go ' PHILOSOPHICAL TRANSACTIONS. [aNNO 1770. 



consideration, because the calculations from the solar tables give the apparent 

 places of the sun, or its longitude with the effect of aberration included, and 

 therefore always about 20" too little. But from this observation a conclusion 

 will follow very different from that which the objection supposes. The retarda- 

 tion mentioned, is properly the time that the calculated phases of a transit of 

 Venus will precede the apparent phases, supposing the tables, from which the 

 calculation is made, to give the true places of the sun. If they give the appa- 

 rent places of the sun, this retardation, instead of being lessened, will be 

 considerably increased. In order to prove this, it may be remembered, that in 

 deducing, by trigonometrical operations, the geocentric places of a planet from 

 the heliocentric, the earth is supposed to be in that point of the ecliptic which is 

 exactly opposite to, or 1 80° from the place of the sun, and that this supposition 

 is just only when the sun's true place is taken. In reality, the earth is always 

 about 20" more forward in its orbit, than the point opposite to the sun's apparent 

 place ; and in consequence of this it will happen, that in calculating a transit of 

 Venus, from tables which give the sun's apparent places, a greater difference will 

 arise between the calculated and the observed times, than if the tables had given 

 the sun's true places. 



For, let s be the sun, t the earth, v Venus. Were there no 

 aberration of light, the sun would be always seen in its true 

 place, or in the direction Ts. But, in reality, in consequence of 

 aberration, it will be seen 20" less advanced in the ecliptic, or in 

 the direction T.y, supposing sts to be an angle of 20". Now a 

 calculation from tables giving the true places of the sun, would 

 not be the time of the observed conjunction, to the time that 

 Venus gets to ts ; but this, though the time of the true con- 

 junction, would not be the time of the observed conjunction ; 

 for the sun being then really seen in the direction t*, Venus, 

 after getting to ts must move 20", or from a to c, before the 

 apparent conjunction can take place. 



But if the calculations are made from the apparent places of the sun, the 

 conjunction will be fixed to the time Venus gets to f s, or a line drawn through 

 s parallel to jt; for in this case t will be the point of the ecliptic opposite to 

 the apparent place of the sun, and the longitude of the sun seen from t will be 

 20" less than its true longitude, and therefore the same with its apparent 

 longitude. But the earth being then really at T, Venus will, at the calculated 

 time of a conjunction, be observed at a distance from the sun equal to the angle 

 LT5. This angle, supposing vt 277, and vs 723, may be easily found to be 

 72".2. Add to this 3".7, the proper aberration of Venus at the time of a transit, 

 removing it more towards e, and the whole visible distance of Venus from the 



