56 



Hence in order to calculate T for a definite value of g, for the 

 case /; ^ '2, q=z 2, we can make use of the equations (37) and 

 (38). The thus obtained value is found in column 3 of table 3. 



§ 15. If we put /9 = 3, q = 'd, (22) and (23) change into: 



g = {\-e-^^^Y (39) 



7'= 7, \(\-e-^kt^^ .^ {i^e-^kiy j^ i _ g-3i-£| . . (40) 

 from which : 



^=Va.|^ + //3 + ^V3| (4i; 



In column 5 of table 3 are found the values of 100 7" calculated 

 by the aid of this equation. The curve E of fig. 2 represents the 

 corresponding values of 100 T and 100^ for this case graphically'. 

 It touches the boundary line B at g =1 T=0. 



With a deviation < 0,3"/o equation (41) holds also for the case 

 p=rl, gr =: 23. This will be more fully discussed in § 21. 



§ 16. For p^=\, 5' = 00 (22) and (23) change into: 



g=z\ -\- 2 g-3^< — 3 e--^ki (42) 



7'=1 + g-3^-' — 2e-2^', (43) 



from which 



{\ + g-2Ty = {\ i-2y - ^Tf (44) 



If T is solved from this, we find : 



T = V, |1 + 4^^ + 2 l/^Hf^ . cos (120° - V, ff% 



(45) 



in which 



85,^ + 205^-1 



cos (f = ■ 



l/(H-8.^)' 



The values of 100 7" calculated from this are found in column 6 

 of table 3. 



§ J 7. If we put i) = S, ^ = 00, (22) and (23) become: 



^ = 1 — 2 e-^^' + e-e'^-' (46) 



T = 1 - 7, e-3A:^ + 7, e-^kt (47) 



from which : 



T=^/,{2g^~[/g) (48) 



In column 7 of table 3 are found the values of 100 T calculated 

 from this. The curve F of fig. 2 represents the corresponding values 

 of 100 T and 100^ for this case graphically. It touches the boundary 

 line B at g= T=0. Equation (48) will be more fully discussed 

 in § 20. 



