7 



upon this is well known to mathematicians. The celebrated principle 

 of least action, as it is applied in mechanics and astronomy, consists in 

 showing that a certain integral v d s, v being the velocity at each point, 

 and d s the element of its motion, must be the minimum. If I take 

 the points A and B in the planets' path, s representing the sun, I only 

 require to know those points A and B and the sun, s, to calculate for 

 you, from the principle of least action — which I can do to the mil- 

 lionth part of an inch at each portion of this orbit— the path that the 

 planet must describe, on the supposition that it is a lazy, intelligent ani- 

 mal, trying to swim round the sun in such a manner as to give the least 

 trouble to itself. It is perfectly well known to astronomers that the 

 imaginary idea of Kepler may be converted into a real fact ; and that, 

 if we grant the hypothesis that the earth is an intelligent animal swim- 

 ming round the sun, we can calculate and predict its path as certainly 

 as we could from the Newtonian law of gravitation. 



Pondering this idea over in my mind, it seemed to me to afford in 

 such a science as Animal Mechanics a possible key which would unlock 

 the secrets of that science. It was an hypothesis invented by Kepler 

 in the early ages of astronomy when more perfect hypotheses were im- 

 possible, but which, when carefully followed out, would lead to results 

 as accurate and as perfect as the exact hypothesis ; and the hypothesis 

 I have to lay before you as the foundation of the science of Animal 

 Mechanics is similar to that of Kepler, and will ultimately, I doubt not, 

 be replaced by a higher and more perfect law, such as that with which 

 Newton replaced Kepler's law. My hypothesis is, that in every arrange- 

 ment of bones, muscles, joints, and parts of animals, the motion 

 must be such as it would be on the hypothesis that the muscle 

 were a living intelligent thing, trying to save itself trouble. We 

 can calculate, as I shall show you in the subsequent lectures, with a 

 certainty as perfect as we can calculate the path of a planet, the posi- 

 tions of bones and sockets as we find them in nature. If, therefore, I 

 can prove my hypothesis, we are entitled to regard it as a key for 

 present use, to be replaced ultimately by some higher law, but a valuable 

 and precious key to unlock for us the secrets of animal mechanics. 



Before proceeding to apply it to the muscles, I must give you one or 

 two more illustrations of it, to show you the power of the instrument 

 which I propose to use. When a ray of light passes from one medium 

 into another, it always describes a bent path. A ray of light passing 

 from the air into a glass of water will be bent at the junction of the two 

 bodies. Taking the point A (diagram) to be the ray of light in the air, 

 and point B the ray of light in the glass, if I imagine the fiction that the 

 molecule of light is a living, intelligent, lazy animal, trying to go from 

 A to B with the minimum of trouble to itself, I can predict, as certainly 

 as by the law of refraction and reflection, the path which it would de- 



