134 PERIOD OF VIBRATION OF STEAM VESSELS. 



The general formula for motion involving space, time and acceleration is — 



J = y2ae (56) 



Substituting 5 for s and the value of t in formula (32), we find 



8 



TV 



S 



(57) 



Q 



This shows that the average accelerating force is — times the maximum 



accelerating force. 



For the vessel of Plates 56 and 57, the "load" is 2,100 tons, and the weight to 

 be raised or lowered is 15,700 tons. The accelerating force would be 2,100 

 tons if amplitude of vibration were such as to straighten out the deflection. 

 Taking t as .197 second, corresponding to 76 vibrations per minute, and a as 



gy. —, corresponding to an amplitude of vibration in each direction of one- 



15700" n^ 



tenth of the deflection, we find from formula (56) that .? =: .00678 foot. 



DISCUSSION. 



The Chairman : — Gentlemen, the paper is ready for your discussion now, and I trust 

 you will not be unduly frightened by the mathematical characters which you find liberally 

 sprinkled throughout the paper. The Chair will take advantage of his position to refrain 

 from further comment. v 



Mr. a. Schein, Visitor: — Mr. Gatewood speaks about the primitive method which 

 was introduced in measuring the vibrations on the tested steamer. That is why I wish to 

 mention the fact that Mr. Elmer A. Sperry has recently completed a pallograph for measur- 

 ing the vibrations of ships, for the use of the U. S. Navy engineers and also at the Model 

 Basin, at Washington, D. C. 



Briefly, the pallograph is an instrument which simultaneously records vertical and 

 horizontal transverse vibration. Of equal importance is the introduction of pencils for indi- 

 cating revolutions of the ship's shafts for each propeller separately, and prime mover, indi- 

 cating seconds. 



When the pallograph is in operation the pendulum appears to oscillate and vibrate rap- 

 idly, whereas in reality it is standing absolutely still, as the ballistics of the apparatus is so 

 adjusted as not to be in synchronism with the vibration of the ship. The apparatus, which 

 weighs hardly ninety pounds, can be placed in any part of the ship so as to detect the cause 

 and location of vibration. The pallograph could doubtless be procured either from the offi- 

 cers of the Navy or from Mr. Elmer A. Sperry. 



