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gauging of couches, that the several dips should be noted down as they are taken, and the memorandum preserved for future reference, if necessary. In other cases, when some experience has been gained, the averages may as a rule be formed mentally except where it is found that a charge of duty will arise.
The number of dips in each instance must, of course, be proportioned to the magnitude of the surface, and to its greater or less apparent evenness. No general directions can be given for the guidance of officers in this particular. It may, however, be stated, that in the gauging of couches the dips should seldom be more than 36 inches apart, in the direction either of the length or the breadth of the frame. No trouble should be spared to obtain as accurate an account as possible of the quantity of grain in couch; and under ordinary circumstances, the greater the number of dips at regular intervals, the nearer will be the approach to a correct and indisputable result.
On no account should officers accustom themselves to the taking of a constant number of dips, such as 5, 10, 20, &c., regardless of the extent and the irregularities of the surface, merely because a particular number serves as an easy divisor in the formation of an average. Unless the surface be so narrow that two sections crosswise are sufficient, 10 dips, however convenient, are never admissible. When the breadth exceeds one-third of the length, 6, 9, 12, or some other multiple of 3 is the best number of dips. In no case can 5, 7, 11, or generally any of the prime numbers be used with propriety. (See on the subject of couch gauging-Loftus's Inland Revenue Almanack for 1864, page 2)."
In the mental computation of average depths, no difficulty will be experienced, after a little practice, in adding rapidly together any short series of inches and tenths, where none, or only a few of the gauges exceed 10 inches. The number of dips that will suffice on each occasion, and the best manner of distributing them over the grain should first be decided upon: the dips should then be taken, as nearly as possible, in the middle of regular equi-distant rows, as has just been explained.
When the gauges all exceed 10 inches, it will simplify the mental reckoning to add together only the excesses above 10, 20, 30, &c. inches; and when the average is formed upon these, to increase the result by the necessary number of tens.
It is the practice of some officers to make the first dip serve as a standard or start-point, which they modify as they proceed, by adding to it or subtracting from it the tenths only of each succeeding higher or lower gauge respectively. For this purpose it is convenient to regard all the inches and tenths in excess or defect of the first dip as so many equivalent tenths.
• The division of the grain into so many equal rectangular masses, and the taking of a dip in the middle of each, is the only foundation of a true average, since the entire bulk is thus resolved, as it were, into a definite number of equal parallelopipedons or smaller couches, the area of each of which is an aliquot part of the area of the whole; and each such area multiplied by its particular depth, and the products added together, must give the same result as the multiplying of the total area by the average of tho different depths. To show by an example the correctness of this view, and therefore the necessary inaccuracy of any other method, suppose the area of a couch-frame to be 2 bushels, and that 4 dips of the grain laid in it are deemed sufficient. If the surface be marked out into 4 eqnal sections, there will be 4 equal areas of one-half a bushel each ; and if each of these be multiplied by its particular depth, the total will be the same as that produced by multiplying the area of the entire mass by the average of the 6 dips. Thus,
Now, as the equality of the four sections is the reason of the agreement of the two processes above illustrated, and as there is no convenient, readily-applied method by which we can lay out a surface into 3, 5, 7, or any other prime number of equal spaces, and at the same time ensure a sufficiency of dips, unless the surface be extremely parrow, it must be evident that the only proper way of proceeding in ordinary cases where more than a single row of dips is necessary, is to use some multiple of the row of dips taken in the direction of the length or the breadth of the utensil. But such numbers as 3, 5, 7, &c., are not multiples of any other numbers
Example. Suppose a series of 6 dips to be, 14:3, 14-9, 15.3, 15-6, 13:8 and 16-0 inches. Here, taking 14 inches as the standard, 15-3, 156, and 16-0 would be reckoned as equal severally to 14 + 13-10ths, 14 + 16-10ths, and 14 + 20 tenths; and 13.8 as equal to 14 - 2-10ths. The operation of forming the average would be, accordingly, 5 tenths + 9 tenths = 14 tenths, + 13 tenths = 27 tenths, + 16 tenths = 43 tenths, less 2 tenths = 41 tenths, +20 tenths = 61 tenths, and 61 tenths divided by 6(the number of dips) = 10 tenths, or one inch, which added to 14 inches, gives 15.0 inches as the average dip. But unless the surface be so level that the dips do not differ by more than a few tenths from each other, this process is apt to confuse, and will not, on the whole, be found less troublesome than the simple additive method above described.
