112 JOURNAL OF THE 



The series is very converging for the small values of a 

 used, and in fact would answer for much larger values of a 

 if desired; hence we see that we are concerned here with a 

 very converging series; in fact, the same series used in 

 computing a table of sines and co-sines, so that we can 

 find X and y accurately to any desired number of decimal 

 places. 



The angle made by a chord from station o to station ;/ 

 with the axis of Y will be designated by a„ . This angle 

 is readily found from the formula, 



tan A„ r= . 



Y„ 



100.078 



Thus for A, 2) we have tan A^g ^ 7 whence a, 2 = 



1192.44 



4°47'5i". 



The angles made by the chords from sta. ^ to the suc- 

 cessive stas. I, 2, 3, . . . . , 12, with the Y axis are given 

 in the previous table, and the values of <7 = 6 N" (in min- 

 utes), eq. (7), are placed above for comparison. 



It will be observed from this table that if we express a 

 to the nearest minute that we have, except for N =: 15, 



A =3 — = 2 N^ {in minutes) (19)- 



3 

 If we include N ^ 15, the extreme error made b 



the formula a = — is 35 seconds corresponding to N := 15, 



3 

 a matter of no practical importance. 



If we should continue the table for greater values of N 

 than 15, we should find the error in using (19) to increase, 

 which explains why N =: 15 is taken as the extreme limit 

 of the table; besides we rarely have need for more than 15 



