426 PROFESSOR W. THOMSON ON THE REDUCTION OF 
bably none approaching to their accuracy. The slightly different numbers to which 
we have been led by the preceding investigation are no doubt still more accurate. 
40. To reduce these results to any other scale of linear measurement, we must 
clearly alter them in the inverse ratio of the square of the absolute lengths chosen 
for the units.* The length of a French foot being 1:06575 of the British standard 
foot, we must therefore multiply the preceding numbers by 1:13581, to reduce 
them to convenient terms. 
41. We may, lastly, express them in terms of the most common unit, which 
is the quantity of heat required to raise the temperature of a grain of water by 1°; 
and to do this we have only to multiply each of them by 7000 x 62°447, being the 
weight of a cubic foot in grains. 
42. The following table contains a summary of our results as to conductivity 
expressed in several different ways, one or other of which will generally be found 
convenient :— 
TABLE XIT.—THERMAL CoNDUCTIVITIES OF EDINBURGH STRATA, IN BRITISH ABSOLUTE UNITS 
[Unit oF LENGTH, THE ENGLIsH Foor]. 

Conductivities in Terms of be. see batt Conductivities in 
Description Thermal Capacity of Unit Bulk oe Sie: nS as Terms of Ther- 
of Terrestrial of Substance oP Wee Pe mal Capacity of 
Substance. ( k (k) One Grain of 
=) ; Water. 
Per Ann. | Per 24+. Per Second. | Per Ann.} Per 24,. | Per Second. Per Second. 
Trap-rock of f : . 
Galion (Eni } 267°0 | -7310 | -000008461 | 141:1 | -3863 | -000004471 1:9544 
Sand of Ex- 
perimental 295:9 | -8100 | -000009875 88-9 | :2435 | -000002818 1-2319 
Garden, 
Sandstone of 
Craigleith 7845 |2-1478 | -00002486 362°7 | :9929 | -00001149 5:0225 
Quarry, 


43. The statements (§§ 36 and 37) by which the signification of ~ has been 
defined and illustrated, require only to have cubic feet of water substituted for 
* Because the absolute amount of heat flowing through the plate across equal areas will be 
inversely as the thickness of the plate ; and the effect of equal quantities of heat in raising the tem- 
perature of equal areas of the water will be inversely as the depth of the water. The same thing may 
be perhaps more easily seen by referring to the elementary definition of thermal conductivity (foot- 
note to § 11, above). The absolute quantity of heat conducted across unit area of a plate of unit 
thickness, with its two sides maintained at temperatures differing by always the same amount, will be 
directly as the areas, and inversely as the thickness, and therefore simply as the absolute length 
chosen for unity, But the thermal unit in which these quantities are measured, being the capacity of 
a unit bulk of water, is directly as the cube of the unit length, and therefore the numbers expressing 
the quantities of heat compared will be inversely as the cubes of the lengths chosen for unity, and 
eee as these simple lengths: that is to say, finally, they will be inversely as the squares of these 
engths. 

