Part 10 (1/2)

When contact ensues between the tooth _D_ and pallet _C_ the tooth _D_ will attack the pallet at the point where the radial line _A v_ crosses the tooth face We have now explained hoe can delineate a tooth or pallet at any point of its angular e in actual practice

PRACTICAL PROBLEMS IN THE LEVER ESCAPEMENT

To delineate our entrance pallet after one-half of the engaged tooth has passed the inner angle of the entrance pallet, we proceed, as in former illustrations, to establish the escape-wheel center at _A_, and from it sweep the arc _b_, to represent the pitch circle We next sweep the short arcs _p s_, to represent the arcs through which the inner and outer angles of the entrance pallet move Now, to comply with our statement as above, we must draw the tooth as if half of it has passed the arc _s_

To do this we draw froh the point _s_, said point _s_ being located at the intersection of the arcs _s_ and _b_ The tooth _D_ is to be shown as if one half of it has passed the point _s_; and, consequently, if we lay off three degrees on each side of the point _s_ and establish the points _d ular extent of the tooth to be drawn

To aid in our delineations we draw fro through the points _d m_ The arc _a_ is next drawn as in forth of the addendule of our escape-wheel tooth being located at the intersection of the arc _a_ with the radial line _A d'_

As shown in Fig 92, the impulse planes of the tooth _D_ and pallet _C_ are in contact and, consequently, in parallel planes, as e 91 It is not an easy ular motion of the escape wheel such condition takes place; because to deterher mathematics, which would require more study than most practical men would care to bestow, especially as they would have but very little use for such knowledge except for this proble with epicycloidal curves for the teeth of wheels

For all practical purposes it will make no difference whether such parallelisularaction The great point, as far as practical results go, is to determine if it takes place at or near the tireatest resistance fro that parallelisrees of angular ular movement for the tooth to escape It is thus evident that the relations, as shown in our drawing, are in favor of the train orresistance as three is to thile the average is only as eleven to ten; that is, the escape wheel in its entire effort passes through eleven degrees of angular rees The student will thus see we have arranged to give the train-power an advantage where it isinfluence of the hairspring

[Illustration: Fig 92]

As regards the exalted adhesion of the parallel surfaces, we fancy there is more harm feared than really exists, because, to take the worst view of the situation, such parallelism only exists for the briefest duration, in a practical sense, because theoretically these surfaces never slide on each other as parallel planes Mathematically considered, the theoretical plane represented by the impulse face of the tooth approaches parallelism with the plane represented by the impulse face of the pallet, arrives at parallelism and instantly passes away from such parallelism

TO DRAW A PALLET IN ANY POSITION

As delineated in Fig 92, the impulse planes of the tooth and pallet are in contact; but we have it in our power to delineate the pallet at any point we choose between the arcs _p s_ To describe and illustrate the above rerees of angular motion of the pallet Now, the irees We do not draw a radial line frole of the impulse plane commences, but the reader will see that the iree on the arc _p_ below the line _B e_ We continue the line _h h_ to represent the ile _B n h_ and find it to be twenty-seven degrees Now suppose ish to delineate the entrance pallet as if not in contact with the escape-wheel tooth--for illustration, say, ish the inner angle of the pallet to be at the point _v_ on the arc _s_ We draw the radial line _B l_ through _v_; and if we draw another line so it passes through the point _v_ at an angle of twenty-seven degrees to _B l_, and continue said line so it crosses the arc _p_, we delineate the ile _i n B_, Fig 92, and find it to be seventy-four degrees; we draw the line _v t_ to the sale with _v B_, and we define the inner face of our pallet in the new position We draw a line parallel with _v t_ from the intersection of the line _v y_ with the arc _p_, and we define our locking face If noe revolve the lines we have just drawn on the center _B_ until the line _l B_ coincides with the line _f B_, ill find the line _y y_ to coincide with _h h_, and the line _v v'_ with _n i_

HIGHER MATHEMATICS APPLIED TO THE LEVER ESCAPEMENT

We have now instructed the reader how to delineate either tooth or pallet in any conceivable position in which they can be related to each other Probably nothing has afforded more efficient aid to practical raphic solution of abstruce mathematical problems; and if we add to this the means of correction by hest mathematical acquirements, we have approached pretty close to the actual require 93]

To better explain e93, where we show preli a lever escaperaphic method the distance between the centers of action of the escape wheel and the pallet staff We iven scale, as, for instance, the radius of the arc _a_ is 5” After the drawing is in the condition shown at Fig 93 we measure the distance on the line _b_ between the points (centers) _A B_, and we thus by graphic means obtain a onoth of the line _A f_ (radius of the arc _a_) and all the angles given, to find the length of _f B_, or _A B_, or both _f B_ and _A B_ By adopting this policy we can verify the raphic method that the distance between the points _A B_ is 578”, and by trigonometrical computation find the distance to be 57762” We know from this that there is 0038” to be accounted for somewhere; but for all practical purposes eitheris about thirty-eight tihteen-size movement

HOW THE BASIS FOR CLOSE MEASUREMENTS IS OBTAINED

Let us further suppose the diameter of our actual escape wheel to be 26”, and ere constructing a watch after the lines of our drawing

By ”lines,” in this case, we eneral form and ratio of parts; as, for illustration, if the distance from the intersection of the arc _a_ with the line _b_ to the point _B_ was one-fifteenth of the diaood in the actual watch, that is, it would be the one-fifteenth part of 26” Again, suppose the dia is 10” and the distance between the centers _A B_ is 578”; to obtain the actual distance for the watch with the escape wheel 26” diameter, we make a statement in proportion, thus: 10 : 578 :: 26 to the actual distance between the pivot holes of the watch By computation we find the distance to be 15” These proportions will hold good in every part of actual construction

All parts--thickness of the pallet stones, length of pallet arms, etc--bear the same ratio of proportion We e drawing and find it to be 47”; we make a similar statement to the one above, thus: 10 : 47 :: 26 to the actual thickness of the real pallet stone By coular relations are alike, whether in the large drawing or the small pallets to match the actual escape wheel 26” in dia 93, the impulse face, as reckoned frorees

MAKE A LARGE ESCAPEMENT MODEL

Reason would suggest the idea of having the theoretical keep pace and touch with the practical It has been a grave fault with ical matters that they did not make and measure the abstractions which they delineated on paper We do not mean by this to endorse the cavil we so often hear--”Oh, that is all right in theory, but it will not work in practice” If theory is right, practice must conform to it

The trouble with many theories is, they do not contain all the ele 94]