There is a very useful calculation connected with cistern and couch-gauging, which should frequently be practised by officers. It consists in estimating the per-centage of the amount of the best couch-gauge over that of the first cistern-gauge-when the latter has been taken soon after the time of wetting—and also the per-centage of the couchbushels over the amount of the highest cistern-gauge. The first of these calculations shows, approximately, the total swell of the grain, and the second enables us to judge whether the whole of the contents of the cistern has boen transferred, without undue compression, into the couch-frame. In fairly worked houses, and in ordinary seasons, the increase of bulk during steeping should not be less than 23 per cent., while the excess of the best couch over the best cistern-gauge should average, at least, from 3 to 4 per cent. Although, however, as a general rule, the grain should, for obvious reasons, lie less compactly when first emptied from the cistern than during the latter stages of the steeping, it must be recollected that in warm weather, or owing to various exceptional circumstances, “cistern charges” will sometimes arise where no fraud has been committed.
Example. Suppose the amount of a cistern gauge taken immediately after wetting to be 75 bushels, and of the best couch-gauge, 97 bushels; to estimate the increase per cent.
75 : 100 : 97 :: 129. And 129 - 100 29 per cent. Answer. This computation may be performed very readily and with sufficient exactness by means of the A and B lines on the slide-rule, as already exemplified on page 237. The increase from the best cistern to the best couch-gauge may be similarly estimated.
Floor Gauging.–The grain, as soon as the time has expired during which it is legally deemed a couch, becomes what is technically called a floor.” On removal from the couch-frame the mass is spread out in heaps of greater or less thickness, according to the temperature of the air, or the peculiarities of the mode of working. By law, the maltster is required to lay his floors with straight lines or edges, or so that they may be conveniently gauged. Except in the case of "young floors,” which are generally piled in thick prismoidal heaps should the weather be cold, the masses of vegetating grain are, in most instances, laid between the walls of the malt-house in a rectangular shape, the ends being made straight and even. There are, of course, occasional unavoidable divergencies from this regularity of outline, such as when the walls of the building are not parallel, &c., &c. But by taking average or intermediate dimensions, almost every floor may be reduced without any material error to the form of a rectangle, and gauged accordingly.
Let A B C D represent the end of a piece of malt with slanting sides. Half way between A and C let a stick, as m n, be set up
B perpendicularly, and another, as vx, half-way ry between B and D. Then extend a tape from r to s, or from m to v, parallel to rs, the latter being regarded as the breadth of the floor. If the ends bo slanting, it will be necessary to measure the lengths in a similar manner.
Otherwise, fix the tape at the innermost sloping edge of one end, as at D, by passing a stick through the ring; then extend the tape in a horizontal direction, D B, to the outermost sloping D edge of the opposite end of the floor, which may bo found, pretty nearly, by dropping a grain of corn from the point at which the tape is held, and observing whether it touches the outer edge; the E &
A length of the floor will thus be obtained, for what is lost at one end is gained at the other.
Again, let M N O P represent the ends of a piece of malt with one side slanting, and
N the other laid against a wall.
Set up a stick at one end perpendicularly, half-way between M and 0, and extend the tape from r to s.
When, from any cause, à floor is laid in the form of a trapezoid, it will be best, as directed at page 178, to add together the lengths of the two parallel sides, and to multiply
the sum by half the perpendicular distance between them. In this case, as in all others, the greater of the two superficial dimensions should be entered as the length, and the less as the breadth of the floor. Whenever a floor is laid in a shape that is not nearly rectangular or trapezoidal, the officer should require the workman to alter it to one of these forms, as the gauging of grain disposed in various uncertain figures would be attended with considerable inconvenience and be liable to error. Average lengths and breadths should always be taken where the edges of the ends or sides appear to deviate materially from straight lines. This precaution is especially important as regards the gauging of floors in deep masses with both the ends and the sides slanting.
Incumbrances in malt-floors, or small unoccupied spaces in any portion of the area, must be allowed for by a proportionate reduction of the gross dimensions. The simplest and most expeditious method of making such allowances is as follows:
Measure the length and breadth, or the diameter, of the space or object, and compute the area in square inches. Then from the gross length or breadth of the floor deduct as many inches as will, when multiplied by the other dimension, give an area equal to that of the incumbrance, &c.
Example. Let the gross length and breadth of a floor be respectively 410 and 265 inches; and suppose the dimensions of an oblong space in some part of the area (such as the opening above a ladder) to be-length 66, breadth 43 inches. To compute the net dimensions of the poor for insertion in the survey-book. Space, 66 X 43 = 2838 square inches. Floor length, 410, multiplied by 7 = 2870 (6 would be too small and 8 too large a multiplier). Breadth of floor, 265, less 7 = 258, the net or modified breadth, which, multiplied by 410, gives the net area of the floor as correctly as is ever requisite in practice. Thus, 410 x 265
108650 66 x 43 = 2838
By abatement from the breadth, 410 x 258 = 105780. Net area 105812 The difference of the two results amounts only to one-hundredth of a bushel on the area.
