248 
MR. A. W. RtiCKBR AND DR. T. E. THORPE ON A MAGNETIC 
On the whole then, the risk of introducing fictitious disturbances by attempting to 
include the whole country under one simple law would be very great. 
We decided, therefore, in calculating the lines of equal Horizontal Force, to employ 
different formulse for districts to the north and south of the 1‘7 line. 
Taking the southern district first, the lines may be regarded as straight, but, inas¬ 
much as they run across the whole breadth of the kingdom, a very small error in the 
calculated slope is important. A rather complicated formula is therefore unfortunately 
necessary. 
If c be the mean distance, expressed in degrees of latitude and measured along 
longitude 5° W., between any line and that which corresponds to 1‘85 units, we have 
a relation of the form 
1'85 — H = ac, 
where a is a constant. 
The 1'85 line cuts longitude 5° W. in latitude 49°‘83, and thus the equation to the 
isodynamic through c is 
I — 49-83 = - (X - 5) m + c, 
where m measures the slope of the line. 
Neither a nor m are quite constant, but both are functions of c, so that 
1/a = 24-47 (l + ^ ; 
' \ 1000 / 
ni = -157 — ’0019c — *0155 sin (50c). 
Thus, if we wish to find where the line corresponding to H cuts longitude X, we 
find c from the equation 
c = 24-47 (1-85 - H) -b 0-001 c^ 
where the value of c, used in the small term in c^, is the approximate value obtained 
by neglecting it. From this m is found, and I is then known. 
If the latitude and longitude are given, and the Horizontal Force is required, we 
first find c apj)roximately from the formula 
c' = 1 - 49-83 + 0-157 (X - 5). 
Subtracting from this 
c" = (X - 5) (0-001 9 c' -b 0-0155 sin (50 c')}, 
the difterence is c, whence H is found. 
Taking next the district north of the 1-7 line, there is no particular difficulty in 
finding similar equations to express the mean direction of the lines with great 
exactitude. If we write 
