PENDULUM. 



PENDULUM. 



3T 



stuns pi*" <w through a wall The ] minium in generally suspended 

 tram a oook on UM tack of the frame, but it may be (mpporte.1 n a 

 triangle standing ou the ruing board, or even from the back of the 

 cMo/but there it then a fear that the axis of uiotioo may not be in the 

 axi* of the palleU, or may not keep to. The clock being fixed, the first 

 Up i* to put it into txal, that i. to make the beat* follow at equal 

 interval*. TIi. clL maker doe* this in couiinun cloclu by U'li.liiu- 

 UM crutch, but when the discrepancy U not great, any one may produce 

 the desired equality by tilting the frame a little ; in table-clock* there 

 are generally fooUercwi for the purpose, or if not, the feet may be 

 propped by piece* of wood, card, Ac. In astronomical clock*, the angle 

 which UM crutch make* with the pallet* admit* of a small adjustment 

 by two sore**, which act on oppoaite aide* of the crutch, and the 

 operation U performed a* follow* : Make the beat* nearly correct by 

 ear, and by touching the screw* : note which screw belongs to the 

 longer leg ; then by softly deadening the pendulum aa it rises, make 

 it jiut nul escape on one aide. By very gentle pnshee cause it to escape 

 on that aide, and *ee whether it escapes on the other ; U it does not, 

 une screw miut be screwed up and the other released. After a few 

 trail and error* it will be found that when the pendulum jiut escape* 

 on cither aide, it will just escape on the other, and if there be a very 

 wall inequality indeed, a little tightening of one of the crutch screws 

 will complete the adjustment. The pendulum should then be brought 

 to rc*t, and the zero of the plate on which the arc of vibration is read 

 olf, be fixed just behind the pointer of the pendulum, shown at c, 

 fyi. '20, '21, in HOKOLUUY. In that article the rule for bringing a 

 clock to time is given. 



In an observatory it is always desirable that a clock should have a 

 email losing rate, and be slow rather than fast (the corrections for 

 clock error and clock rate are then additive), so that it would be better 

 to add a smaller weight than 46 grains ; and in any case it is more safe 

 to destroy the rate by two operations, especially if the preceding rates 

 were not very carefully determined. 



The final adjustment of the compensation can be best accomplished 

 when the clock has gone several months, and when the gain or loss in 

 two of the warmest months in the year U compared with the gain or 

 loss in two of the coldest. Suppose the tneaa temperature in the 

 summer months of trial to be 30 higher than in the winter months, 

 and that the clock loses 1* more in summer than in winter ; it is there- 

 fore utuUr-compciuated, and requires more mercury. Add 1 Ib. of 

 mercury, and bring it to a close rate exactly as before ; and now let it 

 be onr-compensated, so that an increase of 24 in the temperature 

 causes it to gain 0"4 per day, which, by simple proportion, is tl\e same 

 as a gain of 0"5 by SO 9 of temperature. Hence it is clear that as 1 Ib. 

 of mercury cause* an alteration of 1"5 in the variation due to tempe- 

 rature, if a third of a pound be withdrawn the compensation will be 

 nearly correct. A second trial will perfect the compensation, which 

 should never be afterwards disturbed. 



The researches respecting resisting media have already been referred 

 to. There existed for some time a discrepancy between Poisson's 

 factor, by which the correction for buoyancy is to be multiplied, to 

 give the whole effect observed, and Mr. Baily's : the one being 1*5, and 

 the other 1*8. Professor Stokes has reviewed the subject in a memoir 

 published in the ' Transactions of the Cambridge Philosophical Society.' 

 In this inquiry the internal friction of the fluid or medium is taken 

 into account. In the case of a ball-pendulum the resistance U propor- 

 tional, not to the surface, but to the radius of the sphere, so that the 

 quotient of the resistance divided by the mass increases very rapidly 

 a* the radiu* decreases. Hence the terminal velocity of a minute globule 

 of water, descending through the air, depends almost entirely on the 

 internal friction of air ; but since the index of friction is known from 

 Baily'* experiment* this terminal velocity can be calculated numerically 

 i'..r .1 globule of given diameter. This velocity is so small in the case 

 ule.4, such as those of which clouds are probably formed, that 

 according to Mr. Stokes, the suspension of clouds need not offer any 

 difficulty. 



