I 



that the generally-received Rule of Malcolm is not correct. 271 



equated time is owing to the very assumption made in it, which 

 directs us to find the " time when the interest of the debt kept 

 after it is due from its term to the equated time shall be etiual 

 to the discount of the debt, for the time it is paid before due/' 

 But here this time (which is so restricted as to agree in such 

 particular respect) I contend is arbitrarily assigned by our own 

 express convention ; so likewise is the principle; neither of which 

 arises out of the known and obvious conditions involved as well 

 as aimed at in both the rules (if they did, then the rule would be 

 strictly correct), viz. " that the gain and loss being equal, neither 

 party can sustain injury." For as well might we change the 

 principle above, assuming as another the converse of it, and then 

 investigate a rule for such case accordingly. But as to the truth 

 of what is contained in the foregoing inferences, I shall further 

 proceed in an attempt to establish by the solution of a practical 

 example agreeably to both rules : and so as to abridge the resulting 

 process, I shall introduce the case of two payments only; since, 

 according to the principle on which the common rule depends, 4f 

 it can he proved to be the true rule for two payments, it must 

 necessarilv be so for n. payments. A owes B 205/. 100/. to be 

 paid one year and 105/. three years hence: required the equated 

 time to pay the whole. First by the common rule. 



100x1 = 100 



105x3 = 315 



205 205-T-415 = 2^'-j- years the equated time. 



203 + (100. x05x2)=215--(100. x05.x2) = 21-5 



(21-5^-42)^=420-25^ = 20-5 



21"5— 2()-5 = l year from the first pay- 

 ment, or two years the equated time. 



Now according to the first solution neither party will be the 

 loser : it is therefore obvious this circumstance cannot arise from 

 the latter. Hence resuming the question under a different form of 

 calculation by allowing the true proportion of discount only ; 

 let us observe how the result accords with that just obtained. 



When the time for the fir^t payment arrives, let it be sujiposetl 

 that A chooses to make them both: then if a. is the first debt, and 



Z'. the second, (c/+ will be the sum to he paid down, or 



^ I +rl ' 



■ the discount to be allowed. In this view of the question, 



then, it is jjlain that B will not sustain a loss ; for ihi? is a cir- 

 cumstance on his part wc ought not to lose siglit of any more 

 than that of A. Now whether A adjusts the payment in tliis 

 manner, or retains the sum L until the period it is (Ino, is equ illy 

 iudlfferent j as it is certain when that auivcs he will be in pos- 



scsaiun 



