356 On a new and certain Method of ascertaining the Figure 



been speaking, may be much greater. It increases greatly as the 

 line MV (or the ver-sine of the arc) becomes smaller: if, for ex- 

 ample, it were 30", the duration of the occultation under AB 

 would be 14'. 20"; and, under DE, 12'. 10", being a difference, 

 in the duration, of 2'. 10" of time*. In such a case, a difference 

 of 500 feet in the length of the earth's radius might be rendered 

 evident: since such a variation would produce a difference of one 

 second of time in the duration of the occultation f- 



§ 12. I am well aware that it scarcely ever happens that the 

 apparent path of the star is rectilinear, and at the same time per- 

 pendicular to the vertical circle which passes through it, at the 

 moment of the middle of the occultation, as in the case 1 have 

 supposed. But such a supposition may be readilv conceded, as 

 being a mean between the possible cases. For, if the actual phae- 

 iiomena do in some cases deviate therefrom, so as to render the 

 effect of the compression less upon the duration of the occultation 

 than when calculated on the above hypothesis, it will on the other 

 hand often occur that they are greater J. Hence I have no he- 

 sitation in asserting that the means, which I have pointed out, 

 are not dependent on any hypothesis, and are the most certain 

 of any that have yet been suggested for determining the variation 

 in the curvature of the earth's surface. 



§ 13. With respect to the penduhim, the differences in its 

 length are not only too minute and too difficult to be measured 

 with precision, but are also too much influenced bv the unknown 

 internal density of the earth to be brought at all into comparison 



* In this case, CM = (15'.45"-30") = 15'. 15"; consequently AM = 



60' 



3'. 56",2 : which being multiplied by ' ^o, 55,, 5 ^ -> ^^ '" ^^^ preceding cases, 

 vrill give 14'. 20",4 for the time of the star's passing from A to B. But, sup- 

 posing the depression the same as in the former instance, we should have 

 CL=]5'.23",5; consequently DL=LE=3'.20",4: which, multiplied also by 



GO 



^a ■■■- r X 2, will give 12'. 10",2 for the time of the star's passing from D to 

 E, as mentioned in the text. B. 



f According to my calculation, a difference of only 400 feet in the length 

 of the earth's radius would produce a difference of one second of time in the 

 duration of the occultation. But, if the line MV were only 15", a difference 

 of less than 200 feet would produce a difference of one second of time in the 

 duration. And, agreeably to these principles, it will be evident that the du- 

 ration of such occultations will vary according to the elevation of the spot 

 (from which they are observed) above the level of the sea ; and will sensibly 

 differ when observed in valleys, or on the tops of high hills and mountains. 

 A fact which perhaps has not been sufficiently attended to, either in obser- 

 vations of occultation.s, or in calculations wherein the parallax of the moon 

 is involved. B. 



X I confess I do not see the accuracy of this conclusion : for it appears 

 to me that the effect of the compression, on the duration of the occultation, 

 must be greatest when the apparent path of the star is perpendicular to the 

 vertical circle. B. 



with 



