I will give one proof of the certainty of this rule, by setting down the state of this first mash from it.

15,18
212
———
3036
1518
3036
———
A.3218,16Number of degrees of heat in 14,66 barrels of boiling water.
16,00Barrels of water to first mash.
15,18Barrels made to boil.
———
,82Barrel to cool in.
40Heat of cold water.
40Heat of cold water.
B.32,80Number of degrees of heat in 1,34 barrels of cold water.
15,18Boiling water.
,82Cold water.
6,32Volume of grist.
———
C.22,32Barrels, volume of the whole mash.
6,32Barrels, volume of the 11 quarters of malt.
,40Heat of the grist.
———
252,80Number of degrees of heat in the grist.
32,80B.
3218,16A.
———
C.22,32 )350376(157 degrees of heat required in thefirst mash, as above.
2232
———
12717
11160
———
15576
15624
———

So long as the mixture consists only of two quantities of different heat, as is always the case of the first mash, the preceding solution takes place. But in the second and other mashes, where three bodies are concerned, each of different heat, viz. the boiling water, the cold water, and the mash, are to be mixed, and brought to a determinate degree, the rule must be different; yet, like the former, it is the same with what is used in similar cases of allaying, when different metals are to be melted down into a compound of a certain standard, or different ingredients of different value to be blended, in order to make a mixture of a determinate price. What the different density of the metals, or the different value of the ingredients are, in these cases, the different degrees of heat of the boiling water, the grist, and the air, are in this.

Rule to ascertain the heat of the second mash, and of the subsequent ones.

Let the same letters stand for the things they signified before, and d express the actual heat of the grist, then will

—— ——
x =c — b × m +c — d × n
——————————
a — b

or in plain terms, the heat required less (-) the heat of the air, multiplied (×) by the quantity of water used.