310 



Mk power, on the prevention of the 



But if the direction of F passes lower than the centre of gravity, an an- 

 gular velocity about D must necessarily result, the magnitude of which 

 is proportionate to the distance h at which the impulse passes below G. 



If the impulse passes above G, h changing its sign, a assumes a 

 negative value, which is impossible 

 so long as D is supposed to remain 

 in contact with the plane; we must 

 in this case regard E as the point 

 which remains in contact with the 

 plane, and calling R' the vertical 

 reaction at E, 



a the distance EL, 

 a the angular velocity about E, 

 we have, as before, 



Ma a' - R\ 

 Mk*a' = Fh - R'a'; 

 whence M (a' 2 + ¥) a' = Fh, 



a Mia'" + *»)' 

 which shows, as before, that if the direction of F passes through G, 

 no angular rotation will be communicated; and further, that if the 

 direction of F passes higher than G, an angular velocity, whose mag- 

 nitude is proportionate to the distance GH, will be generated, by 

 virtue of which D will be carried upwards, E remaining in contact 

 with the plane. 



The preceding results may be regarded as near approximations to 

 the truth, in the case of a wheeled carriage, when the mass of the 

 wheels is inconsiderable compared with the mass of the carriage. 



But as the wheels and connecting axles in locomotive engines are 

 very massive, it may be useful to inquire what influence the mass of 

 the wheels and axle, about which the rotatory motion takes place, may 

 have in modifying the preceding results. 



The carriage with its wheels not constituting a single rigid body, 

 as in the last case, the problem becomes much more complicated, and 

 it is extremely difficult to avoid sources of error in applying to it the 



