48 LECTURE VII. 



gravity coincides with the centre of motion, or when its path would be a 

 horizontal right line, the equilibrium has been called insensible, but may 

 more properly be termed neutral, and the body will rest in any position, 

 without tending either to fall or to return to its original situation. It is 

 obvious that the centre of gravity cannot move without descending, when 

 it is vertically over the fixed point, nor without ascending, when it is 

 immediately below it ; so that in the one case the equilibrium is tottering, 

 and in the other stable. Hence we may understand the reason of fixing 

 the moveable handles of a vessel of any kind at its upper part, in order that 

 the centre of suspension may be always above the centre of gravity. If 

 they be fixed too low, the vessel will be liable to overset, unless there be 

 sufficient friction to retain it in its proper situation. (Plate III. Fig. 40.) 



An oval surface, placed on a horizontal plane, is capable of a stable 

 equilibrium, when it rests on its side, or on the extremity of its lesser axis, 

 and of a tottering equilibrium, when it stands on the extremity of its 

 greater axis. But the equilibrium of a circle or a sphere is always neutral, 

 for, when disturbed, it neither recovers its first position, nor deviates 

 further from it. ' A flat body, resting on a sphere, will have its equilibrium 

 tottering or stable, accordingly as its centre of gravity is more or less than 

 the semidiameter of the sphere above the point of contact. (Plate III. Fig. 

 41, 42.) 



The stability of a body supported on a flat basis of a given extent, is of a 

 different kind, and is independent of equilibrium. For here, if the centre 

 of gravity move either way, it must begin its motion in an inclined direc- 

 tion, instead of describing a curve which is initially horizontal. The 

 stability of such a body becomes less and less as it is more and more 

 inclined, till, when the centre of gravity is vertically over the margin of 

 the basis, there is a tottering equilibrium ; and if the inclination be still 

 further continued, the body will faU. (Plate III. Fig. 43.) 



The broader the basis and the lower the centre of gravity, the steeper 

 must the path of that centre be, and consequently the greater the stability. 

 Thus the disposition of the weight in a carriage may considerably affect its 

 stability by altering the place of the centre of gravity. A waggon loaded 

 with iron is much less easily overturned than when it is loaded with an 

 equal weight of hay ; supposing the inequality of the road or any acci- 

 dental obstacle, to elevate one side of the waggon, it will always recover its 

 position, provided that the centre of gravity remain within the vertical line 

 passing through the point of contact of the lower wheel and the ground ; 

 and it is obvious that the higher the centre of gravity is situated the sooner 

 it passes this line. If the velocity of the motion were very great, the wheel 

 which is elevated might be lifted off the ground by the momentum, and the 

 centre of gravity might thus be carried beyond the vertical line, by means 

 of an obstacle which would not have overset the waggon, if it had been 

 moving slowly. (Plate III. Fig. 44.) 



If a person be sitting or standing in a carriage, the part of the carriage 

 on which he sits or stands may be considered as representing the place of 

 his weight, provided that his situation be always perpendicular ; but if the 

 motion be rapid he will not be able to remain constantly in a posture per- 



