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force too is dividedbetween the friction on the rails and that 
of the air passed through. The action of rolling surfaces 
such as wheels and pinions of watches, clocks, and other 
machinery, is amply explained, and rules given for minimum 
friction, in the works of Berthoud, Camming, and Halton, on 
clocks and watches, by Camus on the teeth of wheels, and in 
D Fairbair n’s work on mill-gearing, wherein we see that if 
the rolling surfaces were all smooth, hard, and of curvatures 
adapted to such motion, they would offer no friction. 
The motions of shafts on fixed bearings, if the metal sur- 
faces come in contact, will draw in and compress the air, and 
by heating the shaft prevent safe working; hence lubi mating 
matter is used to limit the contact of the metals, so that only 
some of their prominent parts touch, to produce attrition, or 
friction. 
The motion of bodies through water involves several kinds 
of resistance of a more complex nature, the measure of which 
has not been given by any of the able writers on that subject, 
nor has any formula been applied thereto for solving the 
questions of the compound resistances to be overcome by 
ships and other bodies moving through water. Some 
authors have taken the measure of this resistance to be as 
the squares of the velocities ; but this fails because the 
different kinds of resistance arc not alike called into action 
in the different cases adduced. Those of cannon balls 
ricocheting from water, the sinking of plummets in deep 
soundings, and floating bodies at different depths from the 
surface, present, each of them reacting forces (go complex to 
admit of any simple rule of measurement, the separate nature 
of which need not be here repeated ; but it may be said that 
the aggregate of the resisting forces called friction must of 
