Remarks on the Lunar Theory. 13 



In 39512 solar years are contained 488695 lunations, wonting 

 about 5" only of the line of conjunction of the O and ]) . The 

 D 's acceleration during this period amounts to upwards of two 

 complete revolutions of the j to the ©, or nearly 760°. The 

 acceleration of the ]) 's longitude in a period of 600,000 years, 

 acfv,;ding witli the present established theory, would exceed her 

 -mean motion by 3373 revolutions of the ecliptic!!! Hence the 

 absurdity of instituting such long periods is evident. If in any 

 period we could recognise a coincidence in the solar and lunar 

 motions (including their anomalies and accelerations), the same 

 circumstance would not again obtain, from the known perturba- 

 tions in the lunar theory, or at least not till after a lapse of per- 

 haps millions of years ; for, on account of the irregularities in 

 the lunar motions, their circuits must undergo new computations, 

 in order to assign their relative situations during a preceding or 

 subsequent ])eriod. The Chaldean Period is the most i.ncient 

 and correct of any established; it consists of 223 mean lunations, 

 which, according to mean motions at the commencement of 

 the present century, is performed in 6585'' 1^ A'2' 24". 4 ; the 

 motion of the ]) 's anomaly 11^ 27" 10' 9".4; the O's anomaly 

 0' 10° 29' 34".7j O to the D 's node— 11^ 29° 31' 33".5'; 

 whence the comp. © to the D 's node 28' 26''. 5. Mr. Fergu- 

 son states it at 28' 12".5. There is about 18° on each side 

 of the ]) 's node within which there is a possibilitv cf eclipses; 

 consequently the period of eclipses, so far as it affects the earth, 

 contains a space of about 36° about that node, which taken from 

 360^ leaves 324'^ remaining for the eclipse to travel in the ex- 

 pansium; and as this 36' is not gone through in less than 1370 

 years, the remaining 324° cannot be so gone through in less than 

 12330 years. The falling back of the line of conjunctions'or 

 oppositions of the © and J) being 2S'^ 26". 5 with respect to 

 the line of the nodes in every Chaldean period will wear it out in 

 process of time, or in about 1370 years, as above stated; and after 

 that time, it will not return again in less than 12330 years. The 

 eclipses of the © which liappen about the ascending node, and 

 begin to come in at the north pole of tiie earth, will advance a 

 little southerly at each return, till they go off the earth at the 

 south pole ; and tliosc which happen about the descending node, 

 and begin to come in at the south pole of the earth, will proceed 

 a little nortlierly at each return, till at last they quite leave the 

 earth at the north pole. 



The entire period of any respective eclipse is comprised in 

 about 760 Chaldean periods, or about 13700 years; the whole 

 terrestrial phacnomena being completed in about 76 Chaldean 

 periods, or 1370 years. But the irregularities in the lunar mo- 

 tions may lengthen or protract this period 100 years. The I) 's 



acceleration 



