Let the small part. F C lie so cut that c ti may be parallel to the horizon, then the lusly will be supported by the two walls. at c and D. For it' n t, n K. and c L. be drawn perpendicular to the horizon, these lines. hieing produced, may be •supposed to meet at an infinite distance.
To find the pressure on the walls. juin L c, and produce the vertical line K G to meet it in L; then, if a be supposed to be the weight of the body, the pressure on n will be EcXo D C D I.Xc• and the pressure on c will be D C Example 4. Figure the body, A ti C n, he With its tipper end against the vertical face of a wall at c. it is required to find the position of a plane supporting the lower end, D, so that the body may be at rest. Dram the vertical line a E, and draw c E perpendicular to the litce of the wall, c L; join E u, and draw D F perpendicular tel E 13; then D F is the position of the plane required. Complete the parallelogram E II I K : then the pressure on D and c, and the weight of the body, are to each other as E it. F. K. F. I.
The following, from Professor Robinson, w ill al.- .) be found interesting : Figure 1 I.—If a body, or any part of a body, be at once pressed in the two directions A A C. and if the intensity or force of those pressures be in the proportion of these two lines, the body is affected in the same manner as if it were pressed by a single force acting in the direction A D, is the diagonal of the 'undid/1gram Antic formed by the two lines, and whose intensity has the same proportion to the intensity of each of the other two that A D has to A B 01' A C.
This proposition has been already treated at some length under the article LEVER. And D. Bernouilli has demon strated it in the first volume of the Comment. Pefrnind. to which, as well as to D'Alembert's improvement, in his Ointsc/eg, and in the Comment. Tourint as. the reader is referred for a very accurate view of the subject. But nothing can possibly conduce so fully to the practitioner's advan tage as to verify the theoretical demonstratious by actual experi merits.
Figure I 2.—Let the threads A d. A F h, and A E c, have the weights d, b, and c, appended to them, and let two of the threads be laid over the pulleys F and E. By this apparatus, the knot A will he drawn in the directions A B, A C. and A K. It' the sum of the weights 1, and c be greater than that of the single weight d, the as,eni binge will of itself settle in a certain detei mined form ; it' the knot A be pulled out of its place, it w ill always return to it again, and will rest in ill) other tion. ["or example, if the three weights be equal, the threads
will always make equal angles, of 1-2.0 degrees each, round the knot. It' one of the weights be three pounds, an( ither fimr, and the third live, the angle opposite to the thread stretched by five pounds will be always square, &e. When the knot A IS dills 111 equilibria, we must infer. that the action of the weight (1, in the direction A d, is in direct opposition to the combined action of b, in the direction A 13, and of c, in the direction A C. Therefore, if d A lee produced to any point, 11, and A D br taken to represent the magnitude of the force, or pressure exerted by the weight d. the pressures exerted on A. by the weights h and c, in the directions A B. A e, will i11 fiut be equivalent to a pressure in direction A a, whose intensity is represented by A D. we 110W by a scale on A r and A E the lilies A 13 Mid A C, having the same proportions to A 1) that the weights L and c to the weight d, and if we draw D D and D e, we shall hind u C to lie equal and parallel to A B. and n it parallel to A c; so that A D is the diagonal of a parallelogram A 13 n C. This will always be the ease, whatever weights be made use of; only care must be taken that the weight acting without the intervention of a pulley be less than the sum of the (Awn two : for if any one of the weights exceed the sum of the other two, it will prevail, and drag them along with it.
Now, since we know that the weight d would just balance an equal weight, g, pulling directly upwards by the inter vention of the pulley ; and that it just balances the weights b and c, acting in the directions A n, A c, we must infer, that the knot A is a&cted in the saine manner by those two weights, or by the single weight y; and therefore, that two pressures, acting in the directions, and with the inten sities, A n, A C, are equivalent to a single pressure having the direction and proportion of A D. In like manner, the pres sures A 13, A K, are equivalent to A n, which is equal and opposite to A C. Also A K and A c are equivalent to A I, w hich is equal and opposite to A B.