THE INCLINED PLANE, WEDGE AND SCREW. 



307 



THE INCLINED PLANE AND WEDGE. 



From Dr. Dion. Lardner's Lectures, now in course of publication by Greeley & McElrath of New-York. 



Although the connection between these two 

 Mechanical powers and practical Agriculture, 

 may not be apparent at first sight, let tlie reader 

 say, after perusal, whether any young man 

 ought to be, and be satisfied to remain, ignorant 

 of such matters, whose verj* business every day 

 requires the practical use of contrivances by 

 which he is enabled, at so little expense, to make 

 vast additions to the animal power at his com- 

 mand ? So it may be said of the lever and the 

 pulley which shall be in like manner clearly 

 explained in our next, from the same luminous 

 author. 



Thus do v/e proceed to demonstrate tl^t we 

 have many things in store for the accomplish- 

 ment of young Agriculturists, besides telling 

 them how much a hog of a favorite breed may 

 be made to weigh in a given time on a given 

 quantity of corn. y 



The inclined plane is the most .simple of all 

 machines. It is a hard plane surface forming 

 some angle with a horizontal plane, that angle 

 not being a right angle. ^Vllen a weight is 

 placed on such a plane, a twofold effect is pro- 

 duced. A part of the effect of the weight is re- 

 sisted by the plane and produces a pressure 

 upon it ; and the remainder urges the weight 

 down the plane, and would produce a pressure 

 against any surface resisting its motion placed 

 in a direction perpendicular to the plane. 



Let A B, fig. 1, be such a plane. B C its hori- 

 zontal base, A C its bight, and A B C its angle 

 of elevation. Let W be a weight placed upon 



it. This weight acts in the vertical direction 

 W D, and is equivalent to two forces — W F 

 perpendicular to the plane, and W E directed 

 down the plane. If a plane be placi'd at right 

 angles to the inclined plane below W, it will 

 resist the descent of the weight, and sustain a 

 pjiessure expressed by W E. Thus, the weight 

 W resting in the corner, instead of producing 

 one pressure in the direction W D, will produce 

 two pressures : one expressed by W F upon 

 the inclined plane, and the other expressed by 

 W E upon the resisting plane. These pressures 

 respectively have the same proportion to the 

 entire weight as W F and W E have to \V D, 

 or as D E and W E have to W D, because 

 D E is equal to W F. Now the triangle W E 

 (C07) 



D is in all respects similar to the triangle ABC, 

 the one dilFering from the other only in the scale 

 on which it is constructed. Therefore the three 

 lines A 0, C B, and B A, are in the same pro- 

 portion to each other as the lines W E, E D, 

 and W D. Hence A B has to A C the same 

 proportion as the whole weight has to the 

 pressure directed toward B, and A B has to 

 B C the same proportion as the whole weight 

 has to the pressure on the inclined ijlane. 



We have here supposed the weight to be sus- 

 tained upon the inclined plane, by a hard plane 

 fixed at right angles to it. But the power ne- 

 cessary to sustain the ^veight ^vill be the same, 

 in whatever way it is applied, provided it act 

 in the direction of the plane. Thus a cord may 

 be attached to the \\-eight, and stretched toward 

 A, or the hands of men may be applied to tlie 

 weight below it, so as to resist its descent 

 toward B. But in whatever way it be applied, 

 the amount of the power w^ill be determined in 

 tlie same manner. Suppose the ^veight to con- 

 sist of as many pounds as there are inches in 

 A B, then the power requisite to sustain it upon 

 the plane will consist of as many pounds as 

 there are inches in A C, and the pres.sure on the 

 plane will amount to as many pounds as there 

 are inches in B C. 



From what has been stated, it may easily be 

 iufen'ed that the less the elevation of the plane 

 is, the le.ss will be the power requisite to sus- 

 tain a given v/eight upon it, and the greater 

 will be the pressure upon it. Suppose the in- 

 clined plane A B to turn upon a hinge at B, 

 and to be depressed so that its angle of eleva- 

 tion shall be diminished, it is evident that as 

 this angle decreases, the bight of the plane de- 

 creases, and its base increases. Thus, when it 

 takes the position B A', the bight A' C is less 

 than the former bight A C, while the base B C 

 is greater than the fonner base B C. The 

 power requisite to support the weight upon the 

 plane in the position B A' is represented by 

 A' C, and is as much less than the power requi- 

 site to sustain it upon the plane A B, as the 

 bight A' C is less than the hight A C. On the 

 other hand, tlie pressure upon the plane in the 

 position B A' is as much greater than the pres- 

 sure upon the plane B A, as the base B C is 

 greater than the base B C. 



The power of an inclined plane, con.sidered 

 as a machine, is therefore estimated by the pro- 

 portion which the length bears to the hight. 

 This power is always increased by diminishing 

 the elevation of the plane. 



Roads which are not level may be regarded 

 as inclined planes, and loads drawn upon them 

 in caiTiages, considered in reference to the po\N'- 

 ers which impel them, are subject to all the con- 

 ditions which have been established for inclined 

 planes. The inclination of the road is estimated 

 by the hisrht corresponding to some proposed 

 length. Thus it is said to rise one foot in fifteen, 

 one foot in twenty, &c., meaning that if fifteen 

 or twenty feet of the road be taken as the length 

 of an inclined plane, such as A B, the coires- 

 ponding hight will be one foot. Or the same 

 may be expressed thus : that if fifteen or twen- 



