Fan. 13, 1870 | 
NATURE 
there, then, any independent probability of the truth of 
this hypothesis? It is well known that the formation of 
spots occurs chiefly between particular parallels of 
latitude, and that the numbers are greater in the northern 
than in the southern hemisphere. It seems, therefore, at 
least not improbable that a like difference may exist in 
regard to Jongitude. “Sdmmering directs attention to 
the fact, that there are certain meridian belts on the sun’s 
disc, in which he had never observed a solar spot for 
many years together.” * Buys-Ballot, of Utrecht, has 
found, from an elaborate discussion of a great number of 
meteorological observations, that there is a short period 
of variation in the amount of solar heat received by our 
planet ; the period from maximum to maximum coinciding, 
at least approximately, with that of the sun’s rotation with 
respect to the earth. Sir William Herschel also believed 
that one side of the sun, on account of some peculiarity 
in its physical constitution, was less adapted to radiate 
light and heat than the other. 
On Dr. Kirkwood’s hypothesis, the sun-spot period 
would be equal to the interval between two conjunctions 
of the disturbing planets on the heliographic meridian 
(designated by M) of that’ part of the surface most sus- 
ceptible to their influence. It would depend, therefore, on 
the ratio of the sun’s period of rotation to the interval 
between two consecutive conjunctions of such planets. Or, 
as Mercury’s influence is extremely variable, a maximum 
would be produced by this planet’s perihelion passage, 
when the most susceptible part of the sun’s surface had 
the same, or nearly the same, heliocentric longitude. In 
order, then, to test this hypothesis, we must first inquire 
what is the most probable period of the sun’s rotation? 
On account of the frofer motion of the solar spots, 
the time of the sun’s rotation as determined by their 
apparent motion across the disc, varies from about 25 to 
29 days. The roger motion of the spots has recently 
been discussed with great labour and ability by Professor 
Sporer, of Anclam, and Mr. Carrington, in England, who 
have shown conclusively that the rapidity of movement 
varies regularly with the latitude. The equatorial portions 
have the greatest angular velocity; in other words, the 
proper motion of the spots is in a direction contrary to 
that of the sun’s rotation. The formule by which the 
astronomers named expressed the law for the dependence 
of the sun’s apparent period of rotation on the latitude are 
as follows :-— 
According to Carrington, =865’— 165’ sz 7 (1) 
Phan Sporer, €=16°8475°—3°3812° six 
Gus esygeGie po oe D og 0 o oon () 
where & is the arc described in a solar day. The true 
time of rotation is supposed to be that indicated by an 
equatorial spot ; and on this assumption, (1) gives 
P=24°9711d.=24d. 23h. 18.235. . . . . . (3) 
or, (2) gives 
=24°62447d.=24d. 14h. 5971.05. . . . . . (A) 
The true value is probably between the results here given. 
But will this modifying element in the theory of 
planetary action afford a satisfactory explanation of the 
periodic recurrence of maxima and minima of solar spots ? 
Let us consider. 
(a.) The 11-Vear Cycle—The anomalistic period of 
Mercury is 87'9702d., and 
87'9702d. X 46=4046°6292d.=11'077y.=T, . . (5) 
This is very nearly equal to Wolf’s value of the cycle, 
and agrees at least equally well with recorded facts.+ 
* Humboldt’s Cosmos, vol. iv., p. 378. 
+ The following astronomical cycles are also nearly equal to this period of 
variation :— 
1. 18 periods of Venus = rr‘074y. | re, 
2. 35 syn. per. of Mer. = 11104 5. 287,= 11082 
3. 1 period of Jupiter = rr°860 6. 453 = 11063 
where ¢;= the syn. per. of Venus with respect to Jupiter; ¢,= Syn. per. of 
177; = 110309. 
(6) 
which is nearly a mean between Sporer’s and Carring- 
ton’s values of the sun’s period of rotation. With this, 
therefore, as the time of the sun’s axial revolution, we 
have 46 times the period of Mercury—equal to 163 times 
that of the sun’s rotation.- The recurrence of maxima at 
mean intervals of 11°077 years would thus be accounted 
for.* Again, the epochs at which sun-spots were seen 
before the invention of the telescope may be presumed, 
with much probability, to have been nearly coincident 
with the maxima epochs of Schwabe’s cycle. Now, it is 
a remarkable fact that all of those dates, except perhaps 
the last, harmonise with the value which we have adopted 
Again, ~é = 24'82594d.= 24d- 19h. 4Qm. 215. . . 
for Schwabe’s period of variation. Thus : 
From 321, A.D. to 1860, we have 139 periods of 11-072 + yrs. each. 
x 321 ” 807 ” 44 ” It 045 ” 
y7 80722 35 $40°5 ” 3 ” 1L'093 ” 
be) 840°5 7” 1090 ”? 23 ” Ir 10g > 
» 1096 ,, 1161 _ ,, 6 5 107833 ” 
99 1161 ” 1590°9 ” 39 ” 11024 ” 
2? 1590°9 3? 17590 39 I4 ” 11 °367(?) 39 
», 1750°0 ,, 18290 ,, 7 os 11286 np 
” 18290 ” 1860°5 ” si ” 10°500 ” 
The variability of the 
sidered. 
(6.) Wolfs Cycle of 56—57 Vears.—The synodic revolu- 
tion of Mercury is 115°87748d., and 
115°87748d. X 177 =205 10°31396d. =56°15324y.=T, (7) 
In this period the line of conjunction of Mercury and 
the earth advances 56°15324 revolutions. Now, 
Saba gag 28 820284 = 24d. 19f. 4972. 505. . . (8) 
period will be hereafter con- 
This value of the sun’s period of rotation differs from 
that in (6) by only 29 seconds. Adopting it, therefore, we 
find that Mercury and the earth will be in conjunction on 
the same heliographic meridian at regularly recurring 
epochs of 56 years and 56 days. 
(¢.) The 233-Day Pertod—The mean interval between 
the consecutive conjunctions of Venus and Jupiter is 
236°992¢. The close agreement of these periods leaves 
little room to doubt that the latter is the true period of 
spot variation. 
(@.) The 27-Day Period —This is at once satisfactorily 
accounted for. 
(e.) The 584-Day Period.—The identity of this period 
with that of the synodic revolution of Venus has already 
been indicated by De la Rue, Stewart, and Loewy. 
Remarking that Dr. Kirkwood advances other facts in 
support of his argument, we pass at once to his con- 
clusions. 
1. A connection between the behaviour of sun-spots 
and the configurations of certain planets has been placed 
beyond reasonable doubt. 
2. The theory, however, of spot formation by planetary 
influence is encumbered with anomalies and even in- 
consistencies, unless we admit the co-operation of a 
modifying cause. 
3. The hypothesis that a particular part of the solar 
surface is more susceptible than others to planetary dis- 
turbance is rendered probable by the observations of 
different astronomers. 
4. The 11-year cycle of spot variation is mainly de- 
pendent on the influence of Mercury. 
5. The marked irregularity of this period from 1822 to 
Mercury with respect to Venus; and #3= that of Mercury with respect to 
Jupiter. 
* It is not probable that Mercury is on the meridian M precisely at the 
epoch of perihelion passage. It is only necessary to suppose this coincidence 
to occur when the planet is zea7 the perihelion point. Even at the distance 
of 20° the diminution of the disturbing power would be extremely small. 
