74 U. S. COAST AND GEODETIC SURVEY 
of tabulations, letting ¢ represent the same time in the middle day, the 
limits of the group interval for the day following the middle one, are 
(Pe a nd (1+ 972 +53 NEES p) If we let n=—3, —2, —1, 0, 
+1, +2, +3, respectively, for ne teed successive days represented 
by a single page of original tabulations, the limits of the group interval 
for any day of the page may be represented by 
360pn__15p’’ | 360pn =i 
4 woke and (14-7 +—- 
218. Formula (311) gives the mean value of the B ordinate for 
grouping of the A summations. The mean value of (311) obtained 
by combining the groups falling in any particular day of page of 
tabulations in the limits indicated above is 
b Se 
isp? PB cos (bt+ B) dt 
360pn _ 15p’ 
a OD 
asf OY : FB) sin(bt+ 6+ 2° 
mw 5p’ 
aoe hon sy 
auf 24 ye : Lop 360pn 
=( aa FB cos (bet epee ) 
=F\F)B cos Ee pp *) (312) 
OUI a ) 
1 15p’ ; 
if we put R= a sin aie for brevity. 
219. Formula (312) represents the mean value of the B ordinate 
for a particular day of the page record. The average value for the 
7 days may be written 
n=+3 
1F\F,B >) cos (4+ + 00Pt ) 
n=—3 
= B | cos (bt +8) cos (—3 SOP.) sin (bt+ 8) sin (— 3 oe) 
+cos (bt+ B) cos (—2 se) sin (bp+ B) sin (— 2 20re ) 
+cos (bf+ 8) cos (-1 sone) — sin (bt+ 8) sin (-1 sO") 
+cos (bt-+ 8) cos 0—sin (b¢-+ 8) sin 0 
-+cos (bt+ 8) cos (See) — sin (bt+ 8) sin sr ) 
(Formula continued next page) 
