'268 PHILOSOPHICAL TRANSACTIONS. [aNNO I765. 



sun was near the horizon, and at higher altitudes, we may safely conclude that 

 the observations will be made with sufficient accuracy when the sun is at such 

 altitudes above the horizon, as not to be greatly affected by the vapours. At the 

 observatory at Upsal, when the sun's altitude at the ingress was 3-j- degrees, 

 three observers differed 22' ; whereas at the egress, when the sun was 44-j^° high, 

 the difference amounted only to 6^ It should seem therefore, that observers 

 ought not to be sent to places where the sun will be much less than 3° high at 

 the time of either of the contacts. 



It appears by computation, that the joint effect of the parallaxes, both in lon- 

 gitude and latitude, to lengthen the total duration, will be the greatest to those 

 places which are about 24" or 25° to the east of Greenwich, in the 66th or 67th 

 degree of n. latitude, when the sun's altitude is about 5° at each contact; or it 

 the sun's altitude at each contact be required = 10°, the latitude of places under 

 the same meridian must be 73° or 74° n. In the former case, this transit may 

 be very advantageously observed at Tornea°, Kittis, and the adjoining parts of 

 Swedish Lapland; in the latter at Wardhus, and in the neighbourhood of the 

 North Cape; for an error of one or two degrees either in longitude or latitude 

 will make but a very inconsiderable difference in the parallactic time; as will suffi- 

 ciently appear from an inspection of the following table, which contains the joint 

 effect of the parallaxes of longitude and latitude in accelerating the times of the 

 two internal contacts at Tornea°, Kittis, and Wardhus, for each of which places 

 the parallactic angle, or the angle made by a vertical circle with the orbit of 

 Venus, was carefully computed. 



First internal Second internal Total eflFect of Total effect of Difference for 



contact. contact. par. = 8".7. par. = 9".7. l"of parallax. 



Tomea" 6"" 53' 4"^ 47' -f 1 1"* 40' -|- 12'" 58' 1™ 18' 



Kittis 6 51 4 43 -f- 1 1 34 +12 51 1 17 



Wardhus 6 38 4 41. ..-^11 I9 +12 37 . . . . 1 18 



Having determined the greatest effect of parallax in lengthening the total du- 

 ration at such places to which observers may conveniently be sent, let us exa- 

 mine how far we may be enabled to obtain observations in such part of the earth's 

 surface where the effect of parallax will be contrary; and consequently where the 

 total duration will be as short as possible. By the assistance of calculation it 

 may be found, that in the latitude of about 54° south, and in 155° of west lon- 

 gitude nearly, the total duration will be the shortest, when the sun's altitude is 

 5°; or in about 47° of south latitude under the same meridian, when the sun is 

 10° high. And accordingly, by computing the parallactic angle for the latitude 

 of 55° south, and the meridian opposite to that of Tornea°, Mr. H. finds that 

 the total duration will be shortened by parallax no less than 12"" 53', supposing 

 the sun's parallax = 8".7, and consequently that there might be observed a di£- 



