at even hours- of apparent local time, and that those which have been made will be reduced to such hours. We have however found, and shall demonstrate in the sequel, that the phase of the diurnal oscillations depends more on the position of the sun relatively to the magnetic meridian of a given place (i. e. relatively to the azimuth of the plane of the mag- netic meridian) than on the relation to the geographic meridian. Second Law. — " The pole of the needle which is least distant from the sun makes a double diurnal excursion, in the following manner : — It is at its maximum of western excursion four or five Phil. Mag, S. 4. Vol. 8. No. 53. Nov, 1854. 2 D 394 M. A. Secchi on the Periodical Variations hours before the sun passes the meridian of the place; it then turns eastward with increasing celerity, of which the maximum occurs near the passage of the sun through the magnetic meridian, and it reaches its limit of eastern excursion one or two hours after the said passage. As the sun declines, the needle returns back ; and as the sun passes the inferior meridian, there is repeated in the night the same variation as that which took place during the day, but restricted within narrower limits. The limiting hours of these changes vary with the seasons, and are generally earlier in summer and later in winter ; and the magnitudes of the ex- cursions are in the proportion of the diurnal to the nocturnal arc/' Declaration. — The wood-cut will make this law better under- stood. Let EW be the equator or the parallel described by the \ s \ y S' \ \ / / »* 21* 0^ f* f ?" 1^" IS ^ »' e' / \ \ « / / \ '■v \ N K' TS' jgm sun, and T, H, two places situated in opposite hemispheres as respects the sun; between the hours of 19^ and 21^ (7 and 9 A.M.) the two needles will be in the positions shown on the line SN; from 1 to 2 p.m., in the position shown on the line S'N'; between 9 and 10 p.m., as shown on the line S"N"; and, finally, between 14^ and 15^ (2 and 3 a.m.), as on the line The case here represented is exactly that of Toronto (T), and Hobarton (H). Colonel Sabine describes the diurnal oscillation at Toronto as follows: — ^*The mean diurnal variation of the declination at Toronto, as derived from the two-hourly observa- tions in 1841 and 1842, consists in an easterly movement of the north end of the magnet from 2 to 10 hours inclusive ; a small return movement towards the west then takes place till 14 hours, when the easterly progression is resumed, and continues until 20 hours, at which time the north end of the magnet reaches its eastern limit. From 20 hours the movement is continuous towards u \ of Terrestrial Magnetism, 395 the west until 2 hours, which is the period of the extreme west- ern limit/' (Toronto Observations, vol. i. p. 14.) And at Ho- barton as follows : — " The north end of the magnet has two eastern and two western elongations or turning-])oints, at both periods of the year; from October to February the principal eastern elongation is at 2^, and the minor one at 15^; from April to August the hours of these turning-points become respectively 3^ and 16^; from October to February the principal western elongation is between 20^ and 21^, and the minor one at ll^j whilst from April to August the corresponding pha3- nomena occur at 22^ and ] 1^." Then, comparing the figures which represent these movements with those of Toronto, he concludes that they are identical, only having opposite signs, except that the turning-points or periods are earlier at Toronto than at Hobarton. The opposition of these movements is shown in our figure in a manner easily to be remembered. The two stations may be regarded as [within limits, Ed.] the type of all that happens out of the torrid zone. Within or near the tropics the law holds good, providing we have regard to the hemisphere in which the sun is, the places being considered as in the southern hemisphere when the sun is in the northern hemisphere, and in the northern hemi- sphere when he is in the southern. If there should sometimes appear to be an exception, it would be only an apparent one, as we shall soon demonstrate. In the meantime, to facilitate com- parisons, we may establish the following : — Corollary 1. — All the variations are the same in both hemi- spheres, providing we change the name of the pole influenced ; and if we take as the type the north pole and northern hemi- sphere, we shall have identical variations for the south pole in the southern hemisphere; and the variations of the north pole in the southern hemisphere will be opposite to those in the northern hemisphere. Remark. — Perhaps, to avoid any misunderstanding, and the confusion of poles with hemispheres, and for greater convenience in the indication of the antagonistic forces of poles in which the pole called north is the true south pole of the needle, it might be better to retain the name of marked pole, formerly used by some, and especially by English writers, to designate the fundamental pole, to which all is referred, and which in our part of the world looks to the north. Corollary II. — As the points of inflexion of the diurnal curve depend on the sun's passage of the magnetic meridian, it follows that if two places in the northern hemisphere have opposite magnetic declination, i. e. the one east and the other west de- clination, the second will be in its phases later [Qu. earlier, Ed.] 2D2 896 M. A. Secchi on the Periodical Variations than the other. If the two places which we are considering are in opposite hemispheres, this new opposition will have to be taken into account, that is to say, we shall have to make the product of the algeliraical signs relatively to their positions and to their names. This rule will be useful to us presently. It is a conse- quence of the complete antagonism which exists in the two hemi- spheres relatively to magnetic phsenomena. Corollary III. — A consequence of the dependence on the magnetic meridian is the advancement or retardation of the phases with the seasons, as in the course of the year the sun arrives at the same azimuth from the geographical meridian by describing a different horary angle, greater in winter and less in summer ; but the discussion of this point will be more suitably placed in the consideration of the elementary movements of the needle. We will not however omit to notice here one important point. The needle, in its nocturnal oscillation, and especially in winter, makes an excursion which sometimes exceeds the diui-nal one. This has sometimes caused it to be believed, that the maximum of deviation, especially of western deviation, was subject to great displacement. But the case is otherwise. The proper maxima of the semi-diurnal excursions always remain at nearly the same hours ; but if it should happen that the nocturnal should exceed the diurnal, we are not therefore to say, without qualification, that the maximum occurs in the evening ; the times and the periods are to be distinguished, and all will be clear ; for if the absolute maximum may happen at night, the relative maxima however (eliminating the perturbations) follow constantly the period above enounced; and it is these relative maxima and minima which constitute the characteristic properties of the variations of the magnetic as distinguished from the meteorolo- gical period. Remark. — The two laws hitherto enounced are themselves no other than corollaries of another more general law, which we will now proceed to expose ; but I have thought it well to pre- mise them, and to enunciate them separately, in order to pro- ceed afterwards with greater clearness. Third Law, — " The diurnal excursion of the needle is the sum of two distinct excursions, of which the first depends solely on the horary angle, and the second depends besides on the sun's decli- nation. These two fluctuations being variously superimposed upon each other, produce by their interferences all the phenomena of the ordinary diurnal and annual variations/' Declaration. — Nothing is in appearance more bizarre than the curve traced by the magnetic needle in a single day; but as there is no real iiTCgularity in natm-e, it is obvious to presume of Terrestrial Magnetism. 397 that the appearance of irregularity only arises from our being ignorant of the fixed periods, as well as of the accidental causes which influence the needle. Desiring to treat this subject with systematic order, it is necessary to restrict ourselves to the regu- lar variations only. In order to give an idea of the annual variations of the declination without too much multiplying words, we will refer to Sabine^s work (Toronto, vol. ii. p. 20) for the curves traced by him, representing the position of the needle in the two six-monthly periods when the sun is on either side of the equator, at the four observatories of Toronto, St. Helena, Cape of Good Hope, and Hobarton. In these figures the red line indicates the excursions of the needle in the months when the sun is in the northern signs, or in the tropic of Cancer ; and the blue line the same in the months when the sun is in the southern signs, or in the tropic of Capri- corn. These curves include only the hours of the day, as being the most marked. The north pole of the needle deviates to the east when the curve is above the axis of the abscissae, and to the west when it is below it. From a simple inspection of these curves, we may draw the following conclusions : — At Toronto, the needle at 8 in the morning is throughout the year to the east of its mean position; and in the afternoon, towards 2 p.m., it is always to the west ; 2nd, the excursion is greater in summer than in winter, and the annual difference in this respect is represented by the distance between the two curves ; 3rd, in the intermediate months the needle is between the two limiting curves. For Hobarton we get the same laws, but with contrary deno- minations, as we have already said (under Law II. Corollary II.). For St. Helena there is the nbtable circumstance, that the curves are seen to bend alternately south and north of the equa- tor, moving with the sun ; yet it is not to be overlooked, that the curve of the months of the June solstice wants the second inflexion, which it would require in order to be symmetrical with the curve of the opposite six months. At the Cape of Good Hope the phases are transitional between those of St. Helena and Hobarton. These curves are the gra- phical result of the observations, and we have now only to see whether it is possible that they may have originated from more simple periods, which, being separated from each other, may throw light on the physical cause of the phsenomenon. These curves are traced by taking the mean of the six months, and hence they appear more regular than if taken from the dif- ferent months singly ; for if we examine each of the constituent monthly curves separately, we shall find some peculiarities and notable differences, which tend further to confirm the belief that On the Periodical Variations of Terrestrial Magnetism* all these curves conceal simple periods, which being superim- posed give complicated results. That such periods being superimposed upon each other may produce curves of irregular appearance, will not be doubted by any one who may have once seen the multifarious curves, obtained by the superim position of one or two waves, in the little machine invented by "Wheatstone for representing the interferences of luminous undulations ; and it is just the application of these principles to the theory of terrestrial magnetism which reduces these facts, in themselves highly intricate, to a surprising degree of simplicity. In order to render more intelligible what we are about to say, it will not be without its use if we conceive a wave of which the elementary curve is the ordinary one of simple sines, having for its equation y=k sin [x-\-a)f and a second wave of double period, and of the equation y = k sin (2^ + fl). If we superimpose these two forms, we shall have a figure distinct from either. We here suppose the two components to have equal excursions ; but by giving different values to the con- stants which enter into the curve, we may get the share belonging to the minor diurnal inflexions to be almost sensibly rectilinear ; and vice versa we may have more exaggerated inflexions. In the equations of these curves we will distinguish the con- stants by special names for the sake of brevity and clearness, call- ing k the modulus, the arc x the argument, and a the parameter. This being premised, we come to the demonstration of the law which has been enounced, which will be no other than a corollary of the observed facts. And first, from an extended and comparative analysis of all the magnetic observations, the sun is seen to be the principal cause, not only of the diurnal, but also of the annual variations ; and we have only to form to ourselves a clear idea of the manner in which it operates. Colonel Sabine, in vol. ii. of the Toronto Observations, p. 20, briefly sums up the fundamental points, comparing the curves which we have cited, and calls attention to two things, — 1st, the opposition of the movements of the needle in the two observatories situated beyond the tropics in the two opposite hemispheres (i, e. at Toronto and at Hobarton) ; and 2nd, the opposite direction induced by the sun^s passage of the equator in the declination of the needle at St. Helena and at the Cape of Good Hope, which phases place beyond doubt the in- fluence of the sun's declination. He does not however proceed further with the analysis. Now it seemed to me that this germ :might be considerably more developed, and might become fer- tile in very important consequences. It seemed to me strange M. Matteucci on the Electricity of Flame. 399 that the sun should act thus oppositely by his change of declination in these two places and not in the others, limiting itself in these last to only diminishing the fluctuations. It was added, that the changes at St. Helena and at the Cape not having reference to the sun's zenith-distances, his influence ought to be due to an astronomical rather than to a geographical and local cause. It may however naturally be expected that such a period is marked by the many convolutions and superim- positions of difi'erent causes acting on the needle; to extricate it was not easy, and would have been actually impossible without the previous labours of Colonel Sabine, which I have happily found sufficient for the purpose. [To be continued.] L. On the Electricity of Flame, By M. Matteucci*. My dear Grove, IHxiVE gladly taken advantage of a few days' leisure in the country to comply with your request, and at the same time satisfy my own -curiosity, by making some experiments on the electricity of flame, and I now send you the little which I have gathered from my own observations on the subject. I began by studying the conductibility of flame, and employed for this pur- pose a galvanometer constructed by Ruhmkorfi*, similar to that of M. du Bois Reymond, the fine copper wire of which makes 24,000 evolutions round a good astatic system. The flame used in most of my experiments was that of a common spirit-lamp_, or of a double current lamp belonging to the laboratory. The circuit, which contained two DanielFs couples, was formed by two platinum wires, two-thirds of a millimetre in diameter, placed horizontally, and leaving between them a fixed interval of 8 mil- lims. All was perfectly insulated, and the flame completed the circuit. On seeking to ascertain the conducting power of the diiferent parts of the flame, it is soon found that this conducti- bility increases rapidly in going from the base or root of the flame towards the summit. To give an idea of this difierence, I mention here that I had from 4° to 5° of deflection at the base, 8° to 10° at the middle, and from 30^ to 40° at the upper part of the flame. By placing the platinum wires in the flame of a double current lamp, much more striking efl'ects are obtained, which are evidently in proportion with the temperature of the gas composing the flame. If we hold the platinum wires at a less interval apart, that is, from 2 to 3 millims., over the flame of the double-current lamp, which can be diminished at pleasure, we can ascertain the precise moment at which the conductibility of the flame begins ; I found in my experiments that this moment * Communicated by W. R. Grove, Esq- "#80 M. Matteucci on the Electricity of Flame, was that in which the two wires are of a clear red, without having been visibly reached by the flame. This is, as far as I remember, the result obtained by M. E. Becquerel, and accords with what .we know to be the case with all bodies excepting metals, that is, that their conducting power increases by heat. Now is this an eflfect similai- to that undergone by liquids, in which conductibility and electrolygation go on together, or is it rather a discharge like that of the voltaic arc, favoured chiefly by the high temperature of the electrodes which are thus disposed to a disaggregation ? I have often seen a great deflection of the needle persist for a •certain time, when the wires heated to a white heat are moved from the upper to the middle portion of the flame, but this is a subject which can only be discussed by the help of other experi- ments, which I hope that you, who have begun this subject so successfully, will find time to undertake. When, instead of an alcohol flame, that of oil or stearic acid is employed, we find at first that the passage of the current is .yearly null ; but by taking means to prevent the formation of a •fitratHm of black matter on the electrodes, we soon find that the conducting power of these flames is greater than that of alcohol. In order to efi'ect this, I heat the platinum wires in a spirit-flame, which I replace rapidly by that of the substances just named, and I then find that the conductibility of these flames is much greater than that of alcohol. Proceeding in the same manner, I ascertained that the conducting power of the flames of camphor or of gutta percha was much less than that of alcohol. If between the eleotrodes a thin plate of platinum is inter- posed, which may be said to cut the flame in half, the conducti- bility remains unaltered ; and if this plate has been heated pre- viously, we find, on the contrary, that the conducting power is increased. By making use of salt of strontian, or boric acid, or chloride of copper dissolved in small quantities in alcohol, I have been enabled to work with flames which, as is known, present different colours due to volatilized matter : the conductibility of these flames is greatly diminished, and this is particularly the case with the flame rendered green by chloride of popper. The conducting power is visibly increased by a jet of vapour of iodine or of mercury sent into the midst of the flame, and the power is lessened by a jet of steam from water, or by holding burning sulphur in contact with the flame. It would be very curious to study the conducting power of steam at diffierent atmospheres and densities, and above all, to ascertain whether this conductibility is accompanied by electro-chemical decom- position. I now proceed to the development of electricity by flame. I had no difficulty in verifying the results which you have obtained, and which I will express as follows:— We find in the flame M. Matteucci on the Electricity of Flame. 401 of alcohol or of hydrogen gas, and probably in all flames, an electric current, the direction of which current in the flame itself is from the portion called by chemists reductive to that called oxidizing ; in other words, the current of the flame is directed from the metallic plate which is in contact with hydrogen or vapour of alcohol, to that which is in contact with oxygen or atmospheric air. You have clearly proved that this current does not depend on the difference of temperature between the two platinum wires placed in the flame, for it is obtained when the wire surrounded by oxygen is held above the flame so as to be less heated than the other. It may be added, that the current obtained by touching directly the greater and the less heated platinum, would only occasion a deflection of a few degrees, instead of which, in operating with the flame, we have a deflection of 40 or 50 degrees in an opposite direction. The currents obtained by employing plates of platinum are much stronger than when wires are used, and the best arrangement is that of holding one of th^ platinum plates so as partly to envelope the flame, while the other is placed in its centre. I have obtained similar results, though the currents have been rather weaker, with copper or iron wires, and from the state of these wires we can judge more distinctly of the portion of the flame which contains hydrogen, and of the external part where oxygen predominates. As to the explanation of the production of electricity in flame, I do not for a moment hesitate to consider the case as identical with that by which I think I have explained M. Pouillet^s old experiment and secondary polarities, which formed your start- ing-point in your beautiful discovery of the gas battery ; it is that of an electrical current developed between two metallic plates, and principally between two plates of platinum when plunged in water, being or having been in separate contact, the one with hydrogen, the other with oxygen gas. You are aware that, in the case of flame, I have supposed that these two gases were separated by a stratum of steam. It is known that the electrostatic signs of flame accord perfectly with those obtained with the galvanometer, as well also as with those from the gas battery. Before coming to the experiment, which seems to me to leave no doubt as to this interpretation of the electrical phsenomena of flame, allow me to describe some experiments on electrical currents, obtained with platinum wires attached to the extre- mities of the wires of the galvanometer, and immersed in distilled water. I take a platinum wire 3 or 4 metres in length ; after having left this wire for some hours in a mixture of nitric and hydrochloric acids, I wash it repeatedly in hot water. I then cut this wire in two equal parts, and join each half to one of the extremities of the galvanometer which I have already described. 402 M. Matteucci on t/ie Electricity of Flame. If I plunge the two ends of platinum wire into distilled water at the same time, the needle seldom remains at zero, but generally after a deflection of a few degrees returns to zero, the circuit having been left closed. If I then withdraw the two wires simultaneously from the water, and after some minutes plunge them again into the water, there is no deflection of the needle. The same result is obtained if the two wires are wiped dry with linen or paper before replacing them in the water. I have suc- ceeded in obtaining very strong and constant currents in the following way : if one of the wires is moved rapidly in the liquid, if this wire alone is withdrawn from the water and after some time replaced, if the wire is wiped and rubbed with linen or paper andthen put into the liquid, if, finally, this wire has been heated over char- coal,— in all these cases there is a strong current on closing the circuit, and the direction of this current shows that the wire which has undergone these changes becomes as the zinc of the voltaic bittery. It is easy to show, as may be done with pla- tinum plates which give secondary polarities, that these currents exist only in presence of the liquid interposed between the two platinum wires. In order to prove this, we have only to with- draw the two wires from the water, and then to heat or rub one wire more than the other; if then this wire is plunged into mercury, no current is obtained, whereas by employing water a current is obtained. In order to explain these results, we must admit with M. De la Rive, that platinum decomposes, or tends to decompose water at the ordinary temperature, and we may suppose that this tendency is increased by the circumstances which I have described. I will now give, in the last place, the experiment which serves to explain the production of electricity by flame. I place two platinum wires so that one is in contact with the centre of a flame of a spirit-lamp, and the other with the outer margin or apex of this flame. I make the experiment as before described, and the needle, as we already know, deflects so as to indicate a current the direction of which is from the base towards the apex of the flame. After a certain time I take away the flame, I leave the wires to cool, and close the circuit with water. I have then a strong current in the same direction as when I employed the flame. It is hardly necessary to tell you that I assured myself of the truth of this result by alternating the position of the two platinum wires in regard to the flame, as well as by holding the two wires at the same level in the flame, in which case no current is obtained either with flame or with water. I have also ascer- tained in this experiment, that when the two wires, after being kept in the flame, are put into mercury, no current is obtained, whereas when they are plunged into water there is a strong current. • I do not therefore hesitate to conclude, that the electric current M. Matteucci on the Electricity of Flame. 403 which you obtained from the flame of alcohol or of hydrogen is of the same nature as that which is obtained if the two platinum wires are placed in water after having been in contact, or while in contact, the one with hydrogen, the other with oxygen gas : the current in the former case is feebler, owing to the bad con- ducting power of flame. We should thus be led to suppose, — 1st, that the action between the platinum and the gases takes place even at a very high temperature, which supposition is in accordance with experiment ; 2nd, that vapour, like water in a liquid state, is decomposed by the electrical current, which remains to be proved. I must not close this letter without observing that I am not, nor has there been time for me as yet to be, acquainted with the works of the German savants Bufi" and Hankel, of which you speak. Should it appear to you that these few observations ofi*er any interest, I should feel greatly obliged by your communica- ting them, as a proof of my gratitude, to the Editors of the Phi- losophical Magazine. Ever yours, Pise, September 26, 1854. C. Matteucci. To the Editors of the Philosophical Magazine and Journal. Gentlemen, In communicating the above interesting experiments, I am tempted to add a few words of comment ; for though I do not differ much from the interpretation of the flame-current given by my friend M. Matteucci,, it interests me in a different point of view. This I can best explain by stating a conviction I very early acquired from the chemical theory of Voltaism, and which has led to many of the experimental results that I have from time to time communicated to the Philosophical Magazine. It is, that every chemical synthetic action may, by a proper dispo- sition of the constituents, be made to produce a voltaic current. This proposition may probably appear to many a direct and necessary consequence of the chemical theory, but I do not recollect to have seen it broadly stated. Thus the dissolution of gold by aqua regia I showed might produce a voltaic current. The gas battery was, in my mind, a similar deduction, and was arrived at by considering the chemical action in the Dobereiner lamp, and not by the experiments of M. Pouillet and M. Mat- teucci, with which I was unacquainted at the time of my first experiments, though doubtless those would have been an equally ready step to the result. The production of a voltaic current from phosphorus and iodine, solid non-conductors, the nitric acid battery, &c., were derivatives of the same thought. . It has often occurred to me, that if, instead of using zinc and 404 Mr. W. R. Grove on the Electricity of Flame. acidSj which are manufactured, and comparatively expensive materials, for the production of electricity, we could realize the electricity developed by the combustion in atmospheric air, of common coal, wood, fat, or other raw material, we should have at once a fair prospect of the commercial apphcation of electri- city ; but in the experiments I have mentioned, and others of the same class, an electrolyte is a sine qua nan. Hence I was led to- experiment on flame, which appears to me to differ from the above in the absence of an electrolyte ; but M. Matteucci seems, if I rightly read his letter, to regard the steam in the flame as having an electrolytic action, being, in fact, the substitute for the water of the gas battery. Here I to some extent diverge from his views. Water in the liquid state cannot exist in the blowpipe flame, it must be in the state of vapour or gas, and the transfer would not be electrolytic, the which, to my mind at least, involves the idea of a liquid. Vapour is, as I have shown, decomposed by the electric spark, but not, as far as I am aware, by the mere transfer of electricity. It would be very hasty to say a thing cannot be because it has not been, but I cannot at present assume theoretically the elec- trolysis of steam, and I believe the general opinion would be against it ; it may be polarized, but not, I think, electrolysed. It does not, however, seem to me that this hypothesis is needed; there is throughout the course of flame a chemical action going on, each molecule of carbon or hydrogen is com- bining with a neighbouring molecule of oxygen, and there is nothing which theoretically opposes the supposition that such a chain of chemical action should conduct electricity, even though the gases in a chemically dormant state should not do so. As there is more oxygen at one extremity, more hydrocarbon at the other, there must be, irrespective of the molecular combinations, which do not contribute to the voltaic current, a certain number of particles as to which the chemical action has a definite direc- tion j this, to my mind, should produce an electrical current, which should, as it does in fact within certain limits, increase in intensity with the length of the interposed flame. Flame to me presents a difi^erent medium, electrically viewed, from water or from gas, whether simple, compound or mixed, and this gives it a high interest. I will take this opportunity of stating, that with the flame battery which I used for an evening meeting at the Royal Insti- tution, I readily decomposed iodide of potassium, a result I had not obtained when I made my former communication to the Philosophical Magazine. I have the honour to remain. Gentlemen, Your obedient Servant, Etr^tat, Frwioe, Oct. 6, 1854. W. R. Grove. [ 405 ] LI. Intelligence and Miscellaneous Articles. ON SOME NEW DERIVATIVES OF CHLOROFORM. BY PROF. WILLIAMSON. ACCORDING to the results of recent researches in the constitution of salts and the methods thence introduced of explaining chemical reactions, it is equally correct to represent such a reaction as that of hydrochloric acid on hydrate of potash, as consisting in an exchange of hydrogen of the one for potassium of the other, or of chlorine in one for peroxide of hydrogen in the other. In Mr. Kay's researches as described in the following brief outline, this notion has obtained very striking illustration; for he has obtained a peculiar body in which the chlorine of chloroform is replaced by peroxide of sethyle by the action of chloroform on three atoms of sethylate of sodium, which product may be equally well conceived to be a body in which the hydrogen of three atoms of alcohol is replaced by the tribasic radical of chloroform. According to the older theories of the capacity of saturation of salts, this compound would contain a tribasic modification of formic acid, for it has the same relation to formic aether as a so-called tri- basic phosphate has to a monobasic one. To one equivalent of chloroform were added, by degrees, three equivalents of dry and powdered sethylate of soda, a violent action taking place with the evolution of much heat ; the liquid was entirely distilled from the residue (chloride of sodium) by means of an oil- bath, and then subjected to a series of fractional distillations, which yielded a small distillate between 50° and 60° C, smelling strongly of vinous aether, a large distillate (about three-fourths of the whole) between 77° and 78° C., which was chiefly alcohol, and another small distillate (about one-sixth) between 145° and 145°' 3 C. The distillates obtained by the above process, except that of alcohol, being small, the following modification was adopted. Sodium was dissolved in absolute alcohol until the action became feeble, chloroform was then added, care being taken to keep the liquid alkaline ; more sodium was then added, and the process re- peated several times, until the chloride of sodium precipitated be- came very bulky. The liquid was then distilled off and chloroform added to the residue, and also distilled off. To this first distillate sodiuni was again added, and treated with the last distillate instead of pure chloroform, the same precautions being used as before. This method gave similar distillates, and in about the same proportion as that first used ; the highest distillate however boiled constantly at 146° instead of at 145°-3 C. This compound which boils at 145° to 146° C. is a colourless limpid liquid, only slightly soluble in water, having a strongly aro- matic odour, readily inflammable and burning without much smoke ; its specific gravity is '8964 ; it remained liquid at 0° F. Several analyses made of this ])ody agree in giving to it the for- mula O H16 03, which would also be the empirical formula of a tribasic formic- aether ; the density of its vapour also corresponds very closely with the same formula. 406 Intelligence and Miscellaneous Articles. Pentachloride of phosphorus added to a portion of the compound produced a heavy liquid having the odour of chloroform. A small quantity of the body was dissolved in alcohol, distilled upwards for two or three hours with solid hydrate of potash and then distilled off; the residue was next dissolved in water and made exactly neutral by hydrochloric acid, filtered to remove the turbidity, and then a few drops of chloride of mercury added ; after a little time and by the application of heat, a very slight precipitate of subchlo- ride of mercury was formed; also the colour of sesquichloride of iron was a little darkened by anotlier portion of the solution, thus showing that the action of potash on the compound had produced formic acid, but in very small quantity. An equivalent of dry hydrochloric acid was passed into a portion of the compound ; the gas was wholly absorbed, a considerable amount of heat being evolved and the liquid assuming a brownish colour ; the liquid after the absorption of the gas still remained perfectly neutral. It was next distilled with the thermometer : it began to boil at 20" C. and rose gradually to 100°; it was collected in three portions, the first (about one-sixth of the whole) passing over between 20° and 50°, the second (about one -third) between 50° and 68°, the third (one-half) between 68° and 100°. I was unable to carry these distillations further in consequence of the small quantity of the liquid available. Two equivalents of dry hydrochloric acid were passed into a larger quantity of the compound ; towards the close the gas was absorbed less freely, a portion passing through ; after this treatment, the liquid fumed and was highly acid ; it was distilled upwards for eome time, by which a portion of free hydrochloric acid was expelled, and then distilled fractionally ; about one-third came over between 56° and 60° C, one-fourth between 60° and 70°, one-sixth between 70° and 80°, and the remainder (about one-fourth) between 80° and 88°. To the lowest distillate about an equal bulk of water was added ; the substance floated on the surface and seemed to be little, if at all dissolved by the water ; a suflScient quantity of carbonate of soda was next added to neutralize the free acid, and the liquid pipetted from the water, it was then distilled upwards for some time with dry chloride of calcium, and afterwards distilled off; this distil- late was found to boil constantly at 55°'5 C. An analysis made of this body agrees closely with the formula C H'* O*. The distillate which came over between 60° and 70° aftei being treated in the same way as the lower distillate, also yielded a liquid which boiled at 5 6° C. As both methods hitherto used for the purpose of obtaining the body C7 H'° O^ afforded only small quantities, the treatment of chloroform with an alcoholic solution of potash was tried ; for this purpose 12 oz. of solid hydrate of potash and 20 oz. of quick lime were added to about three pints of absolute alcohol, and the alcohol distilled upwards for six or seven hours ; 6 oz. of chloroform were then added gradually, the upward distillation being continued about two hours longer ; the liquid was next distilled off to dryness by means of an oil-bath, and submitted to fractional distillation ; by this method a much larger quantity of the compound was obtained than Intelligence and Miscellaneous Articles. 