March 29, 1894J 



NA TURE 



521 



given by the craniometric methods of Broca and Jhering. M. 

 Lapouge measured the skulls exactly one year after Dr. Wilser, 

 and during the whole of that time they had been thoroughly 

 dried under the sunny roof of his laboratory at Montpelier. He 

 also made a double series of measurements of the length and 

 breadth of the skulls, first, by Broca's method, with a pair of 

 calipers, and secondly, with Ammon's sliding compass, and 

 after the method of Jhering, in precisely the same manner as 

 Dr, Wilser's observations had been made. The results ob- 

 tained are exceedingly interesting, and show that, in competent 

 hands, it is a matter of perfect indifference which instrument is 

 used, and that although, as one would naturally expect, the 

 cephalic index is slightly greater when Jhering's method is em- 

 ployed, yet the difference is so small as to be almost insignificant. 

 By Jhering's method the mean index of the series is 82'54, 

 while Broca's index is 81 "87. Both the length and breadth of 

 the skull appear to be somewhat increased by drying, and the 

 value of the cephalic index is a little raised, that obtained by 

 Dr. Wilser from the fresh skulls being 8i"84, while M. 

 Lapouge's measurements of the dried skulls gave an index of 

 82*54. It will be observed that the difference is almost 

 exactly the same as the excess of Jhering's index over Broca's. 

 The flattening of skulls under the influence of desiccation is 

 a phenomenon well known to all anthropologists, and in the 

 case of these Karlsruhe skulls the mean diminution of height 

 was more than a centimetre, so that, although the hygro- 

 metric conditi'-ns under which skulls are measured do not 

 seem to affect the cephalic index of a series to an appreciable 

 degree, the vertical and transverse indices of damp and dry 

 crania are not comparable with one another. 



SOCIETIES AND ACADEMIES. 



London. 



Physical Society, March 9.— Prof. A. W. Riicker, F.R.S., 

 President, in the chair. — Prof. O. Henrici, F.R. S., made a 

 communication on mathematical calculating machines, especially 

 a new harmonic analyser. After mentioning the general 

 principles on which such machines are based, the author 

 showed a new arithmometer devised by Prof. Selling, in which 

 the jerky motions of the numeral wheels common in such instru- 

 ments are eliminated, and the operations simplified. Another 

 arithmometer of very compact design, named the "Brunsviga," 

 had been placed on the table by Prof. Boys. The simple and 

 ingenious "hatchet" integrator was then shown. It resembles 

 a small hatchet with a tracing-point projecting at right angles 

 to, and at the end of, the handle. Moving the point from near 

 the centre of mass of any closed curve, round the curve once 

 and back to the starting-point, the distance between the initial 

 and final positions of the hatchet-head is a measure of the area 

 of the curve. The instrument has been found very useful for 

 indicator diagrams. A Hine and Robertson's planimeter (lent 

 by Prof. Perry), an Amsler planimeter combined with a pento- 

 graph for measuring small areas, an Amsler integrator to give 

 areas and first moments, and a beautiful sphere and cylinder 

 rolling-integrator of great accuracy, by Coradi of Ziirich, were 

 shown, as well as an ingenious integraph devised by Abdank 

 Abakonowitcz. Passing on to harmonic analysers, Pref. 

 Henrici explained the object of such instruments, viz. to deter- 

 mine the coefiicients in Fourier's expansion for any periodic 

 curve, 



j' = Ao-l- Aj cos 0-f A, cos 20- 



4-Bi sine -J- Bo sin 20 + 



and briefly described Lord Kelvin's instrument now in use at 

 the Meteorological Office. This machine gives the first term 

 and three pairs of coefficients A and B, but is large and expen- 

 sive. The author had endeavoured to devise a simple and more 

 portable instrument, and now described the various stages in 

 the evolution of his new analyser. Using Clifford's method of 

 wrapping the curve round a cylinder, he saw that by imparting 

 a simple harmonic motion to a plane tangential to the cylinder, 

 which plane carried an Amsler planimeter whose tracing point 

 followed the intersection of the plane with the curve, as the 

 cylinder rotated, any coefficient A„ or B„ could be determined. 

