298 



SUPPLEMENT TO OHAP. XTV. 



[CHAP. iv. 



H = P. 



(S) Horizontal thrust. 



Eliminating M from HI. and YL we obtain, after reduction, 



2 sin a fooe /3 cos a + (1 + ) ft rin ft | (1 + c) a (sin* a + sin* ft) 

 8 [~(1 + ) a (a + Bin a oos o) 2 sin 2 a 1 



If we put Ai = 2 sin a (cos /3 cos a + /3 sin ) a (sin* a + sin* /3), 

 A = a (sin* a + sin* j8) 2 /3 sin a sin /9, 

 Bi = 2 a (a + sin a cos a) 4 sin* a, 

 B, = 2 a (a + sin a COS a), 



A B A 



and let A = -^, B = =*-, and H = =^ P, we have 



= H 



1-A* 



where H is the value of H from the above formula, when terms containing 

 K are disregarded. 

 Transforming by series, we have 



H = 



A= 



From the exact formula (46) above, we have the following tables : 

 TABLE FOB H . 



