290 DR. S. CHAPMAN ON THE DIURNAL VARIATIONS OF THK 



become non-convergent to obtain results which can be got less simply in other ways. 

 Whether the final result is convergent depends in this case only on p, and not on tl it- 

 processes of analysis used to deduce II from p. Added June 11, 1913.] 

 We shall write, therefore, 



00 



K = Cae 2 d f cos 7 * <D, = COCK, 



o 



where C, e, and a are constants (introduced for convenience) whose meaning will be 

 explained later, and the coefficients d p are given numbers. Expanding cos p w in terms 

 of n, we have 



where 



0> 



and (since 



2*~V* = 2 m ~ 1 cos ra (x + ) = co8m(\ + t) 

 f p is given (for jo = 0) by 



00 



/,= s 



4 = 



B> 



Here we have written 



In virtue of the definitions of e p and a pq , we have 



Next we consider the differential coefficients of *. We have 



~ 



We shall write f f for ; evidently we have 



cos - sn 



D 



