TRANSACTIONS OF SECTION G. 



515 



although this irregularity may not be distinctly visible to the naked eye. These 

 surfaces, if examined under a sufficiently strong microscope, would be found to be 

 somewhat as represented in the accompanying diagram, No. 9. 



If the upper body be moved in the direction of the arrow, s, by a force, p, the 

 point, a, of the upper surface would mount the incline, formed by the corresponding 

 portion of the lower body, until 

 it reached its summit at a'; from 

 this moment it would begin to 

 descend the next incline, from a* 

 to 6 ; provided the force, p, acting 

 in the direction of the arrow, s, 

 would leave it time to do so. The 

 incline from b to c would have to 

 be mounted next, causing a cer- 

 tain amount of resistance during 

 the time the body traversed the 

 distance d c. But if we increase 

 the speed in the direction of the 

 dart s, so that the body will re- 

 quire less time to traverse a' d than 

 to fall through d b, in such case a' would not arrive at b, but at some other point, 

 V, and then only the portion of the incline V c would have to be mounted, pre- 

 senting a smaller amoimt of resistance than in the former case. This illustrates 

 what occurs. 



The fact that the coefficient of friction diminishes with speed sufficiently ex- 

 plains why a skidded wheel affords less resistance than one which still rotates, 

 because the resistance occasioned by the rotating wheel is only limited by the 

 adhesion of the wheel on the rail, and this, as already shown, is the same as static 

 friction, since the point of the wheel is stationary as regards the forward movement 

 of the train at the moment it touches the rail ; whilst when the wheel is skidded 

 and slides, the friction is that due to the speed at which the wheel moves on the 

 rail, and is therefore less than the other. 



Some special experiments were made with blocks of small area. The brake- 

 blocks generally used in these experiments were 12 inches long, by 3 inches wide, 

 giving a surface of 36 square inches ; the small brake-blocks were made so as to 

 afford a surface of pressure against the wheel of only one-third of this amount, or 12 

 square inches, thus making the pressure per square inch three times as great as 

 before. The diminution of surface was obtained by casting projections upon the 

 face of the block. The author is not prepared to say that any greater coefficient 

 of friction was obtained by the extra pressure per square inch, although in one of 

 the experiments, at a velocity of sixty miles an hour, the rotation of the wheels 

 was arrested by these blocks, whilst this effect had not been produced at that speed 

 in other experiments. The experiments on this form of block were stopped because 

 the blocks were entirely worn down in the course of about twelve experiments. 



Mr. Rennie showed * that high pressures per square inch produced a greater co- 

 efficient of friction between surfaces either moving very slowly or nearly at rest ; 

 but it must be borne in mind that the author's experiments were made with high 

 velocities, whereby a serious element of disturbance is introduced, viz., the grinding 

 away of the surface ; and it is, therefore, probable that the increase in the co- 

 efficient of friction due to increased pressure, may have been neutralised by the 

 lubricating effect of the fine particles ground off the surfaces. 



While no certain opinion can be expressed as to the relation which the co- 

 efficient of friction bears to pressure, so far as these experiments are concerned, it 

 is quite clear that in proportion as the pressure is increased or diminished, so will 

 the actual friction obtained be increased or diminished. When the friction which 

 exists between the brake-blocks and the wheel reaches a certain point, the wheel 

 ceases to rotate, and becomes fixed. This point is reached when the frictional 



1 Phil. Trans, for 1829, p. 159. 

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