407 by the former processes ; it was found to boil constantly at 146° C, and its analysis agreed almost exactly with the formula. In this process the lowest distillate had the same smell of vinous £ether which was before observed in the other methods. An attempt was made to produce the intermediate compounds CHC12, AeO, and CHCl, 2AeO, by adding dry and powdered sethylate of soda very gradually to a large excess of chloroform ; but the liquid after being separated from the precipitate, was found, on distilling fractionally, to resolve itself into chloroform, alcohol, and the body (C? H'^ O^) already obtained, the presence of no other sub- stance being observable. With a view of obtaining a compound analogous to the body C7 H'^ 03, in which amyle should be introduced instead of sethyle, dry amylate of soda was prepared, to three equivalents of which one equivalent of chloroform was added, the liquid separated from the precipitate and then distilled fractionally ; a large proportion of fusel- oil was obtained, together with a small proportion of a body which boiled at a high temperature, — from 260° to 290° C, but chiefly from 260° to 270°; the purification of this substance was not carried further, as at each distillation a considerable portion was decomposed even in an atmosphere of hydrogen, the small quantity of the liquid available precluding any more attempts at distillation. — From the Proceedings of the Royal Society, June 15, 1854. METEOROLOGICAL OBSERVATIONS FOR SEPT. 1854. Chiswick. — September 1. Very fine. 2. Slight fog : very fine. 3. Foggy: very fine. 4. Foggy : slight haze : excessively dry air. 5. Very fine : hazy : fine. 6 — 10. Very fine. 11. Dense fog : clear : quite cloudless : very fine. 12. Dense fog : very fine. 13. Cloudy : rain. 14. Cloudy : slight rain : overcast. 15. Very fine. 16. Overcast. 17. Very fine. 18. Fine : cloudy : rain. 19. Overcast and vsrindy : shght rain. 20. Cloudy : rain. 21. Clear : quite cloudless : fine : light- ning in the evening. 22. Very clear : fine. 23. Densely overcast. 24, 25. Very fine. 26 — 29. Foggy, with very heavy dews in the mornings : very fine throughout the days : clear and cold at nights. 30. Dense fog throughout. Mean temperature of the month 56°*93 Mean temperature of Sept. 1853 55*45 Mean temperature of Sept. for the last twenty-eight years... 56 '98 Average amount of rain in Sept 2*57 inches. Boston.— ^e^i. 1—4. Fine. 5. Cloudy. 6. Fine. 7—9. Cloudy. 10—12. Fine. 13. Cloudy. 14. Rain a.m. 15— 17. Cloudy. 18. Fine. 19. Cloudy : rain a.m. 20. Rain a.m. 21, 22. Fine. 23. Cloudy : raiji a.m. 24. Cloudy: stormy a.m. and p.m. 25 — 29. Fine. 30.- Foggy. Sandwick Manse, Orkney. — Sept. 1. Cloudy a.m. : clear p.m. 2. Clear a.m. : cloudy P.M. 3. Clear, fine a.m. : clear p.m. 4. Rain a.m. : clear, fine p.m. 5. Cloudy, fine a.m. : cloudy p.m. 6. Drizzle a.m. : rain p.m. 7. Drizzle a.m. : cloudy P.M. 8. Cloudy a.m. : clear, fine, aurora p.m. 9. Clear, fine a.m. and p.m. 10. Bright, fine a.m. : clear, fine p.m. 11. Rain a.m. and p.m. 12. Clear, fine a.m. : cloudy P.M. 13. Clear a.m. : rain p.m. 14. Clear a.m. : showers p.m. 15. Showers a.m. and p.m. 16. Showers a.m.: cloudy p.m. 17. Bright a.m.: showers p.m. 18. Showers a.m. and p.m. 19. Bright a.m. : clear p.m. 20. Showers a.m.: cloudy p.m. 21. Bright a.m.: clear p.m. 22. Bright a.m.: cloudy P.M. 23, 24. Rain a.m. : clear p.m. 25. Showers a.m. : cloudy p.m. 26. Showers a.m. : clear p.m. 27. Clear a.m. : cloudy p.m. 28. Clear, fine a.m. : clear p.m. 29. Cloudy a.m. and p.m. 30. Hazy a.m. : clear p.m. Mean temperature of Sept. for twenty-seven previous years . 52°'32 Meaii temperature of this month , 55 '07 Mean temperature of Sept. 1853 53 •28- Average quantity of rain in Sept. for fourteen previous years 2 81 inches. •H3tMpa»s •uo^soa •^MnqD II ^ o 11 P 8 •Hawkptres •ao)8og •ni'd I •^9mnq3 : t ti fi p J* : VO 00 »r> o ; 00 \o •^^ i : o o o • O O O i i ^ i I «^ s s § i - i • - ^ E li ^ & >^ ^ >^ ii i I » ^ li i i i ' ^ i »ll 1 «l »r » i 5 i I s^ 6 s •= ^ g M ^ ■* si N ««i»»srfssgss8i^i»g!isiJi»»i-)iovo»OVOVOiOio«Oiou^ioi^vo»OVni/^^w^u-iT4-iou-)vr(vriu-(iO t>.00 r< H ^vo rt tr^oo t^ M n m t^ vr> t^ OvOO a>0O ^ t^ u-i*c O t^ 0\ H »^ •»!• ir> vr»vO u-> lo vr> vr> vr> vn utvo vo >ovr)iovo»OiOw-)U->vr>vi^ir>^^vovo»ovntr> 'uo^Bog r~ ov en t^ tJ- vo ^00 00 M r) o t^^l-w osv/^K^boo *t^r^«*>-i o '-' •*oo m vr> tr>\o v^vo u^vO "^ vrno wvo \o vo vo vo vo «ovo vn »r> <^ vrivo vo tr> vn u^ ^ ut VO mo " ^t< Tl-t<^0 POrJ-M r^ «nvo w p» N O •-• O vo vooo •^ O Ov Ov tJ- O M H rt rh to N CO « HI pvoo lo ■»!- 5*^ y^ ."+ f^ 5^ t^ y^ ."^ o *o »^ p o o ovoo « b b b b b b b b b b>oo b\ bv b> b\ c\ bs on bv bv b b on b\ b b b bv "o^ b eotnrot<^c*icncntorocJ5 p^?* r^ p .^9® r* 5' r* *^ b b b b b b b b b b b on bv bv b> b> bs b bv bv b b b b o o o o o o tnto«ocococof*^roeotOtoH m ci f< rj r« con H tototocococococococo - O t1- O « 00 t^ CO c< CO n p O »-« ^(0«*>N» MOO t^M ^tH tJ-vo n ^mvo OvO OvO cOrfOO COO O cJOOVO Ov M tocoiOf< t^coH l-^0\t^>-i M M lot^OvCTvOvO Ov"-. « 0\0 •'I-COCOO vo »otococO'»*-cOf« H M M M O OnOO OvOO OOOOvO'-iconocococommw |5 t w tl to 4* »ovo (^00 o\ d « rt ^ vovo t^OO OS Q w tJ to t}- vovo t^OO On d iHi>ii-iMMM«^t4t4Ht4Ht4f4c1(«m THE LONDON, EDINBURGH a.nd DUBLIN PHILOSOPHICAL MAGAZINE AND JOURNAL OF SCIENCE. [FOURTH SERIES.] DECEMBER 1854. LII. On the Mechanical Energies of the Solar System. By Professor William Thomson*. THE mutual actions and motions of the heavenly bodies have long been regarded as the grandest phsenomena of mechanical energy in nature. But their light has been seen, and their heat has been felt, without the slightest suspicion that we had thus a direct perception of mechanical energy at all. Even after it has been shown f that the almost inconceivably minute fraction of the sun's heat and light reaching the earth is the source of energy from which all the mechanical actions of organic life, and nearly every motion of inorganic nature at its surface, are derived, the energy of this source has been scarcely thought of as a development of mechanical power. Little more than ten years ago the true relation of heat to force, in every electric, magnetic, and chemical action, as well as in the ordinary operations of mechanics, was pointed out J ; and it is a simple corollary from this that the sun, within the historical period of human observation, has emitted hundreds of * From the Transactions of the Royal Society of Edinburgh, vol. xxi. part 1 ; read April 17, 1854. t Herschel's Astronomy, Edition 1833. See last Ed., § (399). X Joule " On the Generation of Heat in the Galvanic Circuit," com- municated to the Royal Society of London, Dec. 17, 1840, and published, Phil. Mag., Oct. 1841. "On the Heat evolved during the Electrolysis of Water," Literary and Phil. Soc. of Manchester, 1843, vol. vii. part 3, Second Series. " On the Calorific EiFects of Magneto-Electricity, and the Mechanical Value of Heat," communicated to the British Association, August 1843, and pubhshed, Phil. Mag., Sept. 1843. " On the Changes of Temperature produced by the Rarefaction and Condensation of Air," Phil. Mag. S. 4. Vol. 8. No. 54. Dec. 1854. 2 E 410 Professor W. Thomson on the times as much mechanical energy* as that of the motions of all the known planets taken together. The energy — that of light and radiant heat — thus emitted, is dissipated always more and more widely through endless space, and never has been, pro- bably never can be, restored to the sun, without acts as much beyond the scope of human intelligence as a creation or annihi- lation of energy, or of matter itself, would be. Hence the question arises. What is the source of mechanical energy, drawn upon by the sun, in emitting heat, to be dissipated through space ? In speculating on the answer, we may consider whether the source in question consists of dynamical energy, that is, energy of motion f, or of "potential energy'' (as Mr. Rankine has called the energy of force acting between bodies which will give way to it unless held) ; or whether it consists partly of dy- namical and partly of potential energy. And again, we may consider whether the source in question, or any part of it, is in the sun, or exists in surrounding matter, until taken in and sent out again by the sun, or exists as energy only convertible into heat by mutual actions between the sun and surrounding matter. If it be dynamical and entirely in the sun, it can only be primitive heat ; if potential and in the sun, it can only be energy of chemical forces ready to act. If not in the sun, it must be due to matter coming to the sun (for it certainly is not a mere communication of motion to solar particles from external energy, as such could only be effected by undulations like sound or radiant heat, and we know that no such anti-radiation can be experienced by a body in the sun's circumstances) ; but whether intrinsically in such external matter, or developed by mutual action between this matter and the sun, and whether dynamical or potential in either case, requires careful consideration, as will be shown in the course of this communication. We see, then, that all the theories which have been yet proposed, as well as every conceivable theory, must be one or other, or a combination of the following three : — I. That the sun is a heated body, losing heat. II. That the heat emitted from the sun is due to chemical action among materials originally belonging to his mass, or that the sun is a great fire. III. That meteors falling into the sun give rise to the heat which he emits. communicated to the Ro5'al Society, June 1844, and published, Phil. Mag., May 1845. Joule and Scoresby "On the Powers of Electro-magnetism, Steam, and Horses," Phil. Mag., June 1846. * Once every twenty years or so. See Table of Mechanical Energies of the Solar System, appended. f " Actual energy," as Mr. Rankine has called it. Mechanical Energies of the Solar System. 4J1 I^ alluding to theories of solar heat in former communica^ tions to the Royal Society, I pointed out that the first hypo- thesis is quite untenable. In fact it is demonstrable, that, unless the sun be of matter inconceivably more conductive for heat, and less volatile, than any terrestrial meteoric matter we know, he would become dark in two or three minutes, or days, or months, or years, at his present rate of emission, if he had no source of energy to draw from but primitive heat*. The second has been not only held by the Fire-worshipers, but has probably been conceived of by all men in all times, and considered as more or less probable by every philosopher who has ever speculated on the subject. The third may have occurred at any time to ingenious minds, and may have occurred and been set aside as not worth considering ; but was never brought forward in any definite form, so far as I am aware, until Mr. Waterston communicated to the British Association, during its meeting at Hull, a remarkable speculation on cosmical dynamics, in which he proposed the theory that solar heat is produced by the impact of meteors falling from extra-planetary space, and striking his surface with velocities which they have acquired by his attraction. This is a form of what may be called the .Gravitation Theory of Solar Heat, which is itself included in the general meteoric theory, The objects of the present communication are, to consider the relative capabilities of the second and third hypothesis to account for the phsenomena ; to examine the relation of the gravitation theory to the meteoric theory in general ; and to determine what form of the gravitation theory is required to explain solar heat consistently with other astronomical phsenomena. In the first place it may be remarked, that in all probability there must always be meteors falling into the sun, since the fact of meteors coming to the earth f proves the existence of such bodies moving about in space ; and even if the motions of these bodies are * This assertion is founded on the supposition that conduction is the only means by which heat could reach the sun's surface from the interior, and perhaps requires limitation. For it might be supposed that, as the sun is no doubt a melted mass, the brightness of his surface is constantly refreshed by incandescent fluid rushing from below to take the place of matter falling upon the surface after becoming somewhat cooled and con- sequently denser — a process which might go on for many years without any sensible loss of brightness. If we consider, however, the whole annual emission at the present actual rate, we find, even if the sun's thermal capa- city were as great as that of an equal mass of water, that his mean tempe- rature would be lowered by about 3° Cent, in two years. We may, I think, safely conclude that primitive heat within the sun is not a sufficient source for the emission which has continued without sensible (if any) abatement for 6000 years.— (May 4, 1864.) t To make the argument perfectly conclusive, it would have to be as- sumed that meteors not only are, but have been, always falling to the 2E2 412 Professor W. Thomson on the at any instant such as to correspond to elliptical or circular orbits round the sun, the effects of the resisting medium would gradually bring them in to strike his surface. Also, it is easy to prove dynamically that meteors falling in to the sun, whatever may have been their previous state of motion, must enter his atmo- sphere, or strike his surface, with, on the whole, immensely greater relative velocities than those with which meteors falling to the earth enter the earth's atmosphere, or strike the earth's surface. Now, Joule has shown what enormous quantities of heat must be generated from this relative motion in the case of meteors coming to the earth; and by his explanation* of "fall- ing stars,'' has made it all but certain that, in a vast majority of cases, this generation of heat is so intense as to raise the body in temperature gradually up to an intense white heat, and cause it ultimately to burst into sparks in the air (and burn if it be of metallic iron) before it reaches the surface. Such effects must be experienced to an enormously greater degree before reaching his surface, by meteors falling to the sun, if, as is highly pro- bable, he has a dense atmosphere ; or they would take place yet more intensely on striking his solid or liquid surface, were they to reach it still possessing great velocities. Hence it is certain that some heat and light radiating from the sun is due to meteors. It is excessively probable that there is much more of this from any part of the sun's surface than from an equal area of the earth's, because of the enormously greater action that an equal amount of meteoric matter would produce in entering the sun, and because the sun, by his greater attraction, must draw in meteoric matter much more copiously with reference to equal areas of surface. We would have no right then, as was done till Mr. Waterston brought forward his theory, to neglect meteoric action in speculating on solar heat, unless we could prove, which we certainly cannot do, that its influence is insensible. It is in fact not only proved to exist as a cause of solar heat, but it is the only one of all conceivable causes which we know to exist from independent evidence. To test the possibility of this being the principal or the sole cause of the phaenomenon, let us estimate at what rate meteoric matter would have to fall on the sun, to generate as much heat earth for some immense period of time. The conclusion, however, appears sufficiently probable with the facts we know. * See Philosoj)hical Magazine, May 1848, for reference to a lecture in Manchester, on the 28th April 1847, in which Mr. Joule said, that "the velocity of a meteoric stone is checked by the atmos])here and its vis viva converted into heat, which at last becomes so intense, as to melt the body and dissipate it in fragments too small probably to be noticed in their fall to the ground, in most cases." Mechanical Energies of the Solar System. 413 as is emitted. According to Pouillet^s data*, '06 of a thermal unit Centigrade is the amount of heat incident per second on a square foot directly exposed to solar radiation at the eartVs distance from the sun_, which being 95,000,000 miles, and the sun^s radius being 441,000 miles, we infer that the rate of emission of heat from the sun is ^^ /95,000,000\2 ^^^^ XT, 1 -^ •06 X ( 441 000 ) =^^^1 thermal units per second per square foot of his surface. The mechanical value of this (obtained by multiplying it by Joule^s equivalent, 1390) is 83-4x(?^^00^y=386,900ft.lbs. V 441,000 / ' Now if, as Mr. Waterston supposes, a meteor either strikes the sun, or enters an atmosphere where the luminous and thermal excitation takes place, without having previously experienced any sensible resistance, it may be shown dynamically (the velocity of rotation of the sun^s surface, which at his equator is only a mile and a quarter per second, being neglected) that the least relative velocity which it can have is the velocity it would acquire by , solar gravitation in falling from an infinite distance, which is equal to the velocity it would acquire by the action of a constant force equal to its weight at the sun^s surface, operating through a space equal to his radius. The force of gravity at the sun^s surface being about 28 times that at the earth's surface, this velocity is 2 X 28 X 32-2 X 441,000 ^^_ ., , . ^-^qt: ' = 390 miles per second; and its mechanical value per pound of meteoric matter is 28 X 44] ,000 X 5280 = 65,000,000,000 ft. lbs. Hence the quantity of meteoric matter that would be required, according to Mr. Waterston's form of the gravitation theory, to strike the sun per square foot is 0*000060 pound per second (or about a pound every five hours). At this rate the surface would be covered to a depth of 30 feet in the year, if the density of the deposit is the same as that of water, which is a little less than the mean density of the sunf. A greater rate of deposit than this could not be required, if the hypothesis of no resistance, except in the locality of resistance with luminous reaction, were true ; but a less rate would suffice if, as is pro- bable enough, the meteors in remote space had velocities relative * Memoire sur la Chaleur Solaire, &c., Paris 1838. See Comptes Ren- dus, July 1838; or Pouillet, Traits de Physique, vol. ii. t This is rather more than double the estimate Mr. Waterston has given. The velocity of impact which he has taken is 645 miles per second, in the calculation of which, unless I am mistaken, there must be some error. ^/ 4li Professor W. Thomson on the to the sun not incomparably smaller than the velocity calculated above as due to solar gravitation. But it appears to me that the hypothesis of no sensible re- sistance until the " sun's atmosphere '* is reached, or the sun's surface struck, is not probable* j because if meteors were falling in to the sun in straight lines, or in parabolic or hyperbolic paths, in anything like sufficient quantities for generating all the heat he emits, the earth in crossing their paths would be, if not in- tolerably pelted, at least struck much more copiously by meteors than we can believe it to be from what we observe ; and because the meteors we see appear to come generally in directions cor- responding to motions which have been elliptic or circular, and rarely if ever in such directions as could correspond to previous parabolic, hyperbolic, or rectilineal paths towards the sun. If this opinion and the first mentioned reason for it be correct, the meteors containing the stores of energy for future sun^light Inust be principally within the earth's orbit i and we actually see them there as the "zodiacal light,'' an illuminated shower or rather tornado of stones (Herschel, § 897). The inner parts of this tornado are always getting caught in the sun's atmosphere, and drawn to his mass by gravitation. The bodies in all parts of it, in consequence of the same actions, must be approaching the sun, although but very gradually; yet, in consequence of their comparative minuteness, much more rapidly than the planets. The outer edge of the zodiacal light appears to reach to near the earth at present (Herschel, § 897) ; and in past times it may be that the earth has been in a dense enough part of it to be kept hot, just as the sun is now, by drawing in meteors to its surface. According to this form of the gravitation theory, a meteor would approach the sun by a very gradual spiral, moving with a velocity very little more than that corresponding to a circular ■path at the same distance, until it begins to be much more resisted, and to be consequently rapidly deflected towards the sun ; then the phsenomenon of ignition commences ; after a few seconds of time all the dynamical energy the body had at the fcOmmencement of the sudden change is converted into heat and radiated off; and the mass itself settles incorporated in the sun. It appears, therefore, that the velocity which a meteor loses in entering the sun is that of a Satellite at his surface, which (being -^ of that due to gravitation from an infinite distance) is 276 miles per second. The mechanical value (being half that bf a body falling to the sun from a state of comparatively slow motion in space) is about 82,500,000,000 ft. lb. per pound of meteoric matter ; hence the fall of meteors must be just twice * For a demonstration that it is not possible^ see Addition No. 1. Mechanical Energies of the Solar System. 415 that which was determined above according to Mr. Waterston's form of the theory, and must consequently amount to 3800 lbs. annually per square foot. If, as was before supposed, the density of the deposit is the same as that of water, the whole surface would be covered annually to a depth of 60 feet, from which the sun would grow in diameter by a mile in 88 years. It would take 4000 years at this rate to grow a tenth of a second in apparent diameter, which could scarcely be perceived by the most refined of modern observations, or 40,000 years to grow 1", which would be utterly insensible by any kind of ob- servation (that of eclipses included) unassisted by powerful telescopes. We may be confident, then, that the gradual aug- mentation of the sun^s bulk required by the meteoric theory to account for this heat, may have been going on in time past during the whole existence of the human race, and yet could not possibly have been discovered by observation, and that at the same rate it may go on for thousands of years yet without being discoverable by the most refined observations of modern astronomy. It would take, always at the same rate, about 2,000,000 years for the sun to grow in reality as much as he appears to grow from June to December by the variation of the earth^s distance, which is quite imperceptible to ordinary observa- tion. This leaves for the speculations of geologists on ancient natural history a wide enough range of time with a sun not sensibly less than our present luminary : still more, the meteoric theory affords the simplest possible explanation of past changes of climate on the earth. For a time the earth may have been kept melted by the heat of meteors striking it. A period may have followed when the earth was not too hot for vegetation, but was still kept, by the heat of meteors falling through its atmosphere, at a much higher temperature than at present, and illuminated in all regions, polar as well as equatorial, before the existence of night and day. Lastly ; although a very little smaller, the sun may have been at some remote period much hotter than at present by having a more copious meteoric supply. A dark body of dimensions such as the sun, in any part of space, might, by entering a cloud of meteors, become incandescent as intensely in a few seconds as it could in years of continuance of the same meteoric circumstances ; and on again getting to a position in space comparatively free from meteors, it might almost as suddenly become dark again. It is far from improbable that this is the explanation of the appearance and disappearance of bright stars, and of the strange variations of brilliancy of others which have caused so much astonishment*. * The star which Mr. Hind discovered in Aprd 1848, and which only remained visible for a few weeks, during which period it varied coimiderably 416 Professor W. Thomson on the The amount of matter, drawn by the sun in any time from surrounding space, would be such as in 47^^ years to amount to a mass equal to that of the earth. Now there is no reason what- ever to suppose that 100 times the earth^s mass drawn in to the sun, would be missed from the zodiacal light (or from meteors revolving inside the orbit of Mercury, whether visible as the " zodiacal light '' or not) ; and we may conclude that there is no difficulty whatever in accounting for a constancy of solar heat during 5000 years of time past or to come. Even physical astronomy can raise no objection by showing that the sun's mass has not experienced such an augmentation ; for according to the form of the gravitation theory which I have proposed, the added matter is drawn from a space where it acts on the planets with very nearly the same forces as when incorporated in the sun. This form of the gravitation theory then, which may be proved to require a greater mass of meteoric matter to produce the solar heat than would be required on any other assumption that could be made regarding the previous positions and motions of the meteors, requires not more than it is perfectly possible does fall in to the sun. Hence 1 think we may. regard the adequacy of the meteoric theory to be fully established. Let us now consider how much chemical action would be re- quired to produce the same effects, with a view both to test the adequacy of the theory that the sun is merely a burning mass without a supply of either fuel or dynamical energy from without, and to ascertain the extent to which, in the third theory, the combustion of meteors may contribute, along with their dynamical energies, to the supply of solar heat. Taking the former estimate, 2781 thermal units Centigrade, or 3,869,000 foot-lbs. as the rate per second of emission of energy from a square foot of the sun's surface, equivalent to 7000 horse-power, we find that more than '42 of a lb. of coal per second, or 1500 lbs. per hour would be required to produce heat at the same rate. Now if all the fires of the whole Baltic fleet were heaped up and kept in full combustion, over one or two square yards of surface, and if the surface of a globe all round had every square yard so occupied, where could a sufficient supply of air come frora to sustain the combustion ? yet such is the condition we must suppose the sun to be in, according to the hypothesis now under consideration, at least if one of the combining elements be oxygen or any other gas drawn from the surrounding atmosphere. If ..the products of combustion were gaseous, they would in rising check the necessary supply of fresh air ; or if they be solid or in appearance and brightness, but was always of a " ruddy " colour, may have not experienced meteoric impact enough to make its surface more than red-hot. Mechanical Energies of the Solar System. 417 liquid (as they might be wholly or partly if the fuel be metallic) they would interfere with the supply of the elements from below. In either or in both ways the fire would be choked^ and I think it may be safely affirmed that no such fire could keep alight for more than a few minutes, by any conceivable adaptation of air and fuel. If then the sun be a burning mass, it must be more analogous to burning gunpowder than to a fire burning in air ; and it is quite conceivable that a solid mass, containing within itself all the elements required for combustion, provided the pro- ducts of combustion are permanently gaseous^, could burn off at its surface all round, and actually emit heat as copiously as the sun. Thus an enormous globe of gun-cotton might, if at first cold, and once set on fire round its surface, get to a permanent rate of burning, in which any internal part would become heated by conduction, sufficiently to ignite only when nearly approached by the diminishing surface. It is highly probable indeed that such a body might for a time be as large as the sun, and give out luminous heat as copiously, to be freely radiated into space, without suffering more absorption from its atmosphere of trans- parent gaseous products t than the light of the sun actually does experience from the dense atmosphere through which it passes. Let us therefore consider at what rate such a body, giving out heat so copiously, would diminish by burning away. The heat of combustion could probably not be so much as 4000 thermal units per pound of matter burned J, the greatest thermal equivalent of chemical action yet ascertained falling considerably short of this. But 2781 thermal units (as found above) are emitted per second from each square foot of the sun; hence there would be a loss of about '7 of a pound of matter per square foot per second. Such a loss of matter from every square foot, if of the mean density of the sun (a little more than that of water), would take off from the mass a layer of about '5 of a foot thick in a minute, or of about 55 miles thick in a year. At the same rate continued, a mass as large as the sun is at present would burn away in 8000 years. If the sun has been burning at that rate in past time, he must have been of double diameter, of quadruple heating power, and of eight-fold mass, only 8000 years ago. We may quite safely conclude then that the sun does not get its heat by chemical action among particles of matter primitively belonging to his own mass, and we must therefore look to the meteoric theory for fuel, even if we retain the idea of a fire. Now, according to Andrews, the heat of * On this account gunpowder would not do. \ These would rise and be regularly diffused into space. X Both the elements that enter into combination are of course included in the weight of the burning matter. 418 Professor W. Thomson on the combustion of a pound of iron in oxygen gas is 1301 thermal units, and of a pound of potassium in chlorine 2655 ; a pound of potassium in oxygen 1700 according to Joule; and carbon in oxygen, according to various observers, 8000. The greatest of these numbers, multiplied by 1390 to reduce to foot-pounds, expresses only the 6000dth part, according to Mr. Waterston's theory, and, according to the form of the gravitation theory now proposed, only the 3000dth part, of the least amount of dynamical energy a meteor can have on entering the region of ignition in the sun's atmosphere. Hence a mass of carbon entering the sun's atmosphere, and there burning with oxygen, could only by combustion give out heat equal to the 3000dth part of the heat it cannot but give out from its motion. Probably no kind of known matter (and no meteors reaching the earth have yet brought us decidedly new elements) entering the sun's atmosphere from space, whatever may be its chemical nature, and whatever its dynamical antecedents, could emit by combus- tion as much as ^ ^'^^dth of the heat inevitably generated from its motion. It is highly probable that many, if not all, meteors entering the sun's atmosphere do burn, or enter into some chemical combination with substances which they meet. Pro- bably meteoric iron comes to the sun in enormous quantities, and burns in his atmosphere, just as it does to the earth. But (while probably nearly all the heat and light of the sparks which fly from a steel struck by a flint is due to combustion alone) only y^i^odth part of the heat and light of a mass of iron entering the sun's atmosphere, or ^th of the heat and light of such a meteor entering our own, can possibly be due to combustion. Hence the combustion of meteors may be quite disregarded as a source of solar heat. At the commencement of this communication, it was shown that the heat radiated from the sun is either taken from a stock of primitive solar heat, or generated by chemical action among materials originally belonging to his mass, or due to meteors falling in from surrounding space. We saw that there are suf- ficient reasons for utterly rejecting the first hypothesis ; we have now proved that the second is untenable; and we may con- sequently conclude that the third is true, or that meteors falling in from space give rise to the heat which is continually radiated off by the sun. We have also seen that no appreciable portion of the heat thus produced is due to chemical action, either between the meteors and substances which they meet at the sun, or among elements of the meteors themselves ; and that whatever may have been their original positions or motions relatively to one another or to the sun, the greater part of them fall in gradually from a state of approximately circular motion, and Mechanical Energies of the Solar System. 419 strike the sun with the velocity due to half the potential energy of gravitation lost in coming in from an infinite distance to his surface. The other half of this energy goes to generate heat very slowly and diffusely in the resisting medium. Many a meteor, however, we cannot doubt, comes in to the sun at once in the course of a rectilineal or hyperbolic path, without having spent any appreciable energy in the resisting medium; and, consequently, enters the region of ignition at his surface with a velocity due to the descent from its previous state of motion or rest, and there converts both the dynamical effect of the potential energy of gravitation, and the energy of its previous motion, if it had any, into heat, which is instantly radiated off to space. But the reasons stated above make it improbable that more than a very small fraction of the whole solar heat is obtained by meteors coming in thus directly from extra-planetary space. In conclusion, then, the source of energy from which solar heat is derived is undoubtedly meteoric. It is not any intrinsic energy in the meteors themselves, either potential, as of mutual gravitation or chemical affinities among their elements ; or actual, as of relative motions among them. It is altogether dependent on mutual relations between those bodies and the sun. A portion of it, although very probably not an appreciable portion, is that of motions relative to the sun, and of independent origin. The principal source, perhaps the sole appreciably efficient source, is in bodies circulating round the sun at present inside the earth^s orbit, and probably seen in the sunlight by us and called ^^ the zodiacal light.''