Temperature of Mercury in a Siphon Barometer. 259 



placing the body of the column below it. Suppose then the parts 

 of the column in the vicinity of the circle HI to have such a hor- 

 izontal tendency towards the axis of the tube, without disturbing 

 the column below, as to cause the meniscus HBI to take the form 

 of EAF. We shall then have this equation : 



Meniscus EAF=meniscus HBI+cylinder HEFI. (11.) 



Put height AD of meniscus EAF=H. 



Height BC of meniscus HBI=H^ 



Radius of tube ED=r. 



Correction AB=a7. 



Height of cylinder CD=«/. 



Circumference of a circle whose diameter is unity =n. 

 And let the capacity of any meniscus EAF be represented by (nr^ ) 

 multiplied by a function F (H) of its height. Equation (11) 

 therefore becomes 7rr^.F(H)=7rr^.F(H'')+7rr-y. 



From the figure we have 'ii='H.'-\-y-\-x. 



Dividing the first of these equations by {^r'^,) and eliminating (y,) 

 we have a;=H-H'+F(HO -F(H.) (12.) 



It remains only to determine F (H,) F (H',) which depend 

 upon the form of the meniscus. 



If the tube is small, the meniscus differs insensibly from the 

 segment of a sphere, (Mecanique Celeste, 9334.) And generally, 

 since the meniscus in barometer tubes is a small portion of the 

 solid of revolution of which it is a segment, every practical pur- 

 pose would be answered by considering it a common paraboloid. 

 This being so, we have F(H)=^H, and F(H')=JH'; and con- 



H-H' 



sequently (12) becomes x= — ^ — j (^^O Wherefore (a') is cor- 



H-H' 



rectedto a'+ — „ — 5(14.) 



In like manner, denoting the corresponding heights of the me- 



niscuses in the lower branch by (h,) (h^,) we shall find (6') to be- 



h — h' 

 come b^— — « — j (l^j) ^^^ consequently {a' — h') becomes, after 



H+/i W+h' , „ , , , 



correction, a' — b'-\- — h — — — o — , ( 16. ) Hence, to find the cor- 

 rection for the difference "of readings [a' — h',) we subtract the 

 half sum of the heights of the meniscuses which terminate this 

 column from the half sum of the heights of the meniscuses which 

 terminate the column of which the readings are (a,) (&.) 



