6 PHILOSOPHICAL TRANSACTIONS. [aNNO 1763. 



falls in the node at the end of the 38th period. In each succeeding period, the 

 conjunctions of the sun and moon will be gradually farther and farther from the 

 node, by the quantity of 28' 1 1" ; which will cause the moon's shadow to pass 

 dver the disk of the earth farther and farther on the opposite side from its 

 centre, till it quite leaves the earth, and travels in expansion for about 1 2,492 

 years, before it can come upon the earth again at the same pole as before. 



The reason of this will be plain, when we consider, that 1 8° from either of the 

 nodes of the moon's orbit is the greatest distance at which her shadow can touch 

 the earth at either of its poles. And as there are 1 8° on each side of the node, 

 within the limits of a solar eclipse ; and twice 1 8 make 36, these are all of the 

 360 degrees of the moon's orbit about either of the nodes, within which there 

 can be an eclipse of the sun : and as these eclipses shift through 28' 1 1" of these 

 36 degrees, in every Chaldean or Plinian period, they will shift through the whole 

 limit in ^^ periods, which include 1388 years and 3 months. And then the 

 periods have the remaining 324 degrees of the moon's orbit to shift through, at 

 the rate of only 28' 12'' in each period, before they can be near enough to the 

 same node again, for the moon's shadow to touch the earth ; and this cannot 

 be gone through in less than 12,492 years ; for as 36 is to 1388, so is 324 to 

 12,492. - " , 



The eclipse, April 1st, 17 64, fell in the open space, quite clear of the earth at 

 each return, ever since the creation, till a. d. 1295, June 13th, old stile, at Ti** 

 52" 39' p. M. when it touched the earth at the north pole, according to the mean 

 (or supposed equable) motions of the sun and moon ; their conjunction being 

 then 17° 48' 27" from the moon's ascending node, in the northern part of her 

 orbit. In each period since that time, the conjunction of the sun and moon has 

 been 28' 12" nearer and nearer the same node, and the moon's shadow has there- 

 fore gone m-ore and more southerly over the earth. In the year I962, July 18th 

 old stile, at lO'' 36"" 21' p. m. the same eclipse will have returned 38 times; and 

 as the conjunction will then be only 24' 45" from the node, the centre of the 

 moon's shadow will fall but a little northward of the centre of the earth's en- 

 lightened disk. At the end of the next following period, the conjunction of the 

 sun and moon will have receded back 3' 27'' from the moon's ascending node, 

 into the southern part of her orbit ; which will cause the centre of her shadow 

 to pass a very small matter south of the centre of the earth's disk. After which 

 in every following period, the conjunction of the sun and moon will fall 28' 12" 

 farther and farther back from the node, and the moon's shadow will go still far- 

 ther and farther southward on the earth, till a. d. 2665, September 12, old stile, 

 at 23*^ 46"" 22* p. M. when the eclipse will have finished its 77th period, and will 

 finally leave the earth at the south pole ; and cannot begin the same course over 

 the earth again in less than 12,492 years, as above mentioned. And thus, if the 

 motions of the sun and moon were equable, the same eclipse would always return 



