1907-8.] On the Theory of the Leaking Microbarograph. 449 
Case 7. If the sharp-pointed disturbance of case 5 be repeated 
periodically, we may determine the nature of the barogram as follows i — 
After the variations have settled down to periodicity outside and 
inside, the pressure at the beginning of each period must be the same as 
at the end, and there is no acceleration or retardation of the sharp turning- 
points. 
Let us measure the time from the beginning of one of the periods, i.e. 
when the atmospheric pressure is at a minimum. Then we have 
pe = A + /a dttte^ , 
where A is obviously the inside pressure when t = 0. Hence, since A must 
also be the pressure at time T, we must have 
p rr 
Ae^ = A + /x dt(zz 0 + yt)e ^ + /x dt(rz r 0 + yT - yt)e ^ . 
Jo JbT 
This last equation gives 
(e^ T - 1)A = (e^ T - l)or 0 + (y//x)(el wT - 1 ) 2 , 
that is, 
A = V 0 + (y/p)(e^-l)/(e^ + l); 
or A = Z3 0 + (y Ip) tanh . 
Using this value of A, we get for the ascending branch of the micro - 
barogram 
Similarly, we get for the descending branch 
From (35) or (36) we get 
Vm in. = - (y/n) tanh J/xT . 
2/max. = + (yin) tanh 1/xT 
(36). 
(37) ; 
(38) : 
and the graphs of vs — vr 0 and vr —p are OABCDEF and GHIJKLM in fig. 7. 
As might have been expected a priori, the microbarogram fluctuates about 
the axis of t, i.e. about the line corresponding to p = m — 
It should be observed, however, that tz 0 is not the mean outside 
pressure. This last is so that the mean pressure outside is 
higher than the mean pressure inside by JyT. 
VOL. XXVIII. 
29 
