146 WHAT IS SCIENCE? 



precisely how it is measured) ; and I might have 

 asserted either of them, without knowing the third. The 

 third law is not merely an expression in different words 

 of something known before ; it is a new addition to 

 knowledge. 



But we have added to knowledge only because we have 

 introduced an assertion which was not contained in the 

 two original statements. The deduction depends on the 

 fact that if one thing (A) is proportional to another thing 

 (B) and if B is proportional to a third thing (C), then A is 

 proportional to C. This proposition was not contained 

 in the original statements. But, the reader may reply, 

 it was so contained, because it is involved in the very 

 meaning of " proportional " ; when we say that A is 

 proportional to B, we mean to imply the fact which has 

 just been stated. Now that is perfectly true if we are 

 thinking of the mathematical meaning of " propor- 

 tional," but it is not true if we are thinking of the 

 physical meaning. The proposition which we have really 

 used in making our deduction is this : If weight is pro- 

 portional (in the mathematical sense) to density, when 

 weight is varied by taking different substances, then it 

 is also proportional to density when weight is varied by 

 compressing more of the same substance into the same 

 volume. That is a statement which experiment alone 

 can prove, and it is because we have in fact assumed 

 that experimental statement that we have been able to 

 11 deduce " a new piece of experimental knowledge. It 

 is involved in the original statements only if, when it is 

 said that density is proportional to pressure, it is implied 

 that it has been ascertained by experiment that the law 

 of density is true, and that there is a constant density 

 of a gas, however compressed, given by dividing the 

 weight by the volume. 



The conclusion I want to draw is this. When we appear 

 to arrive at new scientific knowledge by mere deduction 



