i64 PHILOSOPHICAL TRANSACTIONS. [aNNO 1715. 



verse axe of the ellipse was to its conjugate, very nearly as radius to the sine of 

 40°, or as 1000 to 643 proxime; and made an angle of 59°, or very little 

 more, with the meridian passing at that time through the centre of the shade. 



Next as to the direction and the velocity of the motion with which the centre 

 of the shade passed over England, it is to be observed that the shadow passes 

 in a very compound curve, which in the former is not in piano, and only 

 describable on the surface of the sphere; nor is its motion equable, but com- 

 pounded of many elements, producing a great variety. By what method its 

 points, and its tangents in those points, are to be obtained, I reserve to the 

 next opportunity, this account being designed for the curious in general; only 

 I must acquaint them, that for so small a part of the curve as went over Eng- 

 land, it may be esteemed a right line, with more exactness than we usually find 

 in most of our geographical charts. And the like may be said for the velocity, 

 which, though in our present instance it was continually decreasing, may, for 

 so short a time, be supposed to have been the same without sensible error. 



By a careful calculation I have determined the velocity of the motion, at the 

 time of the middle of the eclipse at London, to have been nearly 2Q geogra- 

 phical miles in a minute of time; and that its way made an angle of 52° 45 

 with the meridian towards the east of the north ; therefore the said way made 

 an angle with the axis of the ellipsis of 68° 1 5'. And the greatest duration of 

 total darkness having been 3"^ 57% as before shown, it will follow that that 

 diameter of the elliptic figure, according to which the shade passed, was no less 

 than 11 44- geographical miles. And from the elements of the conies it is easy 

 to be proved, that supposing the figure of the shade a true ellipse, whose axes 

 are as radius to the sine of 40% the greater axis would be 1 7 1 geographical 

 miles, and the lesser 110; and the nearest distance between the limits, supposed 

 parallel, 164 such miles. 



And this length of the axis of the shade, derived purely from the continu- 

 ance of total darkness, is fully confirmed by the observed distance of the parallel 

 limits; the one passing by Badsworth in Yorkshire, the other by Cranbrook in 

 Kent. For by the two latitudes 53° 37' and 51° 6', with the difference of lon- 

 gitude 7"^ 40* of time, or 1° 55% the distance of these two places is given 166^ 

 geographical miles: with the mean angle of position 25° from the north west- 

 wards; therefore this arch makes an angle with the track of the shade of 77-t°; 

 and hence the nearest distance of the parallels becomes 163 such miles, which 

 by the other way was found l64. 



If therefore we conclude the axis of the shadow, when the sun was just 40° 

 high, to have extended over 2° 50' of a great circle, we may securely determine 

 the difference of the sun and inoon*s diameters at this time. For the difference 



