The mathematical principles of mechanical philosophy, and their application to elementary mechanics and architecture, but chiefly to the theory of universal gravitation / [John Henry Pratt].
- Pratt, John H. (John Henry), 1809-1871.
- Date:
- 1842
Licence: Public Domain Mark
Credit: The mathematical principles of mechanical philosophy, and their application to elementary mechanics and architecture, but chiefly to the theory of universal gravitation / [John Henry Pratt]. Source: Wellcome Collection.
70/670 page 30
![STATICS. ONE RIGID BODY. therefore the condition iVthat (Z.X) L + (2. Y)M+ (2.Z) N R.G = °’ or (2 . X) L + (2 . F) A/ + (2. Z) J\T= o, unless R or G vanishes. This is no condition when R = 0 : that is, when 2. A = 0, 2. Y= 0, 2. Z = 0, for the above equation is then identical. In fact we then have only the couple G : which does not admit of a single resultant. Also this is no condition when G = 0, for then L = 0, M = 0, JV = 0, and the equation is again identical. But in this case it is evident we have a single resultant R. Prop. When the forces are reducible to a single resultant, required the magnitude of this force and the equations to the line in which it acts. 54. In this case the force R is in the plane of the couple of which the moment is G. Let the arm of the couple be turned about its extremity A (see fig. 15), and in the plane of the couple, till it is perpen¬ dicular to the force R : and let AB = « be the arm of the couple: then the force of the couple (R') = G -f- a ; and the single resultant equals R acting at C in the direction CR pa¬ rallel to AR, C being in BA produced and determined by the equation AC = ~ AB = —. R R 55. We must now find the equations to the line in which this resultant acts. Leta?!?/]#! be the co-ordinates to some point in this line; then, transferring the origin to this point, it is clear that the body must have no tendency to revolve about the origin. Therefore the new values of LMN when we put + a?, yi + y, + # for x y % must = 0 ;](https://iiif.wellcomecollection.org/image/b29286700_0070.jp2/full/800%2C/0/default.jpg)
