With Jonathan, it had been **instantaneous** as well.

In a couple of years, I won't have so many problems searching the memories. It'll be **instantaneous**, like that! he said and snapped his fingers.

His success was **instantaneous** and complete.

The **instantaneous** centre of CD will be at the intersection of AD, BC, and if CD be drawn parallel to CD, the lines CC, DD may be taken to represent the virtual velocities of C, D turned each through B a right angle.

52, if an infinitesimal deformation is possible without removing the bar CF, the **instantaneous** centre of CF (when AB is fixed) will be at the intersection of AF and BC, and since CC, FF represent the virtual velocities of the points C, F, turned each through a right angle, CF must be parallel to CF.

The whole effect is summed up in the value of the **instantaneous** impulse, which is the timeintegral of the force.

Thus if an **instantaneous** impulse ~ changes the velocity of a mass m from u to u we havtt mumu=f.

Again, if the **instantaneous** position of G be taken as base, the angular momentum of the absolute motion is the same as the angular momentum Of the motion relative to G.

Coincide withthe **instantaneOus** positimi of G, we have ~, 5i, z=o, and the theorem follows.

The kinematical relations above explained now lead to the conclusion that in calculating the effect of extraneous forces in an infinitely short time t we may take moments about an axis passing through the **instantaneous** position of G exactly as if G were fixed; moreover, the result will be the same whether in this process we employ the true velocities of the particles or merely their velocities relative to G.

CG2.61, by 3, since the body is turning about the line of contact (C) as **instantaneous** axis, and the potential energy isMgh cosO.

~(m.PN1)=Iw2, (4) where I is the moment of inertia about the **instantaneous** axis.

Drawn in the direction of the **instantaneous** axis, we have I I=M4/p(~ II); hence w varies asp. The locus of J may therefore be taken as the polhode (f 18).

Thus the relative motion of the wheels is unchanged; but I is considered as fixed, and 2 has the total motion, that is, a rotation about the **instantaneous** axis I, with the angular velocity cii+a1.

It is seemingly **instantaneous** at last.