28 PHILOSOPHICAL TRANSACTIONS. [aNNO 1735, 



232, the same as Sir Isaac Newton found in a different manner; for he makes 

 it as 230 to 231, and as 230 to 231, so is 231 to 232.004. 



6. In the same manner the proportion of the diameters of any planet may 

 be found, if it lias a satellite; for instance, in Jupiter, he turns about his axis 

 in 9*^ Sd™, or in 5q6 minutes: and his third satellite revolves about him in 7'' 3^ 

 42™ 36% or in 10302.6 minutes, at the distance of 1 5.141 of his semidiameters. 

 Therefore, as the cube of 15.141 to unity, so is the square of 10302.6 to 

 30579, the square of the number of minutes in which a satellite would revolve 

 about him at the distance of his semidiameter; and as this last number is to 

 355216, the square of 596, so is unity to I 1-f, or the centrifugal force at his 

 equator, to the mean force of gravity on his surface. There is no need of 

 correcting this number, as in the former article, because the periodic time of 

 Jupiter round the sun is vastly greater than that of his third satellite round him. 

 The third satellite is here chosen before any of the rest, because its greatest 

 elongation was observed by Dr. Pound, with a micrometer adapted to a telescope 

 123 feet long; and he also took the diameter of Jupiter by the transit of the 

 satellite, which is a much more exact way than with a micrometer. But as the 

 planes of Jupiter's satellites almost coincide with the plane of his equator, the 

 diameter, determined by the transit of the satellite, is his greatest; and the 

 distance of the satellite, which ought to have been given in his mean diameters, 

 is assigned in his greatest; for which reason the force of gravity already found, 

 must be augmented in the triplicate ratio of his greatest diameter to his mean 

 one; that is, if a represent the mean diameter, and d the difference of the 

 longest and shortest, in the proportion of 2a + 3d to 2a very nearly. Hence, 

 as the centrifugal force at his equator, is to the mean force ot gravity on his sur- 

 face, so is unity to 1 l-f X -^ — • ■^"^' ^^ ^^^^^^^ ^t 1 '-f X •^-—- — : 1 :: a : 

 ^d, or 20 aa = \%%ad + 27Qdd; which makes a to d, as 108 to 10; and 

 hence the axis is to the equatorial diameter, as 108 — 5 to 108 + 5, or as 103 

 to 113; that is, as 12 to 13-J-; which agrees nicely with the observations of 

 both Dr. Pound and Mr. Bradley, made with Huygens's long telescope; the 

 former making it as 12 to 13, and the latter as 25 to 27, which is very nearly 

 the same. And if this theory agrees so well with observations in Jupiter, there 

 is no doubt but it will be more exact in the earth, whose diameters are much 

 nearer to equality. 



7. By experiments made at Jamaica, Philos. Trans. N° 432, in the latitude 

 of 1 8°, with a very curious clock, contrived by Mr Graham, it was found that 

 the London pendulum went slower there by 2"" 6% in a sydereal day, than at 

 London. But it was found by experiments made with thermometers, that 9^ 



