552 Mr. W 1LDB0RE on 
This matter M. Euler confiders in a fome what different 
light, by finding the initial axis , or that about which, if the 
body were perfectly at reft, it would be firft urged to turn by 
accelerating forces ading upon it ; and from Scholium i. Prop. 
IY. above it appears, that if the body were at reft, and aded 
upon by three external accelerating forces-? , - , and it would 
be urged to turn the firft inftant about fome axis whofe pole is 
' ' 2 t_ " 2 _1_ ri- 1 
E by a fingle forcerr — - — -- — —> fuch that the five forces, 
? , Z , j and ~ will be refpedively as radius, 
cof. EA, cof. EB, cof. EC, and cof. EO, or 
t x coi. EA 
y — 
55 
ixcof. EB ixcoi. EC /xcoi. EO 
- , and fince when the body is in 
motion, and that motion difturbed by the unequal ad ion of its 
own particles which generates accelerating forces, fuch forces 
confidered Amply in themfelves muft ftill have the fame ten- 
dency to turn the body about fome axis whofe pole is E dif- 
ferent from that whofe pole is O, and fuch that the above 
equation may ftill obtain, and if the above-found values of 
Z Z and ? , be fubftituted therein, by means of a calculus 
i i i 
fo inftituted, the value of *, and confequently a will come 
out the very fame as by the preceding methods. 
2. It ftill remains to be fhewn, that the point Z now deter- 
mined has the properties (hewn to be requifite in the fifth Pro- 
pofition above, viz . that it is at reft in abfolute fpace, and 
therefore at reft both with refped to the motion of the fpheri- 
cal furface, and to the velocity with which O the pole of the 
momentary axis fliifts its place. Now, by Scholium i. Prop. 
IV. 
