84 MATHEMATICS 



solid and fluid bodies in the gross, has been from 

 the beginning in such close contact with Mathe- 

 matics that theoretical mechanics has always been 

 regarded as an integral part of Mathematics. This 

 arose from the fact that the phenomena involved 

 are of such a character that they lend themselves 

 easily to measurement, and comparatively easily 

 to the formulation of laws expressible in precise 

 terms. Mechanics may then be regarded as a 

 science that is rationalized in a degree only less 

 complete than is the case in the model instance of 

 Geometry. In those parts of Physics such as 

 Sound, Light, Heat, and Elasticity, in which the 

 subtler properties of matter are involved, the line 

 of progress has consisted largely of reduction, 

 with ever increasing success, to dynamical treat- 

 ment, in which the detailed representation of the 

 phenomena is sought in the extension of Mechanics 

 to the smallest parts of matter, or as in the case 

 of light, to the parts of a hypothetical medium in 

 which the light is regarded as being propagated. 

 The application of ever more refined mathematical 

 methods to the determination and tabulation of 

 the motion of the heavenly bodies has proceeded 

 rapidly in our own time and has as yet by no 

 means reached its zenith. The foundation on a 

 dynamical basis of the Science of Celestial Mechanics 

 by Newton has been regarded as probably the 

 greatest and most far reaching contribution to 

 the advance of Science ever made in our country. 



