444 Proceedings of the Royal Society of Edinburgh. [Sess. 
Hence 
or 
y =TS-jp=- (e^-l)e-^; 
/i z 4 - n l 
y 1 = - a cos 2 ^ (e^ T - \)e~^ .... (14). 
Since y 1 is negative, and has no turning-point, y must have (in addition 
to the quasi-minimum for t = 0) both a maximum and a minimum in the 
interval 0<^T. 
We have, in fact, since m = n tan x, 
and 
dy 
dt 
dyh 
dt 
na cos x{ sin (nt + x) - sin^e - ^} 
wa sin ^ cos ^(e^ T - l)e - ^ . 
. (15); 
• ( 16 ). 
By drawing the graphs of sin ('fti + x) an d s ^ n if is eas y f° see that 
the maxima and minima points above mentioned correspond to values of t 
given by 
nt + x = 7r ~^i an( f n t + X = ^7r + £ 2 , 
where ^ and are two small positive quantities. 
Fig. 4 (not drawn to scale) shows the general character of the graphs of 
7tX — m 0 and w ~p, the former being represented by O ABC, the latter by ODEF. 
It is important to notice that a maximum on the microbarograph 
precedes the maximum in the atmospheric pressure which causes it ; and, 
as we shall see presently from a numerical example, this acceleration may 
be considerable. 
A minimum following a maximum on the microbarogram does not 
necessarily involve a depression following the elevation in the atmospheric 
pressure. 
The equations for calculating and ^ 2 , as above defined, are : — 
/(^)fe= sin ^ 1 -sinxe _tan x( 7r -x-li) = 0 . . . . (17); 
^(^ 2 ) = sin - sin x e- tan x( 27r -x+^)= 0 .... (18). 
