218 SIR W. THOMSON ON VORTEX MOTION. 



and, at the same time, to conform to a common usage, we shall call them 

 impressed forces. 



4. From the homogeneousness as to density of the contents of the fixed 

 bounding vessel, it follows that the centre of inertia of the whole system of liquid 

 and solids immersed in it remains at rest ; in other words, the integral momentum 

 of the motion is zero. Hence (Thomson and Tait's " Natural Philosophy," § 297) 

 the time integral of the sum of the components of pressure on the containing 

 vessel, parallel to any fixed line, is equal to the time-integral of the sum of the com- 

 ponents of impressed forces parallel to the same line. This equality exists, of 

 course, at each instant during the action of the impressed forces, and continues to 

 exist for the constant values of their time integrals, after they have ceased. Thus, 

 in the subsequent motion of the solids, and of the fluids compelled to yield to 

 them, whatever pressure may come to act on the containing vessel, whether from 

 the fluid or from some of the solids coming in contact with it, the components of 

 this pressure, parallel to any fixed line, summed for every element of the inner 

 surface of the vessel, must vanish for every interval of time during which no im- 

 pressed forces act. If, for example, one of the solids strikes the containing vessel, 

 there will be an impulsive pressure of the fluid over all the rest of the fixed con- 

 taining surface, having the sum of its components parallel to any line, equal and 

 contrary* to the corresponding component of the impulsive pressure of the solid 

 on the part of this surface which it strikes [see § 8, and consider oblique impulse 

 of an inner moving solid, on the fixed solid spherical boundary]. But, after the 

 impressed forces cease to act, and as long as the containing vessel is not touched by 

 any of the solids, the integral amount of the component of fluid pressure on it, 

 parallel to any line, vanishes. 



5. If now forces be applied to stop the whole motion of fluid and solids [as 

 (§ 62) is done, if the solids are brought to rest by forces applied to themselves 

 only], the time integrals of the sums of the components of these forces, parallel 

 to any stated lines, may or may not in general be equal and contrary to the time 

 integrals of the corresponding sums of components of the initiating impressed 

 forces (§ 3). But we shall see (§§ 19, 21), that if the containing vessel be infinitely 

 large, and all of the moving solids be infinitely distant from it during the whole 

 motion, there must be not merely the equality in question between the time 

 integrals of the components in contrary directions of the initiating and stopping 

 impressed forces, but there must be (§ 21) completely equilibrating opposition 

 between the two systems. 



6. To avoid circumlocution, henceforth I shall use the unqualified term impulse 

 to signify a system of impulsive forces, to be dealt with as if acting on a rigid body. 

 Thus the most general impulse may be reduced to an impulsive force, and couple 



* I shall use the word contrary to designate merely directional opposition ; and reserve tin' 

 unqualified word opposite, to signify contrary and in one line. 



