>ji6 Mr. Wildbore on 
0 to the great circle BOQj which force being in a direction 
parallel to and in the fame plane with the motive force a£ting 
at O perpendicular to the fame tangent muft be equal to it ; 
that is, the motive force which a£ts perpendicular to E at O is == 
x Dj/=Mr. Landen’s force E /7 . And this may alfo be 
3 
deduced by finding by refolution the motive forces along CO 
and AO, and reducing them into the diredtion of the great 
circle DOE at O, in the fame manner as the accelerating forces 
are managed in Prop. iv. above. Now, thele forces E and E r/ 
not being the only perturbating ones that difturb the motion 
of the body, but others arifing from the non-equilibrium of the 
particles in motion round the axes which are perpendicular to 
the, planes of the varying momentary great circles BOQ, 
DOE, they will neither divided by their refpeftive inertia — x 
M 
b z + c + d z — b r . s 2 and — X d 1 4- b z -f- y x c — b z — s z . a z — b z 
3 
give the accelerating forces along thofe circles, nor are pro- 
portional to them ; but, by the general properties of all motion 
as proved in Prop. iv. the accelerating forces in thofe circles are 
- x % (/ = that of the time) ^ X e z sy$ — 
g t v ' t t d- + c ~ ' 
2 / 2 * • 
O _ /m£? \ 1 
(b) and 
5 * X 
- X 
s t 
TO x e ^y = %? x w ~ to x 
x y$ % gy y(2 . . d z 
2 ^ 
g i 
eg* 
g t 
X - +-Xt -*4 = iL-x 
L zXe yS+ 7 -X C l~Xer^+gX 
g t 
d Z -b Z 
g 
s 
d* + c 
<“ + 
z 3$ 
a' 
a 
<b 
X 
d z -c z ^ c z ~b r 
X 7+b z " ' d z + b 
+b z a 2 + b 
d z -b z 
Xy z + 
d z — b z 
d z + b z 
)= 
__ e 2 $ 
g 
d 2 + b z 
(d z + S 
thefe equations (S) and (Q) there refults the analogy, as 
X y z + ~ — - ) = - (Q). And from 
d -f b J gt v 
d z -c z 
+ 6 
X e z gyf ~ 
C’ YP 
X e gyt : — x 
g 
( 
d"-+c 
‘ +- 
J 0 
d Z + b 2 
X y 
~r* 
