340 PETER GUTHRIE TA1T 



generally greater the narrower it is. Then it falls almost uniformly in a nearly 

 straight path, considerably inclined to the vertical. The deflection is always towards 

 the side to which the edge of the strip which is at any instant the lower, and 

 therefore the foremost, is being carried by the rotation. If the longer edges be 

 not quite horizontal, the path is usually a nearly perfect helix, the successive posi- 

 tions of the upper surface being arranged very much like the steps of a spiral 

 staircase. This is an exceedingly simple, as well as a beautiful and instructive 

 experiment ; and, besides, it has an intimate relation to our subject. 



Finally, we need only refer to Robins' musket, which virtually solved the problem 

 of shooting round a corner. The barrel was slightly curved to the left near the 

 muzzle ; and the bullet (made purposely to fit loosely) rolled on the concave (right- 

 hand) side of the bore, and thus behaved precisely like a sliced golf ball, starting 

 a little to the left, and then skewing away to the right. 



4. As the transverse force due to the spin is always in a direction perpen- 

 dicular to that of the ball's motion, it has no direct influence on the speed of the 

 ball. Its only effect is on the curvature of the path. Thus, so long as we are 

 dealing only with paths confined to one vertical plane, the axis of rotation must be 

 perpendicular to that plane, and the effect of the transverse force is merely, as it 

 were, an unbending of the path which would have been pursued had there been no 

 rotation. From this (very inadequate) point of view we see at once why, other 

 things being the same, even a moderate underspin greatly lengthens the carry, especi- 

 ally in the case of a low trajectory. But such analogies give us no hint as to the 

 actual amount of the lengthening in any particular case. They lead us, however, 

 to suspect that too great a spin may, in its turn, tend to shorten the carry ; and 

 that, if of sufficiently great amount, it might even bend the path over backwards 

 and thus lead to the formation of a kink. Nothing but direct calculation, however, 

 can give us definite information on these questions. And, unfortunately, we must 

 trust implicitly in the accuracy of the computer, for we have no independent means 

 of checking, from stage to stage of his work, the results of his calculations. In 

 dealing with the case of an unresisted projectile, such numerical work can be checked 

 at any stage by a simple and exact geometrical process. Even the more complex 

 conditions of a path in which the resistance is as the square of the speed admit of 

 exact analytical expression ; but when the transverse force due to rotation is taken 

 account of, the equations do not admit of integration in finite terms, so that the 

 computer has to work out the approximate details of the path by successive little 

 stages, say 6 feet at a time (or somewhere about 90 in all), and any errors of 

 approximation he may make at any stage will not only themselves be faithfully 

 represented in the final results, but will necessarily introduce other errors by furnish- 

 ing incorrect data for each succeeding stage of the calculation. As all of his work 

 was carried out to four places of figures at least, such errors are unlikely to have 

 any serious consequence. I have endeavoured to obtain a rough estimate of the 

 probable amount of error thus inevitably introduced by testing my computer (as 

 well as the formula which I gave him) upon examples in which I had the means 

 of independently calculating the exact result at each stage. His work bore this 

 severe test very well. Unfortunately for my present application, it was based through- 



