Daily Variation of Solar Radiation, etc. 541 



E m being used for the integral 



cos S. cos InddO, 



Jo 



or I Jl — sin- e sin 2 6 . cos 2n6dd. 



The series (21) converge only slowly; they have been used to 

 confirm other work for the latitude of Greenwich and for latitude 

 60°, but in the absence of tables of associated functions calculated 

 with reference to angle, the labour entailed is absolutely pro- 

 hibitive. Accordingly in the case of the even functions % 2 %4--- 

 the formula (3) was used to give particular values for 6 = 0°, 30°, 

 60°, 90°. Knowing the form of the expansion, these are sufficient 

 to determine a a~ 2 a A a 6 on the assumption that a s and subsequent 

 coefficients are negligible. The tabulated results for % obtained 

 in the previous paper (Q there) were obtained directly from finite 

 formulae involving elliptic integrals, and shewed a rapid con- 

 vergence in the numbers a a 2 ..., although in that case also the 

 convergence of the zonal harmonics was slow. The expectation 

 that this would also prove to be the case for % 2 ••• was confirmed 

 by the small values obtained for a 6 , so small that although a 6 was 

 always included in the work, its values are not tabulated, as they 

 only just come into the 4th place of decimals for latitudes 50° and 

 60°. For the odd functions % 3 % 5 • . • and the odd part of ^ only 

 the values for 30°, 60°, 90° are available ; sufficient to give aj a 3 a 5 

 on the assumption that subsequent terms may be neglected. Here 

 also the values of a 5 turned out very small. The calculations were 

 made to 6 places, and two are suppressed. 



As regards the tables it should be mentioned that when 



2 d0_ f 



r " dt 



is used, formula (1) becomes 



2Hd0„ v ,, 



— ^— [iXo + S&coss^J, 



in which the ^'s depend on as shewn in table (A). With one 

 year for the unit of time h = 2wab, also dd — 2irdt [1 + small 

 quantities depending on eccentricity]. 



The transformation to mean time is made as in § 17 of the 

 previous paper, the product % s rZ0 becoming 2ir^ g 'dt, so that 

 formula (1) then stands 



-^ dt [h%o + %v' cos sf], 



