,,4 



of the Earth ly means of Occidtalions of the fixed Stars. 355 



§ 10. Let us suppose AVB a portion of the circumference of 

 the moon's disc opposite to the observer ; C the moon's centre ; 

 and that the radius CV, 

 which divides the arc 

 AVB into two equal 

 parts, coincides with 

 the vertical circle of the 

 place of the observer. 

 Let us further suppose 

 that the line MV (or 

 the ver-sine of the arc) 

 is equal to 60''; and 

 that, during the occul- 

 tation, thechord AB of 

 the moon is that which 

 the star would appa- 

 rently describe if the 

 earth were spherical ; 

 or the chord DE that 

 which it would appa- 

 rently describe if the axis of the earth were compressed j-J—, 

 Then ML will be equal to S'',5 as before mentioned: and, com- 

 puting from the mean rate of the horary motion of the moon, it 

 will be found that the duration of the occultation behind AB will 

 be 20'. 7" of time ; and, behind DE, IS'. 41"*. We therefore 

 see how considerable is this difference of 1'. 26" of time ; and 

 how well such observations are adapted not only to convince those 

 who doubt the reality of the compression of the earth's axis, but 

 likewise to show with very great approximation to truth the re- 

 lative length of the earth's radii in different latitudes. For, in 

 the case just mentioned, the variation of a twenty-thousandth 

 part of that length f will cause a difference of one second of time 

 in the duration of the occultation. 



§11. Moreover, it is evident that the effect, of which I have 



• For, joining C,A, and C,B, we shall have CV=CA = CB = 15'.45", and 

 CM=C15'.45"-(;0") = 14'.45"; consequently AM=MB= V(AC-CM). 

 (AC + CM)=5'. 31",4 ; which, being multiplied by ^„^,\,, , in order to re- 

 duce this distance into time, will give 10'. o",() for the timeof the star's pass- 

 ing from A to M : therefore the time of the star's passing from A to B will 

 be equal to 2 X (10'. .T',(j")=20'. "",2. But, if the depression of the earth's 

 axis cause a variation in the ajjparent heiglit of the moon equal to K",5, then 

 will CL=14'.5.T',5, consequently (as CD=AC) DL=LE= ^'(AC— CL). 

 (AC + CL) =5'. 7",7; which, being also multiplied by ..^ ^.^^ ^ , will give 

 9'. 20",5for the time of the star's passing from D to L: therefore the time 

 of the star's passing from D to E will be equal to 2 X (!V. 20",5) = 18'. 41". B. 



t Or, about 1000 feet. The mean radius of the earth being 20,898,240 

 English feet. B. 



Z2 



been 



