312 HORO 
Mr. Edward Troughton has lately invented a tubular 
pendulum , which afts on the principle of the gridiron pen¬ 
dulum: in this conftruclion the apparent rod is a tube of 
brafs reaching from the bob nearly to the top; this con¬ 
tains another tube and five wires in its belly, l'o difpofed 
as to produce all together (like the nine-bar gridiron of 
Harrifon) three expanfions of Heel downwards, and two 
of brafs upwards; whofe lengths being inverfely propor¬ 
tioned to their dilatation, when properly combined, de- 
■ ftroy the whole effect that either metal would have fingly. 
The linall vilible part of the rod near the top is a brafs 
tube, whofe ufe is to cover the upper end of the middle 
wire, which is Angle, and otherwise unfupported. This 
pendulum we have great reafon to believe will Ihortly fu- 
perlede all the other compenfation-pendulums that have 
preceded it, on account of its poffeffing the following 
properties almoft exclufively: fir ft, it has all the advan¬ 
tages of oppofite expanfions which the common gridiron 
pendulum poll'effes; fecondlv, the arrangement of the me¬ 
tallic parts gives it the fimpiicity in appearance of a fingle 
rod, as well as a diminifhed refiflance of the air in its 
vibrations; thirdly, it has great llrength without much 
weight above the ball; fourthly, its centre of ofcillation, 
compared with the centre of the ball, or with the centre 
of gravity, may confequentlv be very nearly determined ; 
fifthly, the motions of the compenfating parts upwards 
and downwards are not affected by jerks, but are progref- 
iive and Heady, while yet the parts are fufficiently braced 
to prefierve their relative fituations and figures; iixthly, 
thecompenfation not onlyincludes the fpringof fufpenfion, 
and is adjuftable for temperature, but has its adjuftment 
for temperature made, independently of the rate of going, 
by a new pyrometer of great fenfibility, and free from the 
ufual objections againft pyrometers; leventhly, it is capa¬ 
ble of being put into beat without altering the fliape of 
the crutch or of any other part; and, laftly, it is capable 
of adjuftment for rate even while going. 
The Angular Pendulum is formed of two pieces or legs 
like a fedtion, and is fufpended by the angular point. This 
pendulum was invented with a view to diminifh the length 
of the common pendulum, but at the fame time to prefierve 
or even increafe the time of vibration. In this pendulum 
the time of vibration depends on the length of the legs, 
and on the angle contained between them conjointly, the 
duration of the time of vibration increafing with the angle. 
Hence a pendulum of this con(tru<ftion may be made to 
ofcillate in any given time. At the lower extremity of 
each leg of the pendulum is a ball or bob as ufiual. It 
may be eafily ftiown, that in this kind of a pendulum, the 
fquares of the times of vibration are as the fecants of half 
the angle contained by the legs: hence, if a pendulum of 
this conftruclion vibrates half feconds when its legs are 
clofe, it will vibrate whole feconds when the legs are 
opened, fo as to contain an angle equal to 151° 
Triangular Pendulum. In the year 1807, Mr. Rigo laid 
before the Royal Society a propofal for a new compenfa- 
tion-pendulum. In the courfie of various experiments, 
he difeovered, that of all modes of compenfation, that 
of triangles is the belt. He accordingly conilruCled 
one in the triangular form, the two fides being of fteel, 
and the bafe of brafs, or of zink, which expands twice as 
much as fteel ; and hence the expanfion of the fides is 
properly counteracted by that of the bafe. In this way 
Mr. Rigo affirms that pendulums may be conftrufted of 
any feries of triangles, that would continue the fame 
length throughout all climates and feafons. The idea ap¬ 
pears very ingenious, and the principle true; but we have 
not heard of any afitual experiments to afeertain the uti¬ 
lity or correftnefis of it in practice. 
The Conical or Circular Pendulum, is fo called from the 
figure deferibed by the ftring or ball of the pendulum. 
