result pointed to by so many independent researches. Powalky subjected these observations to a new discussion and deduced the value 8"-832, corresponding much more closely than Encke's with the recent determinations. But astronomers were not satisfied with his labours, because he rejected some of the more important observations made in 1769, without assigning sufficient cause, and also because the agreement between those observations which he retained was by no means exhibited satisfactorily. As Admiral Manners said, when addressing the Astronomical Society in 1862, 'The weight of Encke's value could scarcely be said to be affected by Powalky's discussion.'

It was reserved for Mr. Stone, of Greenwich, to solve in a satisfactory manner a difficulty which had long perplexed astronomers. We have seen that there are two phases which an observer of Venus in transit might try to catch-the moment when the connection between the disc of Venus and that of the Sun appears to break at ingress or form at egress, and the moment when the outline of Venus, if undisturbed, would just touch the outline of the Sun. Now, if we consider why Venus is distorted so peculiarly near the time of internal contact, we shall see which of these phases corresponds most closely to the real moment of internal contact. The matter is sufficiently simple. Owing to a peculiarity of vision, every bright object appears somewhat larger than it really is, the borders of the image on the retina affecting the neighbouring part of the retina. It follows obviously that every dark object will

appear somewhat smaller than it really is, for the background on which the dark object is depicted will be relatively bright, and so its image on the retina will encroach on that of the dark object. Thus, suppose the arc s s'v' (fig. 17) to represent part of the true outline of the Sun, then, to the observer, the outline would lie as shown outside this circle; but if the circle s' v v represents the true outline of Venus, her apparent outline would lie as shown inside this circle. It is clear,

then, that the part of the outline of Venus which lies upon the Sun seems to belong to a smaller circle than the part of the outline lying outside the Sun. This is true until the actual moment when the true outlines touch, when the appearance would be that shown in fig. 18, the connecting ligament being the finest conceivable line; and obvicusly (referring to ingress), the undistorted part of the apparent outline of Venus would have seemed to belong to a circle touching the Sun's outline some seconds earlier. Similar remarks apply to egress.

So that if an observer could note the moment when the discs of Venus and the Sun were apparently united by a fine line, as in fig. 18, he would have ascertained

the moment of real contact; whereas if he had noticed the time when the circular part of Venus's outline would touch the Sun's, if continued undistorted, he would have caught quite a distinct phase, which we may call apparent contact. As a matter of fact, only the finest possible telescope, and great care and observing skill on the part of the astronomer, would render it possible to notice the moment when such a ligament as is shown in fig. 18 broke or formed. Usually a much coarser ligament only would be noticed; but the observation of the sudden breaking or formation of the ligament would be regarded as an approximate observation of real contact.*

Now, Mr. Stone (after carefully inferring, from the account actually given by the different observers, whether real or apparent contact was noticed) introduced a definite correction,t according to the best estimate we have of the effects of irradiation in enlarging the solar disc and diminishing that of Venus.

By adopting this definite rule, Mr. Stone not only deduced a solar parallax corresponding closely with that obtained by the various other methods described

* In Appendix A will be found some further remarks on this point, in relation to the expectations connected with the approaching transits. It has seemed to me that the view taken by Mr. Stone of the value of those expectations is altogether too despondent. It is quite true, as he points out, that different observers will see a ligament of different breadth-in other words, will catch a different phase; but we need not therefore fear that a corresponding error will be introduced. If each observer does but note the apparent breadth of the ligament, there will be the means of in large part eliminating this cause of error.

It was in this respect that Mr. Stone's work differed from that of his predecessors in the same process of research.

above, but (which is much more important) he brought the observations of the transit into most satisfactory accordance. To quote the words of Admiral Manners' address on presenting to Mr. Stone the Gold Medal of the Royal Astronomical Society- Mr. Stone's investigation includes every complete observation from internal contacts of the transit, and yet, notwithstanding this circumstance, all the observed durations are represented with a degree of accuracy which is, beyond all doubt, within the limits of probable errors of observation. Mr. Stone has effected this object by simple interpretation of the words of the observer, inferring from his language, and from the accompanying circumstances of the case, whether the phenomenon noticed by him referred to an apparent or a real

contact.'

The result thus deduced assigned to the Sun a parallax of 8"-91, with a probable error of 0"03, corresponding to a distance of about 91,730,000 miles, with a probable error of about 300,000 miles. In other words, the Sun's distance, according to this latest, and in many respects most satisfactory determination, is found to lie between about 92,030,000 miles and about 91,430,000 miles. If we assume 8"-9 as, on the whole, the best value for the parallax, implying, as it does, that as yet we have no knowledge of the next decimal figure, we have for the Sun's mean distance 92,000,000 miles; * as we ought not to admit

The very value, be it noted, which Professor Smyth, Astronomer Royal for Scotland, considers to be recorded in the dimensional features

any significant figures beyond the second. Doubtless, after the observations which are to be made on the transits of 1874 and 1882, astronomers will be able to extend the value of the parallax to a second decimal figure, and so there will be three significant figures in the expression for the distance. (See Appendix A.)

It remains to be noticed that the corresponding value of the Sun's diameter is fairly represented by 850,000 miles, nor is anything gained by expressing this diameter, as is so commonly done, with significant figures down to the units' place. Certainly if the true solar parallax is 8"-94000, for instance, then the exact value of the Sun's diameter is 852,908 miles. But when we see that the value of the solar, parallax can only fairly be presented to the first decimal place, or as 8"-9, we cannot pretend to know the Sun's diameter with greater exactness. The limits of error in our estimate of the Sun's distance being probably four or five hundred thousand miles at the least, it must be admitted that the limits of error in our estimate of the Sun's diameter cannot be less than four thousand miles.

The surface of the Sun is equal to four times the area of a circle having this diameter of 850,000 miles, or in round numbers to 2,285,000 millions of miles. His volume is about 1,250,000 times that of the Earth.

of the Great Pyramid. See also his Life and Work at the Great Pyramid, which, though not dealing with this particular feature—or supposed feature-of the pyramid's dimensions, yet goes far to demonstrate that a number of the facts regarded as recent acquisitions of astronomy were known to the architects of that most remarkable erection.

F