xxxvi 
Introduction to the Makerstoun Observations, 1843. 
to the change of the vertical component of the magnetic force, which would produce 
a disturbance = jj, and hence he shews that the value of the constant tan e will be 
given by the formula 
T' 2 tan f Y 
T 2 X 
= tan e cot 6 
Where 8 is the magnetic dip, T' and T the times of one vibration of the needle, the 
former in a horizontal plane, the latter in a vertical plane. 
50. This method has been found to fail in practice ; the determination of the 
time of vibration in a vertical plane has been proved to be a matter of much diffi- 
culty, if at all possible, mixed up, as it is, with several sources of error, which are 
not easily accounted for or eliminated.* It has been shewn with respect to the 
time of vibration in a vertical plane, 
* The following statical method might be substituted for that of Dr Lloyd : — Let jj be the small 
angle which the magnetic axis of the balance needle makes with the horizontal, then the equation of 
equilibrium is (48) 
m Y cos '/} = W g cos (e + jj) (1.) 
if a magnet, whose moment is M, be placed vertically, with its centre at a distance r from the centre of 
the balance needle, and in the continuation of the magnetic axis of the balance needle when horizontal, 
the needle will then make an angle 8 with the horizontal, and the equation of equilibrium will be 
Y' cos d = W g cos (e + d) (2.) 
m 
where 
Y ' = Y + ^ (30 
From equations (1), (2), and (3), 
c M tan b — tan rj . . 
■j' 3 Y — cot e — tan n v*' 
Now, if X be the horizontal intensity of the earth's magnetism, and 6 be the magnetic dip, 
Y = X tan 6 ; (5.) 
and if the deflecting magnet be placed in the line at right angles to the magnetic meridian passing through 
the centre of a freely suspended magnet, and u be the angle of deflection when the centres of the magnets 
are at the distance r v then (No. 26.) 
c M , r 3 
r 3 X 
By equations (4), (5), and (6), 
if 3 3 
~ tan u -L- tan u 
tan 6 2 tan 6 (tan d — tan »j) — tan u tan » ~~ 2 tan & tan (d — jj)' a PP loximate ty > 
and if »j = 0, or bo very small, as it is in general, when tbe needlo may be considered horizontal, then 
. „ r 3 tan u . 
tanf=— — J (7.) 
2 r 3 tan 0 tan 5 K ' 
If the deflecting magnet be placed at right angles to the suspended magnet (as in Dr Lamont's 
niothod), then sin u must be substituted for tan u. 
The 
