Applicatioii of Analijsis to the Motion of Fluids. 481 



of resistance. I find also that the part of the velocity directed 

 to or from the centre of the sphere varies inversely as the 

 square of the distance, and that in a plane di-awn at any in- 

 stant through the centre of the sphere perpendicular to the 

 direction of its motion, the fluid is stationary. Poisson, by 

 integrating the equation with the term containing the diffe- 

 rential coefficient with respect to 6 included, finds the coeflfi- 

 cient of resistance to be l^, the law of variation of the velocity 

 to be inversely as the cube of the distance, and the velocity of 

 the fluid in the above-mentioned plane and in contact with 

 the sphere, to be half the velocity of the spiiere. With these 

 statements I leave the problem to the consideration of mathe- 

 maticians, not venturing, in a question of so much difficulty, to 

 assert unhesitatingly the correctness of my own views. 



As an objection may be raised against the reasoning in my 

 communication in the December Number, because it takes 

 account only of terms involving the first power of the velocity, 



which, by reason of the small factor — , may not be of larger 



magnitude than rejected terms involving the square of the 

 velocity, I take this opportunity of mentioning that, in a paper 

 submitted to the Cambridge Philosophical Societ}', I have 

 carried the approximation to the next degree, and, as might 

 have been anticipated, I obtain the former result, the pressure 

 depending on the square of the velocity being the same on the 

 preceding as on the following half of the surface of the vi- 

 brating spiiere. In the same paper I have attempted to give 

 an answer to the query proposed at the end of the above- 

 mentioned communication, respecting the motion of a small 

 sphere submitted to the mechanical action of the vibrations of 

 an elastic medium. I find tliat there will be a motion of vi- 

 bration of the sphere depending on the first power of the ve- 

 locity of the vibrating medium, and a permanent motion of 

 translation depending on the second power. This result is 

 important if it serves to explain how the vibrations of the 

 ffither (assuming them to be like those of air) may at the same 

 lime produce two different effects, such as light and heat, or 

 light and chemical action. 



Cambridge Observatory, April 13, 1841. 



Phil. Marr. S. 3. Vol. 18. No. 119. June 184-1. 2 I 



