$8 Mr Whitelaw on a New Escapement. 
of the point of the tooth only is employed, and that slides along 
an arc of a circle. 
Let CLG be this wheel, in which AGHB, Plate I. Fig. 8., 
is the new method of escapement, and IMLK, that of Earn- 
shaw, each being in a state of repose. Also EF, the dia- 
meter of the impulse-pallet, is about fths of OC, the radius of 
the scape-wheel, or nearly a mean between those of Arnold and 
Earnshaw. AB is a straight cylindrical lever, turning about an 
axle passing through H, whose ends work in jewelled holes in 
the frame of the watch as usual, to give a steady motion, and as 
little friction as possible. GH, whose shape may be varied, is 
a detent fixed to AB, on which the wheel rests, in such a man- 
ner that the angle OGH is a right angle, and GH is conse- 
quently a tangent to the wheel at the tooth G. The part or 
face cd is jewelled, and formed into an arc of a circle, of which 
the radius is GH ; and therefore, when it slides along the tooth 
G, it can give no motion to the escape- wheel ; also ab is the 
slight spring fixed at a as usual. 
Now, BGH may be considered as a bent lever, or as a wheel 
and pinion fixed on the same axis* as H. Hence, any power 
applied at B is to the resistance at G as GH is to BH, or 
G x GH = B x BH by mechanics *. Hence, if we suppose 
GH to be | of BH, the power will be to the resistance as 1 to 
4 ; or t of power applied at B, will equal the resistance from 
friction, and the force of the slender spring employed for bring- 
ing the detent into its proper position upon the tooth of the 
scape-wheel at G. 
Now, in the case of Earnshaw’s, if we conceive the bar IK to 
be a lever fixed at I, and turning or bending round M, the 
middle of the spring em, as a centre, which is nearly true, L 
the stud, or detent, in which the tooth of the scape-wheel acts 
as before, ik the slight spring fixed at i, then this will become a 
lever of the second kind, and we have by mechanics *(*, the power 
applied at K, is to the resistance at L, as LM is to KM, or 
K x KM = Lx LM. Hence, if KL is \ of LM, as formerly 
supposed, then the power applied by the balance at K will be 
* Wood, § 96. prop, xviii. — Gregory, vol. i. § 133. cor, 2. 
■f Wood, § 73. prop, xiv.— Gregory, vol. i. § 133. cor. 3. 
