354 On a neiu and certain Method of ascertaining the Figure 



of this kind accurately made in the place, for which the varia- 

 tion of curvature is sought, is sufficient to discover it by means 

 of the comparison of the calculated with the observed mo- 

 ment. 



§ 9. I shall now point out what are, in fact, the circumstances 

 in which the differences of the parallax between two latitudes 

 may be shown in an undoubted manner: and, in order virtually 

 to embrace all the cases, I shall take mean quantities in the ele- 

 ments vvhich enter into this investigation. Let us therefore sup- 

 pose, first, that the moon's apparent semidiameter is 15'. 45", 

 its equatorial parallax 57'. 40", and its horary motion 32'. 56",5 : 

 secondly, that the occultation is observed in north latitude G0°, 

 in which parallel there are three celebrated observatories, viz. 

 Petersburg, Stockholm andUpsal: lastly, that the apparent 

 height of the moon is 10°. If there he no variation in the 

 curvature of the earth's surface the parallax of height will be 

 56'. 47",4 * ; but, if the polar compression amount to -g-i-g- of the 

 earth's radius, the same parallax will be 56'. 38",9t. The pa- 

 rallax would therefore under these circumstances experience an 

 alteration of 8",5 ; a quantity certainly too small to be verified 

 with accuracy by means of observations of the height of the moon. 

 But, this slight alteration produces, in certain cases, effects that 

 are very visible: a fact vvhich escaped the observation of Mau- 

 pertuis; who, it is true, speaks of occultations as a mean of dis- 

 covering the' flattening of the earth J. But, he speaks of them 

 generally; and so slightly as to class them with appulses, as be- 

 ing equally fit to determine it. Now, as appulses are far from 

 being observable with such certainty, in regard to time, as the 

 instantaneous disappearance and reappearance of stars in occul- 

 tations, it is evident that Maupertuis can never have had in view 

 the particular cases which I am about to point out, and which 

 differ materially from ordinary ones. 



* Let p = the horizontal parallax of the moon ; and A= the height of the 

 moon : then t =;?. cos h = the parallax of height. B. 



f Let a = the polar coreipression of the earth, supposed = -j-^-iy; >■ = the 

 latitude of the place ; and the radius of the equator equal to unity : then we 

 shall have the length of any other terrestrial radius = (1 — a. sin''- >.) nearly ; 

 which, being multiplied by »•, will give ■nr='r (1 — a. sin- x)= the parallax of 

 height on the supposition that the earth is an oblate spheroid. Whence we 



also have — = the length of the terrestrial radius at any given latitude. 



'»■ S 



And if i denote any given increase of the parallax, wc shall have — for the 



corresponding increase in the lengtii of the earth's radius. B. 

 X Preface mc discours sur la j)arallaxe de la tune. 



§ 10. Let 



