The spectroscope comes in also to aid in determining the contacts with the utmost precision. The light of the solar photosphere, or body of the sun, when made to pass through the prisms of a spectroscope, spreads into a continuous band of various colors, and crossed by many faint, dark lines. Other bodies, raised to a certain heat, and emitting light, give a spectrum of a totally different character. We see only bright upright lines. There is no continuous band or spectrum of prismatic colors. Now, just outside the solar photosphere, and between it and the chromosphere, is a layer of solar atmosphere which gives just such upright, bright lines. This was first discovered not many years ago during a total solar eclipse, when the direct light of the photosphere was cut off by the interposing moon. Knowing what to look for, the astronomers have since been able so to manipulate their telescopes as to catch these bright lines, even when there is no eclipse. They find them, of course, as they examine, a narrow ring apparently encircling the sun, and immediately around his circumference. Now, when the moment of the beginning of the transit is at hand, the spectroscope is turned to the precise point where Venus will touch the sun's rim, and these lines are clearly brought into vision. So long as they shine, the way is open for the light of that narrow layer or belt to reach the earth. The instant their bright flash disappears, the observer knows that the planet has so moved as to intercept the rays of light, and is just in contact. Their reappearance, at the proper time, on the other side of the sun, will indicate the instant when Venus will have quitted the disk and the transit is over.
It is confidently expected that by some one or by all of these methods the uncertainties of 1761 and 1769 will be avoided, and that the instants of the commencement and the conclusion of each line of the transit may be so accurately determined that for neither of them will the error as to their duration exceed one second. Did the time occupied by Venus in making the transit, as seen from one station, differ from the time as seen at the other by only one minute, the uncertainty of one second would be less than two per cent. But, in fact, the times will differ by fifteen minutes, and, by skilfully choosing the places, a difference of twenty minutes may be obtained. In that case, the error or uncertainty would be less than one-tenth of one per cent. For the present, the scientific world will be satisfied with that degree of exactness.
Let us return to our supposition of two stations north and south, 6,000 miles apart. The two lines of transit, as seen from them, are separated about 35 of an arc. This is as the lines are seen from the earth. If we recur to Kepler's proportion, as stated before—that the distance of the earth from the sun [pg 159] is to the distance of Venus from the sun as 10,000,000 is to 7,233,324—we can make use of a trigonometrical calculation, and easily ascertain that those same lines on the sun, seen by an observer on Venus, would appear about 48-½" apart. Moreover, the lines from the sun to Venus, forming this angle, cross each other at the planet, and, if prolonged, will reach the two stations on the earth. Hence, since opposite interior angles are equal, this (48-½") must be the angle at which the same observer on Venus, turning towards the earth, would see the two stations. We arrive thus at a triangle, in which the base is known—6,000 miles; the angle at the vertex on Venus is also known—48-½"; and the angles at the base are easily ascertainable. A simple calculation leads to the distance of Venus from the earth—about 25,300,000 miles. Again, applying Kepler's formula to this number, we obtain as the result, for the earth's distance from the sun, about 91,450,000 miles. If we give here only rough approximations, we are, after all, as near the truth as the astronomers of to-day can boast of being. In a minute calculation, subsidiary but important points are to be brought in, complicating the calculation and influencing the result.
After this statement of the general character of Halley's method, we may be brief in our notice of the yet more beautiful mode of Delisle. He proposed it before the transits of the last century. But its efficiency so entirely depends on an accurate knowledge of the longitudes of the stations, and the longitudes of distant stations were then so uncertain, that it could not then be used with success.
In this mode, two stations are necessary, east and west, or, rather, along that line on the earth's surface from all points of which the transit will show the same line on the solar disk. The further apart the stations are, the better; for the base between them will be larger. To know the distance between them, we must know their longitudes as accurately as their latitudes. From the longitudes we ascertain with precision the difference of time between them. At one of those stations, the first exterior contact is seen, and the exact time is noted. As Venus moves on, the shadow of this first contact flies along that line of the earth's surface like the shadow of a cloud in spring traversing the fields. It is only after the lapse of a certain length of time that the contact is seen and timed at the other station. This certain length of time is the key to the solution. It may be determined by observations on any one or on all the contacts, or by the observation of any other points of the transit examined and timed at both stations. It is obvious that the contacts, being the most unmistakable in their character, will be all used to check and control each other; the more so, as they serve also, as we saw, for Halley's method. The most careful use of the telescope will be supplemented by the photograph and the spectroscope.
