PEN
' VII. To fini the Length of a Pendulum, which pall make
- ny ajjign'd Number of Vibrations many given Time.
Let the Number of Vibrations requir'd, be 50 in a Min. and the Length of the String, counted from the Point of Suf- penfion, to the Centre of Ofcillation, or round Ball at the End of it be requir'd : 'Tis a fix'd Rule that the Lengths of pendulums are to each other, as the Squares of their Vibrations and Contrarywife : Now 'tis agreed that a 'Pendulum vibrat- ing Seconds (or 60 times in a Minute) is 39 Inches, and f; of an Inch; fay therefore as the Square of 50 (which is 2500) to the Square of <So, (which is 3000) fo is 39, 2, to the Length of the 'Pendulum requir'd: which will be found to be 5 6 In- ches &■
Note, In Praflice, (ince the Produfl of the mean Time, will always be 141 12C0 (that is the Product of the Square of 60, multiplied by 39, 2.) that is 3600 -f. 39, 2. you need on- ly divide that Number by the Square of the Number of Vi- bartions affign'd ; and the Quotient will give the Length of a Pendulum, that (hall vibrate juftfo many times in a Min. VII. The Length of a Pendulum being known,to find the Num- ier of Vibrations it will make in a given Time.
This being the Reverfe of the Former ; fay, As the Length given, fuppofe 56, 4, is to the Length of the Standard Pendu- lum fwinging Seconds, viz. 39, 2 ; to is the Square of the Vibrations of the Standard Pendulum in the given Time, v. gr.a. Minute, to the Square of the Vibrations fought: that is, as 56: 4: 39: 2, 3600: 2500.
And the Square Root of 2500, will be 50, the Number of Vibrations fought.
But for life, here, (as in the former Problem; you need on- ly divide 141 1 100 by the Length ; and it gives the Square of the Vibrations; as there you divided by the Square of the Vi- brations, to find the Length.
On thefe Principles, Mr. T)erham has conftrucfed a Table of the Vibrations of Pendulums of different Lengths in the Space of a Minute.
( 777 )
P E N
Pend.
Vibrat.
Pend.
Vibrat.
length
in a
length
in a
in
Minute
in
Minute
inches
inches
z
375-7
30
6i.6
2
2C5.S
>
3
216". 9
39.2
68.0
4
187.8
5
I6~8.0
40
5S-5
6
153-3
50
5 3-1
7
142.O
Co
48.5
8
132.8
70
44.9
9
125.2
80
41.0
10
118.8
90
39-<>
20
S4.0
100
37-5
Note, Thefe Laws, (£c. of the Motion of Pendulums will fcarce hold ftricfly, unlefs the Thread that fuftains the Ball, be void of Weight, and the Gravity of the whole Weight be collected in a Point.
In practice, therefore, a very fine Thread, and .a fmall Ball, but of a very heavy Matter, are to be ufed. A thick Thread, and a bulky Bali dilturb the Motion ilrangely ; for in that Caie, the Pendulum, of Simple, becomes compound ; it being much the fame as if feveral Weights were applied to the lame inflexible Rod in feveral Places.
The Ufe of Pendulums in meafuring Time in Attronomi- cal Obfervations, and on other Occafi'ons where a great De- gree of Precifenefs is requir'd ; is too obvious to need a De- fcription. Either the Length of the Pendulum may be adjuft- ed before its Application, and made to vibrate the defired Time, v. g. Seconds, half Seconds, i$c. by Article VI. or it may be taken at Random, and the Times of the Vibra- tions afterwards determined from Article VIII.
For the Ufe of the Pendulum in meafuring remote in- acceifible Diftances, iSc by means of Sound, i£c. See Sound.
Pendulum Clock, a Clock, which derives its Motion from the Vibration of a Pendulum.
'Tis controverted between Galileo and Huygens, which of the the two firft applied the Pendulum to a Clock; far the Preten/icms of each. See Clock.
After Huygens had difcover'd that the Vibrations made in Arches of a Cycloid, however, unequal they were in extent, were all equal in Time; he fcon perceiv'd that a Pendulum applied to a Clock, fo as to make it defcribe Arches of a Cy- cloid, would rectify the otherwife unavoidable Irregularities of the Motion of the Clock ; fince, tho' the feveral Caufes of thofe Irregularities lhou'd occalion the pendulum to make greater or lefs Vibrations; yet, in virtue of the Cycloid, it wou'd flill make 'em perfectly equal ; and thus the Motion of the Clock govern'd thereby, wou'd be preferved perfectly equable. Sec Cycloid.
But the Difficulty was to make the Pendulum defcribe Arches of a Cycloid ; for, naturally, the Pendulum being tied to a fix d Point, can only defcribe Arches of Circles about the fame.
