466 Mr. J. B. Dale on the 



Equations of the type E 2 a+^>,Ea 4-p 2 a = were formed 

 and divided into two groups, the equations in each group 

 being added to form a single equation. 



From the two resultant equations the values of p x and p 2 

 were found to be 



£>!== 2-4290, p 2 = l*4188. . . . (10) 



Hence s 1= -*9774, * 2 =-l'4516. . . (11) 



and O^m ^, 6> 2 = 136°-5. . . . (12) 



In order to test how far the assumption of the existence 

 of only two independent periodic terms was justified, the 

 values of H = Wa-\-p l Ea i-p 2 a were calculated with the 

 above values of p-i and p 2 and are placed in column (6). 



It is seen that with one or two exceptions the residuals are 

 small and present no systematic run. Hence it is concluded 

 that the deviations from zero are entirely due to errors in 

 reading the values of y } and would be removed by appropriate 

 corrections. 



5. The determination of corrections is really an indeter- 

 minate problem, for the number of ordinates exceeds the 

 number of equations. Expressed in terms of the y's, each 

 equation Wa r -\-p^a r +jj 2 a r ~0 becomes 



y r+3 + q 1 lJ r+ 2+q 2 l/r + l — q2!/r — q^r-l—yr-2 = 0, (13) 



where q l =p l — 1 and q 2 =r^+P2— Pi (14) 



The observed values, however, differ from the true values 

 by small quantities v, and hence these deviations from the 

 true values satisfy the equation 



To render the problem of finding appropriate values of 

 the v's determinate, we add the condition that the sum of 

 their squares must be a minimum. 



Since the labour involved in obtaining an exact solution 

 of: the system of simultaneous equations arising from the 

 expression of the problem in this form would be extremely 

 great, it was decided to proceed by a method of successive 

 approximation. 



It is clear that any particular v will appear in six equations 

 of the type (15), and these together with the minimum con- 

 ditions will <nve a value for v. This method was tried, but 

 was not found to lead to any more satisfactory results than 

 those obtained by the simple method of obtaining six separate 



