Manchester Memoirs, Vol. xlvii. (^igoT^), No. lij. 13 



The corresponding velocities when the stress becomes 

 infinite are 



V 2vk' 



or period =L^^'^'^^ 



_ _^- • (15) 



v = -J^, or period = ^Z^Aiii'. 

 2 V tvk- V CIg 



The latter period =time of vibration of a free free rod. 



The former period = time of vibration of a free free rod 



of half the lensrth.* 



Appendix III. 



Dimensions of a typical destroyer kindly furnished by 

 Philip Watts, Esq., Director of Naval Construction. 



W=4gy tons, d^y ft. ^ = 224 ft. 7=305 foot 

 units, Maximum breadth ^ 20 ft. 6". 6=11-5 ft. E = 



10,000 tons D". /s-=9-02 tons D". — at 60 miles per 



hour (relative velocity) = ri i. Maximum dynamical stress 

 at centre = 9-32 tons D". Increase of stress = 3^. 

 Stress due to tzvisting when = 45°. 



nL 



— = 4j° /= 100 foot units. (7-= loMbs. per D". 



Stress due to twisting = 0'04 tons per D". 



Stress due to bending = 95 % of stress when 6 = 0. 



.'. Total stress is less. 



* Rayleigh's Sound, p. 247, Vol. I. 



