used hy the Ancient Egyptians. 185 



nological epoch in the eighteenth century before Christ, was, by Laplace's for- 

 mula, 49 'j32 ; that is, 0",78 less than the precession, with which Delambre's 

 tables are calculated. I seek then in those tables the time in which the sun 

 would describe 360°. 0', 0",78, and find it to be 365,242485 days, which I take 

 for the length of the mean tropical year. I find the annual variation of the 

 equation of the centre to be 2'',1125, taking into account both the decrease of 

 the mean anomaly and that of the eccentricity. The time of describing this arc 

 would be 0,000595 of a day. Lastly, the annual decrease of the obliquity of 

 the ecliptic is 0",4238. This must be compensated for by an increase in the 

 longitude of 0",58845 ; and the sun would take 0,000166 of a day to describe 

 this arc. Adding together these three quantities, we hav^ for the value of the 

 tropical year, as the Egyptians would observe it, but independent of lunar and 

 planetary perturbations, 365,243246 days. I now divide 73 days by the excess 

 of the last number over 365, and the quotient is 300,1077 years.* When we 

 consider that this is the value of the cycle, calculated on the supposition that the 

 length of the year at the beginning of the eighteenth century had always been 

 its length ; but that, in point of fact, its length had been for many previous cen- 

 turies constantly decreasing, it will be obvious that the Egyptians, looking to 

 their past observations, could not possibly have estimated the lesser cycle at more 

 than 300 years. I have built nothing on the consideration of this being a round 

 number, though that is a circumstance that would not be likely to be overlooked, 

 even had 301 been a somewhat more accurate cycle ; but I contend that, accord- 



* There can be little doubt that Laplace's formulas give the obliquity and its annual variation in 

 past ages too great, and the precession too small. In the question respecting the heliacal rising of 

 Sirius, the correction of this error would have been in my favour. Here it is the reverse; and, 

 therefore, candour obliges me to notice it, and to estimate its bearing on the strength of my argu- 

 ment. The difference between the precession now and in 1780 B. C, as estimated by Laplace, 

 cannot have exceeded its true value by so much as 0''.06. The excess was probably much less; 

 but I am now taking extreme values. The annual decrease of the obliquity must have been at the 

 least 0". 39. The difference between this and the value in the text would be compensated for by a 

 difference of 0". 047 in longitude. The total difference is less than 0".I07 ; over which the sun 

 would move in 0.00003 of a day. We should thus have 0.243216 for a divisor, in place of that in 

 the text; which would give 300.144 for the quotient, determining the length of the cycle. The 

 difference between this and the value given in the text is evidently immaterial, so far as our present 

 argument is concerned. 



VOL. XVIII. 2 A 



