TOL. LIII.J PHILOSOPHICAL TRANSACTIONS. 33 



centres at the 4 following places, and from each comparison he computed the 

 parallax of the sun, which are as in the following table. 



Cajan. Calm. Tobol. Tornea. Upsal. Stok- Abo. Herno. ^un'sP- 

 ■* '^ mean. 



Tranquebar 8".+8 8".45 8".54. 8"-31 8". 18 8".20 8".52 8".42 8".42 



Madras 8.79 8.76 8.93 8.6l 8.79 8.50 8.82 8.73 8.74 



G. Mount 8.42 8.38 8.45 8.'.24 8.42 8.12 8.45 8.35 8.35 



Calcutta 8.69 8.65 8.81 8.43 8.68 8.35 8.73 8.6l 8.62 



Sun's Par. mean 8.59 8.56 8.68 8.40 8.59 8.29 8.63 8.53 8.53 



The mean of these 32 comparisons gives the sun's parallax = 8 '.53. This very 

 near agreement with the former determinations is somewhat surprising, when we 

 consider the smallness of the base from which they are computed, the greatest 

 scarcely exceeding 20" of an angle. But we are also to consider that the appa- 

 rent least distance of the centres may be found from the duration observed to a 

 very great exactness, and nothing affects the accuracy of it but the errors in the 

 observation. Let us suppose that an error of 6' in time happened in each of the 

 observations of the ingress and egress, both in contrary directions ; the sum of the 

 errors therefore in each comparison will amount to 24' of time: this will produce 

 an error of 1" of space in the apparent least distance of the centres by computation ; 

 but this error of 1 " cannot produce an error of so much as half a second in the 

 determination of the sun's parallax. It therefore follows on the above supposition 

 of an error of 24' of time in the observation, that though we had no other observa- 

 tions of the transit of Venus than two of the above total durations, (suppose that 

 of Cajaneburg and Madras) yet we should have been absolutely certain of the par- 

 allax of the sun within less than an error of half a second, and therefore of course it 

 follows that the mean of so great a number of results must be very near the truth. 



This determination of the sun's parallax by the least distance of the centres, 

 is also a convincing proof that there is no mistake in the observation of Mr. Ma- 

 son at the Cape, as alleged by M. Pingre ; and that there must be a mistake of l" 

 in setting down the time of the internal contact at the egress at Rodrigues, not- 

 withstanding M. Pingre, in the aforesaid memoir, prefers his observation to that 

 of Mr. Mason, because, as he says, that after a strict examination of all the 

 circumstances attending his observation, he could not find any mistake in it, but 

 also because he has proved that no mistake could possibly be committed. In this 

 determination of the parallax by the apparent least distance of the centres, we 

 are not embarrassed with an exact knowledge of the difference of longitude 

 between the places compared ; which therefore in some measure compensates for 

 the smallness of the base. 



The same irrefragable argument, made use of in the apparent least distance of 

 the centres measured at Rodrigues, to prove that the parallax of the sun is very 

 nearly = 8".5, may likewise be deduced from the apparent least distance of the 

 centres computed from the total durations observed at these 12 places, but with 



VOL. XII. F 



