370 Mr Tredgold on the Principles of BromCs Gas Machine. 
■R f 1 V 1 w 0.00035 iO’ ^ .r - 
hut, by our preceding calculation — — =t]ie quails 
tity of gas that will heat the volume x of air ; whence, 
1 4700 V 90 V O OOO.^.f? i ^ 
— the cubic feet of gas that will pro- 
( 1 
500 \ 
V 
450 4- ^ / 
duce the same power as a bushel of coals. This equation 
re- 
duces to 
k459j5^^(450-f 0 
k; (^ — 50) - 
But there is obviously a value of f which gives a maximum 
effect, or rather a minimum consumption of gas ; therefore, con- 
sidering t variable and making the fluxion of this expression 
equal to zero, we And t — 208 degrees. If this value of t be in- 
serted, the expression becomes -^^^^^^ — the cubic feet of gas 
^that will produce the same effect as a bushel of coals. 
If pure olefiant gas be used, we have, from Mr Dalton’s ex- 
periments ^’=; 35.7 grains; and, according to Dr Thomson’s 
tablet, zv = 513.3 grains ; hence, — ^ — ^TO cubic feet of 
gas ; from whence we may conclude that 270 feet of the best 
oil-gas at the expence of somewhat more than 10s., at the Edin- 
burgh price, will be required to do the same work as may be 
done by one bushel of Newcastle coals. 
For carburetted hydrogen gas, g=z36G5 grains, and w—2dlA 
3862 X ^ 
grains from the same authorities; consequently, ^ — ^ = 482 
cubic feet ; and, suppose coal-gas capable of producing the same 
effect, then at the Edinburgh price, 482 feet of coal-gas will 
cost 5s. 9d., and produce no more power than a bushel of New- 
castle coals. 
I have made the comparison with the effect produced by a 
bushel of coals, because that quantity is about equivalent to the 
day’s work of a horse ; that is, a bushel of Newcastle coals per 
day is a sufficient quantity for each horse-power of a steam-en- 
gine, and the engine day's work is ten hours, while a horse 
works only eight hours. 
* Dr Thomson'' 8 System of Chemistry ^ vol. i. p. 148. 5th edition, 
f Idem., vol. iii. p. 25. 
