CEJTTKE OF GRAVITY.] 



MECHANICAL PHILOSOPHY STATICS. 



-15 



of the common centre of gravity of their body and the 

 pole ; as, for example, the centre of gravity of the rope- 

 dancer C A being at A, his line of direction should go 

 Fig. 76. . 



through a, off from the rope ; but by moving the pole 

 towards B, the common centre of gravity of the man 

 Hid pole is brought to C, and the line of direction C D 

 goes through the rope. Those that are well skilled in 

 this art wfll sometimes use their arms only instead of 

 a pole ; and it is very common for several of them to 

 dance with a flag, with which they strike the air the same 

 way that the centre of gravity goes when the line of 

 direction does not go through the rope ; and by the re- 

 action of the air the centre of gravity is brought back 

 to its proper place. 



" The ancients observing that horses and other quad- 

 rupeds, in galloping, lift up their two fore feet, and 

 then their hind feet as soon as the fore feet are set 

 down, did imagine that in walking, as well as pacing 

 and trotting, a horse has two feet off of the ground at 

 one time ; and accordingly, in their brass or marble 

 statues, they have represented their horses with two 

 legs off of the ground diagonally opposite as the right 

 before and the left behind, or left before and right 

 behind. The modern statuaries havo also fallen into 

 the same error, because in the quick walking of a horse, 

 the eye cannot well distinguish ; and therefore Borelli 

 (De motu animalium) has shown from mechanical prin- 

 ciples, that the motion of raising two feet at once in 

 walking cannot be consistent with the wisdom and sim- 

 plicity of nature. 



"Let us consider a horse as an oblong machine sus- 

 tained by the four legs, 

 as four props or columns, 

 resting on the points A, 

 B, C, D, (Fig. 77), which 

 make a rectangular quad- 

 rilateral figure ; then the 

 line of direction will fall 

 perpendicularly on E, a 

 point in or near the 

 centre of the quadri- 

 lateral figure, which will 

 make the station or 

 standing of the horse 

 the most firm. The pro- 

 gressive motion begins by one of the hind feet as, for 

 example, the left hind foot C, which, by strongly press- 

 ing back the ground, moves forward the centre of 

 gravity, and consequently carries on the line of direc- 

 tion from E to G as itself moves from C to F. This 

 done, the foot B is raised and carried forward as far as 

 H, which motion of the foot is easy, because the line of 

 direction first falls within the triangle A B D ; secondly, 

 within the trapezium ABFD that is, the body of the 

 horse is sustained by three or by four columns. Lastly, 



the three feet A, D, F, remaining firm, and taking the 

 line of direction at G, immediately the left fore foot B 

 is carried forward to H ; and by the impulse already 

 made, the centre of gravity is also carried over I 

 namely, the central point of the rhomb A H F D. The 

 motion of the two left feet being completed, the im- 

 pulse and motion of the right hind foot D begins, and 

 then that of the right fore foot, and- so on in the 

 manner above described, as the animal moves forward. 



" Ducks, geese, and the greatest part of the water- 

 fowl, whose legs are set wide asunder for the con- 

 venience of their swimming, and turning quick in the 

 water, have always a waddling motion upon land ; but a 

 cock, a stork, an ostrich, and most other birds that are 

 not web-footed, walk almost directly forward without 

 waddling (especially when they walk slowly), having 

 their legs so placed as to put one foot before the other 

 with greater ease. Thus quadrupeds seldom or never 

 waddle, because they have commonly three feet upon 

 the ground at a time ; so that, however the base receiv- 

 ing the line of direction alters from a quadrangular to a 

 triangular figure, that part of it, in which the line of 

 direction falls, is always in or near the same line. 



" When a man stands in a firm posture (Fig. 73) A B, 

 the distance of his feet is the length of a quadrilateral 

 figure, whose breadth is nearly the length of the feet, 

 and D is the point under the centre of gravity C, 

 where the line of direction falls. Let the lines A C and 

 B C be drawn, then let these two lines and D C be con- 

 tinued to the points E F G so as to make the triangles 

 E C G and A C B equal and similar ; as long as the line 

 ! F D (or a plane going through it) cuts the whole body 

 of the man into two equal parts, the centre of gravity 

 will be at C, and C D will be the line of direction. But 

 if the body be inclined towards the left hand H, the 

 centre of gravity will move from C to H, the line of 

 direction will become HB, and the right foot being 

 easily removed from A, may be carried on beyond B, by 

 which means the man will go on towards the left. In 

 like manner, by inclining towards I, the line of direc- 

 tion will be removed to I A, and the man go to the 

 right. When a man stands upon one foot it is with 

 some difficulty. For example, let the line of direction 

 be C D (Fig. 75 1) ; by the motion of the blood and 

 lungs, and other animal motions, the centre of gravity 

 will be apt to vacillate or totter towards F or G on 

 either side about the centre of motion D, where now the 

 base is but small. If the line of direction come to B, 

 the man must fall forwards, backwards if to E ; and 

 though A be under the heel of the foot, yet in the 

 motion of the said line of direction from D to A, the 

 body will be apt to go towards E, and so bring the line 

 of direction beyond the base. This will more probably 

 happen in the side motion of the body ; so that the 

 body will be in danger of falling, unless the right foot 

 be put down towards that side where the body inclines. 

 Birds stand upon one foot much more easily than men, 

 because their line of direction being much shorter, and 

 the base of one foot a large rhomboidal figure made 

 by the four claws, the line of direction cannot go out of 

 that base, unless the centre of gravity rises, which is 

 impossible without a violent motion." 



When a porter carries a burden upon his shoulders, he 

 must stoop, because, if he should stand upright, the 

 common centre of gravity of the man and burden would 

 be so far brought back, that the line of direction would 

 fall behind the feet. 



PROPOSITION XXII. 



A heavy body rests upon a horizontal plane, to find the 

 pressures produced by its weight upon the points of con- 

 tact by which it is supported. 



When a heavy body rests upon a horizontal plane, the 

 pressures produced by its weight on the points on which 

 it is in contact with the plane can be determined, if 

 these points do not exceed three in number. When the 

 points of contact are more than three, the pressure upon 

 each is indeterminate. 



