460 THE PRINCIPLES OF SCIENCE. [CHAP. 



even attempted the general problem of the simultaneous 

 attractions of four, five, six, or more bodies ; they resolve 

 the general problem into so many different problems oi 

 three bodies. The principle upon which the calculations 

 of physical astronomy proceed, is to neglect every quantity 

 which does not seem likely to lead to an effect appreciable 

 in observation, and the quantities rejected are far more 

 numerous and complex than the few larger terms which 

 are retained. All then is merely approximate. 



Concerning other branches of physical science the same 

 statements are even more evidently true. We speak and 

 calculate about inflexible bars, inextensible lines, heavy 

 points, homogeneous substances, uniform spheres, perfect 

 fluids and gases, and we deduce a great number of beautiful 

 theorems; but all is hypothetical. There is no such 

 thing as an inflexible bar, an iuextensible line, nor any one 

 of the other perfect objects of mechanical science ; they 

 are to be classed with those mythical existences, the 

 straight line, triangle, circle, &c., about which Euclid so 

 freely reasoned. Take the simplest operation considered 

 in statics the use of a crowbar in raising a heavy stone, 

 and we shall find, as Thomson and Tait have pointed out, 

 that we neglect far more than we observe. 1 If we suppose 

 the bar to be quite rigid, the fulcrum and stone perfectly 

 hard, and the points of contact real points, we may give 

 the true relation of the forces. But in reality the bar must 

 bend, and the extension and compression of different parts 

 involve us in difficulties. Even if the bar be homoge- 

 neous in all its parts, there is no mathematical theory 

 capable of determining with accuracy all that goes on ; if, 

 as is infinitely more probable, the bar is not homogeneous, 

 the complete solution will be immensely more complicated, 

 but hardly more hopeless. No sooner had we determined 

 the change of form according to simple mechanical princi- 

 ples, than we should discover the interference of thermo- 

 dynamic principles. Compression produces heat and 

 extension cold, and thus the conditions of the problem are 

 modified throughout. In attempting a fourth approxima- 

 tion we should have to allow for the conduction of heat 

 from one part of the bar to another. All these effects are 



1 Treatise on Natwal Philosophy, vol. i. pp. 337, &c. 



