number, Mr. Jeula found the mean percentage of losses in registered
vessels of the United Kingdom and Channel Islands to be 11·13, and the
mean percentage of losses in the total posted in the entire cycle of
eleven years to be 8·64.
In the four years when sun-spots were intermediate in number, that
is in two years following the minimum and in two years preceding the
minimum, the respective percentages were 11·91 and 9·21.
Lastly, in the three years when sun-spots were most numerous, these
percentages were, respectively, 12·49 and 9·53.
That the reader may more clearly understand what is meant here by
percentages, I explain that while the numbers 11·13, 11·91 and 12·49
simply indicate the average number of wrecks (per hundred of all
the ships registered) which occurred in the several years of the
eleven-years cycle, the other numbers, 8·64, 19·21, and 9·53, indicate
the average number of wrecks (per hundred of wrecks recorded) during
eleven successive years, which occurred in the several years of the
cycle. The latter numbers seem more directly to the purpose; and as the
two sets agree pretty closely, we may limit our attention to them.
Now I would in the first place point out that it would have been well
if the actual number or percentage had been indicated for each year of
the cycle, instead of for periods of four years, four years, and three
years. Two eleven-year cycles give in any case but meagre evidence,
and it would have been well if the evidence had been given as fully
as possible. If we had a hundred eleven-yearly cycles, and took the
averages of wrecks for the four years of minimum solar maculation, the
four intermediate years, and the three years of maximum maculation,
we might rely with considerable confidence on the result, because
accidental peculiarities one way or the other could be eliminated. But
in two cycles only, such peculiarities may entirely mask any cyclic
relation really existing, and appear to indicate a relation which has
no real existence. If the percentages had been given for each year,
the effect of such peculiarities would doubtless still remain, and the
final result would not be more trustworthy than before; but we should
have a chance of deciding whether such peculiarities really exist or
not, and also of determining what their nature may be. As an instance
in point, let me cite a case where, having only the results of a
single cycle, we can so arrange them as to appear to indicate a cyclic
association between sun-spots and rainfall, while, when we give them
year by year, such an association is discredited, to say the least.
The total rainfall at Port Louis, between the years 1855 and 1868
inclusive, is as follows:—
In _Rainfall._ _Condition of Sun._
1855 42·665 inches Sun-spot minimum.
1856 46·230 „
1857 43·445 „
1858 35·506 „
1859 56·875 „
1860 45·166 „ Sun-spot maximum.
1861 68·733 „
1862 28·397 „
1863 33·420 „
1864 24·147 „
1865 44·730 „
1866 20·571 „ Sun-spot minimum.
1867 35·970 „
1868 64·180 „
[Illustration]
I think no one, looking at these numbers as they stand, can recognize
any evidence of a cyclic tendency. If we represent the rainfall by
ordinates we get the accompanying figure, which shows the rainfall for
eighteen years, and again I think it may be said that a very lively
imagination is required to recognize anything resembling that wave-like
undulation which the fundamental law of statistics requires where
a cycle is to be made out from a single oscillation. Certainly the
agreement between the broken curve of rainfall and the sun-spot curve
indicated by the waved dotted line is not glaringly obvious. But when
we strike an average for the rainfall, in the way adopted by Mr. Jeula
for shipwrecks, how pleasantly is the theory of sun-spot influence
illustrated by the Port Louis rainfall! Here is the result, as quoted
by the high-priest of the new order of diviners, from the papers by Mr.
Meldrum:—
Three minimum years—total rainfall 133·340
Three maximum years—total rainfall 170·774
Three minimum years—total rainfall 120·721
Nothing could be more satisfactory, but nothing, I venture to assert,
more thoroughly inconsistent with the true method of statistical
research.
May it not be that, underlying the broad results presented by Mr.
Jeula, there are similar irregularities?
