(3) BREWERY GAUGING.-The mash-tun is the only vessel at a brewery in which it is requisite to take gauges for revenue purposes. When the quantity of grains, as ascertained by gauge, exceeds by 20 per cent., the quantity of malt entered on the brewer's entry paper, the case is to be stated to the Board.

Mash-tuns are generally of the form of a cylinder or a frustum of a cone standing on its greater end; but, occasionally rectangular, elliptical, and other shaped tuns are met with in practice. Whatever be the figure of the utensil, its capacity, at different sections of its depth, is now calculated by the uniform method of taking a number of equi-distant diameters or other dimensions from the bottom upwards, multiplying together the area and depth of each frustum, and making a total of the results.

Example. Let A B C D represent a conical mash-tun, the perpendicular depth of which (a o) is 42.5 inches; and suppose the following cross-diameters* taken in the middle of every 10 inches from the bottom:

At a a, 5 inches from the bottom 49.6 by 50.4

Galls.

50, mean diam. at a a, Area of lowest frustum 7.0814.

bb, do. next higher

7.8967.

c c, do.

8.8829.

(49.650.4) ÷ 2 = (52.653-0) ÷ 2 = 52.8 (55.856.2) ÷ 2 = 56-0 (59.760-3) ÷ 2 = 60.0 The areas in gallons are derived, with the least trouble, from the standard Table of Areas of Circles.

To find the quantity of goods contained in this mash-tun at any assigned depth, say 26.7 inches. For every multiple of 10 inches in the given depth, multiply the proper area by 10, and for the inches above the last multiple of 10, take a proportional part of the content of the corresponding frustum, and add the results together. Thus,

Depth. Galls.

Area of lowest frustum x 10 = 70.814 content of lowest frustum.

Neglecting the decimals of a gallon, the result may now be reduced to qrs., bus., and galls.

That is, diameters measured at right-angles to each other between points horizontally opposite on the sides of the vessel. Any slight variation there may be from the true outline of a circle is sufficiently compensated by this system of taking the mean of each pair of cross-diameters.

This mode of ascertaining the partial or total contents of brewers' mash-tuns gives incorrect results when applied to a vessel having the form of a frustum of a cone, as in the case above supposed. The proper way would be to take diameters at the top and bottom respectively of each successive section of 10 inches deep, instead of in the middle of each section, and to augment the area answering to the mean of these diameters by one-twelfth of the area answering to their difference. A series of areas would thus be obtained the same as by the theoretical process laid down on page 212. But as the quantity contained in the frustum answering to any odd inches in the depth-those above an even multiple of 10-could not be determined accurately by this method without measuring the diameter at the surface of the grains on each occasion, and making a special calculation for that part of the vessel, or preparing a table of the content of the mash-tun at every inch and tenth of its depth; and as extreme exactness is not required when the amount of a gauge must be subjected to a large and variable deduction before it can properly be applied as a test of the traders' honesty, the uniform system of taking dimensions in the middle of certain specified depths, and thus treating each frustum as though it had an equal capacity throughout its extent, is perhaps the best practical expedient that can be adopted.

In finding the depth of the grains in a brewer's mash-tun, an average of several dips should be formed as in other cases."

Circular tuns are gauged in precisely the same manner as those of a conical shape; but where the sides of a vessel are nearly upright, it is evident that the contents of the several sections admit of being found with much greater correctness from the areas of their intermediate diameters than where the sides incline outwards or inwards.

For rectangular tuns mean lengths and breadths should be measured at the appointed distances apart; and as respects elliptical tuns, the process is to ascertain the requisite number of transverse and conjugate diameters.

The rectangular areas may be cast by any of the methods pointed out under the head of "Malt Gauging." Elliptical areas are arrived at by multiplying together the transverse and conjugate diameters, and using the circular divisor or factor for gallons (pp. 253, 254). See also an example at the end of the Table of Semi-squares, in which the Table of the Areas of Circles is shown to be applicable to this purpose. It is necessary to divide the final result by 2, as the values in the table last-mentioned represent whole squares instead of half-squares. The principle of the operation will be evident from what has been stated respecting the construction of these tables, on page 251.

