When Exchange is thus arrested from ceasing to be advantageous, the slightest improvement in the ‹commercial apparatus› gives it a new activity. Between Orleans and Angoulême a certain [p113] number of transactions take place. These towns effect an Exchange as often as they can obtain a greater amount of enjoyments by that means than by direct production. They stop short the moment the cost of obtaining commodities by means of exchange, aggravated by the cost of effecting the exchange itself, surpasses, or reaches, that of obtaining them by means of direct production. In these circumstances, if we improve the conditions under which Exchanges are effected—if the merchants’ profits are diminished, or the means of transport facilitated—if roads and railways are made, mountains levelled, and bridges thrown over rivers—in a word, if obstacles are removed, the number of Exchanges will be increased; for men are always desirous to avail themselves of the great advantages which we have ascribed to Exchange, and to substitute gratuitous for onerous utility. The improvement of the ‹commercial apparatus›, then, is equivalent to bringing two cities locally nearer to each other. Whence it follows that bringing men physically, locally, nearer each other is equivalent to improving the conditions of exchange. This is very important. It is, in fact, the solution of the problem of population; and this is precisely the element in that great problem that Malthus has neglected. Where Malthus saw Discordance, attention to this element enables us to discover ‹Harmony›. When men effect an exchange, it is because they succeed by that means in obtaining an equal amount of ‹satisfaction› at a less expense of ‹effort›; and the reason of this is, that on both sides services are rendered which are the means of procuring a greater proportion of what we have termed ‹gratuitous utility›. Now, you have always a greater number of exchanges in proportion as you remove the ‹obstacles› which impede exchanges, and diminish the ‹efforts› which these exchanges exact. And Exchange encounters fewer obstacles, and exacts fewer efforts, just in proportion as you bring men nearer each other, and mass them more together. A greater density of population, then, is accompanied by a greater proportion of ‹gratuitous utility›. That density imparts greater power to the machinery of exchange; it sets free and renders disposable a portion of human efforts; it is a cause of progress. Now, if you please, let us leave generalities and look at facts.