
MECHANICAL ACTION OF HEAT. 187 
The sixth column contains the common logarithms of the volume of one 
pound of steam of saturation corresponding to the same temperatures. 
The seventh column contains the differences of the successive terms of the 
sixth column, which are negative; for the volumes diminish as the pressures 
increase. 
By the ordinary method of taking proportional parts of the differences, the 
logarithms of the volumes corresponding to intermediate pressures, or the loga- 
rithms of the pressures corresponding to intermediate volumes, can be calculated 
with great precision. Thus, let X+/ be the logarithm of a pressure not found in 
the table, X being the next less logarithm which js found in the table; let Y be 
the logarithm of the volume corresponding to X, and Y—é the logarithm of the 
volume corresponding to X+h; let H be the difference between X and the next 
greater logarithm in the table, as given in the fourth column, and K the corre- 
sponding difference in the seventh column; then by the proportion 
18) le BAe: 
either Y—/ may be found from X+h, or X+h from Y—A. 
In the fifth and eighth columns respectively, are given the actual pressures 
and volumes corresponding to the logarithms in the third and sixth columns, to 
five places of figures. 
In the ninth column are given the values of the quantity denoted by P, V, 
in the formule, 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 multi- 
plying the absolute temperature in centigrade degrees by 153-48 feet. Interme- 
diate terms in this column, for a given pressure or a given volume, may be approxi- 
mated to by the method of differences, the constant difference for 5° centigrade 
being 767-4 feet ;, but it is more accurate to calculate them by taking the product 
of the pressure and volume. 
When the pressure is given in other denominations, the following logarithms 
are to be added to its logarithm, in order to reduce it to pounds avoirdupois per 
square foot :— 
For Millimétres of mercury, : : : : : : 6 0:44477 
Inches of mercury, : 3 ; F : ‘ 3 : 1:84960 
Atmospheres of 760 millimétres, . - : : : . 3°32559 
Atmospheres of 30 inches, . ; F : : 4 : 3°32672 
Kilogrammes on the square centimétre, ; - : : 3°31136 
Kilogrammes on the circular centimétre, ; : : 3°41627 
Kilogrammes on the square métre, ; 3 : ‘ ¢ 1-31186 
Pounds avoirdupois on the square inch, ‘ : : : 2-15836 
Pounds avoirdupois on the circular inch, ; : A , 2:26327 
VOL. XX. PART I. 3D 
