The Indian grammarians who devised this complete and scientific system must have had ears almost as sharp as those of the boy in the old story who was said to be able to hear the grass growing. They distinguished between a number of consonants containing a sound of N,—between "twangs" very slightly differing in sound; and they placed them also in the order of their utterance, beginning with an N uttered from the throat and ending with one spoken with the tongue close to the lips. Our language has two or three different N sounds, but our alphabet does not distinguish them. The French language also has several N sounds not indicated by the alphabet, so that one can not hope to speak French intelligibly, still less accurately, without practice with teachers who can render the different N sounds. The Spanish alphabet tries to indicate a second N by putting a mark over the N—thus, Ñ. Then, too, we have three sounds for which our alphabet has but one letter, S; while the Sanskrit alphabet has three letters, one for each sound of S. In the alphabet, as in many other matters, the more enlightened nations of India put to shame the most advanced nations of the Western World.

Did you ever notice how, in our script, or written characters, for the sake of clearness and to keep some letters distinct from others, we have gradually come to write some of them with tall heads above the upper line, or with long tails below the lower line? And still we are constantly mistaking an l for a badly crossed t, and a g for a j or a y; while some letters that do not go above or below the line, such as m, n, i, w, u, and r, are constantly confounded in rapid writing. We are so used to this confusion that we seldom think of it, and we fail to wonder why some arrangement is not generally agreed to, which would do away with it. By remembering this fact, you will avoid the mistake of thinking because our alphabet, written or printed, is so good, that it could not be better. There is great room for improvement in both departments; in the printed form, the difference between n and u, for instance, is none too great; while in writing hardly one person in ten thousand distinguishes them from each other,—which letter is meant must be guessed by the reader. But the men and women who set up type and correct proofs are much bothered by these defects in our alphabet.

The difficulty of having changes made in existing alphabets is very great, yet this is not necessarily a disadvantage. Much insight into the origin and gradual improvements of sets of letters has been gained by studying the order in which the several letters stand. The order varies greatly in different nations, and varies slightly at different epochs in the same nation. In taking the Phœnician letters, the Greeks dropped some, used others for slightly different sounds, and added a few to express sounds that were important to them or that did not exist in the Phœnician. But this was done very gradually. It never has been easy to induce people to change and improve their alphabets.

But there is another reason why men have refused to change the order of letters by inserting a new and useful letter in the place where it naturally belonged. The Greeks and many other peoples used the letters of the alphabet for numerals. We use our own numbers without stopping to think whence they came. The cumbersome system used by the Romans, and called after them, consisted of strokes (I-II-III-IIII) to indicate the four fingers, and two strokes joined (V) to represent the hand, or five fingers. Ten was a picture of two hands, or two V's (X). Among the Etruscans the half of one, or, as we put it, ½ was >, which we think stood for a forefinger crooked in order to denote the half of one finger. But when the Etruscans and Greeks worked at the higher mathematics or attempted hard sums in arithmetic, they are much more likely to have used letters, in order to avoid the clumsiness of these numerals; in other words, they used what looked like a kind of algebra. We know that they tried to simplify the Roman numerals at Rome by making four and nine with three strokes instead of four, by placing an I before the V and an I before the X (IV and IX).

Our use of the numerals which we call "Arabic" is comparatively recent, and it is believed that the Arabs got these numbers from India several centuries after the Koran was written, or about eight hundred years after Christ. But the fact that the Greeks and others used the letters of their alphabets for numerals, caused the order in which they were written to remain fixed. If alpha stood for 1, beta for 2, gamma for 3, delta for 4, and so on up to ten, then a newly coined or newly adopted letter could not be inserted without great confusion; it had to be tacked on to the end of the alphabet. So, when scholars find in inscriptions letters, adopted from another alphabet, which stand out of their natural order, they can make a shrewd guess at the century in which the inscription was made. Suppose an alphabet, which is also used for numerals, loses a letter in the course of time, because there is very little or no use for it; then that letter is still of service for a numeral, and it can not be dropped as a number, though it drops out as a letter. When it is found still employed as a numeral, it reveals some of the history of the alphabet to which it once belonged. These are only a few of many methods of determining the age of a given inscription. Old coins are very useful in settling what the alphabets of various nations were at different epochs.

Our own numerals are extremely convenient for ordinary arithmetic. Algebra, in which letters stand for numbers, is useful for abstract reasoning in mathematics; it treats of the properties of numbers in general. Whether the Indian numerals were originally part of some ancient alphabet, or a series of shortened signs originally somewhat like the Roman numerals that we still use, is not really decided.

There was a curious fashion among certain grammarians and mathematicians of Old India which may be mentioned here. They liked to increase their own importance by making knowledge hard to attain; as it imposed on their pupils, and even more on the outside world. They also wished to exercise the memories of their pupils, and keep them mindful of certain numbers and dates by means of memorizing words. In works on arithmetic and prosody, they deliberately wrote out long words which meant nothing if looked at as parts of a sentence, but stood for so many numbers if the reader had the clew. If such a grammarian wished to write the number twelve by this method, he would write down "moon, eyes"; because there is one moon and two eyes. If he wished to signify the number 1486, he would write "moon, seas, mountains, seasons"; because in India people believed that in the world there were one moon, four seas, and eight mountain chains, and six seasons during the year. So ingenious were they in hiding plain things under an artificial system! The priestly rulers of Egypt, also moved by pride and the desire to seem learned, began at a remote period to make the hieroglyphics as hard as possible to understand. For a given word they would always choose as little known and seldom used a character as they could think of. And doubtless this did render them objects of greater reverence in the eyes of pupils and of common folk.

But to return to the numbers that we call Arabic and the Arabs call Indian. The numbers used by the peoples of India who wrote in Sanskrit were very like the figures 1, 2, 3, 4, 5, 6, 7, 8, 9, and 0, that we use to-day. Even closer resemblances will be found if one goes back to the earliest forms of our numerals; for, during the last thousand years, our numbers have undergone some slight changes. We took them, as you have heard, from the Arabs, who did not employ them much before 800 A. D.; and the use of them did not penetrate into Europe by way of Italy and Spain until four centuries later. Together with these numerals, the Arabs learned from India how to do sums by algebra. For algebra, though an Arabic word, is a science of which the Arabs were ignorant before they reached India. How long the Indians of Hindostan had used this system of notation along with their alphabet, we can not yet determine; but it is quite possible that the old grammarians who improved the Sanskrit were enabled to fashion its alphabet into so scientific an order of groups because this separate system of numerals existed at even a more remote period, and had been found handier than the signs of the alphabet. Not using their letters as numerals, they could marshal them on the best system they were able to devise, as we, too, have been able to do with our alphabet ever since we got the Indian numerals from the Arabs.

It may be said that the invention of these numerals and of algebra for the higher mathematics stamps the old Hindoos as one of the most wonderful races of the world.

(To be concluded.)