Management of delicate Balances. 357 



Whence it appears, that the centre of gravity in the balance 



above described, is only one-thousandth part of an inch below 



the centre of motion. 



Transposing the formula 



A-B=A+B.x. L . .. . 



— T tang, inclination. 



and if the angle of inclination is taken at 4° we have 



7840 3.894316 



x 7.009924 



7. C.Log 9.154902 



Tang. 4° 8.844644 



Grains . . 0.08012 ^~8.903786 

 or 0.08 grains are required to produce inclination of 4° 

 when Z would give 30', shewing that within any common arc 

 of inclination, equal weights produce equal arcs. 



If the points and knife-edge are supposed to have a sensi- 

 ble diameter, the extremities and edge, then by rolling the 

 length of the arm would be decreased by 



2. sin. inclin. + radius of the points, with two scale pan 

 suspensions, and the centre of gravity would also be thrown 

 on one side of the new centre of motion by a quantity = 



= sin. inclin. + radius of knife-edge ; substituting them in 

 the above formula, we get 



A -f B. sin inclin. (x + R.) 



o . , _ . 



(L-2 sin inclin. R). cos. inclin. 

 When the radius of the points and knife-edge is sup- 

 posed = R = 0.005 inches. 

 L = 7 = • • • • 0.845098 

 Cosin 30' .... 9.999983 



0.845081 =6.99970000 inclin. 



2 z 



