376 
ME. C. CHAMBEES ON THE SOLAE VAEIATIONS OE 
they show very distinctly the consistent character of the semiannual inequality in the 
diurnal variation of declination in different years. 
The half-excess for each hour of the numbers in the last column of Table XI. over 
those in the last column of Table XII., or the semiannual inequality of the mean diurnal 
variation of declination, is as follows, the excesses being written in the order of the 
hours 0 to 23: — 
— 0-905 - 0-952 - 0-843 - 0-473 - 0-137 +0 123 + 0-071 -0 165 -0175 - 0 135 - 0-093 -0 062 
-0002 + 0-072 + 0-152 + 0-188 + 0-279 + 0-496 +1052 + 1-355 + 0-978 + 0-225 - 0-399 - 0-633 
Fig. 21, Plate XXVI. is constructed from these numbers. 
Table XIII. — Showing the mean diurnal variation of Declination for each of the years 
1859 to 1865. 
Bombay 
Astronomical 
Hours . 
1859 . 
1860 . 
1861 . 
1862 . 
1863 . 
1864 . 
1865 . 
h . m 
0 12 
- 1-604 
- 1-711 
- 1-669 
- 1-554 
- 1-562 
- 1-494 
- 1-499 
1 12 
- 1-517 
- 1-540 
- 1-513 
-1345 
- 1-318 
- 1-230 
- 1-250 
2 12 
- 1-086 
- 1-074 
- 0-917 
- 0-619 
- 0-814 
- 0-888 
- 0-768 
3 12 
- 0-557 
- 0-508 
- 0-350 
- 0-160 
-0 325 
- 0-279 
-0174 
4 12 
- 0-106 
+ 0-002 
+0123 
+ 0-227 
+ 0-070 
+ 0-038 
+ 0-148 
5 12 
-0173 
- 0-006 
+ 0-083 
- 0-040 
+0 054 
+ 0-063 
+0124 
6 12 
- 0-275 
- 0-152 
-0009 
-0149 
-0042 
-0073 
+0017 
7 12 
- 0-198 
- 0-141 
- 0-142 
-0156 
-0121 
— 0-117 
+0003 
8 12 
-0143 
-0 157 
—Oil l 
-0197 
- 0-123 
- 0-135 
+ 0-007 
9 12 
- 0-084 
-0123 
- 0-078 
- 0-086 
- 0-028 
-0 051 
+ 0-046 
10 12 
-0011 
- 0-042 
-0028 
-0018 
+0013 
+ 0-054 
+0117 
11 12 
+0096 
+ 0-070 
+ 0-105 
+0 045 
+0138 
+0143 
+ 0-234 
12 12 
+0169 
+ 0-124 
+ 0-162 
+ 0-138 
+ 0-220 
+ 0-233 
+ 0-248 
13 12 
+ 0-227 
+ 0-206 
+ 0-200 
+ 0-223 
+ 0-249 
+ 0-282 
+ 0-271 
14 12 
+ 0-177 
+ 0-177 
+ 0-220 
+ 0-202 
+ 0-242 
+ 0-270 
+ 0-217 
15 12 
+ 0-113 
+ 0-082 
+ 0-118 
+ 0-258 
+ 0-177 
+ 0-183 
+ 0-157 
16 12 
+ 0-008 
+0 029 
+ 0-058 
+0071 
+ 0-064 
+0134 
+ 0-112 
17 12 
+ 0-180 
+ 0-181 
+ 0-169 
+0156 
+0146 
+ 0-125 
+0149 
18 12 
+ 0-802 
+ 0-788 
+ 0-910 
+ 0-763 
+ 0-608 
+ 0-610 
+ 0-568 
19 12 
+ 1-309 
+ 1-455 
+ 1-361 
+ M 79 
+ 1-009 
+ 1-013 
+ 1017 
20 12 
+ 1-805 
+ 1-789 
+ 1-517 
+ 1-333 
+ 1-206 
+ 1-229 
+ 1-091 
21 12 
+ 1-456 
+ 1-381 
+ 1-005 
+ 0-945 
+ 0-825 
+ 0-883 
+ 0-557 
22 12 
+ 0-311 
+ 0-258 
+0028 
-0080 
+ 0-271 
- 0-034 
- 0-280 
23 12 
- 0-895 
- 1-084 
— 1-137 
— 1-117 
- 0-956 
- 0-952 
— 1-115 
14. Remarks on the regular Solar-diurnal Variations . — Although the semiannual 
inequality in the diurnal variation of declination has been established by the researches 
of General Sabine as beyond a doubt a general feature in that variation, possessing the 
same characteristics in all parts of the globe, yet the regular progression from month to 
month in the diurnal variation has not, that I am aware, been much dwelt upon. It is 
shown, however, so distinctly in the Bombay Observations as to lead, on a first inspection 
of the curves, figs. 9 to 20, Plate XXVI., to the supposition that the law of variation is 
identical throughout the year, the extent only (including a reversal of direction) varying 
from month to month. But in this respect a different exposition of the character of the 
variation in different months shows that the first thought would be inaccurate. The 
deviations from the normal position of the magnet (S A ) at each hour ( li ) may be expressed 
by the series 
cosw-j-B, sinw-|-A 2 cos2w+B 2 sin2w+A 3 cos 37iff-B 3 sin3w + &c. . . . (g), 
where n=hx 15°; and it is easy from each complete set of hourly values to deduce the 
