THE LAWS OF FLUID RESISTANCE. 91 



On this view, various formulae were constructed by 

 mathematicians to estimate these reactions, and to count 

 up the sum total of resistance which they would cause to a 

 ship or moving body of any given form. These formulae 

 were not all alike, but they were mostly based on the sup- 

 position that the entire forward part of the body had to 

 exert pressure to give the particles motion outwards, and 

 that the entire afterpart had to exert suction to give them 

 motion inwards, and that there was, in fact, what is termed 

 plus pressure throughout the head-end of the body, and 

 minus pressure or partial vacuum throughout the tail-end. 

 And as it seemed that the number of particles which would 

 have to be thus dealt with would depend on the area of 

 maximum cross section of the body, or area of ship's way, 

 as it was sometimes termed, the resistance was supposed to 

 bear an essential proportion to the midship section of the 

 ship. This idea has sometimes been emphatically embodied 

 in the proposition that the work a ship has to do in per- 

 forming a given voyage is to excavate in the surface of the 

 sea, from port to port, a canal, the cross section of which is 

 the same as the midship section of the ship. 



This theory of resistance was at first sight natural and 

 reasonable ; it was generally admitted for many years to 

 be the only practicable theory, and was embodied in all the 

 most approved text-books on hydraulics and naval architec- 

 ture. But when the theory of stream-lines was brought to 

 bear upon the question, then it was discovered that the 

 reactions, which the inertia of the fluid would cause against 

 the surface of the body moving through it, and which were 

 supposed to constitute the resistance, arranged themselves 

 in a totally different manner from what had previously been 

 supposed, and that, therefore, the old way of estimating 

 their total effect upon the ship was fundamentally wrong. 

 How wrong, I can best tell you by stating that according 

 to the theory of stream-lines a submerged body, such as a 

 fish, for example, moving at a steady speed through the 

 assumed frictionless fluid, would experience no resistance 

 at all. Inj fact, when once put in motion it would go on 

 for ever without stopping. 



The revelation, then, which was brought about by the 

 application of the stream-line theory to the question, 

 amounted to this, that the approved formulae for esti- 



