Which of these three kinds was the first invented?

It is impossible, at the present day, to decide which; but it is most probable that instruments with strings were the last invented of the three kinds; and it is most likely, that of those in which sound is produced by the application of wind, the trumpet or horn was first used.  This instrument, in its rudest form, was ready fashioned to the hand of man; the horn of a ram or of an ox, or some of the larger kinds of sea-shells, were soon discovered to possess the power of producing sound, by being blown into through a small hole at the pointed end.

What improvement in this instrument would naturally follow?

Mankind having discovered the property possessed by a hollow tube of producing a certain sound, soon found that the note varied according to the length and capacity of the tube.  A much greater improvement soon after took place; it was discovered that one tube answered the purpose of many by boring holes in the course of its length, and producing various musical sounds by stopping with the fingers certain of these holes.  Most of our modern wind instruments are but improvements on the ancient inventions.

     Tube, a pipe; a long hollow body.

Was not Vocal Music used before the invention of Instrumental?

Vocal music, namely, that produced by the human voice, (so called to distinguish it from instrumental, that produced by instruments,) was undoubtedly the first:  for man had not only the various tones of his own voice to make his observations on, before any art or instrument was found out; but the various natural strains of birds to give him a lesson in improving it, and in modulating the sounds of which it is capable.

     Modulating, forming sound to a certain key.

To what circumstance did an ancient poet ascribe the invention of stringed instruments?

To the observation of the winds whistling in the hollow reeds.  As for other kinds of instruments, there were so many occasions for cords or strings, that men were not long in observing their various sounds, which might give rise to stringed instruments.  Those of concussion, as drums and cymbals, might result from the observation of the naturally hollow noise made by concave bodies when struck.

What are the most ancient stringed instruments?

The most ancient instruments of this kind, whose form is known, are those of the ancient Egyptians; among these the harp stands pre-eminent.  One of the most celebrated representations of an Egyptian harp was drawn from a painting discovered in one of the caverns in the mountains of Egyptian Thebes, by some travellers:  it is called the Theban harp, and has thirteen strings; its form is extremely elegant.  This harp is supposed to be one of the kind in use before and at the time of Sesostris.  Remains of Egyptian harps of a more simple construction, with only four strings, have likewise been discovered.  Among the monuments of ancient Rome, there are representations of stringed instruments resembling the harp, but not equal in beauty of form to the famous Egyptian harp already mentioned.