PARALLAX. 



PARALLAX OP THE FIXED STARS. 



m 



U equal to the time in which Venus 



i from v to V. or in which she de*cribes the angle ESr round the 

 m with her r;f,r angular motion. But the angle ESr i* twice the 

 mat'* hurtMUl parallax ; hence, ainre the time Upsed between the 

 Ingres* at the two place, is known from observation and from the 

 dUhreno* of longitude*, aod UM hourly angular motiont of Venus and 

 UM earth round the eun are known from the table*, and consequently 

 UM diflen*>c*> of the** motion*, the borixontal parallax of the tun can 

 be found. It i* evident that a* the ingre** i* accelerated at B and 

 retarded at t . so the egreo will be accelerated at and retarded at t, 

 Venn* then occupying the ptltiuiH T", r"'. 



Let n* suppoM further that a apecUtor who saw the ingress at E, 

 and therefor* a* early a* possible, should by the rotation of the earth 

 be ovried to t. where be would *ee the egrees M late a* poasible, while 

 the siMiUKu of the late ingiMi at r ia in like manner carried to E, 

 rter* he MM the earliest agre** * In the first case the time of the 

 transit ia tncraawd a* much a* poasible by the effect of parallax, and in 

 tb Utter cai* it i* equally diminished. Now suppose the parallax of 

 UM *un to have a certain value, the parallax of Venus and the effect of 

 Ump parallaxe* in increasing or diminishing the duration of the transit 

 for any spooned place* of observation can be computed. Hence when 

 the duration* are really observed, the differences between the observed 

 duration and that which would have been observed if the spectator had 

 been placed at the centre of the earth will fix the actual amount of the 

 purify The especial excellence of this method consist* in the 

 niovtyr with which a particular phenomenon can be observed, namely, 

 UM first streak of light which is seen after the interior contact at 

 ingre** and the last streak before the interior contact at egress. Two 

 point* on the earth are chosen where the beginning "and end axe both 

 viable, in one of which the duration is shortened as much a; possible, 

 while it is increased in the other. Every observation of either ingress 

 or egre** can in fact be used for determining the parallax, provided the 

 longitude of the place of observation and the time be sufficiently well 

 known; but where both the ingress and egress ore observed, the 

 duration alone require* care. Transits of Venus were observed in 1761 

 aod 1769, and the parallax of the sun deduced by various geometers. 

 (Lagrange, ' Memoira* de Berlin,' 1736 ; Encke, ' Der Venus Durch- 

 gang.' Gotha, 1824.) The next transits will take place in 1874 

 and 1882. 



In the preceding part of this article the methods of determining the 

 parallaxes, and consequently the distances of the bodies composing our 

 syatem. have been described, and we will now point out the way in 

 which this knowledge is applied. Every observation of the sun, moon, 

 or planet* i* affected by parallax and must be corrected for this pre- 

 vious to further calculation. All celestial bodies are apparently 

 elm stud by the refraction of the atmosphere, and those of our system 

 are depressed by the effect of parallax. In nautical works there are 

 table* for reducing the observed altitude of any heavenly body to ite 

 tnte altitude, namely, to that which it would have if there were no 

 atmosphere and the spectator were at the earth's centre. In most of 

 the problems from which the longitude is determined astronomically, 

 in solar eclipse*, occupations, and lunar distances the great difficulty 

 and trouble is in computing the effect produced by the moon's parallax. 

 Astronomers have invented convenient formula; for this purpose, 

 according to the planes to which the bodies arc referred. Thus in 

 working out an occultation, the moon may be referred to the plane 

 of the Aorison, when the effects of parallax in altitude, and, if great 

 accuracy be required, in azimuth, must be computed ; or again, to the 

 eo,m*octi>il, when the parallax in right ascension and declination is to 

 be calculated ; or finally, to the ecliptic, when the parallaxes in longi- 

 tude and latitude must be found. The rules for these computations 

 are given in treatise* on Astronomy. 



The mean equatorial horizontal parallax of the sun, according to 

 Encke, = 8-6776'. It* true value for every ten days is given in the 

 1 Naut. Alman.' at the end of the ephemeris of the sun and moon. 

 The equatorial horizontal parallax of the moon for mean noon and 

 midnight is at page III. of each month, and the parallaxes of the 

 planeU are in the last column of the planetary meridian ephemeris. 



On* effect of parallax is, that the moon appears under a larger angle 

 when near the zenith than when near the horizon. This is contrary 

 to common opinion, but may be very easily proved experimentally, by 

 any one who can handle a sextant with ordinary cure. When the 

 noon i* in the zenith, the horizontal diameter may be auymrntcd from 

 SO'' to 40''. There U a table for this augmentation of the moon's 

 swnidiameter in most nautical works. 



OMUtoitf of PanUajc (la oon*faM de la paraJUnxe) is the angle 



under which the earth's radius would be seen at the centre of the 



moon when she ia at her mean distance. The radius chosen by La 



ho* i* that which belong* to a latitude of which the square of the 



Th* explanation U only Intended to exhibit the priiulptt on which this 

 very Important problem oVpend.. 



t Tab okMiisliu* MUM not to bate ton quite a* definite aa was expected 



toll* somfuate* was remarked at the point of Interior contact before th 



f the thread of light, a sort of black drop (gntta nlgra). Mr. Ball 



*w eertral black thread* connecting the ede of the sun and moon during t i 



formation and breaking up ..f the annnlns In the ecllp** of May 15, 1938 ('Mem 



A*. Bo* ,' ToL X. p. 1), which atemi to be a phenomenon of tbe Sam* kind. 



