6 feet for 6-pdrs.; 14 feet for 12-pdrs.; 18 feet for 24 or 18-pdrs.; four feet of oak or brick will resist cannon shot. 33. What thickness of ice will admit the passage of infantry, cavalry, and artillery? Ice 3 inches thick, will bear infantry marching in file; from 4½ to 6½ inches, cavalry and light artillery; and beyond that the heaviest gun carriages may pass in safety. Ice 8 inches thick will bear nearly 10 cwt. upon a square foot without danger. 34. How is the size of a rope designated? By its circumference: thus, a two-inch rope is a rope two inches in circumference. 35. How is the strength of a hemp rope, or the weight it will support, ascertained? Square the circumference in inches, and divide by 5, for the weight in tons, that it will bear suspended from it. 36. How can the breadth of a river be ascertained without instruments? As follows: [Sidenote: 157]] [Illustration: _Fig. 6_] 1st. The line _AB_ (the distance to be determined) is extended upon the bank to _D_, from which point, after having marked it, lay off equal distances _DC_ and _Cd_; produce _BC_ to _b_, making _Cb_ = _CB_; then extend the line _db_ until it intersects the prolongation of the line _CA_ at _a_. The distance _ab_ is equal to _AB_ or the width of the river. 2d. Lay off any convenient distance, _BC_, perpendicular to _AB_, erect a perpendicular _DC_ to _AC_, note the point _D_ where it intersects _AB_ produced; measure _BD_; then __ _BC_² _AB_ = —————. [3] _BD_ [3] The 2d method was suggested to me by Captain Vogdes, 1st Artillery, U. S. Army. 37. How can the breadth of a river be ascertained by the means of the peak of a cap, or cocked hat? [Sidenote: 158]] Place yourself at the edge of one bank, and lower the peak of the cap, or point of the hat till the edge cut the other bank, then steady your head, by placing your hand under your chin, and turn gently around to some level spot of ground on your own side of the river, and observe where your peak or point of your hat again meets the ground; measure this distance, which will be nearly the breadth of the river. 38. How do you ascertain the distance of an object by means of the tangent scale of a gun, the height of the object at the required distance being known? Direct the line of metal of the gun on the top of the object; then raise the tangent slide till the top of it and notch on the muzzle are in line with the foot of the object, and note what length of scale is required; then, by similar triangles, as the length of the raised part of the tangent scale is to the length of the gun, so is the height of the distant object to the distance required. 39. What composition may be used for greasing the axle-trees of artillery carriages? Hog’s lard softened by working it. If this cannot be procured, tallow or other grease may be used; if hard, it should be melted with fish-oil. 40. What is the simplest method of bursting open strong gates?