Given a mean effective pressure in a steam engine making its stroke in a given time, or a given weight of water constantly falling through a given number of feet in a given time, tlie meclianical power of each may be at once deduced ; but this power is never wholly utilized in useful work. The resistances which absorb the power of motors may be placed in three categories ; namely, the resistance of the medium in which the several parts of the prime motor and the machinery driven by it move, friction of bearing surfaces, and, finally, the resistances overcome in the materials, the change of form in which is the useful work performed. The proper proportions of wheels cannot be attained without due consideration of tho resistances in the two first categories, as well as those in the latter. It is doubtful, however, whether in the construction of ordinary machinery, all these elements are taken properly into account. In many instances we know they are not. The number of revolutions of a pinion driven by a spur wheel being established by tho proper number of teeth in each, or the speed of pulleys being determined by their circumferences, all other considerations are too frequently lost sight of. In some cases the form of the teeth best calculated to secure least consumption of power from friction is properly taken into account ; but even this is in most cases no more than approximated. If we bear in mind the fact that increase of tie perimeters in gearin g is always accompanied by a reduction of pressure upon the teeth, and vice versa, the work performed remaining constant, it becomes evident at once that the diameters of wheels used to perform a given amount of work is an important clement in determining their proper proportions. As friction is independent of velocity and directly dependent upon pressure, it follows that reduction of pressure is also reduction of friction, and that tiio converse is also true. From this it will be seen that the larger the gearing employed to do a given amount of work the less will be the friction between teeth, all other things being equal. Reduction of friction takes place in a system of pulleys and belts by increasing their size on account of the reduced tension of the belts necessary to do a given amount of work. But increase of size implies generally increase of weight or pressure upon journals, and thus while there is diminution of friction between teeth, or of tension in belting, there will be more or less increase of friction upon the journals from this cause, so that on this account there must be a limit to economical enlargement. Again, increased size implies increased resistance from the medium in which the machinery moves, commonly the air, and this also fixes a limit to economical enlargement. The ratio of the friction of a wrought-iron journal playing in a cast iron bearing, well oiled, is, according to Morin's experiments from -07 to '08 of the pressure. If tho teeth of wheels are perfectly formed their friction ought to be nearly reduced to rolling friction, and the ratio of this to pressure is so slight that it need not perhaps be considered here. But such perfection is only theoretical, and there can be rarely found gears so perfectly cut that there is not more or less sliding friction between their teeth. Tho friction in journals, is, however, increased, all things else being equal, by diminished diameter. A somewhat complicated mathematical formula would be required to express this relative increase, and we will not at this time enter upon its discussion. For practical purposes it is enough to say that when other considerations will admit, it will be found more economical of power, and more conducive to durability to allow a liberal size for toothed gearing and for pulleys than to scrimp the pattern.