358 On a new and certain Method of ascertaining the Figure 



bear in mind the enormous expense and labour required in mea- 

 suring a degree of the eartii's surface. Let us recollect the great 

 xnicertainty that may attend such a measurement from the devia- 

 tion of the pliunb-line made use of in the instruments employed 

 for the astronomical ol)servations, occasioned by mountains and 

 valleys, subterraneous cavities and other irregularities in the upper 

 strata of the earth : and, of what great importance such anomalies 

 may be, we may learn in the celebrated work of Boscovich*. 



§ 15. It may perhaps be objected that the two conditions ne- 

 cessary for my ])ur|)ose may not frequently occur together ; 

 namely, that the altitude of the moon f, and the chord of the 

 lunar disc which passes over the star, must be small. This is pro- 

 bably the reason why this method of ascertaining the compression 

 of the earth's axis has not hitherto been practised. It is true 

 that the greater the altitude of the moon above the horizon, and 

 the nearer to its centre the apparent path of the star, so much 

 the smaller will be the difference of parallax caused by a sphere 

 and an oblate spheroid l : and consequently the more easily might 



the 

 knowledged talents of the persons employed in those surveys ; and prevent 

 us from placing too gi-eat reliance on a method which produces results, dif- 

 fering so widely from each other. The learned Boscovich might well ex- 

 claim that " the greater the number of degrees that are measured, the more 

 uncertain does the figure of the earth seem to be." B. 



* De Expcditione Lltteraria, Lib. v. § 230, ct scq. 



"f" It does not appear that the altitude of the moon should be limited to 

 the quantity mentioned by the author in the text, since the variations, alluded 

 to, will be perceptible at the height of 20, and even 30 degrees. Thus, in 

 the case mentioned in § 9, it appears tliat tiie variation in the parallax of the 

 moon at the heigiit of 10° is S","5 : but, if the moon were at the height of 

 20" above the horizon, the variation would be 8", 1 ; and at 30^ it would be 

 7",4. B. 



X The smaller the chord of the lunar disc (or the smaller the ver-sine of 

 the arc) tlie more perceptible will be the difference in the duration of the 

 occultation in such cases; as will appear from the following table; which 

 shows t':ie duration of an occultation of the star on the supposition that the 

 place of the star, when it passed the vertical circle, would be 60", 30", 15", 

 10", and 8",5 within the moon's disc, provided the earth were a perfect 

 sphere: together with the corresponding durations provided the earth were 

 an oblate spheroid, having the axis compressed = 3577. Latitude of the 

 place eO": height of the moon 10'. 



In 



