240 
MR. A. W. RUCKER AND DR. T. E. THORPE ON A MAGNETIC 
Isogoiial lines were next drawn by tlie aid of the mean values of the Decimation 
given in this Table, the points at which they intersect any particular line of latitude 
or longitude being calculated on the assumption that the rate of change of the Declina¬ 
tion with latitude or longitude may be regarded as constant over a single degree. The 
curves thus obtained are shown in dotted lines in Plate II. As they were deduced 
from the linear district formulse they may be called the district curves. 
By drawing a smootli curve to coincide as nearly as possible with any one of the 
longer of these broken district curves, a close approximation to the corresponding 
isoo'onal could be obtained, but in order that the intervals between the curves mioht 
be properly spaced out, it was thought better to obtain a general formula by which 
they could he expressed. 
It appears from Table V., p. 236, that y increases with the latitude, but is nearly 
independent of the longitude. The values of x are more irregular. After several 
trials it was found that the mean Declinations at the central stations of the various' 
districts could be reproduced very accurately by means of the formula, 
S = 19° lU + 19'T (/ — 49-5) — 3'-5 cos [4.5° {I — 49-5)} 
+ [26'-6 + {I — 49*5)] (X - 4), 
where I and X are the numerical values of the latitude and longitude expressed in 
degrees and fractions of a degree. 
It must be distinctly understood that this formula has no theoretical value except 
in so far as it expresses satisfactorily the equation to smooth curves drawn according 
to a definite rule to represent the general form of the broken district curves. 
In applying it to the various stations the curves given by the periodic terms were 
drawn, and the values corresponding to the latitude and longitude of each read off. 
It is possible that errors of 0'‘2 or 0''3 may have occurred in this process. The mean 
A^alues of the Declinations at the central stations of each district are in the following 
Table compared with the results given by the formula. 
J)eclination at central station. 
llifferonce. 
District. 
]\Iean of values 
observed in district. 
Calculated. 
o 
0 
I. 
21 
38 8 
21 
,39-4 
— 0 6 
IT. 
20 
.5.J-6 
20 
54T 
+ 1*5 
HI. 
19 
39-0 
19 
38-9 
-f O-I 
IV. 
IS 
6-6 
18 
4-4 
+ 2-2 
V. 
22 
4T3 
22 
4T5 
- 0-2 
VI. 
21 
25-6 
21 
26-5 
- 0-9 
\ll. 
19 
6-2 
19 
56 
-i- 0-6 
vni. 
2*2 
35'0 
22 
34'4 
-I- 0 -6 
IX. 
20 
19-7 
20 
19-8 
- OT 