In "fixing" brewers' mash-tuns it is the practice of most officers-no directions being given on the subject-to treat any odd section above that corresponding to the last multiple of 10 inches from the bottom, as having the same area as that of the next lower section. Thus, if the area of the highest 10 inches were 8.75 gallons, and there happened to be an excess of 4-6 inches in the depth over the last multiple of 10, the entire section possessing the depth of 14.6 inches would be referred to the area of 8.75 gallons. As the surface of the grains is generally several inches below the level of the top of the vessel it is not thought necessary to obtain a separate area for the odd section.

It should be observed that the column titled "Depth," in the Dimension and Survey Book, is not meant to contain the successive distances of the points of measurement from the bottom of the tun, as 5, 15, 25 inches, &c., but the depth of the section to which each diameter applies, so that the sum of the depths of the several frustums shall represent the total depth of the vessel.

A depth of 24.8 inches, for example, should be divided and entered as follows:

4.8 10

10

Total depth 24-8

• When the malt used is of good quality and finely crushed, the bulk of the grains, if the liquor be all drained off, will, in general, fall short of the quantity of malt mashed. Under opposite conditions, the amount of the mash-tun gauges may be expected to exceed, either slightly, or sometimes by as much as 10 or 15 per cent., the entry of malt brewed. The high temperature of the grains immediately after draining, and the natural compression produced in deep masses of such closely adherent particles are, of course, to be regarded as modifying circumstances.

GAUGING OF VESSELS USED BY DISTILLERS.

260(c)

Incumbrances. In the centre of the larger class of mash-tuns there is usually a vertical shaft, or set of shafts, carrying two or more horizontal arms or spindles each, such arm extending across the diameter of the vessel. Attached to these spindles, and at right angles to them are the "mashing rakes," which consist of circular iron rods of equal diameter, placed about 3 inches apart, and each about 20 inches in length. To allow for the space taken up by these incumbrances, it is only necessary to deduct the area of the shaft from that of each of the sections into which the vessel is divided, and the areas of the horizontal arms, and the sum of the areas of the mashing rakes, from the areas of the several sections affected thereby.

Example. Suppose an upright circular shaft, mean diameter 5 inches, one rectangular arm 120 inches long, cross sections 2 inches square, fixed at a depth of 11 inches from the bottom, and 300 circular rods, each 20 inches long, and half-an-inch in diameter, 2 inches of the length being included in the arm.

480 cubic inches =

Thus we have-Shaft 5 inches diam. Area 0708 galls. (Table of Circular Areas). Arm 2 inches square by 120 inches long 1-7311 galls. 1-7311÷ 10 (depth of section):

=

1731 galls.

Galls. Area.

Galls.

Rods, diam. of each 0.5 inch. = 0007, X 300 = 2100, total area. Then, from the area of the lowest section (10 inches deep) subtract 0708 (area of shaft) + 2100 (area of rods) =2808 galls.

=

From area of second section subtract 0708 (area of shaft as before) +1731 (area of arm) +2100 (area of rods) 4539 galls. The remaining sections may be supposed to be clear of any incumbrance but that of the shaft, the area of which is all that has to be deducted..

Although this method of treating incumbrances will not always be strictly correct, since in the present and many other instances, one or more sections of a mash-tun are affected only through a portion of their depth, yet there does not appear to be any better practical way of making the allowances, without measuring the points reached by the extremities of each separate incumbrance, and setting forth a greater number of areas than is consistent with despatch of calculation or required by the Instructions. Officers are not enjoined to tabulate mash-tuns, but where there are extensive brewers under survey, it tends both to convenience and accuracy to have tables raised, showing the net content of each tun in quarters, bushels, and gallons, at every inch and tenth of an inch of its depth. (4) GAUGING OF VESSELS USED BY DISTILLERS, RECTIFIERS, SPIRIT Dealers, &c.

