147 



the profit would therefore be £1 ll^. 2d., leaving a balance 

 in favour of smelting the ore by the blast-hearth of 6s. 3d. 

 per ton of ore, or an increased profit of nearly 17 per cent. If 

 Mr. Sadler's estimate be adopted, the balance would be three 

 times this sura. 



" On the whole, I think it fair to conclude that the rever- 

 beratory furnace makes larger returns of lead ; that where the 

 produce of ore is inadequate to the supply of a reverberatory 

 furnace, or where the cost or carriage of fuel and other mate- 

 rials is high, the blast-hearth is not without its advantages ; 

 that it is in vain to inquire, in the abstract, which is the more 

 profitable furnace, as the decision of the question entirely de- 

 pends on the circumstances of the locality." 



April 24th, 1848. 



REV. HUMPHREY LLOYD, D. D., President, 

 in the Chair. 



The Rev. Charles Graves made a communication respecting 

 Mathematical Expressions for Hypothetical and Disjunctive 

 Propositions. 



Adopting the principles and notation furnished by Mr. 

 Boole in his " Application of Analysis to Logic," Mr. Graves 

 suggests that it would be more in accordance with the ordi- 

 nary use of language to express the hypothetical proposition, 

 If A' be true, Y is true, 



by the equation 



x = vy, (I) 



than by that which Mr. Boole has employed, viz. 



^(i-y) = o. (2) 



In the former of these equations the symbol x selects all 



the cases in which the antecedent A' is true, whilst y selects 



N 2 



