An ANAI.YSIS OF TKSTS OF WATER-TIGHT BUlvKHE^ADS. 107 



A/.=£[i-'i] (.6) 



wLto 2/3J 



^A = i/'/. (17) 



The value of T here used is denoted above as Tq and determined by 

 equation (4). The value of Mx is as given in last year's paper, page 427. 



2. STIPPENER AB FIXED VERTICAIvIyY AT BOTH ENDS AND I^OADED BY A COM- 

 BINED UNIFORM AND INCREASING I.OAD. 



p = w (h + x). 



Referring to last year's paper, Appendix II, page 431, we cannot here 

 retain the exponential terms without obtaining very cumbrous expressions, 

 but in order to obtain greater accuracy than was the case in last year's 

 paper, the expansion of the exponential terms has been carried to the sixth 

 power. In fact, it has been found that expansion to the fourth power is 

 not, as stated in last year's paper, always sufficient. We then obtain the 

 following expressions :— 



,(MaT^ a x^T , _, 



TV 

 Let —Ej = k> 



12EI 



12 V 5+4^ / 



"^ 12 V 5 + 4^ * 



D id loh + 2,1 + kl + Shk , V 



Pa = ^^- — (21) 



4 5 + 4^ 