Distillery Vessels.—Minute directions respecting the proper mode of gauging and tabulating distillers' utensils of the kind usually erected, being given in the Distillery Instructions, and the principles of the system of equi-distant ordinates having been fully explained at page 197 of the present work, it is unnecessary to add on this subject any but the following brief practical observations.

As the operation of finding the centre of an elliptical surface, and drawing the diameters by the rule laid down in the official books is somewhat tedious, and as the longer and shorter axes will frequently not intersect at the central point of a figure which deviates in any considerable degree from the form of a true ellipse, many persons prefer to ascertain the dimensions corresponding to I J and K L (see fig. on p. 60 of Dis. Instr.) by simply applying the gauging rods at some point, such as I, and obtaining, by repeated trials, the greatest diameter, IJ, which is then struck with a chalked line. In the same manner may be determined the diameter K L, which is the longest that can be measured within the vessel, perpendicular to I J.

As a vessel is often narrower at the top than the bottom, the distance at which the two extreme ordinates of the first horizontal section are taken from each other, should be rather less than the length of the transverse diameter at the top, in order that all the dimensions of the uppermost section may fall within the vessel. Hence the reason of the injunction in the 4th paragraph, page 61 of the Instructions.

It is to be observed that when a cylindrical vessel is placed in an inclined position, all the sections that are taken parallel to the horizontal surface of the liquor required to cover the bottom, will have the form of ellipses: but as the difference of the diameters will always be of small amount, the sections may be reduced practically to circles by employing half the sum of the cross-diameters as a mean-diameter.

The depth of liquor in the "drip" of a vessel is best determined by the use of spirits, as a more definite mark is thus made on the dipping-rod.

Especial care should be taken on every occasion to lay out the bottom of a vessel accurately, and according to the stated directions, as the correctness of the final result depends chiefly upon the manner in which this part of the operation is performed.

Spirit Vats, Large Store Casks, fc. -The gauging and tabulating of these vessels should be conducted agreeably to the directions laid down in the Distillery Instructions with respect to distillers' utensils, a sufficient number of equi-distant dimensions being taken in each case to compensate any irregularity of construction, and to give a true average result.

This uniform plan of dividing every large vessel into an adequate number of odd sections, and measuring cross diameters or other dimensions in the middle of each of the even number of frustums thus set off may be safely and conveniently adopted, whether the sides of the vessel be straight throughout as in the case of a cylinder, inclined to or from one another as in the case of a conical frustum, or protuberant in the middle as in the case of a cask.

The full content of fixed casks, of a capacity not greater than about 200 gallons, will be most readily and accurately determined by weighing them when empty, and when filled with a liquid of known specific gravity, or lbs. weight, per gallon. The difference of the two weights divided by the weight of a single gallon of the liquid gives the content of the cask. Unsweetened spirits of any kind are best adapted for this purpose, as the weight per gallon, corresponding to every indication of the hydrometer, may be had from the table in Schedule C, of the Act 23 and 24 Vic., c. 114, or at the end of the Distillery Instructions*; but water or any fluid, the weight of a stated measure of which has been carefully ascertained will answer the object when spirits cannot be procured.

It is unnecessary to find any dimension except the length, or to form a table of the partial contents of the smaller fixed casks in the stock of a rectifier, &c., as the process of ullaging, as exemplified on page 245, will, in these cases, furnish the quantity of liquor at any fraction of the depth of the cask with sufficient

exactness.

Movable Casks.-The operation of finding the full content of movable casks by gauge, is not required in the present practice of the Excise, as the system of weighing is much more simple and correct. But, as in taking the stock of a spirit dealer or retailer, or on other rare occasions, it may be inconvenient to determine the capacity of a cask by weight, a few remarks on the subject of caskgauging without the aid of special instruments, will be inserted in the Appendix.