When we consider that the loss of ships depends, not only on a cause so
irregularly variable (to all seeming) as wind-storms, but also on other
matters liable to constant change, as the variations in the state of
trade, the occurrence of wars and rumours of wars, special events, such
as international exhibitions, and so forth, we perceive that an even
wider range of survey is required to remove the effects of accidental
peculiarities in their case, than in the case of rainfall, cyclones,
or the like. I cannot but think, for instance, that the total number
of ships lost in divers ways during the American war, and especially
in its earlier years (corresponding with two of the three maximum
years of sun-spots) may have been greater, not merely absolutely but
relatively, than in other years. I think it conceivable, again, that
during the depression following the great commercial panic of 1866
(occurring at a time of minimum solar maculation, as already noticed)
the loss of ships may have been to some degree reduced, relatively as
well as absolutely. We know that when trade is unusually active many
ships have sailed, and perhaps may still be allowed to sail (despite
Mr. Plimsoll’s endeavours), which should have been broken up; whereas
in times of trade depression the ships actually afloat are likely
to be, _on the average_, of a better class. So also, when, for some
special reason, passenger traffic at sea is abnormally increased. I
merely mention these as illustrative cases of causes not (probably)
dependent on sun-spots, which may (not improbably) have affected the
results examined by Mr. Jeula. I think it possible that those results,
if presented for each year, would have indicated the operation of such
causes, naturally masked when sets of four years, four years, and three
years are taken instead of single years.
I imagine that considerations such as these will have to be taken into
account and disposed of before it will be unhesitatingly admitted that
sun-spots have any great effect in increasing the number of shipwrecks.
The advocates of the doctrine of sun-spot influence—or, perhaps
it would be more correct to say, the advocates of the endowment of
sun-spot research—think differently on these and other points. Each
one of the somewhat doubtful relations discussed above is constantly
referred to by them as a demonstrated fact, and a demonstrative proof
of the theory they advocate. For instance, Mr. Lockyer, in referring to
Meldrum’s statistical researches into the frequency of cyclones, does
not hesitate to assert that according to these researches “the whole
question of cyclones is merely a question of solar activity, and that
if we wrote down in one column the number of cyclones in any given
year, and in another column the number of sun-spots in any given year,
there will be a strict relation between them—many sun-spots, many
hurricanes; few sun-spots, few hurricanes.” ... And again, “Mr. Meldrum
has since found” (not merely “has since found reason to believe,” but
definitely, “has since found”) “that what is true of the storms which
devastate the Indian Ocean is true of the storms which devastate the
West Indies; and on referring to the storms of the Indian Ocean, Mr.
Meldrum points out that at those years where we have been quietly
mapping the sun-spot maxima, the harbours were filled with wrecks, and
vessels coming in disabled from every part of the Indian Ocean.” Again,
Mr. Balfour Stewart accepts Mr. Jeula’s statistics confidently as
demonstrating that there are most shipwrecks during periods of maximum
solar activity. Nor are the advocates of the new method of prediction
at all doubtful as to the value of these relations in affording the
basis of a system of prediction. They do not tell us precisely _how_ we
are to profit by the fact, if fact it is, that cyclones and shipwrecks
mark the time of maximum solar maculation, and droughts and famine the
time of minimum. “If we can manage to get at these things,” says Mr.
Lockyer, “the power of prediction, that power which would be the most
useful one in meteorology, if we could only get at it, would be within
our grasp.” And Mr. Balfour Stewart, in a letter to the _Times_, says,
“If we are on the track of a discovery which will in time enable
us to foretell the cycle of droughts, public opinion should demand
that the investigation be prosecuted with redoubled vigour and under
better conditions. If forewarned be forearmed, then such research will
ultimately conduce to the saving of life both at times of maximum and
minimum sun-spot frequency.”
