June 2, 1892] 



NA TURE 



105 



true year, occurred on the ist Thoth of the established 

 year. We should have, in the subsequent years, the 

 state of things described in the diagram. The solstice 



■'ss ... I I I I I I I I I 

 ■'STAo.h I I I I I I I I I I 



Fig. 2. — Showing the relation between the recurrences of the solstices 

 and the ist of Thoth. 



would year by year occur later in relation to the ist of 

 Thoth. The ist of Thoth would occur earlier, in relation 

 to the solstice ; so that in relation to the established year 

 the solstice would sweep forwards among the days ; in 

 relation to the true year the ist of Thoth would sweep 

 backwards. 



Let us call the true natural year a fixed year : it is 

 obvious that, the months of the 365-day year would be 

 perpetually varying their place in relation to those of the 

 fixed year. Let us, therefore, call the 365-day year a 

 vague year. 



Now if the fixed year were exactly 365J days long, it is 

 quite clear that, still to consider the above diagram, the 

 1st of Thoth would again coincide with the solstice in 

 1460 years, since in 4 years the solstice would fall on the 

 2nd of Thoth, in 8 years on the 3rd of Thoth, and so on 

 (365 X 4 = 1460). 



But the fixed year is not 365 J days long exactly. In 

 the time of Hipparchus 365^25 did not really represent 

 the true length of the solar year ; instead of 365*25 we 

 must write 365-242392— that is to say, the real length of 

 the year is a little less thin 365I days. 



Now the length of the year being a little less, of course 

 we should only get a second coincidence of the ist of 

 Thoth vague with the solstice in a longer period than the 

 1460-years cycle ; and, as a matter of fact, 1506 years are 

 required to fit the months into the years with this slightly 

 shortened length of the year. In the case of the solstice 

 and the vague year, then, we have a cycle of 1506 years. 



The variations between the fixed and vague years were 

 known perhaps for many centuries to the priests alone. 

 They would not allow the established year of 365 days, 

 since called the vague year, to be altered ; and so strongly 

 did they feel on this point that, as already stated, every 

 king had to swear when he was crowned that he would 

 not alter the year. We can surmise why this was. It 

 gave great power to the priests ; they alone could tell on 

 what particular day of what particular month the Nile 

 would rise in each year, because they alone knew in what 

 part of the cycle they were ; and in order to get that 

 knowledge they had simply to continue going every year 

 into their Holy of Holies one day in the year as the 

 priests did afterwards in Jerusalem, and watch the little 

 patch of bright sunlight coming into the sanctuary. That 

 would tell them exactly the relation of the true solar sol- 

 stice to their year ; and the exact date of the inunda- 

 tion of the Nile could be predicted by those who could 

 determine observationally the solstice, but by no others. 



But now suppose that instead of the solstice we take 

 the heliacal rising of Sirius, and compare the successive 

 risings at the solstice with the ist of Thoth. 



But why, it will be asked, should there be any differ- 

 ence in the length of the cycles depending upon successive 

 coincidences of the ist of Thoth with the solstice and the 

 heliacal rising of Sirius ? The reason is that stars change 

 their places, and the star to which they trusted to warn 

 them of the beginning of a new year was, like all stars, 

 subject to the effects brought about by the precession of 

 the equinoxes. Not for long could it continue to rise 

 heliacally either at the solstice or the Nile flood. 



Among the most important contributors to the astrono- 

 mical side of this subject are M. Biot and Prof. Oppolzer. 

 It is of the highest importance to bring together the 



NO. I I 79, VOL. 46] 



fundamental points which have been made out by their 

 calculations. We have determinate references to the 

 heliacal rising of Sirius, to the ist of Thoth, to the 

 solstice, and to the rising of the Nile in connection with 

 the Egyptian year; but, so far as I have been able to make 

 out, we find nowhere at present any sharp reference to 

 the importance of their correlation with the times of the 

 tropical year at which these various phenomena took 

 place. The question has been complicated by the use by 

 chronologists of the Julian year in such calculations ; sa 

 the Julian year and the use made of it by chronologists 

 have to be borne in mind. Unfortunately, many side 

 issues have in this way been raised. 



The heliacal rising of Sirius, of course— if in those days 

 a true tropical year was being dealt with — would have 

 given us a more or less constant variation in the time of 

 the rising over a long period, on account of its preces- 

 sional movement; but M. Biot and others before him 

 have pointed out that the variation in the time of the 

 year at^ which the heliacal rising took place, produced by 

 that movement, was almost exactly equal to the error of 

 the Julian year as compared with the true tropical or 

 Gregorian one. Biot showed by his calculations, using the 

 solar tables extant before those of Leverrier, that from 

 3200 B.C. to 200 B.C. in the Julian year of the chronologists, 

 Sirius had constantly, in each year, risen heliacally on 

 July 20 Julian = June 20 Gregorian. Oppolzer, more 

 recently, usrng Leverrier's tables, has made a very slight 

 correction to this, which, however, is practically imma- 

 terial for the purposes of a general statement. He shows 

 that in the latitude of Memphis, in 1600 B.C., the heliacal 

 rising took place on July i8-6, while in the year o it took 

 place on July 197, both Julian dates. 



The variation from the true tropical year brought about 

 by the precessional movement of Sirius or any other star, 

 however, can be watched by noting its heliacal rising in 

 relation to any physical phenomenon which marks the irue 

 length of the tropical year. Such a phenomenon we have 

 in the rising of the Nile, which, during the whole course of 

 historical time, has been found to rise and fall with ab- 

 solute constancy in each year, the initial rise of the 

 waters, some little way above Memphis, taking place very 

 nearly at the summer solstice. 



Again, M. Biot has made a series of calculations from 

 which we learn that the heliacal rising of Sirius AT THE 

 SOLSTICE occurred on July 20 (Julian) in the year 3285 B.C.,. 

 and that in the year 275 B.C. the j^/j/zV^ occurred on June 

 27 (Julian), while the heliacal rising of Sirius took place, 

 as before, on July 20 (Julian), so that in Ptolemaic times^ 

 at Memphis, there was a difference of time of about 24 

 days between the heliacal rising of Sirius and the solstice, 

 and therefore the beginning of the Nile flood in that part 

 of the river. This, among other things, is shown in 



Fig. 3. 



We learn from the work of Biot and Oppolzer then that 

 the precessional movement of the star caused successive 

 heliacal risings of Sirius at the solstice to be separated by 

 almost exactly 365^ days— that is, by a greater period thaji 

 the length of the true year. So that, in relation to this 

 star, two successive heliacal risings at the ist of Thoth 

 vague are represented by a period of (36 ;i X 4 = ) H^i 

 years, while in the case of the solstices we want 1506. 



Now in books on Egyptology the period of 1461 years 

 is termed the Sothic period, and truly so, as it very nearly 

 correctly measures the period elapsing between twa 

 heliacal risings at the solstice (or the beginning of the 

 Nile flood) on the ist of Thoth in the vague year. 



But it is merely the result of chance that 365 j x 4 re- 

 presents it. It has been stated that this period had not 

 any ancient existence, but was calculated back in later 

 times. This seems to me very improbable. I look upon 

 it rather as a true result of observation, the more so as 

 the period was shortened in later times, as Oppolzer has 

 shown. 



