82 A NEW METHOD OF DETERMINING 
The equation (11) is thus changed into 
a= 1— Jo f(1 +24 H) srar— 2! J (x! sryat 
dt ky Po key/ Do 
(12) 
Te COE os Sir ee WA 
1a ele ) a apy V Po 
The equations (10) and (12) can be put in briefer form. 
Let 
Rex Bs VS s: 
Sass A b) (Bi 5 - 
se 1D 
Then 
a COSTAE (5 Lv Gye 
ae J X,dt += J Y, dt, 
(18) 
dz 1 ) Qy > 
cae ee UEN. Bio gy a (Pe eee 7 
dee loa mA (+ ) Seat Ed tS || Y.d 
The values of «, y, found in these equations we get from 
cA + 5% 1 ce os 
x= a + —"(2—t) + 4.5 (e—t) + ete. 
dy . Wy, \2 CS) 
Y=Yot Fi ee t) +4. ae (g—t) + ete. 
! df 
From the expressions for = ; a , we have also 
Az Zz 
cos f +e, __ ue — Ki 10% : 
Gay LW € ee de ic t)) UC: 
(15) 
sin f 1 fds, PI fgg ; 
Sa a oe CO ce 
The quantities given by equations (14) and (15) are found in equations (13) 
without the integral sign. They can be put under the sign of integration and regarded 
