214 



NA TURE 



{Dec. 31, 1885 



the well-known "dark rings" of quartz. Each ring is due to one 

 wave being retarded in the quartz behind the other by an integral 

 number of wave-lengths, so the measurements give the directions 

 through the plate of quartz corresponding to a series of known re- 

 tardations. The relative retardation is, especially in a crystal of 

 weak double-refracting power like quartz, mainly dependent on 

 the distance between the two sheets of the wave-surface. Thus 

 my observations really give the separation between the two 

 sheets at various points, and it is in this separation that the 

 peculiarities of quartz are most strongly marked, and the various 

 expressions put forward by theory most widely divergent. 



I found it convenient to treat separately the region near the 

 axis, where the abnormal form of the wave-surface of quartz is 

 most obvious. I have compared my results with nine different 

 theories, each of which gives an expression of one of the two 

 following forms : — 



D" = Pi2sin-i(^+D(,=. 



D- = P„-sin-'(j) -t-Do'-cos'i <^ 



Here D is "the number of wave-lengths by which one wave 

 lags behind the other in air, after the light has traversed nor- 

 mally a plate of quartz I millimetre thick, the normal to whose 

 faces malies an angle if) with the optic axis." Dj is the value of D 

 when <J> = o, and is known from the rotatory power, and P, and 

 P.2 are constants to which the theories assign different values. 

 By inserting the observed values of D and 1^, I obtained a value 

 of Pj and P„ from each ring. The results from one plate about 

 20 millimetres thick were as follows : — 



<p ... 4° 24' 5°Sii' 6°5iV 7°4oJ' S° 23J' 9=38' 11° 41' 

 Pi ... I5'054 15-207 15-220 15-260 15-249 I5"258 15-269 

 Po ... 15-220 15-293 15-290 15-311 15-295 15-292 15-292 



Similar results were obtained from a second plate about 

 27 millimetres thick. 



From these figures I concluded that the second expression 

 was the correct one, and that P2=i5-3o± -oi. There is a con- 

 siderable discrepancy in the case of the first ring, of which two 

 possible explanations are given in the paper. 



Cauchy gives P^^ --- = 15-351, where a and b are the wave- 

 velocities perpendicular to the optic axis. 

 Lommel gives P2 = - 

 Kettler ,, P.,= 



a + b a-b 



a + b a-b 



2* 



= 15-486. 



San-au 



The other five, M.acCuUagh, Clebsch, Lang, Boussinesq, .and 

 Voigt, have the first form of expression giving 



T) a + b a-b . 



Pi = =15 306. 



2a a'\ 



Thus Sarrau alone succeeds in explaining the observations satis- 

 factorily. 



For the larger values o{ (p \ calculated on Sarrau's theory 

 what values of a-b were required to give the retardation 

 observed in each ring, and obtained as follows : — 



^fzth' 28- 7i' 

 •0037927 -0037931 



32° 7' 35° 34' 38° 36' 

 0037939 -0037932 -0037936 



a-b ... '0037916 '003792 



The observations on the plate cut parallel to the axis gave — 



<l> ••• - 53° 58' 57°"' 64° 45' 72" 13' 79° 53' 83° 40' 85' 37 

 a-d ... '0037949 -0037947 -0037945 -0037944 -0037943 -0037946 -0037944 



The observations were taken in the Cavendish Laboratory, 

 Cambridge, during the months of March and June, 1885. 



For full details as to the apparatus, the plates of quartz used, 

 the mode of observation, the precautions necessary, the tempera- 

 ture effects, and the calculations, reference must be made to the 

 paper. 



