70 



Lieut.-General Strachey. On the 



a series of 72 terms, which will comply with the conditions, in the 

 following manner : — 



If the original series of the 73 five-day means be represented by 

 the numbers (0), (1), (2), (3), &c, .... (72), it will be apparent 

 that the first term (0) corresponds with noon of the 3rd day of the 

 year, the subsequent terms following each other at five-day intervals. 

 The new interpolated series of 72 terms should begin at hours of 

 the 1st day of the year, and will be designated by the numbers 0, 1, 

 2, 3, &c, .... 71. Then if T and T_ 2 represent, respectively, the 

 mean for 24 hours of the first day of the year under computation, 

 and the last day of the preceding year, the interpolated series 

 will be— 



= KTo+T-!), 



1 =K(0) + (1))+tV((D-(0)) = (0) + H((l)-(0)), 



2 = i((l) + (2))+yV((2)-(l)) = (l)+ff((2)-(l)), 



3 = i((2) + (3))+A((3)-(2)) = (2) + f|((3)-(2)), 



35 = i((34) + (35))+ff((35)-(34)) = (34) +| i ((35)-(34)) k 



36 = i((35) + (36)) + ff((36)-(35)) = (36), 



37 = (37) + T V((38)-(37)), 



71 = (71) + ff((72)-(71)). 



Moreover, for a series of 72 terms the value of z in the fundamental 

 equation will be 5° ; and designating the sums of the cosines and 

 sines, respectively, of the successive multiples of z between z and nz by 

 [cos 45° to 85°], and [sin 45° to 85°], and applying a similar notation 

 to the quantities before designated by the series A, B, 0, D, we shall 



^[cos 5° to 85°] -^[sin 5° to 85°] = 10-95188^-f 

 10-95188(-^ 1 4-^ 1 ), 



^[coslO^o^O^-^sinHTtoSO ] = 5-21503 (p 9 + q 2 ) , 

 5-21503(-^ + 2 2 ), 



^ 3 [cosl5°to 75°]- 23 [sin l5°to 75°] = 3'29788(p s + g s ) t 

 3;29788(-^+ g3 ), 



[D 5 toD 8 ] =_p 4 {l + 2[cos20°to80°]} = 575877^ 4 , 

 2 24 [sin 20° to 80°] = 5-67128&. 



have — 



lAtoAtf] = 

 [A 19 toA 35 ] = 



[B!toB 8 ] = 

 [B 10 toB l7 ] = 



[0^0 0,] = 



[0 7 toC u ] = 

 [D toDJ - 



[B l toD 8 ] = 



