436 PROFESSOR TAIT ON 



space-rate of change of direction is increased, not only by the factor ( W + v)/v in the term 

 due to spin, but by a direct contribution from the resistance itself. The effect of a head- 

 wind in producing upward curvature, even in a " skimmer," is well known ; and we now 

 see that it is, at first, almost entirely due to the underspin which, without being aware 

 of it, long drivers necessarily give to the ball. As soon as sin<£ has, by the agency of 

 the underspin, acquired a finite value, the direct resistance comes in to aid the underspin 

 in further increasing it. We now see the true nature of the important service which (in 

 the hands of a powerful player) the nearly vertical face of a driving putter renders 

 against a strong wind. It enables him to give great translatory speed, with little 

 elevation, and with just spin enough to neutralize, for the earlier part of the path, the 

 effect of gravity. 



9. Before I met with Robins' paper, I had tried his pendulum experiment in a form which 

 gives the operator much greater command over the circumstances of rotation than does 

 his twisting of two strings together. Some years ago, with a view to measuring the 

 coefficient of resistance of air, even for high speeds, in the necessarily moderate range 

 afforded by a large room, I had procured a number of spherical wooden shells, turned very 

 thin. My object, at that time, was to make the mass as small as possible, while the 

 diameter was considerable : — but, of course, the moment of inertia was also very small. 

 So, when I fixed in one of them the end of a thin iron wire, the other end of which was 

 fastened to the lower extremity of a vertical spindle which could be driven at any desired 

 speed by means of multiplying gear, the wire suffered very little torsion except at the 

 moments of reversal of the spin. The pendulum vibrations of this ball showed almost 

 perfect elliptic orbits, rotating about the centre in the same sense as did the shell : — 

 and with angular velocity approximately proportional to that of the shell. These two 

 experimental results are in full accordance with the assumed law for the deflecting force 

 due to rotation. For, the ordinary vector equation of elliptic motion about the centre is 



cr = — m 2 a- . 



If the orbit rotate, with angular velocity O, about the vertical unit vector a, perpendicular 



to its plane, a- becomes 



p = a «»/* <r . 



Eliminate r from these equations, and we have at once 



p = -(m 2 -n 2 )p+2n a p. 



The part of the acceleration which depends upon the motion of translation of the 



bob : — viz. 



2Clap, 



is proportional to the speed, and also to O, that is (by the results of observation) propor- 

 tional to the rate of spin ; and it is perpendicular alike to a and to the direction of trans- 

 lation. These statements involve the complete assumption above. The other part of the 

 acceleration depends upon position alone, and must therefore be — n 2 p, that of the non- 

 rotating ball. Hence we see that 



m 2 = n 2 + D, 2 , 



