THOMSON AND TACT'S NATURAL PHILOSOPHY. 



It to Ugrange. in the first place, that we owe the method which 

 mil m fa answer this question without asserting either more or less than 

 II that ean be legitimately deduced from the observed facts. But though this 

 nethod ha* been in the hands of mathematicians since 1788, when the Mtcanique 

 Amtlytww was published, and though a few great mathematicians, such as Sir 

 W. R Hamilton, Jacobi, Ac., have made important contributions to the general 

 theory of dynamics, it is remarkable how slow natural philosophers at large 

 hare been to make Vie of these methods. 



Now, however, we have only to open any memoir on a physical subject 

 in order to eee that these dynamical theorems have been dragged out of the 

 utctuary of profound mathematics in which they lay so long enshrined, and 

 have been set to do all kinds of work, easy as well as difficult, throughout 

 the whole range of physical science. 



Hie credit of breaking up the monopoly of the great masters, of the spell, 

 and making all their charms familiar in our ears as household words, belongs 

 in great measure to Thomson and Tait. The two northern wizards were the 

 first who, without compunction or dread, uttered in their mother tongue the 

 true and proper names of those dynamical concepts which the magicians of old 

 were wont to invoke only by the aid of muttered symbols and inarticulate 

 equations. And now the feeblest among us can repeat the words of power 

 and take part in dynamical discussions which but a few years ago we should 

 hare left for our betters. 



In the present edition we have for the first time an exposition of the 

 general theory of a very potent form of incantation, called by our authors the 

 Ignoration of Co-ordinates. We must remember that the co-ordinates of Thomson 

 and Tait are not the mere scaffolding erected over space by Descartes, but 

 the variables which determine the whole motion. We may picture them as so 

 many independent driving-wheels of a machine which has as many degrees of 

 freedom. In the cases to which the method of ignoration is applied there are 

 certain variables of the system such that neither the kinetic nor the potential 

 energy of the system depends on the value of these variables, though of course 

 the kinetic energy depends on their momenta and velocities. The motion of 

 the rest of the system cannot in any way depend on the particular values of 

 these variables, and therefore the particular values of these variables cannot 

 be ascertained by means of any observation of the motion of the rest of the 

 system. We have therefore no right, from such observations, to assign to them 



