CONJOINED PROPORTION. 1^9 



ID. If 248 men, in 5 days of 11 hours each, dig a 

 trench 230 yards long, 3 wide and 2 deep *, in how many 

 days of 9 hours long, will 24 men dig a trench of 420 

 yards long, 5 wide and 3 deep ? Ans. 288-^^. 



i 



CONJOINED PR^OPORTION. 



Conjoined Proportion is when the coins, weights, or 

 measures, of several countries are compared in the same 

 question ; or it is the joining together of several ratios, 

 and the inferring of the ratio of the first antecedent and 

 the last consequent from the ratios of the several antece- 

 dents and their respective consequents. 



Note i. The solution of questions, under this rule, 

 may frequently be much shortened by cancelling equal 

 numbers, when in both the columns, or in the first column 

 and third term, and abbreviating those that are commens- 

 trable. 



Note 2, The proof is by so many statements in the 

 single rule of three, as the nature of the question requires, 



CASE I. 



Jf^hen it is required to find how many of the last kind of coin, 

 iveight, or measure, menfmied ifi the question^ are equal tj a 

 given number of the first, 



RULE. 



1. Multiply continually together the antecedents for the 

 first term, and the consequents for the second, and make 

 the given number the third. 



2. Then find the fourth term, or proportional, which 

 will be the answer required, 



EXAMPLES. 



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