LOCOMOTION IN GENERAL. 1U9 



(lie ground sink two centimetres under the pressure of the 

 loot, it is evident that the body will only be raised one 

 centimetre, and the useful work will be diminished by two- 

 tliirds. 



The compression of the soil under the foot certainly con- 

 stitutes work, according to the mechanical definition of this 

 word. In fact, the soil, as it yields, offers a certain resist- 

 ance. This resistance must be multiplied by the extent to 

 which the soil is indented, in order to ascertain the value of 

 the work accomplished in this direction. But this work is 

 absolutely useless with respect to locomotion : it is an entire 

 loss of the motive force expended. 



When a fish strikes the water with his tail, in order to 

 drive himself forward, he executes a double work ; a part 

 tends to drive behind him a certain mass of fluid with a 

 certain velocity, and the other to drive the animal forward in 

 spite of the resistance of the surrounding water. This last 

 work alone is utilized ; it would be much more considerable 

 if the tail of the animal met with a solid point of resistance 

 instead of the water which flies from before it. 



Is it possible to measure the dimiuution of useful work 

 in locomotion, according to the greater or less mobility of the 

 point of resistance ? 



If the ground on which we walk resist perfectly, it must be 

 admitted that no part of the muscular work is lost; but in 

 every case in which a displacement of the resisting surface 

 exists at the same time as that of the body, it is necessary to 

 determine the law according to which this partition is made. 

 A principle established by Newton regulates the science of 

 mechanics ; this is that " action and re-action are equal." 

 Does this mean, in the case before us, that half of the work 

 is expended on the resisting surface, and the other half on 

 the displacement of the body of the animal? This cannot be 

 true, if we may judge by the many cases in which a force acts 

 on two bodies at the same time. 



Thus, in the science of projectiles, the motive force of the 

 powder that is to say, the pressure of the gases which are 

 disengaged in the cannon, acts at the same time on the pro- 

 jectile and on the piece, giving these masses a velocity in 



