96 



NA TURE 



[November 25, 1909 



fractional powers; in (he alg'ebraic theory it is almost 

 impossible to avoid tliis, except by tedious divagations, 

 but in tlie tlieory of numbers sucli symbols ought to 

 be avoided if possible, and their occurrence here may 

 cause some readers a shade of regret. G. B. M. 



LISSAJOUS'S FIGURES. 

 Harmonic Vibrations and Vibration Figures. By J. 



Goold, C. E. Benham, R. Kerr, and Prof. L.' R. 



Wilberforcc. Edited by H. C. Newton. (London : 



Newton and Co., n.d.) Price 6s. net. 

 '"yHE four authors of this book have each contributed 

 ^ an account of the construction and use of appa- 

 ratus which they have invented or brought to perfec- 

 tion, the several parts of the book being independent of 

 one another, but related by the similarity of the sub- 

 ject-matter. Lissajous's figures were originally intro- 

 duced as a convenient method of illustrating optically 

 or mechanically acoustic phenomena, but the beauty 

 and perfection of the results obtained by the compound 

 pendulum of Tislcy, and later by the twin elliptic pen- 

 dulum of Goold, have made the subject sufficiently 

 attractive to be pursued for its own sake. As two 

 leading scientific publishers declined to take the book 

 on the ground that it could not pay, we are indebted 

 to Messrs. Newton and Co. for rescuing and producing 

 a book which will be valued in many quarters. 



Mr. Benham writes the history of the harmono- 

 graph, and describes his own triple pendulum and his 

 own modification of Goold's twin elliptic pendulum. 

 He also gives valuable information to anyone who 

 would construct his apparatus as to the details which 

 are necessary for success. The construction of the 

 ruling pen, choice of inks or dyes, the selection of suit- 

 able paper, interesting dodges with photographic 

 plates or with successive chemicals, are a few only of 

 the tips or dodges described. The extremely beautiful 

 stereoscopic effects obtained by viewing two nearly 

 identical harmonograph figures with a stereoscope arc 

 described and illustrated, as is the curious change 

 which occurs when such a pair of figures are slowly 

 turned round at the same time, so as to change their 

 relative aspect, the series of lines all appearing on the 

 surface of a cylinder in the one position, and gradually 

 merging into a series, each of which lies between the 

 last one and the axis in the other position. In the 

 case of figures drawn by the twin elliptic pendulum, 

 where it would be next to impossible to draw two suc- 

 cessive figures which should be sutTicicntly alike, the 

 ingenious plan is adopted of selecting those which 

 have a two-fold symmetry, but in which the two halves 

 on opposite sides of the centre are not quite identical, 

 and then simply turning one upside down, in order to 

 obtain stereoscopic shell-like structures of wonderful 

 beauty. Several examples of the marvellous beauty of 

 the twin elliptic pendulum's work are given, in which 

 it is difficult to know whether the forms of the curves 

 or the water-mark patterns arc the more to be ad- 

 mired. 



Visitors at soiri^es of the Royal .Society will remem- 

 ,bcr the cuncs drawn by Mr. Goold's big twin elliptic 

 pendulum, ,is also that queer vibrating and droning 

 NO. 2091, VOL. 82] 



steel plate, which gave rise to so many curious phen- 

 omena. One passage from Mr. Goold's description 

 may here be quoted. 



" If ... a small chain be thrown on the vibrating 

 pl.ilc, it will immediately settle itself on the curved 

 lino between the vortices and . . . will crawl away to 

 the nearest vortex, and there coil itself up like a ser- 

 pent, continuing to rotate as long as the plate remains 

 sulliciently excited." 



This is one only of a number of curious results ob- 

 tained by Mr. Goold. 



Mr. Richard Kerr describes a form of geometric 

 pen, capable of producing very beautiful patterns. This 

 is followed by an account of Mr. Lewis Wright's 

 method of projecting Lissajous's figures on .1 screen, 

 using reeds in the place of tuning forks, and Prof. 

 Wilberforce describes his well-known sympathetic 

 vibrations obtained by the aid of one or two torsion 

 springs. 



This is an excellent book for tlie Christmas holidays. 



C. V. Boys. 



OUR BOOK SHELF. 

 Cattle oj Southern India. By Lieut.-Col. W. D. 



Gunn. Department of Agriculture, Vol. III., 



Bulletin No. 60. Pp. 65 ; plates. (Madras : 1909.) 



Price 3i. 

 ;\ltiiougii the existence of a number of local breeds 

 and sub-breeds of Indian humped cattle {Bos indiciis) 

 is familiar to .'\nglo-Indians, comparatively little is 

 known about them in this country, and it is, there- 

 fore, highly satisfactory that Col. Gunn, Superin- 

 tendent of the Indian Civil Veterinary Department at 

 Madras, has furnished us with this elaborately illus- 

 trated account of the various types to be met with in 

 sovithern India. It is, however, a matter for regret 

 that the author did not see his way to make his work 

 complete by including the breeds found in other parts 

 of India. As to the origin of humped cattle, the 

 author is silent, and perhaps wisely so, since, so far 

 as we are aware, nothing definite has hitherto been 

 ascertained with regard to this subject. 



If we rightly understand him — and his classification 

 is by no. means so clear and unmistakable as it might 

 be — the author considers that there are two main types 

 of large-humped cattle in southern India, namely, the 

 .Mvsorc and the Ongolc, or Ncllore. The former, 

 which are characterised by the long, more or less 

 upwardly directed, slightly tapering horns, and gener- 

 ally iron-grey or bluish colour, are, however, 

 divisible into a number of sub-breeds, such as the 

 .\mrat Mahal, Ilallikar, Alumbadi, &c., all of which 

 come under the native designation of Doddadana, or 

 large cattle, in contradistinction to the Nadudana, or 

 ordinary small village cattle. The finest of all are the 

 cattle of the .Amrat Mahal breed, which were formerly 

 owned by Tippu Sultan, but became the property of 

 the British Government after the fall of Seringapatam, 

 although the management of the herds remained for a 

 time under the control of the Maharaja of Mysore, on 

 condition of his supplying a specified number of 

 bullocks. In the old days of Indian warfare these 

 cattle were of the greatest value for transport-pur- 

 poses on account of their rapid pace. 



The Nellore, or Ongole, cattle, on the other hand, 

 carry short and somewhat stumpy horns, which are, 

 however, longer in cows than in bulls, and have an 

 outward and slightly backward direction. Formerly 

 black-and-white was in fashion, but white is 



