325 
HORO 
pendulum AB, which is fufpended upon the hook A. 
The pendulum AB defcribes round the point A an arc 
of a circle alternately going and returning. If then the 
pendulum be once put in motion by a pulh of the hand, 
the weight of the pendulum at B will make it return 
upon itfelf, and it will continue to go alternately back¬ 
ward and forward till the refiftance of the air upon the 
pendulum, and the fridtion at the point of fufpenfion at 
A, dellroys the original imprefled force. But at every 
vibration of the pendulum, the teeth of the balance-wheel 
GH aftfo upon the pallets IK (the pivots upon the axis 
of thefe pallets play in two holes of the potence st ), that, 
after one tooth, H, has communicated motion to the pal¬ 
let K, that tooth efcapes ; then the oppofite tooth, G, 
acts upon the pallet I, and efcapes in the fame manner ; 
and thus each tooth of the wheel efcapes the pallets IK, 
after having communicated their motion to the pallets in 
fuch a manner that the pendulum, inllead of being 
Hopped, continues to move. The wheel EE revolves in 
an hour; the pivot c of this wheel paffes through the 
plate, and is continued to r; upon the pivot is a wheel 
NN with a long focket fattened in the centre; upon the 
extremity of this focket r, the minute-hand is fixed. The 
wheel NN a6ts upon the wheel O; the pinion of which, 
p, afts upon the wheel qq, fixed upon a focket which 
turns along with the wheel N. This wheel qq makes its 
revolution in 12 hours, upon the focket of which the 
hour-hand is fixed. 
From the above defcription it is eafy to fee, 1, That 
the weight P turns all the wheels, and at the fame time 
continues the motion of the pendulum. 2. That the 
quicknefs of the motion of the wheels is determined by 
that of the pendulum. 3. That the wheels point out the 
parts of time divided by the uniform motion of the pen¬ 
dulum. 
When the cord upon which the weight is fufpended is 
entirely run down from off the barrel, it is wound up 
again by means of a key, which goes on the fquare end 
of the arbor at Q, by turning it in a contrary direction 
from that in which the weight defcends. For this pur- 
pofe, the inclined fide of the teeth of the wheel K, fig. 57, 
removes the click C, l'o that the ratchet-wheel R turns 
while the wheel D is at reft; but, as loon as the cord is 
wound up, the click falls in between the teeth of the 
wheel D, and the right fide of the teeth again act upon 
the end of the click, which obliges the wheel D to turn 
along with the barrel; and the fpring A keeps the click 
between the teeth of the ratchet-wheel R. 
We fhall now explain how time is meafured by the mo¬ 
tion of the pendulum; and how the wheel E, upon the 
axis of which the minute-hand is fixed, makes but one 
precife revolution in an hour. The vibrations of a pen¬ 
dulum are performed in a Ihorter or longer time in pro¬ 
portion to the length of the pendulum itfelf. A pendu- 
dulum of 3gi inches in length, makes 3600 vibrations in 
an hour: i. e. each vibration is performed in a fecond of 
time, and for that realon it is called a fecond pendulum. 
