METHOD OP EXAMINING ASTRONOMICAL INSTRUMENTS. 36t 



from the arc of 15°, we shall obtain the first arc of 14°. Method of ex- 

 The first 7° of this arc being measured against the second, y™^| ty. £.* 

 we ascertain the value of the first 7°; and then, by mea- 

 suring the first 4° of the remaining arc of 8° against the 

 second, we shall get the value of the first 4°, which added 

 to the arc of 7°, before determined, will give us the length 

 of the first arc of 11°. The first 2° of the remaining arc 

 of 4° must then be measured against the second, and we 

 shall get the value of the first 2° ; and by adding this arc to 

 the arc of 11°, we shall obtain the value of the arc of 13°* 

 By taking away the first arc of 1° from the arc of 15°, we 

 get the remaining arc of 14°, and then having determined 

 the length of the first 7° of this arc, by measuring them 

 against the second, we must add it to the arc of 1°, and we 

 shall obtain the arc of 8°. The length of the first 4° of this 

 arc will then be easily known, by measuring them against 

 the second, as will afterward that of the first 2° in the arc 

 of 4° itself, by measuring them against the second in the 

 same arc. 



We have still to ascertain the lengths of all the first arcs 

 of 10, 20, 30, 40, and 50 minutes contained in each degree, 

 for I shall only consider fhe case in which the circle is di- 

 vided into parts of 10 minutes. Now the length of the first 

 arc of 30' will be obtained by measuring it against the second; 

 and the lengths of the first and second arcs of 20* (the sum 

 of which will give the arc of 40 ; ) by measuring the first 

 against each of the remaining arcs. The length of the third 

 arc of 20' must likewise be put down ; and then the first arc 

 of 10* being measured against the second of the arc of 20', in 

 which it is included, and also against the two arcs of 10' 

 contained in the last arc of 20', its own value, and that of 

 the last 10* in the degree will be determined from a compari- 

 son with the arcs of 20', in which they arc respectively com- 

 prehended. The length of this last arc of 10' being taken 

 from that of the whole degree will give us the length of the 

 first 50', and complete the operation. 



In order to ascertain the greatest possible errour to which Greatest po> 

 we are liable in the examination, let s denote in parts of a se- sl errour# 

 cond the greatest that can be committed in bisectiug any point 

 upon the limb; then, since this errour may occur at each end 



of 



