5 



would be the production of a third science, perfectly novel and of great 

 value. They compared their observations and notes together and pro- 

 duced a treatise on the motions of the human body, which will always be 

 quoted as a model of accuracy and a standard of scientific observation ; 

 but, from the necessary want of unity and uniformity produced by two 

 minds being brought to bear upon the same subject instead of one, it 

 cannot be regarded as so systematic or complete a treatise as that of 

 the illustrious Borelli. 



The progress of science of every description, and the extraordinary 

 and interesting results that have been produced in recent times by the 

 union of sciences apparently diverse from each other, have rendered it 

 almost inevitable that now, in some quarter or other, a science of 

 Animal Mechanics must arise which shall be worthy of being called an 

 exact science, and worthy of taking its place amongst the most perfect 

 of all our modern sciences. 



In order to found such a science, the great want is the discovery of 

 some general principle. I believe that I have succeeded in discovering 

 the true principle on which this science must be founded, and have 

 been enabled to sketch out the broad outlines of the foundation of such 

 a science ; though it must remain for abler mathematicians and more 

 expert anatomists than I can pretend to be to fill up the details of the 

 outline and bring them to the perfection at which I am confident they 

 will ultimately arrive. The principle on which I propose to found the 

 science of Animal Mechanics is a principle of almost universal applica- 

 tion — it is called the Principle of Least Action. This is well known 

 to mathematicians in its application to inanimate nature ; and, with 

 your permission, I will call your attention to one or two remarkable 

 instances of the application of the principle of least action, well ascer- 

 tained in physics and astronomy, before proceeding to apply it, as I 

 hope to do in these lectures, to the study of organic nature, and parti- 

 cularly of muscular mechanics. 



The celebrated Kepler, who died before Sir Isaac Newton's laws of 

 gravitation were discovered, as must be well known to you all, dis- 

 covered by patient observation the laws of the motions of the planets. 

 He discovered, in particular, the important law that a planet revolves 

 round the sun in an ellipse, the sun occupying a focus of this ellipse ; and 

 that every portion of the path of the planet is an ellipse, each portion of 

 the path being characterised by a velocity of motion peculiar to itself, and 

 different from that which is found in any other part. It is not necessary 

 for me to describe to you the simple laws by which the motion of the 

 planet varies ; but if you will imagine a planet moving from point A to 

 point B (diagram) in its path round the sun, Kepler succeeded in dis- 

 covering that it moves along that path by regular laws, by a regular 

 motion belonging to each part of that path, and never deviating from 



