THEORY OF APPROXIMATION. 87 



heat, disregarded the heat absorbed by the box containing 

 the water heated and by other parts of the apparatus, 

 otherwise he would in Dr. Joule's opinion, have come 

 nearly to the correct result. 



It is surprising to learn the number of causes of error 

 which enter into even the simplest experiment, when we 

 strive to attain the most rigid accuracy. Thus we cannot 

 perform the simple experiment of compressing a portion 

 of gas in a bent tube by a column of mercury, in order to 

 test the truth of Boyle's Law, without paying regard to, 

 (i) the variations of atmospheric pressure, which are com- 

 municated to the gas through the mercury; (2) the 

 compressibility of mercury, which causes the column of 

 mercury to vary in density ; (3) the temperature of the 

 mercury throughout the column ; (4) the temperature of 

 the gas which is with difficulty maintained invariable ; 

 (5) the expansion of the glass tube containing the gas. 

 Although Regnault took all these circumstances into ac- 

 count in his accurate examination of the law , there is no 

 reason for supposing that he exhausted the sources of 

 inaccuracy. 



All the earlier investigations concerning the nature of 

 waves in elastic media proceeded upon the assumption 

 that waves of different length would travel with equal 

 speed. Newton's theory of sound had led him to this 

 conclusion, and experiment, or indeed the commonest 

 observations (see vol. i. p. 344) had sufficiently verified the 

 inference. When the undulatory theoiy came to be 

 applied at the commencement of this century to explain 

 the phenomena of light, a great difficulty was encountered. 

 The angle at which a ray of light is refracted in entering 

 a denser medium depends, according to that theory, on the 

 velocity with which the wave travels, so that if all waves 

 of light were to travel with equal velocity in the same 



Jamin, 'Cours de Physique,' vol. i. pp. 282-3. 



