76 OUTLINES OF NATURAL PHILOSOPHY. 



between the centre of suspension and the centre of 

 gravity, P the load in either scale, and W the 

 weight of the beam, the sensibility of the balance 



is as , fi) p - WV ; ^ * 3 t ^ lere f re greater, the 



greater the length of the arm, the less the distance^ 

 between the two centres, and the less the weight 

 with which the balance is loaded. 



Lastly, The stability, or the force with which the 

 state of equilibrium is recovered, is proportional 

 to (2 P -f W) b, the denominator of the preceding 

 fraction. 



The diminution of Z, therefore, while it increases the 

 sensibility, lessens the stability of the balance, but 

 the lengthening of a will increase the former of these 

 quantities, without diminishing the latter. The 

 above formulas are of great practical utility, because, 

 by means of them, one balance may be made having 

 exactly the same sensibility and stability with ano- 

 ther : it is only required, that the ratio of the lengths 

 of the arms should be the same with that which is 

 compounded of the ratios of the distances of the 

 centres of gravity and suspension, and of the weights 

 of the beams. 



A balance made by RAMSDEN for the Royal Society, 

 is capable of weighing ten pounds, and turns with 

 the ten millionth part of the weight, or little more 

 than the two hundredth of a grain. YOUNG'S Lec- 

 tures ', vol. i. p. 125. Descriptions of balances are 

 always defective, where they do not give the values 

 of 0, 6, arid W, the quantities on which the merit of 

 the balance depends, and by the knowledge of which 



similar 



