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4. Notice of an Instrument intended for the Measurement 
of Small Variations of Gravity. By John Allan Broun. 
Communicated by Professor Tait. 
If we suspend a weight by two wires, and turn the weight sus- 
pended from its position of repose through an angle v by means of 
any force, the wires will no longer be vertical, and the weight will 
be lifted from its lowest position by a gravity equal to l sin i tan i 
where l is the length of a wire and i is the small angle which it 
makes with the vertical. If we represent the force which keeps the 
weight W from its position of rest by /, and the intervals of the 
wires above and below by a and b, it is known, as in the case of the 
bifilar magnetometer, that the equation of equilibrium is — 
.C WT Q'b • 
f— W . sin v. 
I cos i 
If we suppose the force f to be constant, and that only W and v 
vary by small amounts, then we find % 
aW 
= — cott» Av. 
The ratio to the whole weight of any variation, produced by any 
such cause as recession from the centre of the earth, whether by 
climbing a mountain or by changing position on the terrestrial 
spheroid, will thus be determined by observations of v and its varia- 
tion. Small variations of W may be determined if we give v a 
value approaching to 90°, and if we can observe small variations of v. 
The following plan is being adopted for the purpose suggested. 
The weight, a cubic inch of lead, is suspended by two fine platinum 
wires ; the cube has mirrors on three of its vertical faces, two of 
which are capable of adjustment so as to make an angle of about 
86° with the middle mirror : below the cube a fine hair spring, like 
that of a watch balance, but of platinum (so as not to rust), is 
attached by one extremity to a central pin fixed below into the 
weight ; the other extremity is fixed (when the weight hangs freely 
and the spring exerts no force) to a hollow cylinder which turns 
freely round the pin as a centre. In this ring another mirror is 
fixed parallel to the middle mirror of the weight, and immediately 
below and in front of it. A telescope is so placed that when the 
spring has no action on the weight, the central divisions of two scales 
VOL. v. 3 i 
