The arrangement of the curves and slope grades, is such as to avoid, excepting in a few instances, the occurrence of a sharp curve on a heavy grade. Water stations are established ten miles apart, or as near this distance as the circumstances will permit. At each station is a "turn out" about 800 feet in length, to allow two trains to pass each other. It is presumed that it will at a future day become necessary to place "turn outs" intermediately between the present ones. In most instances store-houses will also be erected at the stations for the accommodation of the local business-and dwellings for the persons entrusted with the supervision of the road. The amount expended on account of the road to this date is one million one hundred and eighty-seven thousand seventy-two 55-100 dollars. The respective items of expenditure are as follows: For grading, including bridges and culverts, $518,463 11 137,293 61 167,711 22 13,844 50 22,480 97 13,323 63 922 25 40,016 05 Lumber, 27,924 32 From this amount may be deducted for implements, &c., on hand, Nett expenditure, Our examinations since the date of my last report, have not developed any features in the character of the country, leading me to doubt the sufficiency of the sum estimated at that time for the entire completion of the road, and if the company were at this time in possession of the requisite amount of available funds, there would be no difficulty in having the road in operation to the city of Macon in eighteen months. In our machinery, and transportation departments, we are gradually advancing towards the completion of a system commensurate with the ex 10,964 41 39,605 39 $1,197,072 55 10,000 00 $1,187,032 55 tended business that will undoubtedly be attracted by our road. The works at the Spring Hill depot, comprising the erection of the requisite machine shops, engine houses, passenger houses, store houses, offices, &c., have progressed with less vigor than would have been desirable, in consequence of the difficulty of obtaining a supply of materials, and a sufficient force of mechanics during the summer season; no serious inconvenience has resulted from this circumstance. In our motive power department, we have 5 locomotive engines, 4 of which are in good order, and one under repairs; 4 passenger cars, 13 close 8 wheel cars capable of stowing from 40 to 50 bales cotton each, 2 baggage cars and 8 open platform 8 wheel cars. It was supposed this would be sufficient to accomodate any amount of business that could reasonably be expected, during what may properly be called our first business season -while our road is only about half completed and has not yet approached within striking distance of the section of country from which we expect ultimately to derive our greatest business. We have, however, been obliged to keep every engine and car in constant requisition, for the transportation of merchandize fiom, and cotton to the city; and having been singularly fortunate in the regularity that our trains have run without accident, we have been able to do all or nearly all the business that has offered. We are in daily expectation of the arrival from the north, of two additional engines, two 8 wheel passenger cars, and the requisite machinery for our shops. Our mechanics will be kept constantly employed in the construction of freight cars, until we have a full complement for any immergency. The effect of the road even at this incipient stage of its operations, on the trade and general prosperity of the city, is most manifest. Persons from remote counties, who have not visited the city before for years, have come here for their supplies. We have transported merchandize during the present fall for upwards of fifty different counties; and instances have occurred, when we have had in the same train, goods destined for thirty counties. In confirmation of a remark in my last report relative to the healthiness of Savannah, is the fact, that amid the general prevalence of disease throughout a great portion of the southern cities, and in many parts of the country, during the past season; this city has enjoyed an entire exemption from any epidemic. No instance is known of a person having contracted disease by visiting the city from the country. The present season has afforded abundant demonstration of the benefits that would result from the construction of the contemplated branch road to the city of Augusta. During the past three months, large quantities of merchandize have arrived here for that city-while the epidemic prevailed, wagoners could not be induced to go there from the head of our road. The goods were stored, and with the exception of a portion that have been shipped to Charleston to go up by the Hamburgh road, are now in store here. The unusual drought has cut off all communication by the river, and now that the sickness is abaiting in Augusta, and the fall business is opening, it is almost impossible to appreciate the sacrifices and derangement of business that must result from these circumstances. The immense amount of business that would accrue to both cities furnish a most pressing inducement for the early commencement of the road in question. I will close this communication with a statement of the business of our road for the three months ending 31st October. August, 688 1565 10 875 6278 49 7843 59 2215 50 11844 99 14060 49 231085244 85 $20232 25825477| 10 I am sir, very respectfully, your obedient servant, L. O. REYNOLDS, Chief Engineer. THEORY OF THE STEAM-ENGINE. Section II-Of the velocity of the piston under a given load. In the 6th section of the preceding chapter, we have demonstrated that duringall its action in the engine, the steam constantly remains at the state of maximum density for its temperature; and we have shown that, accordingly, when the steam passes, in the engine, from a certain volume M' to another volume M equally known, and that its pressure varies in consequence, and passes from the known pressure p' to another unknown pressure p, the pressure p may be determined by the following equation : This preliminary relation once established, in order to embrace immediately the most complete mode of action of the steam, we will suppose an engine working with expansion and condensation, and with any pressure whatever in the boiler. Then, to pass afterwards to unexpansive engines, or to those without condensation, it will suffice to make the propper sup pressions and substitutions in the general equations. From what is already known of the proposed theory, the relation we seek between the various data of the problem, will be deduced from two general conditions: the former expressing that the engine has attained an uniform motion, and consequently, that the quantity of work applied by the power is equal to the quantity of action developed by the resistance; the second, that there is necessarily, equality between the mass of steam expended by the cylinder, and the mass of steam generated in the boiler. Let P be