VOL. XXXIX.] PHILOSOPHICAL. TRANSACTIONS. 2Q 



were to be allowed for the lengthening of the pendulum by heat; and therefore 

 it was retarded only 1"' 57* by the decrement of gravity. So that while a pen- 

 dulum of London makes 86164 vibrations, the number of seconds in a sydereal 

 day, the same at Jamaica gives only 86047 vibrations. Therefore the force of 

 gravity at London, is to that in the latitude of 18°, as the square of 86 164, 

 to the square of 86047 ; that is, very nearly as 1 106 to 1 103. And, by article 

 1 and 2, if a denote the mean diameter of the earth, d the difference of the 



greatest and smallest, then a will denote the force of gravity in general 



in any latitude, whose co-sine is to the radius as c to r; where, if instead 

 of c there be substituted the co-sines of 51° 32' and 18°, that is, of the lati- 

 tudes of London and Jamaica, we shall have the force of gravity at the former, 

 to that at the latter, as a — 3870(i to a — Q045d, that is, as II06 to 1103. 

 Hence the mean diameter of the earth, will be to the difference of the axis and 

 equatorial diameter, as 191 to unity; and thence, by article 4, as the mean 

 gravity on the surface, is to the centrifugal force at the equator, so is 191 to 4, 

 or so is 239 to unity. In order to show that this cannot be, we may observe, 

 that when the moon's distance was supposed 60 semidiameters of the earth, 

 as in article 5, it was found that the mean force of gravity was to the centri- 

 fugal force at the equator, as 28^ to J. But if the proportion now found be 

 true, the moon's distance of 60 semidiameters must be augmented in the sub- 

 triplicate ratio of 289 to 239, ^^^ then it will become 64 semidiameters. In 

 like manner, if we compute the ratio of the mean force of gravity to the 

 centrifugal force, by presupposing the magnitude of the earth, as Sir Isaac 

 Newton and Mr. Huygens did, we must suppose a degree to be above 80 

 English miles, to bring it out 239 to unity. Now whereas it is certain that 

 the distance of the moon is about 60 semidiameters of the earth, and that a 

 degree is less than 70 English miles; therefore, that the conclusion, which 

 seems to follow from the Jamaica experiment, cannot be allowed to be true. 

 And the experiments made by Richer, in the island of Cayenna, would still 

 make a greater difference between the diameters of the earth, than those made 

 in Jamaica. And the lengths of the Paris and London pendulums compared 

 together, would make it greater than -j-f,- part of the whole, as it was found 

 in article 5. 



8. From all the experiments made with pendulums, it appears that the theory 

 makes them longer in islands than they are found in fact. The London pen- 

 dulum should be longer when compared to the Paris one, than it really is; the 

 Jamaica pendulum, when compared to the London one, which vibrates in a 

 greater island, should be longer than is found by experience; and the pendulum 

 in Cayenna, a smaller island than Jamaica, should be still longer. This defect 



