ON PRESSUBE AND EQUILIBRIUM. 61 



each other, the 'vholes will do the same. And a similar mode of reasoning 

 may be extended to any number of forces opposed to each other. 



It follows from the laws of the composition of motion, that the result of 

 two pressures, expressed by the sides of a parallelogram, will be represented by 

 its diagonal, and that, if a body remain at rest by means of three pressures, 

 they must be related to each other in magnitude as the sides of a triangle 

 parallel to their directions. ,This may be very completely shown by experi- 

 ment. We attach three weights to as many threads, united in one point, and 

 passing ovev three; pulliies ; then by drawing any triangle, of which the sides 

 are in the directions of ■ the threads, or in parallel directions, we may always 

 express the magnitude lof each weight, by the length of the side of the triangle 

 corresponding to its thread. (.P.late III. Fig. 33.) 



The most important of the problems relating to equilibrium are such as con- 

 cern the machines which are usually called mechanical povj^ers. We are not, 

 however, to enter at present into all the properties and uses of these machines; 

 we have at first only to examine them in a state of rest, since the determination 

 of theirmotion requires additional Considerations, and their application to prac- 

 tice belongs to another subdivision of our subject. 



There is a general law of mechanical ecjuilibrium, which includes tlie prin- 

 cipal properties of most of these machines. If two or more bodies, con- 

 nected together,' be suspended from a given point, they will be at rest when 

 their centre of inertia is in the vertical line passing through the point of suS" 

 pension. The truth of this proposition may easily be illustrated, by the actual 

 suspension of any body, or systenl of bodies, from or upon a fixed point ; the 

 whole remaining in equilibrium, when the centre of inertia is either vertically 

 below the point of suspension, or above the point of support, or when the 

 fixed point coincides with the centre of inertia. And whatever may be the - 

 form of a Compound body, it may be considjered.as a system of bodies cour 

 nected together, the situation of the common centre of the inertia determining 

 the quiescent position of the body. (Plate III. Fig. S^-.JS.) 

 ♦ 



Hence the centpe of inertia is called the centre of gravity ;, and it may be 

 practically found, by determining the intersection of two lines which bccohie 



