ALLIGATION ALTERNATE. 



M3 



•1. Connect or link with a continued line the rate of each 

 simple, which is less than that of the compound, with one 

 or any number of those, that are greater than the com- 

 pound •, and each greater rate with one or any number cf 

 the less, 



3. Write the difference between the mixture rate and 

 that of each of the simples opposite the rates, with which 

 they are respectively linked. 



4. Then if only one difference stand, against any rate, it 

 will be the quantity belonging to that rate ; but if there 

 be several, their sum will be the quantity. 



EXAMPLES. 



1. A merchant would mix v/ines at 14s., 19s. 15s. and 

 22s. per gallon, so that the mixture may be worth i8s. the 

 gallon : what quantity of each must be taken ? 



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18^ 



2. How much wine at 6s. per gallon and at 4s, per gal- 

 lon, must be mixed together, that the composition may be 

 worth 5s. per gallon ? 



Ans. 1 2 gallons, or equal quantities of each. 



3. How 



also the double or treble, the ^ or |- part, or any ^ other ratio of 

 these quantities, and so ou, ad infinitum, 

 \ Questions of this kiad are called by algebraists indeterminate or 

 unlhniied problems, and, by ?.n analytical process, theorems may 

 be raised, that will ^ive all the pcsslbU ao5\vers. 



