48 PHILOSOPHICAL TRANSACTIONS, [anNO 1763, 



And here perhaps it may not be altogether unnecessary to inquire, how far 

 the mistake which Dr. Halley committed, by using the difference of the two 

 angles instead of their sum, would influence the times of the transit as seen at 

 the Ganges and Port Nelson. For this purpose Mr. H. made use of the same 

 elements which Dr. Halley has given in his paper, and calculated the angle of 

 the vertical with the orbit of Venus at the two internal contacts at both places, 

 supposing the orbit to be inclined first only 2° 18' to the equator, agreeably to 

 Dr. Halley's supposition, and also 14° 40', and he found that the duration 

 would be IS™ 13* longer at Hudson's Bay than at the Ganges, on the first sup- 

 position; and 14"" 44', if the circles be duly inclined to each other; the dif- 

 ference being only ig seconds. It has already been found by calculation, sup- 

 posing the latitude of Venus to be about 9^ minutes, that the difference of du- 

 ration at the two places would have been only 4"" 56". It may fairly therefore 

 be concluded, that the transposition of the circles contributed very little 

 towards giving so diflferent a result, the reason of which need not here be men- 

 tioned ; and Dr. Halley seems to have been led into the mistake entirely from 

 supposing the latitude of Venus to be about 4' O", according to the tables which 

 he then used, constructed on the principle that the nodes of that planet were 

 fixed. — Having determined that the difl^erence of duration at the two places 

 above mentioned would be IS"" 10* (differing only 3' from the method Mr. H. 

 used, which is independent of projection) the doctor proceeds to show, that if 

 Venus had no latitude at the time of the middle of the transit, the difl^erence 

 would be 18"" 40' ; and if the planet should pass 4' O' to the north of the sun's 

 centre, that difference would be 21"" 40'; and would become still greater, if the 

 planet's north latitude should be further increased. And such would have been 

 the event had the motion of the nodes been progressive. But, agreeably to 

 the principles of universal attraction, their motion is really retrograde, and this 

 Dr. Halley says he himself suspected. And therefore it is somewhat surprising 

 that he did not determine by calculation, what would have been the difference 

 in the whole duration between the two places, if Venus should pass more to the 

 southward of the sun's centre, than he had supposed. He would then immedi- 

 ately have perceived that the two stations were not so advantageously placed as 

 the solution of the problem required. 



Observers were therefore to be sent to other places, in order to determine the 

 sun's parallax agreeably to the method proposed by Dr. Halley. The city of 

 Tobolski in Siberia is so situated, that the interval between the two contacts 

 was perhaps as short as could possibly be observed on any part of the earth's 

 surface : to this place was sent the Abbe Chappe d'Auteroches, one of the 

 French astronomers. Near Hudson's Bay, and in 60" of latitude, the duration 

 would have been 5 minutes longer, supposing the sun's parallax = g". At 



