Mr. Herapath published a most able and searching analysis of M. Mallet's report; but, from the great length we have already devoted to this part of the subject, we can do little more than notice bis observations upon the amount of power expended in relation to the mechanical effect obtained.
He observes that "the relative areas of the air pump, and of the tube, and the number of strokes made by the air pump per minute, being known, we obtain the length of main that could be exhausted in an hour, which is the rate the load should travel per hour, if there were no loss from leakage. Again, having the exhaustion of the main in inches of the barometer, and the sectional area of the main, we get the tractive power, supposing there was no friction in the main. This tractive power multiplied by the velocity, gives the dynamic effect (or momentum) which the atmospheric railway should have, if there was no leakage or friction of the piston with its gear: hence, comparing this with experiment, we get the waste of power employed, or the expenditure to produce a given effect, independently of knowing the power of the engines.
"We have shown that the air cylinder would extract 73.154 yards of the main at every stroke, consequently, there being 22 strokes a minute, we have 73.154 X 22 X 60 / 1760 = 54.865 miles per hour for the velocity of a train, if there was no leakage at all. Either up hill, or on a level, this velocity should be the same if the apparatus was perfect. Moreover, the sectional area of the main being 176.71 inches, and the pressure of a column of mercury one inch high being 49lbs., we shall have for the pressure of an exhaustion of 24.75 inches - that at which the last experiment (p. 492) was made, - 176.71 X 49 X 24.75 = 2143. llbs. But a ton of goods going up an incline of .00719, gravitates backwards 16. l0lbs, and if the road friction of the carriages is 8lbs. per ton, we have 24. l lb. for the tractive force to draw one ton up an incline of .00719. Therefore 2143.1 / 24.1 = 88.923 tons.
Hence, the atmospheric should take 88 . 923 tons up the Dalkey incline, at the rate of 54 . 865 miles per hour, but it only takes 71 . 4 tons at a speed of 15 . 92 miles an hour. Therefore, what the apparatus does do, is to what it should do, as 71 . 4 X 15 . 92: 88 . 923 X 54 . 865 :: 1: 4 . 3. That is, between friction and leakage, the useful effect is not a fourth of what it ought to be, and this, it will be observed, is on the maximum effect of the plan."
On the subject of the cost of working the line, taking Mr. Bergin's statement, that the expense amounts to £1,171 per annum for the whole line, he observes, that this is equal to £781 per mile, and gives the following comparative view of the cost of motive power on the atmospheric and the locomotive systems.
Great Western locomotive . . . . . . . . . . . . . . . . . . . . . .
london and Birmingham ditto . . . . . . . . . . . . . . . . . . .
Dalkey Atmospheric . . . . . . . . . . . . . . . . . . . . .
Again, comparing the working expenses at Dalkey with those of the Camden station, where fixed engines and ropes are employed, he computes the cost of fuel and wages at Dalkey by the same scale as these items are charged at the Camden station, and he makes the cost of the Dalkey line to be £1,950, £l,300 per mile. By the statement of Mr. Creed, the secretary to the London and Birmingham line, it appears that the expenses of the Camden station for the year 1843, amounted to £1,441, and the line being 1 mile 4 chains in length, this is equal to £1,372 per mile.