448 SUPPLEMENT. 



A. The arms of the cross stand at right angles to the 

 middle part ; and the top of it, from a to n is of equal 

 length with either of the arms n e or m k. 



Having set the middle line f u to the latitude of your 

 place, on the quadrant, the board A level, and the point 

 N northward by the needle ; the plane of the cross will 

 be parallel to the plane of the equator ; and the machine 

 will be rectified. 



Then, from III o'clock in the morning, till VI, the 

 upper edge k I of the arm i o will cast a shadow on 

 the time of the day on the side of the arm c m : from 

 VI till IX, the lower edge i of the arm i o will cast a 

 shadow on the hours on the side o q. From IX in the 

 morning to XII at noon, the edge a b of the top part 

 a n will cast a shadow on the hours on the arm n e f: 

 from XII to III in the afternoon, the edge c d of the 

 top part will cast a shadow on the hours on the arm 

 k I m: from III to VI in the evening, the edge g h will 

 cast a shadow on the hours of the part p q; and from 

 VI till IX, the shadow of the edge e f will shew the 

 time on the top part a n. 



The breadth of each part, a b, e f, &c. must be so 

 great as never to let the shadow fall quite without the 

 part or arm on which the hours are marked, when the 

 sun is at his greatest declination from the equator. 



To determine the breadth of the sides of the arms 

 which contain the hours, so as to be in just proportion 

 to their length ; make an angle A B C of 231 degrees, 

 which is equal to the sun's greatest 

 declination : and suppose the length qf 

 each arm, from the side of the long 

 middle part, and also the length of the 

 top part above the arms, to be equal 

 to B d. 



Then, as the edges of the shadow, ***.../ 

 from each of the arms, will be parallel 



