522 
HOROLOGY. 
be called the line of centres. Now there are three different 
ways In which the teeth of one wheel may aft upon the 
teeth of another; and each of thefe inodes of action re¬ 
quires a different form for the teeth. 
I. When the teeth of the wheel begin to aft' upon the 
leaves of the pinion juft as they arrive at the line of 
centres ; and, when their mutual aftion is carried on af¬ 
ter they have palled this line. 
II. When the teeth of the wheel begin to aft upon the 
leaves of the pinion before they arrive at the line of cen¬ 
tres, and conduct them either to this line, or a very little 
beyond it. 
III. When the teeth of the wheel begin to aft upon 
the leaves of the pinion before they arrive at the line of 
the centres, and continue to aft after they have palled 
this line. 
1. The firft of thefe modes of aftion is recommended by 
Camus and De la Hire, the latter of whom has invefti- 
gated the form of the teeth foiely for this particular cafe. 
"When this mode of aftion is adopted, the acting faces of 
the leaves of the pinion Ihould be parts of an interior epi¬ 
cycloid generated by a circle of any diameter rolling upon 
the concave fuperficies of the pinion, and the acting faces 
of the teeth of the wheel ihould be portions of an exterior 
epicycloid formed by the fame generating circle rolling upon 
the convex fuperficies of the wheel. 
Now it is demonftrable that, when one circle rolls 
within another whole diameter is double that of the roll¬ 
ing circle, the line generated by any point of the latter 
will be a firaight live, tending to the centre of the larger 
circle. If the generating circle, therefore, mentioned 
above, Ihould be taken with its diameter equal to the 
radius of the pinion, and be made to roll upon the con¬ 
cave fuperficies of the pinion, it will generate a ftraight 
line tending to the pinion’s centre, which will be the form 
of the aching faces of its leaves ; and the teeth of the 
wheel will, in this cafe, be exterior epicycloids, formed 
by a generating circle, whole diameter is equal to the ra¬ 
dius of the pinion, rolling upon the convex fuperficies 
of the wheel. This form of the teeth, viz. when the 
afting faces of the pinion’s leaves are right lines tending 
to its centre, is perhaps the molt advantageous, as it re¬ 
quires lefs trouble, and may be executed with greater ac¬ 
curacy than if the epicycloidal form had been employed : 
it is j.uftly recommended both by De la Hire and Camus 
as particularly advantageous in clock and watch work. 
2. Having hitherto fuppofed, that the mutual aftion of 
the teeth does not commence till they arrive at the line of 
centres, let us now attend a little to the form which mull 
be given them, when the whole of the aftion is carried on 
before they reach the line of centres, or when it is com¬ 
pleted a very little below this line. This mode of aftion 
is not fo advantageous as that which we have been con- 
fidering, and ihould, if poftible, always be avoided. It is 
evident that the tooth of the wheel afts upon the leaf of 
the pinion before they arrive at the line of centres, that 
It quits the leaf when they reach this line, and that the 
tooth works deeper and deeper between the leaves of the 
pinion the nearer it comes to the line of centres. From 
this halt circumltance a confiderable quantity of friftion 
ariies, becaufe the tooth does not, as before, roll upon the 
leaf, but fades upon it; and from the fame caufe the pinion 
loon becomes foul, as the dull which lies upon the afting 
faces of the leaves is pulhed into the hollows between 
them. One advantage, however, attends this mode of 
action, for it allows us to make the teeth of the large 
wheel reftilineal, and thus renders the labour of the me¬ 
chanic lefs, and the accuracy of his work greater, than if 
they had been of a curvilineal form. If the teeth there¬ 
fore of the wheel are made reftilineal, having their fur- 
faces direfted to the wheel’s centre, the afting faces of the 
leaves mult be epicycloids formed by a generating circle, 
whofe diameter is equal to the radius of the wheel, added 
to the depth of one of its teeth, rolling upon the circum¬ 
ference of the pinion. But, if the teeth of the wheel and 
the leaves of the pinion are made curvilineal, the afting- 
faces of the teeth of the wheel muft be portions of an in¬ 
terior epicycloid formed by any generating circle rolling 
within the concave fuperficies of the large circle, and the 
afting faces of the pinion’s leaves muft be portions of ail 
exterior epicycloid produced by rolling the fame generating 
circle upon the convex circumference of the pinion. 
