CHAPTER XXI.
The French army lay before a fortified place near the Rhine, which we will call Philipsburg.
This army knew Bonaparte by report only; it was commanded by generals of the old school.
Philipsburg was defended on three sides by the nature of the ground; but on the side that faced the French line of march there was only a zigzag wall, pierced, and a low tower or two at each of the salient angles.
There were evidences of a tardy attempt to improve the defences.

In particular there was a large round bastion, about three times the height of the wall; but the masonry was new, and the very embrasures were not yet cut.
Young blood was for assaulting these equivocal fortifications at the end of the day's march that brought the French advanced guard in sight of the place; but the old generals would not hear of it; the soldiers' lives must not be flung away assaulting a place that could be reduced in twenty-one days with mathematical certainty.

For at this epoch a siege was looked on as a process with a certain result, the only problem was in how many days would the place be taken; and even this they used to settle to a day or two on paper by arithmetic; so many feet of wall, and so many guns on the one side; so many guns, so many men, and such and such a soil to cut the trenches in on the other: result, two figures varying from fourteen to forty.

These two figures represented the duration of the siege.
For all that, siege arithmetic, right in general, has often been terribly disturbed by one little incident, that occurs from time to time; viz., Genius INside.

And, indeed, this is one of the sins of genius; it goes and puts out calculations that have stood the brunt of years.