ON THE STUDY OF PHYSICS. 53 



may be stated and in the correlation of the parts of the system, vary- 

 ing all the way from mathematics, which is the science of exactness, 

 to certain branches of natural history, which are no more than cata- 

 logues of the forms of life arranged in arbitrary classes and termed 

 science only because they are sciences in the making, the first step 

 always being to arrange the facts in order, even though it be an arbi- 

 trary one. Because these differences are often forgotten and sometimes 

 ignored with consequent misapprehension and even serious error, they 

 deserve further review and illustration. 



Every science starts with a few postulates suggested by universal 

 experience. These assumptions thus become for that particular science 

 the ultimate things, in terms of which all its conclusions are stated, 

 and they are not, at least as far as that science is concerned, capable 

 of further simplification. The simplest illustration may be seen in 

 the case of mathematics, though many of its followers do not recognize 

 that it is a physical science at all. 



Number is a common and easily distinguishable property of all 

 bodies and of all phenomena. By the process of grouping and count- 

 ing we derive the fundamental laws concerning collections of bodies, 

 such as the associative law, the distributive law, the permutative 

 law, etc. Having secured its fundamental data from the physical world, 

 mathematics withdraws, so to speak, into the realm of thought and, 

 aided by reason alone, weaves its material by successive steps into 

 those remarkable systems which we call arithmetic, algebra, the in- 

 finitesimal calculus, the theory of functions, etc. In a sense mathe- 

 matics is the most fundamental of the sciences, for without it com- 

 parisons would lose that element of exactness which alone endows 

 them with the rank of science. 



Geomet^, though often reckoned as a branch of pure mathematics, 

 is more definitely a physical science than the science of number, since 

 it deals with extension in space, a phenomenon entirely within the 

 domain of physics. But geometry having derived its postulates, or 

 axioms, as they are commonly called in this connection, from experience, 

 like the science of mathematics retires with these data into a world of 

 abstractions ; a world deprived of all realities save spatial relations and 

 the laws of thought, and here develops a system self-contained, i. e., 

 requiring no further appeal to the physical world or to human ex- 

 perience. 



A procedure similar to this is indeed frequently employed in the 

 other sciences, where, having selected a few facts derived from experi- 

 ence, we divest them of all associations which are for the moment 

 inconsequent, and proceed to derive by a course of reasoning, new 

 relations which were not obvious in the premises; but there is this 

 noteworthy difference that while in geometry and analysis the appeal 



