method of representing on a map the steepness of a road at every part.
Contours, of course, show how far one has to go to rise 50 or 100 feet,
but as to whether the ascent is made uniformly or in an irregular
manner, with steep and level places, they tell us nothing. Let the
course of a road be indicated by a single line where it is level, and by
a pair of lines where inclined. Let the distance between the lines be
everywhere proportional to the steepness, then the greatest width will
show the steepest part, and an intermediate width will show places
of intermediate steepness; the crossing of the lines, which must be
distinguishable from one another, will show where the direction of the
slope changes. Further, the size of the figure bounded by the two lines
will show the total rise; a great height being reached only by great
steepness or by great length, a large figure being formed only by great
width or by great length. Those who are mathematically inclined will
recognize here that I have differentiated the curve representing the
slope of the bill, and laid the differential curve down in plan.

Having wandered off my subject, I must return to more mechanical things,
and give the results of some experiments which I have made on the balls
of ball bearings. There is no necessity to argue the case of ball vs.
plain bearings, the balls have so clearly won their case, that it would
be waste of time to show why. Of the wear of the twelve balls forming
one set belonging to the bearings of the wheels of my Otto, I have on a
previous occasion spoken; I may, however, repeat that in running 1,000
miles, the twelve balls lost in weight only 1/20.8 grain, or each ball
lost only 1/250 grain. The wear of the surface amounted to only 1/158000
inch; at the same rate of wear, the loss in traveling from here to the
moon would amount to only 1/34.3 of their weight. I examined each ball
every 200 miles, and was surprised to find that on the whole the wear of
each, during each journey, varied very little. The balls experimented on