OUR COMMON ROADS—MURPHY. 459 
by the shortest or most direct line; (2) to avoid all unnecessary 
ascents and descents within the smallest practical limits; (3) to 
adopt such slopes or gradients for the centre line of the road 
as the kind of conveyance used may require; (4) to give the 
centre line such a position with reference to the natural surface 
of the ground, and the various obstacles to be overcome, that the 
cost of labor for excavations and embankments required by the 
gradients adopted and also the cost of bridges and other access- 
ories, shall be reduced to the smallest amount.” (Prof. Mahan.) 
GRADES AND TRACTIVE FORCE. 
“Upon common roads the grades, or the angles which the axis 
of the road should make with a horizontal line, depend so much 
upon the kind of vehicles employed for traffic, the character of 
the road coverings adopted for the surface, and the condition in 
which the surface is maintained, that no empyrical rule can be 
laid down. The grade should not be as great as to require the 
application of brakes to the wheels in descending, or to prevent 
ordinary vehicles carrying passengers at a trot. In general, the 
gradient should be somewhat less than the angle of repose, or 
angle upon which the vehicle in a state of rest would not be 
set in motion, by its own weight, but would descend with slow, 
uniform velocity if very slight motion be imparted to it. The 
grades, therefore, suitable for any road will depend upon the con- 
dition with respect to smoothness and hardness, in which the 
surface is to be maintained, and hence upon the kind of road- 
covering used; and as the force of gravity is the same whether 
the road be rough and soft, or smooth and hard, steep grades are 
more objectionable on good roads than upon bad.” (General 
Gilmore.) 
The general conclusions arrived at by M. Morin from his ex- 
perience on draught are as follows :— 
The resistance to rolling of vehicles on solid metalled roads and 
pavements is proportional to the weight and inversely proporti- 
onal to the diameter of the wheels. 
On solid roads the resistance is very nearly independent of the 
