proposed by Dr. Young. 417 



and accurately taken. But, this new method being modified 

 by discretional allowances, the change would not be attended 

 with any advantages ; for these allowances would be far more 

 difficult to approximate near the truth, and more perplexing 

 to the mind, than those in the present method. 



With respect to the assertion that the new method would 

 be at least as accurate as the old, I would observe that this 

 question can only be decided by experiments on a large scale. 

 But however, since the elements employed in casting the con- 

 tents are (with the exception of the length) the same in both 

 methods ; and the method of casting the middle frustum of a 

 spheroid by the sliding rule is known to be nearly true (it is 

 not accurately true, as I have demonstrated in my small 

 treatise on Cask Gauging) ; it follows that the comparative 

 merits of the two methods rest entirely on the present mode 

 of reducing the length. But the casks, Nos. III. and 9, it' 

 cast by the old method, would each require 9 or 10 tenths of 

 an inch to be allowed in the length, to produce the true 

 contents; and would require 17 or 18 tenths to be allowed to 

 produce the contents as given by the new method; which 

 last, since the casks are port pipes, is an allowance which no 

 gauger in his senses would ever think of making ; though he 

 might not hit exactly upon the first. Similar observations 

 apply to various other casks; and it is therefore only fair 

 to inter that the old method is in general likely to be the 

 most correct. 



I have, with Dr. Young's algebraic theorems, making use 

 of the wake, calculated the content of each of the 21 casks in 

 the table, both by the superior and by the inferior parabolus; 

 and the result tends to confirm my opinion that no depend- 

 ence should be placed on corrections derived from the wake. 



In addition to what has been said, seeing that, could this 

 sliding rule perform all the things proposed, an additional in- 

 strument would be required (for Dr. Young's four lines would 

 occupy the whole face of the rod, and therefore it could not 

 be used as a head-rod), causing thereby a considerable ex- 

 pense to the revenue, and care and trouble to the gauger, for 

 the sake, principally, of shortening an operation which al- 

 together does not, in general, occupy the space of half a 

 minute, — and that, after all, the operation of ullaging will re- 

 main as at present, subject to the settings of the slide, 1 think, 

 on the whole, that the adoption of this new plan of gauging 

 would, instead of being an advantage, be a detriment to the 

 service. I am, gentlemen, 



Your obedient servant, 

 Portland Place, Hull, May 18, 1824. Wm. WlSEMAN. 



Vol.63. No. 314. June 1824. 3G LXIX. Let- 



