502 
MAJOR-GENERAL SABINE ON THE LUNAR-DIURNAL 
I’he curves obtained from the values comprised in this Table are represented to the 
eye in fig-. 2, the fainter lines corresponding to the variations in the separate periods 
1844 to 1846, and 1846 to 1848, and the stronger line to the mean of the whole 
period of five years. The formulae by which these curves have been computed are as 
follows : — 
1844 to 1846, A^= + -006 — •092sin (a+0°-5)+-036sin (2a-f 345°T), 
1846 to 1848, -OH — •028sm (a+354°-5) -l--058 sin (2a+31675), 
1844 to 1848, A,= --005 — •058sin(a+2°) + -()48sin(2a+330°). 
The coefficients are decimals of a scale-division, and a is reckoned in hours (muiti- 
plied by 15°) from the epoch of the moon’s superior culmination. 
Inclination and Total Force . — ^The lunar-diurnal variations of the Inclination and 
of the Total force are derived from those of the horizontal and vertical components 
of the force by the formulae 
A^=sin 
'COS 
Y ■ 
■■X 
Aip 2 , • 9 
— — cos^ ^ ^ + siffi ^ 
§ being the Inclination, <p the Total force, X its horizontal and Y its vertical compo- 
nents. The variation of the Inclination is expressed in seconds of arc, the + sign 
implying an increase of the dip of the north end of the magnet. The variation of 
the Total force is expressed in parts of the total force at Toronto, of which force the 
approximate absolute value is !3’9 in British units. 
Table III. presents the variations of the Inclination and of the Total Force pro- 
duced by the moon at the different hours of the lunar day, derived from the observed 
variations of the horizontal and vertical components of the force by the formulae 
above stated. 
Table HI. 
Lunar 
hours. 
Lunar-diurnal 
variation 
Lunar 
hours. 
Lunar-diurnal 
variation 
Lunar 
hours. 
Lunar- diurnal 
variation 
of the 
Inclination. 
of the 
Total Force. 
of the 
Inclination. 
of the 
Total Force. 
of the 
Inclination. 
of the 
Total Force. 
Parts of the 
Parts of the 
Parts of the 
,, 
Force. 
Force. 
Force. 
0 
-0-56 
-•0000013 
8 
-t-6-05 
— ‘0000031 
16 
— 6-22 
-t- -0000063 
1 
— 1-44 
-1- -0000004 
9 
+ 0-17 
-•0000058 
17 
+ 0-37 
-f -0000053 
2 
-2-07 
-f -0000019 
10 
0-00 
— •0000050 
18 
-f 1-31 
-{-•0000033 
3 
-2-26 
-f -0000026 
11 
-0-32 
— •0000034 
19 
+ 1-92 
-1- -0000006 
4 
-2-05 
+ -0000021 
12 
-0-75 
— •0000010 
20 
-f 2-14 
— •0000020 
5 
- 1-61 
+-0000008 
13 
— 1-07 
-|-•0000021 
21 
+ 1-93 
-•0000031 
6 
-0-97 
— •0000012 
14 
— 1-08 
■f -0000044 
22 
-f 1-33 
—•0000033 
-0-33 
-•0000034 
15 
-0-76 
-1- -0000060 
23 
-f 0-42 
— •0000026 
'I'he values contained in this 'fable are represented to the eye by the stronger lines 
in figs. 3 and 4; the two fainter lines in each of these figures exhibiting the values 
