THEORY OF APPROXIMATION. 89 



In a similar manner Fourier's theory of the conduction 

 and radiation of heat was based upon the hypothesis that 

 the quantity of heat passing along any line is simply pro- 

 portional to the rate of change of temperature. But it 

 has since been shown by Forbes that the conductivity of a 

 body diminishes as its temperature increases. All the 

 details of Fourier's solution therefore require modification, 

 and the results are in the meantime to be regarded as 

 only approximately true 9. 



We ought to distinguish between those problems which 

 are physically and those which are merely mathematically 

 incomplete. In the latter case the physical law is cor- 

 rectly seized, but the mathematician neglects, or is more 

 often unable to follow out the law in all its results. The law 

 of gravitation and the principles of harmonic or undula- 

 tory movement, even supposing the data to be correct, 

 can never be followed into all their ultimate results. 

 Dr. Young explained the production of Newton's rings by 

 supposing that the rays reflected from the upper and 

 lower surfaces of a thin film of a certain thickness were in 

 opposite phases, and thus neutralized each other. It was 

 pointed out, however, that as the light reflected from the 

 nearer surface must be undoubtedly a little brighter than 

 that from the further surface, the two rays ought not to 

 neutralize each other so completely as they are observed 

 to do. It was finally shown by Poisson that the dis- 

 crepancy arose only from incomplete solution of the 

 problem ; for the light which has once got into the film 

 must be to a certain extent reflected backwards and 

 forwards ad infinitum; and if we follow- out this course of 

 the light by a perfect mathematical analysis, absolute dark- 

 ness may be shown to result from the interference of the 

 rays r . In such a case as this we used no physical laws 



<i Tait's 'Thermodynamics,' p. 10. 



r Lloyd's ' Lectures on the Wave Theory/ pp. 82, 83. 



