14 Mr. WHEWELL on the 
Mr. Wildbore will not, I think, be found so simple and easily 
intelligible as might be wished; and the following method 
appears to me to possess these advantages in a great degree. 
It would be taking up too much time to trace Mr. Landen’s 
mistakes from their first principles; the general foundation of 
them may be stated to be the assumption which he makes, that 
if one force will produce the same effect as another in affecting 
the motion round the avis, it may be substituted for that other ; 
not observing that forces equivalent in that respect will not 
necessarily produce the same effect in other respects. 
The error of principle with which he charges other writers 
is “the resolving a force productive of rotatory motion into three 
forces, and considering each of these forces as acting separately 
on the body impelled.” (Math. Mem. xiv, p. 79). Now there can 
be no doubt that with respect to a single point in motion, we may 
resolve the forces which act upon it in the direction of three 
co-ordinates, and consider the motion of the body in the direction 
of each co-ordinate as affected only by the force in that direction; 
and we shall find that this reasoning will lead us to conclu- 
sions on the subject of rotation. 
The case which TI shall take is where the system is acted 
upon by no extraneous forces whatever. Let three lines at right 
angles to each other pass through a point O, and at the extre- 
mities of the lines, suppose. three material points m, m’, m’. Let 
these points be joimed by lines mm’, mm", m'm'. If now the six 
lines Om, Om', Om", mm', mm", m'm', be supposed to be rigid 
rods without weight, the system will be perfectly unalterable 
in form, and the whole mass will be collected at the points 
m, m', m’. Let this system be supposed to move any how about 
the point O, being left to itself, and not acted on by any force ; 
then the only forces which act on the poimts m, m', m’, are the 
tensions of the six rods just mentioned; and by resolving these, 
