72 Royal Society. 



836 + A + « 



^-11 = 60158-71 . (1+0-002845 cos 2L) 



900 



which Delcros has transformed (in the ' Annuaire Meteorologique de 

 la France' for 1849) to the equivalent of 



/*-n = G015871 x [log B-log 5-0-00003892/8 . (M— m)~\ 

 836 + A + « vPv [\ ^-H + 52251 Hi 



x 900 -* - L + r + m 



The last factor may he split into the two 



r. Then, since 

 6015871 xA+ ^£1^=60309-19 



without sensible error. Then, since 



and 60309-19 x 0-00003892/8 = 2-34770, 



if we put h — H for the product of the three first factors on the 

 right-hand side in (c), we find 



A-H=[60309-19.(logB-log5)-2-34770.(M-m)]. 836 



900 



+ *=Jx 2-625- cos 2L + ^ 



Putting 2-35 for 2-34770, and /, h", H" for their values, this form 

 (d) will be identical with (a), provided that 



60309-19. (logB-log5) = 52400.?— |+c . . (e) 

 Now putting B — b=yB, we have 



B— b y \.'( ,\ -o . 1 3 , 1 4l \ 1 



log B-log b=\og— =fj..(y+ iy 2 + iy 3 + ±y*+ ...\=fi(z + d), 



where \x is the modulus of the tabular logarithms, and 



d=-Ly>+ -V..., 



always a convergent series as y is always a proper fraction, and smaL 

 when y is small, as it is for moderate heights. 

 Hence 



60309-19. (logB-logi) = 60309-19x 2/i 5^ + 60309-19. i/rf 



B + o 



=52384 1^| + c'. 



