356 MISCELLANEOUS STUDIES 



(\n \ 

 H- - ) added, x is the distance north or south from the latitude 

 bz ' 



chosen for reference, z is the distance from the same point measured 

 in the direction of flow, making an angle \f/ with the x direction ; there- 

 fore x equals nz where ^ is measured from the positive (north) direc- 

 tion of x, and n equals cos ^. Making this substitution in equation 

 (46) gives 



l23l 

 oi oz 



(47) 

 Solution for the case in which the flow is constant. 



To solve equation (47) let 



e = & -f e" + o"' 



where 0' is the solution already found (equation 22, p. 344) correspond- 

 ing to H Q, 0" a function of y and t only is to be determined, and 

 ff" is a general solution of the part left after substituting (ff + #") 

 Substituting the value 6' + 6" + 6'" for 6 in equation (47) we have 



A/J/ A/)" A/J'" 



+- - +TI = B[(a l + a 2 nz) cos at -f a 3 nz + 1] e~ 

 ot ot ot 



(48) 



dz dz dz 



From the definitions of 6 1 , 0" and 0'" this equation reduces to 



~dT" + dtf~ ~dz~ ~dz~ 



which can be broken up into two equations 



and 



_ i_ Tfff" I JJ Q (51 \ 



From equation (22) which gives the value of ff we have 

 off Ba,n . Ba.,nr 



oz k'^/- ' - -- - 



sin at)] (52) 



