Military power depends on logistics and global reach

Which country had the third-best military at the time?

It depends on whether the measure is size or global reach; logistics, carriers, and expeditionary support can produce a different ranking from raw force totals.

There is no useful third-place ranking until the criterion is defined. A large regional force and a military able to deploy globally are different measures. The answer places the United States first for reach, treats China as a growing second whose overseas logistics were still developing, and compares Britain and France through carrier availability and expeditionary capacity. Hull counts or personnel totals cannot substitute for bases, transport, sustainment, and deployable aviation.