176 The Rev. E, Hincks on the Years and Cycles 



ference of the indications. The cause of this diversity may be easily seen. At 

 the end of 365 days, the altitude of the sun would not be precisely the same as 

 at the beginning, but about 5' greater, his altitude decreasing something more 

 than 20' a day. If the standard were copied on the first day of this next year, 

 the length of the shadow would evidently be, as compared with the original 

 standard, too small, in the proportion of the cotangent of the altitude, increased 

 by these five minutes, to the cotangent of the altitude itself. The consequence 

 would obviously be, that the new standard would indicate a different series of 

 years of 366 days from the original standard ; it would point out the same first 

 of Thoth in three out of four years, but one a day earlier in the fourth. To 

 obviate this error, it would probably be soon agreed, that the standards should 

 only be copied at the end of the years of 366 days, when the altitude would be 

 nearly the same as at first. But this would only diminish the evil. In the first 

 place, it could not in every instance be certainly known before-hand, whether 

 the current year would consist of 366 days ; it might be a matter of doubt, until 

 the shadow decided the question, whether such a protracted year would, on this 

 particular occasion, occur at the end of three or of four common years. But, 

 setting aside this consideration, the copy taken at the end of a year of 366 days 

 could -aeyex perfectly represent the original standard. The altitude at the end 

 of four years would be somewhat different from what it was at the beginning ; 

 and though the copy then taken would agree with its original in indicating the 

 first few years of 366 days, it would before long indicate different ones, its quin- 

 quennial periods being interspersed among the quadrennial ones in a different 

 manner. 



Under these circumstances, we cannot wonder that the Egyptians should 

 consider the existence of these years of 366 days as a nuisance, and should 

 in course of time determine to get rid of it. Had they occurred at settled 

 intervals, they might have been tolerated ; but, occurring as they did irre- 

 gularly, and the standards in different parts of the country indicating different 

 times for their occurrence, they would be a constant source of annoyance and 

 contention. It was at length resolved that there should be no more intercalation, 

 but that the twelve months and the five celestial days should constitute the entire 

 of the year. The period when this change took place is indicated by the names 

 of the months, hieroglyphically given to those of the year when a fixed one, and 



