to 



NATURE 



[Nov. 1 6, 1876 



artistic world of music, great as the individual acquire- 

 ments of some members as executants may be, is essen- 

 tially a world of handicraftsmen ; practising indeed a very 

 subtle art, but led entirely, according to Aristotle's defini- 

 tion, by rules, and not by laws. 



The function of the scientific man is to expand these 

 technical rules of art into the conscious and explained 

 laws of science. How nobly this duty has been performed 

 by Chladni, by Savart, by Wheatstone, and above all by 

 Helmholtz, few artists are aware ; nor indeed has there 

 been hitherto any easy mode for their obtaining such in- 

 formation. They have been somewhat in the habit 

 of sneering at the theorist as a "mathematician ;" nor is 

 it very remarkable that the other party, like the Dublin 

 fishwife whom O'Connell called a parallelopipedon, should 

 retaliate with even more opprobrious epithets. Hence 

 old threadbare jokes about " catgut-scraping," Lord Ches- 

 terfield's contempt of musicians, and the like, which 

 culminate in the epigram on Handel and Buononcini. 

 This century is beginning to recognise that varying styles 

 of musical art are not a mere question of " Tweedle- 

 dum and Tweedledee, ' and that the " fiddler," though in 

 an utilitarian point of view unnecessary to the main- 

 tenance of life, is highly conducive to education and 

 civilisation. If artists are to maintain the improved 

 position of later years it must be by cordially fraternising 

 with the man of science, for thus only can their art 

 hope to acquire the dignity and generalisation which are 

 the prerogatives of em(rTi]fj.r). 



It is to be noticed that this view of the case appears to 

 have been taken by many of our best professional mu- 

 sicians ; for the list of members whicii heads either volume 

 of these "Proceedings" is far more remarkable for indi- 

 vidual eminence of the names than for their multitude. It 

 is to be hoped that such a conviction will continue to 

 extend. The number of points in which music is con- 

 terminous with pure science is considerable, and is daily 

 increasing. Music, moreover, is among the most power- 

 ful means we have for cultivating that delicacy of the 

 senses on which all accurate observation depends. It 

 has, as yet, been too apt to fall into the hands of a sect 

 or clique, whose disposition is naturally exclusive, and 

 whose objects have often been the reverse of elevated. 

 But with the great advance which has of late years 

 taken place in general musical knowledge throughout 

 England, and by the fostering care of societies like the 

 present there is ground for anticipation that the science 

 of music may rise to the esteem and consideration as an 

 educator and humaniser which it once held in the writings 

 of Plato, and in the palmiest days of old Greek thought. 



W. H. Stone 



ON THE RESISTANCE OF THE AIR TO THE 

 MOTION OF PROJECTILES 



n^HE experiments made by Hutton to determine the 

 -*■ resistance of the air to the motion of shot were 

 carried out by fir;ng small spherical balls into the receiver 

 of a gun-pendulum. As little confidence could be felt in 

 applying his results to the large service shot at present 

 in use, on the formation of the Advanced Class of Royal 

 Artillery Officers, Woolwich, in 1864, it was thought de- 

 sirable that a systematic course of experiments should be 

 made with elongated shot, and upon a much larger scale.' 

 Afterwards, similar experiments were made with round 

 shot. 



The method of experimenting pursued by Hutton ap- 

 peared to have been carried to its useful limits, and 

 although a large ballistic pendulum had been constructed 

 for Government, it was practically useless. The chrono- 

 graph used in the experiments above referred to was 

 invented and constructed for that purpose by the Rev, F. 

 Bashforth, at that time Professor of Applied Mathematics 

 to the Advanced Class, and Official Referee to the Ord- 



nance Select Committee. This instrument is now in the 

 Loan Exhibition, South Kensington. 



A complete collection of the " Reports on Experiments 

 made with the Bashforth chronograph, 1865-1870" 

 (marked 84, B, 1941), has been published by Government, 

 at the nominal price of one shilling.^ It will therefore 

 be sufficient here to state that the first set of experiments 

 was made to test the new chronograph, in which the velo- 

 city of the shot varied from about 1,150 fs. to 1,060 fs. 