PARALLAX, ANNUAL, is the angle under which the earth's orbit 

 i* Men by a superior planet. 



PARALLAX OK THE FIXED STARS. When Copernicus pro- 

 posed hi* hypothec!* of tbe earth's motion, one striking <utnmmical 

 objection was, that the enormous displacement of the spectator's place 

 which hi* system supposed was not supported by a corresponding 

 change in the positions of the fixed stars. Every improvement in 

 instruments, in the art of observing, or in the science of computation, 

 seemed to increase the distance of the sun, and consequently the orbit 

 of the earth, and still no sidereal change could be detected. Hence, 

 until the discoveries of Newton brought forward physical arguments, 

 i' which, however, the collusiveness i* not immediately visible, the 

 'opcniican hypothesis was embraced on the grounds of its symmetry 

 and simplicity rather than on demonstration. Opponents might 

 always ask for the erperimentnm cntcit, the effects of the earth's 

 motion in the apparent displacement of the fixed stars, and this could 

 not be supplied. 



Many attempts were, however, made. Hooke erected a zenith sector 

 .t his chambers in Gresham College, and made some incomplete obser- 

 vations in which he fancied he could trace the effects of parallax, 

 'lamsteed found variations in the north polar distances of fixed stars, 

 which he attributed to parallax, although, aa was shown by Casaini and 

 ioemer, this would have produced results with a totally different law. 

 loemer himself, after many efforts to deduce parallax from observa- 

 iuns in declination, renounced the attempt, on account, as he says, of 

 ' a certain variation in the declinations of stars which can neither be 

 attributed to refractions nor parallaxes," and pursued his investigation 

 >y observations in right ascension, in which it seems he believed him- 

 self to be successful. At length Bradley commenced the research with 

 ar better astronomical means, and by his discoveries of aberration and 

 nutation, fully explained the phenomena which bad perplexed his pre- 

 decessors. It is curious that Roetner, who had discovered the gradual 

 .ransmission and finite velocity of light, should have been perplexed 

 vith the necessary results of this very property in another shape ; and 

 .hat Bradley, while pursuing the problem of parallax, which had been 

 originally interesting as a proof of the earth's chanye of place, should 

 lave hit upon phenomena which satisfactorily proved the earth's 

 aulion, and so confirmed the Copernican hypothesis by evidence 

 lifferent from what he sought. Bradley'n observations further showed 

 ,hat the effect of parallax hi any of the stars observed by him could 

 not amount to 2" and probably was not 1". 



The nature of the changes in the places in the fixed stars, which the 

 change of position in the earth would produce, may be seen from the 

 following figure. Let s be the place of the sun, E . 

 ;hat of the earth, and that of a fixed star. Then ' 

 ;he star is seen from the earth in the direction r. >, 

 and from the sun in the direction s t ; the difference 

 n these two directions is the angle E s, that is, the 

 angle of parallax. If s ",', be drawn jarallel to 

 E , E s, and the observations mode from the earth 

 oe referred, as observations of this kind are always 

 supposed to be, to the sun, the true place of the 

 star is at t, while the place which is assigned to it 

 by observation ia '. At the end of half a year the 

 place of the earth will be at E', and the star is seen 

 in the direction r.'i. Hence it is referred to the 

 tion s" in respect of s. It is evident that the 

 effect of parallax is to cause the star to appear to 

 describe an orbit round its true place in a plane 

 parallel to the ecliptic, similar and equal to the 

 earth's orbit round the sun ; and further, that 

 parallax is always in a plane passing through the star, sun, and i-.u th, 

 and that its effect is to diminish the angle which the sun and star 

 subtend at the earth. When this is clearly conceived, it will also 

 be seen that this ellipse, which is similar to the earth's orbit, will 

 be seen obliquely from the earth, and consequently be projected into 

 another ellipse with altered proportions. The same figure would serve 

 for an explanation of aberration, except that aberration is in a plane 

 defined by the star and the direction of the earth's motion, which 

 direction is at right angles to the line joining the earth and sun, > 

 that the phenomena of parallax and aberration are Kiinil.-ir, only the 

 effect of parallax is at right angles to the effect of aberration. This 

 affords a convenient mode of computing the coefficient of parallax 

 when that of aberration is known.* 



There ia another view of parallax. Suppose a spectator at the 

 star ; then ho would see the earth's radius vector s E under the angle 

 of parallax. The earth's orbit may be considered to be circular, and 

 as the plane is inclined to a spectator anywhere except in the pole of 

 the ecliptic, the earth will appear to describe on ellipse about 8 as 



Thin similarity between aberration and parallax Is not rigorous, but nearly 

 >. It would be strictly true if the earth moved uniformly in a circle. There 

 are convenient tables for computing aberration for Riven conitant of aberration. 

 Calculate the aberration by these tables for Q + 90', being the sun's longi- 

 tude at the time, divide by the seconds of the constant of aberration, nnd you 

 have the cocfflc ent of parallax, tbe parallax being supposed = 1". Also the 

 times when the parallax In right ascension or declination Is the greatest 

 po-sible will be when the effect of aberration In those directions is 0, and rice 

 ttrtS. 



