66 



Lieut.-General Strachey. On the 



The results obtained by the two methods of calculation will there- 

 fore have no sensible difference of accuracy, and as the method now 

 proposed is believed to be both simpler and less liable to arithmetical 

 error it may without objection be preferred. The preliminary com- 

 putations on both systems, consisting of combinations of the observed 

 quantities by addition and subtraction, are identical up to a certain 

 point, but the formula? (2) involve more frequent use of tables, and 

 greater chance of error in algebraical signs, in the final operations. 

 Tt may be added that much additional labour is often needlessly 

 created by employing the hourly differences from the mean value, 

 instead of the hourly values themselves, which are obviously sufficient 

 for the computation of the coefficients. 



The probable errors of the values of the coefficients obtained from 

 the equations (1), will be sensibly larger than those above stated, and 

 on the same assumptions will be as follows : — 



For p 1 and q 1 





e = -577e, 



„ p 2 and q 2 



= iV(2). 



. e = -371e, 



„ p s and q s 



= */(3). 



, e = -289e, 







= -250e, 



» 24 





. e = -202e. 



The probable error of a pair of observations being rather less than 

 f ths of that of a single observation, the greatest possible error of the 

 coefficients thus found will only be about T %ths of the probable error 

 of one of the original observations, and when great precision is not 

 aimed at the results thus obtained may suffice, and will not be found 

 to differ materially from those got by the more tedious methods of 

 calculation. 



6. 



If the original expression for the value of a n is transformed into 

 the series 



an = p + P : (sin nz + T 2 ) + P 2 (sin 2nz + T 3 ) + &c, 



it follows that P x = ^(Pi 2 + q\) \ tan T x = pjq^ and so with all the 

 other terms of the series. 



The most convenient method of computing the values of P l and T l 

 is as follows : — 



log tan T = log p —log q ; 

 from this log sin T may at once be obtained, and 

 log P = p— log sin T. 



