Somewhere on this line is located the center of the balance staff, and it is the problem in hand to locate or establish this center. Now, it is known the circles which define the peripheries of the escape wheel and the impulse roller intersect at e e^2. We can establish on our circle A where these intersections take place by laying off twelve degrees, one-half of the impulse arc on each side of the line of centers a f on this circle and establishing the points e e^2. These points e e^2 being located at the intersection of the circles A and B, must be at the respective distances of 5” and 21/2” distance from the center of the circles A B; consequently, if we set our dividers at 21/2” and place one leg at e and sweep the short arc g^2, and repeat this process when one leg of the dividers is set at e^2, the intersection of the short arcs g and g^2 will locate the center of our balance staff. We have now our two centers established, whose peripheries are in the relation of 2 to 1.
To know, in the chronometer which we are supposed to be constructing, the exact distance apart at which to plant the hole jewels for our two mobiles, i.e., escape wheel and balance staff, we measure carefully on our drawing the distance from a to c (the latter we having just established) and make our statement in the rule of three, as follows: As (10) the diameter of drawn escape wheel is to our real escape wheel so is the measured distance on our drawing to the real distance in the chronometer we are constructing.
It is well to use great care in the large drawing to obtain great accuracy, and make said large drawing on a sheet of metal. This course is justified by the degree of perfection to which measuring tools have arrived in this day. It will be found on measurement of the arc of the circle B, embraced between the intersections e e^2, that it is about forty-eight degrees. How much of this we can utilize in our escapement will depend very much on the perfection and accuracy of construction.
[Illustration: Fig. 139]
We show at Fig. 140 three teeth of an escape wheel, together with the locking jewel E and impulse jewel D. Now, while theoretically we could commence the impulse as soon as the impulse jewel D was inside of the circle representing the periphery of the escape wheel, still, in practical construction, we must allow for contingencies. Before it is safe for the escape wheel to attack the impulse jewel, said jewel must be safely inside of said escape wheel periphery, in order that the attacking tooth shall act with certainty and its full effect. A good deal of thought and study can be bestowed to great advantage on the “action” of a chronometer escapement. Let us examine the conditions involved.