Mr. Lubbock on Cask-Gaging. 331 



The rule which is given by Symons, p. 217, for finding the 

 ullage of a cask lying, by the pen, is erroneous, and I appre- 

 hend of no utility. 



In practice, the sliding-rule (or head-rod) is invariably used 

 in gaging casks, and the content of the cask, considered ge- 

 nerally of the first variety, is sought by adding to the head 

 diameter a certain quantity, depending only on the difference 

 of the bung and head diameter, and considering the sum so 

 obtained as a mean diameter, and the content of the cask to be 

 the same as that of a cylinder of the same altitude or length, 

 with that quantity as the diameter of the base. 



In the first variety, 



content = ---{ c lb l +h°), 

 1 Z 



if 2& 2 + /r = 3{h + qY 



h + q = / ** +JP . ; and since b = h + b-h 



= \/h-+ — {b-h)+~^— 



- *'+ I (b-h) + ^- + &c. 



q — %{b-h) nearly. The error of the content 



obtained by this approximate method = — — {b—hy. 



This, however, is only to be considered as a rough approxi- 

 mation, and the quantity q cannot be made strictly to depend 

 only upon b—h. If we take a cask of which the dimensions 

 are / = 46-9, b = 31 '2, // = 26'1 (which are those of an 

 average brand v piece,) the content of which is accurately 

 116-37 gallons,' we find q = |(5'1) = 3-4, h + q = 29*5, and 

 the content is found by the approximate method above equal 

 to 115-61 gallons. It is obvious that the error will be nearly 

 constant for the same kind of cask, and hence either a correc- 

 tion may be obtained experimentally or by calculation to be 

 added in all cases for each kind of cask, or this correction 

 may be included in that due to the variety. The direction 

 given by Symons is, "Look for the difference of the bung and 

 head diameters on the line of inches on the edge of the rule, 

 and whatsoever number stands opposite to it on the respective 

 lines of varieties add to the head diameter, and the respective 

 sums will be mean diameters, or diameters of cylinders equal 

 to the solidities of the cask when the altitudes of those cylin- 

 ders and the lengths of the casks correspond." When this 

 was written the four varieties were introduced on the sliding- 

 rule ; nowonlv the spheroid is placed there, and I find opposite 

 5-1, 3-5 instead of 3-4. How this difference arises is difficult 

 2U2 