Edinburgh 



Royal Society, December 7.— Mr. J. Murray, Ph.D., 

 Vice-President, in the chair.— .Sir W. Thomson read a paper 

 on certain cases of motion of a liquid filling an ellipsoidal 

 hollow ; and a paper on the communication of motion from a 

 liquid to a rigid containing shell. He showed that the motion 

 of a hquid when rotating about the long axis of a prolate spheroid 

 IS essentially unstable, so that no great speed of rotation can be 

 got up in the liquid in this case by making the containing shell 



rotate about the long axis. — Prof. Turner showed that the 

 relative length and breadth of the sacrum may be taken as a test 

 of development in different races of mankind. In the higher 

 races the length exceeds the breadth. — Prof. Crum Brown read 

 a paper on a case of interlacing surfaces. In this paper he 

 extended the problem of the locking of threads to surfaces, 

 pointing out that only certain surfaces can be covered over by 

 such an interlacing system. For example, the sphere cannot be 

 so covered, while the cylinder and anchor-ring can. — Prof. Tait 

 communicated an elementary examination of the laws of collision 

 of two systems of spheres, showing as clearly as possible what 

 assumptions are necessary in obtaining average results, and how 

 they are justified. The case in which one system of spheres 

 gains energy from without, while the other loses to external 

 objects, is investigated, and shows that the final average energy 

 is not the same in the two systems, thus affording an escape 

 from the difficulties raised by Botzmann's theorem. — In a second 

 paper Prof. Tait defined Ihe mean free path as the average of 

 the free paths at any moment being described by all the particles. 

 The definition, as usually given, is the average speed of a 

 particle divided by the average number of collisions per particle 

 per second. When the former definition is employed, the factor 

 by which the mean free path is reduced in consequence of the 

 motion of the other particles, is found to be o'6S nearly, instead 

 of 0'7i nearly, as found from the second definition. 



Royal Physical Society, November iS. — Mr. B. N. Peach, 

 the retiring President, delivered an address on some of the rela- 

 tions of Palteontology to Geology, illustrated chiefly by examples 

 from the Scottish rocks. 



December 16. — Prof. Duns, Vice-President, in the chair. — 

 Prof. Turner, F.R.S., was elected President, and Mr. J. Harvie 

 Brown, Prof. Duns, and Prof. Ewart were elected Vice-Presi- 

 dents. — The Secretary read a paper by Mr. Robert Kidston, on 

 the species of the genus PalKo.xyris, occurring in British Car- 

 boniferous rocks. — A paper was read by Prof. Ewart, on the 

 hatching of herring in deep water. Prof Ewart pointed out 

 that during recent years the herring- fishing had undergone 

 marked changes in several respects : — (i) There had been a 

 great increase in the " take." In 1S20 only 450,000 barrels 

 were cured, while in 1885 neaidy 1,500,000 barrels were cured. 

 (2) There h.ad been a change in the fishing-ground ; tlie greater 

 number of the fish during the autumn are now caught from forty 

 to sixty miles offshore. (3) The herring captured during the 

 last few years off the east coast during the autumn were much 

 smaller than those captured some ten years ago. The Iierring 

 having, to a great extent, deserted the spawning-grounds in 

 the Moray Firth, it was feared that the shoals might diminish 

 in numbers, owing to the ova being unable to develop on the 

 deep off-shore banks. A reference to the charts showed that 

 the North Sea was, on the whole, very shallow — the fifty-fathom 

 line running from fifty to thirty miles from the coast — and that 

 there was only one small area (off Fraserburgh) where there 

 was 100 fathoms of water. By depositing artificially-fertilised 

 eggs in ninety-eight fathoms of water in Lochfyne, off Tarbert, 

 it was proved that the ova develop normally, and that the only 

 difference is one of time, the hatching being delayed owing to 

 the lower temperature of the deep water. It was pointed out 

 further that there was abundance of food for the fry in the off- 

 shore waters of the Moray Firth, and that the fry, on the second 

 day after hatching, were able to ascend at the rate of too fathoms 

 in five hours. — A communication was read from Mr. A. Smith 

 on the sucker fishes, Liparis and Lepadogaster. — Mr. Brook 

 called attention to a peculiar method of cell-division in the early 

 segmentation stages of fish ova. A series of vacuoles form in 

 the plane of cleavage either at the surface or in the interior of 

 the cell-protoplasm. By an increase in the size of these vacuoles, 

 the two new cells become separated. Several cells may, how- 

 ever, remain connected together by bridge-like strands of the 

 cell-plasma. This method of cell-division has been observed in 

 .Salmonidas and Gadidre, but most distinctly in the herring. — 

 Mr. Gulland read a paper on the sense of touch in Astacus, in 

 which he described the distribution and nature of the tactile 

 setcB and their corresponding nerve end-organs, and discussed 

 their origin and relations, and also the nature of certain glands 

 in the great claw. 



Mathematical Society, December II. — Dr. R. M. Fergu- 

 son, Presitlent, in the chair. — Prof. Tait communicated a paper, 

 which was read by Mr. William Peddle, on integrals occurring 

 in the kinetic theory of gases. Mr. Peddie explained a method 



