450 Proceedings of the Royal Society of Edinburgh. [Sess. 
Further, 
Inside range _ tanh ^/xT j * _ 
Outside range ^/xT 
In the particular case where T = 30 min ‘ and /x = 1/3000, ^/xT = *15; and we 
find 
Inside range = >9925 . 
Outside range 
so that the damping is very slight. For T = 2 h the corresponding ratio 
is *8951. 
Case 7. Lastly, let us take the case where the graph of tct — tet 0 is an 
isosceles trapezium, ODEC in fig. 8. This may be supposed to represent 
the effect of the passage of a rain-cloud heavily charged with water 
vapour. By making EC nearly vertical we might represent the effect of 
a sudden release of pressure by condensation, resulting in a shower. 
If the times between 0 and D, D and E, and E and C be T, U, T re- 
spectively, we may represent the atmospheric pressure by 
5*1 = ST 0 + 7 t for T ; 
^2 = c:r o + y T .. T«T + U; 
£7 3 = S7 0 + 7 T-yC-T-U) „ T + U«2T + U; 
= „ 2T + U«oo . 
* See my Algebra , ii., ch. xxix., § 29. 
