654 PHILOSOPHICAL TRANSACTIONS. [aNNO 1/34. 



Without entering into the dispute about the figure of the earth, Mr. Bradley 

 at present supposes, with Sir Isaac Newton, that the increase of gravity, as we 

 recede from the equator, is nearly as the square of the sine of the latitude, 

 and that the difference in the length of pendulums, is proportional to the aug- 

 mentation or diminution of gravity. On these suppositions Mr. Bradley col- 

 lects, from the abovementioned observations, that if the length of a simple 

 pendulum, that swings seconds at London, be 39.126 English inches, the 

 length of one at the equator would be 39.UO, and at the poles 39.206. And, 

 abstracting from the alteration on account of different degrees of heat, a pen- 

 dulum clock, that would go true time under the equator, will gain 3™ 484-'* in 

 a day at the poles; but the number of seconds which it would gain in any other 

 latitude, would be to 3"^ 48-^', nearly as the square of the sine of that latitude, 

 to the square of the radius; whence it follows, that the number of seconds a 

 clock will lose in a day, on its removal to a place nearer the equator, will be to 

 3"! 48-{-^, nearly as the difference between the squares of the sines of the lati- 

 tudes of the two places, to the square of the radius. Thus the difference of 

 the squares of the sines of 51-i-'' and 18°, the latitudes of London and Black- 

 river, being to the square of the radius, as 118 to '126^, the clock will go 1"' 

 58' in a day slower at Black-river than at Loudon; as was found by obser- 

 vation. 



It may be hoped that Mr. Campbell's success in this experiment, and the 

 little trouble there is in making it, will induce those gentlemen who may here- 

 after carry pendulum clocks into distant countries, to attempt a repetition of 

 it after his manner; that is, by keeping or restoring the pendulums of their 

 clocks to the satne length in the different places, and carefully comparing 

 them with the heavens; and at the same time taking notice of the different 

 degrees of heat, by means of a thermometer. From a variety of such expe 

 riments we should be enabled to determine how far Sir Isaac Newton's theory 

 is conformable to truth, with nuich greater certainty than from those trials 

 which are made by actually measuring the lengths of simple pendulums; be- 

 cause a difference of the 100th part of an inch, in the length of a pendulum, 

 corresponds to 11 seconds in a day, and it being easy to observe how much 

 a clock gains or loses in a day, even to a single second. It is certain, that by 

 means of a clock, compared in the manner abovementioned, we may distin- 

 guish a difference in the lengths of isochronal pendulums, of ) 000th part of 

 an inch, or less; whereas it will be scarcely possible to measure their true 

 lengths, without being liable to a greater error than that. Besides, by taking 

 notice how much a clock gains or loses, on the falling or rising of a thermo- 

 meter, we can better allow for the different degrees of heat in this, than in the 



