442 MOssoTTi ON fbaunhofer's reticular spectra. 



equation need only be subjected to a single transformation. 

 First, since when in it we make X = Aq, .v must be = 0, we have 



sinl(^ + 4. )^ 



sin I 4> ^ ' 



If now i be eliminated by means of this expression, and twice 

 the product of the cosine of half the sum into the sine of half 

 the difference be substituted for the difference of the sines, we 

 obtain 



[(^«) -ijsinj, LV^/ J 



In using this formula for determining the two constants h and k, 

 we must substitute the respective values of jt, for the rays situ- 

 ated upon the six lines B, C, D, E, F, G, 



DB. DC. DE. DF. DG. Dll. 



— 12' 20" 25 -9'4"-2; ll'5o"-0; 22'23"-9; 42'47"-8; 6l'5"-8; 



and correspondingly, 



A = 688 656 526 484 428 393, 



\q being = 589. 



On carrying out the calculation, we get the six equations, 



0027291 =h + 1-7329^ 

 0-027650 = h + 1-8061 k 

 0-027519 = 7/ + 2-2539 A 

 0-027494 = // + 2-4809^ 

 0-028527 = h + 2-8850 yfc 

 0-028903 = /« + 3-2463^; 



whence, by the method of least squares, 



h = 0-025555 k = 0-000975 ; 

 and we then obtain from the equation (3.) 

 i= 1-608506. 

 With these numerical values, the refractive index of flint- 

 glass, of which the prism used by Fraunhofer in his experiments 

 was composed, is expressed in function of the length of waves in 

 vacuo for the different coloured rays, by 



^ = 1-608506 + 0-025555 (M + 0-000975 (^) . 



To determine to what degree of accuracy this formula \'(ould 

 represent the observations, I calculated by means of the equa- 