3. The third way in which one wheel may drive ano¬ 
ther, is when the aftion is partly carried on before the 
afting teeth arrive at the line of centres, and partly after 
they have palled this line. This mode of aftion, is 3 
combination of the two firft modes, and confequently par¬ 
takes of the advantages and aifadvantages of each. 
IV. Of the SCAPEMENT. 
We have feen the manner in which the moving power, 
which is the main-fpring, communicates its influence to 
the wheels. Nov/ that part of a clock or watch which con¬ 
nects the impulfe of the wheels (which move always in one 
direction) with the regulator, whether pendulum or ba¬ 
lance, is called the scapement. We have already ex¬ 
plained the mode in which the pallets of the verge of the 
balance work in the balance-wheel, which is properly the 
fcapement-wheel: in clocks it is called the fwing-wheel. 
When a tooth of this wheel, afting on the pallet, has 
given the balance or pendulum a motion in one direction, 
it muft quit it, that it may get an impulfion in the oppo- 
fite direction 5 and it is this efcaping of the tooth of the 
wheel from the pallet, or of the latter from the former, 
whichever we pleafe to call it, that has given rife to the 
general term, efcapement, or lcapement. 
The parts neceffary to be Ihown in deferibing a fcape¬ 
ment are, the pendulum or the balance, the pallets that 
work in the fcapement-wheel, and that wheel itfelf; toge¬ 
ther with any compenfation that may be applied to the 
balance or its fpring, or both. In fpeaking of clocks or 
watches upon different principles, the difference in the 
lcapement is chiefly meant, for this is the part of a time¬ 
piece that is melt frequently varied. And thus it appears 
that confiderable fcientinc fkill as well as mechanical in¬ 
genuity may be difplayed in the conllruftion of fcape- 
ments ; and the judicious confideraticn of them becomes 
of great importance to the artift: yet, notwithftanding 
this, no material improvement was made in them from the 
firft application of the pendulum to clocks till the days of 
Mr. George Graham ; nothing more was attempted before 
his time than to apply the impulfe of the fwing-wheel in 
fuch manner as was attended with the leafl friftion, and 
would give the greateft motion to the pendulum. Dr. 
Halley discovered, by fome experiments made at the Royal 
Obiervatory at Greenwich, that, by adding more weight 
to the pendulum, it was made to vibrate larger arcs, and 
the clock went falter; by diminifhing the weight of the 
pendulum, the vibrations became Ihorter, and the clock 
went flower: the refult of thefe experiments being diame¬ 
trically oppofite to what ought to be expected from the 
theory of the pendulum, probably firft roufed the attention 
of Mr. Graham, who was not only tkilful in praftice, but 
had much mathematical knowledge, and was well quali¬ 
fied to examine the fubjeft fcientifically: he foon made 
fuch further trials as convinced him, that this feeming 
paradox was occafioned by the retrograde motion which 
was given to the fwing-wheel by every conflruftion of 
fcapement that was at that time in ufe ; and his great fa- 
gacity foon produced a remedy for this defeft, by con- 
Itrufting a fcapement which prevented all recoil of the 
wheels, and reftored to the clock-pendulum, wholly in 
theory, and nearly in praftice, all its natural properties 
in its detached fimple ftate. 
Scapenients, whether for clocks or watches, and how¬ 
ever various, may be reduced to four kinds: the recoiling 
fcapement; the dead-beat; the horizontal, which is fimi- 
lar in effeft to the dead-beat; and the free or detached 
fcapement. 
1. The old recoiling fcapement y vt\\\zh. has been in ufe for 
clocks 
