Prof. Ch. V. Zenger on a New Steam-gauge. 



V\ 4-^ + ^3 + ^4 = 



347 



1= volume occupied by the contained ait* 

 under a pressure of one atmosphere ; 

 ^2 + ^3 + v 4 =. I; = volume occupied by the air under a pres- 

 sure of two atmospheres ; 

 v 3 + v 4 =l= volume occupied by the air under a pres- 

 sure of three atmospheres ; 

 v 4 = I = volume of the air under four atmospheres. 



This gives for the capacities of the separate tubes : 



1 1 







1 



273' 



1 

 37T 



v A — 



These equations indicate the general form of the expressions 

 for the capacities of the separate tubes of a manometer to be di- 

 vided so as to show pressures up to n atmospheres ; and from 

 the capacities the radii of the tubes and terminal globe are at 

 once obtained : thus — 



v\ = 



Capacities. 

 1 

 173' 



1 



1 

 374' 



v„ = 



v»-i = 



V n = 



1 



1 



t\ = 



Radii. 



1 



y/torh 



1 



1 



1 



y/(n— \)mrh 

 1 



\/%nir 



If the length h of each tube is made equal to the unit of length, 

 an inch for instance, it becomes unnecessary to express it in the 

 above values of the radii. 



In order to diminish the number of tubes required for the con- 

 struction of the apparatus, it is sometimes convenient to arrange 



