82 
Proceedings of the Royal Society of Edinburgh. [ Sess. 
y 
30° 
45° 
60° 
75° 
0 
o 
05 
I V/maf 
•025 
•116 
•313 
•620 
1-000 
SI/I : Sa/a 
. -9-42 
-4-05 
-220 
- P39 
- LOO 
Thus the efficacy of this device of compensation is much greater when 
y is small. This would correspond to / small for a given impulse, or a 
more massive impulse piece moving slowly ; but this introduces other con- 
siderations, especially the question of concentrating the impulse in the 
neighbourhood of the vertical position. A few particulars as to the 
numerical values of the quantities referred to above, in the actual running 
of the clock, are given below, p. 112. It may be mentioned here that the 
value of y appears to be in the neighbourhood of 60°, where the factor is 
about double its limit —1. If, however, the roller disc, whose curved 
surface causes variation in the factor, be dispensed with and replaced by 
a wedge-shaped pallet, we could secure greater condensation of the impulse. 
This will now be considered. 
Cases 2, 3. — Wedge-shaped Pallet. 
We may take these together, the second being merely a particular case 
of the third. 
Let h be the height and 2 i the angle of the wedge, </> the angle of 
friction ; then if the pallet is moved transversely with uniform velocity, 
there is zero acceleration of the impulse piece vertically between its guides ; 
whence 
mf= P (sin i + cos i tan <£) 
and the pressure on the pendulum is 
P (cos i — sin i tan cf>) = mf cot (i + <j>) > 
t ™f h 
V 
tan i 
tan ( i -(- cf>) 
(0 
the whole impulse is 
