238 Gen. Roy’s Account of 
relative heights of thefe Rations have been determined by taking 
_ *__th of the arc of diRance for the effect of terreRrial 
I o 
refradlion. 
Art. III. General Theorem. 
Let C (Plate X. fig. 1 1 ) be the center of the earth confi- 
dered as a fphere ; Si the fur face ; H b two places at the fame 
height above the furface ; HO the horizontal line, or apparent 
level at the place H ; and ho the horizontal line, or apparent 
level at the place h ; alfo, let Cm bifedt the angle at C. 
Then, becaufe the angles m HC and mn H are right 
ones, the angle mHn, or mhn, is equal to the angle m CH 
or mCh ; that is to fay, if two places H, h, are of equal 
heights, the one as fieen from the other is depreffed below the 
horizontal line of the place of obfervation, by an angle equal 
to half of the arc of the great circle contained between them, 
or half the angle at C. Hence it follows, that any diftant 
obje£l is higher or lower than the place of obfervation, accord- 
ing as the depreffion is lefs or greater than half the contained 
arc, fuppofing no fuch effect as refraftion to exift in nature. 
Art. IV. Determination of the refraShon between Dover Cajlle 
and Folkfone Turnpike . 
Let D (fig. 12.) be the place of the axis of the telefcope on 
the north turret of the Keep in Boyer Caflle ; T the ground at 
the Ration near Folkftone Turnpike ; DO the horizontal line; 
and SL=CD» 
The diRance of the Rations is 31554.6 feet, which, taking 
the obliquity of the direction into confideration, gives 61 188 
fathoms =i°; and confequently f 9". 4 for the length of the 
contained 
