190 F. A. P. Barnard on the Pendulum. : 
density, and upon changes in its own temperature. In studying 
experimentally the subject of compensation, it would not be 
difficult to eliminate the effects of the first of these causes, s0 a8 
to exhibit truly the merit or defect of any given mode of com 
pensation for the expansion and contraction of the materials of 
the pendulum. | 
he remontoir escapement does not perfectly fulfil these con- 
ditions; but it is believed that the electric clock herewith pre- 
sented does so completely. 
This pendulum has an additional advantage over an escape 
ment remontoir; which arises from the fact that its are of 
vibration may be reduced much lower than is at all practicable — 
with a clock driven by a train. All the errors of the pendulum, 
except those arising from the varying temperature of the 10d, — 
increase with the arc. It is believed that this pendulum may be 
run with so small a motion as to make such errors quite u 
sensible. The degree, moreover, to which external forces aflect 
the rate without altering the are, is proportional to the forces 
themselves; and these, in the present case, must necessarily 
less as the arc is less. 
d2y _ 
Teo 7 (sin g—rf(¢)+mf' (»)). 
The maintaining force, in the present case, is a weight aP bbe 
at the extremity of an arm of the pendulum at the height ofthe 
centre of motion. Represent the weight by w, the lengt ae we 
Sa, is, in this case, nothing but the atmosphen” : 
inertia, so long as the impulse lasts; after this, the. ere . 
ated 
of equal weight with the pendulum, and presenting 92°75. 
surface of resistance, calige: to be scoalseatel by gravity 4 
