1907-8.] On the Theory of the Leaking Microbarograph. 447 
Case 4. To get an idea of the effect of an elevation followed by a 
depression of barometric pressure, we may suppose 
Zo 1 = VS Q + a sin nt for 0^<^27r/w ; 
^2 = ^0 ” 27r/?Z^/^CO . 
It is easily found that the corresponding values of vs —p are given by 
where 
2 / 1 = ttcos^{sin (nt + x) - sin x e } • • • • (23) 
y 2 = - asinxcos-^l - e~^ T )ef xt .... (24): 
tan x = fi/n. 
The general form of the corresponding graphs of vs — vs 0 and vs — p are 
given in fig. 5 by OABCD and OEHKLM. 
Case 5. As very sharp turning-points often appear on the micro- 
barogram, it will be interesting to consider the effect of a symmetric 
elevation of barometric pressure whose graph is an isosceles triangle. 
W e may take vs = vs 0 + yt when 0<y^T ; vs = vs 0 + yT — y t, when 
JT<^CT; vs = vSq, when bT<t< +co ; so that T is the time of passage of 
the disturbance. 
Then, if 0<t<^T, 
whence 
If J-T<£<T, 
■f 
Jo 
Pl e^ = ST 0 + fx\ dt(VS o + y t)e ^ ; 
Pl = VS 0 + y{t-l/fi + e tf/n} 
p 2 e ^ = VS 0 + pi dt(VJ 0 + yt)e^ + p dt(TV 0 + yT - yt)e ^ 
IhT 
If T«+oo, 
= vs 0 e^ + y{(T -t + + - 2e-^ T )} 5 
-P2 = ^o + 7{( T " * + V/*) + (V^)(l - 2e-^ T )e-^} 
P T 
i dt(vs 0 
Jo 
p tfP* = C7 0 + fx | dt(vs 0 + yt)&# + dt(n T 0 + yT - ytj&d + 
4T 
= + (y//x)(e^ T - 1 ) 2 j 
Ps = ra o + (y// l )(e i, ‘ T - 
• (25). 
• (26). 
dtTSf.e* 1 , 
• (27). 
