ACCORDANCE OF QUANTITATIVE THEORIES, <bc. 197 



eclipses and transits, he was able to argue inversely, and 

 assign the ellipticity of the planet's section by theory. 

 The ratio of the polar and equatorial axes thus deter- 

 mined was very nearly that of 13 to -14; and it agrees 

 well with such direct micrometrical measurements of the 

 planet as have been made ; but Laplace believed that the 

 theory gave a more accurate result than direct observation 

 could yield, so that the theory could hardly be said to 

 admit of direct verification. 



The specific heat of air was believed on the grounds of 

 direct experiment to amount to 0*2669, the specific heat of 

 water being taken as unity ; but the methods of expe- 

 riment were open to considerable causes of error. The 

 late Professor Eankirie showed in 1850 that it was possible 

 to calculate from the mechanical equivalent of heat, and 

 from other thermodynamic data, what this number should 

 be, and he found for it 0-2378. This determination was 

 at the time accepted by him and others as the most 

 satisfactory result, although not verified ; subsequently in 

 1853 Regnault obtained by direct experiment the number 

 ' 2 377> proving that the prediction had been well 

 grounded. 



It will be readily seen that in purely quantitative 

 questions verification will be a matter of degree and 

 probability. A less accurate method of measurement can- 

 not verify the results of a more accurate method, so that 

 if we arrive at a determination of the same physical 

 quantity in several distinct modes it will often become >a 

 delicate matter of investigation to decide which result is 

 most reliable, and should be used for the indirect deter- 

 mination of other quantities. For instance, Joule's and 

 Thomson's ingenious experiments upon the thermal phe- 

 nomena of fluids in motion involved, as one physical 

 constant, the mechanical equivalent of heat ; if requisite, 



c ' Philosophical Transactions' (1854), vol. cxliv. p. 364. 



