432 PROFESSOR TAIT ON 



2. I next considered how to take account, in my equations, of the effects of the 

 rotation ; and it appeared to me most probable that this could be done, with quite 

 sufficient approximation, by introducing a new force whose direction is perpendicular at 

 once to the line of flight and to the axis of rotation of the ball : — concurrent in fact with 

 the direction of rotatory motion of the foremost point of the surface. Various considera- 

 tions tended to show that its magnitude must be at least nearly proportional to the speed 

 of rotation and that of translation conjointly. Among these there is the simple one that 

 its direction is reversed when either of these motions is reversed. This may be general- 

 ised ; for if the vector axis, e, be anyhow inclined to the vector of translation, a, the 

 direction (why not then the magnitude also, to a constant multiplier pre's) of the deflect- 

 ing force is given by Vea. Another is that, as the resistance (i.e. the pressure) on the 

 non-rotating ball is proportional to the square of the speed, the pressures on the two 

 front semihemispheres of the rotating ball must be (on the average) proportional to 

 (v + eco) 2 and iv — ew) 2 respectively : — where v is the speed of translation, o> that of 

 rotation, and e a linear constant. The resultant of these, perpendicular to the line of 

 flight, will obviously be perpendicular also to the axis of rotation, and its magnitude will 

 be as v<o. But I need not enumerate more arguments of this kind. In the absence of 

 anything approaching to a complete theory of the phenomenon we must make some 

 assumption, and the true test of the assumption is the comparison of its consequences with 

 the results of observation or experiment. This I have attempted, with some success, as 

 will be seen below. 



3. Another associated question, of greater scientific difficulty but of less apparent 

 importance to my work, was the expression for the rate of loss of energy of rotation 

 by the ball. Is it, or is it not, seriously modified by the translation ? But here I had 

 what seemed strong experimental evidence to go on, afforded by the fact that 1 had often 

 seen a sliced or heeled ball rotating rapidly when it reached the ground at the end of its 

 devious course. This is, of course, what would be expected if the deflecting force were 

 the only, or at least the principal, result of the rotation : — for, being always perpendicular 

 to the direction of translation, it does no work. But, on the other hand, if the friction 

 on a rotating ball depends upon its rate of translation, the ball while flying should 

 lose its spin faster than if its centre were at rest. This is a kind of information which 

 might have been obtained at once from Magnus' experiments, but unfortunately 

 was not. 



4. As I felt that there was a good deal of uncertainty about the whole of these 

 speculations, I resolved to consult Sir G. G. Stokes. I therefore, without stating any 

 arguments, asked him whether my assumptions appeared to him to be sufficiently 

 well-founded to warrant the expenditure of some time and labour in developing their 

 consequences : — and I was much encouraged by his reply. For he wrote : — 



" if the linear velocity at the surface, due to the rotation, is small compared with 

 the velocity of translation, I think your suggestion of the law of resistance a reasonable 

 one, and likely to be approximately true. This would make the deflecting force vary as 



