322 GENERALIZED COORDINATES 



A man introduced into the room beneath will have no opportunity 

 of inspecting the machinery above, but he can manipulate it to a 

 certain extent by pulling the different ropes. If on pulling one 

 rope he finds that the others are set into motion, he will under- 

 stand that the different ropes must be connected above by some 

 kind of mechanism, but will not be able to discover the exact 

 nature of the mechanism. 



This concealed mechanism may be supposed to represent those 

 parts of the mechanism of the universe which are hidden from our 

 view, while the ropes represent those parts which we can manipu- 

 late. In nature, there are certain acts which we can perform, cor- 

 responding to the pulling of the ropes in our analogy, and we see 

 that these are followed by certain consequences, analogous to the 

 motion of the other ropes ; but the ultimate mechanism by which 

 the cause produces the effect remains entirely unknown to us. 

 For instance, if we press the key of an electric circuit, we may 

 find that the needle of a distant galvanometer is moved, but the 

 mechanical processes which transmit the action through the wires 

 of the circuit and through the ether surrounding the galvanometer 

 needle remain unknown. 



263. Now suppose that the imaginary man is at liberty to handle 

 the ropes and that he wishes to study the connection between them. 

 He may begin by conjecturing that the connecting mechanism in 

 the room above consists of arrangements of, say, levers, pulleys, and 

 cogwheels, and he may work out for himself the manner in which 

 the ropes ought to move if his conjectures are correct. This proced- 

 ure would be analogous to that we have described in 260; it is 

 not the procedure we are going to follow here. 



On the other hand, without any conjecture at all as to the 

 nature of the mechanism above, the man will know that certain 

 laws will govern any manipulation of the ropes, if the ropes are 

 connected by mechanism of any kind whatever, such that each 

 particle obeys Newton's laws of motion. 



To explain this, let us take the simplest case, and suppose that 

 there are two ropes only and that when A is pulled down ijH^ an 



