82 



MECHANICS. 



[Lesson VI. 



insert a piece of wire into the hole. If you 

 push one end down (/;) with your right 

 hand, taking care to hold the wire fast with 

 the other, you will cause the opposite end 

 (c) to be raised, and vice versa. Now, 

 this is just the principle on which the 

 acts. 



69. T. How can a wheel act like the 

 straight piece of wood? 



P. We have only to call the parts 

 by other names, and you will immediately 

 see that it is so. Let us call the wire at 

 a the fulcrum, or fixed axis, and b c the 

 arms of the lever ; we shall now have two 

 arms, spokes, or radii of a wheel, and we 

 have only to multiply or increase the 

 number, and we shall then increase the 

 leverage, as in the case of the wheel by 

 which a vessel is steered. 



70. T. What do you mean by the peri- 

 phery of a wheel ? 



P. It is the circumference or rim ; the 

 name being derived from two Greek words, 

 peri (irfpi) about ; and fero (<j>fpo) I carry. 



71. T. What do you mean by the radii 

 of a wheel ? 



P. They are the spokes or arms, which 

 radiate from a centre ; therefore that part 

 of a wheel which is situated between the 

 centre and the circumference is said to be 

 a radius. If we draw a line directly through 

 the circle or circumference of a wheel, so 

 as to touch both its sides, it is called the 

 diameter, which is nothing more than two 

 radii or semi-diameters joined together in 

 the same line of direction. All the radii 

 or spokes of a wheel are kept together in 

 the centre by a cylindrical piece of wood, 

 which serves as the common fulcrum for 

 all the wheel, and at the circumference by 

 the rim. 



72. T. Have all wheels their axes in 

 the centre ? 



P. No, some have not, and are called 

 eccentric wheels , but we must leave the 

 consideration of them for another time. 



73. T. What is the usual arrangement 

 of a wheel and axle ? 



P. The wheel is fixed to an axle or 

 spindle, which revolves horizontally on 

 its two ends, which are supported in some 

 manner (usually by upright pieces of wood), 

 and around this axle is coiled the rope, 

 which sustains the weight, while the peri- 



phery of the wheel has another rope coiled 

 round it, in a contrary direction, with the 

 power suspended to it. [See /'/>. 1, and 

 description in foot note.] 



74. T. What is the fulcrum of the 

 wheel and axle? 



P. The centre of the axle, which is 

 common to the whole machine. 



75. T. How does the machine act ? 



P. When the wheel revolves, of course 

 the axle does the same ; and as the rope 

 is fixed to the axle, with the weight hanging 

 at its end, it is wound round the axle, and 

 so raises the weight. 



76. T. How can you balance this ma- 

 chine, or produce an equilibrium ? 



P. By proportioning the two powers to 

 the diameter of the wheel and the axle, so 

 that the one power or weight may be made 

 to balance the other power or weight. 

 Suppose that the machine is made to move 

 rapidly, it will then be found that the 

 velocity of the power will be to that of the 

 weight as the circumference of the wheel 

 is to that of the axle; because it is quite 

 clear that the power must sink through a 

 space equal to the circumterence of the 

 wheel, before it can raise the weight 

 through a space equal to the circumference 

 of the axle. Now that we know this much, 

 we have next to find the momentum, which 

 is done by multiplying its velocity and 

 weight together. It is therefore evident, 

 that if the number of inches of the circuit 

 of the wheel, multiplied by the number of 

 pounds in the power, produce a sum equal 

 to the product of the measure of the axle 

 multiplied by the number of pounds in the 

 weight, the machine will remain in a state 

 of equilibrium. 



77. T. What does the effect of the 

 wheel depend upon ? 



P. The superiority of the radius, or 

 diameter of the wheel to that of the axle. 

 In 7-V/r. 20, we observe that the weight (T) 

 corresponds to the counteracting force (P) 

 in an inverse ratio to the arms of the lever; 

 that is, inversely to the radii (A B, and r> c) 

 of the wheel. Let us suppose that the 

 radius (A B) of the axle, is lour times less 

 than the radius (D c) of the wheel, we may 

 equipoise a weight of eighty pounds by a 

 force of twenty pounds. 



78. T. Give me some examples of the 