-' The store of energy for future sunlight is at present partly dynamical, that of the motions of these bodies round the sun; and partly potential, that of their gravitation towards the sun. This latter is gradually being spent, half against the resisting medium, and half in causing a continuous increase of the former. Each meteor thus goes on moving faster and faster, and getting nearer and nearer the centre, until some time, very suddenly, it gets so much entangled in the solar atmosphere as to begin to lose velocity. In a few seconds more it is at rest on the sun's surface, and the energy given up is vibrated in a minute or two across the district where it was gathered during so many ages, ultimately to penetrate as light the remotest regions of space. Explanation of Tables. The following tables exhibit the principal numerical data re- garding the mechanical energies of the solar system. In Table I., the mass of the earth is estimated on the assumption that its mean density is five times that of water, and the other 420 Professor W. Thomson on the masses are shown in their true proportions to that of the earth, according to data which Professor Piazzi Smyth has kindly com- municated to the author. In Table II., the mechanical values of the rotations of the sun and earth are computed on the hypothesis, that the moment of inertia of each sphere is equal to the square of its radius multiplied by only one-third of its mass, instead of two-fifths of its mass, as would be the case if its matter were of uniform density. These two estimates are only introduced for the sake of comparison with other mechanical values shown in the table, not having been used in the reasoning. The numbers in the last column of Table II., showing the times during which the sun emits quantities of heat mechanically equivalent to the earth's motion in its orbit, and to its motion of rotation, were first communicated to the Royal Society on the 9th of January 1852, in a paper " On the Sources Available to Man for the production of Mechanical Efi^ect.^' These, and the other numbers in the same column, are the only part of the numerical data either shown in the tables, or used directly or in- directly in the reasoning on which the present theory is founded, that can possibly require any considerable correction ; depending as they do on M. Pouillet's estimate of solar heat in thermal units. The extreme difficulties in the way of arriving at this estimate, notwithstanding the remarkably able manner in which they have been met, necessarily leave much uncertainty as to the degree of accuracy of the result. But even if it were two or three times too great or too small (and there appears no possi- bility that it can be so far from the truth), the general reasoning by which the theory of solar heat at present xiommunicated is supported, would hold with scarcely altered force. The mechanical equivalent of the thermic unit, by which the solar radiation has been reduced to mechanical units, is Mr. Joule's result — 1390 foot-pounds for the thermal unit Centigrade-^ which he determined by direct experiment with so much accuracy, that any correction it may be found to require can scarcely amount to j^^ or y^o^*^ ^^ ^*® ^^^ value. Mechanical Energies of the Solar System, 4^1 Table I. — Forces and Motions in the Solar System. Masses in pounds. Distances from the suns's centre, in miles. Forces of attraction towards the sun, in terrestrial pounds. Velocities, in miles per second, Sun 4,230,000,000x1021 I 1x2021 870x1021 10,530x1021 11,920x1021 1,579x1021 4,037,000x1021 1,208,000x1021 201,490x1021 236,380x1021 (surface) 441,000 441,000 36,800,000 68,700,000 95,000,000 144,800,000 494,300,000 906,200,000 1,822,000,000 2,854,000,000 28-61 per lb. of matter 286,100x101? 35,710x1017 124,200x1017 73,490x1017 4,211x1017 919,400x1017 81,855x1017 3,377x1017 1,615x1017 (equator) 1*27 277 30-36 22-22 18-89 15-28 8-28 611 4-31 3-44 Imaginary solid planet close to the sun Earth Mars Jupiter Saturn Uranus Neptune ......... Distances from earth's centre. Attraction towards earth in terrestrial pounds. Velocities rela- tively to earth's centre, in miles. Moon 136x1021 237,000 3,956 378x1017 1 per lb. of matter. 0-615 0-291 Earth's equator. Table II. — Mechanical Energies of the Solar System. Potential energy of gravitation to sun's surface. Actual energy relatively to sun's centre. In foot-pounds. Equivalent to supply of solar heat, at the present rate of radiation, for a period of In foot-pounds. Equivalent to supply of solar heat, at the present rate of radia- tion, for a period of Sun 967,000x1030 333x1029 347x1030 2,252x1030 1,843x1030 160x1030 119,980x1030 19,580x1030 1,625x1030 1,217x1030 116 yrs. 6 days. 1-44 ... 15-2 ... 98-5 ... 80-7 ... 70 ... 14yrs.l44 2... 127 ... 71-2 ... 53-3 ... Imaginary planet of 1021 lbs. of matter, close to the sun 1 57x1033 697X1033 790x1033 105 X 1033 268,800x1033 80,440x1033 13,430X1033 15,750x1033 6 yrs. 214 days 83 ... 227 ... 94 ... 303 ... 12 ... 252 ... 32,240 9,650 1,610 1,890 Mercury Venus Earth Mars Saturn Uranus ... To the earth's surface. Relatively to earth's centre. 2,846x1027 3-0 hours. 2,347x1025 14,310x1025 1-48 min. 9-03 ... Tlnrfli ^rntntinn^ Total 380,000x1033 45,589 years. 1,114,004x1030 134 years. Professor W, Thomson on the Additions (May 9, 1854), No I. Conclusion of Physical Astro- nomy against the Extra-planetary Meteoric Theory. Meteors which when at great distances possessed, relatively to the centre of gravity of the solar system, velocities not incom- parably smaller than the velocity due to gravitation to the sun^s surface, must strike the surfaces of the earth and of the other planets not incomparably less frequently than equal areas of the sun's surface, and with not incomparably smaller velocities, and consequently must generate heat at the surfaces of the earth and other planets not incomparably less copiously than at equal areas of the sun's surface. But the whole heat emitted from any part of the sun's surface is incomparably greater than all that is gene- rated by meteors on an equal area of the earth's surface, and therefore is incomparably greater than all that can be generated at his own surface by meteors coming in with velocities exceeding considerably the velocity due to his attraction from an infinite distance. Hence upon the extra-planetary meteoric theory of solar heat the quantity of matter required to fall in cannot be much, if at all, less than that required upon the hypothesis that the work done by the sun's attraction is equal to the mechanical value of the heat emitted from his surface, and must therefore be, as found above, about -000060 of a pound per square foot per second, or 1900 lbs. per square foot in a year. The mean density of the sun being about 1^ times that of water, the matter in a pyramidal portion from his centre to a square foot of^ his surface is about ^ X 441,000 X 5280 x 1^ x 64=62,100,000,000 lbs., and the whole annual addition of meteoric matter to the sun would therefore be 1900 _ 1 62,100,000,000 ~ 32,400,000 of his own mass. In about 6000 years the sun would there- fore be augmented by j(/oo ^^ ^lass from extra-planetary space. Since the time occupied by each meteor in falling to the sun from any distance would be much less than the periodic time of a planet revolving at that distance, and since the periodic times of the most distant of the planets is but a small fraction of 6000 years, it follows that the chief eflfect on the motions of the planetary system produced during such a period by the attraction of the matter falling in would be that depending simply on the aug- mentation of the central force. To determine this, let M be the sun's mass at any time t, measured from an epoch 6000 years ago; to the earth's mean angular velocity, and a its meftn Mechanical Energies of the Solar System, 423 distance at the same time ; and 2 h the constant area described by its radius vector per second. Then we have — M a)^a=-^ (centrifugal force), a)a^=h (equable description of areas) ; from which we deduce, and M2 Now, if M(j denote the mass of the sun at the epoch from which time is reckoned, since the annual augmentation is about 72^ oVolTo ^^ *^^ ™^^® itself, we have and ^"~^n^ "^32,400,000/' ^"""^^^^V^"^ 32,400,000/' Hence, if Hq and Ht denote the angular velocities at the epoch and at the present time, T ; the angular velocity, which is uni- formly accelerated during the interval, will have a mean value, ii, expressed as follows : — n=i(n„+a.) ="T{i-i^«}=n.(i-3^^^) ; and if S denote the angle described in the time T, we have / T^ \ ^^^H''' ""32,400,000/- To test this conclusion for the case of the earth, let T' denote the number of revolutions round the sun in the time T. Then, if the unit in which T is measured be the time of a revolution with the angular velocity Ot^ we have rvl rp ^ ~ 32,400,000* Thus, if T be 4000 years, we have or only 3999^ actual years in a period of 4000 times the present 424 Professor W. Thomson on the year. Similarly, we should find a loss of ^th of a year on a period of 2000 years ago ; that is, of about a month and a half since the Christian sera. Thus, if we reckon back about 2000 times the number of days at present in the yeai*, we should find seasons, new and full moons, and eclipses, a month and a half later than would be if the year had been constantly what it is. Now we have abundant historical evidence that there is no such disloca- tion as this, either in the seasons, or in the lunar phsenomenaj and it follows that the central attracting mass of the solar system does not receive the augmentation required by the extra- planetary meteoric theory of solar heat. But the reasoning in the preceding paper establishes, with very great probability, a meteoric theory of solar heat ; and we may therefore conclude that the meteors supplying the sun with heat have been for thousands of years far within the earth's orbit. No. II. FHction between Vortices of Meteoric Vapour and the Sun's Atmosphere the immediate Cause of Solar Heat. It has been shown that the meteors which contribute the energy for solar heat must be for thousands of years within the earth's orbit before falling to the sun. But a meteor could not remain for half a year there, unless it were revolving round the sun, with, at each instant, the elements of a circular or elliptic orbit. Hence meteors, on their way in to the sun, must revolve, each, thousands of times round him, in orbits which, whatever may have been their primitive eccentricities, must tend to be- come more and more nearly circular as they become smaller, by the efl'ects of the resisting medium. The resistance must be excessively small, even very near the sun ; since a body of such tenuity as a comet, darting at the rate of 365 miles per second, within one-seventh of his radius from his surface, comes away without sensible loss of energy. If, as is probable, the atmo- sphere of that part of space is carried in a vortex round the sun by the meteors and other planets, it may be revolving at nearly the same rates as these bodies at different distances in the prin- cipal plane of the solar system ; but we cannot conceive it to be revolving in any locality more rapidly than a planet at the same distance. At one-seventh of the sun's radius from his surface, this would be about 258 miles per second ; and therefore a comet approaching so near the sun, could not have a less velocity rela- tively to the resisting medium than 107 miles per second, and, if going against the stream, might have as great a relative velo- city as 623 miles. On the other hand, the great body of the meteors circulating round the sun, and carrying the resisting medium along with them, may be moving through it with but Mechanical Energies of the Solar System. 425 small relative velocities ; the smaller for each individual meteor, the smaller its dimensions. The effects of the resistance must therefore be very gradual in bringing the meteors in to the sun, even when they are very near his surface ; and we cannot tell how many years, or centuries, or thousands of years, each meteor, according to its dimensions, might revolve wiihin a fraction of the sun^s radius from his surface, before falling in, if it continued solid ; but we may be sure that it w^ould so revolve long enough to take, in its outer parts at least, nearly the temperature of that portion of space ; and therefore, probably, unless it be of some substance infinitely less volatile than any terrestrial or meteoric matter known to us, long enough to be wholly converted into vapour (the mere fact of a comet* escaping from so near the sun as has been stated, being enough to show that there is, at such a distance, no sufficient atmospheric pressure to prevent evapo- ration with so high a temperature). Even the planet Mercury, if the sun is still bright when it falls in, will, in ail probability, be dissipated in vapour long before it reaches the region of in- tense resistance, instead of (as it would inevitably do if not vola- tile) falling in solid, and in a very short time (perhaps a few seconds) generating three years^ heat, to be radiated off in a flash which would certainly scorch one-half of the earth^s sur- face, or perhaps the whole, as we do not know that such an extensive disturbance of the luminiferous medium would be confined by the law of rectilineal propagation. Each meteor, when volatilized, will contribute the actual energy it had before evaporation to a vortex of revolving vapours, approaching the sun spirally to supply the place of the inner parts, which, from moving with enormously greater velocities than the parts of the sun's surface near them, first lose motion by intense resistance, emitting an equivalent of radiant heat and light, and then, from want of centrifugal force, fail into the sun, and consequently become condensed to a liquid or solid state at his surface, where they settle. The latent heat absorbed by the meteors in evapo- ration, and afterwards partially emitted in their condensation at a higher temperature, is probably as insensible, in comparison with the heat of friction, as it has been shown the heat of any * That a comet may escape with only a slight loss by evaporation, if the resistance is not too great to allow it to escape at all, is easily understood, when we consider that it cannot be I'or more than a few hours exposed to very intense heat (not more than two or three hours within a distance equal to the sun's radius from his surface). If it consist of a cloud of solid me- teors'the smallest fragments may be wholly evaporated immediately; but all whose dimensions exceed some very moderate limit of a few feet would, unless kept back by the resisting medium and made to circulate round the sun until evaporated, get away with only a little boiled off from their sur- faces Phil. Mag. S. 4. Vol. 8. No. 54. Dec. 1854. 2 F 426 Professor W. Thomson on the combustion or chemical action they can experience must be, or, as we have tacitly assumed the heat is which is taken and kept by the meteors themselves in approaching from cold space to lodge permanently in the sun. We may conclude that the sun's heat is caused, not by solids striking him, or darting through his atmosphere, but by friction in an atmosphere of evaporated meteors, drawn in and condensed by gravitation while brought to rest by the resistance of the sun's surface. The quantity of meteoric matter required, if falling in solid, would, as we have seen, be such that half the work done by solar gravitation on it, in coming from an infinite distance, is equal to the energy of heat emitted from the sun, and would therefore amount to a pound every 2*3 hours per square foot of the sun's surface ; and it will be the same as this, notwithstanding the process of eva- poration and condensation actually going on, if, as appears pro- bable enough, the velocity of the vortex of vapour immediately external to the region of intense resistance in all latitudes be nearly equal to that of a planet close to the sun. No. III. On the Distribution of Temperature over the Sun's Surface. Not only the larger planets, but the great mass of meteors revolving round the sun, appear to- revolve in planes nearly co- inciding with his equator, and therefore such bodies, if solid when drawn in to the sun, would strike him principally in his equatorial regions, and would cause so much a more copious radiation of heat from those regions than from any other parts of his surface, that the appearance would probably be a line or band of light, instead of the round bright disc which we see. The nearly uniform radiation which actually takes place from different parts of the sun's surface appears to be sufficiently accounted for by the distillation of meteors, which we have seen must, in all probability, take place from an external region of evaporation at a considerable distance (perhaps several times his radius) inwards to his surface where they are condensed. What- ever be the dynamical condition of the luminous atmosphere of intense resistance, it is clear that there must be a very strong tendency to an equality of atmospheric pressure over the pro- bably liquid surface of the sun, and that the temperature of the surface must be everywhere kept near that of the physical equi- librium between the vapours and the liquid or solid into which they are distilling. A lowering of temperature in any part would therefore immediately increase the rate of condensation of vapour into it, and so bring a more copious influx of meteoric matter with dynamical energy to supply the deficiency of heat. The various deviations from uniformity which have been observed in Mechanical Energies of the Solar System. 427 the sun's disc are probably due to eddies which must be con- tinually produced throughout the atmosphere of intense resist- ance between his surface (which at the equator revolves only at the rate of 1*3 mile per second) and the great vortex of mete- oric vapour, which a few miles outside revolves at the rate of 277 miles per second about the equatorial regions, and (if not at the same) certainly at enormously great rates a few miles from the sun's surface in other localities. Such eddies may ordinarily be seen as the streaks which have been compared to ''the streamers of our northern lights'' (Herschel, § 387), and when any one of them sends a root down to the sun's surface it may cause one of the " minute dark dots or pores " which have been observed, and which, when attentively watched, are found to be always changing in appearance (Herschel). A great rota- tory storm, like the tropical hurricanes in the earth's atmosphere, may occasionally result from smaller eddies accidentally com- bining, or from some disturbing cause originating at once an eddy on a much larger scale than usual, and may traverse the sun's surface, preventing the distillation of meteoric vapour over a great area, and consequently checking both the supply of dynamical energy for radiant heat in the luminous atmosphere of resistance, and the torrents of condensed meteoric vapours falling to the surface below it. The consequence would be, that the meteoric rain (Herschel's " cloudy stratum") would be cleared away for a certain space under the central parts of the storm by falling down to the liquid or solid surface, and the luminous atmosphere would lose intensity over a larger space bounded very irregularly by a region of minor eddies, which would cause varying streaks of light. These are exactly the circumstances assumed by Sir William Herschel to account for the great spots with their dark centres surrounded by sharply terminated penumbrse inside the abrupt ragged boundaries of the bright surface, and the branching luminous streaks or *' faculse" in the bright surface outside in their neighbourhood. (Sir John Herschel's Astronomy, § 388.) No. IV. (Added August 15, 1854.) On the Age of the Sun. The moment of the sun's rotatory motion (according to the hypothesis mentioned above in the "Explanation of the Tables" regarding the moment of inertia of his mass) is one-third of his mass multiplied by his radius, multiplied by the linear velocity of his equator, and is therefore equal to that of a planet at his 1*27 1 surface having a mass equal to ^ — 977 ~fi^ ^^ ^^^ ^^^ mass. This is equal to the quantity of meteoric matter which would fall in during 25,000 years, at the present rate ; and therefore 2F2 428 Professor W. Thomson on the 25,000 years is the time the sun would take to acquire his actual motion of rotation, by the incorporation of meteors, if these bodies were each revolving in the plane of his equator im- mediately before entering the region of intense resistance. But it has been shown to be probable that a great space round the sun is occupied by a vortex of evaporated meteors, and that the incorporation of meteoric matter takes place in reality by the condensation of vapour in a stratum close to his surface all round. It appears not improbable that the tangential velocity of this vortex immediately external to the radiant region of intense resistance may be found to be, in all solar latitudes, very nearly that of a planet close to the sun. If it be so, the moment of the motion communicated to the sun by any mass of meteoric matter will be ."' of what would be communicated 4 by the incorporation of an equatorial planet of equal mass : as much as 3^Q of the sun's mass would have to fall in to produce his present rotation : and 32,000 years would be the time in which this would take place, at the present rate of meteoric incorporation as estimated above. It will be a very interesting hydrodynamical problem to fully investigate the motion of the meteoric vortex; and among results to be derived from it will be strict estimates of the con- tribution to the sun's rotatory motion, and of the quantity of heat generated, by any amount of meteoric matter in becoming incorporated. With these, and with an accurate determination of the rate at which the sun radiates heat, we should be able to fix with certainty the augmentation of his velocity of rotation actually taking place at present from year to year, and to esti- mate the time during which the existing rotation would be acquired by meteoric incorporation going on always at the pre- sent rate and in the present manner. Whatever this time (which I shall call T years, to avoid circumlocution below) may be, probably will not be found to differ very widely from the preceding estimate of 32,000 years. Now, from the fact that the sun's equator, the planets' orbits, and the zodiacal light, all lie nearly in one plane, it appears highly probable that the sun's present motion has really been acquired by the incorporation of meteors. It is certain that the present manner and rate of meteoric action cannot have been going on for more than the indicated period (T), without giving the sun a greater rotatory motion than he has, unless (which is very improbable) he were previously rotating in a contrary direc- tion round the same axis : and, at only the present rate, it cannot have been going on for less than that time, unless the sun has been created with a rotatory motion round his present Mechanical Energies of the Solar System. 429 axis, or has acquired such a motion from some independent mechanical action. The actual rate of solar radiation in time past may, for all we know, have been sometimes much greater and sometimes much less than at present ; and there probably has been a time before, when meteors in abundance fell direct to the sun from extra-planetary space, some getting stopped on their way by the earth, and illuminating it by friction in its atmosphere and impact at its surface. But the kind of meteoric action now going on, has in all probability produced neither more nor less than T times the quantity of heat now emitted from the sun in one year. All things considered, it seems not improbable that the earth has been efficiently illuminated by the sun alone for not many times more or less than 32,000 years. As for the future, it will be a most interesting problem to determine the mass of the zodiacal light (that is, matter external to the sun^s mass, and within the earth^s orbit), by the pertur- bations it may probably enbugh be discovered to produce in the motions of the visible planets. It could scarcely, I think, amount to j th of the sun-s mass (probably not to nearly as much), without producing such perturbations as could not have been overlooked in the present state of astronomical science; and we have seen that meteors amounting to j^^^^dth of the sun^s mass, must, at the present estimated rate, fall in in 3000 years. I conclude that sunlight cannot last as at present for 300,000 years. The continual acceleration of the sun's rotatory motion, which the preceding theory indicates, must, sooner or later, be tested by direct observation. The rate of acceleration (which for many thousands of years past and to come must remain sensibly constant, if the solar radiation continues so) is such that the angular velocity is increased annually by y^ of its present value. If T be 32,000, according to the preceding conjectural estimate, the effect in fifty-three years would amount to diminishing the period of the sun's revolution by an hour ; and the actual effect cannot, according to the theory, be incomparably greater or less. It is just possible that a careful comparison of early with recent observations on the apparent motions of the dark spots may demonstrate this variation ; but as some of the most accurate of recent observations of this kind have led to estimates of the pe- riod of revolution* differing from one another by as much as Days. Hours. Minutes. * According to Bohm 25 12 30 Laugier 25 8 10 Petersen 25 4 30 (See Encyc. Brit., Sth edit. vol. iv. p. 87.) The discrepancies are probably due to proper motions of the spots, which, from the explanation given above in Addition III.., may be expected to be very considerable. 430 On obtaining rapid Adjustments with Wollaston's Goniometer, eight hours, it is more probable that, unless some way be discovered for taking into account the motions of the spots themselves with reference to the mass, centuries will elapse before direct evidence can be had either for or against the anticipated acceleration of the sun's rotatory motion. LIII. On a Method of obtaining rapid Adjustments with Wol- laston's Goniometer. By C. Greville Williams*. CHEMISTS who have been in the habit of using WoUaston's goniometer are aware of the trouble and sometimes diffi- culty of making each face of the crystal so reflect the black lines, that, on moving the instrument until both approximate, they shall be truly parallel, and at length, as the movement is continued, perfectly coincide. Most operators find it difficult, in moving the crystal with the fingers on the wax, to prevent disturbing the first adjustment while making the second. With some crystals this is compara- tively easy, with others great loss of time is occasioned by it. The fact is, that the movements of the fingers are too coarse, and it occurred to me that it would be extremely easy to make an instrument that should possess one motion for one face of the crystal, and a second for the other. -p- j^ Fig. 1 represents the contrivance I have adopted before being attached to the gonio- meter, fig. 2 shows it in its place. It will be seen that any chemist can con- struct it with the tools to be found in every laboratory. A small ring of brass is pierced with two grooves exactly opposite each other, through which passes an axle supporting in its centre a small ball, which in its turn has a hole drilled through it, and tapped so that a vertical screw carrying two milled heads can be inserted. One of these milled heads sup- ports the crystal, the other serves to move it, and thereby com- municate a horizontal motion. A lateral motion is obtained by the horizontal axle, which enables it to be moved to the left or right. The whole system is screwed into the small brass plate usually used to support the crystal ; the entire arrangement is seen in fig. 2. The pivot in fig. 1 is made to move stiffly by means of two small plates screwed tight on to the grooves in which it works ; moreover, from the vertical rod being formed from a screw, it can be depressed so as to make the face of the crystal lie exactly in the axis of the instrument. * Communicated by the Author. On a General Method in the Theory of Probabilities. 431 Fig. 3. By the use of this little contrivance, perfect adjustments which would otherwise require a very considerable time, may be made in a few seconds. LIV. On a General Method in the Theory of Probabilities. By George Boole, LL.D., Professor of Mathematics in Queen's College, Cork"^. Preliminary Statement of Principles. 1. nnHE class of questions which I propose to consider here A is that of which the data consist of — 1 st. Probabilities of events, or of combinations of events, capable of being expressed by the signs of ordinary language ; 2nd. Absolute connexions or conditions among events capable of similar expression ; and of which the qusesitum or element sought is also the pro- bability of some event or combination of events whose expression is known. Thus the elements of the question considered in my paper (On the Conditions by which the Solutions of Questions * Communicated by the Author. 432 Prof. Boole on a Gerieral Method in in the Theory of Probabilities are limited, Philosophical Maga- zine, vol. viii. p. 91) are. Data, Probabilities, Prob. x^c^ Prob. y=c^ 1 ,,. Prob. xz=c^p^ Prob. yzz=c^p^j Absolute connexion, z(\-x){\-y)=0 •• . (2) Quasitum. Prob. z. Here, beside the probabilities of the several events whose logical expressions are x, y, xz, and yz, we have given the abso- lute connexion z{\—x){\—y)=0, denoting (in the language of the Calculus of Logic) that the event z cannot happen in the absence of the events x and y. The qusesitum is the probability of the event whose expression is z. I design to investigate a general method of solving problems of this kind. Such a method, viewed through the range of its consequences, is entitled to be regarded as a general method in probabilities, because all solvable questions may be referred either directly, or through some intermediate principle, to the above class. And the hope which moves me to repeat here without substantial change the demonstration of such a method contained in my treatise on the Laws of Thought, is that of being able to set forth with greater fulness the distinctive principles upon which the demonstration depends, and of annexing to the final statement of the rule to which it leads, an important addition, 2. Probability I conceive to be not so much expectation, as a rational ground of expectation, and its numerical measure I de- fine with mathematicians generally* as follows. Definition. If, respecting any event, the mind is only able to form a number n of similar and mutually exclusive hypotheses, to none of which it is entitled to give any preference over any other, and if m of those hypotheses are favourable to the event, i. e, such that any one of- them being realized, the event will happen, while the remaining hypotheses are unfavourable to it, * To quote, for example, Laplace's definition, " La theorie des hasards consiste i r^duire tous les evenements du me me genre a un certain nombre de cas egalement possibles, c'est a dire, tels que nous soyons egalement indecis sur leur existence ; et a determiner le nombre de cas favorables a I'ev^nement dont on cherche la probabilite. Le rapport de ce nombre k celui de tous les cas possibles est la mesure de cette j)robabilite, &c." — Essai philosophique sur les Probabilit^s, p. 7. Subsequently, Laplace speaks of the different " cases " as " hypotheses," which, indeed, they are. the Theory of Probabilities. 433 i. e. favourable in the above sense to its not happening, the pro- 171 bability of the event is measured by the fraction — . It does not, I think, need proof that the principles of the theory of probabilities must be derived either, — 1st, from the nature of probability as set forth in its measure ; or 2ndly, from its connexion with logic and language. Commencing with the former source, I remark that it is implied in the definition that probability is always relative to our actual state of information and varies with that state of information. Laplace illustrates this principle by supposing the following case. Let there be three urns, A, B, C, of which we are only informed that one contains black and the two others white balls ; then, a ball being drawn from C, required the probability that the ball is black. As we are ignorant which of the urns contains black balls, so that we have no reason to suppose it to be the urn C rather than the urn A or the urn B, these three hypotheses will appear equally worthy of credit ; but as the first of the three hypotheses alone is favourable to the drawing of a black ball from C, the proba- bility of that event is ^. Suppose, now, that in addition to the o previous data it is known that the urn A contains only white balls, then our state of indecision has reference only to the urns B and C, and the probability that a ball drawn from C will be black is ^. Lastly, if we are assured that both A and B contain white balls only, the probability that a black ball will issue from C rises into certitude. {Essai Philosophique sur les Probabilites, p. 9.) Here it is seen that our estimate of the probability of an event varies with our knowledge of the circumstances by which it is afiected. In this sense it is that probability may be said to be relative to our actual state of information. Let us, in further illustration of this principle, consider the following problem. The probability of an event x is measured by the fraction — , that of an event y by the fraction -, but of the connexion of the events x and ^ absolutely nothing is known. Required the probability of the event xy, i. e. of the conjunction of the events x and y. There are (see definition) a cases in which x happens, to m cases in which it happens or fails; and concerning these cases the mind is in a state of perfect indecision. To no one of them is it entitled to give any preference over any other. There are, in like manner, b cases in which y happens, to n cases in which it happens or fails ; and these cases are in the same sense equally 434 Prof. Boole on a General Method in balanced. Now the event an/ can only happen through the com- bination of some one of the a cases in which x happens, with some one of the b cases in which y happens, while nothing pre- vents us from supposing any one of the m cases in which a: hap- pens or fails from combining with any orie of the n cases in which y happens or fails. There are thus ab cases in which the event xy happens, to mn cases which are either favourable or unfavourable to its occurrence. Nor have we any reason to assign a preference to any one of those cases over any other. Wherefore the probability of the event xy is — . Or if we represent the probability of the event x by jo, that of the event y by q, the probability of the combination xy is pq. It cannot be disputed that the above is a rigorous consequence of the definition adopted. That new information might alter the value of Prob. xy is only in accordance with the principle (already exemplified from Laplace) of the relative character of probability. It is only so far forth as they are known, that the connexions, causal or otherwise, of events can aff'ect expectation. Let it be added, that the particular result to which we have been led is perfectly consistent with the well-known theorem, that if X and y are known to be independent events, the probability of the event xy is pq. The difference between the two cases con- sists not in the numerical value of Prob. xy, but in this, that if we are sure that the events x and y are independent, then are we sure that there exists between them no hidden connexion, the knowledge of which would affect the value of Prob. xy ; whereas if we are not sure of their independence, we are sensible that such connexions may exist. Again, it is perfectly consistent with the known theorem, that if the probability of x is p, and the probability that if x happen y will happen is q, then the probability of the combination xy is pq. For if we know nothing of the connexion ofx and y, the occurrence of x will not affect our expectation of the occurrence of y, so that the probability that if X happen y will happen, will, in the actual state of our informa- tion, be the same as the simple probability of y, i. e. as q. 4. As from the simple data Prob. x=p, Prob. y=qwe deduce Prob. xy==pq, so from the same data we should have ?roh.x(l-y)=p{l-q), Vroh.