394 



Mb airy, on the INTENSITY OF LIGHT 



As the increments in the 6th and 7th sections were the same, the 

 calculations for these two sections were conducted without the inter- 

 ruption which was necessary at the separation of the other sections. 



The values of w and '^ (uf - m.w) corresponding to the middle of 

 each interval were then computed, and the appropriate value of 



cos X («'' -m.w) 



was formed. Thus, in the first section the computations were made 

 for w = 02, 06, 10, &c: in the 4th section, for w = 1447, 1461, 

 1-475, &c. For a reason that will be shortly mentioned, the values of 



cos - (w' - m . w) were also computed for two values of w preceding 



the first, and two values following the last, of each section. These values 

 were then differenced as far as the 4th order: which operation, besides 

 giving a means of checking most severely the accuracy of the compu- 

 tations, supplied the numbers necessary (in the next process) for con- 

 verting the sum into an integral. 



Now, suppose, that u^ is a function of x, and that the quantity 

 // is so small that the furictions u,^^, m,.+2*. admit of being expressed 

 with sufficient accuracy by the formula u^^ + b.h + c.h- + d.fi^ + e .h\ 

 v„ + b. {2/i) + c . i^hy + d.(2h') + e. (2hy. This assumption is abundantly 

 accurate for the numbers of which we are treating here. Set down two 

 values preceding «, and two following it, and take their differences as 

 far as the 4th order, thus 



u,- bh+ ch'- dh'+ eh* 



I/.+ bli+ ch'+ dh'+ eh* 

 u,^2bh + 4:ch' + 8dh^+i6ek* 



1st Differences. 

 bh-3ch'+7dh'-\5eh' 

 bh- ch'+ dh3- eh* 

 bh+ ch'+ dh'+ eh* 

 bh + 3ch'+7dh'+15eh* 



2d Differences. 



2ch'-6dh^+lieh* 

 2ch' + 2e/i* 



2ch' + 6dh'+lieh' 



3d Differences. 



6rfA'-12eA* 

 6dh^+l2ek* 



4th Diff. 



24cA* 



