It is a difficult matter to find a basis of comparison of the strength of the world's navies which will give satisfactory results. There are so many elements that affect naval efficiency, and the military value of these elements differs so widely, that it is simply impossible to make a comparison based upon any one of them, which will give a reliable result. A mere statement of the total number of ships in each navy will not suffice, since these ships vary in size, speed, armor, and armament. It has been claimed that a comparison based on the total number and weight of guns carried would suffice; but the value of a gun depends greatly upon the character of the ship which carries it, the kind of mount upon which it is placed, the degree of armor protection, and so forth. Because of these modifying conditions, a 12nch gun in one ship may expect to have two or three times the battle-life and efficiency of a 12-inch gun in some other ship. Nor will a comparison on the basis of armor protection suffice; for a fleet which is powerful only in its defensive qualities, and in which the area and thickness of its armor plating has been increased at the expense of the armament and the speed, would be wanting In that mobility and power to swiftly concentrate and deliver a telling blow at the critical moment, upon which the success of a naval campaign so greatly depends. So also, a comparison on a basis of speed would be misleading; for high speed is one of the most costly elements in a warship, costly in the large demands which it makes upon displacement, and it is a fact that, unless the size of the units be very large, unusually high speed in warships is always associated with limited gun power and inadequate protection. A f'.eet of exceedingly fast, but moderately-armed and moderately-protected ships, might sweep the seas of the smaller unprotected cruisers and the general seaborne commerce of an enemy; but it would be powerless to force the issue by a decisive line-of-battle engagement. Then, lastly, and perhaps most important of all, there is the question of age. We do not recall any product of human industry which, as the years go by, depreciates so rapidly in value as the warship; and the most elaborate estimate of the relative value of the fleets of the world is not worth the paper it is written on, unless the question of the age of the ships be most carefully considered. Warships built to-day have at least twice the value of those built ten years ago, and from four to six times the value of those built twenty years ago. Great Britain awoke to this fact and acted upon it in the most trenchant way, when she swept over one hundred warships off the list, and placed them under the auctioneer's hammer. For some years past the SCIENTIFIC AMERICAN has claimed that the only true basis of comparison of naval strength is one based upon total displacement, modifled by considerations of age. Unless there be glaring faults in the design, a ton of displacement in one ship iE> worth about as much as one ton in another ship of the same class and date. The profession of naval architect is one of the most expert in the world, and it is represented by an exceedingly able body of men. Let three leading architects—English, French, and American—compete in the design of a battleship of given displacement, and though the ships may differ in details, the total fighting value will be about the same for all three. It must be admitted, however, that the enormous value given to the heavy, long-range, armor- piercing gun by the results of the Japanese war, has called for a modification in the above method of comparison. If the present popular theories are correct, the navy which can place on the shortest battle line the largest number of 12-inch, or other heavy pieces of modern design, is certain to win the fight; and an estimate of the strength of the navies on this basis will greatly modify the results obtained on a basis of displacement and age only. We give elsewhere the results of a comparison in which is included no gun that is not able to pierce heavy armor at 5,000 yards range, and which includes no piece in the respective guns below the 50-caliber 9.2-inch gun, the 45-caliber 10- inch, the 40-caliber modern ll-inch, the 35-caliber 12- inch, and the 35-caliber 13-inch and 13%,-inch. This reservation excludes from the table all the battleships of the “Royal Sovereign” class of the British navy; the “Iowa,” whose 12-inch gun has only about 2,000 foot- seconds velocity, in our navy; all the battleships of the “Wittelsbach” and “Kaiser Friedrich III.” classes of the German navy, which carry an old model 9.4-inch gun, and those of the “Brandenburg” class, mounting an old model 11-inch. The result shows that England can place in the battle line 292 heavy armor-piercing guns; that France is second with 160 such guns; the United States third with 144 guns; and Japan and Gerny are equal, each with 118 guns. This comparison takes in all the ships authorized, under construction, and already built. The large number of heavy guns carried in the Japanese navy in proportion to displacement shows how they are applying the lessons of their own war.