164 The Rev. E. Hincks on the Years and Cycles 



was in fairness entitled to do ; and that, if he had not done so, the epoch of coin- 

 cidence between the heliacal rising of Sirius and the solstice would have resulted 

 much later than he makes it. It is, however, not unworthy of being noticed, 

 that the rigorous coincidence, which he alleges to have taken place in the year 

 3285 B. C, and on which he appears to lay so much stress, did not really, even 

 on his own hypothesis, take place in that year. The following are the solstitial 

 dates in that year and in the two preceding and two following years, given pro- 

 leptically, both according to the Julian computation and to that of the Egyptian 

 wandering year. That for 3285 is taken from M. Biot's memoir, adding 1.93 

 hour for the difference between Parisian and Memphitic time ; the others are 

 deduced from this by addition and subtraction of 365 days 5.82 hours, which was 

 in that age about the average interval between successive summer solstices. 



Years B. C. Hours after Memphitic Midnight. 



3287 July 21st Pachon 1st 10.92 



3286 21st 1st 16.74 



3285 20th 1st 22.56 



3284 21st 2nd 4.38 



3283 21st 2nd 10.20 



u. -t- •/ being the arc of the equator between the first point of Aries and the horizon, at the time 

 when Sirius is rising ; 



COS. tu. cos. (fi + v) — sin. ui. tan. a . 

 : — ^—^. — r =: cot. 9o ; 



6o being the arc of the ecliptic between the first point of Aries and the horizon ; 



sin.y.sin.fl. . ,. . . 



f ^ ° — sin Sy — a„;) 



COS. a. sin. (jj,-\-y) 



fly being the arc of the ecUptic between the first point of Aries and a parallel of altitude, the vertical 

 depression of which below the horizon is y. 



The morning, on which the sun's longitude^»'«< exceeds 9y, is the morning on which Sirius is 

 said to rise heliacally. 



Now 9y is, as we have seen, a function of five quantities, a, y, X, /x, and w. The three last are 

 determined, the time being given ; but they vary with the time of observation. The two former are 

 independent of the time ; but a, is different for different places of observation, and y for different 

 stars. The more brilliant the star, and the more remote its place of rising from the part of the hori- 

 zon whick is over the sun, the less will y be. 



