VOL. XL.J PHILOSOPHICAL TRANSACTIONS. ISQ 



Some new Statical Experiments. By J. T. Desaguliers, LL. D. F. R. S, 



N° 445, p. 62. 



When a long and heavy body, lying on the ground, is to be raised up at 

 one end, like a lever of the second kind, while the other end keeps its place, 

 and becomes the centre of its motion; the prop used to support it at any point 

 in its whole length, sustains a certain pressure from the beam. Now these ex- 

 periments are to show, by a force drawing always in the direction of the prop, 

 what is the quantity of the pressure on the prop, according to its length, and 

 to the angle which it makes with the beam, or with the horizon, and to the 

 distance from the centre of motion of the beam at which the prop is applied. 

 For when the prop is taken away, the force drawing in the direction of the 

 prop will keep the beam in equilibrio ; and a force ever so little superior to the 

 friction added to the power, will make it overpoise the beam, and raise it 

 higher ; but overcome the power and bring down the beam, if it be added or 

 applied to the beam. 



Though in every case and experiment we have this analogy, taken from me- 

 chanical principles, viz. that, — The intensity of the power : Is to that of the 

 weight : : As the distance of the line of direction of the weight : Is to the 

 distance of the line of direction of the power; — ^yet to find those distances 

 nicely in the several applications of the prop, we must have recourse to geo- 

 metrical constructions and reasonings. With these and the algebraical ex- 

 pressions of the same, the experiments exactly agree. 



In the machine here used, the iron bar, or parallelipiped representing the 

 heavy body, weighs 12 drams, 12 dwt. 12 grains, or 6060 grains; and its 

 centre of gravity is at the distance of 2O-I- inches from its centre of motion. 

 The props used are, the one of 5, and the other of 10 inches. To over- 

 come the friction, allowed for by certain rules in all cases, the Dr. used a nice 

 brass pulley, of 3 inches diameter, its pivots only -j-J-^ of an inch in diameter ; 

 so that the 6oth part of the power added to it, will in all cases overcome the 

 friction. 



Case I. In which the Prop is perpendicular to the Horizon, exemplified by 



two Experiments. 



Exper. 1. — The prop is 5 inches, and placed under a point in the bar, 10 

 inches from the centre of motion. Here the power acting in the direction of 

 the prop, able to keep the bar in that situation, or the pressure sustained by 

 the prop, will be found 250 oz. 1 7 dwt. 1 5 grains ; and the friction 8 dwt. 

 15 grains. The foot of the prop is to be at 8 inches and -^ from the centre 

 of motion. 



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