﻿444 Prof. K. W. Zenger on the Tangent-balance. 



We obtain from this 



tan u= {p-x+yo+y^—j 



—h-^h- 



_L_i 



md ' 



and 



Now if 



then 



ttmu=y — y Q . 



But the losses of weight are the weights of equal volumes v of 

 sulphuric ether and of a denser liquid ; and therefore 



tanu=v(s— s ), 



in which s and s are the specific gravities of the two liquids. 

 If the volume is equal to the unit of volume, we obtain 



tanw = s— s , 

 and finally 



s = s -\- tanw; 



for which, making the above supposition, and designating the 

 densities by d and d, we may write 



d=d i- tanw. 



The tangent-balance (PI. VI.) gives the density without using 

 sets of weights, by merely reading the angle at the index of the 

 balance, which plays on a circular limb 5 inches in length and 

 divided into half degrees, the centre of which is in the axis of 

 rotation of the beam. 



The beam is provided with an adjustment, by means of which 

 it may be raised and lowered so as to immerse the glass rod 

 suitably. 



The liquid is placed in a small beaker, which need not hold 

 more than 2 or 3 cubic centims., so that a minimum of liquid 

 can be used with entire certainty. The delicacy of the balance 

 is such that a deflection of 1° indicates a weight of 17 milli- 

 grammes ; and as the division extends to half degrees, and one 

 tenth of a division may be estimated, it is possible to read 

 to the twentieth of a degree; so that the balance indicates 

 0*8 milligrm. 



The density of a liquid, measured by the tangent-balance, is 

 found by adding to the density of ether, or of any other liquid 

 which corresponds to the zero of the division, the natural tan- 

 gent of the angle of deflection which the index gives when the 



