20 On the Nature and Laws of Friction. 



carriages : — and to the nature of the resistance which such car- 

 riages would experience on an uniform plane, I propose to con- 

 fine my inquiry. The effect of small eminences and asperities, 

 and other circumstances of an accidental nature, has often been 

 considered ; but that kind of resistance which is constant has not, 

 that I am aware of, been attempted on any sound principles. 



Accidental obstructions may be rendered less frequent, or in a 

 great measure removed, by improving the art of road-making; but 

 there is a resistance which wheel-carriages experience, that is 

 independent of these obstructions, and which will be only more 

 uniform in its action the better roads are made. It is from the 

 investigation of this kind of resistance only, that maxims for the 

 construction of wheel-carriages can be drawn ; consequently, the 

 importance of anv attempt to investigate it must be evident,what- 

 ever may be the result. 



When a physical problem is of a complicated nature, it is 

 sometimes necessary, and at other times convenient, to simplify 

 the operation. This may be done in two ways. The one consists 

 in neglecting certain physical circumstances, of which we have 

 numerous examples in works on Mechanics : thus, in the inves- 

 tigation of the mechanical powers the effect of friction is neg- 

 lected ; yet it is impossible that a mechanical power can act 

 without friction : — and various other instances might be noticed. 

 The other way consists in neglecting certain quantities that are 

 very small when compared with the principal qwantities in the 

 equations. This is perhaps the mobt certain of the two methods ; 

 because it is easier to form some notion of the extent of the error 

 introduced by it than by the preceding one; though both have 

 sometimes led to very erroneous conclusions. But it is so great 

 an advantage to express the laws of resistance in simple terms, 

 that even a distant approximation to truth is fully compensated 

 by it. 



A. — When a rolling body, such as the wheel of a carriage, moves 

 upon an uniform horizontal plane, the resistance which opposes 

 its motion is of two kinds. 



For a wheel is retarded by the rubbing of the parts at the axis, 

 which is properly called friction ; and it is also retarded at the cir- 

 cumference by that partof the plane immediatelvbefore the wheel; 

 as that part must be depressed to the same level as that on which 

 the wheel had previously borne, otherwise the wheel must be sup- 

 posed to move over the plane without making an impression pro- 

 portional to its weight and time of action, which would be ab- 

 surd. 



Of 



