Management of delicate Balances. 343 



are considered good ones by the first rate chemists of Eng- 

 land. 



To explain the principles of the following remarks upon 

 the construction and modes of adjustment of a balance, it 

 will be first necessary to take a general view of the principles 

 of the instrument. 



The balance is a lever, having two arms nearly in the same 

 straight line, at the extremities of which the weights and load 

 are hung at nearly equal distances from a central axis, or cen- 

 tre of motion between them. 



The force acting upon the ends of the arms or points of 

 suspension, is the force of gravity due to weights and load. 

 The force at each end of the lever acts in parallel and vertical 

 lines, and the effect to put the system in motion will be the 

 moments of these forces, or the force itself multiplied into the 

 perpendicular upon the direction of its action from the centre 

 of motion. 



The perpendicular from the centre of motion upon the 

 direction of each force, will be equal to the line of the angle 

 which the arm of the balance makes with the vertical multi- 

 plied by the length of the arm. 



The moment of the force acting upon each end of the 

 balance will be equal to the product of the weight, the length 

 of the arm, and line of the angle which it makes with the 

 vertical line from the centre of motion. 



Let A and B be the weights at each end of the arms. 



a and /3 the length of the arms. 



e = angle included between the arms. If the arms do not 

 form equal angles with the vertical, but the angle with the 

 arm A is the greatest, then the moments of the forces acting 

 upon each arm will be 



A. a. Sin (^e -f- Inclin.) 

 B-j3. Sin (|e — Inclin.) 

 As the forces act upon opposite sides of the centre of mo- 



