Il8 JOURNAL OF THE ' 



tersection of chord SL and OD), and since arc a nearly 



FD a 



and A = — we 



LD ^ 



2 



KL X 



or since CG = = — . •. FD = ^ x, 



2 2 



and DC = FC — FD = x — y^ x ^^ % x = q. 



X 



From the table we see that Q = — = Vi nearly through- 



9 

 out. 



We have shown above likewise that CE = x^ = }4, x 



nearly, and as ^ = 14^ .r nearly, we have, nearly, 



cn = y,ci} = y, q; 



so that the curve SEL nearly bisects the gap q between the 

 tangent and the circular curve. 



We shall now deduce an approximate formula for finding 

 the successive angles ^ in terms of N and N,, the numbers 

 of the stations between which the chords are drawn. 

 Neglecting all terms of (14) after the first, and calling 

 x^ the approximate value of ,r, we have 



^' 



— =L y^ a =^ [\ iXo nearest minute of arc). 

 s 



We should naturally infer, within this same limit of 



accuracy, that the arc i can be expressed by a similar 



approximate formula, 



- 1 



I 