This pendulum was invented by Mr. Huygens, and is alfo 
claimed by Dr. Hook. In order to underftand the prin¬ 
ciples of this pendulum, it will be neceffary to premifie 
the following lemma, viz. The times of all the circular 
LOGY, 
revolutions of a heavy globular body, revolving within 
an inverted hollow paraboloid, will be equal whatever be 
the radii of the circles deferibed by that body. In order, 
therefore, to conftruCI the pendulum fo that its ball may 
always deferibe its revolutions in a paraboloid furface, it 
will be nedeflary that the rod of the pendulum be flexible, 
and that it be fufpended in fuch a manner as to form tile 
evolute of the given parabola. Hence, let KH, (fig. 36,) 
be an axis perpendicular to the horizon, having a pinion 
at K moved by the laft wheel in the train of the clock; 
and a hardened fteel point at H moving in an agate pivot, 
to render the motion as free as poffible. Now, let it be 
required that the pendulum fhall perform each revolution 
in a fecond, then the paraboloid furface it moves in muff 
be fuch whofe latus reElum is double the length of the 
common half-fecond pendulum. Let O be the focus of 
the parabola MEC, and MC the latus reElum-, then make 
AEe:MO=jMC“ the length of a common haffi- 
fecond pendulum. At the point A of the verge, let a 
thin plate AB be fixed at one end, and at the other end 
B let it be faftened to a bar or arm BD perpendicular to 
DH, and to which it is fixed at the point D. The figure 
of the plate AB is that of the evolute of the given para¬ 
bola MEC. The ftring of the pendulum muff be of fuch 
a length that when one end is fixed at B, it may lie over 
the plate AB, and then hang perpendicular from it, fo 
that the centre of the bob may be at E when at reft. Now, 
the verge K H being put into motion, the ball of the pen¬ 
dulum will begin to gyrate, and thereby conceive a cen¬ 
trifugal force which will carry it out from the axis to fome 
point F, where it will circulate feconds or half-feconds, 
according as the line AE is~9'8 inches or 2^ inches, and 
AB anfwerable to it. One advantage poflefled by a clock 
having a pendulum of this conftruftion is, that the fecond- 
hand moves in a regular and uniform manner, without 
being fiubjeft to thofe jerks or ftarts as in common clocks j 
and the pendulum is entirely filent. 
Balance Pendulum. Befides the effects of heat and cold 
on the length of the pendulum-rod, and of courfe on its 
ifochronifm, it may certainly be worth while, in the con- 
ltruftion of clocks intended to meafure time with the ut- 
moft poffible exafitnefs, to take Into confideration the re- 
fiftance of the air, which, by its unequal denfity, varying 
the weight of the pendulum, muft in a fmall degree acce¬ 
lerate or retard its motion. The celebrated David Ritten- 
houfe, who paid particular attention to this fubject, eftk 
mates the extreme difference of velocity, arifing from this 
caule, at half a fecond a-day; and he oblerves, that a re¬ 
medy dependent on the barometer will not be ftrifMy ac¬ 
curate, as the weight of the entire column of air does not 
precifely correlpond with the denfity of its bafe. He pro- 
pofes, therefore, as a very Ample and ealy remedy, that 
the pendulum fhall, as ufiual, confift of an inflexible rod 
carrying the ball beneath, and continued above the centre 
of fufpenfion to an equal (or an unequal) diftance upwards; 
At this extremity is to be fixed another ball of the fame 
dimenfions (or greater or lefs, according as the continua¬ 
tion is {hotter or longer), but made as light as poflible. 
The ofcillations of this upper ball will be accelerated by 
its buoyancy by the fame quantity as thofe of the lower 
would be retarded ; and thus, by a proper adjuftment, the 
two effects might be made to balance and correCt each 
other. Our author made a compound pendulum on thefie 
principles, of about one foot in its whole length. This 
pendulum, on many trials, made in the air 57 vibrations 
in a minute. On immerfing the whole in water, it made 
59 vibrations in the fame time; fhowing evidently, that 
its returns were quicker in fo denfe a medium as water 
than in the air. (This is contrary to what takes place 
with the common pendulum.) When the lower bob or 
pendulum only was plunged in water, it made no more 
than 44. vibrations in a minute. 
Wooden Pendulums. —The expanfion or contraction of 
ftraight-grained fir-wood letigthwife, by change of tempe¬ 
rature, is fo fmall, that it is found to make very good pe«- 
duium- 
