344 
NATURE 
[ Aug. 25, 1870, 
generally rejected by investigators, not only from their necessary 
inaccuracy, but because the time of “‘apparent contact ” depends 
upon the amount of irradiation, which varies with the observer 
and the telescope. If there is no irradiation at all, the time of 
apparent contact and that of true contact will be the same, as 
shown in Fig. 2, while, when the cusps are enlarged by 
irradiation, apparent contact will not occur until the planet 
has moved through a space equal to double the irradiation. 
Let us return to the phenomenon at actual contact. Accord- 
ing to the theory as it has been presented, the formation or 
rupture of the black ligament connecting the dark body of Venus 
with the dark ground of the sky is a well-marked phenomenon, 
occurring at the moment of true internal contact. This was, I 
believe, the received theory until Wolf and André made their 
experiments on artificial transits in the autumn and winter of 
7868 and 14869. They announced, as a result of these experi- 
ments, that the formation of the ligament was not contem- 
poraneous with the oceurrence of internal contact, but followed 
it at the ingress of the planet, and preceded it at egress. In 
other words, it appeared while the thread of light was still cam- 
plete. They furthermore announced that with a good telescope 
the ligament did not appear at all, but the thread of light 
between Venus and the sun broke off by becoming indefinitely 
thin. 
The result is not difficult to account for. Irradiation has 
already been described as q spreading of the light emitted from 
each point ef the surface viewed, so that every such point appears 
asasmallcircle. The obvious effect of this spreading isa dilution 
of the light emitted by a luminous thread, whenever the diameter 
of the thread is less than that of the circle of irradiation, In 
consequence of this dilution, the thread may be invisible while 
it is really of sensible thickness, a given amount of light pro- 
ducing a greater effect on the eye the more it is concentrated. 
Since the thread of light must seem to break when it becomes 
invisible at its thinnest point, the formation or rupture ef the 
thread marks, not the moment of actual contact, but the moment 
at which the thread of light becomes so thick as to be visible, or 
so thin as to he invisible. The greater the irradiation, and the 
worse the definition, the thicker will be the thread at this 
moment. 
An interesting cbservetion, illustrative of this point, was made 
by Liais at Rio Janeiro, during the transit of Mercury of Novem- 
ber 1, 1868, Ile had two telescopes, one much smaller than 
the other. He watched the planet in the small one till it seemed 
to touch the disc of the sun, then looking into the large one, he 
sxw a thread of light distinctly between the planet and the sun, 
and they did not really touch until several seconds later. f 
Reference to the figures will make it clear that there is no 
generic difference between the phenomena commonly called the 
rupture of the black drop and that of the foymation of the thread 
of light. If the bright cusps are much rounded, as in Fig. ta, 
the appearance between them is necessarily that of a drop, while 
if they are seen in their true sharpness, as in Fig. 1, the form 
ef the drop will not appear. It has been shown that with dif- 
ferent instruments the phenomenon of contact may exhibit every 
gyadation between these extremes. The only well-defined phe- 
nomenon which all can see is the meeting of the bright cusps and 
the consequent formation of the thread of light at ingress, and 
the rupture of the thread at egress. 
To recapitulate our conclusions— i f 
1. The movement of obseryed internal contact at ingress is 
that at which the thread of light between Venus and the sun be- 
comes thick enough to be yisible. 
2, The least yisible thickness varies with the obseryer and the 
instrument, and, perhaps, with the state of the atmosphere. 
3. The apparent initial thickness of the thread varies with the 
irradiation of the telescope. 
Two questions are now to be discussed. ‘The observed times 
yarying with the observer and the instrument, we must know how 
wide the variation may be. If it be wide enough to render un- 
certain the results of observation, we shall inquire how its 
injurious effects may be obviated, ; 
The first question can be decided only by comparison of the 
observations of different obseryers upon one and the same phe- 
nomenon. For such comparison [ shall select the observations 
of the egress of Mercury on the occasion of its last transit over 
the disc of the sun. This selection is made for the reason that 
this egress was observed by a great number of experienced ob- 
seryers with the best instruments, while former transits, whether 
ef Venus or Mercury, haye been observed less extensively or at 
a time when practical astronomy was far from its present state ot 
perfection, and that the transit in question would therefore 
furnish much better data of judging what we might expect in 
future observations. The comparison was made in the following 
| way :—I selected from the ‘‘ Astronomische Nachrichten,” the 
“* Monthly Notices of the Royal Astronomical Society,” and the 
“*Comptes Rendus,” all the observations of internal contact 
at egress which there was reason to believe related to the breaking 
of the thread of light, and which were made at stations of known 
longitude. Each observation was then reduced to Greenwich 
time, and to the centre of the earth. 
