62 PROCEEDINGS OP THE AMERICAN ACADEMY. 



gave unmistakable evidence that one band belonged to the ordinary, the 

 other to the extraordinary ray. In no case did either of the bands dis- 

 appear entirely, owing to the fact that they overlap, which makes it 

 impossible to have complete transparency with the Nicol in any posi- 

 tion. No measurements have as yet been made of the values of the 

 extinction coefficient in different parts of the spectrum, owing to the diffi- 

 culty of preparing a film thin enough to transmit light within the absorp- 

 tion baud. Though it is possible to get a wedge-shaped film between 

 a lens and a flat plate which transmits all wave-lengths to a certain 

 degree in its thiuest portions, a film of this nature is quite unsuitable for 

 quantitative measurements of the absorption. Probably by working with 

 solutions in glycerine of different concentrations and thicknesses a fairly 

 correct idea of the absorption curve could be obtained by calculation, 

 though this method would be open to some objections. Until the sub- 

 stance has been investigated in the infra-red and uutil the dielectric 

 constant has been determined, the dispersion formula cannot be applied 

 to it to the best advantage. 



At the present time facilities for investigating these two points are not 

 at my disposal, but I expect in the near future to investigate them. In 

 the meantime it is instructive to apply the formula to the results which 

 have already been obtained. 



The Dispersion Formula. 



For parts of the spectrum in which the extinction coefficient has a 

 small value the dispersion is represented by the formula 



2 i , X W * A2 



* 2 = 1 + Z ji 



- \S 



in which X K are the wave-lengths of the centres of the absorption bands 

 (nearly) and m K constants for these bands, the summation being taken for 

 all of the absorption bands, whether near or far removed from the por- 

 tion of the spectrum under consideration. If the bauds are far removed 



A' 2 



from this region the fraction —^ ; is practically equal to unity and 



A" — A K 



the constants m', m", etc., have merely to be added or subtracted accord- 

 ing to whether they lie on the more refrangible or less refrangible side 

 of the spectral region under investigation, i. e., according as the sign of 



X 2 . . . 



-~ -, is positive or negative. 



A" — A K " 