But a pendulum of inches makes 7200 vibrations 
in an hour, or two vibrations in a fecond of time, and 
is called a half-fecond pendulum. Hence, in conftmct- 
ing a wheel whofe revolution mull be performed in a 
given time, the time of the vibrations of the pendulum 
which regulates its motion mull be confidered. Sup- 
pofmg, then, that the pendulum AB, fig. 56, makes 7200 
vibrations in an hour, let us confider how the wheel E 
lhall take up an hour in making one revolution. This 
entirely depends on the number of teeth in the wheels 
and pinions. If the balance-wheel confifts of 30 teeth, it 
will turn once in the time that the pendulum makes 60 
vibrations; for at every turn of the'wheel, the fame tooth 
afts once on the pallet I, and once on the pallet K, which 
occafions two feparate vibrations in the pendulum ; and 
the wheel having 30 teeth, it occafions twice 30, or 60, 
vibrations. Confequently this wheel mull perform 120 
revolutions in hour; becaufe 60 vibrations, which it oc- 
eafions at every revolution, are contained 120 times in 
LOG Y, 
7 Z 30 , the number of vibrations performed by the pendu¬ 
lum in an hour. Nov/, in order to determine the num¬ 
ber of teeth for the wheels EF and their pinions ef; it 
muff be remarked, that one revolution of the wheel E 
muff turn the pinion e as many times as the number of 
teeth in the pinion is contained in the number of teeth 
in the wheel. Thus, if tlm wheel E contains 72 teeth, 
and the pinion e 6, the pinion will make 12 revolutions 
in the time that the wheel makes 1; for each tooth of 
the wheel drives forward a tooth of the pinion, and, when 
the 6 teeth of the pinion are moved, a complete revolu¬ 
tion is performed ; but the ivheel E has by that time only 
advanced 6 teeth, and has Hill 66 to advance before its 
revolution be completed, which will occafion 11 more re¬ 
volutions cf the pinion. For the fame reafon, the wheel 
F having 60 teeth, and the pinion f 6 , the pinion will 
make 10 revolutions while the wheel performs 1. Now, 
the wheel F, being turned by the pinion e, makes 12 re¬ 
volutions for one of the wheel E ; and the pinion f makes 
10 revolutions for one of the wheel F; confequently, the 
pinion f performs 10 times 12 or 120 revolutions in the 
time the wheel E performs one. But the wheel G, which 
is turned by the pinion f occafions 60 vibrations in the 
pendulum each time it turns round ; confequently the 
wheel G occafions 60 times 120 or 7200 vibrations of the 
pendulum while the wheel E performs one revolution ; 
but 7200 is the number of vibrations made by the pen¬ 
dulum in an hour, and confequently the wheel E per¬ 
forms but one revolution in hour; and fo of the reft. 
From this reafoning, it is eafy to difeover how a clock 
may be made to go for any length of time without being 
wound up. 1. By increafing the number of teeth in the 
wdieels. 2. By diminifliing the number of teeth in the 
pinions. 3. By increafing the length of the cord that 
fulpends the weight. 4. By increafing the length of the 
pendulum. And, 5. By adding to the number of wheels 
and pinions. But, in proportion as the time is augment¬ 
ed, if the weight continues the fame, the force which it 
communicates to the laft: wheel GH will be diminiflied. 
We are next to notice the number of teeth in the 
wheels wdiich turn the hour and minute hand. The wheel 
E performs one revolution in an hour; the w'heel N N, 
which is turned by the axis of the wheel E, muff likewife 
make only one revolution in the fame time; and the mi¬ 
nute-hand is fixed to the focket of this wheel. The wheel 
N has 30 teeth, and afts upon the w'heel O, which has 
likewife 30 teeth, and the fame diameter ; confequently 
the wheel O takes one hour to a revolution; now the 
wheel O carries the pinion p, which has 6 teeth, and which 
a£ts upon the wheel qq, of 72 teeth; confequently the 
pinion p makes 12 revolutions while the wheel qq makes 
one, and of courfe the wheel qq takes 12 hours to one re¬ 
volution; and upon the focket of this wheel the hour- 
hand is fixed. All that has been laid here concerning the 
revolutions of the wheels, See. is equally applicable to 
watches as to clocks. 
A portable eight-day clock differs from an ordinary 30- 
hour clock principally in five refpe&s : in the firft place, 
it is actuated by a fpring; fecondly, it has a Ihorter pen¬ 
dulum ; thirdly, it has confequently a higher train; 
fourthly, it requires a fufee; and, laftly, it has frequently 
a crown-wheel fcapement; in {hort, it may be confidered 
as a watch on an enlarged fcale, except that it has ufually 
the ftriking- mechanifm, which is introduced in the repeat¬ 
ing watches only. But a portable clock, fuch as we have 
here deferibed, is eafily converted into a clock with a 
long cafe, and a fufpended weight for the maintaining 
power, by fubftituting a cylindrical barrel for the fufee 
on the arbor of the great wheel, on which barrel the chain 
is wound, in (lead of being made to furround the fufee ; 
for, as a fufpended load acts at all times with the fiune 
power, it is neceffary that the barrel fiiould have the fame 
diameter at every part of it. Of this conftrufHon are the 
eight-day houfeliold clocks in general ufe. Alfo, by in¬ 
troducing a wheel and pinion between the great and cen¬ 
tre wheels, the clock may be made to go a month or 
3 more. 
