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



ing to the principles laid down for computing the value of the tropical year, it 

 is such as will lead to 300 and not 301 years, as the time in which the sun 

 would descend to the standard altitude on the seventy-fourth day of a year made 

 to consist always of 365 days. 



Counting back six of these periods of 300 years from A. D. 34, I arrive at 

 1767 B. C, in which year the commencement of the wandering year was on the 

 8th November. On that day, therefore, the new system must have been 

 adopted ; and the first Egyptian year of 365 days must have been the one, of 

 which that was the first day. The longitude of the sun on that day was about 

 211°. 39'; and its declination about 12°. 18' south. We may therefore safely 

 conclude that 12^° w^ nearly the standard declination ; and that up to this 

 epoch (1767 B. C.) the first day in which the surCs south declination exceeded 

 12^°, was the first day of the year. I will only add, that the first day of the 

 year, computed in this manner, will occur at the end of 300 years on the 

 109574th day from the introduction of the system ; those 300 years containing 

 109573 days, or 300J Egyptian years of 365 days. And not only so, but this 

 will continue to be the case for no less than ten periods of 300 years, or two com- 

 plete revolutions of the seasons. I find that on the 19th October, A. D. 1234, 

 which was 3002 years of 365 days from 8th November, 1767 B. C. ; and which 

 would have been the 1st Thoth of 3003rd Egyptian year, had such continued in 

 use ; the sun's declination was less than 12°. 35' ; and consequently this was the 

 first day of its exceeding 12°. 15' ; for the diurnal increase of the declination 

 was, at that time, and in that part of the orbit, near 21'. If we trace the period 

 backward, in place of forward, its accuracy is considerably greater. In the 900 

 years preceding 1767 B. C. the change of declination would not amount to a 

 minute ; and in the preceding ages, if we choose to calculate what would have 

 occurred before the colonization of Egypt, the cycle would be so exact, that the 

 change of declination in 300 years would be scarcely observable. 



VI. I now proceed to mention some important verifications of these results, 

 which I have obtained from independent considerations, since I first arrived at 

 them. These verifications respect first the length of the cycle, and secondly the 

 date of its epochs. 



1 . It is a very remarkable circumstance, that the double period of 300 years, 

 or the time in which the attainment of 12J° south declination by the sun would 

 pass from the first to the 147th day of the wandering year, is a lunisolar cycle of 



