MECHANICS. 



is eqftal to the time in which the same 

 Space would be described by an uniform 

 equable motion, with half the final velo- 

 city of the accelerated motion, and that 

 in every motion uniformly accelerated 

 from rest, the spaces described are in the 

 duplicate ratio of the times of description : 

 after this he applied the doctrine to the 

 ascent and descent of bodies on inclined 

 planes. For a more particular account 

 we may refer to Dr. KeiPs " Physics." 

 Under the articles CENTRE of gravity, 

 DYNAMICS, ELASTICITY, FORCE, GRAVITA- 

 TION^ MOTIOX, &c. will be found much 

 relating to the doctrine of mechanics ; we 

 shall therefore in this place chiefly treat 

 of the mechanical powers, which are 

 usually reckoned six in number : viz. thfr 

 lever; the wheel and axis, or, as it is fre- 

 quently called, " the axis in peritrochi o ;" 

 the pulley ; the inclined plane ; the 

 wedge; and the screw. Some writers on 

 this subject reduce the six to two, viz. the 

 lever, and the inclined plane; the pulley, 

 and wheel and axis being, in their estima- 

 tion, assemblages of the lever ; and the 

 wedge and the screw being modifications 

 of the inclined plane. 



When two forces act against each 

 other, by the intervention of a machine, 

 the one is denominated the power, and 

 the other the weight. The weight is 

 the resistance to be overcome, or the ef- 

 fect to be produced. The power is the 

 force, whether animate or inanimate, 

 which is employd to overcome that resist- 

 ance, or to produce the required effect. 

 The power and weight are said to ba- 

 lance each other, or to be in equilibrio, 

 when the eftbrt of the one to produce 

 motion in one direction, is equal to the 

 effort of the other to produce it in the 

 opposite direction; or when the weight 

 opposes that degree of resistance which 

 is precisely required to destroy the action 

 of the power. The power of a machine is 

 calculated when it is in a state of equilibri- 

 um. Having discovered what quantity of 

 power will be requisite for this purpose, 

 it will then be necessary to add so much 

 more, viss. one-fourth, or, perhaps, one- 

 third, to overcome the friction of the ma- 

 chine, and give it motion. 



The lever is the simplest of all ma- 

 Chines, and is a straight bar of iron, wood, 

 or other material, supported on, and 

 moveable about a prop called the fulcrum, 

 in the lever, there are three circum- 

 stances to be principally attended to : 1. 

 The fulcrum, or prop, by which it is sup- 

 ported, or on which it turns as a centre of 

 notion : 2. The power to raise and sup- 

 por f ('->.- "-^ in-lit -j, The resistance or 



weight to be raised or sustained The 

 points of suspension are those points 

 where the weights really are, or from 

 which they hang freely. The power and 

 the weight are always supposed to act at 

 right angles to the lever, except it be 

 otherwise expressed. The lever is distin- 

 guished into three sorts, according to the 

 different situations of the fulcrum, or 

 prop, and the power, with respect to 

 each other. 1. When the prop is placed 

 between the power and the weight, as 

 in steel-yards, scissars, pincers, &c. 2. 

 When the prop is at one end of the lever, 

 the power at the other, and the weight 

 between them, as in cutting knives, fast- 

 ened at, or near the point of the blade ; 

 also in oars moving a boat, the water be- 

 ing the fulcrum. 3. When the prop is at 

 one end, the weight at the other, ami 

 the power applied between them, as in 

 tongs, sheers, &c. 



The lever of the first kind is principally 

 used for loosening large stones; or to raise 

 great weights to small heights, in order 

 to get ropes under them, or other means 

 of raising them to still greater heights : it 

 is the most common species of lever. 

 ABC (Plate I. Mechanics, fig. 1.) is a. 

 lever of this kind, in which F is the ful- 

 crum, A the end at which the power is 

 applied, and C the end where the weight 

 acts. To find when an equilibrium will 

 take place between the power and the 

 weight, in this as well as in every other 

 species of lever, we must observe, that, 

 when the momenta, or quantities of force, 

 in two bodies are equal, they will balance 

 each other. No\v, let us consider when 

 this will take place in the lever. Suppose 

 the lever AB, fig. 2, to be turned on its 

 axis, or fulcrum, so as to come into the 

 situation DC ; as the end D is farthest 

 from the centre of motion, and as it has 

 moved through the arch AD in the same 

 time as the endB moved through the arch 

 BC, it is evident that the velocity of AB 

 must have been greater than that of B. 

 But the momenta being the products of 

 the quantities of matter multiplied into the 

 velocities, the greater the velocity, the 

 less the quantity of matter to obtain the 

 same product. Therefore,- as the velocity 

 of A is the greatest, it will require less 

 matter to produce an equilibrium than B. 

 Let us now examine how much more 

 weight B will require than A, to balance. 

 As the radii of circles are in proportion 

 to their circumferences, they are also pro- 

 portionate to similar parts of them ; there- 

 fore, as the arches, AD, CB, are similar, 

 the radius, or arm, DE, bears the same 

 proportion to EG that the arch AD 



