Cuff. — The Cam-lever Balance. 



193 



This great defect is entirely removed by applying to the scale-pan 

 arm a correctly shaped cam, which prevents the too rapid shortening of the 

 virtual length of the scale-pan arm for any given increase in the deflection 

 of the counterpoise arm. The scale-pan is suspended by a tape or cord 

 which passes over the curved surface of the cam and is attached to it on 

 its farthest side. 



With any gravity balance the condition of equilibrium is attained when 

 the product of the length (or the virtual length) of the arm multiplied by 

 the weight on one side of the fulcrum is equal to the product of the length 

 (or the virtual length) of the arm multiplied by the weight on the other 

 side of the fulcrum. The product of the said factors on either side of the 

 fulcrum is called the "moment of force" on that side. 



As an example : Let the length of the counterpoise arm be 140 mm., 

 and the limit of weight to be measured by the balance (including the weight 

 of the scale-pan) be 45 oz., at a distance of 20 mm. from the fulcrum ; then 

 the moment of force on the scale-pan arm would be 45 x 20 = 900, and the 

 counterpoise weight must be 900 divided by 140 (the length of its arm), or 

 6-4286 oz., or very nearly 6-43 oz. (See fig. 1.) 



/40 



o 



6 43oz 



Fig. / 



' ryg.2 



6 4-3 oz 



It is required that when the weight suspended at the end of the scale- 

 pan arm be reduced to any given proportion — say, one-third of the maxi- 

 mum—then the counterpoise arm should rest in equihbrium at the same 

 proportion of its total range — that is, at one-third of 90° (or 30°) from the 

 vertical. In this position (see Fig. 2) it is seen that although the actual 

 length of the counterpoise arm has remained the same, yet its virtual 

 length for reckoning its balancing - power has been reduced to one-half, 

 or 70 mm., and the moment of force on its side of the fulcrum has been 

 reduced from 900 to 700 x 6-4286 = 450. Then, the length (or the virtual 

 length) of the scale-pan arm must be 450 divided by one-third of the maxi- 

 mum weight — that is, one-third of 45 oz. (or 15 oz.). This gives 30 mm. 

 as the required length of the scale-pan arm in this position, instead of 

 20 mm. as in the first position. 



To make the scale regular, the scale-pan has to be suspended at a 

 different distance from the fulcrum for every different angle of deflection 

 of the counterpoise arm. 



Let A = the angle of deflection of the comiterpoise arm from the ver- 

 tical, and L = the actual length of the counterpoise arm, which agrees 

 with its effective length only in its horizontal position, or when A = 90° : 

 then L x sin A = the virtual length of the counterpoise arm for any angle A. 

 Let C = the weight of the counterpoise : then L x sin A x C = moment 

 7— Trans. 



