240 Intelligence and Miscellaneous Articles. 



I have succeeded in finding the exact equation of the emergent 

 wave and comparing it with that of Airy. I have deduced from it 

 the value of the coefficient a 2 for a rainbow of the order K, 



^■fta COs'lCK + l) 8 



sinIK(K + 2) ; 

 as a particular case we have for the first bow, 



3 sin I 

 E being the radius of the sphere of liquid, and I the angle of inci- 

 dence of the ray of light of minimum deflection. 



By the help of this value it will be found that the deflection of 

 a complementary band is given by the formula 



m (\ 2 sinl)* I 

 tan0= (54)i cos I m 

 m being the number calculated by Stokes which refers to the band 

 in question, and X the wave-length of the light employed. 



Comparing the numbers obtained experimentally by Miller with 

 those furnished by the last equation, I have found a disagreement 

 which increases with the number of the order of the band in 

 question. I have likewise compared with the theory the experi- 

 ments recently made by Piilfrich on glass cylinders, and I have 

 found the same want of agreement. 



The theory of Airy appears thus to need supplementing. For this 

 purpose the position of the supplementary bands must be determined 

 bv the aid of the exact equation for the emergent wave which I 

 have obtained, and the results be compared with those obtained by 

 experiment. 



But the preceding formula shows that the deflection of a band 

 is greater the smaller the radius of the drop or cylinder, and the 

 feebler the index. In order to produce experimentally cylinders of 

 very small index, I had recourse to liquid veins which I caused 

 to jet vertically inside a rectangular glass trough filled with a 

 liquid which did not mix with the former, and of an index nearly 

 the same. While a thread of water in air gives between the two 

 former supernumerary bands a deviation of 40°, a thread of petroleum 

 jetting into water enables us to obtain a deflection of 2° between 

 these two bands ; ether, lastly, under the same conditions gives more 

 than 5°. 



But these experiments present great difficulties owing to the 

 instability of the vein. Thus I now use small cylinders of crown 

 glass with a radius of about 0-4 millim., and which I place ver- 

 tically in the centre of the trough filled with liquid. These 

 experimental determinations amplify the angular distance of the 

 bands, and increase the accuracy of the measurements. 



They have enabled me to prove that for great deflections the 

 discrepancy between theory and observation only increases. Airy's 

 theory is then only a first approximation, and I hope soon to be in 

 a position to introduce into it the necessary corrections. — Comptes 

 rendus, May 28, 1888. 



