TUOMBOX AKD TArrt KATUBAL PHILOSOPHY. 



Mopping all the ropes at onoe, and feeling what sort of tug each rope gives. 



If the? Uke the trouble to ascertain how much work they have to do in 



to dime the rope* down to a given set of positions, and to express 



i in tenM of tbej* positions, they have found the potential energy of the 



,1,1MB Jn term* of the known co-ordinates. If they then find the tug on any 



one rope arising from a velocity equal to unity communicated to itself or to 



any other rope, they can express the kinetic energy in terms of the co-ordinates 



These data am sufficient to determine the motion of every one of the 

 when it and all the others are acted on by any given forces. This is 

 all that the men at the ropes can ever know. If the machinery above has 

 degrees of freedom than there are ropes, the co-ordinates which express 

 degrees of freedom must be ignored. There is no help for it. 



Of course, if there are co-ordinates for which there are no ropes, but which 

 into the expression for the energy, then, if the motion of these co- 

 ordinates is periodic, there will be "adynamic vibrations" communicated to the 

 ropes, and by these the men below will know that there is something peculiar 

 going on above them. But if they pull the ropes in proper time, they can 

 cither quiet these adynamic vibrations or strengthen them, so that in this case 

 these co-ordinates cannot be ignored. 



There are other cases, however, in which the conditions for the ignoration 

 of co-ordinates strictly apply. For instance, if an opaque and apparently rigid 

 body contains in a cavity within it an accurately balanced body, mounted on 

 frictionless pivots, and previously set in rapid rotation, the co-ordinate which 

 expresses the angular position of this body is one which we are compelled to 

 ignore, because we have no means of ascertaining it. An unscientific person on 

 receiving this body into his hands would immediately conclude that it was 

 bewitched. A disciple of the northern wizards would prefer to say that the 

 body was subject to gyrostatic domination. 



Of the sections on cycloidal motions of systems, we can only here say 

 that the investigation of the constitution of molecules by means of their 

 vibrations, as indicated by spectroscopic observations, will be greatly assisted by 

 .1 thorough study of this part of the volume. 



We have not space to say anything of what to many readers must be 

 one of the most interesting parts of the book that on continuous calculating 

 machines, in which pure rolling friction is taken from the class of unavoidable 



