SURVEY OE THE BRITISH ISLES FOR THE EPOCH JANUARY I, 1891. 509 
used as the basis of any calculation, the approximate assumption was never applied to 
an interval greater tlian half a degree. 
The errors introduced were in all cases very small, and we assured ourselves that 
they were far less than those due to experiment or to the correction for secular 
change. 
As the method was therefore legitimate, it was better to employ it when so many 
stations were involved. The absolute saving in labour was very great, and the calcu¬ 
lations were more easily checked. 
The preliminary calculations made in the selection of the formulae for the iso¬ 
magnetics were, for the most part, based directly on the formulae themselves. 
We think it better, however, to adhere to one method throughout this paper, and 
the figures here given are deduced from the Table. The agreement between observa¬ 
tion and calculation is in some cases a little less close than it would otherwise have 
been, but the differences only amount to two or three tenths of a minute of arc in the 
case of the Declination, and are equally unimportant in the case of the other elements. 
The evidence for the satisfactory character of the formula is as follows ;—• 
(1.) The formula expresses with great accuracy the values of the Declinations at 
the Central Stations. 
This is proved by the following Table : — 
District. 
Declinations at Central stations. 
Mean value observed 
in district. 
Calculated. 
Difference. 
I. 
20 58-4 
20 59-4 
-I'-O 
II. 
20 7-9 
20 4-9 
-h3-0 
III. 
18 51-8 
18 51-3 
+ 0-5 
IV. 
17 45-7 
17 44-7 
+ 1-0 
V. 
22 3-9 
22 4-5 
-0-6 
VI. 
20 46-0 
20 45-4 
+ 0'6 
VII. 
18 38-4 
18 40-7 
-2-3 
VIII. 
21 53-9 
21 54-0 
-OT 
IX. 
19 35-5 
19 34T 
+ 1-4 
(2.) The formula expresses the general form of the district curves in the centre of 
the kingdom with great accuracy. There is some divergence in the North of Scotland 
and in the South-east of England. 
In the following Table the points at which the isogonals calculated from the 
District Lines (Table II.) and from the formula respectively, cut given lines of 
latitude are compared. The longitudes of the points of intersection are given. 
The lower number in each square is that given by .the district curve, the upper is 
that calculated from the formula. The latter calculation was made direct, and also by 
means of Table III. The results were in due accord. In the following Table the 
numbers are those deduced from Table III. 
