19 
Assuming small inclinations dg and dw this expression can be written 
  
€ (de — do) 
dx E e (45) 
2b'11— 2» (dpa — dq) 
  
After developing (45) into series and neglecting terms of second and 
higher order we find the simple expression 
C 
do == ; (de, — dox) (46) 
20 
Next we use differentials in the expressions (40)— (43). 
The coordinate transformation formulae will then become 
| i: B C y c 
gm AG) + dp +75 p (do, — de) (47) 
C ase 
y = (uu 0m p (de, — do) (48) 
C ^c 
| x" = (x") + 5 dp; + b! (do) — dex) (49) 
| 2 2b 
| 
C rz" 
| y" — (y") — 2 do, — y (de — do) (50) 
2 2b 
If dq, do, dy, and do, are corrections the corrections of the (x') 
ete. coordinates can therefore be written 
C y 
dz’ dq, + — (do, — do 51 
9 /1 b 2 1 
C | x’ a 
dy" 2 | y 1] do, — x dw, (52) 
dz’ == + "n d T (de — do | (53) 
^ 9 | Va p va 0 | f 
C X "H x" 
dy" 2 | yp de x + 1) dw, (54) 
After substituting the expressions (51)—(54) into the differential for- 
mulae (3) and (4) we find the expressions for the corrections of the