Chapter XXVI: Section XI

_Of the Proportion of cold Water to be added to that
which is on the point of Boiling, in Order to obtain the
desired heat in the Extract._

The degree of heat, which causes water to boil is determined, by Farenheit’s scale, to 212. It is in our power to give to any part of the extracting water this degree of heat; and by adding to it a sufficient proportion of water of an equal heat with that of the air, and blending these two quantities with the grist, to bring the whole to the required temperature. The rules for obtaining this end are extremely simple, and cannot be unknown to those, who are skilled in arithmetical operations. But as our view is to render this part of our work generally useful, we think it will be proper briefly to lay down these rules, and to illustrate them by the examples of our two brewings.

_Rule to ascertain the heat of the first Mash._

Let _a_ express the degree of boiling water, _b_ the actual heat of the air, _c_ the required degree for the extract, _m_ the whole quantity of water to be used, _n_ the volume of the malt; _x_, that part of the water, which is to be made to boil, will be determined by the following equation.

----- -----
c - b × m + n

x = ----------------------

a - b

The quantity of water used, added (+) to the volume of the grist.

Their sum (_z_) multiplied (×) by the heat required, less (-) the heat of the air.

This produce divided (÷) by the heat of boiling water (212) less (-) the heat of the air will quote how much is to be made to boil or brought through (212) that is how high the copper is to be charged, the remainder of the length of the whole liquor for this mash, is the quantity to be cooled in.

The first example is that of a brewing of small beer, when the heat of the air is at 60, (see page 232.) The volume of the 6 quarters of malt was estimated at 3,42 barrels, (see page 268;) the first liquor is 14-1/2 barrels, (see page 247) and the heat required for the first mash 154 degrees, (see page 247.)

_First Mash._

_m_ = 14,50 Barrels of water

_n_ = 3,42 Volume of grist
------
_m_ + _n_ = 17,92 _c_ = 154 Heat of the first
mash,

94 _b_ = 60 Heat of the air,

---- ----

(_a_) heat of _c_ - _b_ = 94

boiling water, 212 7168

_b_ heat of the
air, 60 16128
---- ------
_a_ - _b_ = 152 )168448 (1108 barrels of water, to
152 be made to boil out of
---- the 14 + 1/2 barrels which
164 are allotted for the first
152 mash. The incidents to
---- be mentioned, are not
1248 considered in this calculation.
1216
----

The next example of a brewing is that of a grist of eleven quarters of malt for porter or brown beer; the medium heat of the air is forty degrees, the volume of the grist, 6,32 barrels, (see page 268) the first liquor to mash with sixteen barrels, (see page 245) and the heat expected in the mash, one hundred and fifty-seven and a half[29] degrees. (See page 245).

_First Mash of brown strong beer._

16,00 Barrels of water
6,32 Volume of malt
-----
157 Heat required in the
mash, vide page 247.
22,32
117 40 Heat of the air.
------ -----
Heat of boiling 15624 117
water, 212 2232 -----

Heat of air, 40 2232
----- -------
172 )261144 (15,18 barrels of water, to be
172 made to boil out of the
16 barrels.
-----
891
860
-----
314
1324
-----

Iwill 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. 3218,16 Number of degrees of heat in 14,66 barrels
of boiling water.

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

The heat required less (-) the heat of the goods, multiplied (×) by the volume of the goods.

Their sum (z) divided (÷) by the heat of boiling water, (212) less (-) the heat of the air.

Will quote the quantity to be made to boil, or to be brought through (212) the remainder part of the whole liquor for the mash is consequently the quantity to be cooled in.

We may now collect the circumstances of the two brewings, and find the quantity of boiling water, required for their second and subsequent mashes, exclusively of the incidents which will hereafter be mentioned.

The first mash for the six quarters of small beer, had 154 degrees of heat, but this and every mash loses, in the time the extract is parting from it, 4 degrees, which reduces the heat to 150 degrees. The volume of this grist, in its dry state, was 3,42 barrels, but now, by being expanded, and having imbibed much water, it occupies three times that space, or 10,26 barrels; the air is supposed to continue in the same state of 60 degrees of heat. The length and heat to be given to the three remaining mashes, are as follows. (See page 247.)

Degrees of heat, 154 166 170 174
Barrels of water, 14-1/2 14-1/2 11 11
Liquors, 1st 2d 3d 4th
╰━━━v━━━╯ ╰━━v━━╯
1 wort. 2 wort.

