32 THE APPLICATIONS OF PHYSICAL FORCES. [BOOK i. 



then takes a vertical position; but when a body is placed in the 

 pan, the action of this weight at the end of the arm of the lever 

 A moves the needle and causes it to traverse the divisions of an 

 arc of a circle properly graduated. This instrument does not require 

 the use of any weights. Its graduation is deduced from a very 

 simple mechanical principle, namely, that the weights placed in the 

 pan are proportional not to the angles that the needle makes with 

 the vertical, but to the tangents of these . angles, that is to say, to 

 the distances CT, CT' . . ., which the direction of the needle pro- 

 longed determines on the horizontal line drawn from the point c 

 in the vertical line of and tangent to the arc of the circle described 

 from the point as centre. 



FIG. 13. Roberval's balance. 



We conclude this description of weighing instruments employed 

 in commerce and the arts by a few words on Roberval's balance. 

 The two pans of this balance rest, on the upper part of the beam, 

 on two upturned knife-edges, and are fixed to two equal movable 

 rods, connected at their lower extremities by rings to the two ends 

 of a lever also movable on an axis at its centre. This arrange- 

 ment, which changes none of the conditions of equilibrium, renders 

 the use of this balance very convenient. The bodies to be weighed 

 and the standard weights may be placed and taken away without 

 interfering, as in the ordinary balance, with the cords or suspending 

 strings of the pans. This form of balance is very extensively used 

 in the present day. 



