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



Julian year as a middle term. The heliacal rising, he alleges, always occurred 

 on that day ; the solstice occurred on that day in 3285 B. C. In that year, 

 therefore, they rigorously coincided. This appears plausible ; but I would ask, 

 in the first place, did the heliacal rising of Sirlus occur in every year on the 

 20th of July ? Would not the intercalation, which threw the solstice from the 

 21st to the 20th, have thrown the heliacal rising from the 20th to the 19th ? 

 We are, perhaps, not in a state to answer these questions, either affirmatively or 

 negatively, from our ignorance of the precise amount of the change that the posi- 

 tion of SIrius has undergone, in the long interval of 5000 years, from its own 

 proper motion and from the precession of the equinoxes.* But, secondly, 

 admitting that the rising of Sirius on the 20th July was the heliacal rising, was 

 this the rising that coincided with the solstice ? Is it not obvious, on the con- 

 trary, that the rising in the early morning of the 21st was the rising which 

 coincided with an event that occurred at half-past ten in the preceding night ? 

 There was then no real coincidence between the heliacal rising of Sirlus and the 

 solstice in 3285 B. C. M. Biot must admit that there was none in the preceding 

 or following years ; and that which, he endeavours to show, took place in this 

 year is only a colourable one, depending on the arbitrary commencement of the 



88°. 32'. 1"4- 25", 95 1 = fl^ = 89°. 30'. 30" 

 we have 



25",95<=68'.29"; 

 t = 135. 



If then the values of A, /x, and ui that I have used be correct, the coincidence occurred in 3150 

 B. C. ; or a few years earher, as the coefficient of f was positive, and the average rate of increase of 

 fiy in 133 years was on this account somewhat greater than the rate at the commencement of the 

 period. The coincidence would continue for as many years before and after this date as fly would 

 take to increase 29'. 30", or whatever was the exact value of the sun's motion in longitude for half a 

 day. That is to say, it would continue from about 3215 B. C. to about 3083 B. C. 



* If the value of fly for 3285 B. C. be correct, the sun would have attained that longitude about 

 thirty-six hours before the solstice ; that is, about half-past ten in the morning of the 19th July. He 

 would consequently have been some ten or eleven minutes less than 11° below the horizon at the 

 time when Sirius rose. I should think this was within the limits of probable error in the computa- 

 tion. The occurrence of the heliacal rising of Sirius on the same day of the Julian calendar, which 

 was the case for a great number of centuries, is owing to the excess of the mean Julian year, 363.25 

 days, over the tropical year, being very nearly equal to the time that the sun would take to pass over 

 the annual increa,se of fly. ' 



