November 28, 1901] 



NA TURE 



95 



on which the properties of the instrument depend is a unicursal 

 curve of the sixth degree, and Prof. Chrystal showed how, by 

 making a templet in the form of part of the curve, the tri- 

 section of a given angle could be easily effected with the use 

 of a pair of compasses. 



Cambridge. 

 Philosophical Society, November ii. — Mr. W. Bateson, 

 vice-president, in the chair. — The unit of classification in 

 systematic biology, by Mr. II. M. Bernard. The writer 

 described the difticulties he had experienced in grouping the 

 stony corals into genetic groups, and maintained that the time 

 had come when for such unstable groups a new technique was 

 urgently required. The present unit of classification, the only 

 one we had at our disposal, was the species. Hence if these 

 are not discoverable the work is brought to a standstill. His 

 work with the stony corals had suggested to him a geographical 

 method of designating the varying forms as the units for work. 

 These forms he proposed to arrange in geographical lines. 

 Upon the chart of each genus thus obtained he proposed to 

 arrange the different structural variations exhibited within the 

 genus, and hoped to find in this way a powerful and searching 

 instrument for morphological study by means of which in time a 

 natural classification may be built up. — An exhibition of fishes 

 and amphibians to illustrate new methods of mounting 

 specimens for museums, by Mr. J. S. Budgett.— Notes on the 

 development of Sagitia, by Mr. L. Doncaster. The paper 

 confirmed O. Hertwig's account of the development in most 

 points, but showed that Btitschli's account of the formation of 

 the head-ccelom was correct. Sections were described showing 

 the temporary obliteration of the ccelom and the origin of the 

 muscles. The genital cells were described, and the origin of 

 the posterior septum between them during larval life. The 

 development of the genital ducts was discussed, and this, 

 together with the mode of origin of the transverse septa and 

 absence of nephridia, led to the rejection of the view that the 

 Chajtognatha are connected with Annelids. 



Dublin. 

 Royal Irish Academy, November ii.— Prof. R. Atkinson, 

 president, in the chair.— Prof. Charles J. Joly read a paper on the 

 interpretation of quaternions as point-symbols. The author 

 explained a convention by means of which a quaternion may 

 be interpreted as the symbol of a weighted point. He assumes 

 an arbitrary origin, and writing 



?=(i-t-OQ)S?, OQ = V?/S?, 

 he interprets the quaternion q as denoting the point O at the 

 extremity of the vector VV/Sy drawn from the origin. The 

 weight attributable to this point is Sry— the scalar part of the 

 quaternion— so that multiplication by a scalar leaves the repre- 

 sentative point unchanged and merely alters the weight. He 

 gave some examples of applications to projective geometry, and 

 pointed out that the equations 



S'/(/+/')'/ = o, S^( /•-/')/ = 

 represent respectively the eqiiation of the general quadric surface 

 and the equation of tlie general linear complex, /being a linear 

 quaternion function and/' being its conjugate. The equations 

 of the reciprocals of these loci are simply 



The principle of duality presents itself with perfect naturalness, 

 and a quaternion may also be regarded as the symbol of a plane! 

 Thus two objections to the calculus of quaternions have been 

 removed— the want of a point symbol and of a concrete in- 

 terpretation for a quaternion— and, what is in the author's 

 opmion of much greater importance, the whole field of pro- 

 jective geometry is rendered easily tractable by quaternion 

 methods. —Prof. Joly also read a paper on quaternion arrays. 

 In the previous paper the author employed and extended a most 

 useful but neglected notation of Hamilton's (" Elements," art. 

 365 [6]) in order to define lines, planes and volumes in terms 

 of two, three and four quaternions or points. In this paper the 

 notation is further extended, and the vanishing of the array with 

 ijuaiernion constituents 



( a,, a.,, a^ a„ \ 



5^1, A„ ^3 bJ , 



j > (« columns, m rows), 



\Px, A. /3 ■■■■'■■"pu) 

 NO. 1674, VOL. 65] 



expresses the possibility of determining n scalars /[, A,, /„, 



so that 



2^131 = 0, 2/'iii = o, »-/i = o. 



