we get 



344 M. R. Riihlmann on the Alteration produced by Heat 



evidently regular system of values by means of a mathematical 

 formula. 



The idea which immediately suggested itself was to try whether 

 a formula similar to the one usually employed for the coefficients 

 of expansion did not satisfy the experiments. In order to try 

 the fitness of different curves corresponding to these values, some 

 of the observations for the sodium-line were taken, from which 

 four so-called standard values (Normalorte) were chosen. 



t. 0°. 10°. 40°. 70°. 



n t 1-33380 1-33340 1-32910 1-32115 



By the help of these the values of the constants were approxi- 

 mately reckoned. It seemed possible to assume, without in any 

 way departing from the truth, that a formula suitable for the 

 index of refraction for D would be applicable as far as concerned 

 its form to the other two rays. For a curve of the form 



n t =a-{-bt + ct' 2 



7^= 1-3338 - 1-0000332 £-0-000002107 f . (1) 



from the standard values 0°, 40°, 70°. 



This line gives all the first values too small, agrees pretty well 

 at mean temperatures, and diverges rather considerably from the 

 last found values. 



w,= l-3338-0-00001099*-0-000002980* 8 \ (0) 



+ 0-000000007936 i 3 J >• 



This equation certainly agrees remarkably well with the ob- 

 servations. On comparing the first terms, it is seen that the 

 lineal term is very small compared with the others ; and I there- 

 fore tried whether any great difference would be made by neg- 

 lecting it*. The calculation was therefore repeated for 



n t — a -\-ct 2 + dt 3 , 



* It appears, under correction, to the translator that the author's rea- 

 soning is here unsound. Calling the terms 



1-3338, 0-00001099^, 0-000002980 * 2 , 0-0000000093G* 3 



respectively 



A, B, C, D, 



o o 



from t= to t= 3'7, the terms are in the order of magnitude ABCD, 

 „ t= 3-7 to t= 37 „ „ „ ACDB, 



„ t= 37 to (=375 „ „ „ ACDB, 



„ t= 3/5 to temperature beyond the thermometric range ADCB. 



Since up to 37° B >- D, it is not clear why the linear term should be re- 

 jected rather than the cubic one. — F. G. 



