An American base--say at Guantanamo--would be very effective in embarrassing hostile operations _west_ of Guantanamo, because it would be on the flank of the line of communications extending from Europe; but it would be comparatively ineffective in embarrassing operations east of it, since the hostile line of communications would be protected from it by the interposition of its own main body; this interposition necessitating the despatch of defending forces around that main body. The coming hostile force would push before it all resistance, and leave the sea free for the passage of its auxiliaries and supplies. A defending force, operating from Guantanamo, in endeavoring to prevent a hostile fleet from establishing a base to the _eastward_ of it, would act much less effectively than a force operating from Culebra. Not only would the force from Guantanamo have to pass around the main body to attack the train; it would again have to pass around the main body to get back to Guantanamo; whereas a force operating from Culebra could make a direct attack upon the enemy's train, and then a direct retreat to Culebra. This comparison assumes, as has been said, that the matter of resources and strength are not in question; that is, that they are equal in our two supposition bases. But, as in practice they would not be equal, the practical point to consider is how much strength and resources can compensate for inferiority of position, and how much position must be insisted on. Of course, no correct quantitative answer can be given, except by accident. The problem, unfortunately, cannot be solved by mathematics, for the simple reason that no quantitative values can be assigned to the various factors, and because no mathematical formula now exists that expresses their relations to each other. It may be pointed out, however, that if a position be good, strength and resources can be artificially supplied; and that the cost of doing this, even on a tremendous scale, is relatively small compared to the cost of the fleet which the base will support, and in distress protect. In other words, we may be able to form an estimate of the relative values of bases, say at Guantanamo and Culebra, even if we cannot ascribe arithmetical values to each, and compare arithmetically those arithmetical values. If, for instance, we see that a fleet costing $500,000,000, would, if it operated from a base at Culebra, be 10 per cent more effective than if it operated from Guantanamo, and that it would cost $20,000,000 more to make a strong base there than to make an equally strong one at Guantanamo, we should conclude that, since 10 per cent of $500,000,000 is $50,000,000, it would be wise to spend that $20,000,000, even if we had to forego the building of one battlesbip.