62 IX the centra 

 of gravity will !; in 

 the vertical linr \ I ' 

 pasting through the 

 body when it has at- 

 tained a position in 

 which it i perfectly 

 at red We now 

 suspend it ('.') from 



the po- 



of th< when 



it ii at rest, this lino 

 will intersect tlio 

 previous line A B in 

 the point G, which 

 will be the centre of 

 gravity of the body. In many cases we shall thus be 

 enabled to estimate tho position of the centre of gravity. 

 If the body A C B D (2) be bounded by plane surfaces, 

 and be of uniform thickness throughout, we know that 

 if the lint-* A 15 and O D be traced on both parallel sur- 

 face*, the centre of gravity will lie in the middle of the 

 straight lino joining the two points of intersection of 

 these lines. 



To 6nd the centre of gravity of a walking-stick, which 

 U supposed to be symmetrical with respect to an axis 

 passing through its centre, aiid has a heavy head or 

 handle, we have only to balance it on the sharp edge of 

 a body, as indicated in Fig. 03, and we know the 

 Flf. . 



L: 



centre of gravity will lie in the point where the vertical 

 plane passing through tho edge intersects tho axis of the 

 stick. 



In thc.se experimental determinations of the centre of 

 gravity it does not signify whether the body be homo- 

 geneous or not : thus, the adjacent figures show the 



Flf. 64. 



method used by Dcsagnliers for estimating the <> 

 gravity of a human body or skeleton, in the positions 

 there indicated. 



BTA] ' EQ1 [LIBRIUM. 



Theoretically we say that a heavy body nn<l>T ii. 

 of gravity, may be in equilibrium in a cvrt 



we may not be able practically or apnuntoUlly 

 to demonstrate it, because the slightest (listurlmnce of 

 the position nf the body may destroy the conditions of 



librium. Thus, theoretically, a cone will be in a 

 position of equilibrium whether it rest on a table 

 (Tig. 66 1) on its apex, or (2) on its base. In tin- 

 former cam, however, -t possible in- 



to the one side or the other will destroy tin; equilibrium. 

 The equilibrium which in thwrrtirally but not practically 



possible. U called wutnJilr, wli:!.- that which is |.i .. 



U called itablf. An egg will rest on its side in a posit' 



0f HabU gMtiarmm, while the attempt to balance it 



the well-known method Columbus used, to destroy its 

 unstable equilibrium. A body may be said to be in stable 

 equilibrium if after a slight disturbance it recovers its 

 position of equilibrium ; and in vnttabl- i if 



after a slight disturbance it does not recovor it. \\ h< n 

 a body is supported by its centre of gravity, it will rest 

 in every position about that point ; this has been called 

 indifferent equilibrium' Thus, a circle or any plane 

 figure, of uniform thickness, will rest in every position, 

 on an axis passing through its centre of gravity. 



PROPOSITION XX. 



The equilibrium of a body will be stable or unstable ac- 

 cording as its centre of gravity is in the lowest or hijhc.it 

 I-' Won pot ftt . 



If a body be in a state of equilibrium, suspended by 

 an axis at A (Fig. 0(11), about, which it is capable of 



i i, ' ;.. 



freely, or resting on a point A (2), any 

 nbiinoe will cause the body to move to the 

 tight or left, as shown by the dotted Imrs, :m<! 

 centre of g vibe a small arc (! C 1 ; but th.' 



centre of gravity, having moved, however slightly, Wow 

 tho point G, the tendency of JW " '" 



evidently be to remove the centre of gravity further 

 from tlie original position G. But if the centre of 

 gravity be in its lowest position G (3) after any distur- 

 bance which should remove the point G to G', the ten- 

 cl.'iiry of the weight will be to restore the body to its 

 original position, and the point G' to G. 



The tendency of the centre of gravity to 

 place if removed from its lowest to a higher position is 

 well illustrated by fixing the half of a bullet {*), or any 



