PHYSICS AND MATHEMATICS 83 



would contain within themselves, in the form of 

 postulates, every element which could be supplied 

 by physical observation, and would no longer be 

 dependent for their future progress upon the work 

 of the experimenter. Laboratories would then be 

 useful only for illustrative, didactic, and suggestive 

 purposes, just as drawings and models are still 

 used in Geometry, but they would no longer hold 

 their present indispensable position in relation to 

 research. The progress of these sciences would, 

 as in the case of Geometry at present, consist in 

 a detailed development of the schematic represen- 

 tations of the phenomena. The actual state of 

 these departments of Science is of course vastly 

 different from the ideal state to which reference 

 has been made, but there exist in almost all depart- 

 ments of science coherent tracts within which 

 mathematical methods become applicable. In the 

 course of advance in each department, as it reaches 

 the stages in which it is possible to come to closer 

 grips with the phenomena under examination, 

 there arise increasing demands for the application 

 of mathematical methods and reasoning, some- 

 times of course of only an elementary kind, but 

 often later on of a more advanced character. 



The connection of Physics, cosmical and terres- 

 trial, with Mathematics is so close that all parts of 

 the subject are accessible in greater or less degree 

 to mathematical treatment. The part of Physics 

 which was developed earliest, the Mechanics of 



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