﻿Prof. K. W. Zenger on the Tangent-balance. 445 



glass rod is immersed in a denser liquid than the normal liquid 

 (sulphuric ether) . 



If this liquid, for instance, is concentrated sulphuric acid, 

 and the angle of deflection 48°, the density is 



c?=0-736+tan 48° =0-736 + 1-1106= 1-8466. 



For solids a double pan is provided ; the lower is immersed in 



water by depressing the beam ; the upper one is loaded with 



pieces of the solid until the index stands at zero ; thereupon the 



solid is placed upon the lower pan under water. If the angle of 



deflection of the unloaded beam is u, while u l is the angle which 



the index gives when the solid is on the lower pan under water, 



then the density 



j tanw 



a= > 



tan u x 



taking the density of water as unity. 



Unloaded, the tangent-balance gives an angle w = 19°; gar- 

 nets are added until the index shows zero ; and these are then 

 placed on the pan which is under water, when the index gives the 

 angle ^ = 10°; the density is therefore 



tan 19° _ 0-3443 



tan 10° " 0-1763' 

 for which we may write 



d= tan 19° cot 10°=0'3443 x 5-6713, 

 d= 3-4697. 



The pyknometer gave d— 3-470. 



For higher specific gravities this method becomes inaccurate ; 

 and therefore a load is placed upon one pan, which places the 

 index at 45° to 50° when the lower pan is dipped in water; a 

 piece of the body is laid upon the upper pan and the angle u 

 noted; the piece is next brought under the liquid and the angle u Y 

 noted; if u is the angle for the unloaded balance, we have 

 for the density 



-_* tan u — tan u x 

 ~~ tan u } — tan u 



Thus, with an angle of 45° for the unloaded balance, three 

 garnets upon the upper pan gave w = 40° 10*, and upon the 

 lower one ^ = 41° 25'; hence the density is 



tan 45°- tan 41° 25' l-Q-882 



tan 41° 25'- tan 40° 10' ~ 0*882 -0-848 ' 

 0118 __ 

 D -0^034- 347 * 



