the Strengths and Values of Spiiituous Liquors. 337 



FUthly, 



'•245881 f '35127 = the proportion by 



weight oi' 127 

 1 . o J •21272 = that of 1 16 



x:-91498:<j -07177 =: that of each of 

 those of 102 and 87 

 17745 = that of C7. 



= '39491, the proportion by measure of 



•e4017:< 



And 



•16990 

 •05 024 



•12421 



•?:;t27 

 •8iiy+8 



•9°47 3 

 •07177 



127 (or 27 O.P.) 

 = -26828, that of 116 (or 16 O.P-) 



'orm _ .07781^ that of 102 (or 2 O.P.) 

 •91239 



•07177 



•93954- 



•17^4 



= -07639, that of 87 (or 13 U.P.) 



iI-1: = -18517, that of 67 (or 33 U.P.) 



But these making 1-00256, the concentration by mixture 

 15 therefore -00256 of the whole ; and, multiplying each of 

 these by the required quantity, 774 gallons, we get 

 305- 66 Vallons for the requisite quantity by measure of 127 



■^ (or 27 O.P.) 

 207-65 eallons for that of 1 16 (or 16 O.P.) 



60-23 gallons for that oF 102 (or 2 O.P.) 



59-13 gallons for that of 87 (or 13 U.P.) 

 143-33 gallons for that of 67 (or 33 U.P.) 



776. gallons in the whole, composing after the mixture 

 the 774 gallons required; the concentration in this case 

 being exactly 2 gallons. 



It will easily be perceived, that, when the proportions of 

 more than two of these different kinds of spirit arc undefined, 

 as in the preceding question, the problem admits of many 

 answers, and the quantities of each kind of liquor may ac- 

 cordingly be variously proportioned. 



A variety of other problems may be proposed and solved 

 by means of these tables, which the mathematician will 

 sufgest to himself without any difficulty. 1'here is, in facl, 

 lu/ possible question respecting these matters, of whicii, 

 with the pro|.er application of arithmetic or algebra, we 

 mavnot liere find the solution. Tlie authors of this essay 



Vol. XVII. No. C8. Y conccivt 



