The Continental navy next in present interest to that of France is the Italian, owing to the fact that the Italian government, although largely abstaining from the use of armor, has applied itself urgently to developments of gun-power and speed in large war-ships. The _Duilio_ and _Dandolo_ (illustrated on page 105) were considered in the chapter on the French navy, and their resemblance to the _Inflexible_ type pointed out. They are nearly as large as the _Inflexible_, although differing greatly in proportions and form from her. They appear to me to be more objectionable, from the want of armored stability, if one may so speak, than even the _Ajax_ and _Agamemnon_, which are themselves, as we know, more objectionable than the _Inflexible_. The cause of this is to be found in the fact that in designing the British ships, whatever else they may have lost sight of, the Admiralty constructors saw that the more you contracted the length of the armored citadel, the more necessity there was for giving the ship great breadth. The reason of this can be made clear. The fractional expression which represents the statical stability of a ship has in its numerator the quantity _y^3x_, in which _y_ represents the half-breadth of the ship at the water-line, and _x_ the length of the ship. If we regard the stability of the armored citadel only, and neglect the unarmored ends, _x_ represents the length of that citadel, and _y_ its half-breadth. Now if we take two rectangular citadels, one, say, 100 feet long and 60 feet broad, the other the same length, but only 50 feet broad, then the value of _x_ will be the same for both, but the values of _y^3_ will be 216,000 and 125,000 respectively, the ship 60 feet broad having, _cæteris paribus_, nearly double the citadel stability of the 50-feet broad ship. On the other hand, if you wish to give the narrower ship the same citadel stability as the broader one, it will be necessary to make her citadel no less than 172-8/10 feet long. Now the citadel of the _Duilio_ is 107 feet in length,[31] and the breadth is 64 feet 9 inches—say 65 feet. The citadel of the _Inflexible_ is 110 feet long, and its breadth 75 feet, the figures for the _Ajax_ being 140 feet and 66 feet. Now presuming the citadels to be rectangular in each case, we shall have, Inflexible _y^3x_ = 618,750 Ajax _y^3x_ = 453,024 Duilio _y^3x_ = 452,075