THE LAWS OF FLUID RESISTANCE. 107 



the beginning. Therefore the sum total of the forces (in 

 other words the only force) brought to bear upon the 

 body by the motion of the fluid in the direction of its flow, 

 is nil. 



Another instructive way of regarding the same problem 

 is this. Suppose each and every one of the streams into 

 which we have subdivided the ocean to be inclosed in an 

 imaginary rigid pipe made exactly to fit it, throughout, the 

 skin of each pipe having no thickness whatever. The 

 innermost skin of the innermost layer of pipes (I mean 

 that layer which is in contact with the side of the body), 

 the innermost skin, I say, of this layer is practically 

 neither more nor less than the skin or surface of the body. 

 The other parts of the skins of this layer, and all the 

 skins of all the other pipes, simply separate fluid from 

 fluid, which fluid ex hypothesi would be flowing exactly as 

 it does flow if the skins of the pipes were not there ; so 

 that, in fact, if the skins were perforated, the fluid would 

 nowhere tend to flow through the holes. Under these cir- 

 cumstances the flow of the fluid clearly cannot bring any 

 force to bear on any of the skins of any of the pipes, 

 except on the innermost skin of the innermost layer. Now 

 we know that the fluid flowing through this system of 

 pipes administers no total endways force to any one of the 

 pipes or to the system as a whole. But it produces, as we 

 have just seen, no force whatever upon any of the skins 

 which separate fluid from fluid ; consequently if these are 

 removed altogether, the force administered to the remainder 

 of the system, will be the same as is administered to the 

 whole system, namely, no total endways force whatever. 

 But what is this remainder of the system which has no 

 total endways force upon it ? Simply the surface of the 

 body, which is formed, as I have already said, by the inner- 

 most skins of the innermost layer of pipes. Therefore no 

 total endways force is administered to the body by the 

 flow of the fluid. 



I have now shown that an infinite ocean of frictionless 

 fluid flowing past a stationary submerged body cannot 

 administer to it any endways force, whatever be the nature 

 of the consequent deviations of the streams of fluid. The 

 question, what will be in any given case the precise con- 

 figuration of those deviations, is irrelevant to the proof I 



