XXXVI INTRODUCTION TO THE MAKERSTOUN OBSERVATIONS, 1843. 
to the change of the vertical component of the magnetic force, which would produce 
a disturbance = 7, and hence he shews that the value of the constant tan ¢ will be 
given by the formula 
T?  tane Y 
a x 
= tane cot 0 
Where @ 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 Luoyp :—Let 7 be the small 
angle which the magnetic axis of the balance needle makes with the horizontal, then the equation of 
equilibrium is (48) 
mY cosy = Wgcos(€+7) - - - - » - ~ (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 6 wiih the horizontal, and the equation of equilibrium will be 
mY’ cop8= Wgecos(E+8)..-. . - =. ~ (2) 
where 
Sar ried rasmus tse: AFD 
From equations (1), (2), and (3), 
cM I tan é6— tan a ) 
22. cot € — tau 7 CU Rasa ap cand ag ote Se 
Now, if X be the horizontal intensity of the earth’s magnetism, and 4 be the magnetic dip, 
liblag oN, fs cPLA sito oie nomaty. Jou erg Caks ae 
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,, then (No. 26.) 
ae 
vy =f, a Coa Cee tO SO ap Noes i 
pa tant (6.) 
By equations (4), (5), and (6), 
3 3 
r r 
— tanu tan uv 
7 r 
tan € 
= 2 tan 6 (tan 6 — tan n) — tan wu tan 7 = 2 tan @ tan (6 — 1) appr aeeei: 
and if 7 = 0, or be very small, as it is in general, when the needle may be considered horizontal, then 
73 tan wu 
tan € =—,4—__ . . ww ew ew we 
ne =97* tan @ tan 0 Wa) 
If the deflecting magnet be placed at right angles to the suspended magnet (as in Dr Lamont’s 
method), then sin « must be substituted for tan w. 
The 
