ON PRESSURE AND EQUILIBRIUM. 47 



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 repra- 

 sented 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 com- 

 pletely shown by experiment. We attach three weights to as many 

 threads, united in one point, and passing over three pullies ; 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 of 

 each weight by the length of the side of the triangle corresponding to its 

 thread. (Plate III. Fig. 33.) 



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

 concern the machines which are usually called mechanical powers. 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 their motion requires additional considerations, and their 

 application to practice belongs to another subdivision of our subject. 



There is a general law of mechanical equilibrium, which includes the 

 principal properties of most of these machines. If two or more bodies, 

 connected together, be suspended from a given point, they will be at rest 

 when their centre of inertia [gravity ] is in the vertical line passing through 

 the point of suspension. The truth of this proposition may easily be 

 illustrated by the actual suspension of any body, or system of bodies, 

 from or upon a fixed point ; the whole remaining in equilibrium, when 

 the centre of inertia [gravity] is either vertically below the point of sus- 

 pension, or above the point of support, or when the fixed point coincides 

 with the centre of inertia [gravity]. And whatever may be the form of a 

 compound body, it may be considered as a system of bodies connected 

 together, the situation of the common centre of the inertia [gravity] deter- 

 mining the quiescent position of the body. (Plate III. Fig. 34 . . 38.) 



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

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

 become vertical in any two positions in which the body is at rest. Thus, 

 if we suspend a board of an irregular form from any two points succes- 

 sively, and mark the situation of the vertical line in each position, we may 

 find by the intersection the place of the centre of gravity : and it will 

 appear that this intersection will be the same whatever positions we 

 employ. (Plate III; Fig. 39.) 



The consideration of the degree of stability of equilibrium is of material 

 importance in many mechanical operations. Like other variable quanti- 

 ties, the stability may be positive, negative, or evanescent. The equili- 

 brium is positively more or less stable, when the centre of gravity would 

 be obliged to ascend more or less rapidly if it quitted the vertical line : 

 the equilibrium is tottering, and the stability is negative, when the centre 

 of gravity would descend if it were displaced ; but when the centre of 



* Seepage 19 and last page. For demonstrations of this property consult also 

 Poisson, Traite de Mecanique, i. 43. Duchayla, extracted in Pratt's Mec. p. 7, 

 note ; and WhewelTs Mechanics. 



