224 APPENDIX. 



length of the stroke of the piston, add the length of the clearance, and call the sums the 

 increased distance and the increased stroke. Divide the increased stroke by the increased 

 distance, and the quotient will express the true relative expansion of the steam. With this 

 number take out the multiplier from the table, and multiply it into the increased stroke ; the 

 product will represent the entire effort of the steam. From this subtract the length of clear- 

 ance, and the remainder will be the actual effort. Lastly, multiply the actual effort by the 

 full pressure per square inch in the cylinder, and divide the product by the actual length of 

 stroke, and the result will be the mean pressure of the steam exercised upon each square inch 

 of the piston. 



The latter part of the rule may be more simply performed thus : having taken out the 

 multiplier, subtract it from 1-0000, multiply the remainder by the length of the clearance, and 

 divide the product by the true length of stroke. Subtract the quotient from the multiplier, 

 and the remainder will be the corrected multiplier, to be multiplied into the full pressure to 

 get the mean pressure. 



Example. Take the preceding example, and suppose the clearance of the cylinder to be one 

 inch at each end. 



Distance 16 inches Stroke 54 inches 



Clearance 1 Clearance 1 



17 55 



17) 55 (3-235, relative expansion 

 51 



40 

 34 



60 

 51 



90 



With 3-235 we find multiplier, from table, 0-6721. 

 1-0000 

 0-6721 0-6721 



0-3279 

 Clearance 1 



Stroke 54) -3279 (61 - - - Subtract 61 

 324 

 0-6660 



39 Pressure 50 tfes. 



Mean pressure 33-300 tbs. per square inch. 



The former rule, which supposes no clearance, gave 32-83. It hence appears that the addi- 

 tional -f^th'of the quantity of steam used only increases the mean pressure by 0*47, or about 

 \ Tb. on each square inch. 