 This arrangement had considerable friction, and only gave one 

 coefficient at a time ; it also necessitated readjustment of the 

 period of the harmonic motion for each pair of terms. Another 



machine founded on integration by parts was then constructed, 

 in which the relative periods of cylinder and registering wheels 

 was adjusted by a disc and roller, the motion being transmitted 

 to the wheels by bands driven from the disc spindle. This gave 

 A;, and B„ at one operation. Mr. A. Sharp used this machine 

 for some time and then designed an inversion of it, in which 

 the curve was laid out flat and the machine rolled over it. This 

 arrangement greatly facilitated the multiplication of registering 

 wheels, and thereby enabled several pairs of coefficients to be 

 determined at once. The first machine of this kind showed 

 several small errors which were avoided in a second instrument, 

 a specimen of which, made by Coradi, was exhibited and de- 

 scribed. A rectangular frame carried on three rollers (two 

 being fixed to the ends of a long axis) traverses the paper in 

 the direction of y, and the tracing point is fixed to a carriage 

 whicli moves on the frame in a direction perpendicular to y, 

 i.e. in the direction of 0. A band is attached to this carriage 

 and imparts a motion proportional to to two horizontal axes 

 (one for the A coefficients, and one for the B's), placed above 

 and parallel to the long roller axis above mentioned. Each of 

 the two axes carries five pinions having teeth in the ratios I, 2, 

 3, 4, 5, respectively, which gear with crown wheels fixed to 

 vertical spindles. The latter, therefore, rotate through angles 

 proportional to 0, 29, 36, 46, and 50. To the lower ends of 

 these spindles horizontal rings are attached, in which the bear- 

 ings of a registering wheel are formed ; each wheel rests on a 

 cylinder carried by the long axis, and rolls or slides thereon 

 according as its axis is parallel or perpendicular to that of the 

 cylinder. Moving the tracing-point once round the curve gives 

 five pairs of coefficients. By changing the driving-band to other 

 pulleys so as to turn the pinions at different rates relative to the 

 Q movement, the 6th, 8th, loth, and 7th and 9th pairs can be 

 determined. The chief drawback of the instrument is that the 

 registering wheels are not easy to read, whilst the back-lash of 

 the crown wheels and pinions introduces small errors. In the 

 latest form of instrument toothed wheels are dispensed with, 

 and glass spheres carried in frames on the vertical spindles roll 

 on the horizontal cylinders ; each sphere actuates two register- 

 ing wheels on fixed areas at right angles to each other, and 

 these give respectively the sine and cosine coefficients. The 

 number of vertical spindles is therefore halved, and the instru- 

 ment greatly simplified. These details have been introduced by 

 Coradi. A working drawing of another analyser, designed by 

 Mr. Sharp, which gives the amplitude and epoch of the curve 

 resulting from each pair of terms in Fourier's expansion, was 

 exhibited. The discussion on Prof. Henrici's communication 

 was postponed until next meeting. — Mr. H. Wilde, F.R. S., 

 then exhibited and described his " magnetarium," This con- 

 sists of a hollow geographical globe, wound all over the inner 

 surface with insulated wire in planes parallel to the equator. 

 Within this globe is a sphere wound with wire on its surface, 

 and having its axis inclined at 23 i° to that of the outer globe. 

 By me:ins of epicyclic gearing the spheres can be made to rotate 

 at slightly different rates. When electric currents of suitable 

 strength are passed through the two windings, the magnetic 

 condition of the earth can be imitated, both as regards distribu- 

 tion at any epoch, and the secular variations. A better result 

 was obtained by putting sheet iron over the land areas, and a 

 still closer approximation by using thin iron over the water 

 areas. A magnetic chart and tables giving the magnetic ele- 

 ments at various places for different epochs as determined 

 by the magnetarium were shown. The author mentioned 

 that recent observations by the United States Survey 

 at Ascension Island, and by Prof. Thorpe in Senegambia, 

 had confirmed results obtained by his instrument. The 

 President said he had tried the apparatus, and found the 

 Siberian oval closely imitated. The secular variations at 

 Greenwich were also well shown. In South America the 

 approximation was not so good. In reply to a question by Mr. 

 Blakesley, Mr. Wilde said the present position of the pole of 

 the inner sphere was 84' W,, 67° N, 



Geological Society, March 7. — Dr. Henry Woodward, 

 F,R.S., President, in the chair.— The Secretary announced 

 that a portrait of the late Sir Richard Owen had been pre- 

 sented to the Society by Mr. Ernest Swain. — The following 

 communications were read :— The systematic position of the 

 Trilobites, by Mr. H. M. Bernard. The author, in his work 

 on "The Apodidas," endeavoured to show that Apus was 

 the ancestral form of all existing Crustacea except the ostracoda, 



NO. 1274, VOL. 49] 



