GAUGING. 



Prismatic vessels are measured accord- 

 ing to the first explanation, and frustrated 

 or pyramidical vessels are disposed of in 

 the same manner as those whose side or 

 sides regularly augment, or vice versa. 

 Truncated cones, likewise, come under 

 the same rule ; only treating their termi- 

 nations as circles, instead of computing 

 them as squares, or rectilinear bases. 

 The following very easy mode of ascer- 

 taining the contents of a conic frustum 

 is given by the ingenious Newton. Mul- 

 tiply each diameter (*. e. of top and bot- 

 tom) by itself; then the one by the other, 

 and the aggregate of those products by 

 the altitude ; multiply also the last pro- 

 duct by 78539, (the superficial content of 

 a circle whose diameter is 1000) ; a third 

 part of the product is the measure of the 

 frustum. 



Therefore, when vessels have their 

 sides composed of straight ribs, proceed- 

 ing in right lines from one to the other 

 end of the conic frustum, the measure- 

 ment is easily made ; thus we may, with- 

 out difficulty, ascertain the contents of 

 great coppers, mashing-tubs, corn-binns, 

 and a great variety of similar vessels. But 

 we rarely see casks of any description 

 formed by the union of two frustrated 

 cones ; their usual shape is more sphe- 

 roidal ; that is, they have an arched or 

 swelling course from the bung to the 

 chimb or end ; consequently these con- 

 tain more than such as are truly conical. 

 This occasions the necessity for allowing 

 something for the bulge or swell, and of 

 taking the diameter at the centre, be- 

 tween the bung and the chimb, which 

 diameter will give a true medium. The 

 thickness of the cask may easily be as- 

 certained by aid of calibre compasses 

 applied to the proper part. The length 

 of the cask may be measured internally, 

 by putting a rod or wand in at the tap 

 hole, and the internal diameter may be 

 taken in a similar way at the bung ; bat 

 such can only be done when the cask is 

 empty, or, at least, opened for the pur- 

 pose : whereas casks that are filled and 

 sealed must often be measured ; for this 

 purpose the calibre compasses are ex- 

 tremely useful, since they embrace the 

 outside measure. To correct the com- 

 putation, we must usually allow an inch 

 and a half in the whole length, and the 

 same in the whole diameters at the bung 

 and chimb, thus exteriorly taken, for the 

 thickness of the cask itself. This deduc- 

 tion being made, we must compute ac- 

 cording to the form or swell of the staves. 

 If they be much raised, we multiply the 

 difference between the diameter at the 



bung, and at the end, by .7; if less raised, 

 or swelling, we multiply the difference 

 by .65 ; if nearly straight, by .6, and if 

 rectilinear, or truly conical, by .55 ; the 

 product added to the diameter at the 

 end, or head, will give a mean diameter. 

 Suppose the diameter within the bung to 

 be 32 inches, at the head 24, and that the 

 length within be 40 ; the difference be- 

 tween 32 and 24 is 8, which, multiplied 

 by .7, gives 5.6 ; add thereto the diameter 

 at the head, 24, and the medium will be 

 29.6 ; multiply by the length 40, and di- 

 vide by 359.05, and the quotient will be 

 ale gallons 97.4. And thus, with the other 

 multipliers, according to the apparent 

 bulge or swell between the bung and the 

 chimb, and according to wine or ale mea- 

 sure. 



To find the ullage, or quantity of liquor 

 deficient in a cask, we have the following 

 rule. Take the diameter at the bung, and 

 ascertain the number of inches and parts 

 that are dry ; say that of 29 inches 13 be 

 dry ; also that the whole cask measures 

 80 gallons. Divide the dry inches 13 by 

 29, the bung diameter ; the quotient will 

 be .148 ; find the two first figures, .44 

 under V. S. in the annexed table, and its 

 sequent will be .4238, to which add a 

 proportional part for the 8, and the whole 

 sequent will be .4343, which, multiplied 

 by the contents of the cask, will shew a, 

 deficiency of 34.664 gallons. This mea- 

 surement, however, applies to cylinders 

 only ; if the cask be conical, you must 

 find the mean diameter, which should be 

 deducted from that at the bung ; and not- 

 ing half the difference, which is to be de- 

 ductedfrom the wet inches, and reserved,, 

 Then, as the mean diameter is to 100, so 

 is the reserved difference to a versed line 

 in the table : and if the segment (to be 

 found in the table, be multiplied, as be. 

 fore shown, into the contents, the product 

 will be the quantity of liquor in the cask. 



Example. Let the bung-diameter be 32* 

 the mean-diameter 29.6, and the whole 

 measure 97.4 gallons : say there be 19 

 inches wet : 



From 32.0 From 90 



deduct 29.6 take 1.2 



re m ai n 2,4 re mai n 1 7. 8 rese rved . 



its half is 1.2 



Now as 29.6 is to 100, so is 17.8 to .60, 

 the versed sine. The segment to 60 is 

 .6265; which, multiplied by 97.4, the 

 whole contents, the product gives 61 gal- 

 lons of liquor remaining. By working; 

 upon the dry inches, you would have 

 found the ullage, or deficiency. 



