On Diurnal Variation of Barometric Pressure. 



21 



consider the case where the land and water are represented by 

 semi-infinite planes, the coast hne being represented b}^ the 2/-axis. 

 In this case, it will not be far from truth, if we assume 



= «1 ± a„ tanh a{x ^ Xq) 



(20) 



where the upper or the lower sign is to be taken according as the 

 water lies on the east or west side of the ^/-axis. We have then 



— -— = ± ao.^ sech^ a{x '^ x^^, 

 ax 



â?a 



dx 



- = q: 2 a,- «2 tanh a (x q= x^ secb^ a (a? =F x^. 



Hence, 



ai oc «1^ ± 2«! «2 ta-iih a{x + x^) [1 + 2 a^ sech^ a{x '^ a-o)] ' 

 + o..i tanh^ a{x + a?«) [1 + 2 a' sech^ a{x T Xo)Y 

 + ia?a.^ sech^ a{x T Xq), 



(b = tan-' ~ «i + «2 tanh a{x ^x^ {l + 2a^ sech^ a {x^^x^} 

 ' ± 2aa2 sech^ a{x^ Xq) 



(21) 



+ ^ + t:. 



In order to get some idea of the magnitudes of the constants «i, a^, a 

 and Xo, the data for some South African stations given by J. R. 

 Sutton were utilized, according to which we obtain 



for a; = , a = 4°C., 



X = 117 km., a = TC, 

 X = 420 km., a = 8°C., 



Let us assume also a = 8° for a;=oo and a = r for a;=— c»; 

 then we may put approximately 



«J = 4°. 5 , «2 ^= 3.°5, 



a = 0.00855 1/km. or 54300 cos <p radian"', 



26.5 X 10-^ 



Xn = 16.9 km. 



or 



cos ^ 



radian of longitude. 



1) J. R. Sutton, Trans. South African Phil. Soc, 11, 1902 ; Met. Zs., 1904, p. 40. 



