6 The Rev. H. Lioyp on the Determination of the Intensity 
that, in order to apply the method most advantageously, this ratio must be taken 
in such a manner, that the probable error, Aa, shall be the smallest possible. This 
condition gives 
d ee + il 
Sos amar ) =0; 
dg’ g-— 1" 
whence we obtain the following equation for the determination of q: 
3q°— 5q¢° —2=0. 
In order to solve this equation we may observe that, g being greater than unity, 
the last term of the equation may, in a first approximation, be neglected in com- 
parison with the others; so that we have, approximately, 
37°—5=0, g=V iar. 
And setting out from this value, we find, by any of the known methods of ap- 
proximation, 
g= 15325 
or 14, very nearly. Accordingly the smaller distance, 7, being determined by 
the condition that the third term of the series shall be insensible, the greater 
distance should be 1°32 7. 
: : : : A ; 
If we substitute this value of q, in the expression for = above obtained, we find 
from which we can calculate the least probable error corresponding to any given 
angle of deflection, the probable error of reading being known.* 
* In the Dublin Magnetical Observatory the deflecting bar hitherto employed is 12 inches in 
length, and the least deflecting distance therefore 4 feet. The deflection produced by it at this 
distance is about 3° 56’; and the probable error of observation does not exceed 5”. Hence, in 
this case, 
Ag 5: 563 
—_— = —#—_——_—_ = 2. . 
Q 236 x 12 ee 
The absolute intensity,x, varies inversely as the square root of q; so that 
Ax _, Ae 
x so. 
Consequently, the resulting probable error in the determination of the absolute intensity, made 
according to the usual method, is, at this Observatory, about the ;;;,th part of the entire quantity. 
