XXXil INTRODUCTION. 
§ 5. BALANCE oR VERTICAL ForcE MAGNETOMETER. 
36. The Balance Magnetometer is by Ropinson of London. It is composed 
of a needle 12 inches long, and about 1 inch broad, with knife-edge axle, resting on 
agate planes ; at the extremities of the needle are brass rings, each carrying a cross 
of spider’s threads. The needle is placed horizontally, at right angles to the mag- 
netic meridian It is accurately adjusted by means of two fine brass screws; one 
working horizontally towards one extremity balances the needle, the other near the 
other extremity, working vertically, regulates its sensibility. 
The apparatus is covered by a rectangular box, having glazed openings on two 
sides, opposite the spider’s crosses; those on one side allowing light to be thrown 
on the crosses from two small mirrors, those on the other for viewing them, and 
determining their position, which is done accurately by means of microscopes car- 
rying micrometers. There is a thermometer within the box for giving the tempe- 
rature of the magnet. 
37. If m be the moment of free magnetism of the needle, Y the vertical com- 
ponent of the earth’s magnetic force, W the weight of the needle, g the distance 
from the centre of motion to the centre of gravity, € the angle contained by the line 
joining these two centres, and the magnetic axis of the needle on the horizontal, the 
magnetic axis being at right angles to the plane of the magnetic meridian; then the 
equation of equilibrium is 
mY = Wg cose 
Whence differentiating the equation and dividing by it 
— = tan e€Ae — ae 
Yj m 
a, or the varying angle which the magnetic axis makes with the horizontal, is 
; : 3 ; Am ; 
obtained from observations with the micrometer ; for —, See section on temperature 
correction. 
It is conceived that € cannot be determined with accuracy by the practical 
method of inversion, and Dr Luoyp has shewn that it may be obtained from the 
following formula : 
"2 
tan € = cot TE} 
T’ and T being the times of one vibration, the former in the horizontal plane, 
the latter in the vertical plane, and 4 the magnetic dip. 
38. Adjustments, &c. 
June 16, 17, 1841. Experiments were made to determine thie effect of tem- 
perature on the balance magnet. See subsequent section. 
39. Values, in are, of the divisions of the micrometer heads. A brass needle 
