the gross percentage of waste is made less in the proportion of this division. The heat and steam rejected as waste by internal transfer without transformation from the first cylinder, are utilized in the second nearly as effectively as if they were received directly from a boiler at the pressure of rejection from the first cylinder. In so much, therefore, as the pressure can be increased and the increase utilized by the addition of another cylinder, gain is secured. If the total ratio of expansion can thus be raised, under the best working conditions for each case, from, we will say, four up to eight, we should hope to secure a reduction of coal consumed from two and a half, we will say, to two pounds per horse power and per hour, which is about the average figure in good practice. The practical questions thus meet the engineer: To what extent can this principle be availed of? What range of pressure and what ratio of expansion should be assigned to a single cylinder? and how many cylinders should be adopted to give the best results with the highest steam pressure practicable for a specified case? Common experience aids in solving this problem, by showing that the very best results are ordinarily obtained, in each class of multi-cylinder engines, when, the engine being properly designed for its work, terminal pressure for the system can be economically made something above the sum of back pressure in the low-pres- will be here assumed. The fundamental principles are now easily perceived. There are three main facts upon which to base our theory of the multi-cylinder engine. These are: (1) Economical expansion in a single cylinder has a limit due to increasing internal wastes, which is found at a comparatively low ratio of expansion. (2) The method of expansion may be, for practical purposes, such as are here in view, taken to be approximately hyperbolic; the terminal pressure being somewhat above that which corresponds to the sum of all useless resistances, and which may be here taken, as for example, about ten pounds per square inch above vacuum. The division of the initial pressure by this terminal pressure will thus give an approximate measure of the desirable ratio of total expansion for the best existing engines. (3) All steam entering any one cylinder will be rejected, as steam, into the succeeding cylinder, external wastes being neglected, and into the condenser; and the full amount of steam condensed at entrance by absorption of heat by the interior surfaces of the cylinder will be re 1 evaporated later, and will pass into the condenser or into the next cylinder, and heat transferred in the one direction, in the one process, will be transferred in precisely equal amonnt in the opposite direction in the other. The last point is a very important one, and it is very easily established. The cylinder, when in steady operation, is neither permanently heated nor permanently cooled; no progressive heating can go on, as it would, in that case, become heated above the temperature of the steam and become a super-heater; no progressive cooling can occur, since in that case the cylinder would become a condenser of indefinite capacity. It must, therefore, transfer to the next element of the system all the heat which it receives, assuming that external radiation and conduction may be neglected, and that the Rankine and Clausius phenomenon of internal condensation, by transformation of heat into work, is ignored. It also further follows that the introduction of one or of many cylinders between the terminal element and the boiler does not, through cylinder condensation, affect the operation of the latter cylinder, however great that condensation may be, provided the operation of the added elements is effected by raising the steam pressure commensurately, leaving the final element of the series the same initial pressure as before. The total waste by this form of loss is thus evidently measured, in the case of the multi-cylinder engine, by the maximum waste in any one cylinder. If all are equally subject to this loss, the rejected steam of reevaporation from any one cylinder, supplies precisely what is needed to meet the waste by initial condensation in the next; and so on through the series. Thus the use of a series of cylinders, in this manner, divides the total waste for a single cylinder, approximately at least, by the number of cylinders; and it is in this manner that the compound system gives its remarkable increase of efficiency. As stated by the writer,* many years ago, "The serious losses arising from condensation and re-evaporation within the cylinder, and which place an early limit to the benefit derivable from expansion, affect both types of engine, and so far as seems now known, equally;" but the modern type permits the interception of the heat wasted from one cylinder, for utilization by its successor, in such manner that the total waste becomes, practically, that of the low pressure cylinder alone. If any one cylinder wastes more than another, the total waste is, as above stated, measured more nearly by the loss in the most wasteful member of the system. Thus the three principles which have been *Thurston. above enunciated give a means of constructing a philosophy of the multi-cylinder engine, which will meet the essential needs of the designer and of the student of its theory. The first principle shows that a limit existing to economical expansion in a single cylinder, the advisable number of cylinders in series may be determined, when that limit is ascertained, either by experiment, by general experience, or by rational theory and computation. The second principle shows that we may find a tentative measure, at least, of the desirable ratio of expansion for maximum density when the best terminal pressure for the chosen type of engine is settled upon. This total range is divided by the admissible range for a single cylinder, raised to a power denoted by the number of cylinders. Combining thus the two considerations referred to, we obtain a determination, probably fairly approximate, of the proper number of cylinders in series. The third principle permits an estimate to be made of the probable internal wastes of the series, and the probable total expenditure of heat and of steam, and a solution of all problems of efficiency for the compound engine of whatever type. The first step in the process is evidently the determination of the best ratio of expansion, under the assumed condition of operation and for the given type of engine, for a single cylin |