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value of the freight, are not the only losses involved in the adoptionof an insufficient speed. The value of the time of the train, and ofthe train hands, is also to be considered, and enters into the completeexpression of the actual cost of transportation. If the engines andcars, and the men who conduct them, do less duty than they mightaccomplish by the adoption of a higher velocity, the value of the timeof the increase of stock and force which will be required to effect thesame duty at the slower rate, must obviously be charged against thatvelocity.

It is true that there are cases in which the speed to be adopted isgoverned by the necessity of accommodating a certain amount oftrade, or making room for a large passenger conveyance, which couldnot be adequately provided for on a single track, without maintaininga speed determined by the circumstances. Of course the companymust submit to this necessity; they must adopt a high velocity wherethese or other imperative conditions exact it. But the question nowis, what is the value of velocity or time, where they have the powerto exercise their own discretion in the selection of the speed?

In all such cases, the slower the motion of the train the less will bethe expenses of the company, unless it be reduced so low that the in-terest on the cars and engines which convey the freight, and the lossof the time of the engine and train hands, more than compensates forthe reduced charges for repairs of the road and machinery.

Wo will designate by F the value of the locomotive engine in dol-lars ; by/the value of the stock in cars for each ton of freight; by m'the value of the time of all the hands in the train for one hour; andby q the number of tons of merchandize in the train.

The value of one hour for the whole train will be, at 6 per cent.,

ioL< F+ ' / 'f> + “' i (L)

and if we represent this quantity by H, the difference between thevalues of the velocity V' and that of V, will be for each ton, and forone mile,

H/V — V\7 V V'V /•

(M)

This is the difference per ton per mile to the company between thevalues of these velocities, where no imperative conditions obtain.

Now let 11 s see what value this expression exhibits under differentcircumstances; and for this purpose we will put F = 5000; f— 100;<7 = 50; m = 8760\ m' = ^, all of which are very common values, andsuppose, in the first instance, that the business of the line may betransacted by an adequate supply of engiues, men and cars, at som.e