{l-x)(l-y) = {l-p){l-q)kc. And generally it may be shown, that if the probabilities of any events x, y, z are simply given, the probability of any combina- tion of them expressed by F {x,y, z . .) will be found by sub- stituting in that expression for x,y,z . . their given probabilities. The general principle involved in the above deductions may be thus stated. the Theory of Probabilities, 485 Principle I. — Probability is always relative to our actual state of information. Upon the actual connexions of events it depends no further than as such connexions are known to us. This doctrine of the nature of probability, it may be added, has been fully recognized by acute and thoughtful minds ap- proaching the subject from a point of view different from the mathematical one*. I proceed to the statement of an important principle founded on the nature of language as an instrument of expression. It is, that in the theory of probabilities, as in every other branch of science, the solution of a question ought to depend upon the in- formation conveyed in the data, and not upon the special elements or constructions of the language which may serve as the vehicle of that information. Now one very important point in which languages are observed to differ, is the selection of the objects or events to which simple terms are appropriated. In the rude infancy of nations, the number of such terms is small, and their application is confined within the limits of daily experience. With the progress of society the need of a wider vocabulary is felt, not merely for the expression of things unknown to former experience, but also for the purpose of abbreviation. Simple terms are invented, not solely for the representation of things wholly new, but for the more simple expression of things which it was before possible to express by a combination of terms. Whensoever in this gradual advance of language the combination of two simple terms is replaced by a new simple term, a defini- tion or an equivalent series of ordinary propositions is introduced. Thus, if every combination of rain with snow becomes repre- sented, for abbreviation, by the simple term " sleet,'^ we virtually carry with us, whenever we use that term, the definition " sleet is rain with snow,^^ or the equivalent train of propositions, " If there is sleet there is rain with snow,^' " If there is rain with snow there is sleet -/' and that definition, or its equivalent pro- positions, we must, if need be, express as well as assume. Now it is manifest that there is no limit to this invention of simple terms, and consequent implication of propositions. In a lan- guage possessed of an infinite copiousness of diction, every object of experience, every combination of events, might thus be ex- pressed by a simple term. Supposing that we had such a lan- guage at command, it is evident that we might in various ways express the data and the object of a question in the theory of probabilities. The events whose probabilities are given might, according to one mode of expression, appear as compound events * For instance, it is stated with great clearness in an extract from the commonplace book of Bishop Copleston, recently pubhshed by Archbishop Whately. 486 Prof. Boole on a General Method in expressed by combinations of simple events ; according to an- other mode, as simple events connected together by definitions or by implied propositions. Now the principle which I wish to assert is, that it is wholly indifferent which mode of expression we employ, provided that it be adequate to convey all the infor- mation we possess. Perhaps that principle may be more defi- nitely stated as follows. Principle II. — Any events which suffice simply, or by combina- tion, for the expression of the data may be assumed as simple events and symbolized accordingly, provided that we expUcitly determine the whole of the relations which implicitly connect them. To make plain my meaning, let it be supposed that ob- servation has furnished the following elements of a problem : — Probability of rain =p, Probability of rain with snow = q ; the qusesitum of that problem being Probability of rain without snow. The expression of this problem by an observer in whose lan- guage there should exist no word for " snow,^' but in which every combination of rain with snow should be termed " sleet,'' would be as follows : — 1st. Probability of rain =jo, 1 2nd. Probability of sleet =q, ^Data. 3rd. Sleet always implies rain. J Required probability of rain without sleet. It is then affirmed that these two statements are equivalent. The expectation of a phaenomenon cannot be affected by the mere mode of statement of it, and of the circumstances upon which it depends. As respects the two modes of statement in the above instance, it will be seen that in the former of them, one of the given probabilities is that of a compound event ; in the latter, both the given probabilities are those of simple events between which an absolute relation (3rd) is affirmed to exist, and in terms of which the event whose probability is sought is directly expressed. Now, beside that it is the most obvious course of procedure to determine directly the event whose probability is sought in terms of those whose probabilities are given, an object which we can always effect by the Calculus of Logic, there is a special reason why we should take this course. Consider the problem employed for the purpose of illustration in the first section of this paper. Representing the events xz and yz, since their probabilities are given, by s and t respectively, its data become Prob. a7=c„ Prob. y=c^, Prob. s=CiPi, Prob. t=c^p^] (3) the elements x, y, 8 and t, here assumed (Principle II.) as the Theory of Probabilities. 48f simple events, being connected by the relation xyst-\-x{l-y)s{l-t) + (l—x)y{ls)t-{-xy{ls){l—t) 4-^(l-2/)(l-5)(l-/) + (l-%(l-^)(l-/) + {l-a:){l-y){l-s){l-t) = l; ..... (4) and the event whose probability w is sought being under the same conditions a!yst-^w{l—y)s{l'-t)-{-{l—x)y{l—s)t. ... (5) These results (4) and (5) are both given by the development (Laws of Thought, p. 322). The probabilities (3), together with the relation (4), are equivalent to the data of the problem as expressed in terms of a?, y^ and z in the section referred to, Now I remark that the mere probabilities (3) do not of them- selves furnish any relations connecting sc, y, s and t. The whole of the relation connecting those elements is given by (4), and it is given in the form of a logical equation, i. e. of an equation interpretable into a proposition. We possess of that relation an eocplicit and available knowledge. But it is not so with the rela- tion connecting the elements x, y, z, when, as in the primary statement of the problem, these are assumed as simple events. We are explicitly informed that these elements are connected by the relation 2'(1— {xy y, z) =;?, Prob. •>^{xy y, z) = 9, &c. . . (1 ) Annexed absolute conditions : — (9(a7,y,^..)=0, &c (2) Qusesitum, or probability sought : — Prob. F(^,2/,r..) (3) Now the most obvious mode of procedure is to seek to express the event whose probability is sought, explicitly in terms of the events whose probabilities are given. To do this, we must, in accordance with Principle II., regard all these as simple events, expressing them by new logical symbols Wy s, t, &c. Let then {xyyyZ ,.)=zsy '\lr{xyy,z,.)=ty ¥{XyyyZ..) = w. (4) From the logical equations (2) and (4) we can now determine w in terms of s, /, &c. The solution will be of the form w;=A + 0B+5c + iD (5) Here A, B, C, D are functions of s, t, &c., and the several terms of the development are, by means of their coefficients, thus in- terpretable. Ist. A represents those combinations of the events s, t, &c. which must happen if w happen. the Theory of Probabilities. 439 2nd. B those combinations which cannot happen if w happen, but may otherwise happen. 3rd. C those combinations which may or may not happen if w happen. 4th. D those combinations which cannot happen at all. And the above representing all possible combinations, we have A + B + C + D = l (6) Now there are many problems in which the combination de- noted by C does not present itself. Such is the one considered by Mr. Cayley and myself, and commented on by Mr. Wil- braham. As the principle of solution is the same in this as in the more general class of problems in which C does appear, I shall, for simplicity, confine myself to the simpler case. The event w, then, consists solely of that combination of the simple events s, t, &c. which is denoted by A, and the sole condition to which those events are subject is D = 0, or A-fB = l; (7) these logical equations being, by virtue of the necessary equa- tion (6), strictly equivalent when C does not make its appearance in the development. The problem may now be briefly stated as follows. The events s, t, &c. are subject to the condition (7), and at the same time their respective probabilities are ^ Prob. s=Pj Prob. t=q, &c. Required the value of Prob. A. Now let us consider whether, upon the familiar notion of an urn containing balls, we can construct a problem whose expressed data shall be in all respects the same as the above, and which shall at the same time admit of definite solution. And, in the first place, it is manifest that any event or combi- nation of events may be represented by the issuing of a ball possessing a particular quality, or combination of qualities from an urn. Thus the event s may be represented by the issuing of a ball possessing a particular quality which we will term the s-quality, the event t by that of a ball possessing the Equality, and so on. In like manner the event st, or the combination of the events s and t, may be represented by the issuing of a ball possessing at once the qualities s and t. And generally the events A, B, D, whatever combinations of the symbols Sj t ,. these letters may stand for, may be represented by the issuing of balls possessing the corresponding qualities or combinations of qualities. And as every species of events can thus be represented by the issuing of a ball of a particular species from an urn, so every 440 Prof. Boole on a Genei^al Method in problem relating to events may be represented by a correspond- ing problem relating to the issuing of balls from an urn. If, in such imagined problem, any events s, t, &c. so enter as that nothing is known or can be inferred respecting their connexion, they must be treated (Principle I.) as if they were independent, and therefore the balls by whose issue they are represented must be regarded as free from any nexus affecting their issue. On the other hand, if the events s, t, &c. are subject to any condition as D=0, such condition must be introduced by the supposition of a neanis simply forbidding the issue of balls of the species D, without affecting the freedom of the other balls. Such a nexus we may suppose to be established by the attachment of every ball of the species D by a thread to the walls of the urn. All pos- sible issues are thus restricted to balls of the species A or B, so that the condition D=0 is equivalent, as we have before seen, to the condition A + B = 1 . The general problem may therefore be represented as follows : — An urn contains balls whose species are expressed by means of the qualities s, t, &c. and their opposites, concerning the connexion of which qualities nothing is known. Suddenly all balls of the species D are attached by threads to the walls of the urn, and this being done, there is a probability p that any ball drawn is of the species s, a probability q that it is of the species t, and so on. What is the probability that it is of the species A, supposing that A and D denote mutually exclusive species of balls, each defined by means of the properties s, t and their opposites ? Let us, for simplicity, represent A + B by V, and let us repre- sent by Vg the aggregate of constituents in V of which s is a factor, by V^ the aggregate of constituents of which ^ is a factor, and so on. Then, according to the principles of the Calculus of Logic, we shall have the following interpretations, viz. — V= that event which consists in the drawing of a ball which is not of the species D. V,= that event which consists in the di'awing of a ball which is of the species s and is not of the species D. V<= that event which consists in the drawing of a ball which is of the species t and is not of the species D. Now let the total number of balls in the urn be N, and let S be the number which are of the species s, T the number which are of the species /, &c. Hitherto s and / have been used only as logical symbols expressing events. Let us now introduce a new set of symbols s, t, &c., to be used in a quantitative acceptation, ST to denote the numerical ratios :j^, ^j^, &c. Then we have the Theory of Probabilities. 441 s (quantitative) = probability,, before the nexus, of the event s, t (quantitative) = probabiUty, before the nexus, of the event t, and so on. And hence V, V^, V<, &c. quantitative, representing what the same expressions logical become when we change, as above, the signification of 5, t, &c., we have the following derived probabilities (Principle I.). Probabilities before the nexus : — V (quantitative) = probability of the drawing of a ball not of the species D. V^ (quantitative) = probability of the drawing of a ball of the species s but not of the species D. V^(quantitative) = probability of the drawing of a ball of the species t but not of the species J), A (quantitative) = probability of the drawing of a ball of the species A. Now, after the nextis, the probability of the drawing of a ball of the species s is obviously the same as the probability before the nexus, that if a ball not of the species D be drawn, it will be of the species s. Hence Prob. (before nexus) of s not D pzrz ^ ^ Prob. (before nexus) of not D V =Y- (^) And thus we form the series of quantitative equations, Y=P' r =?'&<= (9) Again, the probability after the nexus, of the event A, is equal to the probability before the nexus, that if a ball not of the species D be drawn it will be of the species A, _ Prob. (before nexus) of A not B " Prob. (before nexus) of not D __ Prob. (before nexus) of A ~~ Prob. (before nexus) of not D* Since the events A and D are mutually exclusive, A Hence representing Prob. w by u, we have u = ^. ....... (10) The solution of the problem is now completed. The values of phil. Mag, S. 4. Vol, 8. No. 54. Dec. 1854. 2 G 442 Prof. Boole on a General Method in the ratios s, t, &c. being found from (9), must be substituted in (10). These ratios being positive fractions, we must employ a set of values of 5, /, &c., which consists solely of positive frac- tions. It will hereafter be shown, that when the problem is a real one, the system (9) furnishes one, and only one set of values answering the required description : that set must therefore be taken. This is the only addition required to the general rule as given in the Laws of Thought. The combined systems (9) and (10) may be elegantly deduced by the following method, originally communicated to me by Professor Donkin. The probabilities, before the nexus, of the events V, V„ V<. . and A are the corresponding quantitative functions V, V„ V< . . and A. The probabilities of the same events after the nexus are 1, jo, 9 . . and u respectively. Now the only effect of the nexus is to exclude a number of hypotheses unfavourable to the hap- pening of the above events, without affecting the cases favourable to their happening. Hence the several probabilities have to each other the same ratio before the nexus as after, and therefore V:V.:V,..:A=l:j9:^..;t^; or p q ' ' u ' a system equivalent to the system (9) and (10). The investigation is conducted in the same manner when the function C presents itself in the final logical development (5), and the general rule thus established is the following : — Rule.—Yoxm the symbolical expressions of the events whose probabilities are given or sought, and equate such of them as relate to compound events to a new set of logical symbols, s, t, &c. Express also any absolute conditions which may be given in the data. From the combined system determine by the Cal- culus of Logic, Wj the event whose probability is sought in terms of all the events s, /, &c. whose probabilities are given, and let the result be «.;=A+0BH-5c+iD. Then representing the aggregate A -f B + C by V, and the sum of those constituents in V of which 5 is a factor by V„ and so on, form the algebraic system of equations ^=^..=V, (L) p q Prob. u;= :^-t£^, (IL) wherein p, q, &c. are the given probabilities of s, t, &c. the Theory of Probabilities. 4a4S If the problem be a real one, the system (I.) will furnish one set, and only one set, of positive fractional values of s, t, ^c., which, substituted in (II.), will determine Prob. w. The interpretation of c, when it appears in the solution, is Prob. Cw Prob. C ' and it indicates the new experience requisite to complete the solution of the problem. If the system (I.) does not furnish a single ' system of positive fractional values of s, t, &c., the problem is not a real one, and does not in its statement represent a possible experience. The passages in italics contain the additions to the rule as it is presented in the Laws of Thought. In concluding this paper, I shall briefly consider the only two objections which have at any time occurred to my own mind as likely to occasion a difficulty in the reception of the above results. 1st. It may be, and indeed it has been, urged that the logical calculus upon which the investigation proceeds does not consti- tute a science or represent " reality,^^ being only based upon a system of '^ substituted ratios.^^ To this it is replied, that pure science, as such, is concerned only with ratios or relations. To know things as they are in themselves, is the professed but unattainable object of a so-called philosophy proper. It is, however, here maintained that the logical calculus does represent reality and constitute science, in- asmuch,— 1st, as the laws of thought upon which it is founded, and which it expresses by the fundamental equations xy=yx, x^=-x, &c. are not fictitious, but are derived from a real analysis of the intellectual operations ; 2nd, as it is a fact, and not an assumption, that the laws thus determined are formally identical with the laws of a certain properly defined species of arithmetic ; 3rd, as it accords with the catholic objects of science to avail itself of all discovered laws and relations, without regard to the fashion of the schools or the prescription of ancient usage. 2nd. It may be objected, that, although in the representative problem of the urn we can readily pass in thought from a system of balls having an actual physical nexus to the same system free from that nexus, \Ye cannot, in the represented problem in which the events s, t, &c. are subject to the logical and therefore ne- cessary connexion D = 0, interpret to ourselves the same events as freed from that connexion ; and therefore the problem of the urn does not completely and adequately represent the problem for which it is substituted, inasmuch as in the one case the nexus or condition implied by the equation D = 0 is merely actual, while in the other case it is not only actual but necessary. 2G2 444 Mr. W. J. M. Rankine on simultaneous Observations of It is replied, that this necessity may be regarded as merely posterior to some act of limitation by which the events s, t, &c., previously of larger comprehension, became restricted to that particular interpretation in terms of sc, y, &c. which they bear in the problem, and which is the foundation of the logical necessity referred to. What that larger ccTmprehension is, it is wholly unnecessary to attempt to define. It suffices, upon the general grounds of symbolical algebra, to apply to the inverse process of the removal of a nexus, the formal laws which are derived from the direct and always interpretable case of its imposition. I regard this as a principle, which, though capable of verification in innumerable instances, does not rest simply upon the cumu- lative evidence afforded by such instances, but has a real foun- dation in the intellectual constitution. Finally, as respects the mode in which the aforesaid logical necessity has been represented in the example of the urn, it may be remarked that it involves no more than is implied in the various figures by which, in difl*erent languages, the idea of ne- cessity has been symbolized. For in each of those figures we have presented to us the notion of something which has once been free, but has ceased to be so through a material act, or a positive determination*. And any one of these modes of illus- tration might with equal propriety have been adopted. The verification of these results will be considered in my next paper. Lincoln, Sept. 30, 1854. LV. On some simultaneous Observations of Rain-fall at differ- ent points on the same Mountain- Range. By W. J. Macquorn Rankine, Civil Engineer, F.R.SS. Lond. and Edinb. ^-c.f 1. npiIE question of the relative proportions of rain which fall A at points having different situations, levels, and aspects on the same mountain-range, is one which, besides its scientific interest, is of great practical importance, especially with reference to the water-supply of large towns. 2. The observations here recorded are intended as a small contribution to our knowledge of this subject. They were made ♦ Witness the supposed derivation of the Latin necesse from nexus, of the Greek (IfiapufVTf, from a verb signifying division by the casting of lots, of the \>ord/(:/^e, &e. The higher limitation implied by the addition of such terms as absolute {e. g. absolute necessity) is curiously derived, not from the direct idea of physical restraint, but from the converse one of the removal of all restraint upon the restraining power. t Communicated by the Author; having been read to the British Asso- ciation for the Advancement of Science, Section A, at Liverpool, Sept. 1854. Rain-fall at different points on the same Mountain-Range. 445 daily and simultaneously for a period of 151 consecutive days, from the ISth of July to the 12th of December 1845^ at two points on the north-western slope of the Pentland Hills near Edinburgh. The long lapse of time previous to their publication has been occasioned by the fact, that the fair copy of the obser- vations, with various calculations founded on them, accidentally passed out of my possession not long after it had been prepared ; and it was only a short time since that I happened to find the original registers, which 1 have reduced anew. 3. The range of the Pentland Hills extends in a north-east and south-west direction for about thirteen miles. Its north- east extremity is about five miles from Edinburgh towards the south, and seven miles from the Frith of Forth. For about four miles in the middle of its course the range is double, consisting of two parallel chains of summits separated by a deep and nar- row valley called Glencorse, from which a considerable portion of the water-supply of Edinburgh is derived. This valley is tra- versed by a stream which runs towards the north-east, then turns at right angles and escapes towards the south-east through a gorge, now occupied by the embankment of one of the reser- voirs of the Edinburgh Water Company. 4. The summits of the Pentland Hills vary from 1400 to 1900 feet in height above the sea; the ridges between them, from 1000 to 1300 feet. The highest summits are in the double chain, near the middle of the range. 5. The south-west extremity of the Pentland Hills is a point of divergence of tributary streams of the Forth, Clyde and Tweed. To the west and south-west of this point rise some small tribu- taries of the Clyde. From the south-eastern face of the hills, near the point of divergence, flow some tributaries of the Tweed ; further towards the north-east and from the central valley, tri- butaries of the Frith of Forth. On the north-western face of the range are the sources of the water of Leith and some smaller tributaries of the Frith of Forth ; and on the same face, near its south-western end, some sources of the Almond, also a tributary of the Frith of Forth. From the south-western extremity of the Pentland range already referred to, a range of low hills of from 1000 to 800 feet in height extends towards the west-north-west, being part of the boundary between the basin of the Forth and that of the Clyde. \ 6. The surface of the Pentland Hills is covered chiefly with pasture and heath, with a few patches of peat. Ample details of the topography and geology of this range may be found in Mr. Charles Maclaren^s work on the Geology of Fife and the Lothians. . 7. The two points at which the observations of rain-fall now 446 Mr. W. J. M. Rankine on simultaneous Observations of referred to were made, were situated on the north-western face of the Pentland range near its south-western extremity, amongst the sources of the river Almond. Both the gauges were placed as near as possible to the surface of the ground, in open and regularly-sloping pasture, far from any sheltering objects. The lower gauge, designated by H, was about 700 feet above the level of the sea, three miles and a quarter to the north-west of the line of summits of the Pentland Hills, about four miles to the north-cast of the range of low hills before mentioned, and ten miles southward from the Frith of Forth. The higher gauge, designated by G, was about 900 feet above the level of the sea, or 200 feet above the gauge H, one mile and a half to the north-west of the line of summits of the Pentland Hills, one mile and three-quarters to the north-east of the range of low hills, and two miles and a half from the gauge H in a direction south-by-west. 8. The rain-fall was recorded by a different observer for each gauge every morning about nine o'clock. Although minute fractions were not attended to in the readings, so that compari- sons between the quantities of rain at the respective gauges on single days are of little value, yet I am satisfied of the accuracy of the result of any comparison embracing a period of several days. The vicinity of situation and similarity of aspect of those two gauges naturally caused them to receive the rain-fall of the same masses of cloud, so that very few instances occurred of rain fall- ing at one gauge without a fall also taking place at the other within the space of a few hours, if not simultaneously. 9. In the first of the annexed tables, therefore, the depths of rain-fall at the gauges G and H are compared for each period of rainy weather. There are seventeen of these periods in the table, varying in length from two to eleven days, and separated by periods of drought. The first period, however, from the I3th to the 20th of July, must be taken with the qualification, that the quantities of rain set down for it are merely the sums of a number of brief showers occurring at intervals. At the foot of the table the total depths of rain are compared for the whole period of observation, 151 days. The mean ratio set down at the foot of Table I. in the fourth column, shows that the total rain-fall at the gauge G exceeded that at the gauge H in the ratio of one to one and a quarter. The ratios for the seventeen periods of rain deviate from this mean amount, upwards and downwards, in a somewhat irregular manner, but evince, on the whole, a tendency to increase with the approach of winter. 10. In the second table, the depths of rain-fall at the gauges H and G are compared for each of the calendar months, August, Rain-fall at different points on the same Mountain-Hang e, 447 September, October, and November 1845, and for the period consisting of these four months. The ratios for the several months in the fourth column of this table show a much less extent of deviation from the mean ratio of one to one and a quarter than those for shorter periods ; and in them also is evi- dent a tendency to increase on the approach of winter. 11. It is a question of some interest whether the excess of the rain-fall at the gauge G above that at the gauge H is principally caused by the greater elevation of the ground at the former gauge, or by the greater proximity of the gauge G to the chain of summits of the mountain range. In order to throw some light on this question, there are added in the fifth column of Table II. the depths of rain, as published by Mr. Beardmore during the four months referred to, at a gauge which I have designated by F, 734 feet above the sea, situated near the embankment of the Edinburgh Water Company in the gorge of the Valley of Glencorse, and in the immediate vicinity of some of the highest summits of the range. In the sixth column are given the ratios of the depths of rain at the gauge F to those at the gauge H for the four months separately, and for the whole period. From these data it appears, that although the gauge F was at nearly the same elevation with the gauge H, it received during the four months in question a depth of rain somewhat greater than that at the gauge G, nearly 200 feet higher. This was most probably the effect of the greater proximity of the gauge F to the highest summits of the range. The ratios of the depth of rain at F to that at H for the dif- ferent months vary in a very irregular manner ; probably because those points are separated by the mountain-range, and receive the rain-fall of different masses of cloud and different winds. 12. In the third table the total depths of rain-fall during the four months at each of the gauges H, G, F, are compared with the depth registered in a gauge denoted by E during the same period at the residence of Mr. Adie, immediately to the south of Edinburgh, and a little more than 200 feet above the sea. The rain-fall at this last point is very much less than that at any one of the points on the mountain-range. 13. The rain-fall at points still nearer the summits of the hills than the gauges G and F must have been considerably greater than that indicated by these gauges. This appears from the facts, that the total flow of water during the period of obser- vation, of a tributary stream of the river Almond, gauged by me at a point near G, corresponded to an effective depth of rain-fall only one-thirteenth part less than that recorded by the rain- gauge; and that the flow from the valley of Glencorse, as gauged by 448 On Rain-fall at different points on the same Mountain-Range. Mr. Beardmore in 1846 and 1847, corresponded to an effective depth of rain-fall somewfiat exceeding that at the rain-gauge F. 14. I do not bring forward the limited number of observations and comparisons here recorded as possessing any great value in themselves, but as capable of contributing to the attainment of useful conclusions when combined with other data of the same kind. Table I. — Comparison of Rain-fall by periods of Bain. Dates (days commencing at 9 A.M.). Gauge H, inches. Gauge G, inches. Ratio G h' 1845, July 13 to 30. ... 31 to Aug. 5. Aug. 7 to 9. ... 10 to 13. ... 18 to 22. ... 23 to 27. Sept. 14 to 17. ... 18 to 20. ... 21 to 23^ ... 25 to Oct. 6. Oct. 7 to 14. ... 15 to 22. ... 27 to 31. Nov. 6 to 12. ... 17 to 21. ... 25 to Dec. 4. Dec. 5 to 12. 0-5 0-9 03 11 0-9 0-6 0-2 1-5 10 4-4 0-6 1-2 10 0-4 11 1-7 0-4 03 10 0-4 13 1-2 07 0-3 1-7 0-9 41 0-8 2-3 1-8 0-4 1-5 2-8 0-8 0-60 Ml 1-33 118 1-33 117 1-50 113 0-90 0-93 1-33 1-92 1-80 100 1-36 1-65 200 Total for 151 days 17-8 223 1*25 mean ratio. Table XL— Comparison of Rain -fall by Calendar Months. Months. Gauge H, inches. Gauge G, inches. Ratio G H' Gauge F, inches. Rati* F H* August 1845 3-5 4-3 5-6 2-9 42 50 6-9 4-3 1-20 115 1-23 1-48 5-38 4-83 801 2-90 1-54 112 143 1-00 September October .\ November Total rain and mean ratios... 16-3 20-4 1-25 2112 1-30 Table III. Gauge H, inches. Gauge E, inches. Ratio E h' Inverse ratio H E' Ratio G e' Ratio F E* Aug., Sept., Oct. and Nov. ... 