Take a string made up of pieces alternately black and white, each exactly as long as the wheel is high, and stretch it between the mark and the top of the wheel. If there are n pieces of string included, the slope is 1 in n, for by similar triangles the diameter of the wheel is to the length of the string as the vertical rise is to the distance on the road. This gives the average steepness of a piece sufficiently long to be worth testing, because an incline only a few feet in length, of almost any steepness, can be mounted by the aid of momentum.

There is only one process, with which I am acquainted, which supplies a 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 were a new set obtained from Mr. Bown. I also had from him one ball of each of each of the following sizes 3, 4, 5, 6, and 7 16ths of an inch in diameter, as I was curious to know what weight they would suppport without crushing.

As as preliminary experiment, I placed a spare 5/16 ball between the crushing faces of the new testing machine at South Kensington, and applied a gradually increasing force up to 7 tons 9½ cwt., at which it showed no signs of distress. On removing it I found that it had buried itself over an angle of about 60° in the hard steel faces, faces so hard that a file would not touch them. Those marks will be a permanent record of the stuff of which the ball was made. The ball itself is sealed in a tube, so that any one who is curious to see it can do so. Finding that the crushing faces were not sufficiently hard, I made two anvils of the best tool steel, and very carefully hardened them. These, though they were impressed slightly, were sufficiently good for the purpose. In the following table are the results of the crushing experiments:

3/16 ball at 2 tons 13 cwt. did not break, but crushed on removing part of the weight.

¼ ball at 3 tons 15 cwt. did not break, but crushed on removing part of the weight.

5/16 ball at 4 tons 9 cwt. broke.

3/8 ball at 8 tons 6 cwt. did not break, crushed under another 120 lb.

7/16 ball crushed before 3 tons, with which I was starting, had been applied. Examination showed that the steel bar of which it was made had been laminated.

These experiments do not tell much of importance; they are curious, and perhaps of sufficient interest to bring before your notice. The fragments are all preserved in tubes, and labeled, so that any one who likes to see them can do so.

Of the advantage which a machine which will collapse or fold up when desired, but retain its form on the road, offers in convenience, it is unnecessary for me to speak.

Of double machines, the Rucker tandem bicycle seems to me to be in every respect the best, but I should add that I speak only from imagination and not from experience. The independent steering, the impossibility of capsizing forward or sideways, the position of the rider over his work, the absence of any little wheel with its mud throwing and vibrating tendencies, combine to make a machine which ought to be superior in almost every desirable quality to any other; what it may be in practice I hope to hear in the discussion.

Of double tricycles, the Sociable has been tried by many, and is practically a failure in so far as traveling quickly and easily is concerned. The Tandem, though it presents so objectionable an appearance, seems likely to become a favorite, for it surpasses any single tricycle, and rivals the bicycle in speed. How it may compare in comfort or in safety with the single machine, perhaps those few who are well acquainted with them will say; at any rate, in the case of the Humber, greater stability is given to the steering, owing to the weight of the front rider.

Time will not allow me to say more of these machines, or to attack the subject of steam, electric, or magic tricycles, which I had hoped to do. With steam and electricity we are well acquainted; by magic tricycles, I mean those driven by a motor which, without any expense, will drive one twenty miles an hour, up or down hill, with perfect safety. Highway regulations, and certain reasons not well understood, have at present prevented these contrivances from making a revolution.