CHAP. IV.] 



SUPPLEMENT TO CHAP. XIV. 



299 



For the values of the quantities A and B we have the following table : 

 VALUES OF A AND B. 



From the above tables it is easy to find the thrust for any given position of 

 load, and any given span and rise. The preceding table gives the reac- 

 tion ; it only remains to determine the moment M at crown. 



(c) Moment at crown. 



From VII. we have 



M = iHr/2 cos a \ -iPr^ illa ~ B]n * m 



\ sin a / sin a 



Substituting the value of H, already given, eq. (46), we obtain 

 2 M |(1 + K) a (a + sin a cos a) 2 sin 2 a~j 



= Pr j sin a sin a cos (a 13)+2 sin a (cos ft cos a) sin a (sin a sin ft) sin ft 

 a (cos ft cos a) (1 + K) {a (sin* a + sin 2 /3) 2)3 sin a sin /3} 



+ (1 + K) (a /3) (a + sin a cos a) sin ft I. 

 In similar manner, as before, for H we have 



Mo = Moo 



where M 00 is the value of M when terms containing Tc are disregarded, 

 and B has the same value as above. By series we have 



and 



+ ^(3a + 6a 3 /3+45a*^ l + 808a^ 8 +154 4 ) |, 



o= 86 



a*(3a 2 -10a-5/3 2 ) 



