448 Proceedings of the Royal Society of Edinburgh. 
From (25), (26), and (27) we get 
For 0«iT, Vl = Zi = .... 
„ |T«T, yMfi -p 2 = (y/p ) { - 1 + ( 2e^ T -\)e~^} 
„ T<^+oo, 2/ 8 = ^-i? 3 = -(yi/^){e^ T - l} 2 e~^ . 
Also 

d h = - y(2ei<‘ 1 ' - lje-M* ; = y/ »(2eJ»*® - l) e -e« 
(XP 
The graphs of V5 - tiy 0 and tzr — p are OCBK and ODEF in fig. 6. 
[Sess. 
(28); 
(29) ; 
(30) . 
(31) ; 
(32) ; 
• (33). 
It should be noticed that here there is no retardation or acceleration of 
the turning-points on the microbarogram ; but there is a pseudo-minimum. 
The parts of the microbarogram ODEF are congruent with portions 
of the exponential curve y = e~ fMm , and it should be noticed that the amount 
of the discontinuity of the gradient is the same at D and E as at C and B 
respectively. 
In the particular case where T = 30 min- = 1800 sec ’ and /u = 1/3000, we have 
£/*T = '3, l-e-^ T = *74082, (1 - e~^ T ) 2 = -06718 . 
AC = 900y , AD = 778y , BE = 202y. 
Hence the range of the microbarogram is 980y, that is to say, greater 
than the range of the outside air pressure ! 
Case 6. Periodic sinusoidal barometric disturbance ts — t*y 0 + a sin nt. 
We have merely to drop the term containing e ~ flt , which becomes 
infinitely small after a considerable time has elapsed ; and we get 
y = - a cos x cos (nt + x) .... (34). 
The acceleration is x! n > an d the ratio of damping cos x- 
Thus, if x = ’P i’ e ‘ T = 27r/^ = 31-43 min -, then l/'ft, = 30003 ; and the 
acceleration of the maximum (and also of the minimum) is 30 sec - 
