186 Dr Searle, A Simple Method of determining : 
$4. Formula for viscosity. In the experiment the mass of 
the air which passes through the tube is deduced from the fall of 
pressure of the air in the vessel during a time ¢ seconds. 
Let the volume of the vessel up to the end «=0 of the flow 
tube be Sc.c. and let the mass of air in the vessel at any time ¢ be 
M grms. Then if, as is assumed, the temperature be 0,, we have | 
MSc = Sc,P/P,... ee (11) 
The rate at which mass escapes from the vessel is o,U, grms. per | 
sec. and this is equal to —dM/dt. Hence, by (11), 
re ae 
Gendt es eee 
Using this value of U, in (10), we obtain the following differential 
equation for P, viz. 
ie 
SEEPS Ge tea 
Pi dt SiG6yl eel 
Putting 1/(P? — P,”) into partial fractions, we have 
(ae 1 PSG 
= = seat date (12) 
TP) VPESP) SPP \ eae lees 
Integrating from t=0 to t=#, we have 
A Pigg, Pt Ea]. att 
OP. 2 P=, i, © lense 
If P, and P, be the pressures in the vessel at t=0 and at t=7, 
then 
TAP ot Be : 
is = )\, PoudnnoDdDDOodoadadDOOLOOS (13) 
é mes (P, =a VER PRP; + P, 
where dX. = log, 1B Sa eE Pt . Pee ee (14) 
_ mail t 
Hence NS Teg #40 ee ee (15) 
From the last expression 7 can be determined. The value of Py — 
on the right side of (15) must be expressed in dynes per sq. em. 
Thus, if the barometric height be h, cm. and the density of — 
mercury at the temperature of the barometer be p grms. per ¢.c., — 
Po = gphy- 
Since only ratios are involved in the formula (14) for A, the pres- 
sures in that formula may be expressed in cm. of mercury. 
In the experiment it is the differences P,—P,, and, Pw 
