308 



MONTHLY JOURNAL OF AGRICULTURE. 



ty feet be measured upon the road, the differ- 

 ence of the levels of tlie two extremities of the 

 distance measured is one foot. According to 

 this method of estimating the inclination of the 

 roads, the power requisite to sustain a load upon 

 them (setting aside the effect of friction) is al- 

 ways proportional to that elevation. Thus, if a 

 road rise one foot in twent3-, a power of one 

 ton will be sufficient to sustain twenty tons, and 

 so on. 



On ahoiizontal plane, theouly resistance which 

 tlie power has to overcome, is the friction of the 

 load with the plane, and the consideration of this 

 being for the present omitted, a weight once put 

 in m jiion \vould continue moving forever, with- 

 out any farther action of the power. But if the 

 pline ce inclined, the power will be expended 

 in rais'nz the weight through the perpendicular 

 ti^ht cf .he plane. Thus, in a road which rises 

 one foot in ten, the power is expended in raising 

 the weight tlirough one perpendicular foot for 

 everj- ten feet of the road over which it is moved. 

 As tlie expenditure of power depends upon the 

 rate at which the weight is raised perpendicu- 

 larly, it is evident that the greater the inclina- 

 tion of the road is, the slower the motion must 

 be with the same force. If the energj- of the 

 power be such as to raise the \\eight at the rate 

 of one foot per minute, the weight may be moved 

 in each minute through that lengtli of the road 

 which corresponds to a rise of one foot. Thus 

 if two roads rise, one at the rate of a foot in fif- 

 teen feet, and the other at the rate of one foot in 

 twenty feet, the same expenditure of power 

 ) will move the weight through fifteen feet of 

 the one, and twenty feet of the other at the same 

 rate. 



From such considerations as these, it will 

 readily appear that it may often be more expe- 

 dient to carry a road through a circuitous route 

 than to continue it in the most direct course ; 

 for. though the measured length of the road may 

 be considerably greater in the former case, yet 

 more may be gained in speed ■with the same ex- 

 penditure of power, than is lost by the increase 

 of distance. By attending to these circum- 

 stances, modern road-makers liave greatly 

 facilitated and expedited the intercourse be- 

 t\N een distant places. 



If the power act oblique to the plane, it will 

 have a twofold effect : a part being expended 

 in supportmg or drawing the weight, and a part 

 in diminishing or increasing the pressure upon 

 the plane. Let W P. fig. 1, be the power, 

 i . Tiis v.-iU be equivalent to two forces, W F', 

 ^•^'Srpendicnlar to the plane, and W E', in the 

 ) direction of the plane. In order that the pow- 

 ) er shonld su.stain the weight, it is necessary that 

 ^ tliat part W E' of the power which acts in the 

 direction of the plane, should be equal to that 

 part W E, fig. 1, of the weight which acts down 

 the plane. The other part \V F. of the power 

 acting perpendicular to the plane, is iimnediate- 

 ly opposed to that part 'W' F of the w eight 

 which produces pressure. The pressure upon 

 the plane will therefore be diminished by the 

 amount of W F'. The amount of the power, 

 which will equilibrate with the weight, maj-, in 

 this case, be found as follows : Take Vi E' 

 equal to W E. and draw E' P perpendicular to 

 the plane, and meeting the direction of tlie pow- 

 er. The proportion of the power to the weight 

 will be that of W P to W D. And the proportion 

 of die pressure to the weiirht will be that of the 

 difference between ^V F and W F' to W D. 

 If tlie amount of the power have a less propor- 

 (GO^) 



tion to the weight than W P has to W D, it will 

 not support the body on the plane, but will al- 

 low it to descend. And if it had a greater pro- 

 portion, it will draw the weight up the plane to- 

 ward A. 



It sometimes happens that a weight upon one 

 inclined plane is raised or supported by another 

 weight upon another inclined plane. Thus, if 

 A B and A B', fig. 2, be two inclined planes, 

 forming an angle at A. and ^V W be two 

 weights placed upon these planes, and connect- 

 ed by a cord passing over a pulley at A, the one 

 weight vvill ei- 

 ther sustain the 

 other, or one 

 will descend, 

 drawing the 

 other up. To 

 ^ determine the 

 circumstances 

 under which 

 these effects will ensue, draw the lines W 

 D and W D' in the vertical direction, and 

 take upon them as many inches as there are 

 ounces m the weights respectively. W D and 

 W IM being the lengths thus taken, and there- 

 fore representing the weights, the lines \V E 

 and W E' will represent the effects of these 

 weights respectively down the planes. If W 

 E and W' E' be equal, the weights will sus- 

 tain each other without motion. But if WE 

 be greater than W E', the vv-eight \V will de- 

 scend, drawing the weight ^V up. And if W 

 E' be greater than 'W E, the weight W will 

 descend drawing the weight W up. In every 

 case, the lines W F and W F' will represent 

 the pressures upon the planes respectively. 



It is not necessarj- for the effect just described, 

 that the inclined planes should, as repre- 

 sented in the figure, form an angle with each 

 other. They may be parallel, or in any other 

 po.sition, the rope being earned over a sufficient 

 number of wheels placed so as to give it the 

 neces.sary defiection. This method of moving 

 loads is frequently applied in great public 

 works where rail roads are used. Loaded 

 wagons descend one inclined plane, while oth- 

 er wagons, either empty or so loaded as to per- 

 mit the descent of those with which they are 

 connected, are dra\\Ti up the other. 



In the application of the inclined plane, 

 which we have hitherto noticed, the machine 

 it.self is supposed to be fixed in its position, 

 while the weight or load is moved upon it — 

 But it frequently happens that resistances are to 

 be overcome which do not admit to be thus 

 moved. In such cases, instead of moving the 

 load upon the plane, the plane is to be moved 

 under or against the load. Let D E, fig- 3. be a 

 heavy beam secured in a vertical position be- 

 "' " tween guides, F Q 



and H I, so that it is 

 free to move upward 

 or downward, but not 

 lateralh-. Let ABC 

 be an inclined plane, 

 the extremity of 

 which is placed be- 

 neath the end of the 

 beam. A force ap- 

 plied to the back of 

 this plane A C, in the 

 direction C B, will 



urge the plane under 



C B the beam, so as to 



raise the beam to the position represented in 



