26 
MR. C. CHAMBERS ON LUNI-SOLAR VARIATIONS OF 
The mean variations f c .i(h), f s . x (h) (lines g and h of Tables 11 to 18), are curved in 
order in figs. 22 to 37. 
15. Extending now the process of elimination described in paragraph 11, so as to 
further clear the observed variations of their elements f c .i(b), fs.\(h), &c., as shown on 
lines a and b of Tables 11 to 18, we subtract f c .i(h) from the observed lunar diurnal 
variation at new moon, commencing with 0 hours ; subtract f s .i(h) from the observed 
variation at first quarter, commencing with 6 hours; add to the observed varia¬ 
tion at full moon, commencing with 12 hours ; and add to the observed variation 
at last quarter, commencing with 18 hours; thus reducing the residuals formerly 
obtained to four new residuals, the mean of which may be taken as the residual lunar 
diurnal variation for the quarters of the moon. A similar process, using lines c and cl 
of Tables 11 to 18, in lieu of lines a and b, leads to the residual lunar diurnal variation 
for the eighths phases. These residuals, for each quarter of the year and for both the 
magnetic elements, were found to be practically insignificant, the hourly numbers in 
all of them lying between the limits dr ‘000002. From this we conclude that, in each 
quarter of the year and for each magnetic element separately, our extended formula 
practically embodies the whole of the observed lunar diurnal variation for the full 
lunation. 
16. Coefficients of the harmonic equivalents of the typical variations, expressed in 
the form 
• 2tt (2tt \ , (2ir \ 
cq cos —h + b 1 sin —h + a 2 cos 2 ( —h j + b. 2 sin 2 ( ~hj + &c., 
were calculated for each case, the data being taken from Tables 9 and 10, and from 
lines g and h of Tables 11 to 18, and their values are exhibited in Tables 19 and 20. 
Table 19. 
Declination. 
«] 
*>1 
a 2 
&2 
A, 
Ao 
Bo 
'um . 
+ •0000005 
--0000034 
+ -0000006 
+-0000004 
i(ft> • 
+-0000023 
+-0000023 
+-0000010 
--0000003 
November to January -j 
+ '0000031 
+ -0000026 
+-0000097 
+ -0000040 
... 
... 
--0000030 
+-0000031 
- -0000055 
+ -0000077 
r/c-iM • 
- '0000032 
--oooooio 
+-0000009 
+-0000009 
/,■#) • 
+ ’0000008 
--0000006 
--oooooio 
•ooooooo 
February to April . . 
/«■*<&) : 
+ -00000U 
--0000022 
+-0000023 
--0000009 
U-#) • 
--0000014 
--0000001 
--0000002 
+ -0000016 
fAl(A) • 
-•0000014 
--0000019 
--0000001 
--0000011 
/>• l(ft) • 
+-0000029 
+-0000008 
+ -0000002 
-•oooooio 
May to July . . . . -! 
f'M r 
- -0000043 
^0000000 
--0000078 
+-0000013 
... 
... 
... 
- '0000024 
- -0000049 
--0000017 
- -oooooso 
- -0000004 
+ -0000020 
--0000007 
+ -0000003 
* 
iW • 
... 
- -0000001 
-•0000004 
- -0000017 
- -0000016 
August to October. . 
- -0000054 
+ -0000008 
- -0000076 
+ -0000047 
L/.. a (A) • 
... 
... 
- -0000016 
- -0000040 
- -0000050 
- -0000048 