The laws of expansion and of manipulation of these quaternion 

 arrays are explained, and it is pointed out that the quotient of a 

 two-row and a one-row array 



^fa,fbjc,fd\,^ ^ , 



\ a, b, c, d, j ' ' ' ' ' ' 

 comprises all the Hamiltonian invariants of the linear quaternion 

 function y— a result easily extended to the case of any number 

 of functions by increasing the number of rows in the first array. 

 As another example of the use of these arrays, if ju is the couple 

 and A. the force of a wrench, the origin being base-point, the in- 

 variants of an «-system of screws are at once deducible from the 

 array, 



f Ml. Ma. Ma 



M„l 



— Mr. Frederick Purser read a paper on the application of 

 Bessel's functions in the theory of elasticity. This paper 

 attempts to use Bessel's functions in the discussion of the 

 elastic equilibrium of a right circular cylinder. It is shown 

 that the elastic forces and displacements at any point when no 

 bodily forces act can be expressed as the sum of two series, one 

 of which proceeds by products of exponential functions of c and 

 ordinary Besselians in r, the other by products of trigonometrical 

 functions of 2 with Besselians in r of imaginary argument. The 

 method is also apphed to certain cases of applied bodily force, 

 and various practical problems are considered both with a view 

 to approximate solution and as illustrating the St. Venant 

 theory of equipollence, on which it is conceived the present 

 method throws some light. 



Paris. 

 Academy of Sciences, Nov. 18.— M. Fouque in the chair. 

 — On the periods of double integrals in the theory of algebraic 

 functions of two variables, by M. Emile Picard.— On a modifi- 

 cation in the mode of use of an electrical thermometer, for the 

 determination of subterranean temperatures at the Museum of 

 Natural History, by M. Henri Becquerel. A description of a 

 new method of applying the thermocouple to the determination 

 of temperature at a distance. A d'Arsonval galvanometer, the 

 deviations of which are proportional to the intensities of the cur- 

 rents, is used, and the scale of this galvanometer is calibrated in 

 degress by direct comparison with the thermocouple and a 

 mercury thermometer. One junction of the thermocouple is 

 then placed in the point the temperature of which is required, 

 and the other in mercury along with a thermometer. Since the 

 deflection of the d'Arsonval is now proportional to the difference 

 of these temperatures, the graduated scale is displaced parallel 

 to itself in such a manner that the zero of the galvanometer 

 coincides with the line indicating the temperature of the junction 

 in the mercury. On closing the circuit the reading on the scale 

 now indicates the temperature of the distant junction. — The 

 stu'By of ammonium amalgam, by M. Henri Moissan (see p. 89). 

 —On the Perseids of 1901, by M. Perrotin. There has been 

 an increase in the number of meteors from the Perseids during 

 the present year. The observations at Nice were somewhat 

 incomplete on account of the weather. On August 10 there 

 was an average of 10 stars per hour, on the nth, 25 to 30 per 

 hour, on the 12th, 32 were counted during the 40 minutes 

 observations were possible, and only 24 were seen on the two 

 following nights.— Observations of the Perseids made at Athens, 

 by M. D. Eginitis. These stars were seen on the four nights 

 commencing on August 9, and were counted up to the sixth order. ' 

 About 500 meteors were observed in all, the maximum display 

 being on the nth, when on the average 31 per hour were seen. — 

 On a manometric differential log, by MM. Emile Raverot and 

 Pierre Belly. The two sides of a manometer are connected to 

 two tubes under the water in the same horizontal plane, one tube 

 opening in the direction of motion of the vessel, the other being 

 at right angles. In the case of the tube in the direction of 

 motion, the pressure depends partly upon the velocity of the 

 vessel and partly upon the variable static pressure due to its 

 depth below the surface of the water. The latter effect is com- 

 pletely compensated by the second tube, and by the introduc- 

 tion of a suitable damping arrangement the readings of the 

 manometer are a function of the speed of the vessel alone. 

 The scale is graduated empirically by runs over a measured 

 distance. — The law of radiation at low temperatures, by M. 

 Compan. A series of experiments were carried out on the rate 



