182 Mr. W. J. M. Rankine on the Mechanical Action of Heat. 



and K the con-esponding difference in the seventh column ; then 

 by the proportion 



H : K : : A : ^, 



either Y — k may be found from X + h, or X + A from Y — k. 



In the fifth aud eighth columns respectively are given the 

 actual pressures! and volumes corresponding to the logarithms in 

 the third aud sixth columns, to five places of figures. 



In the ninth column are given the values of the quantity 

 denoted by PjV, in the formula?, which represents the mechanical 

 action of unity of weight of steam at full pressure, or before it 

 has begun to expand, in raising an equal weight. Those values 

 are expressed in feet, being the products of the pressures in the 

 fifth column by the volumes in the eighth, and have been found 

 by multiplying the absolute temperatm-e in Centigrade degrees 

 by 153'48 feet. Intermediate terms in this column, for a given 

 pressure or a given volume, may be approximated to by the 

 method of differences, the constant difference for 5° Centigrade 

 being 767 '4 feet ; but it is more acciu'ate to calculate them by 

 taking the product of the pressure and volume. 



When the pressure is given in other denominations, the fol- 

 lowing logarithms are to be added to its logarithm, in order to 

 reduce it to pounds avoirdupois per square foot : — 



For millimetres of mercmy 0"44477 



For inches of mercmy 1 "84960 



For atmospheres of 760 millimetres . . . 3'32559 



For atmospheres of 30 inches 3"32673 



• For kilogrammes on the square centimetre . . 3"31136 

 For kilogrammes on the circular centimetre . 3'41627 

 For kilogrammes on the square metre . . . 1'31136 

 For pounds avoirdupois on the square inch . 2' 15 836 

 For pounds avoirdupois on the circular inch . 2'26327 

 To reduce the logarithm of the number of cubic metres occu- 

 pied by one kilogramme to that of the number of cubic feet 

 occupied by one pound avoirdupois, add 1 "20463. 



The logarithms are given to five places of decimals only, as a 

 greater degree of precision is not attainable in calculations of 

 this kind. 



(33.) The second table is for the purpose of calculating the 

 mechanical action of steam in expansive engines. 



The first column contains values of the fraction of the entire 

 capacity of the cylinder which is filled with steam before the 



expansion commences (being the quantity - of the fomiulse), for 



every hundi'edth part, from I'OO, or the whole cylinder, down 

 to O'lO, or one-tenth. 