Here M. Huygens hit on a Secret which all the World is now ter of: The Iron Rod or Wiar which bears the Bob at Bot- tom, he tied a Top to a Silken Thread, placed between two Cycloidal Cheeks, or two little Arches of a C>cloid, made of Metal. Hence the Motion of Vibration, applying inceflantly from one to t'other of thofe Arches, the Thread, which is ex- tremely flexible, eafily affumes the Figure thereof; and by- Means hereof tis demonflratcd, that the Weight fufpended at the other End of the Rod, will defcribe a juft Arch of a Cycloid.
This is doubtlefs one of the moil ufeful and ingenious In- ventions many Ages have produced : By means whereof, we have Clocks which won't err afingle Second in feveral Days.
'Tis true, the Pendulum is lyable to its Irregularities ; how minute foever they may be; M. de la Hire thinks there is ftill room to improve it.
The Silk Thread by which it is fufpended, he obferves Ihortens in moift Weather, and lengthens in dry; by which means the Length of the whole Pendulum, and coofequently the times of the Vibrations are varied.
To obviate this Inconvenience, M. de la Hire, in lieu of a Silk Thread, ufed a little fine Spring ; which was not indeed fubject to fhorten and lengthen ; but which he found grew fliffer in cold Weather, and made its Vibrations falter than in warm.
He had therefore recourfe to a fliff Wiar or Rod, Firm from one End to t'other. Indeed, by this means he renounced the Advantages of the Cycloid ; but he found, as he fays, by Experience, that the Vibrations in Arches of Circles are per- formed in Times as equal, provided they ben't of too preat Extent, as thofe in Cycloids. But the Experiments of Sir J. Ahor and others, have demonilrated of the contrary.
The ordinary Caufes of the Irregularities of pendulums, Mr. 'Derham afcribesto the Alterations in the Gravity, and Temperature of the Air; which increafe and diminilh the Weight of the Ball, and by that means make the Vibrations greater and lefs : An Acceffion of Weight in the Ball being tound by Experiment to accelerate the Motion of the Pen- dulum.
A Weight of Six Pound added to the Ball, Mr. "Derham found, made his Clock gain 1 3 Seconds every Day.
A general Remedy againfl thefe Inconveniences of Pendu- lums, is to make 'em long, the Bob heavy, and to vibrate but a little way: this is the ufual means in England ; the Cy- cloidel Cheeks being generally overlook 'd.
To corretl the Motion of Pendulum- Clocks ; the ufual Me- thod is to fcrew and let down the Ball ;but a very fmall Alter- ation here having a very great Effect ; Mr. IDerham prefers Hmgens's Method, which is to have a fmall Weight or Bob to Aide up and down the Rod above the Ball, which is to be immoveable: tho' he improves on the Method, and recom- mends having the Ball to fcrew up and down, to bring the Pendulum near its Gage ; and the little Bob to ferve lor the nicer Corrections, as the Alteration of a Second, &c.
Mr. Huygens orders rhe Weight of this little Corrector to be equal to that of the Wiar, or 50' of that of the great Bail : He adds a Table ot the Alterations, the feveral fhittings there- of will occafion in the Motion of the pendulum ; Wherein it is obfervable, that a fmall Alteration towards the lower End of the Pendulum, makes as great an Alteration in Time, as a greater riling or tailing does when higher.
Pendulum Royal, a Name given among us to a Clock, whofe Pendulum fwings Seconds, and goes eioht Days ; fhewing the Hour, Minutes, and Seconds. See Clock.
The Numbers of fuch a Piece are thus calculated ; firft caft up the Seconds in 12 Hours, and you will find them to be 43200=: 12X So* (To. The fwing Wheel mutt be 30 to fiving So Seconds in one of its Revolutions : Now let ~ 43200 — 2160c, be divided by 30, and you will have 720 in the Quo- tient, which mutt be broken into Quotients; the firft of them mult be 12 tor the great Wheel which moves round once in 12 Hours. 720 divided by 12, gives 60, which may alfo be conveniently broken into 8 ) 96 (12 two Quotients, as 10 and 6, or 5 and 12, or 8 8 ) 64 ( 8 and 7 \ ; which latt is moft convenient: and 8 ) 60 ( 7 |
if you take all your Pinnions 8, the Work will . ■ .
ftand thus. 30
According to this Computation, the great Wheel will go about once in 12 Hours, to fhew the Hour ; the fecond Wheel once in an Hour, to fuew the Minutes ; and the fwing Wheel once in a Minute, to fhew the Seconds. See Movement and Clock-work,
PENECILLA, in Pharmacy, a Lozenge, made round by rolling ; the fame as TurundiJa ; thus call'd from Penecilltis a, Pencil, which it refembles in fhape.
PENECILLUS, among Chirurgeons, is ufed for a Tent to be put in Wounds or Ulcers. See Tent.
S M PENE-
