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may be employed, such as foot, metere, centimetere, millimetere or other measures of length; also tons, ounces, grams, kilograms, etc, or any other measure of pull or resistance.

In lever designs, to be able to proportion the levers so that they will be strong enough bout not too strong—for the wieght must be kept down—it is necessary to know or to determine the magnitude of the factors, and judgment is sometimes called into play, because while a given pull may be adequate, yet even so a greater pull may be adequate, yet even so a greater pull may be exerted in any such case. The strain upon the lever will be that due to the greater possible pull, rather than to the necessary pull.

Let us assume a case as follows: We will say the motorist can exert a maximum pull of 100 pounds at F. notwithstanding the fact that 20 pounds might be ample for his purpose. We must then provide for the 100 pounds effort.Let us also assume that l is 18 inches; P,6 inches, and A 24 inches; then

$W{=}{\frac {F\times L}{l}}{=}{\frac {100\times 18}{6}}=300$pounds.

The pull will then be 300 pounds at W. Hence (a) the cable must be capable of safely withstanding a pull of 300 pounds, thus requireing the use of a three-six-teenths inch diameter pliable steel cable, preferably "plow steel" with nineteen strands. In ordering cable specify circumference in inches, quality and number of strands.

The shape of the lever arm will affect (a) its weight for a given weight. If steel castings are preferred it may be expedient to fix upon an I section; if forgings are used, the rectangular—rounded corners—section works out well. In any case the section must be settled upon, else the strength may not to be estimated. Levers are pure and simple "cantilever" beams. Hence formulae that apply to this class of beams will suffice for the purpose.

Emprical formulae for use in designing levers will suffice for the purpose, and simplify the problem to a marked extent. A great many designers say the best way is to duplicate a lever that did not give trouble. Indeed! The Pyramids of Egypt did not fall down. They were duplicated. But the Pyramids answered no useful purpose. In any case a "printer's devil" or a "plumber's cub" could figure out a final resting place for an Egyptian monarch in one minute, that would offer equal security and cost but an infinitesimal fraction of the cost of a Pyramid.

Note.—The safe working load of wire rope—such as is used on motor car brakes—is given by Klien thus: $d-0.0087{\sqrt {\frac {P}{n}}}$= diameter of each strand in inches,

In which P is the safe working load in pounds and n the number of wires in cable, or strands. Plow steel cable will do somewhat better than pliable hoisting cable.

The width of levers should be about one-twentieth of the length from the fulcrum to the point of pull, but in cases in which the width, for any reason, is reduced below this ratio, a corrective factor should be applied as follows:

Width of Lever	Allowable proportion of Calculated Load.
1⁄20× length	Full allowance
1⁄30× length	90%"
1⁄40× length	80%"
1⁄50× length	70%"
1⁄60× length	60%"
1⁄70× length	50%"

The levers proportioned after these formulæ will be subjected to a very much greater strain than that usual with cantilever beams, because in the working of levers in motor cars the load is not quiescent. When levers are 'eccentric" an extra allowance must be made, to compensate for torsion, otherwise permanent deformation may result.

The formulæ comtemplate the use of well worked 40 to 50 carbon steel. Mild steel does not offer the desired resistance to deformation, and in the event of the use of mild steel an extra allowance of metal must be made.

The most likely chance of trouble with non-eccentric levers is at the fulcrum, as the fastenings are rarely secure. The best way to avoid trouble is to fasten to a flange, as illustrated in Fig. 7. The next

best fastening detail is shown in Fig. 8. A large diameter of the shaft to which a lever may be keyed introduces troubles of a serious nature, unless something is done, for a large diameter of shaft means great weight. Hollow shafting is the best recourse, and in this connection it is possible that a résumé of hollow shaft advantages will serve a useful end. The comparative strength of a hollow to a solid shaft is shown by the following formulæ :

For equal torsional strength