248 sun and Venus, if all the telescopes were alike, if all the telescopes were in perfect focal adjustment, and if the atmo spheric conditions of definition at all the stations were per fect or identical. But if these conditions are not realized (and they cannot be realized in practice) the same appar ent phenomena will not represent corresponding phases ; and, further, the observers at different stations use such different language to express what they saw that it becomes impossible to select even apparent corresponding phases with any certainty. The value of the solar parallax deduced from a series of observations of the contacts of Venus with the sun s limb will therefore entirely depend upon the interpretation put upon the language of the various observers. The result will besides be systematically affected if the state of atmospheric definition is systematically different in the opposite stations. It is thus not surprising that very different results have been arrived at by different astronomers from different transits, and even from different discussions of the same observations of the same transit. Laplace, Mecluinique Celeste transits of 1761 and 1769, 8 81 Kncke, Entfcrnung dcr Somic, p. 108 ,, ,, ,, 8 58 Stone, Mon. Notices R. A. S., vol. xxviii. p. 255. ..transit of 1769, 8 91 Powalky, Ast. Naehrichtcn, Ixxvi. col. 161 ,, 1769,879 Airy, Monthly Notices, vol. xxxviii. p. 16 ,, 1874, 876 Stone, Monthly Notices, vol. xxxviii. p. 294.... ,, 1874, 8 88 Tupnian, Monthly Notices, vol. xxxviii. p. 455. ,, 1874, 8 85 Besides observing the contacts, another method was employed by the Germans, the Russians, the Dutch, by Lord Lindsay s expe dition at the transit of Venus in 1874, and by the Germans in 1882, viz., the heliometric method. This consists in observing with the heliometer (see MICROMETER, vol. xvi. pp. 252-254) the distance of Venus from opposite limbs of the sun along known position-angles nearly in the line of greatest and least distance of Venus from the -sun s limb. The method possesses many apparent advantages, because it affords the opportunity of multiplying the observations and of eliminating many sources of error. At first sight it seems as if the method is free from the necessity for any accurate determination of the scale-value of the instrument, because, if measures are made from opposite limbs of the sun, the sun s diameter may be taken as the standard for all observers, and the place of the planet may be interpolated relatively to the oppo site limbs. Unfortunately it happens that there is a very marked difference in observing the sun s diameter due both to instrument and observer. Thus two observers with different instruments, who have compared scale-value by a number of pairs of stars, or zones of stars, will measure sun-diameters with a marked constant difference. If the sun s diameter is assumed to be constant, it, in fact, determines the scale-value ; hence the distance of centres measured by the two observers will differ by the proportionate part - x Ad, where s is the distance of centres, d the true diameter, and A l the difference of diameter as measured by the two observers. Thus it is only when 5 = (that is, when the planet is near the centre of the sun) that this method can be used, a condition that does not exist in practice. In the case of the transit of Venus fully one-third of the whole of this personality would enter into the result by this method of reduction. For rigid reduction therefore it is absolutely necessary to have a rigid determination of scale-value in seconds of arc. Unfortunately this value, when determined for any uniform instrumental condition of temperature, is liable to change, because, in observations of the sun, difference of temperature be tween the tube, the object-glass, and the scale of the instrument is produced, and the focal adjustment is also disturbed. The scale- value depends on the relation of the focal length of the object- glass to the length of a part of the scale, and is besides affected by abnormal focal adjustment of the eyepiece. Drs Auwers and Winnecke adopted a very complete scheme for determining the scale-value at any instant. 1. The scale-value was determined for a uniform condition of the temperature of the instrument by measuring zones of stars whose places were rigidly determined by meridian observations ; and by the same means the temperature coefficient of the instrument was determined for different temperatures, the various parts of the instrument being assumed of a uniform temperature in observations of stars by night. 2. The effect of a displacement of focus was determined by measuring the sun s diameter and distances of pairs of stars with different positions of the focal adjustment. 