used ly the Ancient Egyptians. . 169 



arc of depression for a star of average brilliancy, it is quite too great for a star of 

 such preeminent brilliancy as Sirius ; especially when the distance in azimuth of 

 its place of rising from the sun was upwards of 60°. M. Biot allows that the obser- 

 vation of heliacal risings admits an uncertainty of three or four days at least ; but one 

 principal cause of this uncertainty is, that the heliacal risings of bright stars must 

 precede, while those of faint ones must follow, the times calculated on the hypothesis 

 of their rays having a uniform power. On the ground of the possible errors of 

 observation, he allows 500 years before or after the epoch of 3285 B. C, as 

 limits, within which the heliacal rising would sensibly coincide with the solstice. 

 It appears to me, that there would be little likelihood of the heliacal rising of 

 Sirius being later than the time calculated on the supposition of the sun's being 

 11° below the horizon, but that there would be every probability of its being 

 earlier. It would, therefore, I contend, be right to lower the epoch on this 

 account by at least half oi this admissible error of 500 years. I have further to 

 add, that there is a different source of errors of observation, which M. Biot has 

 overlooked, but which should evidently be taken into account. He has only 

 considered the possibility of erroneously observing the heliacal rising of Sirius ; 

 but, surely, an error in observing the solstice is to be expected also. He seems 

 to have forgotten, that, in the whole of this argument, what has been called the 

 solstice is not the observed arrival of the sun at the tropic of Cancer, but the 

 observed commencement of the inundation of the Nile. In this observation an 

 error of four or five days might easily take place, which would correspond to 520 

 or 650 years in the epoch. For this admissible error of observation, and for 

 that which may remain in observing the heliacal rising, I conceive that 600 

 years will be a very moderate allowance. To sum up the whole of this argument, 

 I take from M. Biot's epoch 135 years, in which I conceive that he has erred as 

 to the epoch of coincidence between the solstice and the heliacal rising of Sirius, 

 even on his own hypothesis as to latitude and depression. I take 600 years more, 

 in which he has erred by taking the heliacal rising at Memphis in place of that at 

 Thebes ; and 250 years more, which he should have allowed for the superior bril- 

 liancy of Sirius to the average brilliancy of the stars mentioned by Ptolemy in his 

 Apparitions. This reduces the epoch oi accurate coincidence between the heliacal 

 rising of Sirius and the solstice from 3285 B. C. to 2300 B. C. ; and I maintain 

 that there would be a sensible coincidence, within the limits of errors of observation, 

 VOL. xviii. r 



