TRANSACTIONS OF THE SECTIONS. 207 
from a shorter radiant of the lower one. When this state of rest is 
disturbed by loading the scale the balance moves round, and, in the 
progress of its revolution, the opposite eccentricities of the spirals com- 
bine in changing the ratio of the leverage, and thus originate a self- 
adjusting power, by which the loads of both cords are mutually moved 
into equilibrium. The receiving scale thus commences with greater, 
and ends with less mechanical power than the counterpoise—a circum- 
stance which is in harmony with the purpose of employing an un- 
changing weight to measure others both less and greater than itself; 
while the principle is one which concentrates the power and abridges 
the size of the machine. In order, however, that the total amount of 
adjusting power thus generally obtained may be equally drawn upon 
and advantageously distributed throughout the movement of the ba- 
lance, a definite relation is established between the weight of the coun- 
terpoise and the rates at which the accumulating weight of the scale 
and the leverage of the lower spiral increase. The leverage of the 
upper spiral, being derived from these ascertained conditions, is made 
to preserve a rate of decrease which accords with the previously regu- 
lated increase in the leverage of the lower curve; while both spirals 
have their precise form determined by the additional consideration of 
the direction in which the cords exert their power on the circumference 
of the balance. In their calculated formation the two spirals are thus 
dependent on and related to each other, while together they are com- 
ponent parts of one continuous curve, in which the mutual and com- 
bined changes of leverage are made to follow an equable, as well as a 
general progressive gradation ; by which means the balance is moved 
through equal angles by equal weights. In machines intended for 
weights of considerable amount, the balance is made to revolve about 
an axis, which is itself supported, a little above its centre, on knife- 
edge rests, so as to combine the movement of the revolving balance 
with the libration of the common one—the coincidence of a pointer 
from the axis with the ordinary pointer of the machine showing when 
the indication is practically unaffected by friction. In machines for 
weights of still greater magnitude, the articles to be weighed are made 
to act, in part, as their own counterpoise, by adopting differential 
curves to diminish the descending power of the scale ; by which a com- 
paratively small counterpoise is made to adjust the unsupported differ- 
ence of weights greatly exceeding itself. 
_— 
On a Water Filter. By Mr. Tuom. 
Mr. Thom described a self-cleaning filter, similar to those which 
have been in use on a large scale at Greenock for about thirteen, and 
at Paisley for three years, and which purify water, not only in which 
mud and other impurities are mixed or merely suspended, but which 
also free moss-water of its colour and taste, thereby rendering it, in 
both respects, similar to spring-water. The substance which pro- 
duces this effect is a species of trap-rock or amygdaloid, very com- 