It is plain that the allowance may be made on the length instead of the breadth by a similar process—
Breadth, 265 x 11 (nearest whole number of inches) = 2915; 410 – 11 = 399, modified length; and 399 X 265 = 105735, which is less than the exact net area by about 2-100ths of a bushel.
When spaces or incumbrances are circular, the area in square inches may be computed mentally with sufficient nearness by squaring the diameter and multiplying it by 8 (for •7854), or squaring the circumference and multiplying it by :08 (for •07958).
Unless in the case of small spaces or incumbrances, it is advisable, however, to divide the floor into two or more sections, as suggested by its shape, and gauge each separately.
The average depth of a floor having been determined by one of the modes stated in the article on cistern and couch-gauging, the content in bushels may be obtained from the slide-rule, at one operation, by aid of the M D line (see page 238). In order to value the results given on the rule, it is necessary to observe the following directions, until sufficient experience in the use of this part of the instrument has been gained to enable the officer to dispense with precepts.
Note the number of figures expressing the value of the commencement of each of the three lines A, B, and MD. Add these numbers together and deduct 4 from the sum. The remainder shows the number of figures in the whole bushels of the floor, if the result falls within the first half of the slide ; if otherwise, the remainder must be increased by 1.
Example (1). Length 650, breadth 300, depth 4 inches.
Here the commencement of M D (the given depth being 4) contains only one integer; of A and B respectively, 3 integers (the length being taken on one of these lines and the breadth on the other) 1 and 3 are 4 and 3 are 7; and 4 from 7 leaves 3. It is inferred, therefore, that as the result falls within the first half of the slide, there must be 3 integers in the content of the floor, which, by the rule, is found to be 351 bushels.
The method of using the slide-rule to determine the content of rectangular solids in bushels is as follows:
Set any of the three dimensions on B to one of the other two on MD (preferably the length or breadth on B to the depth on M D); then against the remaining dimension on A will be found the content on B.
Example (2). Given the length of a floor 72; the breadth 53, and the depth 14:6 inches, to find the content.
72 on B to 14:6 on MD; under 53 on A is 25 on B. Or, 53 on B to 14:6 on M D, under 72 on A, is 25 on B.
Answer. 25 bushels.
Here the commencement of M D consists of one integer (that is, reckoning up to 14.6 on that line); of B two, and of A, two integers. Then, agreeably to the rule just laid down, we say, 1 and 2 are 3 and 2 are 5, less 4 equals 1. But as the result falls within the second half of the slide, we add 1 to the difference of the integers. There are, accordingly, two integers in the content, or the answer is 25 bushels.
The principle of this mode of valuation may be deduced on a little reflection from the general theory of the slide-rule (see page 235 et Seg.) if it be borne in mind that the beginning of the graduations on the line M D is on the right hand, and of the lines A and B on the left hand.
In casting gauges by the rule it is well always to check the first result by another setting of the dimensions; and if, through difficulty of reading or other causes, there should be any disparity between the two contents thus found, the mean should be taken.*
It need hardly be stated that the areas of malt utensils cannot be determined, by means of the slide-rule, with the accuracy that is required for official purposes.
Young officers are recommended, when they have gauged a malt-floor and cast its content by the rule, to ascertain roughly the per-centage of the quantity in the floor above the number of gross couch-bushels, and then to compare such per-centage with the apparent amount of increase exhibited by the grain in respect of the degree of growth it has attained, and its general condition on the floor. After a little careful practice of this kind in honestly conducted houses, a certain length and thickness of the rootlets and other circumstances affecting the bulk of the vegetating corn, such as recent turning or watering, will become associated in the mind with a certain per-centage of increase, and a valuable criterion will thus be formed by which the fairness of the mode of working may, at any time, be tested in that stage of a trader's operations. Thus, when the bud or rootlet shows itself as a white speck at the base of the grains, the excess above the couch generally amounts to from 10 to 15 per cent. When the rootlets are about an eighth of an inch in length, the per-centage will, as a rule, vary from 20 to 25 per cent., and so on.
Nothing, however, short of regular observation, combined with careful gauging and a proper allowance for the modifying circumstances of each case, will confer accuracy of judgment in this particular.
The slide-rule enables us, as in other cases, to find the per-centage with great facility. Set the number of couch-bushels on B to 1 on A, and over the floor-bushels on B will be the per-centage plus 100 on A.
Example. The couch-bushels are 130 and the amount of a floor-gauge is 182 bushels. Required the increase per cent. 130 on B to 1 on A ; over 182 on B is 140 on A.
Answer. 40 per cent. When the increase in any instance exceeds 63 per cent., a floor-charge is present, which must always be computed to the exact tenth of a bushel by the pen.
