3 
fixed by the keep-pin d, and the loops e, c' for the active position, and c 3 for the 
passive position of the brake. 
In order to determine experimentally the force required : 
1. to unship the brake; 
2. to keep it unshipped; 
the loops A were replaced by dynamometers, and the maximum force indicated 
was about 55 lbs., while a force of only 9 lbs. was found sufficient to release the 
brake. 
These results can be easily explained. Their solution is no other than that of 
the problem: to find at every moment, the value of the power P of given direc¬ 
tion, in equilibrium with a resistance It, of given magnitude and direction, and 
knowing the course followed by the point, at which the power P and the resistance 
It are applied. The direction of the harness traces may be taken as the given 
direction. It may be considered invariable when the horses are about to start the 
carriage. 
The resistance P, being the measure of the force of the spiral springs (80 
lbs.), is exerted at the point U, where the traction rod is attached to the swingle- 
tree hook. The power of the horses, acting at the trace hooks, is applied at a 
point obviously at the same distance from the splinter-bar as the preceding force. 
We may therefore regard as equal the two arcs of circle which these two points 
describe round the splinter-bar when the swingle-tree is turned by the power of 
the horses. (We might, on the other hand, take account of the difference between 
the radii r, r\ of these circles. The courses traced by the two points will be in 
the proportion of r to r\ since the angles of turning round the splinter-bar are equal. 
In the equation below the quantities P and P should be replaced by the values 
P r, P/, proportional to the respective work performed. The radii r, r', can be 
directly measured). 
Similarly, with regard to the traction rods, we may consider their direction known 
and constant, and disregard, owing to their length, the slight displacement of the 
jointed end at the swingle-tree hook. 
The conditions are therefore those of the case propounded :— 
P known in direction ; 
P known in direction and magnitude; 
the direction of both forces being constant. 
Let then {3 be the constant angle which the traces make with the prolongation 
of the traction bars. Let us consider an element ds of the arc described by the 
point U where we suppose P and P to be applied. Let a be the angle which 
this element makes with the prolongation of the traction bar. 
Fig. 1. 
Then the equation of equilibrium gives ; 