16-3 1309 0-80 1-26 1 1-56 1-62 LVI. Observations on Meteorolites or Aerolites, considered Geo- graphicallyj Statistically, and Cosmically, accompanied by a complete Catalogue. By R. P. Greg. [Concluded from p. 342.] THERE is no occasion, in continuation, to enter into details concerning the phsenomena attending the fall of meteorites and fire-balls, &c., or give a list of the analyses which have from time to time been made of various meteoric irons and stones. Suffice it to say, that no new chemical element has yet been dis- covered in these bodies, though several new mineral compounds have been observed. Most, indeed nearly all, the simple chemical elements have been detected in them. Some consist of pure iron ; others of iron alloyed with nickel, perhaps also accompanied with small quantities of carbon, chro- mium, cobalt, arsenic and phosphorus ; and some few are me- chanically combined with crystallized olivine ; the majority have, however, a common or normal character, both internally and externally. They have been variously classified; as by Prof. Shepard in the following way, treating them as it were minera- logically : — Class I. — Metallic. Order 1. Tv/r n ui fSec. I. Pure. Malleable, I m^ -i ^ iv homogeneousi Sec. II. AUoyed / ^'°^^'y crystalline. ° L [ Coarsely crystalhne. Order 2. Malleable. / Amygdalo-peridotic. , . < Amyerdalo-pyritic. heteroi'eneous I r* •<. i I • i => [^Pynto-plumbagmous. * ^ - Orders. - - fPure. ' ' \ Alloyed. Class II. — Stony. Brittle : . , Order 1 Sec. I. Peridotic/^^^'^^-g^^^f^- \ r me-gramed. Trachytic. . . . -^ Sec. II. Pyroxenic. Sec. III. Chladnitic. ^Sec. IV. Carbonaceous. Order 2. Trannean l^^^' ^- Homogeneous, irappean. . . . |g^^ jj Porphyritic. Order 3. Pumice-like. Probably, and partly in connexion with this similarity with the chemical elements and even minerals of our own planet, has been developed the theory of the /iow-e.2;^r«-terrestrial origin of 460 Mr. R. P. Greg on Meteorolites or Aerolites, meteoric irons and stones ; a theory principally supported by the chemists and electricians, as Sir H. Davy, Fusinieri, M. Biot, Prof. Shepard, M. F. G. Fischer and others. Before concluding this paper I shall shortly allude to this theory, as it bears strongly on the general subject. I cannot do better than again quote from Prof. Shepard. (See his Report on American Me- teorites, published in the American Journal of Science.) "The extra-terrestrial origin of meteoric stones and iron masses seems likely to be more and more called in question, with the advance of knowledge respecting such substances, and as additions continue to be made to the connected sciences ; I may therefore take an early occasion of presenting some views, founded partly upon Biotas theory of the aurora borealis, which seem to favour such an origin of meteorites. " The recent study of those frequently occurring and wide- spread atmospheric accumulations of meteoric dust (a single case being recorded where the area must have been thousands of square miles in extent, and where the quantity of earthy matter precipitated must have been from 50 to 500,000 tons in weight), makes known to us the vast scale on which terrestrial matter is often pervading the regions of the upper atmosphere, and pre- pares us to appreciate the mode in which peculiar constituents of meteorites may be translated to those remote distances, where, according to the theory of Biot, the clouds of meteoric dust are retained. " Great electrical excitation is known to accompany volcanic eruptions, which may reasonably be supposed to occasion some chemical changes in the volcanic ashes ejected; these being wafted by the ascensional force of the eruption into the regions of the magneto-polar influence, may there undergo a species of magnetic analysis. The most highly magnetic elements (iron, nickel, cobalt, chromium, &c.), or compounds in which these predominate, would thereby be separated and become suspended in the form of metallic dust, forming those columnar clouds so often illuminated in auroral displays, and whose position con- forms to the direction of the dipping-needle. While certain of the diamagnetic elements (or combinations of them), on the other hand, may under the control of the same force be collected into different masses, taking up a position at right angles to the former (which Faraday has shown to be the fact in respect to such bodies), and thus produce those more or less regular arches, transverse to the magnetic meridian, that are often re- cognized in the phaenomena of the aurora borealis. " Any great disturbance of the forces maintaining these clouds of meteor-dust, like that produced by a magnetic storm, might lead to the precipitation of portions of the matter thus suspended. considered Geographically , Statistically y and Cosmically. 451 If the disturbance was confined to the magnetic dust, iron-masses would fall ; if to the diamagnetic dust, a non-ferruginous stone ; if it should extend to both classes simultaneously, a blending of the two characters would ensue in the precipitate, and a rain of ordinary meteoric stones would take place. "As favouring this view, we are struck with the rounded, hailstone-like form of many of the particles of composition (even though consisting of widely dijQPerent substances) in nearly all stones, and even in many of the iron masses. Nor are these shapes to be referred to fusion ; they evidently depend upon a cause analogous to that which determines the same configuration in hailstones themselves. " The occasional raining of meteorites might therefore on such a theory be as much expected as the ordinary deposition of moisture from the atmosphere. The former would originate in a mechanical elevation of volcanic ashes and in matter swept into the air by tornadoes, the latter from simple evaporation. In the one case, the matter is upheld by magneto-electric force ; in the other, by the law of difi*usion which regulates the blending of vapours and gases, and by temperature. A precipitation of metallic and earthy matter would happen on any reduction of the magnetic tension ; one of rain, hail or snow, on a fall of temperature. The materials of both originate in our earth. In the one instance they are elevated but to a short distance from its surface, while in the other they appear to penetrate beyond its furthest limits, and possibly to enter the interplanetary space ; in both cases, however, they are destined, through the operation of invariable laws, to return to their original reposi- tory.'' That large falls of dust and other substances do occasionally take place is without doubt, as well as that volcanic dust is some- times shot up into the air and carried great distances ; but that it is this same matter which is afterwards sustained or solidified by magnetic action, there is no proper evidence to prove. The fall of a meteorite is usually preceded by an explosion, and a scattering J rather than uniting, of fragments or bodies ; evidence rather of some larger part, or whole, entering our atmosphere from without, and bursting or cracking from sudden heating, into larger or smaller particles according to the original nature and texture of the body itself. Humboldt, in his ' Cosmos,' decidedly expresses the opinion that the nature of these meteoric stones, and the phsenomena accompanying their fall, are such as to pre- clude the idea of their having been condensed from minute mat- ter or from a gaseous state, in a short interval of time : he also states that meteoric masses kindle and become luminous at ele- vations which must be supposed to be almost entirely deprived 462 Mr. R. P. Greg on Meteorolites or Aerolites, of air, aud frequently explode at great elevations. Their enor- mous and probably planetary velocity, their oblique, nay, some- times horizontal direction, frequently in a retrograde or opposite direction to the earth's motion, are all perfectly subversive of the idea of these meteoric masses having a terrestrial or atmospheric origin. And there are other objections to M. Biot's and Prof. Shepard's theory, such as the question, whence comes the large quantity of nickel in meteoric irons ? It is an extremely rare metal on the earth, and is only found in a few localities ; nor does it, that I am aware of, constitute any portion of volcanic matter hitherto analysed. It is not to be denied that there exist some phsenomena of the meteoric class which have an atmospheric and therefore terrestrial origin ; there are, we know, cases of electric action producing certain kinds of fireballs ; there are falls of dust, black rain, and even of viscid substances ; but it is necessary to sepa- rate these cases from the regular meteoric masses, stone or iron, and not indiscriminately attempt to account for all these things by one theoiy, however ingenious, or howsoever in particular cases and to a certain extent, correct. La Grange, Arago and Humboldt all agree in rejecting the atmospheric origin of aerolites. Having thus examined and rejected the theory of a terrestrial origin of meteoric masses, I shall conclude by summing up the principal points I have endeavoured to establish. First. That the deposition of meteoric matter on the surface of the earth has not been, all things considered, otherwise than uniform, ?. e. there is no decided tendency to local deposition. , Secondly. That their origin is not within the limits of the earth's atmosphere. Thirdly. That they are probably distinct from ordinary lumi- nous meteors, as regards both their physical nature and orbits, and may also exhibit periodicity. (See Table F.) Fourthly. That their period of least common occurrence takes place when the earth is on the side of the winter solstice in peri- helion; while, on the other hand, the period of most frequent occuiTcnce is when the earth is in aphelion, and the mean system or mass of the asteroids in their perihelion. Fifthly. That they may reasonably be considered as belonging to the group of planetoids or asteroids, and to partake, therefore, of the proper nature and conditions of planetary bodies. Note I. p. 332. — One circumstance may be mentioned as being rather singular, which is, the extraordinary number of meteoric irons, discovered within a comparatively short period in the United States, considered Geographically j Statistically, and Cosmically. 453 viz. thirty-four ; while only one has been found in France, and but one in Great Britain. In Mexico eight meteoric irons have been discovered and described, but there is no recorded or historic instance of a stone fall ; yet in the United States there have been seventeen falls of stones this century, and one observed iron fall. There is no accounting for these apparent irregularities ; possibly several of the Mexican and United States iron meteoric masses have been the result or produce of one shower or explosion. The proportion of stone to iron falls may be taken at 25 to 1, i. e. 96 per cent, of all that fall consist of stony matter; so that for the thirty-four iron masses found in the United States there may have been 34 x 96 = 3264 stone falls. Note II. p. 334. — It is remarkable, that while December has only nine falls recorded,/!;^ out of these should have occurred on the 13th of the month, and one on the 14th. Five fell within the space of only twelve years, and two fell on the 13th December 1803, at two distinct localities. In looking through Prof. Powell's * Catalogues of Luminous Me- teors,' and various journals, there are described only two meteors and two small falling stars for any 13th day of December. Note III. p. 336. — Professor Cappocci of Naples, in a letter to M. Arago (given in the Comptes Rendus for August 1840), endea- vours, though I think not very successfully, to establish, not only a coincidence in the fall of aerolites and luminous meteors for the 16th and 17th of July, but assigns to them a regular recurring period of five years, and concludes by supposing that they are " the result of an aggregation of cosmical atoms dispersed in space; atoms which are constrained to unite themselves by contrary poles in consequence of magnetic attraction." And he seems to consider comets, aurora boreales, meteors and aerolites as various resultants from bands or currents of nebulous matter, existing in planetary space, in a state of magnetism more or less intense. Note IV. p. 336. — It can hardly be imagined that the small frag- ments and atoms which usually constitute aerolites can have any luminosity, whether reflected or inherent. It is possible, however, they may form the more solid part or nucleus of larger and less solidified bodies. That ordinary faUing stars, and more particularly the luminous meteors observable in the great periodic displays of August and November, are self-luminous can hardly admit of doubt. It may be mentionod that Pallas has probably irregular and angular surfaces, like the majority of meteoric stones, and that Ceres is ap- parently surrounded with a very dense atmosphere ; a circumstance perhaps also sometimes the case, on a far smaller scale, with meteor- olithic fire-balls. Respecting the cause of the supposed breaking up of a planet between Mars and Jupiter, Mr. Nasmyth, at a recent 454 Mr. B. P. Greg on Meteorolites or Aerolites, meeting of the British Association, ingeniously suggested that its disruption might have occurred when the planet had arrived at some such condition or state of tension (whilst cooling) as that known to exist in a Prince Rupert drop, which, as is well known, shivers to pieces on the slightest injury to the surface. Table F. — Showing the days of each month on which aerolites have fallen to the earth. Months. January .. February.. March April May June July August . . September October .. November December idi2 13! 15 6l 8 1112 17 6 4 5 5 3| 5 1317 1313 1803 1628 18,18 1314 1718 191920 23 25 14 25 1315 171822 15j 18:20 101313 1314 29 25 2630 3030 Note a. — Epochs supposed to be periodical in displays of ** lumi- nous meteors," are here inserted for the purpose of comparing the results with Table F. : — April 22-25. July 17-19. August 9-13. October . . . . 16-18. November . . 10-14. Ditto . . 27-29. December . . 8-12. (?) Note b. — Epochs when it would appear that the falls of aerolites may be periodical : — February . . 15-19. March .... 19-25. May 17-20. June 9-16. (?) Ditto 20-22 July 22-26. September. . 9-14. November . . 29-30. December . . 11-14. considered Geographically ^ Statistically j and Cosmically. 455 Table G. Jan. Feb. Mar. April. May. June. July. August. Sept. Oct. Nov. Dec. f I 1825 1824 1810 1796 1853 1848 1847 1839 1830 1827 1825 1824 1818 1815 1814 1796 1849 1843 1841 1820 1818 1813 1811 1807 1806 1805 1798 1796 1851 1844 1842 1838 1812 1812 1808 1804 1799 1795 1848 1846 ?1831 1827 1808 1806 1791 1843 1841 1838 1834 1828 1822 1821 1819 1818 1809 1805 1794 1847 1843 1842 1840 1837 1835 ? 1831 1820 1811 1810 1803 1790 1841 1835 1829 1823 1822 181b 1812 1810 ? 1800 1854 1852 1843 1833 1829 1826 1825 1822 1822 1814 1813 1808 1802 1849 1844 1838 1827 1824 1819 1815 1803 1791 1850 1846 1839 1835 1833 1822 1820 1814 1811 1805 1846 1836 1833 1813 1807 1803 1803 1798 1795 Period of 100 years. , .... -A __ 1717 1697 1683 1622 1785 1671 1647 1683 1654 16o6 1780 1750 1620 1715 1620 1751 1698 1680 1677 1752 1723 1668 1635 1766 1755 1753 1727 1725 1647 1635 1789 1766 1738 1650 1642 1828 1618 1775 1768 1753 1650 1787 1750 1740 1674 1773 1768 1639 1627 -1585 1496 1596 1583 1491 1540 1580 1561 1552 1520 1379 1591 1581 1511 1492 ' 1328 1249 1304 856 Catalogue. — No. I. Stones and Irons. Year. Month and day. Locality. Spec, grav. Iron or stone. Remarks. B.C. 1478 1200 644 570 or 520 343 or654 466 204 211 192 176 Crete. ... Stone. ?do. do. do. do. do. do. do. do. ?do. do. p A shower of stones. Very large stone. A shower. Two falls. Time of Pliny. Orchomenos. China. Crete. Rome Italy. Egospotamos, Pergamus, Thrace. Ancona Italy. China. ...J China. Crustumerian Territory Italy. Vocontii Territory Gaul. 456 Mr. R. P. Greg on Meteorolites or Aerolites, *^ Catalogue. — No. I. [continued). Year. Month and day. Locality. Spec grav, Iron or stone Remarks. I.e. 89 138 to G 46 .D. 2to333 452 About 570 616 823 856 or 889 892 or 897 921 905 951 998 1021 1057 1112 1198 1135 or 1136 1164 > 1249 1280 About 1300 1304 1305 1328 1368 1379 1421 1438 1474 1480 1491 1492 1496 1510 1511 1516 1520 About 1545 1545 1540 China, China, Acilla Africa, Winter (Dec.) China. Thrace EmessaandMountLebanon, Syria. Bender Arabia China. Saxony Egypt- , Japan. Ahmendabad India. Narni , July or Aug Italy. China. Augsburg Bavaria. Magdeburg Prussia. Africa July 26 Oct. 1 Jan. 9 May 26 Mar. 22 Nov. 7 Jan. 28 Sept. May' Apr. 28 Hoanglie China. Aquileia Trieste. Near Paris France Oldisleben, Thuringia. . . Germany. Misnia Saxony. Wiirzburg Franconia Welixos, Ussing Russia. Quedlinbourg Saxony. Alexandria Egypt. Arragon Spain. Friedland, Saale Saxony. Vandals S. Austria. .. In Mortahiah and Dakhalia. Oldenburg Germany. Minden Hanover. Island of Java. Burgos Spain. Viterbo Italy. S. Saxony or Bohemia. Crema Italy. Ensisheim France. Cesena, Romagna Italy. Padua Italy. Crema North Italy. China. Arragon Spain. Neuhof Saxony. Piedmont Italy. Limousin France. 3 50 Stone, do. do. do. do. do. do. do. do. do. ?do. do. do. do. do. do. do. do. ?do. do. do. do. do. do. do. do. do. P p do. Iron. Stone. do. do. do. do. do. do. do. do. do. do. do. Iron. Stone. do. 7 distinct falls. Several stones. 5 distinct falls. 3 large stones. 6th century (?). A shower. Several. 5 stones. A very large one. One. Two. Several. One 12 in. in diam. A shower. 13th century. 13th or I4th cen- A shower, [tury One. i>) Several large ones. One. Many. ? Two large ones. One. 270 lbs. weight [one. (Doubtful). Large number. 6 fragments. considered Geographically, Statistically, and Cosmically. 457 Catalogue. — No. I. {continued). Year. 1552 1559 1561 1580 1581 1583 1585 1591 1596 1618 1620 1622 1627 1628 1634 1635 1635 1636 1639 1642 I Month and day. Locality. Spec, grav. May 19 May 17 May 2 7 July 26 Mar. 2 Jan. June 9 Mar. 1 August Apr. 17 Jan. 10 Nov.27 Aug, Oct. 27 Jun.21 July Mar. Nov.29 Aug 1647 1647 1650 1650 1654 1668 1671 1673 1674 1676 1677 1680 1683 1683 1692 1697 1698 1700 1715 1717 1723 1725 1727 1738 1740 1740- 1741 1750 1751 1752 1753 1753 1755 1766 Feb. 18 August Aug. 6 Sep. 4 ? Mar. 30 Jun. 20 Feb. 27 Oct. 6 May 28 May 18 Jan. 12 Mar. Jan. 13 May 19 Autum. Apr. 11 Jan. Jun. 22 July 3 July 22 Aug. 18 Oct. 25 Winter Thuriugia Saxony. Miscoz Transylvania. Eilenborg, Torgau Prussia, Gottingen (?) Germany Thuringia Germany Piedmont Italy. Castro villari or Rosas? Italy. Kumersdorf? Germany. Crevalcore Piedmont. Murakoz Styria. Jalindher Persia. Devon England Provence France. Berkshire England. Charollois France. Vago near Verona Italy. Calce, Vicenza Italy. Sagau, Silesia Prussia. Mt. Vaison, Maritime Alps, France. Suffolk CO., between Woodbridge and Aldboro' England. Zwickau Saxony. Stolzenau, Westphalia, Germany. Dordrecht Holland. Milan , Italy. Funen Island Denmark. Verona Italy. Swabia Austria. Dietting Bavaria. Glarus canton Switzerland. Orkneys Scotland. Ermendorf. Saxony. Near London England Castrovillari, Calabria Italy. Piedmont Italy. Temesvar Hungary. Near Sienna Italy. Berne Switzerland. Jamaica.. West Indies. Garz, Pomerania Prussia. Larissa Macedonia, Reichstadt Bohemia Mixburg, Northamptonsh., Engl Lilaschitz Bohemia Carpentras France Rasgrad ,... Hungary Greenland Oct. 12 May 26 June 5 July Sept July July Niort, Normandy France. Agram Croatia. Freisengen Bavaria. Tabor Bohemia. Liponas France. Terra Nuova S. Italy. Albereto near Milan S. Italy. Iron or stone. ?Stone. do. do. do. do. do. do. do. do. do. Iron. Stone, do. do. do. do. do. do. do. do. do. do. do. do. do. do. do. do. do. do. do. do. do. do. do. do. do. do. do. do. do. do. do. do. do. do. Remarks. 7-80 3'65 3-66 Several. One. Several. One. 30 lbs. ; one stone, 3 of about 100 lbs. 7 lbs. [each. 59 lbs. Two stones. [S. A large stone, N. to 11 oz. (Doubtful.) One large one. 38 lbs. One. 4 lbs. One stone. A shower. Large ones. A shower. Fell into a boat. Several. Several. Several. A shower. 20 lbs. Several. Several. A large stone. do. Iron. Stone do. do. do. do. A large stone. 71+161bs.W.toE. Several (or 1722). Several stones. Two = 31 lbs. 7 oz. One. Phil. Mag. S. 4. Vol. 8. No. 54. Dec. 1854. 3H 458 Mr. B. P. Greg on Meteorolites or Aerolites, Catalogue. — No. I. (continued). Yea r. Month and day. Locality. Spec, grav. Iron or stone. Remarks. 1766 1768 1768 1773 1775 1775 or 1776 1776 or 1777 1779 1780 1782 1785 1787 1789 1790 1791 1791 1794 1795 1795 1796 1796 1796 1798 1798 1799 ?1802 1803 1803 1803 1803 1804 1805 1805 1805 1806 1806 1807 1807 1808 1808 1808 1808 1809 1809 1810 1810 1810 1811 1811 1811 1812 Aug. 15 Sep. 13 Nov.20 Nov.17 Sep. 19 Apr. 1 Feb. 19 Oct. 1 Aug.20 Julv 24 Oct. 20 May 17 Juneie Dec. 13 Apr. 13 Jan. 4 Feb. 19 Mar. 8 Mar. 12 Dec. 13 Apr. Sept. Oct. July 4 Dec. 13 Dec. 13 Apr. 5 Mar.25 June Nov. Mar. 15 Mavl7 Mar.l3 Dec. 14 Novellara, Modena S.Italy Luc^ France. Manerkirchen Bavaria. Sigena, Arragon Spain Rodach, Coburg Germany Obruteza in Volhynia Russia. Fabriano, Ancona Italy Pettiswood, West Meath, Ireland Beeston England. Turin Italy, Eichstadt Bavaria Khartof, Ukraine Russia. , France. Barbotan France. Menabilly, Cornwall... England. Tuscany Italy. Sienna Italy Wold Cottage, Yorksh., England, 3-50 3-45 3-63 Apr. 19 May 22 Sept Jnne20 Jan. July August Nov.23 Mar.l2 July Apr. 12 Ceylon India. Belaja, Zerkwa Russia. Friexo Portugal. Lusatia Saxony. Salis France, Benares India, Baton Rouge, Mississippi... U.S. Scotland, Apt, Provence France East Norton, Leicestersh.... Engl, L'Aigle France, Massing Bavaria Possil, Glasgow Scotland. Irkutsk Siberia Constantinople Turkey. Asco Corsica. Alais France. Glastonbury, Somerset.. .England. Timochin, Smolensk Russia. Weston, Connecticut... U. States. Moradabad India. Parma Italy. Stanneru Moravia. Lissa Bohemia. Kikina, Smolensk Russia. Lat. 30® 58' N., long. 70° 25' W. Caswell, N. Carolina U.S. Futty-Ghur India. Tipperary Ireland. Panganoor India. Poltawa Russia. Berlanguillas Spain. Toulouse France. 3-65 3*62 3-40 3-85 3-55 3-45 3-36 3-48 3-45 3-26 3-53 317 3-66 1-70 3'64 3-50 3'40 315 3-52 3-49 3-49 3-70 Stone, do. do. do. do. do. do. do. do. do. do. do. do. do. do. do. do. do. do. do. do. do. do. do. do. do. do. do. do. do. do. do. do. do. do. do. do. do. do, do. do. do. do. do. do. .>do. do. Iron(?) Stone. do. do. Doubtful. 7i lbs. Two ; one of 38 lbs. 9 lbs. 6oz. One fell. A shower. 15 inches diameter. Several of 10 and [20 lbs. 12 small ones. 56 lbs. 10 lbs. Or Mar. 8. W.toE. A shower. Belfast Chron. of Several, [the War. 7 lbs. 3000 stones fell. 3i lbs. Contains little iron. S.E. to N.W. y^o, of 7+2ilbs. Contains no iron. [iron. Carbonaceous ; no One, 2i lbs. 160 lbs. 300 lbs.; in frag- [ments. [iron. 250 stones fell ; no 4 or 5 small ones. [board. 6 oz. Fell on ship- 3 lbs. 71 lbs. [13 lbs. Two fell ; one of 3 fell. Several small ones. considered Geographically j Statistically, and Cosmically. 459 Catalogue. — No. I. (continued). Year. Month and day, 1812 1812 1813 1813 1813 1814 1814 1814 or 1812 1815 1815 1816 1818 1818 1818 1818 1819 1819 1820 1820 1820 1821 1822 1822 1822 1822 1823 1824 1824 1824 1825 1825 1825 1825 1826 1827 1827 1827 1828 1829 1829 1830 1831 1833 1833 1833 1834 1834 1835 Apr. 15 Aug. 5 Mar. 14 Sep. 10 Dec. 13 Feb. 3 Sept. 5 Feb. 18 Oct. 3 Mar.30 Feb. 15 June Aug. 10 Jun. 13 Oct. 13 July 12 Mar.21 Nov.29 Jun. 15 Jun. 9 Sep. 10 Sep. 13 Nov.30 Aug Jan. 15 Oct. 14 Feb. 18 Jan. 16 Feb. 10 Sep. 14 Locality. Spec, grav. Erxleben Saxony. Chantonnay France. Cutro, Calabria. Italy. Limerick Ireland. Lontalex, Wiberg Finland. Bacbmut, Ekatherinoslaw, Russia. Agen France. Saros North Hungary. Loodianah India. Chassigny France. Near Nagy Banya Hungary Gov. of Volhynia Russia. Limoges France Seres Macedonia. Slobodka, Smolensk Russia. Jonzac France. Politz, Gera S. Prussia, Lixna, Witepsk Russia, Vedenberg Hungary. Cosenza, Calabria Italy. Juvenas France Iron or stone. Sept. Feb. 27 Oct. 5 or 8 May 9 Angers France. Carlstadt Sweden. La Baffe, Vosges France Futtehpore, Doab India. Nobleboro', Maine U.S. Renazzo Italy. Zebrak Bohemia. Irkutsk Siberia. Oriang, Malwate India. Nanjemoy, Maryland U.S. Owhyhee Sandwich Isles. Ekatherinosloff. Russia. Waterville, Maine U.S Mhow, Ghazeepore India. Bialistock Russia Jun. Sept, Aug. 15 Feb. 15 July 18 Nov.25 Sept. Dec. 28 Jun. 12 ?Nov29 July 30 Nashville, Summer CO., Tennessee, U.S. Richmond, Virginia U.S. Forsythe, Georgia U.S Deal, New Jersey U.S. Launton, Oxford England. Poitiers, Vouille France Blansko Moravia. Wessely Moravia. Okaninak, Volhynia Russia Charwallas India. Raffaten, borders of Hungary and Wallachia. Dickson co., Tennessee U.S. 3H2 3- 3-46 3-64 307 3-42 3-60 3-65 i'io sVo 3-47 3-08 3-39 3-70 310 3-66 3-35 309 3-25 3-60 3-66 3-39 3-77 3-5 317 3-55 3-34 3-50 3-55 3-38 Stone, do. do. do. do. do. do. do. do. do. do. do. ?do. do. do. do. do. do. do. do. do. do. do. do. do. do. do. do. do. do. do. do. do. do. do. do. do. do. do. do. do. do. do. do. do. do. do. Iron. Remarks. 4i lbs. [2 smaller. One of 69 lbs., and Dust and stones. 17+65+24 lbs. E. toW. Contains no iron. 40 lbs. Several ; one of 18 112 lbs. [lbs. 25 lbs. 8 lbs. ; contains no [iron One. ? 15 lbs. One. Contains no iron. 3 fell ; one 7 lbs. 14i lbs. ? A shower of stones. 3 fell; one 220 lbs. Contains only 1*5 iron. [Dir.S.E.toN.W. Several;! of 22 lbs. 16 lbs. (sp.gr. 2-0)? 3 small ones fell, 4 lbs. 5 lbs. 16 lbs. [30 lbs. Two fell ; together 86 lbs. Doubtful, [pounds. One, of several 4 lbs. ; contains no [iron. 3 fell, one 5 lbs., [another 11^ lbs. 4 lbs. 36 lbs. 2^ lbs. 40 lbs. (or May 13). 301b8.(27or29Dec.) 7 lbs. A shower. 9 lbs. ^i60 Mr. R. P. Greg on Meteorolites or Aerolites, Catalogue. — No. I. {continued). Year Month and day Locality. Spec, grav. Iron or stone. Remarks. Stone. 2 lbs. 1-35 do. Contains no iron. 372 do. do. Immense shower. 3*55 do. 19 lbs. do. 3 lbs. ... do. 4 lbs. 3-53 do. 3 fragments. 2-69 do. Many. N.W.toS.E. Carbonaceous. ... do. do. 50 lbs. N.E.toS.W. ... do. do. 11 lbs. 372 do. 2i lbs. 354 do. 75 lbs. ... do. (Or beginning of ... do. 11 lbs. [Sept.) 3-54 do. ... do. 7 lbs. 302 do. 13 lbs.; contains no do. [iron. ... do. do. do. 10 in. in diam. do. Doubtful. ... do. (Or May 8.) 9 do. [stones. ... do. 6 lbs. 2-32 do. 6oz. 3-58 do. 75 lbs. 771 Iron. Two fragments, 42 3-50 Stone. 4 lbs. [and 30 lbs. 3-45 do. Uoz. S.E.toN.W. ... do. A shower. 3-63 do. do. 18 lbs. do. 3 feet in diameter. do. 3-50 do. 18 lbs. S.W.toN.E. 376 do. A large stone. ... do. 6 lbs. 1835 1835 1836 1836 1837 1837 1838 1838 1838 1839 1839 1840 1840 1841 1841 1841 1841 1842 1842 1843 1843 1843 1843 1844 1844 1846 1846 1846 1846 1847 1847 1848 1848 1849 or 1850 1849 1849 1850 1851 1852 1853 1854 Aug. 4 Nov.13 Dec. 11 July 24 August Apr. 18 June 6 Oct. 13 Feb. 13 Nov.29 July 17 May 9 Mar.22 Jun. 12 August Nov. 5 Apr. 26 July 4 Mar.25 June 2 July 26 Sep. 16 Apr. 29 Oct. 2 May 10 Nov. 11 Dec.25 Summ. Feb. 25 July 14 Feb. 15 May 20 Oct. 31 Mar.l9 Nov.30 April Sep. 4 Feb. 10 Sep. 5 Cirencester England. Simond, de I'Ain France. Macao China. Flatten See Hungary Gross-Divina Hungary. Esnaude, Charente France Akburpoor India. Chandakapore, Berar India. Cold Bokkewelde, Cape of Good Hope. Little Piney Point, Missouri, U.S. Naples Italy. Casalc... Piedmont. Kirghiz Steppes Tartary. Griinberg Silesia. Chateau Renard, Loiret... France. Iwan Hungary. La Vendee France. Milena, Croatia Austria. Logrono Spain. Bishopville, S. Carolina U.S. Utrecht Holland. Manegon, Khandeish India. Kleinwinden, Mulhausen, Germ. Killeter, co. Tyrone Ireland. St. Andrew's Cuba. Macerata, Monte Milone... Italy. Lowell, Massachussets U.S. Minderthal Germany. Richland, S. Carolina U.S. Iowa, Linn, co U.S. Braunau Silesia. Dharwar India. Castine, Maine U.S. Tunis N. Africa. Cabarras co., N. Carolina... U.S. Poonah India. Bissempore India. Guterlof Westphalia. Mezo-Madaras Transylvania. Girgenti ..Sicily. Fehrbellin,nr. Potsdam, Germany. Catalogue. — No. II. Iron Meteoric Masses. Year found. Locality. Spec, grav. Pounds weight. Remarks, peculiarities, &c. B.C. 1168 1168 52or56 Crete. ... > } [mass. ? A spongy or vesicular Mount Ida ....Crete. Lucania S. Italy. considered Geographically , Statistically, and Cosmically. 46 i Catalogue. — No. II. [continued). Year found. Locality. Spec, gray. Pounds weight. Remarks. A.D. 1368 1545 1618 1620 1712 1717 1751 1780 1783 1784 1784 1784 1792 1793 1805 1808 1810 1811 1811 1811 1810 1814 1816 1818 1819 1819 1820 1822 1827 1828 1828 1829 1823 or 1824 1832 1834 1834 1835 1835 1839 1839 1840 1841 1841 1842 Oldenburg Germany. Neuhof Saxony. Bohemia. Jalindher Persia. Krasnojarsk Siberia. Senegal W. Africa. Agram Croatia. Lahore India. (Tucuman), Otumpa Mexico. Rio de la Plate S. America- Ziquipilco, Toluca Mexico. Sierra Blanca Mexico. Zacatecas Mexico. Cape of Good Hope... S. Africa. Bitberg Prussia. Texas, Red River U.S. Brahin Russia. Panganoor India. Elbogen Bohemia. Durango Mexico. Rasgata, Santa Rosas, N. Granada. Lenarto Hungary White Mountains, Franconia, New Hampshire U.S. Lockport, New York U.S Burlington, Otsego, N. York, U.S. Baffin's Bay Greenland Guildford, N. Carolina U.S. Randolph co., N. Carolina... U.S, Atacama Bolivia Caille, Departm. du Var, France Bedford co., Pennsylvania... U.S, Bohumilitz Bohemia Kinsdale, between West Moun- tains and Connecticut U.S Walker CO., Alabama U.S Scriba, Oswego co., N. York, U.S. Claiborne co., Alabama U.S Dickson co., Tennessee U.S. Black Mountains, Buncombe co. N. Carolina U.S Asheville,Buncombeco.,N.C.,U.S. Putnam co., Georgia U.S. Cocke CO., Tennessee U.S. Petropawlawski Siberia Newberry,' RufFMountains,' South Carolina. U.S. Greeneco.,'Babb'sMill,Ten.,'U.S. 6-48 772 7 1,600 7-8071+16 7-60 7Q7 7-50 700 6-50 7-70 6-20 774 7-88 7-30 7-7^ 7-50 7-23 7m 7-64 6-91 7 7-2( e's 7-2( 7-90 7-69 7-26 7-76 710 30,000 4,000 2,000 3,460 3,000 200 ''i'90 35,000 1,700 194 20 36 150 28 2 300 1,100 "163 165 8 20 9 Iron; fell in 1368. Fell between 1540 & 1550. Fell 1618. ? Fell 1620, April 17. Cont. crystaUized olivine. Large quantity. Has cry- stalline structure. Two fragments ; shows Widmanstattian figures when polished. Fell 1780. Wid. figures, very perfect. Crystalline structure im- perfect. Large quantity. Shows Wid. figures, do. Does not show Wid. figs. Plenty ; do. do. Wid. figs. ; ? with olivine, do., very distinct. With crystalline olivine. Fell 1811; ?iron. Shows faint Wid. figures. Wid. figures, distinct. Vesicular and malleable. Wid. figs., very distinct. Wid. figs. ; cont. pyrites, do., extremely hard. Large mass. [texture very hard. Crystalline structure faint ; With crystallized olivine. Known 200 years ago. Wid (Doubtful mass.) [figs. With Schreibersite. Several pieces. Has no crystalline struc- Wid. figures. [ture Fell July 30. 30 70 2,000 70 Wid. figures. Crystallized in structure, with graphite & magnetite, 17 Found 31 feet in the soil. 117 Structure crystalline. 12+6 Two. No Wid. figures. 462 Mr. R. P. Greg on MeteoroKtes or Aerolites, Catalogue. — No. II. (continued). Year found. Locality. Spec, grav. Poundi weight. Remarks. 1843 1843 1843 1845 1845 1846 1846 1847 1847 1849 1850 1850 1853 1853 Un- known. 1847 Otsego CO., New York U.S. St. Augustine's Bay, Madagascar. Arva Hungary. Buncombe CO., Mommouey Creek, N. Carolina U.S. De Kalb co., Tennessee U.S. Jackson co., Tennessee U.S. Smithland, Tennessee U.S. Chester co., S. Carolina U.S. Seelasgen Silesia. Fort Singhur, Deccan India. Schwetz Prussia. Pittsberg, Pennsylvania U.S. Tazewell,Claiborneco.,Tenn.,U.S. Long Creek, Jefferson co., Ten- nessee U.S. Haywood co., N. Carolina... U.S. Lead Hills Scotland. Potosi S. America. Steinbach Saxony. Seneca River, Cayuga co., New York U.S. Lion River S. Africa. Oaxaca Mexico. Salt River, Kentucky U.S Murfreesboro', Tennessee... U.S. Charlotte co., Tennessee U.S. Grayson co., Tennessee U.S. Roanoak, Virginia U.S. Alasej Mountains Siberia. Tucson, Sonora New Mexico. Livingston co., Kentucky... U.S. Braunau Silesia. Near the Caspian Sea. 276grs, 71 7-32 7*70 4" 7-77 7- 7-30 7-43 7-42 7-34 813 7-71 218 31 43 60 3 ioz, foz, 9 170 Finely crystalline. Large quantities. Contains graphite and schreibersite. Vesicular, and with a cry stalline structure. No Wid. figures. do. Olivinoid and vesicular. Wid. figures, distinct. Has a crystalline structure Crystalline in structure. Finely crystalline ; very ? Atacama iron. [hard, With olivine. With Wid. figs. & pyrites. Shows Wid. figures. Doubtful if meteoric. Large mass. Large quantity. 42-1-30 Two fragments. Wid. figs. ; very small. Cont. pyrites Fell July 14, 1847. Contains iron, nickel, co- balt and copper. Catalogue.— No. III. Doubtful. Year. LocaUty. Remarlu. ? 648 1095 1673 1676 1676 1753 1756 1776 Daghistan (? Scythia). Constantinople Stone. do. do. } P P Stone. do. do. Fell B.C. April 4. March 21. Fell in the sea. January. ? August 5. France. , France. Copinsha ? Near Leghorn Italy. Eichstadt Germany. France. NovcUara Italy Contribution towards the History of Paraffine. Catalogue. — No. III. (continued). 463 Year. Locality. Remarks. 1783 1785 1799 1805 1806 1810 1809 1814 1813 1817 1817 1822 1824 1826 1826 or 1827 1827 or 1828 1801 ? 1637 1762 1814 1819 England, France. Baton Rouge, Mississippi... U.S. Dordrecht Holland. Basingstoke, Hants England. .....France. South Atlantic. Doab India. Malpas, Cheshire England. Paris France. Baltic. Kadonah, near Agra India. Sterlitamak, Orenberg... Russia. Castres France. Waterloo, Seneca co., N.Y., U.S. Alport, Derbyshire England. Isle aux Tonneliers... Mauritius. Pulrose Isle of Man. Concord, New Hampshire... U.S. Russia. Aifghanistan. Lucerne Switzerland. Canada Years 850, 1110, 1548, 1557, 1652, 1686, 1718, 1796, 1811, 1819 and 1844. Shower of St. August 18. p April 5. Stone. do. May 17. do. p ? Fell into the sea. June 19. ? November 5. Shower of St. In the summer. ? November 3. ? Fell in the sea. May 2. Stone. Aug. 7. Same as the fall at Futtehpore. Hailstones, enclosing cry- ? [stals of pyrites. Sept. Stone. Spec. grav. 2'30. do. Autumn. Stone. do. do. do. Several. Dates unknown. do. (See Comptes Rendus. Dust. ? [1836.) do. Explosions, with meteors. Falls of viscid matter, with luminous meteors. LVII. Contribution towards the History of Paraffine. By Baron Keichenbach *. NEARLY a quarter of a century has now elapsed since I ex- hibited the first specimen of paraffine to the German Asso- ciation of Naturalists at Hamburgh in 1830^ and described the mode of preparing this substance in Schweigger's Journal of Chemistry. With the exception of some analyses by Ettling, Lewy, and others^ very little has been communicated regarding this body since that period. The very valuable properties of paraffine, the power with which it resists the action of concen- trated acids and alkalies, and even of potassium at a boiling temperature, the brilliant whiteness of its flame, which deposits no soot, its beautiful translucency and its lubricating quality, * From the Journal fur praktische Chemie, by Otto Linne Erdmann and Gustav Werther, No. 17, October 1854. 464 Contribution towards the History of Paraffine. recommend this substance for various technical applications ; and I have myself called attention to this fact from its first discovery, without being able, however, to arrive at any satisfactory results in its industrial application. The difficulty which presented itself, was the small quantity which the dry distillation of wood furnishes of this substance. I subsequently showed that paraf- fine might be obtained from vegetable oils, from animal sub- stances, and likewise from pit-coal ; but from all these substances so minute a quantity was obtained that its production for manu- facturing purposes was neither remunerative nor inviting. Thus paraffine remained up to this period an interesting curiosity, un- known except in the collection of scientific chemists. I now hear that in England, which is essentially the country of useful applications, a manufactory of paraffine nipon an ex- tended scale has been carried on by Mr. Young since 1850. This talented chemist has succeeded in finding a method which yields comparatively large quantities of paraffine. Mr. Young obtains 13 pounds from a ton of cannel coal. This discovery renders the preparation of paraffine a lucrative branch of industry, especially since, in addition to the production of paraffine, a large quantity, about 30 gallons, of a lubricating oil is obtained which is saturated with paraffine, and which is said to surpass all other fatty substances as an antifrictional, and to have been already 80 generally adopted, that Young^s works now supply weekly as much as 8000 gallons to the market. The most evident proof of the advantages offered by paraffine, is the rivalry which has already ensued in its production, and is well illustrated by an action at law, which some of the later competitors of Mr. Young have brought against him with the view of upsetting his patents, by attempting to prove that the discovery was not new, and was in fact not capable of being patented. It is true that the dis- covery of paraffine is my own, and I have announced it. To Mr. Young, however, belongs the merit of a second discovery, the merit of having elaborated a method which furnishes a com- paratively lar^e quantity of this substance, and which is suffi- ciently remunerative to the manufacturer ; a result which 1 had vainly endeavoured to realize. I hope that Mr. Young will succeed in convincing the legal authorities of the priority of his practical discovery, which was not part of any purely scientific investigation, and which I cannot claim in any way. May he enjoy the fruits of his invention and of his industry, which he deserves, and to which no other person has a right ! [ 465 ] LVIII. On the Conductibility of Liquids for Electricity. By MM. Van Breda and Logeman. In a letter to Professor Faraday. Royal Institution, My dear Tyndall, Oct. 31, 1854. I SEND the enclosed letter from MM. Van !