A rapid mode of casting the content of floors roughly, when a slide-rulo may not be at hand, is to take the first two figures only of the length and breadth, augmenting the second figure of each by 1, if the third figure of the dimension should be equal to or greater than 5. Then let one number be multiplied by half of the other, one place of decimals pointed off, and the product, diminished by a tenth of itself; the remainder multiplied into the depth gives a tolerable approximation to the quantity in the floor. This process is merely a modification of the first part of the more accurate. method exemplified on page 254.
Example. Length 368, breadth 122, depth 3.6.
87 X 6 = 222; 222 with one decimal place cut off = 22.2; 22.2 less a tenth of itself 20; 20 x 3.6 = 72, the number of bushels (nearly) in the floor.
Many officers will, no doubt, be able to make a computation of this kind mentally.
When the content of a malt-floor exceeds 200 bushels, the slide-rule, owing to the openness of its graduations between the points marked 2 and 10 will not give the result with greater nicety than to the nearest whole bushel, and sometimes not so closely as this.
* Mr. Woollgar, in treating of the slide-rule observes, that when there are two or more methods of performing the same operation, and two or more numbers are given or required, which can be exactly expressed on the rule (that is, by the divisions coinciding), while there is another number which can only be estimated or guessed at (that is, when a space has to be divided by the eye), that mode of operation should be adopted which will place an exact value opposite to an estimated one, and vice versa. Thus, if the dimensions of a floor of malt were, length 460, breadth 183, and depth 10-7, we should set 460 by preferonce to 10.7, as the points corresponding to 183 and 10-7 can only be estimated by halving, with the eye, the spaces between two even divisions.
Kiln Gauging.---Kilns for the drying of malt may be of any shape & maltster thinks fit ; but in most instances, kiln-floors are either rectangular or circular. When a different form presents itself, it will be best as a general rule, to treat the surface as that of an irregular polygon, and to obtain the area by division into triangles agreeably to one of the methods pointed out in the Principles of Mensuration, page 179. If any portion of the floor should bo of the form of the segment of a circle, as is sometimes the case, the area of that portion should be computed separately by aid of the Table of Circular Segments in the Appendix, using Rule III., page 193. To find the diameter of the circle answering to the segment in question, measure the chord of the segment, that is, the straight line connecting the extremities of the arc (A D, fig. page 189), and also the versed sine, or the height of the segment from the middle of the chord to the middle of the arc (as B E, same fig.) Then divide the square of half the chord by the versed sine ; to the quotient add the versed sine, and the result will be the diameter required.
When a kiln is of very unusual or irregular shape a minute description of its figure, or still better, a drawing on a small scale, and an account of the method adopted in measuring it, should be inserted in the Dimension Book.
It is deemed suflicient to measure the dimensions of kilns to whole inches.
The grain on the kiln having been made reasonably level, the average depth is taken and multiplied by the area. This calculation may be performed on the slide-rule.
There is often, from the unevenness of tho surface, some difficulty in obtaining a correct mean dip of grain drying on a kiln. But as gauges in this part of the process are extremely important, officers should exercise the authority vested in them by law, and insist on the surface being rendered as level as circumstances will permit. The maltster froquently alloges a peculiarity in the drying power of the kiln as a reason for laying the grain much more thinly in some parts than others. When this is really the case, it is only necessary to cause the grain to be placed on that portion of the kiln-floor where the drying power is least (usually about a fourth of the entire area), in a wedge-like form, and to take dips in the middle of the slope. The number of dips proper to the level section should be proportionate to tho number taken on the slope. Thus, in a small kiln requiring (say) 8 dips, two of the dips must be obtained in the quarter section forming the incline, and so in proportion as regards any other number of dips.
Gauging on the kiln, when the malt is dry, or nearly so, supplies a useful compare with the quantity chargeable from couch. It may be generally stated that no gauge of dry unblown malt can, in a fairly worked house, equal the gross couch-bushels; or, at the outside limit, exceed the net couch-bushels by more than 10 per cent.
The gross couch-bushels form, upon the whole, the best practical compare, as well as that most readily applied, with the amounts of dry malt gauges, inasmuch as the differences in the quality and condition of the barley, from time to time, nearly expend themselves in the varied yields of the cistern swell. An illustration of this is appended. Dry Barley put
DRY MALT PER CENT.
barley. couch-bushels. (a). 81.5
11.1 (6). 77.0
13.6 (c). 85.0
(c). Ditto of inferior quality, and soft. As a rule, a dry malt-gauge may be considered satisfactory when it gives a quantity less than the gross couch-bushels by at least 10 per cent.
Gauges taken during the process of drying are valuable as checks upon the trader's honesty. It should be observed that the depth of the raw malt upon the kiln diminishes by about one-third from expulsion of tho moisture, and that the rate of decrease is, in most places, pretty uniform throughout.