396 Mr airy, on the INTENSITY OF LIGHT 



the intervals into which iv is divided. And as the same formula 

 applies to every one of the intervals, it applies to the sum of all. 

 And the sum of all the partial integrals through each section is the 

 whole integral through each section. Thus we find, 



Integral through each section 

 = interval x i 



■ sum of computed values of cos - {w^ - m . w) 



+ — sum of corresponding 2d differences 



17 

 — t-rjc.^ sum of corresponding 4th differences 



= interval 



sum of computed values of cos ~(vr — m .w) 



1 1 1st difference following the last term — 1st difference 1 



24 1 preceding the first term J 



_ 17 f3d difference following the last term - 3d difference! 



5760 ( preceding the first term J 



This process was used throughout. For the purpose of forming the 

 ;Jrd difference following the last term and that preceding the first term, 



it was necessary to compute two values of cos ^ (w' - m . tc) following the 



end of each section and two preceding its beginning. 



The values of - {w^ — m . w) were computed by means of Delambre's 



Tables Trigonometriques Decimales. The centesimal division of the circle 

 is, in every instance in which I have used it> far more convenient than 

 the sexagesimal: but in an instance like the present, where there is 

 continual addition or subtraction of arcs, and where the whole arc amounts 

 to several circumferences, the labour and liability to error would be so 

 great with the sexagesimal division, as to make the operation almost im- 

 practicable. The numbers were thus formed in each section. The first 



four values of - vf were computed independently and differenced, and 



with these differences the rest of the series of - uf' was formed: the 



2 



last was also computed independently as a check. The first term of 



