260 Temperature of Mercury in a Siphon Barometer. 



It is evident from (16) that no error will be introduced, and 

 consequently no correction will be needed, even if the forms of the 

 meniscuses do vary, provided the sums of their altitudes for each 

 column are constant ; that is, provided the height of the upper 

 meniscus increases as that of the lower one diminishes, and vice 

 versa. This indeed is the tendency in good tubes properly filled, 

 and furnishes a convenient and useful test. 



Example. I took two observations with No. 365 Bunten's ba- 

 rometer, in which the altitudes of the meniscuses were particu- 

 larly subject to variation. The elements of the first observation 

 were 

 a=A07.75, 6=363.11, H = 1.68, h=l.75; and of the second 

 a'=400.11, 6^=360.09, H^=0.90, h'=1.60. 



According to (16) therefore, the corrected difference of readings 

 is 40.49 ; while the observed difference is 40.02. 



We have hitherto supposed the tubes, within the ranges of the 

 mercurial surfaces, to be of equal and constant diameters. It is 

 desirable to test the accuracy of the instrument in this respect, 

 and, if necessary, to apply the suitable correction for temperature. 

 A correction also for capillarity is equally important, and may be 

 directly applied by knowing the diameter of the tube at the ex- 

 tremity of the column. 



We will suppose the tubes within the ranges of the mercurial 

 surfaces to be frustums of cones ; and, besides the notation and 

 figure employed in determining (9,) 

 Put R = radius of the tube at D, 

 r= radius of the tube at d, 



^=angle which the axis of the tube makes with its side at D, 



6'=angle which the axis of the tube makes with its side at d ; 



and suppose the cylinders, whose altitudes are (p, ) (p^, ) to rest on 



bases at D, d, respectively equal to the horizontal sections of the 



barometric tube at these points. 



Regarding the tubes DD', dd', from the necessary smallness of 

 their heights, as cylinders, we have 



Capacity of the tube DD'=TreR^p(i' — t,) (17.) 



Capacity of the tube dd' = n£r"p'{i'— t,) {IS.) 



Radius at D''=R+(a, -a) sin. 6. 



Radius ^i d" = r+{h,-h) sin. 0'. 



Frustum DD"=g(a/-a) [R3+[R+(a/-a) sin. ^]-+R[R+ 

 (o,-a)sin.^]%] (19.) 



