Waves generated by Impact. 109* 



Since the intensity is proportional to F 2 + G 2 , we see from 

 the above expressions on substituting the values of A 0r 

 A 2 , &c, that the intensity is maximum in the direction of 

 the line joining the centres, and that it gradually decreases 

 and assumes the minimum value in the perpendicular 

 direction. 



Now, if we further diminish the wave-length — that^ is,, 

 if we assume ka = 2, we get 



, ^r. 25 — 50i . 44 + 62*52' 

 ^ = 100 L A °nU2r +As -5$W25 P * {C0se) 



t 405 + 1170*6z' . -\jK*-r+* 



+ A * 1534329-36 P4(C0S ^ +&C ' J —^->- 



= 3Q [3 A (8 - 16?) + 3 A 2 (7-53 + 10-7z)P 2 (cos 6) 



+ &c 



Hence 



r 



F=-8 + 3O\L2P 2 (cos0)+&c.. 

 G = 16+42'8P 2 (cos0)-r-&c. 



We thus see that in this case F 2 + G 2 is maximum at 0° 

 where its value is 3941*44 nearly, and that its value 

 gradually decreases and assumes the minimum value nearly 

 116 at an angle of 61°, and that it again increases and 

 assumes a second maximum value at an angle of 90°, where 

 its value is 558*16 nearly. If we further decrease the wave- 

 length we get results analogous to the above case, namely, 

 that the intensity is maximum in the line joining the centres, 

 and that it assumes a minimum value at some angle inter- 

 mediate between 0° and 90° and a second maximum value 

 at 90° which is much less than the first maximum. We can 

 easily proceed to a second approximation by determining 

 the values of the coefficients in the expression for the 

 prescribed vibration on the surface of the imaginary sphere 

 so as to agree as closely as possible with the actual state of 

 affairs. 



4. Experimental study of the character of the 

 sound-wave. 



The experimental results described before would be very 

 difficult to explain on any hypothesis other than that which 