3. The focal point was determined during sun-observations by adjusting the focus on a telescope fixed in a specially prepared chamber, where its temperature would change very slowly, and the temperature of the scale (and hence its length) were measured by a metallic thermometer ; hence the change of the proportion of the scale-length to the focal length became known. In Lord Lindsay s expedition similar precautions were employed, excepting that in the last case an attempt was made to determine the temperature of the tube by thermometers and that of the object- glass by a thermo-pile, and the position of the focal point was cal culated from these data. The uncertainties of all these operations are considerable, and, though from the extraordinary labour and care bestowed upon the determination of the necessary corrections by the German astro nomers a fairly reliable result may be arrived at, it is certain that the method of determining the solar parallax from heliometric observation of transits of Venus can now be surpassed by methods more direct, more reliable, and at the same time less laborious and costly. If photographs can be obtained during a transit in which the limbs of the sun and Venus are sufficiently well-defined, the distance of the centres of the sun and planet can be determined (as in the heliometer method) provided only that the pictures are affected by no systematic errors. That this latter condition may be fulfilled the following are the essential conditions. 1. The picture must be formed on the photographic plate without distortion, or, if it is affected by distortion, that distortion must be ascertained and allowed for. 2. No change must take place in the process of developing and fixing the picture, or, if such change is possible, means must be provided for its detection and elimination. 3. The angular value of one inch on the plate must be accurately known, so as to convert measured distances into arc for the same reasons as in the heliometer method. It is necessary to employ an image of considerable size, because otherwise the particles of collodion, if magnified so much as to permit measurement of the requisite accuracy, give an irregularity to the limbs that is fatal to accurate estimation. Thus it becomes necessary either to employ a lens of very considerable focal length (40 feet was generally adopted), or to introduce a secondary lens to magnify the image formed in the primary focus. The first of these methods was employed by the Americans, by the French, and in Lord Lindsay s expedition at the transit of 1874, the second by the British, German, Russian, and Dutch expeditions. The use of an object-glass of long focus renders mounting of the lens in the usual manner, though not a practical impossibility, yet at least a matter of extreme inconvenience. Accordingly, where lenses of long focus were employed, the telescope was mounted in a horizontal position, and the sun s rays were reflected by a plane mirror in the direction of the tube s length. It is not easy to con ceive that any sensible distortion in the image can be produced by a lens of such long focus even if only of mediocre quality of figure ; indeed the method may be assumed free from any such error ; but it is undoubtedly exposed to all the errors of distortion which may be produced by the plane. From the perfection now attained in the construction of optical planes, and the means which exist for testing them, the errors due to this cause may also probably be safely neglected, except in so far as the figure of the plane is dis torted by the heat of the sun, and it is not impossible that some sources of systematic error may be thus created. To determine the angular value of one inch (or other unit of length) on the photographic plate, it is only necessary to measure the distance of the plate from the posterior surface of the object- glass, and then to determine the distance of the optical centre of the lens from that surface ; the sum of these two distances is the radius of which lines on the surface of the plate (reckoned from the centre of the plate) are tangents. The French adopted the daguerrotype method of photography, in which it is impossible to imagine any errors due to contraction of the photographic film, as in the collodion process, because the picture is virtually a portion of the silver plate on which it is taken. But in adopting this process the advantage of measuring the photo graphs by transmitted light was lost ; and it is a practical question, which experience has not yet decided, whether the loss or the gain is the greater. The Americans, and Lord Lindsay in 1874, using the collodion process, took the precaution to provide means for the detection of possible contraction of the film during development of the picture or drying of the film. This was done by placing the sensitive plate near to or in contact with a reticule ruled on glass near the primary focus ; this reticule was thus photographed simultaneously with each photograph of the sun ; hence any change produced during the development would cause a similar change in the relative positions of the images of the ruled lines on the developed plate. As a matter of fact the American astronomers have found fairly reliable results from their photographic operations, but the accuracy arrived at is by no means very considerable, the probable
