th in the escape
wheel should divide evenly into the number of beats made per minute in a
watch with seconds hand, it is not, strictly speaking, necessary that it
should do so, as an example will show. We will take an ordinary watch,
beating 300 times per minute; we will fit an escape wheel of 16 teeth;
multiply this by 2, as there is a forward and then a return motion of
the balance and consequently two beats for each tooth, making
16 x 2 = 32 beats for each revolution of the escape wheel. 300 beats are
made per minute; divide this by the beats made on each revolution, and
we have the number of times in which the escape wheel revolves per
minute, namely, 300 / 32 = 9.375. This number then is the proportion
existing for the teeth and pitch diameters of the 4th wheel and escape
pinion. We must now find a suitable number of teeth for this wheel and
pinion. Of available pinions for a watch, the only one which would
answer would be one of 8 leaves, as any other number would give a
fractional number of teeth for the 4th wheel, therefore 9.375 x 8 = 75
teeth in 4th wheel. Now as to the proof: as is well known, if we
multiply the number of teeth contained in 4th and escape wheels also by
2, for the reason previously given, and divide by the leaves in the
escape pinion, we get the number of beats made per minute; therefore
(75 x 16 x 2)/8 = 300 beats per minute.

Pallets can be made to embrace more than three teeth, but would be much
heavier and therefore the mechanical action would suffer. They can also
be made to embrace fewer teeth, but the necessary side shake in the
pivot holes would prove very detrimental to a total lifting angle of
10deg., which represents the angle of movement in modern watches. Some of
the finest ones only make 8 or 9deg. of a movement; the smaller the angle
the greater will the effects of defective workmanship be; 10deg. is a
common-sense angle and gives a safe escapement capable of fine results.
Theoretically, if a timepiece could be produced in which the balance
would vibrate without being connected with an escapement, we would have
reached a step nearer the goal. Practice has shown this to be the proper
theory to work on. Hence, the smaller the pallet and impulse angles the
less will the balance and escapement be connected. The chronometer is
still more highly detached than the lever.

The pallet embracing three teeth is sound and practical, and when
applied to a 15 tooth wheel, this arrangement o