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LVII. On the Tangent -balance, and its application to determining 

 the Density of Solids and Liquids by direct reading. By Pro- 

 fessor K. W. Zenger*. 



[With a Plate.] 



THE degree of delicacy of a balance depends on the weight 

 of the arm m, the distance d of its centre of gravity from 

 the axis of suspension, and finally on the length of the arm /. 

 If p is a weight on one scale and u is the angle of deflection, then 



tan?4= ^-=« 

 ma 



If the balance be so arranged that the constant 



md ' 

 then 



tan u =p. 



The tangent of the angle of deflection is equal to the weighty. 

 If by means of a hook and a fine platinum wire there be sus- 

 pended to one arm of the balance a small glass rod which dips 

 in a liquid, for instance the specifically lightest sulphuric ether 

 (of 0*736 spec. grav. at 0°), and if to the other end of the beam 

 a small brass weight be hung and so arranged that the index 

 stands at zero, we have as the equation for the angle of deflection, 



tantt =(^-a? + y )^, (1) 



where p is the weight of the brass weight, x the weight of the 

 glass rod, y its loss of weight in the ether. 

 As the angle will then be zero, it follows that 



0=p-x + y Q , 



Immersed in another liquid of greater specific gravity, the loss of 

 weight y must be greater, and the index will give an angle u ; 

 we shall then have 



tanw=(i>-#+2/)^ (2) 



The loss of weight may be supposed to consist of two parts — 

 namely, the loss of weight in ether, plus the excess of loss of 

 weight y x in the denser fluid- — from which is obtained 



V =y Q + Vv 



yi=y -y - 



* Communicated by the Author. 



