STARS. 



the diftance of the ftars at, ac, at E, and from thence the 

 parallax P. Let the triangle a b i [Phte XX. jlftroncmy, 

 fg. 12.) reprcfent the fituation of the ilars ; a ^ is the fub- 

 tenfe of 5", the angle under which they are to be feen at O. 



■M 



The quantity ^/3 by the former theorem is found "Vv— - P> 



^hich is the partial parallax that would have been feen by 

 the earth's moving from O to E, if both ftars had been in 

 the ecliptic ; but on account of the difference in latitude, it 

 will be now reprefented by a, 3, the hypothenufe of the tri- 

 angle ab^: therefore in general, putting ab = d, and a ,3 



= D, we have 



s/^^^ 



dd X Mto 



= P. 



Hence, D 

 given, we 



m — M 

 being taken by obfervation, and d, M, and 

 obtain the total parallax. 



If the fituation of the ftars differs in longitude as well as 

 latitude, we may refolve this cafe by the following method. 

 Let the triangle ab ^ [Plate XX. AJlromrr.y, fi^. 13.) repre- 

 fent the fituation of the ftars, ab — d being their diftance 

 Veen at O, a S 1= D their diftance feen at E. Tii?.t the 

 change 3,3, which is produced by the earth's motion, will 



be truly exprefted by — j^-j P, may be proved as before, 



by fuppofing the ftar a to have been placed at a. Now let 

 the angle of pofition ba-j. be taken by a micrometer, or 

 by any other method fufficiently exaft ; then, by folving 

 the triangle a ix, we fhall have the longitudinal and lati- 

 tudinal diff^erenccs a » and ^ a of the two ftars. Put a a 

 1^ X, h a. =:i y, and it will be .v -f i ;3 = a q, whence D =: 



* + 



M 



M; 



P + >.^ ; and 



/D^-^ 



xM 



cM> 



M 



sf 



If neither of the ftars (hould be in the ecliptic, nor have 

 the fame longitude or latitude, the laft theorem will ftiU 

 ferve to calculate the total parallax whofe maximum will lie 

 in E. There will, moreover, arife another parallax, whofe 

 maximum will be in the conjunftion and oppofition, which 

 will be divided, and lie on different fides of the large ftar ; 

 but as we know the whole parallax to be exceedingly fmall. 

 It will not be necellary to mveftigate every particular cafe of 

 this kind ; for, by reafon of the divifion of the parallax, 

 which render^ obfervr.tions taken at any other time, except 

 where it is greateft, very unfavourable, the forixuili would 

 be of httle ufe. Dr. Herfchel clofes his account of this 

 theory with a general obfervation on the time and place 

 where the maxima of parallax will happen. 



When two unequal ftars are both in the ecliptic, or, not 

 being in the ecliptic, have equal latitudes, north or fouth, 

 and the largelt ftar has moft longitude, the maximum of the 

 apparent diftance will be when the fun's longitude is 90° 

 more than the ftars, or when obferved in the morning : and 

 the minimum when the longitude of the fun is 90^ lefs than 

 that of the ftar, or when obferved in the evening. When 

 the fmall ftar has moft longitude, the maximum and mini- 

 mum, a!' well as the time of obfervation, will be the revcrfe 

 of the former. When the ftars differ in latitude, this makes 

 110 alteration in the place of the maximum or minimum, nor 

 in the time of obfervation ; i. e. it is immaterial whether the 

 largeft ftar has the leaft or the greateft latitude of the two 

 ftars. Phil. Tranf. vol. Ixxii. parti, art. 11. 



The diftance of the ftar y Draconis appears by Dr. Brad- 

 ley's obfervations, already recited, to be at leaft four hun- 

 dred thoufand times that of the fun, and the diftance of the 

 jieareft fixed ftar not lefs than forty thoufaad diameters of 



the earth's annual orbit : i. e. the former is diftant from ih<" 

 earth at leaft 38,000,000,000,000 miles, and the latter not 

 lefs than 7,600,000,000,000 miles. As thefe diftances are 

 immenfely great, it may not be unamufing to compare them 

 with the velocity of fome moving body by which they may be 

 meafured. 



The fwifteft motion we know of is that of light, (fee 

 Light,) which pailes from the fun to the earth in eight 

 minutes thirteen feconds, and yet this would be above fix 

 years traverfing the firft fpace, and nearly 1^ year in palling 

 from the neareil fixed ftar to the earth. A cannon-ball dif- 

 charged from a twenty-four pounder, with two-thirds its 

 weight of powder, which moves at the rate of about nineteen 

 miles in a minute (fee Gun), would be three million eight 

 hundred thoufand years pafTmg from y Draconis to the earth, 

 and feven hundred and fixty thoufand years pafling from the 

 neareft fixed ftar. Sound, which moves at the rate of about 

 thirteen miles in a minute, would be five million fix hundred 

 thoufand years traverfing the former diftance, and one mil- 

 lion one hundred and twenty thoufand palling through the 

 latter. 



The- celebrated Huygens purfued fpcculations of this 

 kind fo far, as to believe it not impoflible, that there may be 

 ftars at fuch ir.conceivable diftances, that their light has not 

 yet reached the earth fince its creation. 



Dr. Halley has alfo advanced, what he fays (Phil. Tranf. 

 No. 364. or Abr. vol. vi. p. 41 8. ) feems to be a metaphys- 

 eal paradox, "oiz.. that the number of fixed ftars muft be 

 more than any finite number, and fome of them more than 

 at a finite diftance from others : and Mr. Addifon has juftly 

 obferved, that this thought is far from being extravagant, 

 when we confider that the univerfe is the work of infinite 

 power, prompted by infinite gooduefs, having an infinite 

 ipace to exert itfelf in ; fo that our imagination can fet no 

 bounds to it. 



Stai(.s, The Magnitudes of the Fixed, appear to be very 

 different, which difference may probably arife, not only 

 from a divcrfity in their real magnitudes, but principally 

 from their diftances, which are different. 



The ftars appear of a fenfible magnitude to the bare eye, 

 bccaufe the retina is affected not only by the rays of light 

 which are emitted direftly from thcin, but by many thou- 

 fands more, which, fallii.g upon our eye-lids, and upon the 

 aerial particles about us, are reflected into our eyes fo 

 ftrongly, as to excite vibrations, not only in thofe points of 

 the retina where the real images of the ftars are formed, but 

 alfo in other points at fome diftance round about. This 

 makes us imagine the Itars to be much bigger than they 

 would appear, if we faw them only by the few rays which 

 come direiflly from them, fo as to enter our eyes without 

 being intermixed with others. 



Any one may be fenlible of this by looking at a ftar of 

 the firfl magnitude through a long narrow tube, which, 

 though it takes in as much of the fky as would hold a thou- 

 fand fuch ilars, fcarcely renders that one vifible. 



The more a telefcope magnifies, the lefs is the aperture 

 through which the ftar is feen, and confequently the fewer 

 rays it admits into the eye. Since, therL-fore, the ftars ap- 

 pear lefs in a telefcope which magnifies 200 times, than they 

 do to the bare eye, infomuch that they feem to be only indi- 

 vifible points, we may infer that they are at immenfe dif- 

 tances from us, and alfo that they fhine by their own proper 

 light. If they fhone by borrowed light, they would be as 

 invifible without telefcopes as the fatellites of Jupiter are : 

 for thefe fatellites appear bigger when viewed with a good 

 telefcope than the largeft fixed ftars do. 



The liars, on account of their apparently vai-ious mag- 

 I nitudcs. 



