330 PHILOSOPHICAL TRANSACTIONS. [anNO 1753. 



And this conclusion of my theory quite agrees with experience; for, from all the 

 observations relating to the gravity made in several places of the globe, either by 

 actual measures of the second pendulum, or by the difference of duration of the 

 same pendulum's vibrations, it appears, that the gravity decreases from the north 

 to the south in a greater ratio, than it would be, if the total diminution from 

 the pole to the equator were only -jJ-,-. 



^ 69. Por the proportion of the two diameters. 



Supposing, as in the precedent chapter, the earth originally fluid, it follows, 

 from the ^ 63, that the ratio of the two diameters cannot exceed that of 230 

 to 231 ; since (^ 20) 230 to 231 is the ratio in the case of the homogeneous 

 spheroid ; and as the mensurations of the gravity cannot agree with the supposi- 

 tion of the homogeneity, the diameters of the earth ought to be in a ratio less 

 than 230 to 231. 



Without adhering to the supposition of the earth's being formerly fluid, but 

 admitting, as in the chap. 3 and 4, all generality possible in the variation of 

 density and ratio of diameters of the beds or strata laid down from the centre to 

 the surface, there will still happen a difference of the diameters less than -^^ 

 For, by § 50, the total diminution of the gravity from the pole to the equator 

 being subtracted from -t-ttj the remainder is the difference between the diameters. 

 Now the diminution of the gravity having been found greater than -^-k-^, the 

 ellipticity, or difference of diameters, ought to be less than that fraction, and 

 consequently the ratio of diameters less than 230 to 231. 



That consequence of my theory is not so happy as the preceding; for the de- 

 gree measured in the north, compared to that of France, give the two diameters 

 as 177 to 178, which ratio is greater than 230 to 231 instead of being less, as 

 the theory would require. 



As the measures made in the north have been performed with great care and 

 exactness,* their result seems at first to be preferred to that of my theory. But 

 a reflection on the errors unavoidable in actual measures, and an examination of 

 the limits of these errors, will show that, without violating the measures, they 

 would be brought nearer the theory, and even agree with it. For, by a conve- 

 nient calculation, it will be found, that a diminution less than 6o toises, made 

 to the difference between the degrees of Paris and Tornea, would give the dia- 

 meters in the ratio of 230 to 23 J . And if it be considered what is the smallness 

 of an error of 6o toises, when divided in two operations, which require so great 

 a number of astronomical and geographical observations, it will be thought that 

 an error a little larger may be supposed, without disparaging either our operation, 

 or Mr. Picard's ; and thus theory and experience would agree. 



• Those measures have been since found very erroneous. 