 The resistance of the air was found to vary as the cube 

 of the velocity. The next experiments were made with 

 elongated shot of equal diameters and different forms of 

 head. The velocities here varied from 1,500 f s. to 1,090 f s., 

 and the law of resistance still appeared to be the cubic. 

 Lastly, a course of experiments was made with elongated 

 and spherical projectiles (solid and hoilow) of 3, 5, 7, and 

 9 inches in diameter. The velocities of the elongated 

 shot varied from 800 f s. to 1,750 f.s., and those of the 

 spherical from 800 f s. to 2,400 f.s. At a given velocity 

 the resistance of the air varied as the square of the dia- 

 meter. But when the coefficient of resistance was ob- 

 tained by dividing the numbers expressing the resistances 

 by the cube cf the corresponding velocity, the result 

 was not now constant through these great variations of 

 velocity. This coefficient was found to increase rapidly 

 from 900 fs. up to 1,050 fs.,and from 1,100 f.s. to 1,300 fs. 

 it was nearly constant, and for higher velocities it gradu- 

 ally decreased with the increase of velocity. The pub- 

 lished reports give a full account of every round fired. 

 Unfortunately it has not hitherto been found possible to 

 express the coefficient of resistance by a simple function 

 of the velocity. Mr. Bashforth has made use of the cubic 

 law in his treatise on the motion of projectiles (1873). 

 The trajectory is divided into arcs, and each arc is sup- 

 posed to be described, while the coefficient of resistance 

 retains its mean value for that arc. 



In a tract on the remaining velocities, &c., of several 

 service shot (1871),'-^ Mr. Bashforth stated : — " For ogival- 

 headed elongated shot, the resistance of the air may be 

 said to vary roughly as the sixth power of the velocity for 

 velocities 900-1,100 f s. ; to vary as the third power for 

 velocities, 1,100-1,350 f.s.; and to vary as the second 

 power for velocities above 1,350 f.s." 



General Mayevski, Professor of Ballistics to the Aca- 

 demy of Artillery, St. Petersburg, published a work on 

 Ballistics in Russian, in 1870, at the expense of the State. 

 A translation of the more interesting chapters of this 

 work was published in French by the author, in 1872.^ 

 In the preface to the latter work he states that " Les xi- 

 sultats des experiences faites par M. Bashforth en Angle- 

 terre sur les projectiles oblongs ont €i€ ddduits des 

 donndes insdrdes dans les Proceedings of the Royal Artil- 

 lery Institution, Woolwich, 1868. Les experiences de St. 

 Petersbourg sur la resistance de Fair au mouvement des 

 projectiles sphdriques et oblongs ont €i€ faites par nous en 

 1868 et 1869, etleurs resultats sont pour la premiere fois 

 publids dans notre traitd. Afin que les expressions de 

 la resistance reprdsentent, avec une approximation suf- 

 fisante, les rdsultats de nos experiences et ceux des expe- 

 riences anglaises, faites avec des appareils perfectionnes, 

 et que ces expressions permettent en mecne temps une 

 integration facile, quoique par approximation^ des equa- 

 tions differentielles du mouvement, nous avons 2Axxv\?, pour 

 les projectiles sphei'iqties, dans les limites des vitesses de 

 530""= %. 376™^ (i 739-1230 fs.) la resistance de Fair pro- 

 postionelle au carrl de la vitesse, et nous avons exprimd, 

 &, partir de la vitesse de 376"' (1230 fs.) jusqu'aux 

 petites vitesses, la resistance de I'air par un binome dont 

 le premier terme est proportionel k la deuxifeme puissance 

 de la vitesse, et le second k la quatri^me puissance 

 de la vitesse ; pour les projectiles oblongs, quand leur axe 

 de figure coincide avec la direction du mouvement, nou 



W. Clowes and Son ; AHen ; Mitchell ; Longmans and C ■>- 

 London : Spon. ^ Paris : Gauthier-Viilars. 