the total pressure of the steam in the boiler, and P' the pressure the same steam will have on arriving in the cylinder, a pressure which will always be less than P, except in a particular case, which we shall treat of shortly. The steam then will enter the cylinder at the pressure P', and will continue to flow in with that pressure and to produce a corresponding effect, till the communication between the boiler and the cylinder is intercepted. The arrival of any new steam into the cylinder will then be stopped, but that which is already there will begin to dilate during the rest of the stroke of the piston, producing by its expansion a certain quantity of work, which will go to augment that already produced during the period of the admission of the steam. P being, as has been said, the pressure of the steam in the boiler, and P' the pressure it will assume on reaching the cylinder before the expansion, let be the pressure of that steam at any point of the expansion. At the same time let / be the total length of the stroke of the piston, l' the portion traversed at the moment when the expansion begins, and λ that which corresponds to the point where the steam has acquired the pressure. Lastly, let a be the area of the piston, and c the clearance of the cylinder, that is to say, the vacant space which exists at each end of the cylinder, beyond the portion traversed by the piston, and which necessarily fills with steam at every stroke; this space, including the adjoining passages, being represented by an equivalent length of the cylinder. If the piston be taken at the moment when the portion of the stroke traversed is, and the pressure, it will appear that if the piston traverse, moreover, an elementary space dλ,, the elementary work produced in that motion will be adλ. But at the same time, the volume a (l'+c), occupied by the steam before the expansion, will have become a (λ+c). Hence, from the equation (c), indicated above, there will exist between the two corresponding pressures P' and, the analogy Multiplying the two members of this equation by a dλ, we shall deduce This expression will give then the quantity of elementary work produced by the expansion, while the piston traverses the space dλ; and if the integral be taken between the limits l' and 7, we shall have the total effect produced by the expansion of the steam, from the moment of its being intercepted to the end of the stroke: viz. an expression in which the logarithm is a hyperbolic one. This quantity expressing the work performed in that portion of the stroke during which there was expansion, if we add to it the effect Pal produced during the anterior part of the stroke, or before the beginning of the expansion, we shall have for the total work developed by the steam during the whole stroke of the piston, } But the engine being supposed to have attained uniform motion, the work developed by the mover must be equal to that developed by the resistance. Representing by R the total pressure exerted on the unit of surface of the piston by virtue of that resistance, or rather by virtue of the divers resistances which take place in the engine, the work it will have developed in one stroke, will have for its expression, a a Rl. We must therefore have the analogy a (l'+c) G +P) n al=Ral ༽ + log + c (A), which is the first general relation between the different data of the problem. This equation expressing that the work developed by the power, is entirely found in the effect produced, it will be remarked that, for the analogy to take place, it is not necessary that the motion of the engine be strictly uniform. It may be composed of equal oscillations, beginning from zero of velocity, and returning to zero again; provided the successive oscillations be made in equal times, and that the changes of velocity take place by insensible degrees, so as to suffer no loss of vis viva. It must be observed also, that, if in this expression we make l'=l, which amounts to supposing that the engine works without expansion, the equation reduces itself to P'R; that is to say, the pressure of the steam in the cylinder will, in this case, be equal to the pressure of the resistance against the piston, as we have already demonstrated directly for unexpansive engines, of which we spoke in the first chapter. We have just obtained the first general relation between the data and the incognita of the problem. Let us now seek a second analogy resulting from the equality between the production and the expenditure of the steam. If S be made to express the volume of water evaporated by the boiler in a unit of time, and transmitted to the cylinder, this volume on reaching the cylinder, transformed into steam at the pressure P', will there become, from the relation already given (a), S n + q P' This will then be the volume of steam, at the pressure P', supplied by the boiler in a unit of time, in one minute for instance. On the other hand, a (l'+c) being the volume of the steam expended at each stroke of the piston, if there be K strokes per minute, the expense per minute will be Ka (l'+c). But expressing by v the velocity of the piston per minute, we shall have also v=Kl; which gives K=7. Whence the above expenditure will be va (l + c) し v Since, then, there is an equality between the production and the expenditure of the steam, we shall have the equation which is the second general relation between the data and the incognita of the problem. Consequently, on eliminating P' from the two equations (A) and (B), we shall have as the final relation sought, it is known that these logarithms are deduced from those of the tables, by multiplying the latter by the constant number 2:302585, or approximatively 1+c by 2.303, the term log might, for practical purposes be replaced by l' + c 1+c 2.303 log in which log. would then express an ordinary logarithm. l' + c' But as tables of hyperbolic logarithms are found in several works, and as besides, we shall give in the sequel, a table which will dispense from all research on this head, we will not here make any change in the formulæ. This equation is less simple than that which would be obtained in the same inquiry, by supposing the steam to preserve its temperature through the whole of its action in the engine; but that supposition, though producing often but slight differences in the definitive results of the calculations, is not really exact, since it is incontestable that the steam changes its pressure during the expansion, and that the experiments quoted above prove that it changes temperature in a manner exactly correspondent. The last formula. which we have presented, has then the advantage of taking this important circumstance into account, and consequently of being more accurate in the applications. Besides, if in equation (1) the effect of the change of temperature be annulled, the formula becomes the same that we have presented in the first chapter, supposing the preservation of the temperature of the steam. |