When the diameter of the pallet roller has a consider able proportion to that of the wheel, the angle of 'scapement will be less, and the hold on the face of the pallet will also be less ; but the impulse given will be more direct, and the chance of stopping-, from any counter-action by external motion, will also be greatly lessened. In this angle more must be included than that which is made from the drop of the tooth to its escaping the pallet. The angle of 'scape mem is included between the point where the tooth escapes from the main pallet or roller, and the point to which the lifting-pallet comes in returning, after having passed the lifting-spring. There can be no 'scaping unless the lifting pallet has passed the lifting spring : It is then again ready to unlock the wheel. It is desirable, that the unlocking of the wheel should be made with the least possible resistance to the vibrations of the balance ; which is attained, by hav ing the end of the lifting-pallet as near to the centre of the balance as is consitent with its getting such a hold of the lifting-spring, that in its course, it can readily and easily bring out the detent from locking the wheel. The hold of the tooth on the detent should not be more than the hundredth part of an inch. But, in doing this, the supple xnentary angle becomes greater and increases the angle of 'scapement ; and therefore it may be proper to have the lifting-pallet a little longer. A little additional length will greatly reduce the angle of 'scapement, and not much in crease the evil of a greater resistance to the vibrations of the balance.
In a box chronometer, whet e the balance wheel has twelve teeth, and the whole angle of 'scapement is to be 60°, it is required to find the ratio of the diameter of the wheel to that of the roller. The supplementary angle being taken at 15°, the angle of impulse must then be 45°, which is rather wide as otherwise ; but it will be less than this, when the thickness of the points of the teeth, and the spaces for drop and escape, are not taken into the computation. Now 360° being divided by twelve, the number of the wheel teeth, gives 30° for the quotient ; and again divided by 45, the number of degrees for the angle of impulse, the quotient will be 8°. The diameter of the wheel is supposed to be .6 of an inch. To find that of the roller, say, as 12 : 6 : :8 : 4. Four tenths of an inch is the diameter required for the roller, which will give somewhat less than 45° for the an gle of impulse. The diameter of the roller may be found in another way, sufficiently near for practice. The diame ter of the wheel is .6 of an inch, or .600 ; then say, as 113 : 355 : : .600 : 1.885 ; this last being divided by 12, the num ber of the wheel teeth, gives for the quotient .157, the dis tance between the teeth. This distance taken as a radius for the roller, would give for the angle of impulse.
About one-fourth more of this added, will give .200 for the radius, so that the angle may be about 45°.
Nothing should be overlooked, which can contribute to make the balance unlock the wheel with the least possible resistance. When the wheel is locked by the extremity of the teeth, it must be easier unlocked than when the locking is at a less distance from the centre. The unlocking can not be done easier than with a wheel for such a detached 'scapement as was contrived about fifteen years ago by Owen Robinson, (see Plate CCC1II. Fig. 4 ) a very judi cious 'scapement maker, who wrought long with the late Mr Arnold. This wheel is like that for Tyrer's 'scape mem. The long teeth of arrete rest on the detent, and the upright teeth give impulse. It is evident that the unlock ing with such teeth must be vet y easy, when compared with the teeth of those wheels which are made after the ordina ry way.
Lest what has been said concerning the principle of a detached 'scapement may not be sufficient, we shall endea vour to describe the 'scapement itself, such as it is at pre sent commonly made, so as to give an idea of it, and of the manner by which it acts. The balance-wheel of a pocket chronometer has fifteen teeth not very deep cut, and a lit tle under cut on the face. A notch cut into a round piece of steel or roller, which is thicker than the wheel, forms the face of the pallet. Sometimes a small piece of ruby or sapphire is inserted into the notch at the face of the pal let, for the wheel teeth, to act upon, so that no wearing may ensue. The ratio of the diameter of the wheel to that of the roller, is that of .425 to .175. When the wheel and roller are in their places, the wheel supposed to be locked, the roller roust turn freely between two teeth, having only freedom, and not much more. From the centre of the roller to the point of one of the teeth, that next the last es caped, let a line be drawn at a tangent to this tooth. On this line is placed the detent and lifting springs. The de tent piece on which the wheel is locked, is a small bit of fine stone, either ruby or sapphire, set into steel, formed into a delicate spring, of such a length as to be equal to that of the distance of two or three spaces between the teeth, with a sole and steady pin at one end, which must be fixed to the potence plate by a screw. This is what is called the detent spring, the end of which goes within a little distance of the circle de scribed by the extremity of the lifting pallet. On the left hand side of the detent spring is attached another called the Wang spring, which cannot be too delicate, but is made a little thicker towards the outer or lifting end than anywhere else. This end of the lifting spring projects a very little beyond that of the detent spring. On the arbor of the roller and balance, and placed near the roller, is twisted a short and thick steel socket, in which is set a bit of precious stone, the face of which, is made flat, and nearly in a line with the centre, be hind it is chamfered on towards the point, and made rather thin than otherwise. This is called the lifting pallet. The length or height is made so as to unlock the wheel to the best advantage ; that is. by only carrying the detent a short way beyond the unlocking. This excursion is to be confined to as small an angle as may be. Near to the de tent piece is fixed a stud, in which is a screw to regulate the depth of the detent into the wheel teeth. The point of the screw should be hardened, and have a part of the ruby detent to rest upon it, when the detent spring presses that way. When the balance is at rest, the face of the lifting pallet is very near to the outer side and end of the lifting sluing. If the balance is brought a very little about to the left, the lifting pallet will pass the end of the filling spring. On the balance being now turned towards the right, at the moment of the wheel being unlocked, the main pallet or roller presents itself, tcrreceive the point of one of the teeth, and is impelled with considerable force ; meanwhile the detent falls again to its place, and locks the wheel. The balance, having completed this vibriation, returns. In the returning, the lifting pallet pushes the lifting spring easily aside, being no longer supported by the detent spring when turning in this direction, that is, from the right to the left, the detent is again ready to be disengaged on the next re turn of the balance to the right, and 'so on.