THOMSON AND TAIT's NATURAL PHILOSOPHY. 781 



The phenomena of real bodies are found to correspond so exactly with the 

 necessary laws of dynamical systems, that we cannot help applying the language 

 of dynamics to real bodies, and speaking of the masses in dynamics as if they 

 were real bodies or portions of matter. 



We must be careful, however, to remember that what we sometimes, even 

 in abstract dynamics, call matter, is not that unknown substratum of real 

 bodies, against which Berkeley directed his arguments, but something as perfectly 

 intelligible as a straight line or a sphere. 



Real bodies may or may not have such a substratum, just as they may 

 or may not have sensations, or be capable of happiness or misery, knowledge 

 or ignorance, and the dynamical transactions between them may or may not 

 be accompanied with the conscious effort which the word force suggests to us 

 when we imagine one of the bodies to be our own, but so long as their 

 motions are related to each other according to the conditions laid down in 

 dynamics, we call them, in a perfectly intelligible sense, dynamical or material 

 systems. 



In this, the second edition, we notice a large amount of new matter, the 

 importance of which is such that any opinion which we could form within the 

 time at our disposal would be utterly inadequate. But there is one point of 

 vital importance in which we observe a marked improvement, namely, in the 

 treatment of the generalised equations of motion. 



Whatever may be our opinion about the relation of mass, as defined in 

 dynamics, to the matter which constitutes real bodies, the practical interest of 

 the science arises from the fact that real bodies do behave in a manner 

 strikingly analogous to that in which we have proved that the mass-systems 

 of abstract dynamics must behave. 



In cases like that of the planets, when the motions we have to account 

 for can be actually observed, the equations of Maclaurin, which are simply a 

 translation of Newton's laws into the Cartesian system of co-ordinates, are 

 amply sufficient for our purpose. But when we have reason to believe that 

 the phenomena which fall under our observation form but a very small part 

 of what is really going on in the system, the question is not what phenomena 

 will result from the hypothesis that the system is of a certain specified kind ? 

 but what is the most general specification of a material system consistent with 

 the condition that the motions of those parts of the system which we can 

 observe are what we find them to be ? 



