360 Prof. G. H. Darwin. On an Apparatus for [Dec. 15, 



Tlie method of the last section apparently depends on the com- 

 pleteness of the year, yet, with certain modifications, it may be 

 rendered available for shorter periods. 



We suppose that so much of the year as is available is broken into 

 sets of 30 days by the rules of the last section, and that the means 

 are harmonically analysed. The results of such harmonic analysis 

 for month (T) are given in (11) of 3, but for the purpose in hand 

 they now admit of some simplification. It is clear that it is not 

 worth while to evaluate the very small solar elliptic tides T and ft 

 from a short period of observation. If, then, we denote by P< T ) the 

 ratio of the cube of the sun's parallax to its mean parallax at the 

 middle of the month (T), the first three terms of the third of (11) 



cos 



may be included in the expression P^H S . K S . The last term of this 



sin 



equation really does involve the solar parallax to some extent, and 

 we may, with sufficient approximation, write the third pair of equa- 

 tions 



= #, s C P n 8 ^ + ^^(^'-V''-60 T-29-53). 



Let us now consider the value of PW. The longitude of the solar 

 perigee is 281 or 79, and the ratio of the sun's parallax to its 

 mean parallax is approximately 1 + e, cos (h + 79), and the cube 

 of that ratio is 1 + 3e ( cos(/i + 79) or 1 + 0-0504 cos (7*, + 79). 

 Now &, the sun's longitude at the middle of month (T), is 

 ho + 15 + 30 r; hence 



PW = 1+0-0504 cos (&o + 30 c 



; 1 



p (7) = 1-0'0504 COS (^ + 30 ' 



Thus it is easy to compute the values of 1/PW for the successive 

 months, when we know h the sun's mean longitude at O d O h of the 

 month 0. 



The semi-annual tide, being usually small, may be neglected in 

 these incomplete observations, and the equations (11) now become 



qi M _. A i H sa _ _ , __ 



cos, 

 ~Bin (* -V"~60T-29-53), 



