The motion of a crank is therefore to be compared to the motion of a mathematical point at at an uniform distance around a centre; and which inotion is the result of the action of an infinite number of tangential motives, successively applied. On the other hand, suppose the point i was allowed to follow the tangential impulse for some distance and arrived at k, then the full tangential power would have been developed in conformity with its natural disposition. But, in the case before us, some power must be expended in constantly diverting the impulse from its natural course. And the line kx will represent the amount of that power required to force the point k, back towards the centre, to make it move in the circumference of the circle. We may therefore conclude, that the loss of effect is caused by the abstraction of power from the tangential forces in order to check their natural tendency and to make them conform with a circular motion. For the American Railroad Journal and Mechanics' Magazine. It is stated in a short editorial notice at the end of the Journal of 15th February, that "on examining the article in our last number, on Dr. Lardner's experiments, it appears that the writer has fallen into an error, which vitates much of his reasoning. The article was prepared in haste, and the writer is not at present in the city, but will doubtless make the necessary correction." The writer avails himself of the first opportunity to make these corrections, premising, however, that all the practical views and conclusions in the article referred to are, in his opinion, substantially correct, and that he still considers Dr. Lardner to have "signally failed in his attempts to prove that the resistance of the atmosphere has been underrated, that the frontage is unimportant, and that the resistance increases as the volume of the train." The general results of Dr. L. appeared so palpably erroneous, and it appeared so very easy to show that they were so, that the first part of the article was written without that caution and close examination which should be bestowed even on investigations of the very easiest kind. The assertion, that "the mere ratio of the height to the length of the plane and the velocity which gravity can generate on that plane, are not sufficient to determine the value of the resistances." (p. 73) has some truth when discussing the motion of a body up an inclined plane, but has no application in the present case-hence the remarks contained in pages 71, 72 and 73, even when correct in themselves, have little connection with the subject under discussion. When a body, left free to the action of gravity on an inclined plane, attains a uniform velocity, the power and resistance are necessarily in equilibrio and they may be represented by the weight of the body multiplied by the height and divided by the length of the plane. The same error occurs at page 80, where it is said, "Now, if on a plane of 1-89, the entire force of gravity be absorbed in overcoming the resistance, as previously assumed by Dr. L., whence is derived the power, which, by carrying the train up the next plane, so very nearly compensates for the power expended in the descent of the first ?" It is here overlooked that the entire power is absorbed only, at that velocity, and that the compensating power of the gradients arises exclusively from variations in the speeu. Again, at page 73, speaking of a mode of determining the resistance by observing the actual velocity at the foot of an inclined plane, then calculating the height due to this velocity and subtracting that from the entire height, it is hastily assumed that Dr. L. and Mr. Wood would consider the resistance as represented by the total height of the plane because they so estimate it, and very properly, when calculating the resistance at a uniform velocity. The two cases are, however, entirely dissimilar, hence there is nothing to justify any such supposition. It was said that "the late experiments of Dr. Lardner fully confirm the views of Mr. Brunel," etc. It would be more correct to say some of the experiments, for many of them are utterly irreconcilable with each other, or with the daily experience of the Whiston plane, as Mr. Brunel positively asserts. In addition to what was then said to substantiate these opinions, as well as to show the value of the ordinary modes of calculation, the following ex periments of Dr. Lardner are examined. Tables IV and V give the velocity of one coach (5:35 tons) on a plane of 1-89 as equal to 23 15 miles per hour, being the mean of three experi ments. Tables VI and VIII give the velocity of eight coaches (40-75 tons) on a plane of 1-177 as equal to 25 48 miles per hour, being the mean of four experiments. Now, if the resistance were as the volume of the train, we should have only half the velocity on 1-177, instead of which it is actually greater than on 1-89. In this case then, by increasing the volume of the train 8 times we have diminished the resistance more than one half, or, in other words a train of 8 coaches will descend an inclination of 30 feet per mile more rapidly than a single coach will run, down an inclination of 60 feet per mile. This great difference would, by the ordinary modes of calculation, be as cribed to the frontage, which is the same in both cases, and, supposing this equal to 50 square feet, we have, with the velocity of 25.48 miles per hour a resistance from the atmosphere =50 × 3·25 162-5 lbs. Now, the total resistance was equal to 1-177 of the weight, or 12-65 lb. per ton; and 40-75 × 12 65 515-48 lbs. equal to the entire resistance. Deduct from this the frontage 1625 lbs. +(40-75×5) 203-75 lbs. for the friction aud there remains 149-23 lbs for the resistance of the air to the other 7 coaches or 426 lb. per ton. Now add 5 pounds for the friction, and we have lb. 9-26 per ton, for the traction of all except the first coach at a velocity of 25-48 miles per hour. De Pambour estimated it at 8 lbs. with an average velocity of about 19 miles per hour, and if Mr. Brunel is correct in stating, (C. E. and A. J. p. 70, vol. 2,) "The passenger train, in descending this plane, with the steam shut off the engine, which then causes some considerable resistance, frequently acquires a very high velocity, exceeding forty miles rather than thirty miles per hour, and requiring the use of the brake," then is he fully