Several readers of my W3 site quoted the work of Schove. He made analyses of old auroral reports in northern traditional sources and, plotting them on a time scale, inferred a series of dates for sunspots cycles maxima for the years -300 (before JC) to actual period.

I asked to one of these readers, Ray Tomes, author of a very interesting "Harmonic theory" and who also published on solar cycles, to send me Schove's estimated solar cycle maxima years. Here is the answer :

From: rtomes@kcbbs.gen.nz (Ray Tomes)

Subject: Years of Schove sunspot maxima

Schove dates ssmax

-293 -283 -272 -261 -249 -236 -223 -214 -205 -192 -182 -172 -163 -149 -135 -125 -113 -104 -91 -82 -72 -62 -53 -42 -27 -16 -5 8 20 31 42 53 65 76 86 96 105 118 130 141 152 163 175 186 196 208 219 230 240 252 265 277 290 302 311 321 330 342 354 362 372 387 396 410 421 430 441 452 465 479 490 501 511 522 531 542 557 567 578 585 597 607 618 628 642 654 665 677 689 699 714 724 735 745 754 765 776 787 798 809 821 829 840 850 862 872 887 898 907 917 926 938 950 963 974 986 994 1003 1016 1027 1038 1052 1067 1078 1088 1098 1110 1118 1129 1138 1151 1160 1173 1185 1193 1202 1219 1228 1239 1249 1259 1276 1288 1296 1308 1316 1324 1337 1353 1362 1372 1382 1391 1402 1413 1429 1439 1449 1461 1472 1480 1497 1505 1519 1528 1539 1548 1558 1572 1581 1591 1604 1615 1626 1639 1649 1660 1675 1685 1693 1705 1718 1727 1738 1750 1761 1769 1778 1787 1804 1816 1830 1837 1848 1860 1870 1883 1893 1905 1917 1928 1937 1947 1957 1968 1979

I modified the "plots.pas" program to allow the plotting of Schove's dates along with the other syzygies signals. The Schove's dates are plotted as blue bars, given the same sign as the filtered syzygie quality signal.

I ran the program at first, without believing too much that it could be correlated on such a long period : the results were surprising. I present them on 700 years periods, as plots on a longer time are difficult to read on a screen.

On the 1100 - 1800 period, the correlation is very
good. It seems that some auroras
were a little shifted with the maximum of the syzygies signal, but never more than
three years, which is excellent.

On the 400 - 1100 period, we get almost the
same quality of the correlation.

On the -300 - +400 period, we see that the result
is not so good. The correlation is good down to 260. Before that time, an abrupt
phase shift seems to occur. At -300, there is nearly a 180 phase shift (10 years
difference)

This difference could be due to several reasons :

- I could have reached the limits of calculating ephemerids with single precision 32 bits real numbers on a PC. Or perhaps the numeric values I used (taken in a book) are accurate enough for the twentieth century, not for the first centuries of our era.
- The secular interaction beetween the planets in the central zone of the solar system, especially the Earth - Venus interaction.
- Some errors in the dating of auroras by Schove.

The second hypothese is obvious. I used the actual parameters
of the planets to compute the syzygies, with no secular interaction.
I tried to check what difference in the
angular speed of the planets was necessary to suppress the phase shift on the
-300 - +400 period. For this, I included the following lines at the beginning
of the "syzygies.pas" program :

with planete [rang_venus] do LP := LP * 0.99999 ; with planete [rang_terre] do LP := LP * 1.00001 ;LP being the angular velocity (degrees / days) on the orbit, this means that I slow down a little Venus of minus E-5 and that I accelerate a little Earth of plus E-5, Jupiter being supposed to stay regular. The result shows a perfect correlation on this period. It creates some problems from 400 to 1100, while the 1100 to 1800 result is nearly unchanged. This seems to show that when retro computing the position of a planet through centuries, quadratic angular acceleration terms should be used to model the secular interaction.

Now, for the third hypothese, it would be interesting to know how Schove dated his materials on the -300 - +400 period.

In conclusion, I would just say that I hope I will soon be able to confirm my ephemerids.
If they are valid, being neither a specialist
of secular interaction beetween planets nor of old runic texts, I cannot make my
mind. What would be very helpfull would be to have records of the heliacal cycle
of Venus absolutely dated, around these dates. So, if a specialist of the Mayas
calendars or of the babylonian astronomic tablets could
help...thanks in advance.