The more accurate method of calculating the effect of the expansion from B to C, would involve more advanced mathematical principles than could properly be introduced here; but the result of such a computation would be that the actual average effect of the steam from B to C would be equal to a uniform pressure through that space, amounting to one thousand five hundred and forty-five pounds, being greater than the result of the above computation, the difference being due to the expansive action through each of the ten divisions, which was omitted in the above computation. (91.) It is evident that the expansive principle, as here explained, involves the condition of a variation in the intensity of the moving power. Thus, if the steam act with a uniform energy on the piston so long as its supply from the boiler continues, the moment that supply is stopped, by closing the steam valve, the steam contained in the cylinder will fill a gradually increasing volume by the motion of the piston, and therefore will act above the piston with a gradually decreasing energy. If the resistance to the moving power produced by the load, friction, &c. be not subject to a variation corresponding precisely to such variation in the moving power, then the consequence must be that the motion imparted to the load will cease to be uniform. If the energy of the moving power at any part of the stroke be greater than the resistance, the motion produced will be accelerated; if it be less, the motion will be retarded; and if it be at one time greater, and another [Pg164] time less, as will probably happen, then the motion will be alternately accelerated and retarded. This variation in the speed of the body moved will not, however, affect the mechanical effect produced by the power, provided that the momentum imparted to the moving mass be allowed to expend itself at the end of the stroke, so that the piston may be brought to rest as nearly as possible by the resistance of the load, and not by any shock on any fixed points in the machine. This is an object which, consequently, should be aimed at with a view to the economy of power, independently of other considerations connected with the wear and tear of the machinery. So long as the engine is only applied to the operation of pumping water, great regularity of motion is not essential, and, therefore, the variation of speed which appears to be an almost inevitable consequence of any extensive application of the expansive principle, is of little importance. In the patent which Watt took out for the application of the expansive principle, he specified several methods of producing a uniform effect upon a uniform resistance, notwithstanding the variation of the energy of the power which necessarily attended the expansion of the steam. This he proposed to accomplish by various mechanical means, some of which had been previously applied to the equalisation of a varying power. One consisted in causing the piston