162 Measurement of Time and other Magnitudes. 



is to say, it may happen that unless the assumption is true, 

 some generally accepted theory must be false. But why is 

 the theory generally accepted ? Surely because it predicts 

 true laws. But these laws will involve measured magnitudes: 

 how are we to know that the laws are true unless we can 

 measure the magnitudes independently o£ any assumption 

 that they, or the theory from which they are deduced, are 

 true ? An attempt to found upon theory the measurement of 

 so basic a magnitude as time leads to a circular argument. 

 Of course, scientific truth is so different from mathematical 

 truth and capable of so many degrees that an argument 

 formally circular may not be really valueless. But if it can 

 be avoided, so much the better. I maintain that measurement 

 of all fundamental magnitudes can be stated as a purely 

 experimental process without any appeal to theory. 



(3) In reply to Dr. Silberstein's question, distance is not 

 a fundamental magnitude ; but it is very closely connected 

 with the length of a straight rod, which is a fundamental 

 magnitude and measured by a process precisely similar to 

 that which I sketched for weight and period of time. 



(4) Temperature is certainly not a fundamental magnitude ; 

 it cannot be added. From two bodies at temperature 1, there 

 cannot be produced by any physical means a body at tem- 

 perature 2. The international hydrogen scale is purely 

 arbitrary — as arbitrary as that of the mercury-in-glass 

 thermometer ; it does not express any physical laws. But if 

 hydrogen were a perfect gas, temperature on that scale would 

 be a pure derived magnitude, like density or viscosity. That 

 is to say, it would be a constant in a numerical law relating 

 fundamentally measured magnitudes. 



(5) Lastly, when I said that my observations were 

 " elementary," I used the word in its proper sense to mean 

 that only the elements of the matter, and not the com- 

 plexities, were considered. If Cay ley has really asserted 

 anything contrary to my contentions — I do not think he has, — 

 I w r ould reply that even the giants are liable to error, especially 

 if, being mathematicians, they discourse upon experimental 

 physics. 



Yours faithfully, 



Norman R. Campbell. 