If these hopes are really justified by the facts of the case, it would
be well that the matter should be as quickly as possible put to the
test. No one would be so heartless, I think, as to reject, through an
excess of scientific caution, a scheme which might issue in the saving
of many lives from famine or from shipwreck. And on the other hand, no
one, I think, would believe so ill of his fellow-men as to suppose for
one moment that advantage could be taken of the sympathies which have
been aroused by the Indian famine, or which may from time to time be
excited by the record of great disasters by sea and land, to advocate
bottomless schemes merely for purposes of personal advancement. We must
now, perforce, believe that those who advocate the erection of new
observatories and laboratories for studying the physics of the sun,
have the most thorough faith in the scheme which they proffer to save
our Indian population from famine and our seamen from shipwreck.
But they, on the other hand, should now also believe that those who
have described the scheme as entirely hopeless, do really so regard it.
If we exonerate them from the charge of responding to an appeal for
food by offering spectroscopes, they in turn should exonerate us from
the charge of denying spectroscopes to the starving millions of India
though knowing well that the spectroscopic track leads straight to
safety.
I must acknowledge I cannot for my own part see even that small modicum
of hope in the course suggested which would suffice to justify its
being followed. In my opinion, one ounce of rice would be worth more
(simply because it would be worth something) than ten thousand tons of
spectroscopes. For what, in the first place, has been shown as to the
connection between meteorological phenomena and sun-spots? Supposing we
grant, and it is granting a great deal, that all the cycles referred
to have been made out. They one and all affect averages only. The most
marked among them can so little be trusted in detail that while the
maximum of sun-spots agrees _in the main_ with an excess or defect of
rain or wind, or of special rains with special winds, or the like, the
actual year of maximum may present the exact reverse.
Of what use can it be to know, for instance, that the three years of
least solar maculation will probably give a rainfall less than that
for the preceding or following three years, if the middle year of
the three, when the spots are most numerous of all, _may_ haply show
plenteous rainfall? Or it may be the first of the three, or the last,
which is thus well supplied, while a defect in the other two, or in one
of the others, brings the total triennial rainfall below the average.
What provision could possibly be made under such circumstances to meet
a contingency which may occur in any one of three years? or, at least,
what provision could be made which would prove nearly so effective
as an arrangement which could readily be made for keeping sufficient
Government stores at suitable stations (that is, never allowing such
stores to fall at the critical season in each year below a certain
minimum), and sending early telegraphic information of unfavourable
weather? Does any one suppose that the solar rice-grains are better
worth watching for such a purpose than the terrestrial rice-grains, or
that it is not well within the resources of modern science and modern
means of communication and transport, to make sufficient preparation
each year for a calamity always possible in India? And be it noticed
that if, on the one hand, believers in solar safety from famine may
urge that, in thus objecting to their scheme, I am opposing what might,
in some year of great famine and small sun-spots, save the lives of
a greater number than would be saved by any system of terrestrial
watchfulness, I would point out, on the other, that the solar scheme,
if it means anything at all, means special watchfulness at the minimum
sun-spot season, and general confidence (so far as famine is concerned)
at the season of maximum solar maculation; and that while as yet
nothing has been really proved about the connection between sun-spots
and famine, such confidence might prove to be a very dangerous mistake.
Supposing even it were not only proved that sun-spots exert such and
such effects, but that this knowledge can avail to help us to measures
of special precaution, how is the study of the sun going to advance
our knowledge? In passing, let it be remarked that already an enormous
number of workers are engaged in studying the sun in every part of
the world. The sun is watched on every fine day, in every quarter of
the earth, with the telescope, analyzed with the spectroscope, his
prominences counted and measured, his surface photographed, and so
forth. What more ought to be or could be done? But that is not the main
point. If more could be done, what could be added to our knowledge
which would avail in the way of prediction? “At present,” says Mr.
