the Viscosity of Aur. 185 
is assumed to be equal to @,, the temperature of the surrounding 
atmosphere. 
§3. Calculation of pressure. When the motion is steady, the 
mass of air crossing each section of the flow tube per second is the 
same, and hence 
eater OL ORK Ee nein aac Enea ne (4) 
where o, and U, are the density and volume of the same mass of 
air at temperature @, and at the atmospheric pressure P,. Thus 
a, ee ere (5) 
o P 
Inserting this value of U in (3), we find the following differential 
equation for p, viz. 
IPO jo ae eho 
nia ae she Sy eae Bone eet ee (6) 
In practice the radius of the tube will not be quite constant at 
different parts of the tube, but it will generally vary so slowly as 
we pass along the tube that the conditions of flow for any in- 
finitesimal length dw may be treated as if they were those which 
would exist there if the whole tube had the same radius as the 
element dz. On these assumptions, equation (6) holds good for all 
values of x Integrating it with respect to # from «=0 to v=, 
and remembering that 7 is independent of the pressure, we have 
Lda 
T a 
IED; ‘ Face eee oooD0odODDOYOND (7) 
If the pressure in the vessel, 1.e. where 2=0, be P, then 
O GUIS 2 GP pes ; 
BO.) eR BD Bele tant! oe (8) 
since the pressure at #=/ is the atmospheric pressure P,. With 
moderately good tubes the integral on the left differs very little 
from J/a,‘, where za,” is the value of the cross-section deduced 
from the formula ~ 
THO sa pr wl E aan eRe nae Gch iar (9) 
and M grammes is the mass of mercury, of density p grm. per c.c., 
which fills the tube. The necessary calibration correction is in- 
vestigated in § 6. Neglecting it for the present, the formula 
becomes 
ma P?— P? 
= Teal? Ee SE ams 
an equation due to O. E. Meyer. 
Uy 
