2. Enter these values of t.. in (8) to compute Y/T against Z 1 by graphical 

 or numerical integration. Thus we obtain values of Y/T against t.. 



3. Obtain values of t 3 against Y/T from (10) and (12), in a similar way. 



4. Taking values of t.. and t a corresponding to the same Y/T , T.. can be 

 computed from (14) and T a from (13). 



Thus the problem as stated above is formally solved. Yet it is easily seen 

 that the equations (6), (8), (10) and (12), involving as they do the two independent 

 parameters f and p, do not readily lend themselves to the calculation of a general, 

 dimensionless set of solutions for T.. and T 2 . It will be shown in Appendix IV that 

 a close approximation is obtained by replacing equations (6), (8), (10), and (12) 

 by the following one-parameter set of equations: 



log t. = - c tan - z 1 (6a) 



z 1 



y r J iVi* < 8a > 







1 + z, 



log t, = ■£■ log tj^-g . . . (10a) 



= j ^|r (12a) 



z a 



v 



o 



where c = 2f/p and z^ = pZ 1 , z, = pZ 2 , y = ^ Y. 



Forms more convenient for calculation are obtained by introducing the sub- 

 stitutions 



u = tan" z i and v = i log •] ^* . Then z 1 - tan u and z a = tanh v, 



1 1 "~ Za 1 



and the above equations become 



t 1 = e-° n (6b) 



u 

 y = [ e -011 tan u du (8b) 



o 



t a = e cv (10b) 



v 



I 







y = J e cv tanh v dv (12b) 



Tables 1 and 2 for computing y are based upon equations (8b) and (12b) 

 respectively. For, expanding e into a power series, (8b) becomes 



