2 ART. n.^ATCHT AND TANAKADATE : THEORY OF 



of the rainbow which is due to a source of finite dimensions, 

 the result hohls only approximately. Recently, the colours of 

 the rainbow have been minutely investigated by Pernter*^^ witli 

 the use of Maxwell's theory of compound colours. In that paper 

 Pernter also calculated the colours of the rainbow^ as due to a 

 circular source of light, by a numerical addition of the results, 

 due to seven point-sources in a straight line, each differing by 

 5'. This method of calculation is not exact, and the result only 

 holds as a rough approximation (see ante). 



It is to be remarked that Pernter's values^'^ of Airy's inte- 

 gral /" (z), on which the whole calculation is based, are some- 

 times discrepant from those originally given by Airy. On 

 comparing them with Airy's values, we found three mistakes at 

 z-1.8, 2.2 and 3.6, and Pernter himself, in his second paper, ^^^ 

 remarked that these mistakes came from Mascart's table and 

 that they did not aftect the final result of his calculation. For 

 z>8, on drawing the curve representing Pernter's values, we 

 found considerable irregularity. It seemed therefore advisable 

 to repeat the calculation, using Stokes's semi convergent series 

 (see ante). The results of our calculations were always greater 

 than Pernter's values, excepting the maxima and minima values. 

 Some numerical examples arc given in the following table : 



z /' : Pernter's f' : our's 



8.8 0.189 0.223 



9.4 .100 .125 



10.0 .240 .268 



10.6 .022 .033 



11.0 .170 .189- 



(1) Wien Sitz. Ber. CVI. 2a, p. .135 (1897); Neues über den Regenbogen (Wien, 1898). 



(2) Loc. cit., p. 140. 



(3) Wien. Sitz. Ber. CXIV. 2a, p. 1 (1905). 