^^'eda and Loge- man to you as an Editor of the Philosophical Magazine. If you should judge it proper for insertion in that Journal, I shall be very happy to see it there, but will beg you to accom- pany it on my part with the observation that it is not so con- clusive in proving the negative (a thing very difficult to do) as to move me at present from the reserved condition of mind which I have recently expressed in respect of this matter. Ever yours truly, M. Faraday. To Professor Faraday. Sir, The experiments on electro-dynamic induction in liquids which you have published in a letter to M. de la Rive, have excited our lively interest, not only because the phsenomenon appeared to us to be of importance in itself, but especially because it seemed likely to throw some light upon the manner in which electricity is propagated in liquids. Do liquids conduct exclusively by electrolysis, or do they also possess a proper conductibility, similar to that of metals ? An experiment that we have made may perhaps assist in the solution of this question. It is well known that the conductibility of liquids increases with their temperature, whilst the opposite effect takes place with the metals, a fact which is easily explained if we suppose that liquids^in general oppose less resistance to decomposition in proportion as their temperature is raised. If this explanation be the true one, the next thing to be ascertained is, whether a liquid will also exhibit this increase of conductibility for a current so weak as to traverse it without producing any apparent chemical decomposition. If this were the case, it would appear probable that the decomposition nevertheless took place, and that it was by its intervention that the current passed through the liquid. We have endeavoured to solve this question by the following experiment. We passed the current of a small DanielFs element through a column of distilled water 24 centi- metres in length, contained in a glass tube of about 15 milli- metres in diameter ; the electrodes were of platinum wire. One of these electrodes was connected with the zinc pole of the battery, the other with one end of the helix of a galvanometer of which the 466 MM. Van Breda and Logeman on the wire made 1800 coils, the other end of which communicated with the copper pole. The tube was immersed in a water-bath, the temperature of which could be raised by means of a spirit-lamp. When the water was at 59° F., the needle of the galvanometer deviated 4°. When the lamp was lighted, this deviation was seen to increase regularly. At a temperature of 152°*6 F., the deviation was "7°, and at 190°-4 F. it was 11°. The increase of the conductibility of the liquid by heat was therefore proved, even when traversed by an excessively feeble current. Had any chemical decomposition of the water taken place during this experiment ? Its direct result led to the belief that such was the case, but we were also fortified in this opinion by the follow- ing circumstances. When the liquid was cooled, the communi- cations remaining untouched, the needle of the galvanometer no longer showed any appreciable deviation. When the direction of the current in the column of water was reversed, the needle immediately deviated 8° and returned insensibly, but in a short time to 4°, at which point it remained stationary. It was con- sequently an effect of the polarization of the electrodes that we observed in this case, a polarization which opposed the current at the first moment of its passing, without, however, being able to annul it, but which annulled it completely when it had become stronger by the passage of the stronger current through the heated liquid. But is this polarization the peculiar effect, and consequently the irrefragable proof, of chemical action ? There are many experiments which render this opinion, if not absolutely certain, at least exceedingly probable. We may mention in particular those of Schonbein, who found that the effect continues when the electrodes which have served to introduce a current into a liquid are immersed in another liquid through which no current has been passed, and also that effects exactly similar to those of the plates polarized by the current may be obtained by putting one of them only in contact with a gas (such as hydrogen or chlorine) for a very short time, and afterwards immersing them in acidulated water*. Some physicists, however, still maintain the opposite opinion. They explain polarization by an accumu- lation of electricity of different natures, either in the electrodes themselves, or in the adjacent portions of the liquid ; these two electricities in recombining by a conductor uniting the two electrodes, after the connexion between these and the electro- motor has been broken, would give rise to the current in the opposite direction to that of the latter, which is always observed in such cases. It appeared to us that your beautiful experiment on electro- * PoggendorflPs Annalen, vol. jdvi. p. 109, and vol. xlvii. p. 101. Conductibility of Liquids for Electricity, 467 dynamic induction in liquids might furnish a means of submitting this opinion to an experimental test, by trying whether the electrodes, employed in that experiment to conduct the instan- taneous current of the fluid helix to the galvanometer, are or are not polarized by this current. To obtain a decisive effect it was necessary to reproduce the phsenomenon with more intensity than when, as in your experiments, the question was merely to prove the phaenomenon itself. For this purpose we made use of a tube of vulcanized Indian rubber, of about 1 centimetre in internal diameter and 13 metres in length. We twisted it round the two branches of the large electro-magnet intended for experi- ments in diamagnetism, which, if we are not mistaken, has the same form and the same dimensions as your own ; it is covered by a coil of copper wire 3 millimetres in diameter and 180 metres long. The tube was entirely filled with a mixture of 6 parts by volume of water and 1 part of sulphuric acid. It was terminated at both ends by glass tubes of about 4 centimetres in length ; into each of these passed a platinum wire of 1 millimetre in diameter, the portion of which immersed in the liquid was about 2"5 centimetres in length. All being thus arranged, the ends of the two platinum wires were connected with the galvanometer of 1800 coils which was placed at a distance of 10 metres. We had ascertained previously that at this distance the magnet did not exercise any sensible action upon the needles. The moment the two ends of the copper- wire coil of the electro-magnet were put in connexion with the poles of a Grove's battery of 60 large elements, arranged in a double series of 30, the needle of the galvanometer deviated suddenly about 40°, and returned, after oscillations which occupied between 1 and 2 minutes, to 0°. When the circuit of the pile was interrupted, the galvanometer deviated again about the same number of degrees, but in the opposite direction, returning again to 0° in the same manner. The needle returning in both cases to 0°, one would be tempted, at first sight, to think that there was no polarization of the elec- trodes. But the strong impulsion communicated to the very astatic system of the galvanometer by the induced current, causing the needles to oscillate during a considerable period as we have just stated, the circuit remaining always complete, it appeared possible that the polarization, if it existed, had already exhausted itself before the needles had arrived at a state of repose. To get rid of this difficulty we put the two electrodes in direct communication with each other by means of a copper wire of only 10 centimetres in length, although they still remained in connexion with the galvanometer. The induced current pro- duced when the circuit of the pile was established, then passed by this wire rather than by the infinitely longer wire of the 468 On the Conductibility of Liquids for Electricity. galvanometer, and the needles remained at rest. But when this wire was removed after the establishment of the communication with the pile, we saio the galvanometer deviate instantly in an opposite direction to the deviation produced by the induced current of the preceding experiment, and rest, after a few oscillations, at 10°. By replacing the wire, then interrupting the circuit and again removing the wire, we saw the galvanometer deviate in the contrary direction, and rest, in the same manner, at about 10° on the other side of the divided arc. In both cases the deviation diminished regularly by little and little until it became 0° ; we did not exactly measui*e the time which this occupied, but it appeared to us to be about 30 or 40 seconds. These experiments were frequently repeated, and always with the same result. We need not say that we always took the precautions pointed out by you, to prevent the eiffect of an induc- tion in one of the metallic conductors. Polarization therefore takes place in the electrodes which serve, not only to convey a current into a liquid, but to carry out the current induced in the liquid itself. It appears to us that this fact directly contradicts the theory which attributes polarization to an accumulation of the two electricities upon or around the electrodes ; for in the present case not only would such an accu- mulation be infinitely less probable than in ordinary cases of polarization, but if it existed, it would necessarily give rise to a current not in a direction opposed to that of the principal current, but in the same direction. May we therefore regard all polarization as an effect of elec- trolytic decomposition, and consequently as an irrefragable proof of the existence of this decomposition ? If this be true, we shall be led to regard the opinion of those who admit the possibility of the transmission of a current, or of a portion of a current through a decomposable fluid without the occurrence of any decomposition, as resting upon very slight grounds. Whenever we have passed a current, however weak, through such a liquid, we have always observed an undoubted polarization of the elec- trodes. We shall take the liberty to describe one other experiment, which is still more convincing in this respect than that described at the commencement of this communication. We immersed two plates of platinum, 6 centimetres in length and 5 centimetres in breadth, at a distance of about 1 centimetre from each other, in distilled water. One of these plates communicated with the ground by a metal wire; they had previously been carefully cleaned by heating to redness, and consequently, when put in communication with the galvanometer, did not produce any sensible deviation. But as soon as a single spark from a common Prof. Dove on the Changes of Wind in a Cyclone. 469 electrical machine had been thrown upon the plate which did not communicate directly with the ground, and the communica- tion with the galvanometer had been established, the needle deviated from 3° to 4° in one direction, and the same distance in the opposite direction when the current of the spark was passed through the water the other way. This deviation could be brought to 15° or more by throwing several sparks instead of one upon one of the plates, or by connecting the plate for a very short time with the conductor of the machine during the movement of its plate. We fear that the importance of this letter will not be propor- tional to its length ; if, however, its contents should seem to you to be worthy of attention, we shall be happy to see it pub- lished in any manner you think proper. We remain, Sir, &c., J. G. S. Van Breda. Haarlem, September 1854. W. M. LoGEMAN. LIX. On the Changes of Wind in a Cyclone. In a Letter from Professor Dove of Berlin to Captain Washington, R.N.j F.R.S. 13 Ashley Place, Westminster, Dear Sir, September 12, 1854. IN our conversation yesterday on the subject of cyclones, I made the remark that too wide an extension was given to the theory respecting them when all changes of wind in a par- ticular direction were referred to them, whereas an essential distinction ought to be made between those changes of wind which are produced by the advance of a cyclone over the surface of the earth, and those which are the necessary consequences of the phsenomenon which I have called the law of deflection. Per- mit me to express my meaning in rather more detail. When a cyclone is moving over the earth^s surface in any direction, the place of observation may be in either of two cases. The middle or centre of the cyclone may, in passing, be either over it or on one side of it. In the first case, the place is in a diameter ; and in the second case, it is in a chord of the rotatory storm or cyclone. In both cases the observer sees the wind- vane as a tangent of the cyclone ; only with the difference, that if it is the centre of the storm which passes over him, two winds from directly opposite directions succeeding each other are separated by an interval of calm ; whereas if, instead of being on the diameter, he is on a chord at some distance from the centre, he experiences no such interval of lull, but finds in its place a more or less prolonged time during which the wind veers round. The direction in which it does so is always opposite on 470 Prof. Dove on the Changes of Wind in a Cyclone, the two opposite sides of the middle line. In a cyclone advan- cing towards the north (in the northern hemisphere), the change of wind on its eastern side always takes place from E. through S. to W., or " with the sun -/' on the western side of the storm, from E. through N. to W., or "against the sun/' Now if all changes of wind were more or less direct results of advancing rotatory storms or cyclones, there would necessarily be found in the northern hemisphere as many cases of change of wind of one of these ways as in the other ; for although the cyclones prevail and pass over certain parts of the ocean more especially, yet the preponderance of one direction of the change of wind in one place would be compensated by the opposite preponderance in another, and on the whole there would not remain any prepon- derance. I have, however, shown by special investigations, that there is such a preponderance, and that it is the case in both hemi- spheres; that in the non-tropical zone of the northern hemi- sphere the wind in the majority of cases changes from S. through W. to N. and E., and in the southern hemisphere from S. through E. to N. and W. ; this demonstrated preponderance must there- fore have some other cause, and that cause must be one of general conditions, because it produces opposite effects in oppo- site hemispheres. The space between two meridians is an equilateral triangle, having its base on the Equator and its sum- mit at the Pole. It is evident that the whole mass of air which ascends over the base line in the meridian of calms cannot flow in the rapidly narrowing space up to the point at the summit of the triangle, but that it must ascend again before reaching that point. This descent takes place at the outer limit of the "trade winds,'' but at variable points ; so that while at certain places portions of air are flowing from the upper regions of the tropical atmosphere into the temperate zone, at other places at the same time the contrary may be taking place, causing an extension backwards of the " trade wind," and making it appear to begin earlier than would correspond to its mean outer limit. The currents of air which in the tropics flow over each other, in the temperate zones flow alongside each other and in variable beds. Our phsenomena of weather, therefore, at each particular place of observation depend on two currents, which alternate as each in turn prevails over and presses aside the other, or drives it off the field. When one of these currents prevails in full in- tensity, we have the extremes of climate ; where they strive for the mastery, we have its variability. Let us now suppose that in London a northerly current of air begins, that is to say, that the mass of air between London and a point to the north of the 8hetlands is set in motion ; an observer in London will remark Prof. Dove on the Changes of Wind in a Cyclone. 471 first a north wind, but the further north the place from whence this north wind comes the more will it change into a N.E. wind, as the velocity of rotation of the earth is less in the higher than in the lower latitudes ; therefore the wind that left Edinburgh as a N. wind reaches London, we will say, as a N.N.E. wind; if it left the latitude of Shetland as a N. wind, it reaches London as a N.E. wind; and if it left the polar circle as a N. wind, it reaches London as an E.N.E. wind. It is plain that in these cases we have only to do with one unaltered current, which, the further it proceeds, the more its original direction appears de- flected. Winds between N. and E. are therefore, properly speak- ing, N. winds; in other words, a N.E. wind is a N. wind, which comes from further N. than does the wind which arrives at the place itself as a N. wind; and the N.E. is therefore the heaviest, coldest and driest. If, then, we suppose that after a northerly current gradually changing into an east wind, a southerly current sets in, we see the wind change from E. through S.E. to S., the barometer fall, and the air become warmer and moister. The longer this south current lasts, the greater, therefore, is the distance from which the wind comes, and the more the S. wind will change through S.W. to W. ; for a S.W . wind is no other than a S. wind which has its origin further to the S. than a wind which arrives as a south wind. The winds between S. and W. are therefore south winds. If the cause which produced them continues, the south wind, which has become a west one, will keep back the direct air from the south ; and there will be often repeated unsteady changes between S. and W. with thick weather. If at last the polar current presses forward again, we see the barometer rise with the wind passing through N.W. to north, while the tempe- rature sinks and the clouds break. This regular course prevails in the northern hemisphere, and the opposite in the southern one. We may therefore say that, on the average, the wind, from these causes, turns in both hemi- spheres with the sun, and that therefore the seaman^s adage truly says — " When the wind veers against the sun. Trust it not, for back it will run." It follows, then, in regard to tempestuous movements of the atmosphere, that storms are either " gales or hurrioanes.^^ Both cause the wind- vane to turn round, but in the " gales '' it turns only with the sun ; in the rotatory storms or hurricanes it turns with the sun on one side of the storm, and against the sun on the opposite side. If a ship in the northern hemisphere is on the east side of a hurricane or cyclone advancing towards the north, the navigator cannot tell simply from the way in which the wind turns whether he is in a cyclone or in a gale ; but if he is on the 472 Prof. Sedgwick on the May Hill Sandstone^ west side he can tell, as he may generally infer, when a change of wind takes place against the sun and the wind blows strong, that the ship is in a cyclone. It is not difficult to give for both hemi- spheres independent rules for Judging on which side of the cyclone a ship is. I have given such rules in detail in special memoirs, but I should make this letter too long if I were to enter on them, and they are also somewhat foreign to its imme- diate purpose. Believe me, dear Sir, Sincerely yours, H. W. Dove. To Captain Washington, R.N., F.R.S., Admiralty, LX. On the May Hill Sandstone, and the Palaozoic System of England. By the Rev. Prof. Adam Sedgwick, F.R.S., F.G.S, To the Editors of the Philosophical Magazine and Journal. Gentlemen, HEREWITH I send what might, without impropriety, be called a continuation of the paper you have done me the favour to publish in the October and November Numbers of your Journal. The task undertaken by Professor M'Coy and myself in 1853 was left incomplete; but we have this autumn taken it up where it had been abandoned, and completed our examination of various critical sections, at the junction of the Cambrian and Silurian rocks, which we had not been able to visit during the preceding year. Is there in South Wales any " Middle Silurian '* group in which the characteristic Silurian and Cambrian types are so mixed and confounded as to be inseparable ? In North Wales and Siluria we found no such group. Wherever it had been erroneously laid down as one group we found it separable into two distinct stages — the upper of which contained a cha- racteristic Silurian group of fossils — and the lower, an equally characteristic Cambrian group. But I was informed that near Builth, in some of the eastern hills of Radnorshire, and in several sections near Llandovery, the Government Surveyors had found the veiy mixture of older and newer types which we had sought for in vain during our short excursions in 1852 and 1853. To the places thus indicated (taking the Presteign sections on our way) we first bent our steps, and the results of our examination will be given in the early part of this communication. They are in perfect agreement with what we had before seen in North Wales and Siluria. There is, we believe, no " Middle Silurian group '' like that laid down in the Government Survey — there is no con- fusion of organic types — the May Hill group (though in a dege- nerate and disconnected form) does exist, in the county here and the Palaozoic System of England. 473 alluded to, as a distinct formation — separable from the so-called " Lower Silurian " rocks, and constituting a physical and palse- ontological base to the true " Silurian System :" and lastly, that '' System/^ when reduced to its true base, is, we believe, either in actual position, or in palseontological succession, discordant to the Cambrian rocks on which it rests. If these conclusions be true, there is an end of any legitimate dispute on nomenclature; for we have no example in English geology of two great formations which are, as a general rule, unconformable in their position, yet at the same time belong to a common series, and pass under a common name. Having thus completed our observations on the groups con- nected with the May Hill sandstone, we next examined the sec- tions through the Llandeilo group in the valley of the Towy. The results of this examination, and their bearing on the questions of palaeozoic classification and nomenclature, will form the con- cluding part of the paper, which I now respectfully offer for insertion in the Philosophical Magazine and Journal. I have the honour to be. Gentlemen, Your faithful Servant, | A. Sedgwick. Cambridge, October 31, 1854. I have thought it best to retain the title adopted in my former communication, published in the October and November Num- bers of this Journal. When the substance of this paper was read before the British Association (during September last) at Liverpool, the title was somewhat modified, for the express pur- pose of bringing the communication into a direct comparison with one of the preceding year, read before the British Asso- ciation assembled at Hull, of which an abstract has been pub- lished in their volume for 1853. The above letter to the Editors is perhaps h sufficient intro- duction to the new facts about to be described ; but for the sake of any reader who is not familiar with the questions in debate, I think it best to give, in the first place, a short summary of the facts brought forward in my previous paper, and of the conclu- sions drawn from them. My special object was to prove — (1st) that the May Hill sandstone is the true and only base of the Silurian series (or " system ") ; (2ndly) that the Silurian series, when thus defined, was, as a general rule, either obviously unconformable to the Cambrian series, or overlapped its beds in such a manner as absolutely to conceal the true sequence of the deposits, as we pass from one series to the other. In confirma- tion of these conclusions (and in addition to the sections brought Phil. Mag. S. 4. Vol. 8. No. 54. Dec. 1854. 2 I 474 Prof. Sedgwick on the May Hill Sandstone, before the Geological Society of London, Nov. 3, 1852) the fol- lowing sections were discussed : — The first section was from the Cambrian and Silurian rocks on the line of the Holyhead road, west of the Berwyns, and was as follows {supra, fig. 1 . p. 306) : — 5. Carboniferous series. 4. Devonian series, vei*y degenerate, and unconformable to the Denbigh flag. 3. Denbigh flag, &c. (Wenlock and Ludlow). 2. May Hill sandstone, of great thickness, and ending in a conglomerate. Unconformable to the Cambrian rocks. 1. Cambrian rocks of the Bala group. The second section was taken from the sequence north and south of the valley of the Dee, near Llangollen (supra, fig. 3. p. 30G). 5. Carboniferous rocks. 4. Denbigh flag. (No. 3 of fig. 3. p. 306.) 3. Upper Bala group, with two bands of limestone. 2. Alternations of slate and porphyry, trap-shale (schaalstein) , &c., with many Cambrian fossils. 1. Beds of dark shale, grits, flags, &c., in which fossils gra- dually disappear. Here there is no apparent unconformity, and the stage No. 3 might be almost said to pass into the stage No. 4; but the absence of the May Hill sandstone and conglomerate of the pre- vious section proves that No. 4 has been brought over No. 3 by a great overlap, and that the section is therefore imperfect. The third section was from Mathyrafal near Meifod {supra, p. 306. fig. 2). 4. Wenlock shale, &c. (No. 3 of fig. 2. p. 306.) 3. Beds of shale with many fossils (a good Cambrian stage). ^ 2. Beds of limestone, coarse calcareous conglomerate, &c. 1. Fossiliferous series of the Meifod Hills, &c. Here Nos. 1, 2 and 3 represent a peculiar development of the Upper Bala groups,. and are collectively of great thickness. Between Nos. 3 and 4 there is an obvious discordancy of posi- tion, and the May Hill series is wanting. It is probably over- lapped by, and buried under, the Wenlock shale ; and between Nos. 3 and 4 there was, so far as we saw, no interchange of cha- racteristic Cambrian and Silurian species *. The 4th, 5th and 6th sections from Norbury, the banks of the Onny and Shineton (where the Caradoc sandstone approaches * I may remark, as I have done in a j)revious paper, that all the beds below the May Hill sandstone are here called Cambrian, whatever may have been their supposed sectional place in the " Silurian System." and the Palaozoic System of England, ^^ 475 the banks of the Severn), are described in the Report of the Bri- tish Association (Transactions of the Sections, pp. 58 and 59. 1853). The general results derived from these sections are as follows {supra, p. 313. fig. 4) : — Fourth section, 7. Carboniferous series. 6. Devonian series. 5. Ludlow group, in three stages. r d. Wenlock limestone. 4. Wenlock group, in J c. Wenlock shale. four stages. | h. Lower Wenlock or Woolhope limestone. [ a. May Hill sandstone and Norbury limestone. 3. Caradoc sandstone of Horderley, &c. o ci, 1 p cor.' 1. (With. Aqnostuspisiformis, Olenus'i, Asaphus'^i 2. Shales, &c. of Shmetonj citheropsisAldensis,Siphomtretamicula,kc. I. Longraynd slates. In this section Nos. 2 and 3 are obviously unconformable to the old Longmynd slates. But the base of No. 4 is also (though not so obviously).sunconformable to No. 3. Hence this 4th sec- tion is not a continuous and complete, but is a broken and in- complete, section. It has not therefore been correctly assumed as a typical section ; nor can it, under the name Caradoc sand- stone, be made the foundation of a correct nomenclature *. So far I have been dealing, in the way of recapitulation, with the evidence of my preceding paper : and bearing on exactly the same questions, I now proceed to comment on some additional evidence which fell under the notice of Professor M^Coy and myself during our short recent tour made in a portion of South Wales. I. New Radnor and Presteign Sections. The accompanying sketch does not profess to exhibit an accu- racy of outline or exact proportion among the beds ; but it does, I Old Radnor. Fig* !• 1. Trap. 2'. Limestone dipping S.E. 2. Limestone dipping N .W. 3. May Hill sandstone. 3. Wenlock shale. 2". Reappearance of the limestone near Presteign. believe, exhibit the right order of the several groups, and there- fore may help to illustrate the following remarks. The lower parts of the valley extending from Presteign to Old Radnor are * (See fig. 4. p. 313. supra.) The black line, between Nos. 2 and 3 of this section, is drawn inaccurately. It ought to be parallel to the dividing lines of No. 3 ; for 2 and 3 are perfectly conformable and in an unbroken sequence. 212 476 Prof. Sedgwick on the May Hill Sandstone, probably filled with Wenlock shale, and near the latter place some large protruding bosses of igneous rock have elevated a fine mass of limestone, which dips in a north-westerly direction towards the valley. On the opposite side of the valley, and about two miles from Presteign, rises another and a similar mass of limestone, dipping also towards the valley, in a south-easterly direction and at a great angle. From beneath this second mass of limestone rise some thin beds of arenaceous and calcareous shale, succeeded by beds of yellowish sandstone of considerable thickness, which are thrown into a saddle, and form a pictu- resque ridge. Near the summit of the ridge the sandstone be- comes more coarse, and passes into a conglomerate very like that near the top of the well-known beds of May Hill. As we de- scend from the ridge towards Presteign the dip becomes reversed, and we again meet with the limestone, which (though broken and interrupted) seems to have wrapped round the protruding ridge, so as to dip, wherever it appears, from the sandstone. If the shale of the valley be Wenlock shale, the limestone must be in the place of the limestone of Woolhope ; and its fossils are unquestionably those of the Wenlock group. This conclusion seems now to be admitted, though at one time controverted. But what is the sandstone forming the ridge under the lime- stone ? The beds under the limestone, to a considerable depth, contain many fossils ; while the lower and coarser beds which break out near the summit of the ridge appear (like those near the top of May Hill) to be almost without traces of organic life. We collected during an evening walk the following species, which have been carefully determined by Professor M^Coy. Sandstone Beds. P^/raia (unnamed species, same Strophomena simulans (very as at May Hill). abundant). suhduplicata. Pentamerus oblongus. uniserialis. lens. Hemithyris hemisphcerica (abun- Orthis elegantula, dant). Spirifei'a a'ispa. diodonta. Modiolopsis ? didyma (as at Aymestry). Loxonema elegans ? Murchisonia ? Old Radnor and Presteign Limestone, Stenopora fibrosa (in very great Spirigerina reticularis. abundance). Hemithyris hidentata. Favosites alveolaris, Orthis testudinaria. So far as the above two lists extend, there is in them no spe- cies not well known either at May Hill, or the corresponding beds at Malvern, or in the undoubted Wenlock and Ludlow and the Palaeozoic System of England. 4i77 rocks of other localities. One of the species [H. didyma) had not been found lower than the Aymestry limestone ; and Spiri- fera crispa not lower than the Wenlock limestone. A few of the species, as is well known, have a much wider range. It follows from the above facts, and especially from the list of fossils, that the sandstone of Presteign is a true May Hill sand- stone : but it does not exhibit its relations to any inferior group ; neither does it exhibit any mixture of the characteristic Cam- brian with the characteristic Silurian types. II. Sections through the Llandeilo Flag and the Trappean Hills north of BuiltK (Fig. 2.) The rocks here noticed are too well known to need any elabo- rate discussion, as they are excellently described in the ' Silurian System.^ They break out immediately on the west side of the great terrace which runs into Mynydd Epynt, and is composed of the Upper Silurian rocks (Wenlock and Ludlow). These Builth rocks do not, however, dip under the " Upper Silurian " rocks, hvAfrom them towards the west — where they are overlaid by the Norbury limestone and the Wenlock shale. The shale extends several miles further west through a comparatively low country; and beyond it rise the higher hills of Radnorshire, which in the ' Silurian System ' are coloured as Cambrian ; and have always been considered by myself as a part of the Upper Cambrian series. But the author of the " System,^^ in adopting the nomenclature and colours of his map and sections, took it for granted that the Builth flags were geologically superior to these higher hills of Radnorshire ; and if the assumption be in- correct I am not in any way responsible for the mistake. For I never examined, or profecsed to have examined, the physical base of the so-called " Lower Silurian ^' rocks of South Wales ; nor did I ever see a single section of them between the summers of 1834 and 1846. As a matter of fact, the Builth rocks show no unequivocal relations either to the Cambrian or Silurian series ; being surrounded by a sea of Wenlock shale, which abuts against their lower beds on the eastern side and overlaps their upper beds on the western. The accompanying section may be shortly described as fol- lows : — Fig. 2, Section about two iniles N. of Builth, nearly E. and W. * 5 ^ ^ s 1. Trap. 4. Norbury limestone, &c. 2. Alternations of recomposed trap and shale. 5. Wenlock shale, &c. 3. Tark flagstone ending with a bed of recomposed trap. 478 Prof. Sedgwick on the May Hill Sandstone y 1. Immediately on the west side of the Silurian hills is the rugged trappean ridge which forms the base of the section. Some parts of it are highly cellular and amygdaloidal ; and if it were originally submarine, it must have been formed at least in a very shallow sea. 2. Next follows a remarkable series of beds, which towards the north become greatly expanded, and which on the sectional line are of considerable thickness. They are made up of a kind of trappean breccia, and of a fine granular recomposed trap, in some places forming a good building-stone. And these masses alternate with some beds (especially in the more northern parts of the range) to which the name ash might, I think, be fairly given — though I greatly limit the meaning of the word ashy as used in the Government Survey. In its place I formerly used the term plutonic silt, and afterwards the German term schaalstein ; and in the same sense I now generally use the words trap-shale ; defining thereby a vast series of slaty recomposed rocks derived chiefly from submarine eruptions, which therefore never existed as a time ash. Alternating with such masses are also found several bands of a true shale and flagstone, evidently forming a part of the regular aqueous flagstone of Builth. All the above beds occasionally contain fossils, among which I may mention the Asaphus tyr annus, of which a noble specimen was found in one of the plutonic grits. 