_Second Mash for Small Beer._

_c_ = 166 Heat required in the mash.
_d_ = 150 Heat of the goods.
----
_c_ - _d_ = 16

_n_ = 1026 Volume of the goods.
-----
96
32
160
------
_c_ - _d_ × _n_ = 16416
------
_c_ = 166 Heat required in the mash.
_b_ = 60 Heat of the air.
------
_c_ - _b_ = 106
_m_ = 1450 Barrels of water.
------
5300
424
106
--------
_c_ - _b_ × _m_ = 153700
_c_ - _d_ × _n_ = 16416
--------
_a_ - _b_ = 152)170116(11,19 Barrels of water to be made to
152 boil out of the quantity allotted
_a_ = 212 ----- for the second mash.
_b_ = 60 181
--- 152
152 -----
291
152
-----
1396
1368

_Third Mash._

170 Heat of mash. 170 Heat of 3rd mash.
60 Heat of air. 162 Heat of goods.
---- ----
110 8
1100 Barrels of water 1026 Volume of grist.
------ 3d mash. ----
11000 8208
110
------
121000
8208
-------
152)129208(8,50 Barrels to be made to boil out of the
1216 quantity of water allowed for the
------ third mash.
760
760
-----
8

_Fourth Mash._

174 Heat of 4th mash. 174 Heat of 4th mash.
60 Heat of air. 166 Heat of goods.
------ -----
114 8
11,00 Barrels of water 1026 Volume of goods.
------ for 4th mash. -----
11400 48
114 16
------ 80
125400 -------
8208 8208
------
152)133608(879 Barrels to be made to boil out of the
1216 quantity of water allowed for the
------ fourth mash.
1200
1064
-----
1368
1368
-----

The liquors of this brewing of common small beer, when the mean heat of the air is 60 degrees, must therefore be ordered in the following manner (the incidents hereafter to be noticed, excepted.)

1 Liqr. 2 Liqr. 3 Liqr. 4 Liqr.

Lengths of liquors, 14-1/2 14-1/2 11 11
------ ------ ------ ------
Boiling water; barrels, 11 11-1/2 8-1/2 8-3/4
Cold water; barrels, 3-1/2 3-1/4 2-1/2 2-1/4
------ ------ ------ ------
14-1/2 14-1/4 11 11
------ ------ ------ ------

The heat of the first mash for the 11 quarters of brown beer, was 157 degrees, (see page 245) and after the parting of the extract from it, 153; the volume of the grist, in its dry state, was valued at 6,32 barrels of water, (see page 268) but, for the reasons before mentioned, it now occupies three times that space, or 18,96 barrels. The air is supposed to continue at 40 degrees, and the length and heat to be given to the different mashes, were determined as follows: (see page 245.)

Degree of heat, 157 158 162 164 165
Barrels of water, 16 8 12 9 9
Liquors; 1st 2d 3d 4th 5th
╰━━v━━╯ ╰━v━╯ ╰━━━v━━━╯
1 wort. 2 wort. 3 wort.

_Second Mash of Porter, or brown strong._

212 Boiling water.
40 Heat of air.
---
172

158 Heat of 2nd mash.
153 Heat of the grist or goods.
----
5
1896 Volume of goods
----
158 Heat of 2nd mash 30
40 Heat of air 45
---- 40
118 5
8,00 Barrels of ------
------ water. 9480
94400
9480
------
172)103880(6,03 Barrels of water to be made to boil for
1032 the second mash.
------
680
516
----

_Third Mash._

212 Heat of boiling water.
40 Heat of air.
----
172
162 Heat of 3rd mash.
154 Heat of goods.
------
162 Heat of 3rd mash. 8
40 Heat of air. 18,96
---- ------
122 48
12,00 Bar. of water. 72
------- 64
146400 8
15168 ------
---------- 15168
172)161568(9,45 Barrels of water to be made to boil for
1548 third mash.
------
776
688
------
888
860
------

_Fourth Mash._

164 Heat of 4th mash.
158 Heat of goods.
-----
6
18,96 Volume of grist wetted.
164 Heat of 4th mash. -----
40 Heat of air. 36
------ 54
124 48
9,00 Bars. of water. 6
------- -------
111600 11376
11376 -------
-------
172)122976(7,14 Barrels of water to be made to boil for
1204 the fourth mash.
------
257
172
------
856
688
------
168

_Fifth Mash._

165 Heat of 5th Mash.
160 Heat of Goods.
----
5
18,96
165 Heat of 5th mash. -----
40 Heat of air. 30
---- 45
125 40
9,00 Barrels of water. 5
------- ------
114500 9480
9480
-------
172)123980(7,20 Barrels of water to be made to boil for
1204 the 5th mash.
------
358
344
------
140

The liquors of this brewing of brown beer must therefore be ordered in the following manner:

Barrels of boiling water, 15-1/4 6 9-1/2 7 7
Barrels of cold water, 3/4 2 2-1/2 2 2
------ ---- -------- ---- ----
16 8 12 9 9
Liquors, 1st. 2nd. 3rd. 4th. 5th.

What in the brewery is generally called cooling in, must be settled for this brewing according to the number of barrels of cold water specified as above, the incidents hereafter to be noticed excepted.

Each of these calculations may be proved in the same manner as was done before. This method of discovering the proportion of water to be cooled in, deserves, on account of its plainness and utility, to be preferred to any other, which depend only upon the uncertain determination of our senses.