277 



PARALLAX OF THE FIXED STARS. 



PARALLELOGRAM. 



273 



centre. The nearer the star s U to the ecliptic, the more excentric this 

 ellipse will be,* but in all cases there is a diameter of the earth's 

 orbit, namely, that which is perpendicular to the line joining ss, 

 which is seen in its true proportions without foreshortening. 



Since Roemer and Bradley, many astronomers have sought for 

 parallax by observation in right ascension and declination. Bessel 

 could find no evidence of such an effect in Bradley 's transit or zenith 

 distance observations. Piazzi, from meridian zenith observations, 

 concluded that Sirius had a parallax of 4" and Procyon one of 5"'7 ; 

 Calandrelli found a parallax of 4"'4 in a Lyne. But the most per- 

 gevering and accurate observations for deducing the value of parallax 

 from meridian observations were prosecuted by Dr. Brinkley at Dublin 

 with an 8-foot circle by Ramsden, and by Pond at Greenwich with 

 the 6-foot mural-circle of Troughton. Dr. Briukley conceived that 

 he had established without doubt a sensible parallax in a Lyric, a 

 Cygni, and a Aquilao, while Pond maintained that no sensible parallax 

 was shown in any of those stars, from observations in declination and 

 in right ascension. He further corroborated this result by comparing 

 two stars, a Cygni and j3 Aurigje, which have nearly the same declina- 

 tion and opposite right ascension, with a fixed tube. This controversy 

 continued for several years, and though there can be no doubt now 

 that Dr. Brinkley was mistaken, and that Pond was right in his con- 

 clusions, there is a good deal of interest attached to the discussion. 

 Dr. Brinkley's last memoir is in the ' Transactions of the Royal Irish 

 Academy,' vol. xiv. Mr. Pond's paper on the parallax of a Lyra will 

 be found in the ' Phil. Trans.,' 1823, part i., p. 53. 



Sir William Herschel first pointed out the mode of detecting 

 parallax which affords a probability of success, namely, that which 

 depends upon the measurement of double stars. In his paper, ' Phil. 

 Trans.,' 1782, part i. p. 82, he showed that if the stars which compose 

 a double star be at different distances from the earth, which was at 

 that tune supposed to be the chief cause of differences in magnitude, 

 they must be differently affected by parallax, and therefore that then- 

 apparent distance from each other will be altered by a change of 

 position in the spectator. Now as the apparent distance of two 

 neighbouring stars can be measured with great accuracy ,t the problem 

 dlax is thus reduced to that of finding a double star in which a 

 variation of distance is observable, and following the law which the 

 earth's change of place requires. It was hi this inquiry that Sir 

 William Herschel discovered that very many double stars have a 

 relative motion both in distance and angular position, which proves 

 them to be a connected system, and that unexpected result, which he 

 prosecuted with all his ardour and genius, seems to have led him from 

 the investigation of parallax into his profound and original researches. 

 Sir John Herschel (' Phil. Trans.,' 1826, part iii., p. 266,) extended his 

 father's proposal for the discovery of parallax by showing that the 

 variation produced by parallax in the angle of position of two stars is 

 a more sensible phenomenon and one more easily measured than the 

 variation in distance; and in the ' Phil. Trans.,' 1827, p. 126, he pub- 

 lished a considerable list of stars suitable for his research, with the 

 times of year when the observations would show the greatest effect of 

 parallax. 



It has been shown that the earth's change of place in its orbit causes 

 each star to have an apparent motion in an ellipse of which the major 

 axis is parallel to the ecliptic and equal to the diameter of the earth's 

 orbit as seen at the distance of the star, and the minor axis equal to 

 the major x sine *'s latitude. If then the stars be a connected system, 

 and comparatively near each other, the stars will appear to describe 

 two equal and similar elllipses, and the line joining their apparent 

 places will be equal and parallel to the line joining their true positions. 

 It is therefore in vain to look for any effect of parallax in micro- 

 metrical or relative measures of distance and position in a connected 

 system. But if one of the stars be much farther from us than the 

 other, suppose it ten times farther off, then the apparent ellipse! will 

 continue to be similar, and similarly described, only the dimensions 

 of that described by the more distant star will be l-10th of that 

 described by the nearer star, which comes to the same thing as supposing 

 the more distant star to be fixed, and the nearer star to describe round 

 its true place an ellipse of 6-10ths the actual dimensions. If with Sir 

 William Herschel we measure the apparent dittanea of the two stars, 

 those are best suited to the purpose in which the line joining the stars 

 is in the direction of the major axis of the parallactic ellipse, that is, is 

 parallel to the ecliptic. If we proceed by measures of position, as 

 recommended by Sir .fohn Herschel, those stars are most favourable in 

 which the line joining the two stars is perpendicular to the ecliptic. 

