sun's distance. 289 



of the Earth shall tend to lengthen the duration of transit as seen 

 there ? The transit at southern stations is already the longer by 

 virtue of their southern position; and if to this we could superadd a 

 further lengthening by virtue of the Earth's rotation, we should have 

 a very long duration of transit there which we might hope to com- 

 pare with the very short duration at the north station, with the pros- 

 pect of obtaining a combination which would be most advantageous 

 for obtaining the measure sought. 

 We can select such a station. 



It is essential to remark, that the transit will take place in the 

 month of December, and that at that time the Earth's south pole will 

 be turned towards the Sun, and therefore, that those regions of the 

 earth which are included between the south pole and the southern 

 limit of illumination will be carried by rotation in a direction oppo- 

 site to the direction of movement of all the northern parts of the 

 earth. If we fix our attention on a part of the Antarctic continent, 

 between Sabrina Land and Repulse bay, it will be seen that it is car- 

 ried in the same direction as Venus, that the apparent movement of 

 Venus is therefore made slower, and that the duration of transit is 

 thereby lengthened. And as it is lengthened already by the southern 

 position of the station, it will by the combination of these causes be 

 very much lengthened. Comparing this with the observed duration 

 in the United States, where it is very much shortened, we shall have 

 a large difference, depending entirely upon the proportion which the 

 Earth's radius bears to the distance of the Sun, and most favorably 

 available for the determination of that proportion. The difference of 

 the times of duration would probably be not less than twenty-five 

 minutes. 



Thus the circumstances of the transit of 1882 are peculiarly favor- 

 able (subject only to certain practical considerations, to be noticed 

 hereafter.) for the determination of the proportion of the Earth's 

 radius to the Sun's distance, (usually called the Sun's horizontal par- 

 allax, or more strictly the sine of the Sun's horizontal parallax.) A 

 discussion of the transit of 1874 will show what are the conditions 

 on which this favorable state depends. 



In figure 5, where Venus is seen Fig. 5. 



crossing the northern part of the Sun's reversed. 



disk, it will be perceived that the 

 northern station has (independently of 



the Earth's rotation) the longer dura- / ^^ 7er 



tion of transit and the southern has 

 the shorter. Now when we introduce 

 the consideration of rotation — for 

 which purpose we regard the globe 

 with the meridians of 30° W. and 

 120° W., brought to the vertical to 

 represent the illuminated portions at 

 the ingress and egress, respectively — 

 no selection of stations on the principle adopted for 1882 will tend to 

 exaggerate this difference. If both stations are on the north side of 

 19 



