242 On the proposed Alteration 



An ingenious revenue officer, Mr. J. Overley (by fur the 

 most scientific author who ever wrote in England, as to 



Sauging in particular), states that, according to Ward's Young 

 lathematician's Guide, a spheroidal cask having 31*5 and 

 2^'5 inches for the bung and head diameters respectively, and 

 42 inches for the length, will contain 100"78 gallons of English 

 ale measure. 



In the 1 03d page of the work, he has shown the method to 

 construct a gauging instrument, called a diagonal-rod. 



He states that " this line is constructed tor a cask whose 

 content is 60 ale gallons, and the diagonal thereof 30 inches ; 

 therefore the proposition holds : 



" As 60 is to the cube of 30, so is any other content to the 

 cube of the diagonal" 



Now, gentlemen, I shall undertake to prove that those casks 

 were not both the frusta of the spheroid ; and, as that is the 

 sort of cask fi-om which all gangers draw their conclusions, 

 that the diagonal rod is very considerably in error. My let- 

 ter in your Magazine for August 1818 furnishes me with 

 abundant reason for scepticism ; and I am aware the author 

 took this matter upon trust from Oughtread, who indeed was 

 no mean authority, Tlie theoiy is perfectly true if applied to 

 Ward's cask. The object of this rod is to ascertain the con- 

 tent of any cask. The operation is as follows: — Through tire 

 orifice in the middle of the staff pass the rod, until it meet the 

 intersection of the opposite staff and the head; then just in 

 the centre of the orifice will stand the content of the cask, 

 upon the rod, among a scale of unequal graduations engraven 

 upon it; which graduations result from a tarif formed fi'om 

 the analogy before given ; and since homologous solids are to 

 one another as the cubes of their dimensions, we have a me- 

 thod of proving the justice of my disapproval of the rods now 

 used, which I discover to liave been uniformly constructed 

 from the erroneous cask selected by Oughtread ; if, indeed, he 

 ever applied to a cask at all ; which I have abundant reason to 

 suspect he never did. For it could not have been either of 

 ihejirst, second, or third variety ; but ratlier the frusta of two 

 cones abutting upon one common base ; and which is such a 

 cask as is only known in theory. 



The annexed engraving will be explanatory of the subse- 

 quent exphcations, where 



The length =bg = 42 inches. 

 The bung diam. = cf= 31 '5 inches. 

 The head diam. = ah = 24'5 inches. 



The half length = Zir/ = 21 inches, or base of a triangle, 



of 



