XLVII. A letter from Richard Price, D. D. F. R. S. to Benjamin Franklin, LL. D. F. R. S. on the effect of the aberration of light on the time of a transit of Venus over the Sun . C s j « ] X L V II. A Letter from Richard Price, D .D . F. R. S. to Benjamin Franklin, L L. D. F. RyS.on the EffeSi of the Aberration of Light on the Lime of a Lr anft of Venus over the Sun. D e a r S i r, Read Dec. 20. IT Cannot doubt but that the obferyation 1770 JL made by your ingenious friend in the paper ^ you fent me is right. T h e aberration of Venus muft, I think, a t e d the phafes of a tranfit, by re­ tarding them, and not by accelerating them. This retardation is 554."; for that is the time nearly which Venus, during a tranfit, takes to move over 3 " . ^ This, however, is by no means the whole retardation of a tranfit occafioned by aberration. T here is a retar­ dation arifing from the aberration of the Sun, as well as from that of Venus, T h e aberration of the Sun, it is well known, leffens its longitude about 2 0 ". and the aberration of Venus, agreeably to your friends demonftration, increafes its longitude at the time of a tranfit 3//*7* Venus, therefore, and the Sun, at the inftant of the true beginning of a tranfit, muft be feparated from one another by aberration 2 ^* 7 5 and, hnce Venus then moves nearly at the rate o f 4 in an Ht The paper which occafioned this letter, and which is here preferred to, may be found in p» 35 ̂ *kis volume. hour, 7 D ow nl oa de d fr om h tt ps :/ /r oy al so ci et yp ub li sh in g. or g/ o n 05 A pr il 2 02 1 * hour, it will move over 2 5 ^.7 in A nd confequently, from the inftant of the beginning o f a tranfit, 5 ': 5 5 '' muft elapfe before it can begin apparently. It may, I know, be objected here, that the aber­ ration of the Sun ought not to be taken into confi- deration, becaufe the calculations from the folar tables give the apparent places of the Sun, or its longitude with the effect of aberration included, and therefore always about 2 0 ^ too little. But from this obfervation a conclufion will follow very different from that which the objection fuppofes. T h e retardation I have mentioned is properly the tim e that the calculated phafes of a tranfit of Venus will precede the apparent phafes, fuppofing the tables from which the calculation is made to give the true places of the Sun. I f they give the apparent plkces of the Sun, this retardation, inftead o f being leffened, will be con- fiderably increafed. In order to prove this, I m uft defire it may be remembered, that in deducing by trigonometrical operations the geocentric places of a planet from the heliocentric, the E aith is fuppofed to be in that point of the ecliptic which is^exadlly oppofite to, or 180° from the plaice o f the fun, and that this fuppofition is juft only when the fttn’s true place is taken. In reality, the Earth is always about 2 0 ^ more forward in its orbit than th e , point obpofite to the Sun’s apparent place 5 and in cOnfdquehce of this it will happen, that in calculating a tranfit of Venus from tables which give the Sun’s apparent places, a greater difference will arife between the (Calculated and the obferved times than if the tables had given the Sun’s true places. Vol„LX. Z zz For [ 537 ] D ow nl oa de d fr om h tt ps :/ /r oy al so ci et yp ub li sh in g. or g/ o n 05 A pr il 2 02 1 [ 53» ] For, let S be the Sun, T the Earth, V Venus. Were there no aberration of light, the Sun would be always feen in its true place, or in the dire&ion TS. But, in reality, in confequenee of aberration, it will be feen ao /; lefs advanced in the ecliptic, or in the direction Tx, fuppofing STj to be an angle of 2o//. Now a calculation from tables giving the true places of the Sun, would fix the moment of a conjunction, to th e time that Venus gets to TS j but this, though the time of the true conjunction, would not be the time of th e obferved conjunction $ for the Sun being then really feen in the direction T s , Venus, after getting to TS, muff move 2 0 " , or from a to c, before the apparent conjunction can take place. But if the calculations are made from the appa­ rent places of the Sun, the conjunction will be fixt to the time Venus gets to t S, or a line drawn through S parallel to x T , for in this cafe t will be the point of the ecliptic oppofite to the apparent place of the Sun, and the longitude of the fun feen from t will be 2 0 ^ lefs than its true longitude, and therefore the fame with “its apparent longitude. But the Earth being then really at T , Venus will, at the calculated time of a con­ junction, he obferved at a. diftance from the Sun equal to the angle L T s. T his angle, fuppofing V T 277, and V S 7 2 3 , may be eafily found D ow nl oa de d fr om h tt ps :/ /r oy al so ci et yp ub li sh in g. or g/ o n 05 A pr il 2 02 1 [ 539 1 found to be 72/7.2. Add to this $",7, the proper aberration of Venus at the time o f a tranfit, removing it more towards E , and the whole vifible diftance o f Venus from the Sun’s center at the calculated moment o f a conjun&ion, will be $£over which it will move in 19 minutes of time. A nd this, consequently, will be the retardation of the phafes o f a tranfit of Venus occafioned by aberration, on the fuppofition, th at in calculating, the Sun’s apparent, and not his true place is taken. I believe thefe obfervations have not been attended to by aftronomers j and therefore I am the more defirous o f communicating them to you. I am, Dear Sir, with much refpeft, your obliged humble fervant, Richard Price. Z z z 2 P.-S. In D ow nl oa de d fr om h tt ps :/ /r oy al so ci et yp ub li sh in g. or g/ o n 05 A pr il 2 02 1 [ 54° ] P. S. In a former letter which I fent you, I gave,, by miftake, the error occafioned by aberration lefs. than I have now given it. T he difcovery of this miftake I owe to the kind afliftance and correction with which Mr. Mafkelyne, the aftronomer royal, has been pleafed to favorme; I have, for the fake of more diftin&nefs and clearnefs, fuppofed Venus to move in the plane of the ecliptic. Some differences will arife from the inclination of the path of Venus to the ecliptic, and alfo from taking the aberration of the Sun, and the proportion of Venus's diftance from the Earth to her diftance from the Sun,, exaCtly as they really are at the time o f a tranfit. T hus, at the time of the laft tranfit of Venus, fiippofing light to come from the Sun to the Earth in 8^2, the aber­ ration of the Sun was 1 9//.8. T h e diftance of Venus from the Earth was to its diftance from the Sun as 290* to 726, and therefore the retardation 18A: 16ff. M r. Canton has obferved, that in the . desHempy MV. De la Lande makes the efteCt of aberration at the inferior conjunction of Venus and Mercury to be an augmentation o f their longitudes. Indeed, M r.. Blifs himfelf obferves this 5 and yet, through an over­ fight, makes the effeCt as to time to be an accelera­ tion, Vid. Phil. Tranfi vol. L II. p. 249. s . X L V III. * D ow nl oa de d fr om h tt ps :/ /r oy al so ci et yp ub li sh in g. or g/ o n 05 A pr il 2 02 1