MOSSOTTI ON FRAUNHOFEr's RETICULAR SPECTRA. 447 



which in the second part of the expression of -j-—^ is contained 



Ct A 



between the parentheses. 



If we had eliminated y^ from the latter equation and (6.), and 

 instead of ^^ and x substituted its values (7.) and (2.) in function 

 of A, the resulting equation would not involve any unknown 

 quantity but X, and would be capable of giving the value of 

 this magnitude for that place at which the intensity of the light 

 of the prismatic spectrum must be at its maximum. We shall 

 denote this value by x^. 



The elimination and solution here spoken of would be im- 

 practicable if it were required to be carried out to its fullest extent. 

 We may however remark, that the maximum of G must lie very 

 near to that of /', and that the values of F when near the maximum 

 in general var}^ but little, and still less in our peculiar instance, on 

 account of the form of the equation adopted. As the value of ;^ 

 in the formula (6.) must be rather small, and the exponential 



e ^ becomes a very small magnitude which may be neglected, 

 the equations (6.) and (10.) may be reduced to the form 



~^». = ix -%' + %' 



^m = 3^. H^^^^^ {1 -5x + 3x^ + 9x^}. 



For the purpose of solving these two equations, I have cal- 

 culated a table of five terms, which gives the values of 



■j-'j H -^ — by means of the assumed values of K, and those 



of Km which are very near those of \. Then, assuming a value 

 for p^ which is very near the truth, I calculated from the first of 

 the two equations, that of xr^, then that of £■, from which I next 

 deduced 



An 



A = A^ + 



'■0 



With this value of A, by entering in the table mentioned above, 

 I have deduced that of 



tVH 



A„, — A^ 



"0 



and by means of the second equation obtained a second value of 

 3^. If this value of ^^ coincided with that already obtained from 

 the first equation, I concluded that the assumed value of x ^^"«s 