justified in saying, (p. 70, ibid.) that calculations "if judiciously made, would give more correct results, though not nearly so large as the experiments before us; they would at least be free from several very serious sources of error." On Dr. Lardner's hypothesis the resistances ought to be equal in the two cases and the difference of more than one half cannot be explained, whilst with the ordinary modes of calculation, it is easily and satisfactorily accounted for. With a large train, the resistance would have been still less, as the frontage is constant, besides which, it is possible that part of the resistance, that is, the "friction" of the air on the sides of the carriages, may not increase as the square of the velocity. All calculations necessarily suppose an absolute calm, a rare occurrence, and in nearly every practical case it would be necessary to determine the force and direction of the wind, and make the requisite allowances. This would be attended with immense labor, and could hardly lead to any beneficial practical result, hence it is not likely to be undertaken by competent persons. As observed in the previous "remarks," the subject is more curious than useful, or even interesting," and, did the present state of the public works offer any thing more substantial to discuss, the writer would consider himself bound to apologize to the readers of the Journal for filling up so many pages with these "airy nothings." New York, March 7, 1840. W. R. C GREAT INCOME FROM A RAILWAY.-20 PER CENT. PER ANNUM. We have had placed in our hands, the "Statement of the Directors relative to the Syracuse and Utica Railroad, to 1st Jan. 1840." This road was commenced in 1838 and put in operation, the 3d of July 1839, at the following outlay of capital. The distance is 534 miles. For buildings, coach, engine, wood and water houses, 30,445 65 Deduct to show cost of road, this sum, for iron and stock in cluded in the above, for repairs on hand, The nett income for the first six months, is as follows. 20,500 $893,889 42 The receipt from 3d July 1839 to 1st Jan. 1840 was from 48,483 through, and 34,053 way passengers, 121,972 55 Transportation of freight $850, U. S. mail $2,801 08, 2,651 08 $125,623 63 The expenses of transportation account, are For superintending, collecting and clerk hire, $2,177 38 For services of engineers, firemen, brakemen, and away snow, and sundry work on road, 7,037 06 For incidental expenses, cattle killed, repairs on de- Nett receipts in 6 months, on outlay of $893,889 34,768 11 $90,855 52 Note. "The payments on transportation acconut in Deeember are more than the monthly average, from the fact that in this years disbursements are included the semi-annual expenses at Utica, and nearly all the taxes for the year." 66 The locomotive with business trains have travelled 35,139 miles."This corresponds in a striking manner, with the estimates made by the Chevalier de Gerstner, that it costs $1 per mile on an average for the expenses of the locomotive engine on a well regulated railway. J. E. B. REPORT OF THE CAMDEN AND AMBOY RAILROAD COMPANY. ANNUAL REPORTS OF THE RAILROAD CORPORATIONS IN THE STATE OF MASSACHUSETTS, FOR 1839. The perusal of these documents has afforded a most welcome confirmation of our opinion, made up from long continued observation, that railroads afford the safest and most profitable investment of money in the United States. The continued prosperity of complete and well managed roads, amid the most fearful commercial distress, affords the best evidence of the truth of our statement. Railroads must be made and must be used, and hard times" can have upon them will be a reduction of fare-accompanied by an immense increase of business. the greatest effect that It is well known that no public exposition of the affairs of the Camden and Amboy railroad, and Delaware and Raritan canal joint company, has ever yet been made until the present time. The whole line and its numerous appendages amounting in all to 92 miles of railroad, is now complete, and in successful operation, and the Directors now make a report containing a full exposition of all their doings, a description of the work and an inventory of all their property. This document likewise contains the monthly receipt and expenditure, from the commencement of business on the line, and several comparative tables. If we separate the receipt and expenses of the canal, it appears that the railroad has averaged a nett profit of about 11 per cent., since its opening-an interest superior to that yield-' ed by any other mode of investment. There are many interesting deductions to be made from the facts given in this report, the consideration of which is reserved for another occasion. Before leaving it however, we may remark, that the influence of the present untoward state of affairs, manifests itself in a remarkable manner. It will be found, that in the last three years the receipts have been rather less than in 1836, the period of their maximum, while the expenses have greatly diminished since that time, and that the net profit is still increasing. The Annual Reports of the Railroad Corporations in Massachusetts, to the Legislature of that State, are succinct statements of the condition of the roads, and the amount of expense and income, made under oath, and therefore are to be considered as excellent authority. Some of the works are but just commenced, others are partly finished, while a few have been in operation for some time. The following are those which have declared dividends. It is to be remembered that on several of these works, heavy sums have been expended for large portions of the line which are as yet incomplete, and yet need but little further outlay to finish them. The dividend is therefore on a capital, part of which is not yet productive. That such profits should be made upon roads in a portion of a single State, when bank, insurance and every other stock has depreciated, is most cheering to the friends of Internal Improvement, and to the public generally. It is an evidence that we have abundant resources within ourselves, and that we need railroads for their universal diffusion. It shows, too, that what is most necessary, is most profitable; thereby offering a sure inducement to the gradual and universal extension of railroads. With such prospects we need not despair. Increase of skill and inge |