This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1843 edition. Excerpt: ... the second perpendicularly to it. This last is completely resisted by the plane; whilst the former can only be resisted by some force acting in the direction W C. But suppose this force to be acting in some other direction, as W e; to ascertain its action upon the weight, we must resolve it as before, into ...
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This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1843 edition. Excerpt: ... the second perpendicularly to it. This last is completely resisted by the plane; whilst the former can only be resisted by some force acting in the direction W C. But suppose this force to be acting in some other direction, as W e; to ascertain its action upon the weight, we must resolve it as before, into two forces, of which one, W', shall act in the direction of the plane, and the other gf in a line perpendicular to it. The former, therefore, will act against the force W b which impels tbe body down the plane; and, if superior to it, will cause the body to ascend the plane; whilst the latter, acting upwards perpendicularly from the surface of the plane, will partly counterbalance the downward pressure W d or b a. It is evident that, the steeper the plane, the larger is the proportion which W b will bear to la; that is, the greater will be the tendency of the body to roll down the plane, and the less will its weight be supported by the surface. 354. The mode in which the power of the inclined plane is estimated, may be deduced from a very simple mathematical process; by which the whole triangle abW can be shown to have its three angles respectively equal to those of the original triangle A B C, so that the sides are proportional to each other. (Euclid, Book VI., Prop. 8.) Hence W a is to W b as A C is to B C; and "W a is to b a as A C is to A B. Now W a represents the whole pressure of the body W in the downward direction; and W b that portion of its pressure which causes it to move down the plane, which must be resisted in order to keep the body at rest, and which must be overcome to cause it to ascend. Hence, under all circumstances, the whole weight of the body is to its pull down the incline, as the whole length of the incline A C, is to...
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