THE POPULAR EDUCATOR. 



measured by the number of pounds it will support. We I then, the following rule : Incline the plane till the body is on 



accordingly pass on to consider the nature and effects of the 

 fourth kind, namely, friction. This has been frequently referred 

 to, and, as it often interferes with the accuracy of the results 

 we obtain, it is important to become familiar with its effects. 



If we attempt to cause one body to slide or move over 

 another, we find a certain amount of resistance to our efforts. 

 This resistance or opposition to attempted motion is friction. All 

 surfaces have a degree of roughness or unevenness of texture, 

 and the inequalities of two such surfaces fit into one another, 

 the projections of the one catching those of the other. We find 

 this friction more or less in all cases of attempted motion. If 

 two surfaces were absolutely smooth, there would be none; 

 this, however, we cannot obtain, but the nearer we approach to 

 it, the less friction we have. 



If a block of wood lies on the ground, I may be unable to 

 push it along. Move it now to a surface of clear ice, the 

 resistance will be less ; and if we place it on narrow smooth 

 runners, like those of a sledge, we still further reduce friction. 

 In all cases, however, it exists ; and as we see, it is only called 

 into play when motion is attempted ; and since it prevents the 

 body from moving (unless the force applied be powerful enough 

 to overcome it), its line of action must be contrary to that of 

 the attempted motion, as otherwise it could not neutralise the 

 force applied. 



Now it will easily be seen that it is of great importance to be 

 able to ascertain the amount of friction between surfaces. On 

 a railway we want to know what force is required to overcome 

 the friction of a train along a level part of the line. We can 

 easily, by the principles of the inclined plane, find the additional 

 force required to draw it up an incline. Many practical ques- 

 tions of this sort are constantly met with, and there are two 

 common ways of solving them. 



The most usual method is by the apparatus represented in 

 Fig. 82. A slab of the substance over which the other is to 

 slide, is laid 

 horizontally 

 on a table. A 

 block, A, of 

 the second 

 substance is 

 taken, a cord 

 is fastened to 

 it and passed 



over a pulley at the edge of the table, so as to be parallel to its 

 surface ; at the other end of this cord a scale-pan is fastened. 

 Weights are now placed in this, or, better still, sand is poured 

 into it, until A just begins to move. The weight of the sand in 

 the pan divided by that of A, gives the fraction which expresses 

 the proportion that the friction bears to the weight to be moved. 

 Thus, if the substance weigh 2 pounds or 32 ounces, and a weight 

 of 5 ounces is required to move it, the fraction is ^. This is 

 called the Co-efficient of Friction. 



The other way of ascertaining this quantity is sometimes 

 easier. A block, A (Fig. 83), of one substance is laid on a plane, 

 B c, made of the other, and the end c is then lifted till A is 

 just on the point of sliding down the plane. The full amount 

 of friction is now at work, and we may consider this as a case 

 of a body kept at rest on an inclined plane. The forces which 

 act on A are its own weight in the direction A w, the resistance 

 of the plane in the direction A R perpendicular to its surface, and 



the force of friction 

 which acts up the 

 plane along A F. Now, 

 since there is equi- 



librium, this last force 

 is equal and opposite 

 to the resultant of A B 

 and A w, that is, to AE. 

 The three forces, then. 

 may be represented 

 by the three sides of 

 the triangle w A E, but 

 Fig. 83. this triangle is similar 



to the triangle BCD; 

 therefore we may take B c as representing the weight, and c D 



the friction, and is the co-efficient of friction. We have, 



BC 



Tig. 82. 



the point of motion; the elevation of the end of the plane 

 divided by its length gives the required fraction. 



This suggests the way of making a useful calculation, like tho 

 following : On how steep an incline will a cart stand safely if 

 the co-efficient of friction be gg ? We see that the incline must 

 be somewhat less than 1 foot in 30, as, if it be greater, the cart 

 will run down from its own weight. By these and similar means 

 thousands of experiments have been tried, a few of which are here 

 given as illustrations. You can easily try others yourself. Along 

 a railway friction is reckoned to be from 8 to 10 pounds per ton ; 

 on a good road about ^th of the load ; this amount, however, 

 varies very greatly with the character of the road. The co- 

 efficient of friction for steel on ice is only 5^, while that of oak 

 on oak or elm is over |. 



There are, however, certain general rules, discovered by expe- 

 riment, which are more important to remember. 



1. Friction is proportional to the pressure. If we place 

 weights on A (Fig. 82) so as to double the pressure, we shall 

 find it requisite, also, to double the weights in the pan, and so 

 for any other alteration of the pressure of A. 



2. The amount of friction does not vary with the extent of 

 the surfaces in contact. This at first seems strange, but, if we 

 consider it, we see the reason. Suppose a block of deal two 

 inches thick move over another surface of deal. If the block 

 weigh 10 pounds, the force required to overcome friction will bo 

 about 3i pounds. Now saw the block into two, of half tho thick- 

 ness, and lay them side by side. Each has half the weight of 

 the original block and the same surface, and so the friction of 

 each will be one-half of 3i pounds ; the two together will there- 

 fore move with the same friction as the one did, though the 

 extent of surface is doubled. 



3. The amount of friction varies with the nature of the bodies 

 and the smoothness or otherwise of their surfaces. 



Various ways of diminishing friction are adopted in practice. 

 Those parts of any machine which work together are made as 

 smooth as possible, and oil or grease applied to them. The 

 bearings, too, or boxes in which the axles of wheels turn, are 

 made of a different kind of metal from the axles themselves, and 

 many other expedients are resorted to. Still there is a loss of 

 power from this cause, which often amounts to | or even |. 



There are two kinds of friction sliding and rolling. Sliding 

 friction is that of which we have spoken ; but if a body be made 

 round, and allowed to roll over and over instead of sliding, a 

 different kind of friction comes into action. The rudest appli- 

 cation of this is when a man, instead of pushing a stone along 

 the ground, puts rollers under it, and thus moves it with far 

 more ease, fresh rollers being put under in front when needed. 

 Wheels are a further advance upon this, as they not only save 

 tho trouble of constantly replacing the rollers, but, as they only 

 touch the ground at the sides of the body, and not along the 

 whole width as rollers do, they avoid much of the friction. 



Sometimes when a large axle has to turn in bearings, friction- 

 wheels are introduced. These are small wheels, on the edge of 

 which the axle turns, and they transfer the friction to their own 

 small axles. Many such appliances to avoid friction are con- 

 stantly met with. Castors on chairs and tables, and narrow 

 irons on skates, are familiar examples. 



We must not, however, imagine from all this that friction is 

 always a hindrance. Far from it. If we try and walk along a 

 very glassy surface of ice, we are soon painfully reminded of the 

 absence of the customary friction between our boots and the 

 surface on which we are walking, and hence in frosty weather 

 gravel or ashes are scattered on the paths. All the driving force 

 a railway engine has is from the friction of its wheels with the 

 rails. It was at first proposed that the driving-wheels should 

 be toothed, and notches cut into the rails into which these teeth 

 might catch ; but the friction was soon found to be sufficient. 

 On damp days, however, we frequently see the porters at a 

 station putting gravel on the rails, in order that there may be 

 more friction at starting. The brake, also, which is applied to 

 stop a train or machine, acts by pressing a block against the 

 wheel, and thus causing an amount of friction which is soon suffi- 

 cient to overcome the momentum acquired. So, when a nail is 

 driven into a piece of wood, it is held in its place merely by friction, 

 and the same cause enables the fibres of cotton or hemp to cling 

 together so as to be woven into a cord or rope. We see, then, that 

 friction is one of the most important forces we have to consider. 