When a pendulum is not limited to one plane, but only to the con 

 cave surface of a hollow sphere, we have what is called the 

 pendulum. It* motion* have of late yean been investigated in the 

 pages of the ' Philosophical Magazine,' and elsewhere. 



Ist.ylh of Simj>lt and IntariaUe Pendulum. "The equality of the 

 oscillation* of a weight suspended by a line is said to liave been used 

 by I I'll Jim ix. in linn, and by the Arabian astronomers, for the sub- 

 division of |iortions of tin,.-. (Young, 'Nat Phil.,' vol. i., p. 595.) 

 This property of the pendulum was remarked by Qalileo when a 

 tixlent at Pisa, by observing the vibration* of a lamp swinging from 

 the roof of the cathedral, and was by him proposed as a medical instru- 

 ment for observation, on the pulse. (Drinkwater, ' Life of Galileo, 

 p. .'-.) The simple pendulum was much used a* an astronomical 

 instrument (called perjtfitdiculum in the older writers) before it was 

 adapted by Huyghena to the clock. Mouton (' Obscrvationes Diametro- 

 ruui Soli* et Luna],' Lugd., 1670) applied the vibrations of the simple 

 pendulum successfully to measure the time in which the sun and moon 

 describe their respective diameters, and in the Appendix, p. 427 

 proposes his Nora memurantm geomttriranun idea, that is, a dccirna 

 yitem of measure* bawd on the value of a minute in Km-i. .liV length 

 of a degree. Thi* is his militut, the thousandth part of whirl. 

 a ti'jyu ; and the finds l>y IX|M intent that the rirga, which 



according to Riccioli, i* 5 ft 4-363 in., Bologneae measure, is the 

 ength of a simple pendulum which make* 1*222 oscillations in half 

 an Tiour. 



In l'i 71 Picart was sent to determine the position of Tycho Brabe"s 

 observatory at Uranibourg. He took thi* opportunity of swinging the 

 wnduluni, and found the length of the second* pendulum 3 ft. U in. 84). 

 >ari measure, exactly the same as he had previously found it to be at 

 i'aris, and subsequently at Cette, on the south coast of France. 

 Koemer obtained the same result at London, and these erroneous 

 neasures of Picart, the first astronomical observer of his day, were 

 or a long time cited as objections to the theory of gravitation. 



In 1672 Richer was sent to Cayenne (about 4* 56' N. lat) to ""* a 

 course of observations, and among the rest to observe the length of 

 the seconds pendulum. His words are : " L'uno des plus considerables 

 observations que j'ay faites, est celle de la longueur du pendule K 

 secondea de temps, laquelle s'est trouvoe plus courte en Calenne quit 

 Paris : car la niesme mesure qui avoit estd marquee en ce lieu-la sur 

 une verge de fer, suivant la longueur qui s'estoit trouvce necessaire 

 |nir fair un pendule a secondea de temps, ayant est<5 ap]*>rU<e en 

 France, et comparce avec celle de Paris, leur difference a este' tnnivco 

 d'une ligne et un quart, dont celle de Caienne est moiudre que celle de 

 Paris, laquelle eat de 3 pieds 8f lignes. Cette observation a eati! 

