PARALLAX 249 error of the complete measurements of an average plate amounting to 0" 5. But the difficulties of dealing with systematic errors are enor mously increased when a secondary magnifier is employed, be cause it is theoretically impossible with the present optical glass (employing spherical curves) to construct a perfect secondary magnifier in which the scale value should be absolutely the same in every part of the field ; still less is it possible, when the attempt is made, to combine the visual and photographic rays in the same focus ; hence every photoheliograph of this construction must be separately studied for distortion of the image. The results of actual trial prove that the distortion is even greater than was expected, and is besides not the same in each radius, and the latter error may be produced by a very small error of centring in the lenses which compose the secondary magnifier. The investigation of such errors with the required accuracy would be a laborious and at best an unsatisfactory operation, and is rendered practically impossible by the fact that, whenever the instrument is turned upon the sun, the object-glass becomes heated, its focal length changed, and the optical relation of the secondary magnifier to the image in the principal focus of the object-glass changed also. For these reasons the photographic observations in which second ary magnifiers were employed might be expected to prove a failure, and this expectation has been confirmed by the result of experience. The observation of the transit of Venus on a large scale of national expenditure was certainly justified in 1761 and 1769. In those days there were no refined means of measuring angles with high accuracy, and the employment of the motion of Venus and a time-scale of measurement was the best available method of determining the solar parallax. But since 1820 the art of measurement has so advanced, and such refined instruments and methods have been thus introduced, that it may be a matter of some .surprise and question to future generations of astronomers why so much labour and money were expended upon so imperfect a method in 1874 and 1882. The justification of these expeditions must be found, not in the reliability of the value of the solar parallax determined by them, but in the impulse given to the construction of instruments, the awakening of a widespread interest in astronomy, the stimulus to invention of new methods of research, and the accurate determination of the latitudes and longitudes of a large number of important and previously undetermined stations on the earth s surface. If an opposition of Mars occurs when that planet is near perihelion and the earth near aphelion the planet is then about one-third of the sun s distance from the earth. When these conditions are nearly realized the opportunity is a favourable one for determining the solar parallax. On 1672, October 1, the star ij/ Aquarii was occulted by Mars. Estimations of the distance of the planet from the star were made at well-observed instants of time by Richer, Picard, and Homer, as already noticed, and from these observations the first approximate determination of the solar parallax was made by Cassini, viz., 9" 5. The method of observing Mars that has been most largely employed consists in observing the apparent declina tion of the planet by means of the transit circle at ob servatories both in the northern and in the southern hemi sphere. To increase the accuracy of the result, the same stars near the planet are observed at the various observa tories, so that the method is reduced to measuring the difference of declination between the planet and neigh bouring stars. The effects of periodic error in the gradua tion of the circles, of flexure of the instruments, and of abnormal refraction are thus nearly eliminated, and there remain only the systematic errors which may be supposed to arise from the difference of the habit of the observers in bisecting a star and a planet. To some extent these errors could be eliminated by the use of a reversing prism applied in the place of a sun-shade between the eyepiece and the observer s eye. By the use of such a prism the motion of the spider-web and the limbs of the planet can be reversed with respect to the vertical, and such errors as depend on a different habit of bisecting a similar apparent upper and lower limb would be thus eliminated. But on account of the chromatic dispersion of the atmosphere the lower limb of the planet is coloured red and the upper limb violet ; and in the illuminated field of the telescope it is probable that the observer has a tendency to cut with his spider-web more deeply into the feeble violet limb than into the more glaring red limb. The effect of his so doing would be to increase the value of the resulting parallax, and it seems not improbable that from this cause a larger value of the parallax has been obtained by this than by other methods. The following are the most important series of observa tions, and their discussion by this method : Winnecke (Ast. Nachrichten, lix. col. 261), opposition of Mars 1862 ; from observations at Pulkowa and Cape of Good Hope 8 90 Newcomb (Washington Observations, 1865, Appendix II.); from all meridian observations of Mars in 1862 8 85 Eastman (Wash. Obs., 1877, Appendix III.); from meridian observations of Mars at six observatories in 1877 8 95 Stone, Monthly Notices, xlii. p. 300 ; including observations rejected by Eastman 8 95 In 1872 (Ast. Nach., No. 1897) Dr Galle of Breslau proposed a method of determining the solar parallax which appears to be the foundation of the method of the future, viz., to measure, by means of the equatorial, the difference of declination between selected stars and a minor planet, or rather to interpolate the declination of a minor planet relative to two stars of comparison. A minor planet presents precisely the appearance of a star, and it is impossible to conceive any personality which can affect the observation of such a planet and a star. The interpolation of the planet s declination relative to two including star- declinations (i.e., measurement from stars nearly equally north and south of the planet) entirely eliminates errors due to error of the adopted arc-value of the micrometer screw. It is true that in the case of minor planets the parallax factor can hardly exceed 1^, whilst in the case of Mars that factor may be 3 ; but their disks present objects which are capable of being observed with quite two and a half times the accuracy of Mars. Hence the condi tions of accidental accuracy are equalized for a single opposition, whilst the advantages of systematic accuracy are entirely in favour of the minor planets. Moreover, the opportunities offered by favourable oppositions of minor planets are much more frequent than in the case of Mars. The opposition of the minor planet Flora in 1874 was observed, at the request of Dr Galle, by a considerable number of observers in both northern and southern hemi spheres, but unfortunately only in very few cases with the precaution, care, and perfection of instrumental equipment necessary. In 1882 the minor planets Victoria and Sappho were similarly observed at the request of Gill. The work was taken up by a number of astronomers in both hemi spheres, in a much more complete and systematic manner, with better instrumental means, and with the benefit of former experience. The results have not yet been reduced, but it is believed they will afford a valuable contribution to the problem in question. The results of Dr Galle s discussion of the observations of Flora in 1874 l give for the solar parallax 8" S70"-042 ; but the same results when the relative weights are assigned in a more legitimate manner lead to the value 8" 820"-06. But in any plan requiring numerous and widely spread observers it is very difficult to secure that entire sympathy 1 Ucber eine Bestimmung der Sonnen Parallaxe cms correspond iren den Beobachtungen des Planetcn Flora in October und November 1873 Breslau, 1S75. XVIII. 72
