440 Proceedings of the Royal Society of Edinburgh. [Sess. 
settle down after a long period of undisturbed atmospheric pressure w 0 . 
We should then have p = m 0 , and therefore by (1) v = u = v 0 say, and we 
may now write (1) in the form 
zz-p = v - v 0 (6). 
Also, if w 0 be the value of w in the initial case supposed, we may write 
(5) in the form 
a 2 v + ( b 2 - a 2 )w = a 2 v 0 + ( b 2 - a 2 }w 0 ; 
or 
v- w 0 .=B- (b 2 ja 2 - l)(w- w 0 ) .... (7). 
Hence, finally, 
&-p= - (k 2 /a 2 - l)(w-w 0 ) . . . (8); 
that is, if 0 be the divergence in centimetres of the index of the instrument 
from the position of absolute equilibrium for the temperature supposed, 
and h a constant factor depending on the multiplying power of the 
registering lever or levers, then 
xs - pfe*/® 2 - V)zik . . . . . (9). 
In other words, the reading is proportional to the difference between 
the pressures outside and inside the floating cup. We have supposed the 
excursions of the index so small that the circular motion of the recording 
pen may be taken without sensible error to be proportional to the vertical 
motion of the floating cup. 
On the Variation of Pressure in a Closed Chamber which 
Leaks into the Air through a Capillary Tube.* 
Let V be the volume of the air-chamber. 
v the volume of the air in the chamber at time t when reduced to 
the pressure 
R the radius, and L the length, of the capillary tube. 
p the pressure of the inside air at time t. 
ts the pressure of the outside air at time t. 
ZcTq the common initial pressure outside and inside the chamber, 
which we shall usually take to be the standard barometric 
pressure, viz. 981 x 76 x 13*55 = 1*014 x 10 6 dynes per sq. cm. 
ij the coefficient of viscosity of air at 15° C., say ^ = *00018. 
* This part of the theory will apply equally well to any other form of microbarograph 
in which the reading is proportional to the difference between the atmospheric pressure 
and the pressure in an air-chamber provided with a leak : for example, to the Richard 
statoscope, when its air-chamber communicates with the outer air through a capillary tube. 
