136 KEPORT— 1882. 



matter dissolved in it is placed more towards the red.' He divides the 

 solvents into four groups. While the order of the liquids within each 

 group may change, the second group will always displace the absorption 

 band more towards the red than the first, the third more than the 

 second, and the fourth more than the third. Dr. Claes, who also remarks 

 that the order of the solvents is not strictly that of their dispersive 

 powers, suggests a formula which shall correctly represent the position 

 of the absorption bands in different liquids. If A. is the wave-length of 

 the centre of an absorption band, his equation, when freed from tLe 

 sheltering confusion of ornamental variables, runs thus — 



^'-* = "+K^ .... (1) 



In this equation i represents the dispersive constant of the liquid ; 

 that is to say, the factor of the inverse square of the wave-length in the 

 series which gives the refractive index as a function of the wave-length ; 

 and a, /3 are two constants which, according to Dr. Claes, have to be deter- 

 mined for each absorption band by means of its position in different 

 liquids. Now to ordinary minds the above equation seems simply a 

 restricted case of Kundt's original law that the wave-length increases 

 with the dispersive power, for we can solve for X^ — h, and this quantity 

 must therefore be a constant, which, on the face of it, it is not, as Dr. Claes 

 himself takes some pains to prove. Yet our author shows how the same 

 law in its new shape can with astonishing accuracy explain facts which to 

 most minds show no regularity at all. As it is a point of some importance 

 to possess a method of calculation which shall give such small differences 

 between observed and calculated values as those obtained by Dr. Claes, we 

 may take the trouble to point it out, especially as he might have still 

 further reduced these differences had he been more careful in his calcula- 

 tions with the two last decimal places. The secret consists in substituting 

 in the expression on the right-hand side the observed values of X and then 

 calculating the X on the left side. The differences between these two 

 values Dr. Claes calls the differences between the observed and calculated 

 values of \. It is easy to see how this plan works. "Write A for \^ — h, 

 and call the values which A takes in the two special cases L, and L2 ; 

 then in the way suggested by the author a and /3 have to be determined in 

 terms of L, and Lj, and by substituting these values equation (1) 

 becomes 



A = L, -f L2 - M2 .... (2) 



If we write L, + d for the observed value of A we get 



A _ L, = Lo - ^^ - -^^ 



But the difference between A — L, and d being the so-called difference 

 between the observed and calculated value becomes - — ^-^ — ^ . 



As the total displacement Lo — Lj between any two bands is small, as well 

 as d, this quantity is small compared to d. In other words, as long as 

 A, Lj and Lg differ by small quantities, equation (2) must necessarily be true 

 to quantities of the same order of magnitude, and any discrepancy must 



