598 Mr. AIRY'S supplement TO A PAPER ON THE INTENSITY OF LIGHT 



Jo cos w^dw into its successive positive and negative portions, we have A^ — Ji + A3- Ai+ ... in 



which by -i42„ + i is meant the portion of the integral (taken positively) which occurs from 



M>' = (2 » + 1) - to w' = (2 « + 3) — . The greater n is made, the smaller is the interval of this 



partial integration ; and these successive portions diminish, and diminish without limit, so that the 



series is convergent, and the error always less than the first term rejected. And J^ sin w^dw may 



be treated in the same way. 



"A. DE MORGAN." 



The following numerical values occurring in the application of Professor De Morgan's final 

 series may be conveniently placed here : — 



Log Tj = 0-42796274.93. 



Log r, = 0-1316564916. 



With these series I have computed the values of J^cos — (w^ - m .w) (m = to to = - j ; for 



w = — 5 .6, -5.4, Stc. as far as + 5 . 6 : and I now exhibit a table of the results, compared 

 with those deduced from quadratures as far as the latter were carried. Each term of the series 

 was computed to 6 decimals, and one figure was struck ofi^ in the sum. 



It is impossible to make the calculation for larger values of m, positive or negative, even with 

 10-figure logarithms, on account of the divergence of the first terms of the series. For the values 



