148 MEASUREMENT OF AN ARC ON THE 



60957 fathoms to the degree, 192O8 feet will give an 

 arc of 3' p" very nearl}^, which is the contained arc. 

 And the diflerence between the depression and ele- 

 vation being 2' 58", we have •■' °"-^"' ■'^ ^ " =5",5 for 

 the terrestrial refraction. Hence, since the observ- 

 ed elevation of the stand, plus half, the contained 

 arc would give the angle subtended by the per- 

 pendicular height of the stand above the telescope 

 at the beach, were there no refraction, we shall 

 have 7' \5^ +^''— 5",5=:8' 44" for the true angle 

 subtended by the perpendicular height, which be- 

 ing taken as tangent, to the horizontal distance 

 and radius, we have R : tan. 8' 44" :: 1^208 : 

 48,797 feet the height required. But the axis of 

 the telescope on the beach was determined by 

 levelling down to the water, to be 21,166 feet 

 above the sea. Which, added to the above, give 

 69,963 feet for the perpendicular height of the top 

 of the stand above the \c\c\ of the sea. 



Now the top of the race-stand was determined 

 by leveUing to be 31,25 feet above the north ex-' 

 , tremity of the base ; which taken from the other, 

 leaves 38,/13 for the north extremity 6f -the base 

 above the sea, which extremity being, by the ta- 

 ble, 9.9.,9Q feet above the south extremity, we 

 shall have \5,75?j feet from the perpendicular 

 height of the south extremity of the line above 

 the level of the sea; and from this height the 

 length of the base has been reduced. 



The angles of elevation and depression Vv'ere 

 taken by the circular instrument, from a mean of 

 several observations, and the error of collimation 

 was corrected by turning the transit over, and the 

 horizontal plate half-round. But the weather was 

 rather dull during the whole of these operations. 

 1 



