126 On the Measure of 
A at its centre of gyration around the point, G, 
the result will be as follows : D will be brought 
to rest, G will move off as before with the 
velocity v, and A and B will have a rotatory 
motion about G, with the velocity v at their 
centres of gyration. In both instances, the 
striking forces, if measured by the masses into 
their velocities are the same; and as the strik- 
ing balls are in both instances brought to rest, 
they must have communicated exactly their. 
whole force to the mass which was struck. 
The results, however, are far from being equal. 
If the force of D be no greater than that of C, 
we shall have the rotatory motion produced 
without force, although we have no reason to 
suppose that the rotatory can be produced 
with less force than the rectilinear motion. 
St 
In order to avoid unnecessary calculations 
or analyses, I have stated these cases in the 
most simple forms I could devise. Iam aware 
that there are many who think they may be 
easily solved in the usual way, and that some . 
of the cases will be considered as trivial para- 
doxes. But if we examine the explanations 
which have been given of similar cases, we 
shall find that there is considerable diversity of 
opinion about the principles by which they are 
to be explained ; and that some of the solutions 
_- 
4 
{ 
5 
| 
\ 
