99 



enabled to stretch out the same member in feeling for body when 

 none is actually within reach ; and as in the former case the failure 

 of the effort to discover light results in the sensible impression of 

 black or darkness, so in the latter case the effort unsuccessfully 

 aimed at the apprehension of body will take effect on the intelli- 

 gence in the direct cognition or actual experience of space, viz. of 

 that particular portion of space through which the hand is moved in 

 the unsuccessful search after body. 



Thus the notion of space, like that of body, or of any sensible 

 phenomenon, is traced to the actual experience of the thing itself 

 in concrete existence. The subsequent enlargement of the idea, so 

 as to comprehend the space occupied by the solid substance of bodies 

 and that which stretches away to infinity in all directions around us, 

 is duly accounted for on the same principle ; and that impossibility 

 of conceiving the destruction of any portion of space, on which so 

 much stress has been laid as establishing the necessity of a deeper- 

 seated origin than simple experience, is shown to be the natural 

 consequence of the negative foundation of the idea as explained by 

 the analogy of light and darkness. 



April 15, 1850. 



On the Mathematical Exposition of some Doctrines of Political 

 Economy. By the Master of Trinity. 



The object of this paper was to solve algebraically certain pro- 

 blems which have been solved by Mr. J. S. Mill and others by 

 means of numbers, taken as examples ; the principles of these writers 

 being taken for granted in the algebraical solution. Mr. Mill has 

 rightly observed, that instead of saying that prices are determined 

 by the ratio of demand and supply, we ought to say that they are 

 determined by the equation of demand and supply. This equation 

 may be thus stated. Let p be the price, and q the quantity bought 

 and sold at that price. When p becomes p', let q become q' ; and p' 

 being equal to p(l+n), let p'q'=pq(\ -\-mn) : this is the equation 

 of demand and supply. For different commodities, we have different 

 values. There are such classes of commodities as these : (A.) Con- 

 ventional necessaries, for which m=. 1 : of these the same quantity is 

 bought whatever be the price. (B.) Articles of fixed expenditure, 

 for which m = 0: on these the same sum is always expended, a 

 smaller quantity being bought in proportion as they are dearer. (C.) 

 Common necessaries, in which m is between 1 and : in these, when 

 the price falls, the consumption is increased, but the money ex- 

 pended diminished. (D.) Popular luxuries, in which m is negative : 

 in these, when the price falls, the consumption is so much increased 

 that the money expended on them is increased also. For corn, the 



mean value of m seems to be about - : on this supposition a failure 



of one-fourth in the supply would double the price. The quantity 

 m measures the susceptibility of the price to change when the supply 

 changes, and also the intensity of the demand. 