Balfour Stewart, “the problem has not been pursued on a sufficiently
large scale or in a sufficient number of places. If the attack is to
be continued, the skirmishers should give way to heavy guns, and these
should be brought to bear without delay now that the point of attack is
known.” In other words, now that we know, according to the advocates
of these views, that meteorological phenomena follow roughly the great
solar-spot period, we should prosecute the attack in this direction,
in order to find out—what? Minor periods, perhaps, with which
meteorological phenomena may still more roughly synchronize. Other such
periods are already known with which meteorological phenomena have
never yet been associated. New details of the sun’s surface? No one has
yet pretended that any of the details already known, except the spots,
affect terrestrial weather, and the idea that peculiarities so minute
as hitherto to have escaped detection can do so, is as absurd, on the
face of it, as the supposition that minute details in the structure
of a burning coal, such details as could only be detected by close
scrutiny, can affect the general quality and effects of the heat
transmitted by the coal, as part of a large fire, to the further side
of a large room.
Lastly, I would urge this general argument against a theory which seems
to me to have even less to recommend it to acceptance than the faith
in astrology.[8] _If it requires, as we are so strongly assured, the
most costly observations, the employment of the heaviest guns (and
“great guns” are generally expensive), twenty or thirty years of time,
and the closest scrutiny and research, to prove that sun-spots affect
terrestrial relations in a definite manner, effects so extremely
difficult to demonstrate cannot possibly be important enough to be
worth predicting._
_NEW WAYS OF MEASURING THE SUN’S DISTANCE._
It is strange that the problem of determining the sun’s distance, which
for many ages was regarded as altogether insoluble, and which even
during later years had seemed fairly solvable in but one or two ways,
should be found, on closer investigation, to admit of many methods
of solution. If astronomers should only be as fortunate hereafter in
dealing with the problem of determining the distances of the stars,
as they have been with the question of the sun’s distance, we may
hope for knowledge respecting the structure of the universe such as
even the Herschels despaired of our ever gaining. Yet this problem of
determining star-distances does not seem more intractable, now, than
the problem of measuring the sun’s distance appeared only two centuries
ago. If we rightly view the many methods devised for dealing with the
easier task, we must admit that the more difficult—which, by the way,
is in reality infinitely the more interesting—cannot be regarded
as so utterly hopeless as, with our present methods and appliances,
it appears to be. True, we know only the distances of two or three
stars, approximately, and have means of forming a vague opinion
about the distances of only a dozen others, or thereabouts, while at
distances now immeasurable lie six thousand stars visible to the eye,
and twenty millions within range of the telescope. Yet, in Galileo’s
time, men might have argued similarly against all hope of measuring
the proportions of the solar system. “We know only,” they might have
urged, “the distance of the moon, our immediate neighbour,—beyond
her, at distances so great that hers, so far as we can judge, is by
comparison almost as nothing, lie the Sun and Mercury, Venus and Mars;
further away yet lie Jupiter and Saturn, and possibly other planets,
not visible to the naked eye, but within range of that wonderful
instrument, the telescope, which our Galileo and others are using so
successfully. What hope can there be, when the exact measurement of the
moon’s distance has so fully taxed our powers of celestial measurement,
that we can ever obtain exact information respecting the distances of
the sun and planets? By what method is a problem so stupendous to be
attacked?” Yet, within a few years of that time, Kepler had formed
already a rough estimate of the distance of the sun; in 1639, young
Horrocks pointed to a method which has since been successfully applied.
Before the end of the seventeenth century Cassini and Flamsteed had
approached the solution of the problem more nearly, while Hailey had
definitely formulated the method which bears his name. Long before the
end of the eighteenth century it was certainly known that the sun’s
distance lies between 85 millions of miles and 98 millions (Kepler,
Cassini, and Flamsteed had been unable to indicate any superior limit).
And lastly, in our own time, half a score of methods, each subdivisible
into several forms, have been applied to the solution of this
fundamental problem of observational astronomy.
I propose now to sketch some new and very promising methods, which have
been applied already with a degree of success arguing well for the
prospects of future applications of the methods under more favourable
conditions.
In the first place, let us very briefly consider the methods which had
been before employed, in order that the proper position of the new
methods may be more clearly recognized.
