18 A NEW METHOD OF DETERMINING 
Deduce the values of 8) + &, y, — 7 from (a) and (d), substitute them in (¢), we find 
G — (oS 
eo Sra Ma eas 
The last equation then takes the form 
O= 77-5 — Bo (¥2—$) —4 (70 +S) (Y2—S).S- (¢) 
This equation furnishes the value of £; and with ¢ known, we find &, 7, from equations 
already given. The three equations giving the values of the quantities sought are 
Sar Soa) S se lA +P ban = B70 oo) ho Or y2=0) 
BP Boo = (yar S)G =) (Cr) 
n—y1.n+ (Yo+%) (¥2—4) =) 
Finding the values of ¢, £, 7, from these equations, and arranging with respect to y., 
preserving only the first power, we have 
Belt 
bea =- Bo: ye : 
a (9) 
jae te ty i 
= oom 
hae? ies Ae? 
Substituting these values in equations (16), they become 
q7.5n0Q = Ge ee Yo 
q.cosQ = y,— Fie ga an 
q Csin Q= ao (ait rr 2 
gq. Coos Q= Esty, 
noting that C= y, + ¢. 
If more accurate values of ¢, &, 7, are needed than those given by equations (gq), 
we proceed as follows : 
Substitute the value of ¢ given by (g) in the second term of the first of equa- 
tions (/), we find, up to terms including y,’, 
Pome ReMi Coats » : _ fo: (bts By 18 
GS= 7 2° V2 ap abe Ge aE APP” Yo — 4. Yo: ( ) 