Stills. As the law requires rectifiers to charge their stills in the proportion of 7 parts in 10 of the entire quantity of liquor which each still, inclusive of its head, is capable of containing, officers must ascertain the dimensions of every ordinary still and still-head, when first erected at a rectifying house, and compute the capacity of both, so as to show the vacuity or dry inches when the utensil is charged with 7-10ths of its contents. (See Cautionary Instr., p. 65).

Full directions as to the proper mode of gauging and tabulating stills are appended to most of the older issues of the Distillery Instructions, and are also published in a separate pamphlet, copies of which, when necessary, may, no doubt, be procured on application to the Board.

To these sources officers are referred for information, as it would be of little utility to swell the limits of the present work by an insertion of the particulars.

See the Instructions relative to the Survey of Cautionary Traders, page 73, as read in connection with the General Order of 3rd September, 1862.

GAUGE POINTS, ETC., ON THE SLIDE-Rule.

260(e)

It may be remarked, however, that the method of treating the distinct sections of the still and still-head, as so many mathematical figures, such as cylinders, cones, &c., and finding the capacity of each by an appropriate rule, is both troublesome and inaccurate. A more simple process, and one which affords the

most correct results, is to apply to each section the prismoidal formula laid down on page 216, without paying any regard to the geometrical configuration of the object.

Gauge Points, &c., and Special Lines on the Slide-rule.—A « gauge-point" is merely a technical name for the square-root of a fixed divisor, such as the number of cubic inches in a bushel, a gallon, &c. Thus at 47.1 on the line D is a metal pin with the letters "M S" attached, that number being the « square gauge point" for malt bushels, or, in other words, the square-root or side of a square, the area of which is exactly one bushel. Again, at 18.79 and 53.14 on D are pins with the marks "M G" and "M R," representing, on the same principle, the circular gauge-points for gallons and bushels respectively.

The use of these points is as follows:-Suppose the area of a square were required in bushels, the length of a side being 80 inches. By employing the lines M D, A and B, and setting 80 on B to 10 on M D, under 80 on A would be found 2.88 bushels on B. Now the question thus resolved is one of simple proportion, that is,

Or, as the number of cubic inches in a square, at one inch deep, the side of which is 47.1 inches, is to the number of cubic inches in a square, (at one inch deep) the side of which is 80 inches, so is 1 bushel to 2.88 bushels. But by the property of the lines C and D, as explained on page 239 et Seg., it is evident that we may obtain the same result, if we set 1 on C to 47.1 (at the middle of the pin denoted by M S) on D, and above 80 on D, read off the answer on C. As respects the areas of rectangles, it is necessary to obtain the mean-proportional between the length and breadth-that is, the side of a square the area of which is equal to that of the given rectanglebefore the number of bushels can be determined, as above, by means of the gaugepoint on D. It would appear, therefore, that the areas in bushels of squares and rectangles are much more easily arrived at by the use of the line M D.

Since there is frequent occasion, however, to compute the capacities of cylinders in gallons, and there is no special line laid down on the slide-rule for this purpose, like the scale M D for the contents of rectangular bodies, the circular gauge-point, 18.79 on D, affords a ready method of arriving at the required result. Thus, on the same principle as has just been exemplified with regard to the gauge-point for squares, we may find the capacity of any cylinder in gallons at one setting of the rule, as follows:

Let the diameter of a cylinder be 38 inches and the depth or length 65 inches, what is the content in gallons? Here we have the proportion:

As 18.79 (353.036): 382 :: 14.09.

And 4.09 × 65 = 265.8 gallons. Answer. But, if we set 65 on C to 18.79 (gauge point M G) on D, over 38 on D is 266 on C; and similarly, as respects a cylinder of any other dimensions. The reason of this will be obvious to those who bave studied the mode of graduation of the lines C and D, as treated of at

R***