 reiteree pendant dix rnoia entiers, oil il ne s'est point passe' de aemaine 

 qu'ello n'ait est& faite plusieurs fois avec beaucoup de soin. Lea 

 vibrations du pendule simple dont on se servoit, estoient fort petites et 

 duroient fort sensibles jusques n cinquante-deux minutes de temps, et 

 out est<5 companies a celles d'une horloge tres excellent*, dont lea 

 vibrations marquoient les secondes de temps." (' Kecueil des Obser- 

 vations faites en plusieurs Voyages par ordre de sa Majeste',* p. 66, 

 Paris, 1693.) We have cited this passage textually, not only on 

 account of its importance, but because it is generally merely stated that 

 Richer's clock, which was regulated on Paris time, lost more than two 

 minutes at Cayenne. This misrepresents the eritlcnce of the experiment, 

 and moreover leaves room to suppose that Richer made a rhnntt dis- 

 covery, whereas the determination of the length of the pendulum was 

 one of the special objects of his mission (see p. 2). Neither Picart nor 

 Richer gives any details of his modus operandi. 



In 1673 Huyghens published his 'Horologium Oacillatorium,' perhaps 

 the most remarkable mathematico-uiechanical work which preceded 

 Newton's ' Priueipia.' He therein explains the uodironitm of oscil- 

 lations in a cycloid, and the mechanical means of making the pendulum 

 swing in a cycloid. He gives theorems for finding the centre of oscil- 

 lation of several figures, and thence the length of the simple pendulum, 

 corresponding to a compound pendulum of certain forms ; and in pro- 

 positions 19 and 20 (p. 124-5) proves that when the body is the same, 

 the distances of the axes of suspension from the centre of gravity are 

 reciprocally as the distances of the centre of gravity from the respec- 

 tive centres of oscillation, and that the point of suspension and 

 centre of oscillation are convertible. His proposition 25 (p. 151) is 

 on the mode of fixing a universal and perpetual measure, which lie 

 proposes should be the third part of a seconds pendulum, and names a 

 horary foot. 



Newton, in his ' Principia,' lib. i., s. 10, investigates the oscillations 

 of a body in a cycloid, or in any other curve; lib. ii., s. 6, he considers 

 the effects of a resisting medium on a pendulous body ; and lib. iii., 

 prop. 19, he determines the figure of the earth, supposing it to be fluid 

 and of uniform density, to be a spheroid of which the equatorial and 

 polar diameters are as 220 : 229. In prop. 20 he computes the lengths 

 of the seconds pendulum and of the degrees of the meridian, which are 

 required on the foregoing suppositions ; and he remarks, " Quod 

 inequalitas diametrorum terne facilius et certius per experiment* pen- 

 dulorum deprchendi possit quaui per arena geographice menauratos in 

 meridiano." In the following pages is an analysis of the lengths of the 

 pendulum which had come to his knowledge. 



We have not been able to find any account by Graham himself of 

 two very capital improvements which he seems to have introduced into 

 pendulum experiments. The first is a clock, in which " he carefully 

 contrived that its pendulum might at pleasure be reduced to the same 

 length whenever there should be occasion to remove the clock from 

 one place and set it up in another." (Brodley's ' Account of the going 

 of a Clock by Graham, in London, and at Black River, Jamaica,' ' Phil. 

 Trans.,' vol. xxxviii, p. 302.) Probably this was done by drawing the 

 spring through a clip to a given mark ; for in another description of a 

 similar clock it is said the suspending spring was broken. We do not, 

 however, see need for any adjustment in this respect, if the spring be 

 pinned into the rod and into its upper axis. The pendulum was not 

 compensated, but a thermometer was enclosed in the clock, and as the 

 rate in different temperatures at the same place had been determined, 

 the reduction to a normal temperature was easy. Clocks of this kin<l 

 were supplied to the French expeditions for measuring arc* of the 

 meridian in Upland and Peru. For this latter expedition Graham 

 -u| plitil Godin with a detached pendulum, which Godin thus describes : 

 " Ce pendule est compose' en general d'un til de cuivre, d'une Ixmle 

 da matne inatiero a 1111 de KCS bouts, et d'une piece .IVier taillee en 

 couteau a 1'autre bout, qui est celui de suspension : ce couteau porte 

 sur deux montauts d'acier en deux points qui designent 1'axe du 



Tliii volume contain! Picart'l observation*, a< veil M Iticber't. 



