The art of measuring the capacities of all kinds of vessels Gauging of course forms a part of mensuration, and is accordingly treated of by most writers on that branch of science; but as casks are seldom of any exact mathematical forms, the rules laid down by such authors must be considered as merely theoretical; and in practice, gauging is performed mechanically, by means of the gauging or diagonal rod, or by the gauging sliding rule. The diagonal or gauging rod is a rod or rule adapted for determining the contents of the casks, by measuring the diagonal only; viz. the diagonal from the bung to the extremity of the opposite stave next the head. It is a square rule, having four sides or faces, and is usually four feet long, and folds together by means of joints. Upon one face of the rule is a scale of inches, for taking the measure of the diagonal; to these are adapted the areas, in gallons, of circles to the corresponding diameters. Upon the opposite face is a scale, expressing the contents of casks, having a corresponding diagonal; and these lines constitute the difference between the diagonal rods and the slide rules.

To use the diagonal rods, put the rod in at the bung hole of the cask, until its end touch the opposite stave at the farthest possible distance from the bunghole, and note the inches and parts cut by the middle of the bung; then draw out the rod, and look for the same inches and parts on the opposite face of it, and on them will be found the contents, in gallons. The sliding rule is similar to the common sliding Gunters, (see Gunter's Scale,) but having certain divisors, or gauge points at different points of the scale, pointed out by small brass pins, which divisors are the number of cubic inches in any particular measure, as malt bushels, or imperial gallons, the casks are gauged approximately as cylinders, taking a mean diameter, for which purpose they are generally reduced to what is called four varieties; and if the difference between the head and the bung diameters does not exceed six inches, their mean diameters may be found by multiplying the difference of the first by .68; of the second, by •62; of the third, by .55; and of the fourth, by .5; the respective products of these numbers, added to the head diameter, will make a mean diameter.

Having found a mean diameter, the contents are found by setting the length of the cask upon the line marked B, on the brass slider, against the gauge-point, for gallons, on the upper line A, upon the rule, and against the mean diameter upon the lower line D; upon the rule will be found the contents on C upon the slider. On the back of the rule are four other lines, differently marked. The first line is marked l), and is similar to the same line upon the opposite side, and upon this line are set the circular gauge-point for wine, and various other gauge - points; the second line is upon the slider - it is marked C, and is similar to the same line C upon the opposite face; the third and fourth lines on this instrument are two lines of segments, for ullaging the casks, as it is termed, that is, finding the contents of a cask, only partly full. One of these lines is marked S S, for segment standing, and the other S L, for segment lying; these lines are set upon the rule, and are both numbered alike, from 1 to 10, and from 10 to 100.

To find the ullage of a lying cask by the line of segments, having the bung diameter, the depth of the liquid in inches, and the contents of the cask, set the bung diameter on C to 100, on the line of segments marked S L, and opposite the depth of liquid on C will be a number on the line of segment, which call the reserved number; then set 100 on A to the contents of the cask upon B, and against the reserve number before found upon A is the contents of the cask upon B. To find the ullage of a cask standing, substitute the length for the bung diameter, and the line S S, for the line S L, and proceed as before.

To facilitate computations in gauging, Mr. W. Gutteridge has invented a series of new units of measure, which has received the approbation of every individual member of the Commission of Weights and Measures. These units of measure are numbered 1, 2, 3, 4, 5, 6, 7, 8, No. 4 being the common decimal foot, which is introduced to complete the series. These units are all decimally subdivided into 100 equal parts, and are the roots of the cubic and superficial measures in which the capacities of vessels, or solid contents of bodies are reckoned, as gallons for liquids, and cubic feet for timber. By this means, no division is necessary in computing contents or capacities, for the area expressed in Mr. Gutteridge's system of notation multiplied by the depth gives the contents; whereas, when the dimensions are taken in inches, after multiplying the area by the depth, it is necessary to divide the product by the number of inches in a gallon or a foot to find the contents. Mr. Gutteridge's units of measure, with their data, are as follows:

In connexion with the subject of gauging, we may notice a singular circumstance related by Mr. Gutteridge. He had been called in to gauge a new vat for Messrs. Booth & Co. distillers, and his own system was employed as affording greater accuracy than the inch method in common use. After the dimensions had been taken, a glass tube was fixed on the outside of the vat, for reading off the quantities within, as a means of comparison with the interior dip. That no difference might arise from the effect of capillary attraction, the tube was made of more than an inch bore, and was fixed perpendicularly, with a graduated scale placed closely, so that the zero of the scale coincided with the top of the ungula, which exactly covered the bottom, without producing any sensible depth of wet at the dipping place, from which it was inferred that the interior dip, and the exterior indications of level would be always the same; and upon putting in several determined quantities, those quantities were indicated by the tube exactly; but a difference was afterwards perceived between the interior dip and the exterior level, and the greater the quantity, the greater the difference.

The experiment was frequently repeated, with every precaution to guard against error, one source of which was the difference of temperature in the vat and in the tube, amounting in one instance to 21/2 degrees, which would cause a difference of about .085 of an inch, (the spirit being 41.6 per cent, over proof,) but to save computations of this sort, the time chosen for the principal experiment was when the temperature was alike. With 1400 gallons in the vat, the difference was about .6/10 of an inch; 2200 gallons more were then pumped in, and the difference increased to 98/100 of an inch, and on adding 700 gallons more, the difference amounted to 11/10 inch. It appearing highly improbable that the timbers could compress so much more under the dipping place than under where the tube was fixed a level of the two surfaces was taken, and, extraordinary as the fact may appear there was a difference found in the levels, of 4/10 of an inch, the liquid being that much higher in the vat than the tube. This difference Mr. Gutteridge imputes to a difference in the specific gravity of the spirit within the vat, and that within the tube, and upon assaying them the former was found to be nearly 5 per cent, stronger than the latter.

This variation must have been caused by a greater evaporation on the tube, and it shows that with spirits of such great strength, evaporation is very rapid, and cannot be too carefully guarded against. The remaining difference between the dip and the level in the tube Mr. Gutteridge supposes to have arisen from a compression of the timbers under the dipping place.

The following diagrams of the vat, tube, and timbers, will render the subject more intelligible. Fig. 1 represents a section of the vat, a b being the tube fixed into a metal pipe b c, with a cock at c d, the level of the spirit in the vat; f the level in the tube, and h i the dipping place. Fig. 2. shows the supports of the vat; B the back, and F the front, of which the seven similar parts a a are the immediate rests, each four inches square; b b b the three timbers upon which the former rest, 101/2 inches deep, and 121/2 broad; c c the two sleepers upon which the beams are laid. The places d d d d are supported upon tour upright posts, and under k was placed another support; l the orifice for the tube pipe, and o the dipping place.

Fig. 1.

Fig. 2.