268 M. R. Riihlmann on the Alteration produced hj Heat 



formula 



rc=l-33696-0-00006909/-0-00000085i3* 3 . 



As this method requires the exact determination of the law of 

 alteration of the angle of the axis of the crystalline plate, and is 

 therefore rather complicated, and, further, as every error in the 

 determination of this law is introduced into the determination 

 of the index, I do not think that the method will receive very 

 extensive application to the determination of the dependence of 

 the refraction of liquid bodies upon their temperature. These ob- 

 servations relating to Fraunhofer's line D and water are marked 

 in Plate V. by crossed circles. 



If we cast a glance back at the above experimental researches 

 which have been hitherto published, we are forced to admit 

 that the chief fundamental facts have been indeed established 

 by Fizeau for solid bodies and by Gladstone and Dale for liquid 

 ones, but that the results are, to a very considerable extent, de- 

 ficient in accuracy. The question canDOt be regarded as solved 

 until not only the refractive index (with exactness within cer- 

 tain limits), but also the law of alteration has been given in the 

 form of an interpolation formula. This interpolation formula 

 is best given in the shape 



H t = a + bt + ct* + dP + eP + , 



where the constants a, b, c } d, &c. have been determined with 

 the greatest accuracy and the agreement of the formula with 

 the observations has been established. For solid bodies, Fizeau 

 has furnished these data, while for liquids the only data hitherto 

 given are those of Miittrich, and these merely between 0° and 

 65° C. The numbers of the latter observer differ so much from 

 those of other physicists, that, in spite of their great extension, 

 they can at most only be regarded as relatively true, inasmuch 

 as they must all be affected by a common error, about which we 

 do not even know whether it may not be a function of the tem- 

 perature. 



The problem which is here first to be solved is accordingly 

 to give a formula, either for the alteration of the index of refrac- 

 tion for different luminous rays for as many liquids as possible, 

 or preferably for the constants of a dispersion formula. 



I have endeavoured to give these data for water ; and after I 

 have tested my method by this investigation, I shall seek to de- 

 termine these important physical constants for other substances. 



It appears, from what has been stated above, that it is of as 

 little avail to determine the refraction-indices of substances with- 

 out giving the formula of alteration as it is to give the specific 

 gravity without adducing the coefficient of expansion. 