From these comparisons it appears that the contact was first 
seen by Le Verrier, at Marseilles, at two seconds before nine 
o'clock, Greenwich time. In one second more it was seen by 
Rayet at Paris, Oppolzer at Vienna, Lynn at Greenwich, and 
Kaiser at Leyden. The times, noted by twenty other observers, 
are scattered yery evenly over the following fifteen seconds. Kam 
and Kaiser, at Leyden, did not see the contact until nineteen and 
twenty-four seconds past nine, 
It thus appears that among the best observers, using the best 
instruments, there is a difference exceeding twenty seconds 
between the times of noting contact. This difference cor- 
responds to more than a second of arc, so that really these 
observations were scarcely made with more accuracy than measures 
under favourable circumstances with a micrometer, and are net 
therefore to be relied on. Buta great addition to the accuracy 
of the determination could be made by measyres of the distance 
of the cusps, while the planet was entering upon the disc of the 
sun. It would tend greatly to the accuracy of the results, if the 
observers should meet beforehand with the telescopes they were 
actually to use in observing the transit and make observations in 
common on artificial transits. Jt would be a comparatively 
simple operation to erect an artificial representation of the sun’s 
disc at the distance of a few hundred yards, and to have an 
artificial planet moyed over it by clock-work. The actual time 
of contact could be determined by electricity, and the relative 
positions of the planet and the dise by actual measurement. 
With this apparatus it would be easy to determine the personal 
errors to which each observer was liable, and these errors would ap- 
proximately represent those of the observations of actual transit. 
Still it would be very unsafe to trust mainly to any determina- 
tion of internal contact. Understanding the uncertainty of such 
determinations, the German astronomers have proposed to trust 
to measures with a heliometer, made while the planet is crossing 
the disc. The use of a sufficient number of heliometers would 
be both difficult and expensive, and I think we have an entirely 
satisfactory substitute in photography. Indeed, Mr. De la Rue 
has proposed to determine the moment of internal contact by 
photegraphy. But the result would be subject to the same 
uncertainty which affects optical obseryations—the photograph 
which first shows contact will not be that taken when the thread 
of light between Venus and the sun’s disc was first completed, 
but the first taken after it became thick enough to affect the 
plate, and this thickness is more variable and uncertain than the 
thickness necessary to affect the eye. We know very well that 
a haziness of the sky which very slightly diminishes the apparent 
brilliancy of the sun, will very materially cut off the actinic rays, 
and the photographic plate has not the power of adjustment 
which the eye has. 
But, although we cannot determine contacts by photography, 
I conceive that we may thereby be able to measure the distance 
of the centres of Venus and the sun with great accuracy. 
Having a photograph of the sun with Venus on its disc, we can, 
with a suitable micrometer, fix the position of the centre of each 
body with great precision. We can then measure the distance 
of the centres in inches with corresponding precision. All we 
then want is the value in arc of an inch on the photograph plate. 
This determination is not without difficulty. It will not do to 
trust the measured diameters of the images of the sun, because 
they are affected by irradiation, just as the optical image is. If 
the plates were nearly of the same size, and the ratio of the dia- 
meters of Venus and the sun the same in both plates, it would 
be safe to assume that they were equally affected by irradiation. 
But should any show itself, it would not be safe to assume that 
the light of the sun encroached equally upon the dark ground ot 
Venus and upon the sky, because it is so much fainter near the 
border. 
If the photographic telescope were furnished with clock-work, 
it would be advisable to take several photographs of the Pleiades 
belt, before and after the transit, to furnish an accurate standard 
oa 
