364 THE PEINCIPLES OF SCIENCE. [chap. 



as havin«" a centi-e of gravity, that of tlie sun and earth 

 lying within the sun and only 267 miles from its centre. 



Although we most commonly use the notion of a centre 

 or average point with regard to gravity, the same notion 

 is applicable to other cases. Terrestrial gravity is a case 

 of approximately parallel forces, and the centre of gravity 

 is but a s])ecial case of the more general Centre of Parallel 

 Forces. Wherever a number of forces of whatever amount 

 act in parallel lines, it is possible to discover a point at 

 which the algebraic sum of the forces may be imagined to 

 act with exactly the same effect. Water in a cistern 

 presses against the side with a pressure varying according 

 to the depth, but always in a direction perpendicular to 

 the side. We may then conceive the whole pressure as 

 exerted on one point, which will be one-third from the 

 bottom of the cistern, and may be called the Centre of 

 Pressure. The Centre of Oscillation of a pendulum, dis- 

 covered by Huygheiis, is that point at which the whole 

 weight of the pendulum may be considered as concentrated, 

 without altering the time of oscillation (p. 315). When 

 one body strikes another the Centre of Percussion is that 

 point in the striking body at which all its mass might be 

 concentrated without altering the effect of the stroke. In 

 position the Centre of Percussion does not differ from the 

 Centre of Oscillation. Mathematicians have also described 

 the Centre of Gyration, the Centre of Conversion, the 

 Centre of Friction, &c. 



We ought carefully to distinguish between those cases 

 in which an invariable centre can be assigned, and those in 

 which it cannot. In perfect strictness, there is no such 

 thing as a true invariable centre of gravity. As a general 

 rule a body is capable of possessing an invariable centre 

 only for perfectly parallel forces, and gravity never does 

 act in absolutely parallel lines. Thus, as usual, we find 

 that our conceptions are only hypothetically correct, and 

 only approximately applicable to real circumstances. 

 Tliere are indeed certain geometrical forms called Ccntro- 

 laric} such that a body of that shape would attract another 

 exactly as if the mass were concentrated at the centre of 

 gravity, whether the forces act in a parallel manner or not. 



* Thomson and Tait, Treatise on JS'atural Philosophy, vol. i. p. 394. 