 It is scarcely necessary to say that these conditions are not rigorous, 

 and that stars tolerably near the pole of the ecliptic are equally well 

 suited to either kind of measure, as the apparent ellipse is then almost 

 a circle. Since the application of clock-work to large equatoriak, we 

 think that the measures of the distance of double stars may be made 

 nearly as accurately, and even more easily, than angles of position ; and 

 further, that any telescopes which have yet been constructed may be 

 mounted equatorially and carried by clock-work. Most of the close 



The aerai-axis major l the earth', radian vector, and the semi-aiia minor 

 Is the etrlh'a radius rector x in of ' latitude. 



t It la perhaps more. eaijr to determine the ditnce of a double *Ur to 0-1 

 than to fix an abtolnt* place to 1"-0. t 



double stars are probably connected, and are therefore unfit for the 

 detection of parallax. 



In the last-named property, that of measuring considerable angles, 

 the heliometer is unrivalled, and thus we see its especial use in the 

 researches connected with parallax. It is almost hopeless to attack the 

 problem by any other means at present known ; and the divided eye- 

 piece', which is found very useful for small measures of distance,' is, 

 like the wire micrometer, limited to this object. 



For his researches on parallax, Bessel selected the double star 61 

 Cygni, which is a double star having a large proper motion. This 

 property leads us naturally to guess that it is a comparatively near 

 star, as its actual velocity would otherwise be enormously large. Two 

 stars a and b were chosen, b in the direction joining the component 

 stars of 61 Cygni, and a at right angles to this direction. The obser- 

 vations of b are made by bringing it into the middle of the two stars, 

 those of a by placing it in the same line with the two stars. As the 

 two stars of 61 Cygni are nearly of the same brightness, the observation 

 is exceedingly accurate. These measurements were continued for 

 fourteen months with very little interruption. The stars a and b 

 are so far removed from 61 Cygni as to render any connection highly 

 improbable. Variations were found in these distances, which, being 

 compared with the effect which parallax would produce, are exactly 

 accounted for ; therefore this variation is produced by parallax, for it 

 can be shown that any other known cause of disturbance has been got 

 rid of by the skill of the observer. The result is that the parallax of 

 61 Cygni is 0"'314 ; whence the distance of 61 Cygui is 658,000 times 

 the distance of the earth from the sun, and light from the star is 10.J 

 years hi reaching us. 



This result has received a most satisfactory confirmation from tho 

 researches of Professor Peters, and those of the late Mr. Johnson, 

 director of the Radcliffe Observatory, Oxford. The value deduced by 

 the former of these astronomers, namely, 0"'849, was founded on 

 observations made by himself with a vertical circle at the Imperial 

 Observatory of Pulkowa. In 1852-3 Mr. Johnson measured the dis- 

 tance of the star from two other small stars in its vicinity with the 

 Oxford heliometer, and obtained 0"'384 for the value of its parallax. 



The parallax of a Lyras, was determined by M. Struve. in the year 

 1835. The method employed by him consisted in measuring with a wire 

 micrometer the distance of the star from another bright star in its 

 vicinity. In this way he found the parallax of a Lyra to be 0"'261. 

 The parallax of this star has also been investigated by Professor Peters, 

 M. Utto Struve, and Mr. Johnson. M. Otto Struve, by combining his 

 own value of the parallax of the star with the values obtained by his 

 father and Professor Peters, obtained 0"'1549 for the definitive result. 

 Mr. Johnson obtained very imperfect evidence hi favour of a sensible 

 parallax of the star. 



The late Professor Henderson, of Edinburgh, determined the parallax 

 of the bright star a Centauri, from observations made by himself with 

 the mural circle at the Cape of Good Hope in the years 1832-3. In 

 this case, the resulting parallax was large, amounting to 1 "'16. Mr. 

 Maclear, from observations made at the Cape in the years 1839-40, 

 found the parallax of the same star to be 0"'9128 ; and from subse- 

 quent observations extending down to 1848, he deduced 0"'9187 as 

 the most probable value of the parallax. The parallaxes of several 

 other stars have been investigated in recent tunes, but no trust- 

 worthy results have yet been arrived at. 



PARALLAX, in practical optics, is the longitudinal misplacement 

 of the wires in a telescope or microscope. If the wires are not at a 

 proper distance from the object-glass, the image of the object is 

 not seen distinctly when the wires are so seen. On giving a little 

 motion to the eye, the object will seem to move upon the wires. If it 

 move in the direction of the eye, the cell carrying the wires must be 

 pushed in, and rice rend. There are means for this adjustment in all 

 instruments which require it, and it is a point to which the attention 

 of observers should be very carefully directed. 



PARALLEL. [PARALLELS.] 



PARALLEL PRKSSUiKS. [PRESSURE.] 



PARALLELOGRAM (wapaXATjAii-ypo^a, parallel-drawn figure) is 

 the mathematical term for a four-sided figure of which the opposite 

 sides are parallel. Such a figure may be obtained from any four-sided 

 figure' by bisecting the four sides and joining the adjacent bisecting 

 points. When all the angles of a parallelogram are equal, they are 

 therefore right angles, and the figure is called a RECTANGLE. When 

 the sides are also equal, the figure is a SQUARE : matters of more 

 historical interest are connected with either of these terms than 

 with the generic term parallelogram. Referring therefore to those 

 articles, we shall here give the principal properties of parallelograms 

 in general. 



1. The opposite sides are equal, as AC and BD. 



2. The opponite angles are equal, as Arn and ABP. imd adjdOM 



