ON BALANCES. 55 



centre of gravity, in which case it will require an additional 

 weight to cause it to turn or incline to any given angle, and 

 it is therefore less sensible with a greater load. The fixing of 

 the centre of motion in a balance is consequently of peculiar 

 importance, for on this depends the readiness with which it 

 will be affected by a smaller weight, and will return to a hori- 

 zontal position. And it will be seen that the best position of 

 all is that where the centre of motion is a little above the 

 centre of gravity. It should, however, be proportioned to 

 the distance of the weights from the fulcrum and to the 

 amount of the load, and this object can be attained in different 

 beams only by practical skill and experience. In order to 

 regulate the centre of gravity in balances of precision, they 

 are made to carry a small weight either under or over the 

 centre of motion, and movable with a screw. 



If the beam of an equal-armed balance be adjusted as to 

 its centre of gravity so as to have no tendency to one position 

 more than another, as in a, and the pans be equally loaded, 

 then with a small weight added to one of the pans, the 

 balance will turn, and the point of suspension of this pan 

 will move with an accelerated motion similar to that of fall- 

 ing bodies, but very nearly as much slower in proportion as 

 the added weight is less than the whole weight borne by the 

 fulcrum. The stronger the tendency to a horizontal position 

 in a balance, or the quicker its vibration (as in c and 3), the 

 greater additional weight will be required to cause it to turn 

 or oscillate to an increased angle. If a balance were to turn 

 with iooofrth part of the weight upon the fulcrum, it would 

 move at the quickest 10,000 slower than a falling body; that 

 is to say, the pan containing the weight, instead of moving 

 at the normal rate of a falling body, or through sixteen feet 

 in a second of time, would fall only through about ^-th of an 

 inch, and it would take about thirteen seconds to fall ^ inch. 

 Consequently all accurate weighing with a balance of preci- 

 sion which turns, with a very small difference in the weights 

 placed in the pans, must be slow. 



13. From what has been said it may be seen that if the 

 arms of a balance be unequal, weights which form an equi- 

 poise will be unequal in proportion. A justly constructed 

 equal-armed balance may thus be tampered with and made 

 a fraudulent balance. One common practice with fraudulent 

 dealers is to throw one of the suspending chains of the weight- 



