508 
MR. A. W. RUCKER AND DR. T. E. THORPE ON A MAGNETIC 
The district curves were obtained from these numbers exactly as before. They are 
shown in dotted lines on Map 1. 
A formula was then sought, which should express (l) the values of the Declinations 
at the central stations^ and (2) the forms of smooth curves representing the general 
form of the broken district curves. 
It is perhaps unnecessary to describe in detail the steps by which the final result 
was reached. It will be sufficient to state our conclusions and give d j)osterior{ the 
evidence which we think justifies them. 
We find that the equation to the terrestrial isogonals for 1891 can be obtained from 
that for 1886 by adding to it for the district south of latitude 54° 30' N. the terms*— 
— 34'-0 - 0'-6 (Z — 49-5) - O'U (X - 4) 
+ O'-Ol (/ - 54-5)- (X — 4)'^ 
while for the district north of latitude 54° 30' N. we add the first three terms of this 
expression only, i.e., 
— 34'-0 - 0'-6 (Z - 49-5) - 0'-3 (X - 4). 
In both cases Z and X are the latitude and longitude expressed in terms of degrees 
and fractions of a desrree. 
o 
Hence the equation to the terrestrial isogonals {cf. “ 1890 Memoir,” p. 240) south 
of latitude 54° 30' on January 1, 1891 is 
8 = 18° 37' + 18''5 (Z — 49-5) - 3'-5 cos {45° (Z - 49-5)} 
+ {26'-3 + l'-5 (Z - 49-5)] (X - 4) 
+ O'-Ol (X - 4)- (Z - .54-5)q 
and north of latitude 54° 30' the same expression holds good if the last term, i.e., 
O'-Ol (X - 4)3 (Z — 54-5)^ 
be omitted. 
By means of this formula the calculated Declinations were determined at all points 
given by the intersections of lines corresponding to entire degrees of latitude and 
longitude. The numbers thus found, together with the differences between them, 
are given in the following Table III. 
In the reduction of our earlier survey the calculated values at the difierent stations 
were determined direct from the alcrebralcal formulse for the terrestrial isomametics. 
O O 
In the work described in this paper we have on the contrary used tables such as 
tlmt given on the oj^poslte page and have assumed that the rate of change of the 
elements with latitude and longitude might be taken as constant for intervals less 
than a degree. 
As tlie nearest intersection of whole degrees of latitude and longitude was always 
* In these equations the factors which contain I and X ai’e to be regarded as mere numerals. 
