39 jblfficuhies ef Experiments with Pmduhms, 



hand will be jarred by a blow upwards, owing to the tendency of the outer half of the fticlc to 

 proceed downwards by virtue of its greater velocity. If the obftacle be ftruck with the outer end 

 of the fticlt, the jar will be in the contrary direilion, becaufe the whole, or the greateft part of the 

 force, is exerted within the obftacle ; but if the blow be given at the diftance of one-third part of 

 the outer extremity, it will be more effectual than in other cafes, and the greater velocity of the 

 extarnal portion compenfating for the greater mafs of the part neareft the hand, no blow will 

 be felt, becaufe there is no tendency to rotation. The (lick therefore moves, and if hung up 

 would vibrate as if its whole mafs were collccled at the diftance of two-thirds of its length from 

 the point of fufpenfion. And it is accordingly found, that a fmall ball hung by a thread of 

 that length will vibrate in equal times with the ftick Mathematicians, particularly Huyghens, 

 have determined the places of the centres of ofcillation of bodies, varioufly figured and fufpend- 

 ed. It is enough for our prefent purpofe to have fhewn, that the effectual length of a pendu- 

 lum cannot be determined without admitting the confideration of the figure and magnitude of 

 the pendulous body as an element in the procefs ; or to ftalte the effeiS: more immediately, we 

 may obferve, that if two balls were feparately fufpended, and fet to vibrate through equal 

 arcs, having the diftance between their centres and points of fufpenfion refpeftively equal, 

 the larger ball would vibrate flOweft, becaufe its centre of ofcillation would be furtheft from its 

 centre of gravity. Hence it rriuft follow, that our two obfervers, who are fuppofed to be in 

 fearch of one and the fame meafure, would, independently of the other difficult requifites, find 

 it necefTary to ufe balls either equal or proportioned to each other in a known ratio, a condition 

 which is precifely the difficulty this method is meant to obviate. It will, moreover, be required, 

 in order that the determinations may hold good, that the material, whether metal or any other 

 fub'ftance, fliould be of uniform denfity throughout, as well as that it fliould poffefs great truth 

 of figure ; both which conditions fcarcely require any remark with regard to their praftical 

 difficulties. 5. The force of gravitation is different according to the latitude of the place of ob- 

 fervation, and as far as obfervations have yet been carried, this variation is not governed by a per- 

 fe<aiy regular law. It is not the fame in the northern and fouthern hemifpheres, and is probably 

 afFedled by the vicinity of mountains, and the pofition of the plane of vibration with regard to 

 them. Thefe caufes, which do not afFefl the utility of an inftrument for meafuring time, are of 

 great confequence in the deduflion of our linear meafure. 6. Whether there be any notable ir- 

 regularity in the rotation of the earth, from which our meafures of time are derived, may be 

 queftioned. It is probable, from the evidence of aftronomical clocks, fome of which have per- 

 formed with wonderful accuracy, that there is not ; and this evidence is ftill more confirmed by 

 the correfpondence of the rotations of Jupiter and Mars with refpe£l to that of the earth, con- 

 cerning which, I have heard of no irregularity, excepting in a paper of Dr. Herfchel, in the 

 Philofophical Tranfadlions for 1784. 7. The mechanical determination of the centre of fuf- 

 penfion is not altogether an eafy talk. 



From thefe, and, perhaps, other difficulties, the admeafurement of length by the pendulum 

 had been, for aconfiderable number of years, difregarded, when in the year 1774, the fociety in 

 London, for the encouragement of arts, manufaftures, and commerce, offered a reward of one 

 hundred guineas, for a mode of afcertaining invariable ftandards for weights and meafures, 

 communicable at all times and to all nations, which offer being continued for three fucceeding 



years, 