3. Over the above, on the sectional line, is a considerable series of beds of dark shale and flagstone in which the igneous recom- posed rocks almost entirely disappear. It was from this series (about a quarter of a mile east of Pen Cerrig) that in 1846 I collected, along with my fellow-labourer John Ruthven, a fine suite of fossils, some species of which were new. They are in- cluded in the list of 24 species of Builth fossils given by Pro- fessor M'Coy (Camb. Palseozoic Fossils, p. 354). The locality is stated to be three miles north of Builth, but the true distance is not much above two miles. The series ends just below Pen Cerrig House, where it is over- laid (as seen near a pond and small water-course) by a well- defined bed of recomposed trappean rock, also containing traces of fossils. 4. Next follow calcareous and sandy beds, apparently in per- fect parallelism to the former. They are not more than 8 or 10 feet in thickness, and the more calcareous portions are good types of the Norbury limestone, and contain innumerable casts of the characteristic Pentamerus. 5. Over the preceding, and with the same strike and dip, are beds of shale and earthy calcareous flagstone, with irregular len- ticular concretions parallel to the bedding. These dip down the water-course and form the highest beds visible in the section. and the Paleozoic System of England. 479 The beds (in a quarry under Pen Cerrig House) which are immediately under the recomposed trappean bed are made up of an indurated Builth flag like that of the well-known Well field quarries, and contain Ogygia Buchi and Diplograpsus pristis in considerable abundance. The shales (No. 5) over the Pentamerus beds contain Grapto- lites Ludensisy an unnamed Denbigh flag species of Atrypaj and Orthoceras (?) ; and we found in them no other fossil. To exhibit the evidence in one point of view, I here subjoin a list of fossils we collected from the beds in the above section, in- cluding the flags of Wellfield quarries, which are a little further south, but on the line of No. 3, and not far from its top. 1st. From the Llanelwedd quarries of plutonic grit, &c. (the building-stone of Builth), near the turnpike road. Pyritonema fasciculus, the same as at Tre Cib near Llandeilo. This species has sometimes been mistaken for an Ichthyo- dorulite. Orthis avellana. Leptcena sericea. O. calligramma, Pterinea. All of which are Cambrian species, i. e. are not found, so far as we have seen, in any May Hill or Upper Silurian rocks. 2nd. From a quarry east of Pen Cerrig. (No. 3 of the figure.) Diplograpsus pristis. Ogygia Buchi (abundant). Ampyx nudus (very abundant) . Cytheropsis Aldensis. All the above are Cambrian ; and a much larger number of Cambrian species from the same quarry is given in the pub- lished list of the Cambridge Palaeozoic Fossils (p. 354). 3rd. From a quarry west of Wellfield House. Diplograpsus pristis. Ogygia Buchi (abundant). Ampyx nudus. Siphonotretra micula (in great Agnostus Maccoyi (Salter). abundance). All the above are exclusively Cambrian. In the Wellfield grounds are some beds very much resembling the shales of Shineton near Wenlock. Should the Olenus be found in them, it will appear among its former associates and among rocks of the same age with those of Hollybush and Shineton. 4th. From the quarry below Pen Cerrig House. Petraia (as at May Hill; an unnamed species). Ptylodictya lanceolata (Wenlock). Pentamerus oblongus (in very great abundance). Orthis pecten. No exclusively Cambrian species, and one exclu- .sively Wenlock, hitherto, r GrapioUtes Ludensis. 3. Upper shale, -s Atrypa (an unnamed Denbigh flag species). <;.*,..., ^ f. {. Orthoceras {^) (Wenlock shale). 2. Bands of Norbury limestone, &c. above the trap. 480 Prof. Sedgwick on the May Hill Sandstone, From the above statements the following conclusions seem naturally to follow : — 1st. The Pentamerus beds (or Norbury limestone, No. 4) must be arranged with the shales (No. 5. fig. 2), as their fossils belong to a group which is entirely distinct from that of the Builth flag. The case is exactly like that at Norbury and in the neighbour- hood of Wenlock, where the same beds were cut off from the Caradoc sandstone, and arranged by Professor M'Coy and myself as the base of the upper or true Silurian series. Here (just as in Bohemia) there is, after the intervention of a bed of trap, an immediate change in the fossil fauna — the upper being Silu- nan, while the lower is Cambrian : and a similar remark applies, we believe, to one of Professor Phillips's Malvern sections, which is based on the HoUybush shales. 2ndly. Spite of the almost mathematical parallelism in the bedding of the preceding groups, there can be little doubt but a great geological interval exists between the true Builth flags (No. 3) and the overlying beds (Nos. 4 and 5). The section is not perfect and continuous, and cannot (on that account) give us a guidance to a true nomenclature of the groups. The case is analogous to that already quoted from the section south of Llangollen {supra, fig. 3. p. 306). Ill, Conglomerates, slates and sandstones of Dol Fan, ^c. Under this title is included a large and ill-defined group of slates and sandstones, sometimes passing into a coarse conglo- merate. This group, commencing near the southern end of Radnor Forest, ranges through Dol Fan towards the south-west ; generally contorted and forming saddles with sides of high incli- nation ; the conglomerates not continuous, but breaking off" and reappearing ; first forming a part of the mountain barrier to the comparatively low country of Wenlock shale which runs to the SW. of Builth ; then thrown further back among the western moun- tains ; and at length forming a kind of high rugged plateau near the water-shed of the Cothi and the Towy. That this singular and ill-defined group has a high geological place among the un- dulating masses between Teifi and the Towy can admit of no doubt; and I think it certain (as I have done since 1832) that these undulating masses (as well as many others of a very diff"er- ent type, fm-ther west towards Cardigan Bay) are superior to the Bala limestone. Of what date then are the Dol Fan conglomerates and the associated beds of grit and slate ? The answer can only be sup- plied by the fossils. In my old collection, made in 1846, 1 have but one species from the neighbourhood of Dol Fan, viz. Euom- phalus tricinctus. During the year 1846 I made, however, another traverse and the Palaozoic System of England. * 4^1 through the conglomerates, which are finely exhibited between Llandovery and Pumsant ; and at Bwlch Trebennau I found the following fossils, which were determined by Mr. Salter : — Encrinite stems (abundant). Orthis elegantula (abundant), Favosites andother ill-preserved Atrypa crassa, corals. Calymene, small fragment not Turbinolopsis (a large species). specifically determinable. Lept(Ena sericea (abundant). The parcel containing this list never reached the Cambridge Museum, and Bwlch Trebennau does not, therefore, appear in M^Coy^s alphabetical list of "Lower Palaeozoic Localities*.'' But I lately revisited the same spot, along with hirn ; and we pro- cui*ed from it the two following species, Euomphalus tricinctus and E. triporcatus. Both species are true Cambrian types ; and the former helps us to connect the conglomerates of Trebennau with those of Dol Fan. Taken collectively, the above list, how- ever imperfect, seems clearly to indicate a group below the May Hill sandstone, and is therefore Cambrian. .. IV. Intimately associated. with the above conglomerates, and, I believe, on a lower geological stage, is a very great develop- ment of rather earthy slates, and of arenaceous flagstones, some- times coarse, and almost deserving the name of conglomerates, in which case they are often ferruginous. The shaly slates of this group are well seen in the high hills which form the water- shed between Builth and Llandovery, both on the old road and on the newer road by Llanwrtjd and the Sugarloaf. Beds of the same general age range far up the hills on both sides of the Towy above Llangadoc, and here and there show somewhat rugged crests of hard, brown sandstone or conglomerate. This group is in some places extremely fossiliferous, and may be well seen in an excursion northward from Llandeilo to Taliaris, and round the hills near Garn Fawr. This excursion was made by Mr. Salter and myself in 1846, and we obtained fossils from the following localities, viz. below Taliaris, Park Lodge, Garn Fawr, Cil-y-waun, and other places on our track. I have in my note-book the lists made out by Mr. Salter, with which I will not trouble the reader, as the fossils may be far better studied in the Museum of Practical Geology than in the Cambridge col- lection. But this I may state, on the authority of Professor M'Coy, that so far as my lists and species go, they form a very characteristic upper Bala group, and contain not so much as one species which can be regarded as characteristic of a May Hill or a Wenlock group. * At the same time was lost a small but valuable parcel, containing the fossils from the neighbourhood of Devil's Bridge. 482 Prof. Sedgwick on the May Hill Sandstone, The above great and ill-defined group seems to range through the water-shed last mentioned, and so to pass under the Wen- lock escarpment. On the southern side of the valley between Llandovery and Llangadoc the same group is exposed, and from various quarries (e, g. Pen-y-lan, Goleugod, Cefn llhyddan) I obtained the species described by Professor M'Coy in his List of the Cambridge Palaeozoic Fossils. As among them were some species which rather seemed to indicate a May Hill group, it became important to re-examine some of the localities, which I will notice in the order in which we visited them. 1st. Fenian (or Pen-y-lan), a little more than a mile E.S.E. of Llandoveiy. The quarry with the fossils is near the crest of the hill, and contains some beds of sandstone, alternating with a decomposing flagstone and indurated shale. It' was formerly used for building, but is now deserted. The beds dip at a great angle about N.W. Some of the beds of the ridge, which ranges to the N.E., are nearly perpendicular. In a new quarry, nearly a mile towards the N.E., and at a lower level, we found the beds dipping about S.E. at an angle of 70°. We believe it .almost impossible to determine, by the evidence of sections, what exact relation the Penlan beds bear to the rocks in the immediate neighbourhood ; but among the ruins of the deserted quarry we collected the following species : — Halysites catenulatus. Stenopora fibrosa, Petraia uniserialis. Pentamerus globosus, bina. oblongus (very abun- Palaopora megastoma. dant). This list does not contain any species which has hitherto been regarded as exclusively characteristic of Cambrian rocks, and it gives us a true and characteristic May Hill group of fossils. 2nd. Two quarries from the Goleugod ridge, near the road on its north side, and a third quarry on the cross road to Myddfai gave the following results : — Ist quarry — Halysites catenulatus, , Spirifer percrassus (very abun- Favosites alveolaris, dant). multipora. Pentamerus undatus. Ceraurus Williamsi, Or this calligramma. Lituites comu-arietis. The corals and the Pentamerus are well-known common types, the others are exclusively Cambrian ; therefore the group is Cambrian, as it does not give one exclusively Silurian type. and the Palaozoic System of England. 483 2nd quarry — ^ Petraia uniserialis. Orthis parva. Ceraurus Williamsu elegantula (var a). Orthis protensa (in great turgida. abundance). Leptcena sericea. testudinaria. quinquecostata, flahellulum. This is a very characteristic Cambrian group, containing only two species, which are common to the May Hill beds. The third quarry we had not time to examine in detail, but it contained Leptmna sericea abundantly (a good Cambrian species, never found by us in the May Hill or Wenlock groups) . Here (as in the former case) we are not able to define the place of the Goleugod ridge by help of the sections. The country is broken and faulted, and all the beds are highly inclined ; but there cannot be a doubt that the ridge is, according to our no- menclature. Upper Cambrian — a part of the upper Bala group. It contains no quarry with a group of fossils like that of Penlan. In the gravel over the rocks of the second quarry we, however, found water-worn masses with casts of Pentamerus ohlongus, which seemed to show that other May Hill beds were not far off. V. Quarries on the Hill of Mandinam. The accompanying section, without pretending to any accu- racy of detail, conveys, I believe, a correct idea of the relative Fig. 3. Mandinam Section nearly N, and S. Hill above Mandinam. S. N Quarry 4 3 2 1. Hills of Wenlock shale and Old Red Sandstone. 3. Beds with Cambrian fossils. 2. Confused and mineralized beds. 4. May Hill group. position of the several groups. To the south are the escarp- ments of the Old Red Sandstone, and of the Wenlock and Ludlow groups. Then follows a valley in which the beds are dislocated, mineralized, and penetrated by lead veins, which we had not time to examine, as they are considerably to the east of the line of section. Lastly follows the Mandinam ridge, which is very fossiliferous, 1st. Rocks near the top of the hill. Encrinurus punctatus. Leptana sericea (abundant). Orthis calligramma. quinquecostata. testudinaria. 484 Prof. Sedgwick on the May Hill Sa?ulsto?ie, Two of the above {E. punctatus and O. testudinaria) are some- times found in Silurian rocks, the others are exclusively Cambrian. 2nd. North side of the hill, from an old quarry, and thence down to the level of the river. Stenopora fibrosa. Petraia uniserialis* Spirigerina reticularis, Leptagonia depressa. Pentamerus oblongus (abundant). — . — linguiferus (including undaius). Turrit ella cancellata (?). Here we have not one exclusively Cambrian species, but several which are common to Cambrian and Silurian rocks. Like that of Penlan, it is a good May Hill fossil group. Such were the results of a single day's examination of the very broken and difficult country to the south of Llandovery. It would, perhaps, have been impossible to arrange its beds in any approximate geological order had there been no clearer evidence in any other typical country. There are, however, in this country two very distinct fossil groups, — a May Hill group, and an upper Bala or Cambrian group. These two groups are in the quarries exhibited apart. They do not appear to alternate or interchange places. They have several species in common, but there is no confusion among the typical species. Thus, no truly characteristic Cambrian species was found in the upper or May Hill beds; and, in like manner, no truly characteristic Upper Silurian or May Hill species was found in the Cambrian beds. Such were the facts observed, whatever be the consequences to which they may lead us. The facts are stated fairly and without reserve. VL Section of Castell Craig Gwyddon, ^c. For purpose of illustration, I here exhibit a reduced sketch of a small part of two beautiful sections published by the Government N.W. Fig. 4. Castell Craig Gwyddon. Noedd Grug. | \ i 1 . Old Red Sandstone. 2 and 3. Ludlow and Wenlock. 4. Probably Wenlock. 5. May Hill beds of Castell Craig Gwyddon, probably continued through Noedd Grug. 6. Cambrian group, geologically far above the Llan- deilo flag in tne valley of the Towy. Survey and the author of the ' Silurian System.' Of the general and the Palcsozoic System of England. 485 accuracy of these sections I have no doubt; though I may remark, that the cleavage planes of Noedd Grug are not given in the section of the Survey quite correctly, for they deviate with the flexures of the beds j so that in one place, where the beds are highly inclined, the cleavage planes (if I may trust my remem- brance of the phsenomena after a lapse of twenty years) become nearly horizontal. It was in the hope of solving this peculiarity of structure that in 1834 I accompanied my friend Sir R. I. Murchison over Noedd Grug ; and it was the only instance in this part of Wales in which I went with him towards the beds which he then regarded as the geographical boundary of his system. He placed the boundary a little beyond the northern limit of the ridge. I lament that an attack of indisposition (the only interruption during our short tour) prevented me from accompanying my friend Prof. ^PCoy over the ridge of Noedd Grug ; and he was so entirely unacquainted with the fossil localities that he did not wish to make the traverse by himself. Our observations were therefore confined to the south end of the ridge (Castell Craig Gwyddon), and to the shale beds immediately overlying it. 1st. Respecting the Old Red Sandstone, and the greater part of the great Silurian group (Wenlock, &c.}, there can be no dis- pute. 2nd. As to the stage of shale and earthy slates (No. 4 of the figure) which come next in order, we sought diligently for its fossils, but we did not find so much as one ; and from its mineralogical type, we did not see how it could either be classed with, or separated from, the Wenlock shale. 3rd. The hard, and nearly vertical, beds of gray sandstone which rise from beneath the shale are too well known to need detailed description. In places they become of coarse structure, but they do not, so far as I know, ever pass into a coarse conglomerate, like that of Dol Fan or Bwlch Trebennau. The upper beds of the great precipice contain (as will be shown) a fine May Hill series of fossils. Hence it seems natural to con- clude, that the shales immediately overlying these beds are a true part of the Wenlock shale ; an opinion I should hold, unless the contrary could be proved by fossil evidence, which probably will not be done. Whether the May Hill group of fossils extends through the whole of the contorted sandstone group of Noedd Grug, or is confined to its upper portion, we were unfortunately unable to determine, for the reason above given. But I think I may affirm, from the remembrance of bygone years, that to the north of Noedd Grug, and near Cefn-y-garreg, true Cambrian fossils are met with in abundance. Not, however, to detain the reader with conjectures, I subjoin the list of fossils collected at Castell Craig Gwyddon. - *^ 486 Prof. Sedgwick on the May Hill Sandstone, Stenopora fibrosa, Palaopora interstincta. Halysites catenulatus. Pentamerus linguiferus ( -|- un- Petraia (an unnamed species, datus), same as at May Hill). globosus. bina. oblongtLS. uniserialis, Hemithyris hemispharica, • subduplicata. Leptana transversalis. rugosa (?). Spirigerina reticularis. Of characteristic Cambrian species (i, e. of species which have not been found among any admitted Upper Silurian rocks), not one occurs in the above list. But all the above species are found in the Wenlock or May Hill beds. And I may remark that here (as at Norbury), nearly on the line of demarcation between Cam- bria and Siluria, the common species seem to be crowded together, and we might say that the old characteristic types had disap- peared, and that the new and characteristic Silurian types had not yet found time and place to develope themselves on the section. On the joint evidence of this and the preceding section, we may therefore conclude that we have found a true May Hill group — a palseontological and physical base to the Silurian rocks, — that this base does not lose its character by a blending within it of the characteristic Cambrian and Silurian types, and hence that (spite of the enormous dislocations of the country) it does give us, though in a disjointed and fragmentary form, the ele- ments for the construction of a good geological horizon. I do not, however, believe that this horizon would have been dis- covered in the country above described, had not its place been made out before, by the incomparably clearer sections in North Wales and the bordering English counties. I here conclude the details connected with the establishment of the May Hill sandstone as a group not to be confounded with, or united to, the Cambrian rocks. It was deposited after, or during, great mechanical movements, and it seems exactly to mark the epoch when the characteristic types of an older fauna disappeared, and when the characteristic types of a newer fauna began. If the facts above stated be not invalidated by opposing evidence (and of this I have little fear, as I have now examined the very places where it had been thought that there was some opposing evidence), the discussion of them is no idle battle of mere words, but involves fundamental principles essential to a right classification, and consequently a right nomenclature of our older Palaeozoic series. No classification, therefore, or nomen- clature which has overlooked the place and office of the May Hill sandstone can rest on a basis that is secure, or have any claim for a permanent acceptance. and the Paleozoic System of England, ~ 4^ VII. Llandeilo Flag of the Valley of the Towy, and its relations to the neighbouring groups, I will not detain my readers by any elaborate details respecting this remarkable group. It had long been known to fossil col- lectors from its specimens of Asaphus Buchi and other fossils, and for ages its limestone beds and flags had been quarried for economical use, but the definition of its geological place was first attempted by the author of the ' Silurian System.' It contains many calcareous bands, as may be well seen in the Silurian sections, and still better in the maps and sections of the Government Survey. These limestone bands (some exhibited as mere streaks of limestone, alternating with, and passing into dark shale and flagstone, others as thick and solid masses) are numerous. Within the group are also bands of a brown, arena- ceous flagstone, and sometimes of very hard and coarse siliceous grits passing into a conglomerate. So far as I know, its base is not exposed in any section of the Towy, but its highest beds (as I interpret the group) are on its north side composed of a dark- coloured, pyritous, indurated shale, passing into a slate, which in a few places {e. g. N.E. of Carmarthen, and at Pengoylan near Llangadoc) has been quarried for use. Some of these slates, not being affected by transverse cleavage, show the Diplograpsus pristis in considerable abundance. The group is in the form of a saddle, but these highest bands are not so well exposed on its south side as they are on the north side. They are represented partially, and may perhaps be here and there overlapped and concealed by the Wenlock shale, which (on the south side of the Towy from Llangadoc to Llanarthney) seems to form the immediate southern boundary of the group. Most of these peculiarities of structure are seen in the sections published by the Government Survey, and in the original sec- tions of the ' Silurian System;' and with no idea of blinking the difficulties of the subject, but in the hope of making the relations of the groups clear, I gave an ideal section {supra, fig. 6, p. 314) to show the order of the deposits down the valley of the Towy, through a space of nearly twenty miles below Llangadoc. The disturbing forces that caused the complicated derange- ment of the Llandeilo group aff^ected also the beds much further towards the north-east, but without bringing up the pommel of the saddle; for above Llangadoc, the valley for several miles must originally have been bridged over by the higher geological groups, such as those above described, which ended, here and there, with a kind of top dressing of the May Hill sandstone. The slight ideal sketch (fig. 3, p. 314) above noticed was from memory ; but since my recent visit to the valley of the Towy, I 488 Prof. Sedgwick on the May Hill Sandstone, wish to expunge No. 3 (the Caradoc sandstone) from the section, and to place the Llandeilo flag immediately under the Wenlock shale. The hypothetical interpolation of the Caradoc sandstone did not, however, at all affect the general inference I drew from the sketch. It conveys, however, such an inadequate notion of the thickness of the nearly vertical beds which overlie the north side of the Llandeilo saddle, that I will endeavour to give a better ideal representation of it. Fig. 5. N. and S. section through the valley of the Towy below Llangadoc. 1. Old Red Sandstone, la. Tilestone. 2. Wenlock and Ludlow. 3. Contorted Llandeilo saddle. Hiehly inclined slate rocks, &c. of very great thickness. Commencement of the great undulating groups. If the above sketch convey anything resembling a correct notion of the relations of the great mineral masses, it must inevitably follow that the Llandeilo flag is no true base to the overlying Silurian terrace, and that it has no immediate relation to the Wenlock shale except that of an accidental juxtaposition arising from an irregular overlap of the true Silurian groups ; on the contrary, that it is deeply imbedded in the great Upper Cambrian group, which rolls, in many times repeated and irre- gular undulations, to the coast of Cardigan Bay ; or, if it be crossed on a more northern line, which rolls in like undulations till it is lifted up and arrested near the south-eastern flank of Cader Idris. I call the group Upper Cambrian, because, however different in mineral type, it is the representative of the great Bala group (No. 3) of the Tabular View (supra, p. 362)*. * I once, with a view of bringing the older rocks of Wales into com- parison with those of Cumberland, limited the Upper Cambrian group to the rocks which commence with the Bala limestone and end with (what I now call) the May Hill sandstone. The change I afterwards made (in drawing the Upper Cambrian base hne on the S.E. flank of Cader Idris or the E. flank of great Arenig) involved no change of principle; it was a mere shifting of a line of demarcation among the subdivisious of an un- broken series. Whether the calcareous beds of the Llandeilo group be, or be not, the exact equivalents of the Bala Umestone I do not pretend to determine. The May Hill sandstone, which in the typical Silurian country is of great thickness and continuity, gradually dies away and disappears in the country described in this paper. Hence it sometimes appears and some- times disappears from the base of the overlying Silurian groups ; and in the latter case, the Wenlock shale forms the base of the Siliuian groups and the Palaeozoic System of England, 489 If this be true, the ideal section {supra, fig. 5, p. 313) appealed to for years before and after the publication of the ' Silurian System/ as the basis of nomenclature for its lower groups, was absolutely without meaning. If the fundamental sections were wrong, the nomenclature could not be right. In the determina- tion of the true Silurian groups, the author of the " System '' did incomparable service to the cause of geology, and there is not a geologist in the old or new world who is not grateful for it. But in descending below the groups he had irrefragably esta- blished, he missed the key of his own position, and linked toge- ther groups which had no nearer relation than that of accidental, and often discordant, juxtaposition. When he passed below the horizon of the May Hill sandstone, he did the collector's work alii^_(DH-F)H-(D-F)sec2<^ a« - (J) + F) - (D - F) sec2<^' of Reflexion of Polarized Light, ^ ^ii' ^ 51&; from which and equation (5) we infer a ^^i/— cot (<^ + «) cot (<^ — a) _ (8) - = -/ — tan(^ + u) tan (<^— a) j Equations (7) and (8) serve to calculate the position of the axis major and the ratio of axes from knowing u and e^—e; « is the azimuth measured on the analyser, and e'— e is found by means of the compensator as follows : — It is known from a comparison of the wave theory of thin plates with Newton's experimental laws, that if a beam of light be reflected perpendicularly from a transparent surface, there is a difi^erence of phase of 180° between the incident and reflected light ; a fact which has been admirably illustrated by Dr. Young, by means of the analogy of the impact of elastic balls. The differ- ence of phase, therefore, between the reflected components in, and perpendicular to, the plane of incidence in passing from the incidence 0° to 90°, increases from 180° to 360°, and not from 0° to 180°. By means of the compensator we have the following proportion : — e'_e — 180° : 180° : : the reading of the compensator minus the zero reading : the number of divisions of the compen- sator corresponding to half a wave length. The zero of the compensator used by me is 39*43, and the number of divisions corresponding to different kinds of light for half a wave are as follow : — White lamplight (colza oil) . . . 13-39 Red lamplight (colza oil) . . . 15*43 Red sunlight (same colour) . . . 15*37 If, therefore, C denote the reading of the compensator, we find from the foregoing proportion the equation for red sunlight, 1 oqo e'-e = 180°+(C-39*43)x^^:g^. . . (9) From (9) and the analyser (a) we calculate <^ by means of equation (7), and from and a we calculate the ratio of « to 6 by equation (8) . The calculations in the following section are all made from these equations. 2. Account of the Experiments. The following experiments, unless the contrary be expressed, were made with the same glass as that used in Tables I. and II., the method of observation being as follows : — The polarizer was 6U The Rev. S. Haughton on some new Laws placed at a fixed azimuth, and the angle of incidence increased, as shown in the first column ; the actual readings of the com- pensator and analyser are given in the second and third columns ; the values of e'— e — 180°, deduced from the compensator by means of equation (9), or a similar equation for the white lamplight, are given in the fourth column ; <^ and r, calculated from (7) and (8), are given in the fifth and sixth columns; and a seventh column is added containing the values of the angle whose tangent is jf found as follows : — If A be the azimuth of the polarizer, cos A and sin A will be the components of the incident plane- Eolarized light in and perpendicular to the plane of incidence ; ence if a be the reading of the analyser, we have, since I cos a and J sin a are the corresponding components of the reflected light, Y=tanacotA (10) This column will be found useful in comparing the observa- tions with theory. Table III. Azimuth of polarizer =45°. White lamplight (colza oil). Incidence. Compen- sator. Analjrser. e'-e-180°. 0. a r Tan-(^). 43 37 39-54 18° 30 3 li +18 28 47-79 1§36 48 37 40-07 10 55 10 17 -1-10 45 ^-42 10 55 50 45 40-61 8 10 17 36 + 7 48 23-37 8 10 51 45 4111 6 45 24 22 -}- 6 10 20-70 6 45 52 45 42-67 6 10 45 29 4- 4 21 1303 6 10 54 20 44-46 5 1 69 44 + 1 45 12-15 5 1 65 20 46-30 5 36 94 38 - 0 27 10-23 5 36 56 20 48-18 6 15 120 6 - 3 10 10-68 6 15 57 40 5007 7 35 145 41 - 6 19 13-52 7 35 58 40 51-00 9 39 158 16 - 9 0 16-16 9 39 60 35 51-60 11 10 166 24 -10 53 22-34 11 10 65 40 51-98 18 11 171 33 -18 2 22-84 18 11 75 35 62-60 30 25 178 40 -30 25 Infinity. 30 25 The fifth and sixth columns of this table prove the truth of Laws I. and V. The value of the principal incidence deduced from the values of is 55° 8', at which angle the quantity of light reflected in the plane of incidence (or the major axis of the ellipse) is nearly 104 times the quantity of light in the perpendicular plane (or minor axis) ; because the quantity of light in the plane of incidence is proportional to the square of the ratio of a to b. ' ' of Reflexion of Polarized Light, "^^ Table IV. Azimuth of polarizer = 80°. Red sunlight. ms Incidence. Compen- sator. Analyser. e'-e-180°. ' a b' Tan-(j). 54 30 54 45 55 0 55 15 55 30 4605 46-75 46-90 47 53 4805 43 2^ 43 20 43 8 43 15 45 30 85 38 87 24 94 46 100 51 +37 56 +26 18 + 17 24 -26 49 -47 39 1-25 109 108 Ml 1-21 4 i 4 1 3 59 4 0 4 20 Here we observe the ratio -r approaching unity, while the axis major, as shown by the fifth column, still follows the Law V. Laws L, IL, IIL, V. are verified by this table. The principal incidence is 55° 6', and the ratio of quantities of light reflected in, and perpendicular to, the plane of incidence is 1*17 at the principal incidence. Table VIL Azimuth of polarizer =85° 55^ Red sunlight. Incidence. Compen- sator. Analyser. e'-e-l80°. 0. a r Tan-(^). 54 3& 54 45 55 0 55 15 55 30 45-96 46-65 4700 47-72 48-00 45° 36 45 12 45 5 45 40 46 30 76 24 84 28 88 34 96 59 100 16 +47 7 -1-47 4 +48 19 -50 25 -53 12 1-27 MO 102 113 1-20 4 10 4 7 4 6 4 11 4 18 In this table we have just passed the circular limit, and the column for begins to show Law VI., which will be more fully developed in the succeeding experiments. The principal incidence is 55° 7' ; and the minimum ratio of the quantities of light reflected in, and perpendicular to, the plane of incidence is 1*04. of Reflexion of Polarized Light. Table VIII. Azimuth of polarizer =86°. Red sunlight. 17 ii:t Incidence. Compen- sator. Analyser. e'-e-180°. . a b' ---^Cr); 34 30 39-77 83 20 3 58 +83 2i 120-5 30 53 52 30 4303 53 30 42 7 +56 16 2-73 5 24 53 30 44-67 47 0 61 18 +49 8 1-70 4 17 54 0 45-25 46 20 68 5 +48 34 1-48 4 11 54 30 46-13 46 11 78 23 +50 48 1-23 4 10 54 45 46-48 46 0 82 28 +52 28 114 4 8 55 0 46-91 45 45 87 30 +60 29 1-06 4 6 55 15 47-33 47 0 92 25 -74 27 1-08 4 17 55 30 48-07 48 20 101 5 -60 39 1-25 4 30 56 0 48-86 50 15 111 30 -58 25 1-53 4 48 56 30 49-40 51 30 116 38 -58 37 1-71 5 2 57 30 50-20 57 0 126 0 -63 34 2-26 6 9 73 30 53-69 83 15 166 50 -83 25 37-96 30 35 In this table the value of (/> diminishes from 83° to 48°, and rises then to 60° ; as the incidence approaches the principal incidence the motion becomes more rapid, and at that incidence the axis major is perpendicular to the plane of incidence : having passed this angle, it diminishes again to 58° negative, and then rises again to 83° negative. This motion of the axis major verifies Law VI., and explains the apparent anomaly in the value of in Table VII. A comparison of the values of -r in Tables VII. and VIII. proves the truth of Law IV. The principal incidence is 55° 8', at which angle, since the axis major is perpendicular to the plane of incidence, the quan- tity of light reflected in the plane of incidence is to the light reflected in the perpendicular plane as 1 r 1*12. Table IX. Azimuth of polarizer =87°. Red sunlight. Incidence. Compen- sator. Analyser. e'-e-180°. 0. a b' Tan-((). 34 30 39-48 84 50 0 27 +84 50 Infinity. 30 6 52 30 42-87 60 0 40 14 +63 33 3-27 5 11 53 30 44-06 55 0 54 10 +60 56 2-16 4 17 54 0 44-93 54 20 64 21 +63 59 1-78 4 11 54 30 45-82 54 0 74 45 +70 30 1-52 4 8 54 45 46-34 53 54 80 50 +76 48 1-43 4 7 55 0 46-60 53 55 83 53 + 80 50 1-40 4 7 55 15 47-23 53 34 91 15 -87 59 1-35 4 4 55 30 47-92 55 30 99 20 -78 33 1-48 4 22 56 0 48-40 56 30 104 57 -74 21 1-64 4 32 56 30 49-08 59 30 112 54 -72 28 1-97 5 5 57 30 50-00 64 30 123 40 -72 48 2-72 6 16 73 30 53-54 85 0 165 5 -85 10 44-5 30 55 518 The Bev. S. Haughton on some new Laws An attentive examination of the fifth column proves completely the truth of Law VI. ; and a comparison of the values of t in Tables VII., VIII., IX. proves the truth of Law IV. The principal incidence is 55° 13', and the quantity of light in the plane of incidence is to the quantity of light in the perpen- dicular plane as 1 : 1*82. Having ascertained the truth of the six laws stated at the commencement of this paper, I removed the compensator and made the following direct experiment, by which is shown the possibility of obtaining circularly-polarized light by means of a single reflexion, not total, at the surface of a transparent body : — Angle of incidence . . = 55° (V Polarizer =85° 50'. On turning the analyser round through 360°, it was not pos- sible to detect any change in the intensity of the light, which was therefore sensibly circularly polarized, proving the truth of Law III. directly. The truth of Laws II., III., IV. is made very evident by the following table formed from the preceding tables. Table X. Principal incidence. Polarizer. 