ON A CONSTANT INDICATOR FOR STEAM-ENGINES. 



317 



u,= 



Rm p 



U, - U. = 



(T r- \ sin < 



R 7)1 p 





. (N,- NO- -^(l -?+-") L. 



(T r- X sin i 

 Now N, — No represents the residual number N actually registered by the 

 indicator, and U, — U., represents the whole work U done by the engine 

 upon each square inch of the piston in favour of the load : 



,.U = ^i^^N - (±±i)ZL (3.) 



or- Asm* nitr- 



The Springs. 



Four sets of springs were constructed of the forms and dimensions repre- 

 sented in the accompanying figures. The thickness of each spring, in decimal 

 parts of an inch, at different distances from its extremities, is shown by the 

 numbers upon the corresponding figure. 



No. 1. 



No. 2. 



No. 3. 



No. 4. 



I 



r-Fnsj— 



3 



•Eyi- 



-•201 



■•284 

 -•348 



.•402 

 -•450 



J^ 



-IS- 



L^M 



±-. 



m.^ 



— Ft^ 



•147 



•208 



-•255 



-•275 



294 



312 



V -329 



- -122 



■-.•173 



•245 

 ■309 



-«- 



-^ 



T^ 



-» 



-.•194 

 ■r ^282 

 -,•345 

 ,•398 



- -445 

 488 



X. 



The following tables contain the results of experiments made, witli great 

 care, by Mr. Timme to determine the law of deflection in the springs con- 

 structed for the Committee, and the particular value of the constant A in re- 

 spect to each. 



