ENGINEERING STRUCTURES 

 F 



145 



indicator spring, so that -^ would be the displacement of the 



piston under a steady force F. 



The equation of motion now becomes 



9 



where ' x ' is the displacement of the piston at time ' t ' seconds 

 after the first application of the force F, and the solution of 

 this is 



This shows, that if the time ' t,' during which the force F is 

 applied, is very short, the recorded pressure is less than the true 



pressure at the indicator in the ratio 1 cos\/?= . t, where t= 



I JST 

 4Z -r V p seconds. The value of the term \J gr-= can be obtained, 



experimentally, since the frequency of the natural vibration 



1 / IS 



of the indicator is equal to TJ-V w - Values of 'n' were 



ZTT W 



obtained by mounting the indicator on the cylinder of a gas 

 engine, taking a diagram, and counting the number of oscilla- 

 tions traced out during a definite portion of a revolution. 

 The results of these observations were very consistent and 

 gave the following results : 



The validity of this reasoning was checked by a series of 

 experiments on the pipe line modified as shown by the dotted 



