It puzzles a stranger to see a good military band--and they are excellent musicians here--play upon their instruments in perfect harmony, and at the same time march out of step or cadence with the music. It would seem almost impossible for one possessing a true musical ear to perform such a trick. With any European or American band, both feet and instruments would get out of accord constantly, or fall into it naturally. Like the king's guard in Hawaii, the troops here parade in white linen or cotton uniforms, stout and unbleached, with a plenty of silvered buttons, the cap being white and of the same material as the rest of the simple costume. At times they appear in a plain uniform of dark blue, but this is on special occasions only, as it is considered to be full dress. The officers are nearly all graduates of the military school at Chapultepec, where the best of foreign teachers are employed in the various departments, so that in future it is confidently expected that the army will be found in a more efficient condition than ever before. The common soldiers, we were told, are composed of rather questionable material. A large percentage of them are criminals released from prison on condition of their enlisting and serving for a certain length of time in the ranks of the regular army. On the caps of those serving out a term of imprisonment in this manner are certain marks indicating the same, as well as showing the length of the prescribed service. Punishment is ever prompt in this country, and despotic methods prevail. Any one attempting to evade his term of service, or breaking army regulations, is very apt to have his business settled by a bullet at once, without even the form of a trial. The department of the cavalry seemed to a casual observer to be much more efficient than that of the infantry. The fact is, the average Mexican is an admirable horseman, and appears better in that capacity than in any other. The national or standing army numbers about forty-five thousand of all arms, besides which each state has a regular militia force, but of a poorly organized character, in most instances, as we were informed, being neither uniformed, nor drilled at regular periods. President Diaz is opposed to the employment of criminals, such as we have described, thinking with good reason that it has a tendency to bring disrepute upon the service. This would seem to be such an unquestionable fact as to admit of no argument.