356 On the Construction and 



A. a, — B. |3=A. a. + B. p. cotang \ e tang inclin. 

 Or, 



A. a.—B. /3. . 



cotang inclin=cotang £s. 



A. a.+B. j3- 



If the length of the arms is supposed equal, which will be 

 of no consequence in the present case, we may take a=/3 

 and then the formula becomes 



— =-- cotang inclin= cotang |e 

 A+B. 5 s 



If x = the length of the prependicular from the centre of 

 motion upon the line joining A and B and L == the length 

 of the arm. 



A— B 

 x=L. cotang |t=cotan inclin. + L~ A 



which is the same as if the whole weight at both ends of the 

 lever combined with the weight of the beam was to be consi- 

 dered as acting on the centre of gravity of the system, in a 

 point close below the centre of motion, so as to keep the sys- 

 tem horizontal, and the disturbing weight as acting at the end 

 of the lever to produce the inclination. 



Let the whole weight of the load, counterpoise beam, and 



scale =A+B= 7840 grains. 



A=B= .1 grain. 



100 ° 



Angle of inclination produced by adding JL th grains 

 z=30' and L=r7 inches. 



7840. . . . C.Log 6.105684 



L_ Log 8.- 



100 & 



7 Inches 0.845098 



Cotang inches= 0' 12.059142 



Inclin 0.001. = 7-009924 



