ON ELECTRICAL OBSERVATIONS AT KEW. 115 
cal plane of the centre of the pith-ball when unelectrified, and should be at cuch a distance 
that the arc measured by it may be of sufficient range to determine 
Fig. 1. the length of the sine with tolerable accuracy. The distance between 
the centres of the azimuth circle and pith-ball should, if possible, be 
of such a value in half-Parisian lines as to facilitate the formation of a 
table for obtaining the value of the sine in half-Parisian lines by in- 
spection, so that a simple observation of the bisection of the right and 
left limbs of the pith-ball, which of course would be in arc, and the 
deduced divergence in arc of its centre from its plane of rest when 
unelectrified, would, with the assistance of the table, give at once the 
electric tension in half-Parisian lines ; and these readings might readily 
be converted into terms of Volta’s electrometer No. 1, by properly 
adjusting the straw, pith-ball, &c. to a definite value, so that a diver- 
gence of half a Parisian line may be equivalent to a certain number of 
divisions of Volta’s standard electrometer. In this way, it is clear, the 
tensions might be expressed in terms of Volta’s standard up to 90° 
of Henley without the necessity of applying corrections, unless such 
corrections should be rendered necessary from the effects of gravity on 
the pendulum. 
The whole matter may be rendered plain by the annexed diagram 
(fig. 1). Let A represent the centre of the pith-ball when unelectrified, 
and B the centre of the azimuth circle of the theodolite. The di- 
stance B A will form the base of a right-angled triangle, of which the 
divergence of the pendulum P—A’ is the perpendicular. When the 
‘instrument is electrified, the pith-ball diverges in a plane at right 
angles to the plane passing through its centre when unelectrified, 
and that of the azimuth circle; or in other words, the plane of its 
motion passes vertically through the line A C, and is at right angles 
to the vertical plane passing through the line A B. If now the 
theodolite is so adjusted that the limbs of the pith-ball may be 
bisected, the azimuth circle will measure in arc the sine of the angle 
of divergence, and thus we have given the side and angles of a right- 
B angled triangle from which the linear measure of the divergence may 
readily be deduced. The analogy is as follows :—Radius is to the tangent of the horizontal 
angle, as the distance between the centres of the pith-ball and azimuth circle is to the 
divergence. 
Pe 
Suppose the distance AB = 500 half-lines; 
The azimuthal angle...... =o: 
Then Log AB......... «ee = 27698970 
5 | Log tan 6° 2.,.sd00. = 9-021620 
» Log 5255+ ...... = 1°720590 
Consequently the divergence is equal to 52°55 half-Parisian lines in a plane at right angles to 
the vertical plane passing through the above-mentioned centres. 
N.B. The diagram is constructed in accordance with the above example. 
It is not absolutely necessary to employ a theodolite. A telescope furnished with cross wires 
firmly fixed on a support having its centre of azimuthal motion at a known constant and in- 
_ variable distance from the centre of the pith-ball when unelectrified, the angle being measured 
by an arm sufficiently extended to include the angle subtended by the pendulum when de- 
_ flected from the perpendicular 90°, will be sufficient. A vertical motion should be given to the 
telescope by rackwork by which it can be raised to the level of the pith-ball when electrified, 
and it should be farnished with a level, &c. to ensure horizontality. 
The above remarks have reference to the expression of the electric tension in the linear 
terms adopted by Volta, viz. half-Paris lines, and are principally applicable to the retention 
of Volta’s notation so far as the measurement of the sine of the angle of divergence from the per- 
pendicular is concerned ; but Mr. Ronalds has suggested a much better mode of connecting the 
readings of the two instruments, viz. a conversion of the readings of Volta’s electrometer (half 
Paris lines) into measures of arc, so that the readings of the three instruments, Volta No. 1, 
Volta No. 2, and Henley, and even of the discharger, may all be expressed in degrees of the 
circle, the sines of which are of course readily ascertainable. 
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