PHILOSOPHICAL TRANSACTIONS. 



285 



VOL. LXII.] 



Lexell, in the Petersburg Commentaries, vol. l6, after the method of Mr. Euler, 

 senior, in the 14th vol. of the same Commentaries. This calculation is deduced 

 from the observations made in several places, as mentioned in the title of the 

 paper. Since the observations of the external contacts made at King George's 

 Island, seem not to agree well with those of the internal, the author deems it 

 proper to consider the two cases separately ; the former way according to both 

 the external and internal contacts, and the other the internal contacts only. 

 Now by combining the observations of George Island with those made in Europe, 

 the sun's horizontal parallax found for the former case isp = 8.68 — O.OOT 7y, 

 for the latter p = 8.58 — 0.0080^; where y denotes the correction of Venus's 

 geocentric latitude for the assumed time of conjunction. When in a similar 

 manner the observations made at Prince of Wales's Fort in Hudson's Bay, are 

 compared with the European, he obtains for the former case p = 8.82 — 0.00 1 Qy, 

 and for tlie latter p = 8.74 — 0.0022j/. Lastly, the California observations, 

 compared with the European, give/)=8.6l — 0.0062y. That, among these 

 conclusions, some certain medium may be taken so as to be near the truth, it 

 must be noted that each of these is to be considered as possessing a greater de- 

 gree of certainty, as the co-efficients a:re greater, by which the equations are af- 

 fected, from which those values of the letter p are derived, as then the less is 

 the chance of error in the observation for changing the true value of the paral- 

 lax. The probabilities therefore of the conclusions deduced from the several 

 American observations, estimating in this way, are found to be proportional to 

 the numbers 11,8, and 4. Also to distinguish the best observations from the 

 more uncertain ones, the author adopts 3 hypotheses : viz. 1 . How the medium 

 above mentioned may be taken from the conclusions which are found, when all 

 the observations indiscriminately are used, by which is obtained/? = 8.63 — 

 0.0o63j/; 2dly, by taking into the computation only the times of the internal 

 contacts for George Isle, which gives p = 8.57 — 0.0057^; and 3dly, by ex- 

 cluding the observations of the external contacts made at Hudson's Bay, which 

 gives /> := 8.62 — 0.0065y. But as there does not appear sufficient reason why 

 the times of the exterior contacts should be accounted doubtful, the medium so 

 taken, between the medium deduced from the two latter hypotheses, may safely 

 be taken to give the parallax p = 8.60 — 0.006^. For a final verification of 

 this conclusion, each of the American observations were compared with those 

 made in Lapland, where both the ingress and egress of Venus could be observed, 

 as, for this kind of observations, the errors arising from the longitude of 

 places, in estimating the parallax, are of small moment. Then the me- 

 diums being taken as above said, give, for the three hypotheses, the following 

 values of p : viz. 1st, p = 8.68 — 0.0076^ ; 2d, p = 8.67 — 0.0074^ ; 3d, 

 p =. 8.62 — 0.007 7y, And these conclusions differ not more from those 



