MECHANICAL PHILOSOPHY STATICS. 



[onmt or owrmr. 



In (1) thi* foroe U evidently destroyed by the reaction 

 of the plane, and the body will rind. In (2) thw force 

 has a moment about the point B, which U not counter- 

 acted by the resistance of the plane ; and consequently 

 the body will turn round B till it falls in iuch a pMttha 

 that G \V will lio within the baar on which it rest*. This 

 property i readily shown, experimentally, by Uking two 

 oblique eylinden (Fig. 711 and 2) of uch length* that 

 the vertical pasting through the centre of gravity ..f th 

 one, when placed on a table, ahall fall within its circular 

 bate, and the other without The former will stand and 

 the latter will fall when placed with their circular base* 

 in contact with the taM.- 



If the surface on which the body rest* be inclined in- 



71. 



tteati of horizontal, the same effect will be produced, 

 provided the body be prevented from sliding down the 

 inclined plane by friction or some other force. 



Thus, a loaded waggon 

 passing along an inclined 

 road will not be over- 

 turned so long as the 

 vertical G A (Fig. 72) 

 passing through the 

 centre of gravity G of 

 the load and waggon 

 falls within the points 

 where the wheels touch 

 the road. As soon as 

 the inclination of the 

 road becomes so great, 

 or the position of the 

 centre of gravity of the 

 load be such, that the ver- 

 tical falls without these 

 points, the waggon will 

 be overturned. 

 The broader the base, and the lower the centre of 

 gravity of th body, the firmer will be its stability. A 

 waggon cam-ing a load of straw is more likely to be 

 overturned than if it were laden with an equal weight of 

 iron or some other heavy material ; because, in the first 

 instance, the distance of the centre of gravity of the 

 load and waggon from the ground is much higher than 

 b| !,. !.,r. i 



ii nd tower which in the belfry of the cathedral 

 at Pisa, is 190 feet high, and deviates from the perpen- 

 dicular about 14 feet. At Bologna there is a square 

 tower called Garisemla, 134 feet high, and deviating 9 

 feet from the perpendicular. Both these buildings are 

 supposed to owe their inclination from the depression 

 of the ground under their foundations ; and they have 

 not been overthrown, because the vertical, paaung through 

 their centre of gravity, still fall* within their base. 



Denaguliers, in his Count of Experimental Fhilo- 

 opfcy, has the following interesting observations on the 

 position of the centre of gravity in animal bodies 

 when at rest, or in motion, in various positions. " When 

 we stand upright, with our feet as represented in Fig. 

 73, the line of direction (i. . . the vertical pauing through 

 tW eaUn of gravity) goes through the point C, and 

 pass** between our feet to D, and we may move our 

 heads from E to F or G, and our bodies forward*, 

 backward*, or sideways, as far as I or H, without 

 of falling, or lining our feet, aa long aa the 



line of direction traverses no farther than I A or H B, 

 and falls anywhere with- n,. 73. 



in tlu space AB, which 

 in this situation of our 

 feet makes a pretty large 

 base. But if we set one 

 foot before the other, as 

 in Fig. 74, a little push 

 sideways will make the 

 line of direction (which 

 went through C) fall 

 out of the base to the 

 right or left toward* E 

 or B ; in which case a 

 man must fall if he do 

 not quickly re- 

 move his feet to 

 the position of 

 Fig. 73. 



"When we stand 

 nponeitherleg, we 

 must bring our 



body so much over the foot, that the centre of 

 gravity being directly over it, the line of direc- 

 tion may go through the sole of it ; and in walk- 

 ing, the line of direction must travel through 

 every place where each foot is set down, going 

 successively through the points E, A, D, B 

 (Fig. 75), while the centre of gravity goes through 

 the points G, C, F, &c. ; so that unless a man in walk- 

 Fig. 74. ing straight forward, sets one foot directly before 

 the other, the line of direction will not describe 

 a straight line upon the plane where the man 

 walks, but an indented line ; that is, angles to 

 the right and left, whilst the body of the man 

 goes on in a waddling motion. This we see in 

 the walking of fat people, and all others that 

 straddle in their gait. The line of direction going 

 through the points A, B, C, D, E, describes 

 a straight line in Fig. 75 (2), where the feet are set be- 

 fore one another ; but when the motion of one foot is in 

 a parallel line with the motion of the other, an indented 

 line is described by the motion of the centre of gravity 

 above, and the line of direction as it cuts the ground at 

 A, B, C, D, E (3). 



" It is not strictly true that any man in his common 

 walk sets one foot so exactly before the other as to carry 

 on the bottom of his line of direction in a straight line, 

 as represented in (3) ; because if a straight line be drawn 

 with chalk, it is difficult to walk straight along it : but 

 the plainest proof is the observation of two upright 

 sticks, of about the height of a man, the one painted 

 white and the other black, and set up about ten yanU 

 beyond one another, in the same line that a man walks 

 Fig. 7i. towards them ; for in such a case, 



though he keep one eyo shut, the 

 last stick will appear sometimes on 

 the right and sometimes on the left 

 of the first ; and the more so the 

 nearer the man 

 come* to the 

 sticks. Rope- 

 rs, indeed, 

 go in a straight 

 line ; but it is 

 what they have 

 learned by art, 

 and inured them- 

 selves to by long 

 practice ; yet they 

 must, even after 

 all, have helps to 

 keep their centre 

 of gravity over 

 the rope. They 

 generally keep their eyes on some distant point in the 

 same plane as the rope. They have commonly a long 

 pole loaded at the ends with the balls of lead B b (Fig. 

 70), by the motion of which they can alter the position 



