430 PROFESSOR TAIT ON 



The one novelty in the experiments of Magnus (so far as spherical projectiles are 

 concerned) consisted in blowing a stream of air against the rotating body, instead of 

 giving it a progressive as well as a rotatory motion ; thus, in fact, realizing the idea 

 suggested by Euler in one of the quotations made above. He was thus enabled, by means 

 of little vanes, to trace out in a very interesting and instructive manner the character 

 of the relative motion of the air and the rotating body. This was a cylinder instead 

 of a sphere, so the effects were greater and of a simpler character, but not so directly appli- 

 cable to bullets. Otherwise, his experiments are merely corroborative of those of Robins. 



But neither Robins nor Magnus gives any hint as to the form of the expression for 

 the deflecting force, in terms of the magnitudes of the translatory and the rotatory speed. 

 That it depends upon both is obvious from the fact that it does not exist when either 

 of them is absent, however great the other may be. 



1. For some time my attention has been directed to this subject by the singularly in- 

 consistent results which I obtained when endeavouring to determine the resistance which 

 the air offers to a golf-ball. # The coefficient of resistance which I calculated from Robins' 

 data for iron balls, by introducing the mass and diameter of a golf-ball, was very soon 

 found to be too small : — and I had grounds for belief that even the considerably greater 

 value, calculated in a similar way from Bashforth's data, was also too small. Hence the 

 reason for my attempts to determine its value, however indirectly. The roughness of the 

 ball has probably considerable influence ; and, as will be seen later, so possibly has its 

 rotation. I collected, with the efficient assistance of Mr T. Hodge (whose authority on 

 such matters, alike from the practical and the observational point of view, no one in 

 St Andrews will question) a fairly complete set of data for the average characteristics of 

 a really fine drive : — elevation at starting, range, time of flight, position of vertex, &c. 

 Assuming, as the definite result of all sound experiment from Robins to BASHFORTH,t that 

 the resistance to a spherical projectile (whose speed is less than that of sound) varies 

 nearly as the square of the speed, I tried to determine from my data the initial speed 

 and the coefficient of resistance, treating the question as one of ordinary Kinetics of a 

 Particle. We easily obtain, for a low trajectory, simple but sufficiently approximate 

 expressions for the range, the time of flight, and the position of the vertex, in terms of 

 the data of projection and the coefficient of resistance. If, then, we assume once for all 

 an initial elevation of 1 in 4, the only disposable initial element is the speed of projection. 

 Making various more or less probable assumptions as to its value, I found for each the 

 corresponding coefficient of resistance which would give the datum range. Thus I. 

 obtained the means of calculating the time of flight and the position of the vertex of the 

 path. The greater the assumed initial speed (short, of course, of that of sound) the 

 larger is the coefficient of resistance required to give the datum range, and the more 



* "The Unwritten Chapter on Golf," Nature, 22/9/87 ; and "Some Points in the Physics of Golf," Ibid., 28/8/90, 

 24/9/91, 29/6/93. Also a popular article "Hammering and Driving," Golf, 19/2/92 ; where the importance of under- 

 pin is considered, mainly from the point of view of stability of motion of a projectile which is always somewhat imperfect 

 as regards both sphericity and homogeneity. 



+ " On the Motion of Projectiles," 2nd edn., London, 1890. 



