96 U. S$. COAST AND GEODETIC SURVEY 
n=365 
>) Yn COS 24(n—I1)e 
n=1 
—=4,96A’ —1.51B’—1.70C’ —0.24D’ +182.38 LH’ 
+3.88A” +3.06B” +3.25C” +0.00D” +0.00 E” 
n=365 . 
dS Yo Sin 24(n—1)e 
n=1 
=—0.70A’—0.18B’ —0.21C’+0.01D’+0.00H’ 
+0.68A” —0.17B” —0.20C” + 0.00D” + 182.62 EH” 
(417e) 
274. The numerical value of the first member of each of the above 
normal equations is obtained from the observations by taking the 
sum of the product of each daily mean by the cosine or sine of the 
angle indicated. The solution of the equations give the values of A’, 
A", B’, B’’, etc., from which the corresponding values of quantities 
A and a, B and 8, etc., of formula (405) are readily obtained, since 
LA 
AG & 
A=, (A’)?+ (A’)? and a=tan7! 
In calculating the corrected epoch, it must be kept in mind that the 
t in this reduction is referred to the 11.5 hour of the first day of series 
instead of the preceding midnight. 
275. Before solving equations (417), if the daily means have not 
already been cleared of the effects of the short-period constituents, it 
will be necessary to apply corrections to the first member of each of 
these equations in order to make the clearances. 
The disturbance in a single daily mean due to the presence of a 
short-period constituent is represented by equation (398). Intro- 
ducing the subscript s to distinguish the symbols pertaining to the 
short-period constituents, the disturbance in the daily mean of the 
n= day of series due to the presence of the short-period constituent 
A, may be written 
yslo=aqA —— cos {24(n—1)a,+11.5a,+a;} (418) 
ond 3 
The disturbances in the products of the daily means by 
cos 24(n—1)a and sin 24(n—1)a 
may therefore be written 
[Ysln CoS 24(n—1)a 
1 in 12a, 
oa A ee a 1 [eos {24(n—1) (a,ta)+11.5a,+ a5} 
+ecos {24(n—1) (a4,—a)+11.5a,+a5}] (419) 
and 
[Ysln Sin 24(rn—1)a 
1 I 2 ‘ 
SA eee gin (28 Ge nae Wesoete| 
SIN 3@, 
—sin {24(n—1) (a,g—a)+11.5a,+a5}] (420) 
