DECENNIAL PERIOD OF MAGNETIC VARIATIONS, ETC, 577 
to have found long periods of 56 years and of 80-90 years.* From the pre- 
ceding discussion, the best known epochs seem to show a period of 42 years; 
as twice this period is within the limits of the last of Dr Woxr, we should obtain 
the mean duration, if either be true, by employing an interval of about 84 years. 
We have, fortunately, two very satisfactory epochs for this determination, that 
of 1787°25 deduced from Cassrni’s observations and confirmed by GiLpin’s, and 
the last maximum of 1870°85. From these two epochs, supposing they include 
eight periods between them, we have 
1870:85 — 178725 _ 83-60 
PKS 
8 = 10°45 years. 
28. If, however, we suppose with Dr Wo.r that there were only seven 
periods, then we have 

83-60 
lid 11°80 years. 
As there can be no doubt as to the accuracy of the earlier epoch (confirmed 
as it is also by Dr Wo r’s spot numbers and Professor Loomis’s aurora numbers), 
we may take for comparison with it one of Dr Wotr’s epochs of maximum 
spot frequency upwards of 80 years before; we have then 
17873 = 17055 _ 818 - 45.09 
8 8 
The number of periods here employed is that given by Dr Wotr. We have 
then, according to the astronomer of Zurich— 
By 8 periods, 1705 to 1787, mean period 10°23 years. 
Gs) 1787 to 1871, _ 11:80, 
These two means differ twice as much from each other as Dr WoL¥F’s mean 
of 11:11 years does from that originally found by Dr Lamont, and confirmed 
by this discussion.t 
* See “ Astr. Mitt. xv. Vierteljahrss.” 1863, S. 97, for a notice of a 56 years’ period of the aurore 
by Professor Frirz; also of Otmsrep’s period of 65 years. For the period of 80—90 years see “ Ast. 
Mitt.” xxxviii. S. 378, July 1875. I am not sure that I am acquainted with all the periods which Dr 
Woxr has discovered, nor do I know if one excludes the other. 
+ It is not possible to reconcile the two results deduced from Dr Wotr’s epochs and periods; if 
we take any of the epochs of maximum given by him before that here employed (1705) we always fail 
to reach his period of 11°11 years; thus we have 
9 periods, 1787°3 — 1693-0 94-3, mean 10°43 
TO x » —1685:0 = 1023, , 10°23 
dion: »  —1675:0 = 1123, 4, 10-21 
aes »  —1660:0 = 1273, ,, 10°61 
12) ody »  —1649:0 = 1383, ,, 10°64 
Hef ir » —1639°5 = 147-8, ,, 10°56 
1S) as, 2 eee 6S, ,,. 0775 
ee prcdGip = hAlcs, .,  d0i74 
Little weight can be given to these earlier epochs; but whatever weight they may possess, if we 
start from the sure epoch of 1787 no interval including more than 80 years will be found to satisfy the 
