FORMULAE. 
117 
“_/ ” is the grade in feet per mile. 
u x" is the load drawn, including tender, and is expressed in tons. 
Formulae (2) and (4) are simply deductions by transposition from (1) and (3.) 
In formulae (1) and (3) the numerator expresses the effective adhesive weight; that is to say, it 
expresses the portion of the total adhesive weight which is found by experiment to be really 
effective in drawing a load in certain states of the rail. Now, since we know by experiment that 
on a level a force of eight pounds is necessary to draw one ton, if we divide the effective adhesive 
weight (expressed in pounds) by 8, the quotient will be the load due that effective adhesive weight, 
0.2 A 
and formula (1) will read x — -. 
8 
On a grade we know that, in addition to the force necessary to overcome the friction, it is also 
necessary to apply further power to counteract the effect of gravity. 
Taking a load of one ton, and calling “/” the height of the plane, “Z” the length, (for the value 
of which we may, in the slight inclinations given railway grades, substitute the value of the base 
of the plane, without appreciable error,) we have for the tendency of one ton to move down the 
2240 xf 2240 x f 
plane-, or substituting for l, 5280, the number of feet in a mile-- == 0.4242/ “f ” 
l 52S0 
being the height in feet of a plane whose base is one mile long. 
This expression (0.4242 f) is, then, the measure of the force required to prevent one ton from 
sliding down the plane, and must be added to the force necessary to overcome the friction of a 
ton on a level in order to obtain the force required to keep one ton in motion up a grade. 
Dividing, then, by this sum (0.4242/ + 8) the disposable power of the engine (0.2 A,) we 
have the number of tons that the engine can draw up any given grade. 
Engines usually weigh from 20 to 24 tons: some as much as 30 tons: it is considered desirable 
to reduce the weight of engines as much as possible, in order to diminish the wear and tear of 
the rails. 
Most engines now run with four drivers—the front of the engine resting upon a truck with 
eight small wheels; some engines, particularly those intended for heavy grades, are placed upon 
six wheels, all drivers, in order to increase the effective adhesive weight. The objection to mul¬ 
tiplying the number of drivers consists in the increased number of joints, &c., with the conse¬ 
quent increase of friction and loss of power. 
A common 8-wheel tender weighs, empty. 14,000 lbs. 
Water for 25 miles, (12,000 gallons at 8.35 lbs. per gallon). 10,437 “ 
Wood, (1.44 cord, at 3,180 lbs. per cord). 4,579 “ 
4 passenger cars, for 50 passengers each, at 12,000 lbs. each. 48,000 “ 
2 baggage cars, at 16,000 lbs. 32,000 “ 
200 passengers, at 150 lbs. each. 30,000 “ 
Baggage, at 100 lbs. each passenger. 20,000 “ 
Add for contingencies. 12,224 “ 
Total weight of train of 200 passengers. 171,240 “ 
or 76 tons. 
We will now take a 20-ton engine on four drivers and apply the formula. 
The total adhesive weight will be about. 2S.600 lbs. 
Its maximum load on a level, over a good track. 715 tons. 
Its maximum load on a level, over a track in bad condition, slippery, &c. 511 “ 
By formula (2) we have for the same engine the maximum grade up which it 
can draw the train of 200 passengers, as given in detail above. 159f feet. 
By formula (4) we have for same data a maximum grade of. 109 “ 
