MOS80TTI OiV FRAUNIIOFER's RETICULAR SPECTRA. 445 



In constructing a formula to represent the observed inten- 

 sities with a small number of constants, it is important to pro- 

 ceed to the investigation by direct experiments, which yield the 

 given values for interpolation. The inspection of the values of 



— r previously given, shows that they diminish from the cen- 

 tre towards the extremities in a manner which tends to point 

 to the existence of a similar law of decrease on both sides. In 

 order therefore to repi-esent the intensities of the light in the 

 reticular spectrum, I shall take the ordinates of a symmetrical 

 curve, and select as the axis of the curve the line which passes 

 through that point where the length of the waves A^is = 553*5. 

 I have adopted the following formula : — 



r, 3x (i-%) 1 



-^=iX " _1 • . . • (6.) 



L 1 +4x^e X } 



in which, to render the members homogeneous, I have made 



^ = 3.-^ . . . (7.); x= ^Y- • • • (S-) 



and have assumed the maximum value of T, i. e. that which cor- 

 responds to the axis of the curve, to be taken as unity. 



That this formula may represent the intensity of the reticular 

 spectrum, it must satisfy the two following conditions : — 



Fiist. If by means of it the maximum intensity of light in 

 the prismatic spectrum be calculated, this must fall at the intei-- 

 val DE, about one-fourth or one-third of it from D towards E. 



Secondly. The calculated intensities of light corresponding 

 to the places at the lines B, C, D, E, F, G and H in the spec- 

 trum, must agree very closely with those observed, the values of 

 which we have given in No. 4. « 



6. To ascertain whether the formula (6.) possesses the above 

 property, I may previously remark, that the values of the in- 

 tensity G must generally be deduced from those of F by means 

 of the equation given above : — 



^=«rfA^ (4-) 



. To satisfy the first condition, I differentiate this equation, and 

 in the differential equation make -j- = 0, so that the value of 



