ON THE APPLICATION OF PHOTOGRAPHY AS A MEANS OF DETERMINING THE SOLAR PARALLAX Ir is impossible to read Dr. De la Rue's account of the results of careful measurement applied to photographs of the solar eclipses in 1860 and 1868 without recognising that we have in photography, as applied to the approaching Transit of Venus, one of the most powerful available means of determining the Sun's distance. Within the last few years, solar photography has made a progress which is very promising in regard to the future achievements of the science as an aid to exact astronomy. So that doubtless, in 1874, astronomers will apply photographic methods to the transit of that year, with even greater success than we should now be prepared to anticipate. It has therefore seemed to me that the photographic observation of the coming transit merits at least as full a preliminary inquiry as either Halley's or Delisle's method of direct observation. The result of an inquiry directed to this end has led me to the conclusion that photographers of the approaching transit should adopt for their guidance considerations somewhat different from those which have hitherto been chiefly attended to. It is undoubtedly true, as Dr. De la Rue has pointed out, that the photographer of the transit can readily take a large number of pictures, and by combining these, can ascertain with great accuracy the path of Venus across the solar disc. And by comparing the paths thus deduced for different stations a satisfactory estimate can be formed of the solar parallax. I do not wish to suggest any departure from this course of procedure. On the other hand, it is undoubtedly true, as Major Tennant has remarked, that the greatest effect of parallax will be obtained, for any two stations, when both stations, the Earth's centre, and the centre of Venus, are in one and the same plane. So far as those two stations are concerned, his remark is just, that it is the position of Venus at the instant when the stations are so situated, and not the nearest approach of Venus to the Sun's centre, which should be compared. And further, Dr. De la Rue's comment on this, to the effect that his method in reality includes Major Tennant's, is also correct. In fact, there can be no doubt that the position of Venus at the particular instant referred to by Major Tennant can be far more exactly ascertained by a reference to the complete path of Venus for each station than from any attempt to secure nearly simultaneous photographic records at stations far removed from each other. But it appears to me that the method I am about to suggest, according to which the whole question will be reduced to the determination of a parallactic displacement of Venus on a line through the centre of the Sun's disc, is the one by which the fullest assistance will be obtained from photography; while a source of error, which has not hitherto been specially considered, will be practically eliminated. It must be remembered that in the comparison of photographic records, whether for the determination of the path of Venus across the Sun's disc at a particular station, or for the comparison either of Venus's apparent position or of her path as seen from two different stations, the accuracy of the results will depend in part on the certainty with which two or more pictures may be brought into comparison by means of a fiducial line or set of lines. It seems certain that no method can be devised by which all chance of error from this source can be eliminated. The great point would, therefore, seem to be to render its effect as small as possible. Now let us consider for a moment Major Tennant's proposition, FIG. 3. a b A as giving a convenient illustration of the effects of any error either in the position of the fiducial lines, or in bringing those belonging to two pictures into exact correspondence. Let fig. 3 represent the result of a comparison between two photographs of the Sun. A B and C D are fiducial cross-lines common to both pictures; a is the centre of Venus for one picture, b is her centre for the other; and on the exact measurement of a b depends the determination of the Sun's parallax, so far at least as these two pictures are concerned. Now it is very obvious that if the lines A B, C D, for one picture, have not been B D brought into perfect correspondence with those belonging to the other, the distance a b will be correspondingly affected. In fact, it would appear that if the usual methods for making the correspondence as exact as possible are followed, almost as large an error would be introduced through this cause alone as by errors in the measurement of a b, since the two processes-the measurement of a b and the adjustment of the sets of cross-lines-depend on the very same circumstance, the nicety, namely, with which the eye and the judgment can estimate minute quantities of about the same relative dimensions. But now, if a and b, in place of having the position shown in fig. 3, were situated as in fig. 4, it is clear that the distance ab will not be appreciably affected by any small error in the adjustment of the fiducial lines. Fig. 4. The object, therefore, which it seems most desirable to secure is that Venus, as seen from two different stations at a particular instant, should have a relative parallactic displacement towards the Sun's centre, or as nearly towards the Sun's centre as possible. This amounts to adding to Major Tennant's conditions this further one, that the Sun's centre should be in the same plane with the two stations or rather to making this condition a substitute for that one which requires that the Earth's centre should be in the same plane with the two stations. For as a rule we must not expect to be able to secure that two convenient stations on the Earth, as well as the centres of the Earth, Venus, and the Sun, should be in the same plane. Dr. De la Rue's remark that by taking a series of pictures the position of Venus may be ascertained at any moment is in reality quite as applicable to my suggestion as to Major Tennant's. In fact, were it not, we might despair of securing the desired object, since we have no reason for believing that astronomers are so certain as to the exact progress of the transit, that the conditions could be secured by anticipatory instructions: whereas by applying Dr. De la Rue's method it will be possible, after the transit is past, to determine with any desired degree of accuracy the position of Venus at the proper instant. And further, it is very obvious that no error in the placing of the fiducial lines for pictures taken at the same stations can much affect the accuracy of the result, since the comparison of successive pictures, taken at the same station, does not directly involve the element of the solar parallax, as when we have to compare two pictures or paths determined at different stations. The object, then, of the present paper and the accompanying chart is to determine what stations are most suitable for applying photography to the transit of 1874, on the principles above enumerated. I think the drawing will be found, however, to be also an instructive illustration of the whole character of the transit. In the last essay but one, I showed how all the chief elements of the transit could be deduced by considering the motion of Venus relatively to a pair of cones, each enveloping the Sun and the Earth, but one having its vertex outside the Earth, the other having its vertex between the Earth and the Sun. The remaining positions of the Earth in fig. 5, corresponding to the 11 pictures 3-13 in the illustrative plate, are those occupied by the Earth at successive intervals of 15 minutes, the picture numbered 8 corresponding to the position occupied by the Earth at 16h 6m 31 G.M.T., on December 28, 1874, when Venus makes her nearest approach to the centre of the Sun's disc. Now if we look at figs. 1 and 2, and consider what they represent, we shall see that fig. 2 may be looked upon as exhibiting an inverted picture of the Sun's disc and the transit of Venus's centre across it: we see, in fact, that the apparent position occupied at any instant by any point on the Earth's surface in fig. 2, corresponds exactly to the position occupied by Venus upon the Sun's disc, as supposed to be seen from that point of the Earth's surface at the instant in question. We have only to invert fig. 2, and look at it from behind, to see what sort of path Venus would seem to traverse upon the Sun's disc, either with reference to the Earth's centre, or to any point of the Earth's surface supposed to be properly depicted upon the small discs 1-15 in fig. 10. It follows, therefore, that if we want to determine two stations at which at any instant Venus would appear to have a relative parallactic displacement towards the Sun's centre, all that required is that we select two stations which are on the same radial line from the common centre of the circular sections in fig. 10. The positions of those radial lines which cross the Earth's track c d are exhibited in plate XVII. It will be understood, of course, that the three rows of figures belong in reality to a single row, the numbering of the successive pictures of the Earth indicating the |