250 PAKALLAX with the end in view, that scrupulous care in minute detail, which is essential in the highest class of observation, and it becomes impossible to alter the previously prepared programme in such a case, should circumstances render it desirable to do so; nor does it always happen that distant observatories can be supplied with the necessary instru mental details in sufficient time. In the case of the Victoria and Sappho observations of 1882 the requisite sympathy and care were accorded in a very remarkable degree, but on account of the errors of the planetary tables (discover able only when the observations were begun) the selected stars of comparison were not by any means the most favourable that could have been chosen, and were con sequently not the stars that a single observer would have selected at the time. Hence arises the desirability of a method not requiring co-operation, in which success depends upon a single observer, who may obtain independently by his own observations a complete series of results. In 1857 Airy, in an address to the Koyal Astronomical Society on the methods available for determining the solar parallax during the next twenty -five years, called attention to the favourable opposition of Mars in 1877, and declared his opinion that the best method of finding the solar parallax was to determine at an equatorial station the difference of right ascension of that planet and neighbour ing stars in the evening and early morning, by observing transits of stars and planet across the webs of a well- adjusted rigidly mounted equatorial. The motion of the earth s rotation would transport the observer 6000 or 70UO miles between the evening and morning observations, and the requisite displacement would thus be obtained. In other ^words, the observer would avail himself of the diurnal displacement to determine the parallax of the planet. Of course a very large number of observations would be required, because the observation of a transit over the webs of a telescope is not so exact as the micro- metric comparison of two points. Only one observer availed himself of Airy s suggestion, but a very good series of observations by this method was obtained by Maxwell Hall at the island of Jamaica. The detailed observations are printed in Mem. R. A. ,$ ., vol. xliv. p. 121; the result ing value of the solar parallax is 8"790"-06. In 1874 (in connexion with Lord Lindsay s expedition to Mauritius) Gill, combining the suggestion of Galle as to the employment of a minor planet and Airy s suggestion as to the employment of the diurnal displacement, observed the minor planet Juno, which was at that time favourably situated for the purpose. But instead of employing the method of transits of the planet and stars across spider- webs he used a heliometer, and measured with that instru ment the distance of the planet from the same star in the evening and morning. In order to eliminate the effects of changes in the scale-value, Gill selected stars on opposite sides of the planet, and so arranged his observations as to measure simultaneously the angle between the planet and both comparison stars. That is to say, if the two dis tances in question are called a and b, the measures were ar ranged in the order ,b y b,a or b,a,a,b. Thus any abnormal scale-value of the instrument applicable to the measurement a would be equally applicable to the measurement b. If the places of the comparison stars are thus determined by meridian observations, the scale-value may be derived from the observations themselves with all desirable accur acy, and the effect of chanye in the scale-value (which alone is all-important) be absolutely eliminated. The observations so made at Mauritius showed that the posi tion of the planet Juno relative to two stars of comparison could be so interpolated with a probable error less than -th of a second of arc. A full account of these observa tions, together with a description of the heliometer, is given in the Dunecht Publications, vol ii. Lord Lindsay s yacht, which conveyed the heliometer to Mauritius, unfor tunately did not reach her destination till the most favourable time for making the observations was past; but sufficient observations were obtained to test the method thoroughly and to prove its capabilities. 1 The value of the solar parallax resulting from the observations of Juno at Mauritius was 8"770 "04 In 1877, instead of observing the favourable opposition of Mars of that year by Airy s method, Gill proposed to the Eoyal Astronomical Society to employ a heliometer (kindly lent by Lord Lindsay) to observe the planet in a similar manner to that in which he had observed the minor planet Juno at Mauritius in 1874. The offer was accepted. Gill selected the island of Ascension, and there carried out the necessary observations. The stars of comparison, by the kind and hearty co-operation of astronomers, were observed at thirteen of the principal observatories with meridian instruments, a combination of their results affording standard places of high accuracy. In general the angular distance of the planet was measured both in the evening and morning from each of three surrounding stars. The observed readings of the heliometer were corrected for the effects of refraction and phase, for the errors of division of the scales and of the micrometer screw, and were then converted into arc on an assumed value of one revolution of the micrometer screw (or rather of half an interval of the scale divisions). The tabular apparent distance of the centre of Mars from each star for the instant of each observation was then computed with an assumed approximate value of the solar parallax (8" 80). The calculation of the solar parallax and the elimination of errors of scale-value were then easily effected as follows : Let Aa, AS = the corrections in seconds of arc to be applied to the tabular right ascension and declination respectively to obtain the true right ascension and declination of Mars at the epoch T O . p = the position angle of the planet referred to the star of comparison. S =the approximate mean declination of the star and planet. K = the daily rate of increase of Aa for the epoch T O . K = the daily rate of increase of AS for the epoch T O . T =the Greenwich mean time of observation. n = the number of y^ parts (or the percentage) that the assumed solar parallax must be increased. z =the correction required to be applied to an observed arc of 10000" reduced on the assumed scale-value, the observed distance in seconds of arc Toooo the observed angular distance, computed with the assumed scale-value. C =the calculated or tabular distance computed with the assumed value of the solar parallax. Then each observation furnishes an equation of condition of the following form / Aa +/"A5 +f "n - vz = (0 - C) -/ (T - T O )K -/"(T - T V; where f = sin p cos 8 /" = CQS;J ,, /parallax in R. A. , /parallax in declination = ( ioo ) f + ( ~Too~ -) J the parallaxes in/ " being in seconds of arc. The equations resulting from each group of observations are then combined, care being taken to combine together in one group such observations only as have been made nearly simultaneously and where the value of z may therefore be assumed to be the same. The combination of a group of evening with a group of morning observations (in which the term representing the error of scale- value must then be represented by z and z ) thus affords six 1 A more complete test has since been furnished by observations for stellar parallax, to which reference will afterwards be made.
