THE PATH OF A ROTATING SPHERICAL PROJECTILE. 429 



a homogeneous sphere really amounts to no more than this : — that, since friction is 

 greater where the density of the air is greater, the front of the ball suffers greater friction 

 than does the back. Thus there is a lateral force, which he shows to be very small, 

 tending to deflect the ball as if it were rolling upon the air in front of it. As this is 

 exactly the opposite of the effect described by Eobins, I feared at first that I must have 

 misunderstood Poisson's mathematics. But this feeling gave way to one of astonishment 

 when I read further ; for there can be no doubt of the meaning of the following passage 

 which occurs in his comments on the investigation : — 



" C'est ce que Ton peut aussi regarder comme evident d, priori, si Ton considere que 

 cette deviation est due a l'exces de la densite de l'air en avant du projectile, sur sa densite 

 en arriere ; exces qui donne lieu a un plus grand frottement du fluide, contre l'hemisphere 



anterieur, et a un moindre contre l'hemisphere posterieur il en resultera 



une force horizontale qui poussera ce point [the centre of inertia] dans le sens du plus 

 grand frottement ou en sens contraire de la rotation a laquelle il repond, c'est-a-dire vers 

 la gauche, quand les points de la partie anterieure du projectile tourneront de gauche 

 a droite, et vers la droite, lorsqu'ils tourneront de droite a gauche." Recherches, &c, 

 p. 119. 



In fact, Poisson's elaborate investigation leads to no term, in the expression for 

 the normal component of the force, which can have different values at corresponding 

 points of the two front semihemispheres of the projectile : — and it is to a force of this 

 nature that Newton's remarks and Robins' experiments alike point. 



The paper of Magnus # commences with a historical sketch of the question, but it 

 contains no reference to Newton. The author obviously cannot have read Robins' 

 papers, for he mentions his work only once, and in the following altogether inadequate 

 and unappreciative fashion : — 



" Robins, der zuerst eine Erklarung dieser Abweichung in seinen Principles of 

 Gunnery versucht hat, glaubte, dass die ablenkende Kraft durch die Umdrehung des 

 Geschosses erzeugt werde, und gegenwartig nimmt man dies allgemein an." 



Had Magnus known of the experiments with the crooked gun-barrel and the rotating 

 pendulum, he would surely have employed a stronger expression than " glaubte " ! For 

 Robins says (p. 208) of his own pendulum experiment : — 



" it was always easy to predict, before the ball was let go, which way it would 

 deflect, only by considering on which side the whirl would be combined with the progres- 

 sive motion ; for on that side always the deflecting power acted ; as the resistance was 

 greater here, than on the side where the whirl and progressive motion were opposed to 

 each other." 



This passage strongly resembles part of the extract already made from Newton's 

 letter. But Robins justly adds (two words have been italicized) — 



" This experiment is an incontestible proof, that, if any bullet, besides its progressive 

 motion, hath a whirl round its axis, it will be deflected in the manner here described." 



* Uber die Abweichung der Geschosse, Berlin Trans., 1852. 



