222 fHILOSOFHICAL TRANSACTIONS. [ANNO 1738. 



observations we have made under the arctic circle, and with those of Mr. 

 Picart in France, we may have the true difference of the earth's diameters at 

 the equator and at the poles. Then our theory may be applied, to determine 

 whether the earth is more or less dense at the central parts than at the surface,* 

 or whether it be every where of a uniform density, as it ought to be, if, with- 

 out admitting very gross errors in the observations, it may be concluded, that 

 the earth is really the spheroid of Sir Isaac Newton; and this case would be 

 the simplest and the most natural of all. 



I am here obliged to acknowledge, that if the observations we have made in 

 the north may be relied on,-|- and if we must admit as incontestable as well the 

 measure of a degree as the length of the pendulum, the foregoing theory could 

 not be reconciled to the phenomena. For it follows from our observa- 

 tions, that the diameter of the equator must exceed the earth's axis by more 

 than the 230th part; and that the gravity at the pole must be greater than that 

 at the equator by more than the 230th part also; which will by no means agree 

 with what we have deduced in art. 23. 



As to what concerns the measure of gravity in Lapland, as being not so 

 liable to error as the measuring a degree; the earth may be not quite so flat as 

 Sir Isaac's spheroid requires. By the table of the length of the pendulum, 

 exhibited in the treatise concerning the figure of the earth, published this year 

 by Mr. de Maupertuis, and by art. 22 of the present discourse, the earth may 

 be more elevated at the equator than at the pole by the 266th part, or there- 

 abouts. After the true quantity of the earth's flatness shall be fully settled, if 

 it should be found to have this figure, I should be apt to think it is a little more 

 dense at the centre than towards the superficies. But if on the contrary we 

 should be well ascertained, that the earth is raised higher at the equator than at 

 the pole, by above the 230th part: and if, for any sufficient reason, we may 

 something shorten the length of the pendulum that beats seconds in the north; 

 there would be some grounds to allow, that the earth is not so dense at the 

 central regions as at those near the surface. But if it shall happen, that we 

 can neither diminish the length of the pendulum, nor the excess of the equa- 

 torial diameter above the axe, I must then give up my hypothesis. Yet I shall 

 think it may be of some use to have thus discussed it, because possibly no one 

 would have imagined what might have been the result of it. It appears that 



• It has since been determined, by Dr. Hutton's calculations on the observations made at mount 

 Schehallien, in Scotland, that the mean density of the earth, is about 2 times more than at the sur- 

 face ; and that it is therefore probable the central parts of the earth are still much more dense. See 

 Philos. Trans, vol. 68, part 33. 



+ It has since been found very erroneous. See p. 287, of this volume of Abridgments. 



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