The plan obviously suggested at the outset for the solution of the
problem was simply to deal with it as a problem of surveying. It was
in such a manner that the moon’s distance had been found, and the
only difficulty in applying the method to the sun or to any planet
consisted in the delicacy of the observations required. The earth being
the only surveying-ground available to astronomers in dealing with
this problem (in dealing with the problem of the stars’ distances they
have a very much wider field of operations), it was necessary that
a base-line should be measured on this globe of ours,—large enough
compared with our small selves, but utterly insignificant compared
with the dimensions of the solar system. The diameter of the earth
being less than 8000 miles, the longest line which the observers could
take for base scarcely exceeded 6000 miles; since observations of the
same celestial object at opposite ends of a diameter necessarily imply
that the object is in the horizon of _both_ the observing stations
(for precisely the same reason that two cords stretched from the ends
of any diameter of a ball to a distant point touch the ball at those
ends). But the sun’s distance being some 92 millions of miles, a base
of 6000 miles amounts to less than the 15,000th part of the distance
to be measured. Conceive a surveyor endeavouring to determine the
distance of a steeple or rock 15,000 feet, or nearly three miles, from
him, with a base-line _one foot_ in length, and you can conceive the
task of astronomers who should attempt to apply the direct surveying
method to determine the sun’s distance,—at least, you have one of
their difficulties strikingly illustrated, though a number of others
remain which the illustration does not indicate. For, after all, a
base one foot in length, though far too short, is a convenient one in
many respects: the observer can pass from one end to the other without
trouble—he looks at the distant object under almost exactly the same
conditions from each end, and so forth. A base 6000 miles long for
determining the sun’s distance is too short in precisely the same
degree, but it is assuredly not so convenient a base for the observer.
A giant 36,000 miles high would find it as convenient as a surveyor
six feet high would find a one foot base-line; but astronomers, as
a rule, are less than 36,000 miles in height. Accordingly the same
observer cannot work at both ends of the base-line, and they have to
send out expeditions to occupy each station. All the circumstances
of temperature, atmosphere, personal observing qualities, etc., are
unlike at the two ends of the base-line. The task of measuring the
sun’s distance directly is, in fact, at present beyond the power of
observational astronomy, wonderfully though its methods have developed
in accuracy.
We all know how, by observations of Venus in transit, the difficulty
has been so far reduced that trustworthy results have been obtained.
Such observations belong to the surveying method, only Venus’s distance
is made the object of measurement instead of the sun’s. The sun serves
simply as a sort of dial-plate, Venus’s position while in transit
across this celestial dial-plate being more easily measured than when
she is at large upon the sky. The devices by which Halley and Delisle
severally caused _time_ to be the relation observed, instead of
position, do not affect the general principle of the transit method. It
remains dependent on the determination of position. Precisely as by the
change of the _position_ of the hands of a clock on the face we measure
_time_, so by the transit method, as Halley and Delisle respectively
suggested its use, we determine Venus’s position on the sun’s face,
by observing the difference of the time she takes in crossing, or the
difference of the time at which she begins to cross, or passes off, his
face.
Besides the advantage of having a dial-face like the sun’s on which
thus to determine positions, the transit method deals with Venus when
at her nearest, or about 25 million miles from us, instead of the sun
at his greater distance of from 90½ to 93½ millions of miles. Yet we
do not get the entire advantage of this relative proximity of Venus.
For the dial-face—the sun, that is—changes its position too—in less
degree than Venus changes hers, but still so much as largely to reduce
her seeming displacement. The sun being further away as 92 to 25, is
less displaced as 25 to 92. Venus’s displacement is thus diminished by
25/92nds of its full amount, leaving only 67/92nds. Practically, then,
the advantage of observing Venus, so far as distance is concerned, is
the same as though, instead of being at a distance of only 25 million
miles, her distance were greater as 92 to 67, giving as her effective
distance when in transit some 34,300,000 miles.