132 Dr. WHEWELL, ON THE MATHEMATICAL EXPOSITION OF 



Hence it appears that when m is very nearly equal to I, a small increase in the quantity 



supplied, ( — , — , — , J will produce a large diminution in the price ( — ,-,-). In such 



cases we may say that the price is very susceptible of change, (by alteration of the supply), 

 and since, as m is larger, this susceptibility is greater, we may take m to measure the suscepti- 

 bility of change of price of each commodity. 



15. But if we consider the demand as varying with the price, it is evident that for a given 

 increase of price, a greater increase of money demand indicates a stronger effectual demand : 

 and as this is greater according as m is greater, m may measure the strength of demand for 

 each commodity, as shewn when the price changes. 



16. We may include these two ways of regarding m, by calling it the specific rate of 

 change of each commodity ; meaning thereby, both the change of price when the supply varies, 

 and the change of demand when the price varies. 



17. For an example of the value of m, we may take data given by Mr. Tooke {High 

 and Low Prices, p. 285). He says that to diminutions in the supply of corn we have correspond- 

 ing augmentations of price, in the following proportion : 



12 3 4 5 



Diminution of supply — , — , — , — , — ; 

 rr J 10 10 10 10 10 



„ . 3 8 16 28 45 



Increase of price — , — , — , — , — . 



r 10 10 10 10 10 



Now if we take m = - , we have the following correspondencies : 



12 3 4 5 



Diminution of supply — , — , — , — , — ; 

 rr/ 10 10 10 10 10 



t * ■ H 6 3 15 40 • - • 



Increase of price -» , -« , — , — , infinite. 



r 10 10 10 10 



For a deficiency of supply of one-half, the prices would be infinite. This shews that the formula 



with the value m = -, is not applicable for so great a deficiency of supply : but upon the whole, 



m = - , appears to be near the value of the specific rate of change for corn. 



1 3 17 



If we take the diminution of supply = — , and increase of price = — , we have m = — . 



rr-7 10 r 10 30 



5 . 45 7 



If we take the diminution of supply = — , and increase of price = — .we have m = — . 



r * J 10 ^10' 18 



The former is greater than - , the latter is less than - *. 



2 2 



" It appears that when the diminution of supply is small, I is nearly one-half, the value m = % is too large. Therefore the 

 the value m = J is too small, and when the diminution of supply | function pq(l+mx) is not really the true formula of the 



