416 Mr. Wiseman on the Method of Gauging 



ties of casks met with in practice, this would perhaps have 

 been it. But, without corrections or allowances, the thing- 

 appears to me to be impossible. 



Dr. Young's formula generalized is b" x k 2 -" x l-i-?n = c; or, 

 in logarithms ?iB + (2 — n)H + L — M = C(m being = 294-l 18); 



where n = ~ ~ . Putting this equation into numbers, 



the true value of n will be found for any cask whatever whose 

 true content is previously known. Thus the cask No. III. 

 requires ?i=l '40803; or, if a vulgar fraction with the deno- 

 minator 150 be preferred, the indices of b and h will be fi^ 

 and fin.;— No - IV - requires jf§ and iff;— No. 3, U% and 

 T 9 3%, and No. 8, §M and T 9 7 % ; &c. The average of all these, 

 f £§ and T 9 / 7 , Dr. Young has adopted. But since the values 

 of the indices will in practice vary at least from -j-f §, -f jf to 

 f ji, T 8 j 9 ^, this circumstance alone shows that Dr. Young's 

 rule (where the indices are constant) will in many instances 

 be necessarily very incorrect, and consequently unfit for the 

 purposes of general cask-gauging. Those casks (port pipes, 

 see Nos. III. and 9), which, being made in a more regular 

 manner, are the easiest to determine near the truth, have their 

 contents made furthest from the truth ; so that there would be 

 a certain loss to the revenue of two or three gallons on every 

 cask of that description gauged by this method ! Similar ob- 

 servations might be made with respect to several other varie- 

 ties of casks. 



It follows from what has already been said, that this new 

 method cannot with propriety be adopted unless it can be 

 modified in its operation by discretional allowances in and 

 additions to the length ; something similar to the present 

 practice : for the having recourse to tabular corrections, which 

 Dr. Young himself seems to think may be necessary, is inadmis- 

 sible ; since the operation of taking such a dimension as the 

 wake and applying its corresponding correction, would re- 

 quire, perhaps, tenfold the time and trouble required by those 

 operations which this new method is intended to supersede. But 

 if even tabular corrections could be applied consistently with 

 dispatch, the wake, from the difficulty of obtaining it accu- 

 rately, is the most improper element from which to calculate 

 them. The obvious want of analogy between the series of 

 wakes and that of errors given in the Report, sufficiently shows 

 that no table of corrections calculated with the wake can be at 

 all depended upon. If, as I said before, tabular corrections 

 could be admitted, those calculated with the help of the mid- 

 dle diameter between the bung and head would be most to be 

 depended on ; and this dimension would be far more easily 



and 



