used by the Ancient Egyptians. 167 



artificial day. It seems absurd to lay any stress on a coincidence occurring rigo- 

 rously in any specified year, when the phenomena which coincide approach one 

 another at the very slow rate of about eleven minutes a year, and when they 

 would, of course, continue to coincide for about 130 years. But, as M. Biot has 

 insisted a good deal on this coincidence having rigorously taken place in 3285 

 B. C, it seems proper to show that his statement to that effect is unfounded. 

 The 130 years of coincidence did not begin till about seventy years after this 

 epoch. 



The error which M. Biot has committed in this matter is, however, com- 

 paratively of little importance. I now proceed to show that the suppositions 

 which he has made in his calculation respecting the latitude and the arc of de- 

 pression are altogether unwarranted. The former he assumes to be 30°, and 

 the latter 11°. Now I contend that both of these values have been taken 

 unwarrantably great ; and the extent to which this vitiates the calculation may 

 be judged from the following statement; a diminution either of the arc of 

 depression or of the latitude by one degree will bring down the epoch of 

 coincidence above 150 years.* A person aware of these facts might easily 

 exhibit an apparent coincidence between the phenomena in question on any 

 assigned year of perhaps 1500. He has only in the first instance to choose 

 a suitable arc of depression ; then to calculate under what parallel of latitude, 

 assuming this arc, the star would rise heliacally at the solstice of the assigned 

 year ; and lastly, to invent plausible reasons for using that arc, and for 

 placing his observer under that parallel. It appears to me that this is just the 

 course which M. Biot has pursued. His curious reason for choosing the latitude 

 of 30° seems to prove it. He takes the latitude of Memphis ; " because for 

 epochs so ancient we cannot place the centre of religion in the very lowest parts 

 of Egypt r This one-sided reason shows plainly what was passing in his mind. 



* Using the values of A, /x, and to for 3283 B. C, as laid down in a former note, I find that a 

 substitution of 10° for y, in place of 11°, diminishes 9y by 1°, 19'. 11" ; a substitution of 29° for a, 

 in place of 30°, diminishes 8y by nearly the same quantity, namely, by 1°. 20'. 11". To compensate 

 for this diminution, Oy must be augmented by the terms depending on the time; and, allowing for 

 the increase which the coefficient of t would undergo, as well as for the necessary introduction of 

 the term containing P, it will appear that either of these substitutions must bring down the epoch of 

 coincidence considerably above 150 years. 



