Events were soon to reveal the seriousness of this mistake. It was far more important to strike at Paris through Brittany than to occupy even the richest of the French West Indies. For a triumphant advance of the Bretons and Vendeans must not only have lessened the material resources of the Republic but also have deprived its defenders of one of their chief advantages. Hitherto the Republicans had been better massed together, while their assailants were spread over wide spaces. It is a well-known principle in war that an army operating on an inner arc, or what are termed interior lines, has a great advantage over forces spread over the outer circumference. The Allies then held the Pyrenees, the Maritime Alps, the Rhine, and most of Flanders, Brittany, and parts of the South. The defenders, possessing the central provinces, could mass their units far more quickly and choose the point on that outer curve against which they would aim their blow. This principle was thoroughly understood by Carnot. Near the centre of the circle he massed the levies that were to save the Republic, and, confiding them to zealots who were resolved to conquer or die, he soon had on foot armies which, however contemptible as units, were formidable from their weight and their enthusiasm. As in mechanics the mass multiplied by the speed gives the effective force, so in the campaign of 1793 the _levee en masse_ multiplied by enthusiasm and impelled by the brain power of Carnot begot a momentum which, when brought to bear on light, scattered, and almost stationary bodies, proved to be irresistible. For while Carnot trusted to concentration, the Allies either sank into inertia, or made ex-centric movements which ultimately played into their opponents' hands. The Prussians, after taking Mainz, did little more than rest on their laurels, their only move being towards Luxemburg. Coburg was inclined to follow their example on the ground that an advance to Paris would unite all the French parties against him, while the siege of the remaining fortresses in the North would allow anarchy to run riot at the centre.[229] The argument is a good example of political _finesse_ applied to a military problem, with disastrous results. Coburg therefore set about the siege of Quesnoy.