330 Mr. J. Rand Capron on the Auroral 



observers' distances from the shadow-line, and degrees of 

 "above" or "below" view of the beam's centre relative to 

 the moon's centre as they observed it, into two sums, and then 

 to divide the mileage sum by the degree sum, and the result 

 will be the best average value of the rate that the observations 

 can afford. Exact angular centre differences are only given 

 at Bristol, Guildown, Chatham, St. Ives, and Hewarth (York); 

 and these agreeing very fairly (except the Hewarth one), and 

 the distances being taken from the first presumptive track, the 

 result is found to be a total of 280'5 miles for 14*1 degrees of 

 j) parallax, or an average rate of 5° to 100 miles. This, 

 projected with a protractor, would make the beam's height 

 215 miles over Bordeaux, but with a want of probability of 

 such a height and distance. Abandoning therefore the He- 

 warth observation and accepting the other four, we get in 

 figures as follows: — 



Bristol 23 miles = 1-6 



Guildown... 24-5 „ = 2-0 



Chatham ... 33 „ = 2*0 



St. Ives _3]_ „ = 5-5 



117-5 „ = 11-1 

 .-. 100 „ = 9-4 

 and this gives by projection a height of 92 miles 180 miles 

 south of the shadow-line. Prof. Herschel at this point remarks 

 that, as the result of his experience of the heights of the ray- 

 less milky auroral arches, obtained by good parallaxes of them, 

 he has found they constantly occur within a few miles of 100 

 high, and that possibly the St. Ives observer's parallax may 

 be a little excessive. Taking now a shadow-line inclined 18° 

 to the geographical B. and W. direction (for the moving beam 

 must have lain over a part of France where 18° was about the 

 extent of magnetic variation) , measuring the distances again, 

 and preferring this time to use 5° instead of a mean of 5° and 

 6° as the St. Ives's parallax, we have as follows:— - 



Bristol 17 miles = 1*6 



Guildown ... 24 „ = 2-0 



Chatham ... 27 „ = 2*0 



St. Ives 41-5 ,, = 5-0 



109*5,, =10-0 

 .\ 100 „ = 9-65 = 9f°- 



Projected with the j) 's altitude at Guildown (28J°), these 

 figures will give a height of 100 miles at a distance of 185 miles 

 south of the shadow-line (eee PI. VII. fig. 1); or if, instead of 

 using so large an angle as 9°*6 to protract with, we prefer to 



