Jan. 20, 1871.] 9 (Haupt. 
CompuTarron oF EFFECT oF GREDIENTS, by HerMAN Havrt, C. E. 
(Read before the American Philosophical Society, Jan. 20, 1871.) 
When the maximum load of the same engine on any two different incli- 
nations has been determined by experiment, the data thus furnished will 
suffice to calculate the load on any other inclination, the load on a level, 
the angle of friction at which a train will descend by gravity, the tractive 
power per ton of load required on a level, and the number of pounds 
adhesion for each ton of load. ; 
Let R = resistance of the train on a level, which is equal to the power 
of the engine. 
W = gross weight of train on a level. 
W! — Weight of train on grade a. 
W? = Weight of train on grade b. 
It is proper to assume that the power required to move a train and the 
resistance, which is equal to it, will be in proportion to the gross weight. 
The force of gravity on any inclination is in proportion to the height 
of the plane divided by its length, or as the rise per mile divided by 5280. 
The resistance of the train W! being in proportion to its weight, will 
be expressed by W! R 
fo 
“WwW 
and the resistance of WW, 2 bY. We R 
Wee 
: ‘ W'a 
The gravity of the train W! on the grade a = < 
: < 5280 
; r2 
and of the train W? on the grade bi 
5280 
Tf the engine is supposed to be loaded to the limit of its capacity on 
each gradient, then the power exerted must be the same as on a level and 
We W'a 
a | Med 
We Wl 
wh + F980 =R_ and consequently 
W'r pe eWedeg Wo Wb 
Wicd 2ORBO0, 6 Wo 1 5880 
From which the value of Rin terms of W W' and W? is found. 
Stas ac dae a 
5280 (W'—W?) 
wi Wla 
Take now the former equation R= we 5980 
from which a second value of Ris obtained = oo Wia Bes) 
5280 (W—W'!) 
ae 
A, PS 8-VOU Sir 
