the Wave-length within a Refractive Medium. 333 



2. That in isomeric bodies the same relation obtains closely 

 in a large number of the bodies examined. 



3. In all the cases examined v is a quantity not very far 

 below //.a- 



4. That the substitution of one chemical element for another 



v — 1 



has a very great influence on the quantity — — , and sub- 

 stances with high chemical equivalent have, as far as ex- 

 amined, a far greater influence in increasing the density than 

 in raising the limit. 



5. That the equation a sin 6= sin m0 gives in the cases 

 examined an approximate value for all the other indices, two 

 being assumed as data. In the case of rock-salt this holds good 

 far down in the invisible heat-spectrum, and also in the ultra- 

 violet, but fails somewhat at a certain point in the flint-glass 

 spectrum, and also, to a less degree, at the upper end of the 

 visible spectrum of bisulphide of carbon. 



It is evident that for a certain value of a and 6 the equation 

 asin0 = sinm# becomes impossible. This would mean that 

 there is an upper limit which is given by a certain value 

 of wave-length, beyond which the formula gives impossible 

 results. In the case of selenium only, of the substances ex- 

 amined, is this limit within the visible spectrum. The ana- 

 logy with the critical angle of total reflexion gives this 

 circumstance considerable interest. 



It is evident, then, in the present state of our data, that in 

 all cases examined the formula of Sir Geo. Airey gives an 

 approximate value of an index by means of two others, and 

 in this way they can be calculated ; but that, as a rule, 

 the lower indices come out too high as compared with 

 the upper. A cause for this may perhaps be suggested 

 in the heating of the medium due to the absorption of the 

 rays; and as there seems to be evidence of absorption of 

 short waves above the longer ones, given by recent stellar 

 photometric determinations, this absorption would perhaps, if 

 included in the conditions of the problem, account for some 

 of the outstanding difference. This and anomalous dispersion 

 — itself apparently depending on absorption — opens an in- 

 teresting Held of inquiry, and in this direction I propose to 

 pursue the investigation. 



Since the above was written I have been informed by Dr. 

 Gladstone that he in some cases used a screen of solution of 

 alum, but found that practically nothing was gained by its 

 use. This fact, then, must be taken into account in any 

 attempt to explain the outstanding differences between theory 

 and observation. 



