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.