45 d 104-00 80 0 3-96 85 0 1-58 85 45 117 85 5^ 104 86 0 112 87 6 1-82 From this table it appears that the value of the azimuth, which I have called the circular limit, is 85° 52'. Collecting together the values of the principal incidence, or incidence for which the axes of the reflected elliptically-polarized light he in, and perpendicular to, the plane of incidence, we find Table XI. Polamer. Principal incidence. 4^ d ' 80 0 85 0 85 45 85 55 86 0 87 0 5^ ^ 54 27 54 59 55 6 55 7 55 8 55 13 Mean 55 1 of Reflexion of Polarized Light, 519 This angle should, according to received ideas, coincide with the polarizing angle, or its tangent should give the refractive index; the tangent of 55° 1' is 1*4290, which is very different from the refractive index found directly, which is 1*6229; but I have repeatedly observed the refractive index found by reflexion differ considerably from that found by refraction, and believe that the law of Brewster is only approximate. In order to ascertain this point, I made the following experi- ment on another rhomb of glass having the same refractive index as that used in my former experiments. Table XII. • Azimuth of polarizer =86°. Red sunlight. Incidence. Compen- sator. Analyser. e'-e-180°. . a b' 34 30 39-70 8§26 3 8 +8°3 26 Infinity. 52 30 43-33 53 30 45 37 +56 48 2-53 53 30 44-70 50 0 61 39 +55 11 1-73 54 0 45-60 49 0 72 11 +57 20 1-41 54 30 46-30 47 30 80 22 +58 48 1-21 54 45 46-79 46 45 85 58 +65 30 110 55 0 47-31 46 0 92 11 -QQ 15 105 55 15 47-70 47 30 96 45 -63 20 116 55 30 48-00 48 30 100 16 -62 17 1-24 56 0 48-83 50 30 109 58 -59 50 1-50 56 30 49-10 52 30 113 8 -62 & 1-64 57 30 49-95 57 0 123 5 -64 32 215 73 30 53-40 82 30 163 27 -82 48 26-98 The refractive constants of tfiis rhomb were determined with care, and found to be — Refractive index of extreme red . . . Refractive index of extreme violet . . Refractive index of red used in experiments Dispersive power = 1-6190 = 1-6555 = 1-6230 = 0-0573 The comparison of the values of <^ and j- from this table with the corresponding values in Table VIII. is satisfactory. The principal incidence is 54° 53', which agrees with the values in Table XI., and confirms the deduction I have drawn from that table. The observations contained in the preceding tables were made during the course of the past summer, which was very favourable for such a purpose. I have repeated the more important obser- vations many times, and by using strong sunlight have always succeeded in obtaining the same results. I consider that they 620 Prof. Challis on the Tlieory of the Mom^s Motion. completely establish the six laws laid down by me ; but I could have wished, before communicating them to your valuable Journal, to have had an opportunity of repeating them with dif- ferent substances, particularly with double refracting crystals ; but the short, rainy days of November, and the return of the col- lege duties of Michaelmas term, compel me to postpone further experiments to a i)eriod of brighter sunshine and greater leisure. In the meantime, I think the facts I have already obtained will prove of some interest to such of your readers as are engaged in optical researches. ^i Trinity College, Dublin, . November 4, 1854. LXII. The Theory of the Moon's Motion. — Second Approximation. By Professor Challis*. MR. ADAMS has made no reply to the arguments in the Philosophical Magazine for August, by which I met his objections to my new solution of the problem of the moon's motion. As those objections are all completely answered, I consider myself entitled to assert that the judgement passed on the paper which contained the first approximation of the solution remains unsupported. I have distinctly proved, that, in forming his opinion of it, Mr. Adams relied on false rea- soning. I feel, therefore, no hesitation in extending the method to higher approximations, being well persuaded that such extension will more fully demonstrate its logical accuracy and the soundness of the deductions drawn from it. The object of the present communication is to obtain expressions for the radius-vec1;or and true longitude of the moon to the second ap- proximation, after recapitulating, for the sake of clearness, the reasoning of the first approximation. [1 It will be proper to begin with stating the limitations of the problem. Three bodies being supposed to attract each other according to the law of gravity, and the velocity and direction of the velocity of one of them at a given point of space being given at a given instant, it might be proposed to determine by successive approximations its subsequent motion on the suppo- sition that the motion is principally due to the action of one of the other bodies. This, however, is not the problem relating to the moon's orbit which I propose to solve. I make the addi- tional limitation, suggested by observation, that the moon's motion is such that it always differs to a small amount from uniform motion in a circular orbit of given radius. The problem * Communicated by the Author. Prof. Challis on the Theory of the Moon's Motion, 521 with this limitation is that of which the solution is usually called the lunar theory, although the introduction of the limitation into the reasoning is not usually pointed out. Let M, rrij w! be the attractions of the earth, moon, and sun respectively, at the unit of distance, and at the time t reckoned from a given epoch ; let x, y, z, r and a?, y\ z\ r' be the rectan- gular coordinates and radius-vectors of the moon and sun, referred to the earth's centre as a fixed origin, and to the plane of the ecliptic and the first point of Aries. Then putting />t for M -f m, and P for(^ — a?')^ + {y—y^f + {z—s^Y, we have the known equations, J-t-f+$'+-'(.-y)V-«=o, As it is not my object to obtain exact numerical results, but to exhibit a method of solution, I shall suppose for the sake of simplicity that the sun describes a circular orbit in the plane of the ecliptic at its mean distance («'), and with its mean angular velocity {n^) , Thus a/ = a' cos {n't + e') , y'=a' sin (n't -f e^) , and z' = 0. Hence dx' = — n'y'dt, and dy' = n'x'dt. By taking account of these values of da/ and dy', and putting a' for r', the following result is readily obtained : m^.dr'-?^d.{xa/+yy') + 2m'd.(a'^-^2(a!a/-{-yy')-hrT^. Hence by integration (putting ^ for the angle between the radius-vectors of the sun and moon), ^: dt^ + dt^ ^dt^ ^"""^ dt ^^""^dt ^^'- ^-~cos^ + 2m'{a'^-2a'rcoscj> + rY^, It thus appears that the pi^oblem of three bodies admits of an exact first integral in the case in which the relative orbit of one of the bodies is a circle. I am not aware that this proposition has been proved before. To simplify the question still further, I shall now suppose the moon to move in the plane of the ecliptic, as the principle of the proposed method of solution equally admits of being exhibited Phil, Mag, S. 4. No. 55. Suppl Vol. 8. 2 M 6%2 Prof. Challis on the Theory of the Moon*s Motion, under this restriction. Thus we shall have, 6 being the moon's longitude, dz ^ dx^ . dy^ dr' . 7^d&^ ft-^' dt^ '^ dt^ " dt^ '^ dt^ ' gdO dy doc . /^ , ,, u and the above integral becomes dr^ r''d4>^ ^^ ,2, Also, since 2fi^2m^r r 'W cos (a) dd dd> ^ , J dt dt it follows that dt __ m'r sin <^ {■-( _ d^y d^x -^W^dF |cos,^J)-*}. (b) The equations (a) and (b) between the three variables r, <^ and tf will conduct by successive approximations to the moon's motion and the form of her orbit. By expanding the trinomial 13 r affected with the indices — tt and —77 to the fourth power of—., 2 2 ^ a!' the following approximate equations, in which »'^ is substituted for -f^ will be found : H- -j-f (3cos^ + 5cos3^) + ^2(9+20cob2(^+35cos4<^) (A) d , r (§-') 37»'V dt sin2<^ 2 3n'V Q ; (sin <^ + 5 sin 3) (B) Prof. Challis m the Theory of the Moon's Motion, 523 It may be remarked, that tlie method so far applies as well to the planetary as the lunar theory. First Approximation. * Terms on the right-hand sides of the above equations involving higher powers of r than the second will be omitted. Thus the second equation may be put under the form ^'Alt^'^) 3n'2sin2 ^, — — _ i_ fjif^ «"■) Kf-') But by the hypothesis of the problem, the moon^s longitude 6 always differs by a small angle from a mean longitude nt-\-e. Hence -— +/i'=7i nearly, and dt= — ^. Substituting these cLi n —^ n values in the above equation, integrating, and omitting the square of the disturbing force, we have Hence and ^ 37i'Vcos2(i) rd6 h , 37i'^r cos 2 at r 4i{n—w) r^dffi^ h^ ^ ,, ,22/, , 3cos2<^\ , -^ ^^-^nlh + n'^r^^l + —j-^) nearly. But by the equation (A), to the same approximation, dr^ r^d6^ r, 2m' 2yu, Sti'V Hence by substitution, and altering the designation of the arbi- trary constant, *V^.&-^,o.o ,0 It may be observed, that in obtaining this equation it has not been necessary to employ an approximate value of the radius- vector. It follows, however, from the reasoning, that r differs little from a mean value, because approximately r^(^^ni^^r^n = h. If the equation (C) be supposed to apply to a circular orbit, we 2M2 524 Pi*of. Challis on the Theory of the Moon's Motion, dr have iT=0, and consequently As this equation contains possible but not unequal roots, it is satisfied simultaneously with the derived equation — ^ + Cr-nV=0. Hence Lb Tl Uj = 5 + -^ nearly.. This will afterwards be found to be the value of the mean distance in the first approximation to the orbit. As the equation (C) gives the value of -^ to the second order dr of small quantities, we may deduce from it the value of -j, and therefore that of r, to the first order of small quantities ; and these values, it may be observed, will be independent of the sun's longitude. I proceed next to the integration of that equation. The course which first presents itself is, to substitute for r in the term involving w'^ a mean value a, thus omitting, as hereto- fore, small quantities of the third order. By this process the approximate orbit is shown to be a fixed ellipse described by the action of the central force -^ . This result does not recognize the existence of a disturbing force, although it has been fully taken into account in the investigation. I find also, by carrying the approximation further on the same principle, that terms in- consistent with the hypothesis of the approximation arise, of the same kind as those met with in the usual method of treating the lunar theory when the approximation commences with a fixed ellipse. Since, however, no rule by which approximations are conducted has been violated, some step incompatible with the particular conditions of the question must have been taken. But the only step that has been taken peculiar to the case, is that of substituting a for r in the term -77-, on the assumption that some other term of the equation is of a higher order of value than this term. It must therefore be concluded that the equa- tion (C) contains no term of a higher order of value than that of the term -5—. It is, however, certain that this is not the Prof. Challis on the Theory of the Moon's Motion. 525 case unless the trinomial h^—^fjb7'-\-Cr^ be equivalent to a single term of the second order of small quantities. To satisfy this condition, the constants ^ and C must be related to each other. The required relation may be found as follows. Put for r in the above expression w-\-v, and assume w to be much larger than v. Then the expression becomes h^-2lM{w + v)^-C{w^-vY, and the appropriate condition is satisfied if and Hence it follows that — 2/i- + 2Cm;=0. w=j^ and h^=. ^. The reasoning by which the above relation between h and C is deduced, appears to be perfectly cogent. I cannot, after the fullest consideration, perceive that any step can be called in question. It may be observed that the constant C was intro- duced by an integration performed anterior to any limitation of the question, and that the relation between h and C results from the limitation given to the problem by assuming the moon's true motion in longitude to differ little from a mean motion. It is not my intention to introduce the equation h^C = ^^ into the investigation at present, because I wish to prove, first, that if h and C be regarded as independent of each other, the solu- tion of the lunar problem deduced from the equation (C) is iden- tical with the ordinary solution. It must, however, be borne in mind, that if the foregoing reasoning be good, neither method of solution ought, in strict logic, to be proceeded with until the above relation between the constants has been deduced*. * As in this part of the reasoninp; my method is distinguished from every other that has been applied to the lunar theory, I will endeavour to put the argument in as succinct a form as possible, that it may be the more readily seized. Suppose the expression —Cr^-~}i?-\-'2,}ir-{- —— to contain terms higher in value than the last term. Then the only legitimate process of approximation is to integrate, ne- glecting the small term, so as to obtain an approximate value of r, to sub- stitute this value in the small term and integrate again, and so on. By this process the approximation commences with a fixed ellipse of arbitrary eccentricity, and is found in succeeding steps to introduce terms which may increase indefinitely with the time, and which are therefore in- compatible with the hypothesis that the true values of the radius-vector and the longitude dififer little from mean values. Consequently on that hypothesis the above expression cannot contain 526 Prof. Challis on the Theory of the Moon's Motion. Putting now the equation (C) under the form »'V' y^_Cr«-A»+2/tr+^ it follows from what is shown above, that the integration must be performed as if the quantity under the radical were of four dimensions with respect to r, the last term being treated as vari- able. This cannot be done exactly, but an integral sufficiently approximate for our purpose may be obtained on the same prin- ciple as that applied to the approximate solution of algebraic equations of high dimensions. That is, having ascertained in the manner exhibited above that '- \% an approximate value of r, we may substitute in the above equation ^ -f ?; for r, and expand to the second power of r, to secure an approximation of the first order. This being done, the equation is integrable, and the same results are obtained as those given in mv communication to the Philosophical Magazine for April 1854 (p. 281). It will only be necessary to insert here those results which may be useful in the second approximation. c(«*+.+y)=cos-.^-(.«-(l-9')* - =1 + 6 cos c(^4-y) m being the ratio of the moon's periodic time to the sun's, and a and e being new constants, the relations of which to the con- stants h and C are given by the equations From the last two equations may be deduced the following : Hence A: (■4) terms higher in value than the last term, and the constants C and h must he related to each other in such a manner as to satisfy this condition. The relation between C and h thus obtained is the same that results by supposing the expression to contain the disturbing force as % factor. Prof. Challis on the Theory of the Moon's Motion. 527 The first approximations to the radius-vector and the true longi- tude in terms of the mean longitude as given by this solution, are r—a—aecosc.nt + e + y 6=:nt-^€ + 2eamc.nt + € + y. Second Approximation. The same terms of the equations (A) and (B) are to be used for the second approximation as for the first, the next terms being of a higher order by two degress. Thus the equation (B) gives dSr''(^^+n')y=-'^ n'^r^ sin 2 dt. Putting, for shortness' sake, jo for the angle c(n^ + e + 7), and q for [nt + e) — [nH + e'), and using the values of r and 6 given by the first approximation, it will be found that r^mi2(f> = «2(sin2g' + esm{2q +p) — Sesin {2q — jo)). Substituting in the equation above, integrating, and omitting terms of the fourth order. Hence by squaring, and substituting the approximate value of r in the small term, r^^=!^-2n'h + n'^r^ dt^ r^ + (5e \ cos2g'+ -5-cos(2g'+jo)— 5ecos(25'— jo)j 2 Again, by a like process, r^ cos 2(^ = a^('cos 2g' — 3e cos(2g'— jo) + e cos(2g' +jo)). Hence the equation (A) gives s^+^i^=^^+-«^+y-^-2- + — 2 — (cos2g'— 3ecos(2g'— ;?) + ecos (2g'+p)). Consequently, by subtraction, £ + ^ -y -"P + C = «'V<3cos(3(?-i>) -cos(3g +;>)). (C) It will be seen that this approximation has introduced no new term independent of the sun's longitude. Putting, for brevity, 5^ Prof. Challis on the Theory of t/ie Moon's Motion, h^ 2/L6 w'^r* Q for 2 H 1 — ^ C, the approximate value of dt may be thus expressed : (tv n u e '^^^ VS "" ^Q* ^^ ^^^ ^^^""-^^ ~^°^ ^^^ '''^^'^^^' The first term of the right-hand side of the equation is to be integrated just as in the first approximation. In the other term we may substitute for Q* the approximate value of -p, viz. n^a^e^ sin*/?. Then observing that r&cos{2q-p)-co,{2q+p)^^ 2co8 2g J sin*j9 wsinja ^ we obtain by integration, > ^ . . ,«— r 1 , n'^ cos 20 . c(n/ + e+y)=cos-^ .v/flV— (a— r)2+ -2 ^ — -^ " ae a ^ ' ^ n^e sinjo ^^2 But \/«V--(a— r)*=flesin;3 nearly, and — =m*. Hence it will be readily seen that 1 — e C0SJ9 + X- — -^ cos 2/>— m^ cos 2q ) . Again, by what is proved above, we have to quantities of the second order, de h 3»'2 Hence W = 7^ + ^'"''^9- 'hdt . 3m^ Putting for r the value just obtained, and for h its value wa'( 1— »- j, and integrating, the result is 5g2 11m* . ^ = 71^4- e + 2e sin »-|- —r- sin %p-\ ^— sin2^. We have thus arrived at the values of r and d given by the second approximation. But it does not follow that these are the complete values to the second order of small quantities; because, on proceeding to the next approximation, terms of the third order may rise to the second order by integration. This will be the case with terms of which the circular function con- tains the arc 2{q—p). I propose, therefore, to enter upon the third approximation so far as may be necessary to discover terms which rise to the second order by integration. For this purpose Prof. Challis on (he Theory of the Moon's Motion. 529 the values of r and 0 given by the second approximation will be employedj^ On going through the process exactly in the manner already indicated, it is found that the expression for -^ contains the term which on account of the small denominator m is of the third order. This gives rise in the value of r, to the term -'2 -15^2 co&2{q-p) 2n^eJ ~ 4u. d^x dx^ For greater brevity write — . as Xr. The most cursory consi- deration will suffice to show, irrespective of all calculation, that we should have the following form of expansion, viz. + { (2, 6)^2 . ^6+ (3, 5) . (^3 . ^s) + (4, 4) . (0,-4 . ^J } -^x,^ ~ {(2,2,5)a72.a72.a?5+ (2,3,4) .(a?2.^3-^4) + (3,3,3)fe.a73.iP3)-^a?iio + {(2, 2, 2, 4)(a72 . ^2 . a^a . x^) + (2, 2, 3, 3){x^ . x^.x^.x^)} -r-a?/* — { (2, 2, 2, 2, 3) {x^ . a^g . ^2 • ^2 • ^5) "^^1^^} + (2,2,2,2,2,2)-^^^ In the first group of a single term, 7 is taken in one part, in the second group of 3 terms, 8 is taken in every possible way of partition in two parts, in the third group of 3 terms, 9 is taken in every possible way of partition in three parts, and so on, until finally 12, i. e. the double of the number next inferior to the given index 7, is taken in the sole possible way in which it can be taken of six parts ; I ought to add, that in the groups of indices, unity is always understood to be inadmissible. The groups of indices in the parentheses indicate numerical coefficients to be determined, and the whole and sole real diffi- culty (if any) of the question consists in determining the value of these numerical symbols. Now the law which furnishes these values would be seen on the most perfunctory examination to be the very simplest law that could possibly be stated, viz. any such symbol as (r, s, t, . . .) is to be understood to denote the number of distinct ways in which a number of things equal to the sum of the indices r, s, t, &c. admit of being thrown into combina?^ tion groups of r, s, t, &c. I the Inversion of the Independent Variable. 537 J Thus_, ex. gr. ^"^^ ^^-"1.2x1. 2. 3. 4. 5. 6"-^^ H1 ^^'^^-1.2.3x1.2.3.4.5 = ^^ (4 4) - 1 . 1>^»3.4.5.6.7.8 ^'^^"2 1. 2. 3. 4x1. 2. 3. 4-^^ ^2 9 n^-l 1.2.3.4.5.6.7.8.9 ^ ' '^ "2 ' 1 .2x1.2x1.2.3.4.5 ^9^ ^A^l ■^■3.4.5.6.7.8.9 ^'''^^-l. 2x1. 2. 3x1. 2. 3. 4 ^/q q ON 1 1.2.3.4.5.6.7.8. 9 ^o,o, ^;- 3 3 3 • 1.2.3x1.2.3x1.2.3 rs 9 9 IN- 1 1.2.3.4.5.6.7.8.9.10 ^'''^" 1.2. 3 '1.2x1. 2x1. 2x1. 2. 3. 4 (9 9^^\--L. _L 3 .2.3.4.5.6.7.8.9.10 ^ ' ' ' ^ - 1 . 2 ^ 1 . 2 ^ 1.2x1.2x1.2.3x1.2.3' and so on. The general law is obvious ; and to prove its appli- cability in general, we bave only to show that if it be true for the case of -j^j it is true for _ — —. The proof is as follows. dx"" dx"""^ Let in general [/, m, n, &c.] indicate the value of 1.2.3 (/+W + 71 + &C.) 1.2.../xl.2...mxl.2. ..wx&c' without reference to /, m, w, &c. being equal or unequal inter se. Lemma 1. It is very easily seen that ^^ [/, m, n, &c.] = [/— '1, m, n, &c.] + [/, m — \, n, &c.] + [/, m, n — \, &c.] -f-&c. If now we use the notation [r : ^, s : o-, t '.r, &c.] as an abbre- viated form of the notation [p, p, p . . . to r terms, a, a, a ... to s terms, r, t . . . to / terms, &c.], it is obvious that the equation last written becomes \r:p,s:(ryt:T, &c.] =7* x [p — \, (^ — 1) : p, s:p, r — l>o-, &c., and respectively units when {(T—l)=p, T~l=(7, &c. ; foritwillbeobvious that if a t>»0O OS to p « •w*«wo O o«o O « ^iif^iiiiiif^^ii ^i^^iU^iijiiiii^ 3M ^M iM g S g S « s i^i^m^iii-i^iU^i^^^^i^ r* rj- r« oo On ON o t--vo oo m r-.oo r--oo cooNTi-a\t» «^>-i i~-m u-,| • ,-ie^^^le*'^ >M|0 H|n m{c« m|ci ''I^ He* 5i-Tl-u^u-»Ti-u->u^ir>'^Ti-'^'^^'^Tl-^<^rocOTl-^»ou-iTl- ONO\OnOnO\0\0 OnONOnO O O O\0\0n0n0NO\0n0nOn0nO\On0nOnOnO\OnC\,. I r< t-N *^ •<4- rnoo ONt^Tj-c« m c« 00 "h ^vo r< OnOnOhOnOnOnO 0\OnOnO\0 O O OnOnO\OnOsOnOnOnONOnOnOnO\OnOnOn<^ g O ^ N u-^ wi O p OO Jf^^ ;^ /> .f^ ON c» oo On O t^ •-> oo 00 VO t^OO On On On On On On On On On On On O O On On On OnOO OnOO OnOO 00 OnOO On On On On On On 0>-"^^0>-"ONt~~r OncoN OnwOO COCow-iQ •rj-w On v<^00 no n o t^oo y~> y^ p _onoo o o ■^ ■+ h "-• o f^.'*,'^.'^"^ .^^.^.'^'.^ _t^ n m w b b b\ On 'o\ On O 'o\ On O O O O O O O On On On On On On 'on *On 'on 'on 'c "o *0 u ^ xrwo t^OO On 6 o 4- *ONd t^oo On 6 N to ^ lovd r^oo « rt H r» c< N c< 557 INDEX TO VOL. vin; ! I I Adams (J. C.) on some new theo- rems relating to the moon's orbit, 27. AeroHtes, observations on, 329, 449. iEthyle, new phosphite of, 548. iEthylo -quinine, on the preparation and composition of, 124. Alkalimetry, on a new method of, 553. Ammonia, on the oxidation of, in the human body, 217- Amphibia, on the impregnation of the ovum in the, 224. Ankerite, 137. Arithmetic, on some new theorems in, 187. Atmosphere, on the effect of the pressure of the, on the mean level of the ocean, 318. Atmospherical phaenomena, on the theory of the variations of, 294. Barry (Dr. M.) on the mode of origin of the cell-membrane, and the na- ture of the earliest pores, 282; on the discoveries of Keber on the porosity of bodies, with con- firmations, 287, 370. Becquerel (M.) on the principles which govern the disengagement of electricity in chemical actions, 76; on the production of pyro- electric currents, 323. Beetz (W.) on the power of conduct- ing electricity assumed by insula- tors at high temperatures, 191 ; on the magnitude of galvanic polariza- tion, 380. Bodies, on the porosity of, 287, 370. Boole (Prof. G.) on the theory of probabilities, 87, 175, 431 ; on the conditions by which the solutions of questions in the theory of pro- babilities are limited, 91. Brachiopoda, contributions to the anatomy of the, 225. Braun (A.) on the occurrence of zinc - in the vegetable organism, 156. ^romanil, 38. Bromanilamic acid, 41; bromanil- amide, 38. 2. Bromhydranil, 39. Bromine, on the action of, upon ni- tropicric acid, 36. Bromopicrine, 37. Brown (J. F.) on a general method of substituting iodine for hydrogen in organic compounds, and on the properties of iodopyromeconic acid, 201. Buff (Prof.) on the conductivity of heated glass for electricity, 12.* Burman's law for the inversion of the independent variable, note on, 535. Cambridge Observatory, on the de- termination of the longitude of the, by galvanic signals, 235. Cambridge Philosophical Society, proceedings of the, 234. Carpenter (Dr. W. B.) on a pecuHar arrangement of the sanguiferous system in Terebratula and other Brachiopoda, 541. Cayley (A.) on quantics, 69. Celestine, 139. Cell-membrane, on the mode of origin of the, 282. Cerebro-spinal fluid, examination of the, 213. Challis (Prof.) on certain questions relating to the moon's orbit, 98; on the determination of the longi- tude of the Cambridge Observatory by galvanic signals, 235; on the theory of the moon's motion, 520. Chances, on the theory of, 87, 175, 431. Chemical reactions, on the electricity disengaged in, 7G. Chloroform, on some new derivatives of, 405. Chromatic dynamometer, description of the, 349. Cinnamon oil, on the artificial pro- duction of, 238. Cold, influence of, on the expansion of certain substances, 357. 558 INDEX. Collins (M.) on the attraction of el- lipsoids, 223. Collodion, new process for rendering, more sensitive, 24, 213. Collodion plates, on the methods of preserving the sensitiveness of, 1 11 . Connell (Prof. A.) on a new hygro- meter or dew-point instrument, 81. Creosote, constitution of coal-tar, 55 1 . Cresyle, on some compounds of, 551. Crookes (W.) on a method of pre- serving the sensitiveness of collo- dion plates. 111. Cuminic alcohol, on, 555. Cyclone, on the changes of wind in a, 469. Day (Dr. A.) on the rotation of the pendulum, 19 ; mineralogical no- tices, 137. Dove (Prof.) on the bearing of the barometrical and hygrometrical ob- servations at Hobarton and the Cape of Good Hope on the general theory of the variations of atmo- spherical phamomena, 294 ; on the changes of wind in a cyclone, 469. Electric currents, on the thermal ef- fects of, in unequally heated con- ductors, 62. Electricity, on the conductivity of heated glass for, 12 ; on the prin- ciples which govern the disengage- ment of, in chemical action, 76; on the conducting power of insu- lators at high temperatures for, 19 ; on the conductibihty of hquids for, 465. in equilibrium, on the mathe- matical theory of, 42, of flame, on the, 399. Ellipsoids, on the attraction of, 223. Endosmose, observations on, 151. Erythrozym, on the properties of, 161. Flame, on the electricity of, 399. Fluids, on the thermal eflccts of, in motion, 321. Gerling (Prof.), description of two letter-scales, 113. Glass, on the conductivity of heated, for electricity, 12. Goniometer, Wollaston's, on obtain- ing rapid adjustments with, 430. Graham (Prof.) on osmotic force, 151 . Greg (R. P.) on meteorolites or ae- rohtes, considered geographically. statistically, and cosmically, 329, 449. Griffith (Dr. J. W.) on the relation of the angular aperture of object- glasses to their penetrating power and to oblique light, 70. Grove (W. R.) on the electricity of flame, 403. Hamilton (Sir W. R.) on some exten- sions of quaternions, 125, 261. Hargreave (C. J.) on the law of prime numbers, 114. Hassall (Dr. A. H.) on the frequent occurrence of indigo in human urine, 233. Haughton (Rev. S.) on some new laws of reflexion of polarized light, 507. Huxley (T. H.) on the anatomy of the Brachiopoda, 225. Hydrargyrsethyle, on some combina- tions of, 238. Hydrocyanaldine, composition of, 326. Hydrogen, method of substituting iodine for, in organic compounds, 201. Hygrometer, description of a new, 81. Indigo, on the frequent occurrence of, in human urine, 233. lodmecone, on the preparation and properties of, 206. lodopyromeconic acid, on the pro- perties of, 201. Isotropic bodies, on the double re- fraction temporai-ily produced in, 241, 342. Jones (Dr. H. B.) on the oxidation of ammonia in the body, 217. Joule (J. P.) on the thermal eff'ects of fluids in motion, 321. Keber (F.) on the porosity of bodies, 287, 370. Kraut (M.) on cuminic alcohol, 555. Leblanc (F.) on the electro-chemical decomposition of water, 237. Letter-scales, description of two new, 113. Light, on certain recent investigations m the theory of, 42 ; on some new laws of reflexion of polarized, 507. Liquids, motion of, on some phaeuo- mena connected with the, /4 ; on the conductibihty of, for electri- city, 466. INDEX. 559 Logeman (M.) on the conductibility of liquids for electricity, 465. Lubbock (Sir J. W.) on a graphical method of clearing a lunar distance, 280. Madder, on the action of the ferment of, on sugar, 161. Magnetic declination, on the observa- tions of the, at the Observatory of St. Helena, 139. Magnetism, on the periodical varia- tions of terrestrial, 385. Magnus (Prof. G.) on red and black sulphur, 177. Matteucci (M.) on the electricity of flame, 399. Meteorolites, observations on, 329, 449. Meteorological observations, 79, 159, 239, 327, 407, 555. Mineralogical notices, 137. Moon's orbit, on some new theorems relating to the, 27, 98, 520. Newport (the late G.) on the impreg- nation of the ovum in the Am- phibia, and on the early stages of development of the embryo, 224. Nitro-glycerine, 548. Nitropicric acid, on the action of bro- mine on, 36. Numbers, prime, on the law of, 114. Object-glasses, on the relation of the angular aperture of, to their pene- trating power and to oblique light, 70. Osmotic force, researches on, 151. Ovum, on the impregnation of the, . in the Amphibia, 224. Palaeozoic system of England, on the, 301, 35.9, 472. ParafRne, 463. Pendulum, on the rotation of the, 19. Platinum-sdlts, on the fractional crystallization of, 209. Polarization, galvanic, on the magni- tude of, 380. Porosity of bodies, on the, 287, 370. Price (Dr, A. P.) on a new method of alkalimetry, 553. Probabilities, on the theory of, 87, 91, 175, 431. Pyridine, on the presence of, in the naphtha from the bituminous shale of Dorsetshire, 209. Pyro-electric currents, on the produc- tion of, 323. Quantics, on, 69. Quaternions, on some extensions of, 125, 261. Quinine, on the constitution of, 123. Rain-fall, on some simultaneous ob- servations of, 444. Rankine (W. J. M.) on the expansion of certain substances by cold, 357 ; on some simultaneous observations of rain-fall at different points on the same mountain-range, 444 ; on formulae for the maximum pres- sure and latent heat of vapours, 530. Regnault (V.) on the elastic forces of vapours in vacuo and in gases, at - different temperatures, and on the tensions of the vapours furnished by mixed or superposed liquids, 269. Reichenbach (Baron) on paraffine, 463. Retina, on the circumstances which regulate the production of pictures on the, 544. Robinson (Dr. G.) on the disintegra- tion of urinary calculi by the lateral disruptive force of the electrical discharge, 220. Ross (Capt. Sir J. C.) on the effect of the pressure of the atmosphere on the mean level of the ocean, 318. Royal Institution of Great Britain, proceedings of the, 74. Royal Societv, proceedings of the, 62, 139,213,318,541. Sabine (Col. E.) on some conclusions derived from the observations of the magnetic declination at the Observatory of St. Helena, 139. Saline solutions, on the boiUng-points of, 273. Schunck (Dr. E.) on the action of the ferment of madder on sugar, 161. Scoresby (Rev. W.) on some of the circumstances and principles which regulate the production of pictures on the retina, 544. Secchi (A.) on the periodical varia- tions of terrestrial magnetism, 385. Sedgwick (Rev. Prof.) on the May Hill sandstone, and the Palaeozoic system of England, 301, 359, 472. Silex, on a remarkable form of, 139. Solar heat, on the immediate cause of, 424. 560 INDEX. Solar system, on the mechanical energies of the, 409. Sounds produced by the contact of bodies having different temi)era- tures, on the, 1. Spiller (J.) on a method of preserving the sensitiveness of collocUon plates, 111. Stenhouse (Dr. J.) on the action of bromine on nitropicric acid, 36. Stokes (Prof.) on recent investiga- tions in the theory of light, 42. Strecker (A.) on the constitution of quinine, 123 ; on the composition of tannic acid, 157 ; on the artifi- cial production of taurine, 236 ; on some combinations of hydrar- gyromethyle and hydrargyrajthyle, 238 ; on the artificial production of cinnamon oil, ib. ; on hydrocyan- aldine, 326. Styrone, on some properties of, 238. Sugar, on the action of the ferment of madder on, 161 ; on the presence of, in the cerebro-spinal fluid, 213. Sulphur, on red and black, 177. Sun's body, on the probable nature of the, 24. Sun, on the distribution of tempera- ture over the surface of the, 426 ; on the age of the, 427- Sylvester (J. J.) on some new theo- rems in arithmetic, 187 ; on Bur- man's law for the inversion of the independent variable, 535. Tannic acid, on the composition of. Taurine, on the artificial production of, 236. Terebratulidae, on the anatomy of the, 225, 541. Thermo-electricity, researches in, 62 ; on the phsenomena of, in crystal- line metals, 68. Thomson (Prof. W.) on the mathe- matical theory of electricity in equilibrium, 42; researches in thermo-electricity, 62 ; on the me- chanical energies of the solar sy- stem, 409. Tones produced by the contact of bodies having different tempera- tures, on the, 1. Topaz, 138. Turner (W.) on the chemieal compo- sition of the cerebro-spinal fluid, 213. Tyndall (Dr. J.) on the vibrations and tones produced by the contact of bodies having different tempera- tures, 1 ; on phsenomena connected with the motion of liquids, 74. Urinary calculi, on the disintegration of, by the lateral disruptive force of the electrical discharge, 220. Urine, on the frequent occuiTcnce of indigo in human, 233. Van Breda (M.) on the conductibihty of liquids for electricity, 465. Vapours, on the elastic forces of, in vacuo and in gases, 269 ; formulae for the maximum pressure and latent heat of, 530. Warburton (Mr.) on self-repeating series, 234. "Water, on the electro-chemical de- composition of, 237. Wertheim (G.) on the double refrac- tion temporarily produced in iso- tropic bodies, 241, 342. Williams (C. G.) on the presence of pyridine among the volatile bases m the naphtha from the bituminous shale of Dorsetshire, and on the fractional crystallization of plati- num-salts, 209; on a method of obtaining rapid adjustments with Wollaston's goniometer, 430. Williamson (Prof.) on some new de- rivatives of chloroform, 405; on nitroglycerine, 548; on a new phosphite of aethyle, ib.; on the constitution of coal-tar creosote, 551. Wind, on the changes of, in a cyclone, 469. Woods (Dr.T.) on the probable nature of the sun's body, and on a new process for rendering collodion more sensitive, 24, 213. Zinc, on the occurrence of, in the vegetable organism, 156, END OF THE TH VOLUME. J'kU.Ma^. Ser.^. Vol (9. PL I. 2 % \\ '\ J '^ achuiL si^t. \ \ -^^-te^gs^ \\ A \ \ \ \ !2 'J \0\ -Ar^ Fi^. 1. Thz]..Ma^. Ser. 4.Yo\.8.^U\. Fig. A. I \ V 0 12 Scale, forFws.l&2. H V-^—i h 4- 5 B 7 ScoIa for FigsA.S). &3. #^ m E ^,. ^"^^^SS^ ■U".,. . fsf...' m' ^^'t ^ ^-^^^