The long folding plate pictures the Earth on her course through the positions marked 1, 2, ... 14, 15, in fig. 102. The path of the Earth in this figure is, for convenience of engraving, broken up into three parts, as shown in fig. 103, and the Earth is represented at each part of her progress, precisely poised and rotated, as she would appear if she could be viewed from the Sun during the course of the transit of 1874. Leaving the cross-lines out of consideration for the present, let the student study this plate, interpreting it by reference to figs. 101 and 103, and he will be able to form more exact conceptions of the real relations presented during the transit than he could from a very long and recondite explanation. He sees in the first picture of the Earth those regions whence the sees in the last Those parts of beginning of the transit will be visible. He those regions where the end will be visible. the Earth which appear in both these views are those from which the whole of the transit will be visible. And, finally, those parts which do not appear in either of these views (nor, therefore, in any of the fifteen) are those whence no part of the transit will be seen. But now, having done this, and understanding also that he will presently be invited to return to the consideration of this plate, let him examine the larger and more elaborate views Plate IX. and X., representing the Earth as supposed to be seen from the Sun at the beginning and end of the transit. Of these views the first represents the Earth as she would appear from the Sun when her centre is just crossing the circle v v of fig. 93 at ingress, and the second represents her as she would appear when her centre is just crossing the same circle at egress. So that the first corresponds to an epoch between those represented in the first two Earth pictures of the folding plate, while the second corresponds to an epoch between those represented in the last two pictures of that plate. The seemingly parallel cross-lines in Plate IX. represent the encroaching outline of the circle v v′ (fig. 98) at intervals of a single minute of time between the epochs represented by the first two figures in the folding plate. The corresponding cross-lines in Plate X. represent the same outline gradually passing off the Earth's face between the epochs corresponding to the last two figures in the folding plate. The encroachment and the passing off not being strictly uniform,* these lines are not equi-distant, nor are they strictly parallel. (They should not be absolutely straight, since they really form short arcs of circles; but this consideration is relatively unimportant.) Now, these two plates give us all we require for determining what are the best stations, whether for Delisle's or Halley's method.† For Delisle's, applied as at ingress, consider Plate IX. We * The reason of this will be seen by a reference to fig. 102. Obviously the rate at which the Earth's centre is approaching the centre of Venus (which rate really measures the rate of encroachment) diminishes during ingress, while for like reason the rate of passing off increases during egress. + Properly speaking Plates IX. and X. only represent the Earth accurately for the moment when the outline of v v′ (fig. 102) crosses the Earth's centre. Since, as we see by the cross-lines, no less than 25m. 6s. are occupied by the passage of the outline of v v' over the Earth's face, both at ingress and egress, the Earth's rotation has to be considered. This, however, can very easily be done, since the latitude circles are shown, and the longitude circles are separated by ten degrees, corresponding to the Earth's rotation in forty minutes. Thus from Plate IX. we see that the cross-line marked 7m. on the right of the centre passes near Jeddo. But as the cross-line occupies this position seven minutes before it crosses the Earth's centre, we must put Jeddo back through an amount corresponding to seven minutes' rotation, or about one-sixth of the distance separating two longitude circles in this neighbourhood. |