Let two such stations be chosen which, by their longitudes and latitudes, we know to be 5,000 miles apart. It will be found that the transit, or any special point of it, will be seen at the second station about three minutes of time later than at the first. This means that the shadow of Venus travels 5,000 miles in three minutes on the earth's surface or at the earth's distance from the sun. Applying Kepler's formula, we find that, to [pg 160] produce this effect, Venus herself must have travelled about 3,860 miles in those three minutes. There-fore in 224.7 days—her solar year—she would travel about 416 millions of miles, supposing that, during the transit, she was moving at her mean velocity. This, then, is the length of her periphery of her orbit around the sun. Observations have determined its shape. Now that we know its size, it is not difficult to ascertain what her mean distance from the sun must be. It is about 66,300,000 miles. From this, the usual formula leads us to the earth's distance from the sun—91,650,000 miles. We merely indicate the salient points of the process, and that with summary numbers. An astronomer would enter into minor questions: how far the earth had travelled in her orbit during those three minutes, and what had been the special motion of the second station during the same time, on account of the diurnal revolution of the earth on its axis. He would carefully establish the proportion of the distances between the sun and Venus and the earth, during the transit, to their mean distances as contemplated in Kepler's law, and he would compare the velocity of Venus at that time with her mean velocity. Other points, too, would have to be brought in, complicating the whole process to an extent that would soften the brain of any one but a calculating astronomer.
In Halley's method, the effort is to obtain two transit lines on the sun as widely apart as possible. For that purpose, the stations must differ in latitude as widely as possible. In Delisle's method, on the contrary, the longitude becomes of primary importance. The latitude can be easily determined. Hence, in the last century, Halley's method was almost exclusively adopted. But now we can use both; for we have better instruments and better star catalogues, and can determine longitudes by astronomical observations much more accurately than could ordinarily be done a century ago. In addition, we have now almost faultless chronometers. Besides all these means, we have, and will use to a great extent, the grand American invention of determining the longitude by the electric telegraph with an accuracy which leaves nothing to be desired.
While each method requires at least two stations, a greater number would support and control each other, and allow us to take the average result of a greater number of observations. Four stations at the corners of a large quadrangle on the surface of the earth might give two sets of stations for each method. But this year the stations may be nearer a hundred.
Careful preliminary studies have already determined on what portion of the earth the transit will be visible. The most available points will be turned to account for stations. We say available; for, unfortunately, much of that space is occupied by oceans, while astronomical stations must perforce be situated on firm land. Some of the best points, too, seem almost inaccessible. Still, there is a vast line of posts determined on in the northern hemisphere, and quite a number, to correspond with them, in the southern. Beginning at Alexandria, in Egypt, the line stretches northward and eastward through Palestine, Georgia, Tartary, Middle Asia, and Northern China to Yeddo, in Japan, perhaps to Honolulu, in the Sandwich Islands. Along a great part of this line, the Russian [pg 161] telegraphic wires will give exact longitudes, thus affording a fine field for the use of Delisle's method. In the southern hemisphere, the line may be set down as commencing near the Cape of Good Hope, bending southeastwardly to the lately discovered Antarctic lands, passing south of Australia, then turning upwards towards the equator, and terminating at Nukahiva, in the Sandwich Islands, in the South Pacific Ocean. Along this line, at Crozet Island, at St. Paul's, at Reunion, at Kerguelen Land—further south, if the southern summer will have sufficiently melted the snows and driven back the ice-barrier to allow the observers to land and work—at Campbell Land, in New Caledonia, and in other places, stations will be established, between which and corresponding stations in the northern line Halley's method may be used.
Time, learning, skill, energy, money, everything that man can give, will be devoted to ensure success in the astronomical work to be done on the 8th of December next. Such earnestness commands respect, and wins our sympathy and best wishes.