8 MOTION OF A SOLID THROUGH A PERFECT FLUID. 



be the final value of V. The last term in p will contribute 

 nothing to the final equation, and we obtain merely 



IT 

 P 



= P£^§^(V'-V)cos0. . . . (2) 



Now, the motion in question having been produced from 

 rest in an infinite liquid by the motion of the sphere, the 

 motion is the same at every instant as that impulsively 

 produced from rest by giving instantaneously to the sphere 

 its velocity V (Thomson and Tait, vol. i. part i, page 328 ; 

 Kirchoff, Vorlesungen, chap. xix. &c). The value of the 

 impulsive pressures due to the instantaneous production 

 of the velocity V of the sphere, and which produces the 

 consequent velocities in the fluid is 



^ = *£vcos0, (3) 



where - , of course, only differs from <j> by a constant. 



Now, there need be no difficulty in supposing a fluid 

 capable of transmitting a tension, provided this tension 

 tends to produce no discontinuity of motion or disruption 

 between near parts, as in the present case. But at the 

 surface of the sphere we get 



- = j«Vcos^; 

 P 



and thereupon a maximum of cohesion is needed of the 

 order apY at the extreme rear of the sphere, which is 

 double the mean value required "*. Considering the coeffi- 

 cient of cohesion as constant, all other things being alike, 



* The pressure in front or tension behind a sphere of radius i foot, started 

 impulsively with uni of velocity in water, would be roughly represented by 

 that due to a slab of granite | inch thick falling through 3 inches. 



