181. Q.—­Then by working an engine expansively, the power of the steam is increased, but the power of the engine is diminished?

A.—­Yes.  The efficacy of a given quantity of steam is more than doubled by expanding the steam four times, while the efficacy of each stroke is made nearly one-half less.  And, therefore, to carry out the expansive principle in practice, the cylinder requires to be larger than usual, or the piston faster than usual, in the proportion in which the expansion is carried out.  Every one who is acquainted with simple arithmetic, can compute the terminal pressure of steam in a cylinder, when he knows the initial pressure and the point at which the steam is cut off; and he can also find, by the same process, any pressure intermediate between the first and the last.  By setting down these pressures in a table, and taking their mean, he can determine the effect, with tolerable accuracy, of any particular measure of expansion.  It is necessary to remark, that it is the total pressure of the steam that he must take; not the pressure above the atmosphere, but the pressure above a perfect vacuum.

182. Q.—­Can you give any rule for ascertaining at one operation the amount of benefit derivable from expansion?

A.—­Divide the length of stroke through which the steam expands, by the length of stroke performed with full pressure, which last call 1; the hyperbolic logarithm of the quotient is the increase of efficiency due to expansion.  According to this rule it will be found, that if a given quantity of steam, the power of which working at full pressure is represented by 1, be admitted into a cylinder of such a size that its ingress is concluded when one-half the stroke has been performed, its efficacy will be raised by expansion to 1.69; if the admission of the steam be stopped at one-third of the stroke, the efficacy will be 2.10; at one- fourth, 2.39; at one-fifth, 2.61; at one-sixth, 2.79; at one-seventh, 2.95; at one-eighth, 3.08.  The expansion, however, cannot be carried beneficially so far as one-eighth, unless the pressure of the steam in the boiler be very considerable, on account of the inconvenient size of cylinder or speed of piston which would require to be adopted, the friction of the engine, and the resistance of vapor in the condenser, which all become relatively greater with a smaller urging force.

183. Q.—­Is this amount of benefit actually realized in practice?

A.—­Only in some cases.  It appears to be indispensable to the realization of any large amount of benefit by expansion, that the cylinder should be enclosed in a steam jacket, or should in some other way be effectually protected from refrigeration.  In some engines not so protected, it has been found experimentally that less benefit was obtained from the fuel by working expansively than by working without expansion—­the whole benefit due to expansion being more than counteracted by the increased refrigeration due to the larger surface of the cylinder required to develop the power.  In locomotive engines, with outside cylinders, this condition of the advantageous use of expansion has been made very conspicuous, as has also been the case in screw steamers with four cylinders, and in which the refrigerating surface of the cylinders was consequently large.