THE PATH OF A ROTATING SPHERICAL PROJECTILE. 



499 



a really long run. In such a case the carry will, of course, be still further reduced, 

 unless the initial elevation be very considerably increased. (Some of Mr Wood's 

 numerical results, from which fig. 3 was drawn, were given in the preceding section.) 



In fig-4, a and V are as in fig. 1, but k=l and <£ = 45°. Here we have the kink, 

 of which a provisional sketch (closely resembling the truth) was given in the former 

 instalment of the paper. I have not yet obtained it with a golf-ball, though as already 

 stated I have got the length of producing the cusp above spoken of. But the kink can 

 be obtained in a striking manner when we use as projectile one of the large balloons 

 of thin india-rubber which are now so common. We have only to " slice " the balloon 

 sharply downwards (in a nearly vertical plane) with the flat hand. This is a most 

 instructive experiment, and its repetition presents no difficulty whatever. It is to be 

 specially noticed that, in the particular kink sketched, there is a point of minimum speed 

 somewhat beyond the vertex, and a point of maximum speed, both nearly in the same 

 vertical with the point of projection. The first (where the speed is reduced to 587) is 

 reached in a little more than two seconds, the other (where it has risen to 7 3 '8) in rather 

 more than four. 



It may be interesting to give a few details of Mr Wood's calculations for this case : — 

 selecting specially those near the points of maximum and minimum speed, and along 

 with them those for closely corresponding elevations on the ascending side. Also near 

 the vertex. The equations were 



v*=Wl _i^_4oo sin (1-0-04) 









<f>i = 



rh , 360 



V 



12000 

 s— cos 



V 2 



0(1-0- 



04) 







8/6 



1. 



V 2 



90000 

 # 



V 



300 



l/v 



003 



* 



2(1/,) 

 •003 



4> 



45° 



sin 

 •7071 



2(sin 0) 



•7071 



* 



COS0 



•7071 



2(cos 0) 



•7071 



* 



23. 



24582 

 * 



156-8 



•00638 

 * 



10693 



78°-72 

 * 



•9807 



19-6186 



* 



•1956 



11-3075 



* 



41. 



5583 

 * 



74-7 



•01359 



* 



•27640 



145°-3 



•5693 



35-8751 



* 



-•8221 



6-2814 

 * 



44. 

 45. 

 46. 



4278 

 3974 



3739 



* 



65-4 

 63-0 

 611 



•01529 

 01586 



•01636 



* 



•32038 

 •33624 

 •35260 



166°-46 



174°-58 

 183M6 



* 



•2343 



•0944 



- 0553 



36-9422 



37-0266 



36-9813 

 * 



-■9722 

 - -9955 

 -•9981 



3-4951 

 2-4996 

 1-5015 



* 



48. 

 49. 

 50. 



3475 



3441 



3464 

 * 



59-0 

 58-7 

 58-9 



•01697 

 •01704 



01700 



<* 



•38630 

 •40334 

 •42034 



201°-3 

 210°-5 

 219°5 



-•3633 

 -•5075 

 -•6363 



36-4078 

 35-9003 

 35-2640 



-•9317 



-•8616 

 - -7714 



- -5921 



- 1-4537 



-2-2251 



* 



67. 

 68. 

 69. 



5434 



5443 



5435 

 * 



73-7 

 73-8 

 73-7 



•01357 

 •01355 



•01357 



* 



•67179 

 •68534 

 •69891 



313°-1 



316°-5 



319°-9 



* 



-•7302 

 -•6880 

 - -6446 



20-0274 

 19-3394 



18-6948 

 * 



•6833 

 •7258 

 •7646 



- -3162 



+ -4096 



+ -1742 

 * 



The following data belong to the last elements for which the calculations were 

 made : — 



80. 

 81. 



4374 

 4202 



661 



64-8 



•01512 

 •01542 



•85485 

 •87027 



352°-9 

 355°-8 



-•1224 

 - -0732 



14-6898 

 14-6166 



•9925 

 •9973 



11-2602 

 12-2575 



VOL. XXXIX. PART II. (NO. 16). 



4 F 



