[Footnote 23:  It is distinctly proved by President Goguet, that the course of the moon, and her various appearances, served mankind in general, in the first ages, for the measurement of time.  What is here said of the Otaheitans confirms his observations.  We are told too, in another work, that the natives of the Pellew Islands reckon their time by months, and not by years; in which, however, we see they are inferior to the former as to extent of science.  Now there are two sorts of lunar month, called in the language of astronomers, synodical and periodical; the first is the time from new moon to new moon, consisting of 29 days, 12 hours, 44 min. 3 seconds, which is the month most commonly used by the early observers; the second, consisting of 27 days, 7 hours, 43 min. 5 seconds, is that portion of time which the moon takes to finish her course round the earth.  Neither of these multiplied by 13 will make up the solar year exactly.  In what manner then the Otaheitans reckon, it is not easy to comprehend.  The probability is, that they have no notion of the periodical month.—­E.]

In numeration they proceed from one to ten, the number of fingers on both hands; and though they have for each number a different name, they generally take hold of their fingers one by one, shifting from one hand to the other, till they come to the number they want to express.  And in other instances, we observed that, when they were conversing with each other, they joined signs to their words, which were so expressive that a stranger might easily apprehend their meaning.

In counting from ten they repeat the name of that number, and add the word more; ten, and one more, is eleven; ten, and two more, twelve; and so of the rest, as we say one-and-twenty, two-and-twenty.  When they come to ten and ten more, they have a new denomination, as we say a score; and by these scores they count till they get ten of them, when they have a denomination for two hundred; and we never could discover that they had any denomination to express a greater number:  Neither, indeed; do they seem to want any; for ten of these amount to two thousand, a greater number than they can ever apply.[24]

[Footnote 24:  The reader cannot but be pleased with what Goguet says on the practice of numbering with the fingers, so common in most nations, and adopted we see by the Otaheitans.  “Nature has provided us with a kind of arithmetical instrument more generally used than is commonly imagined; I mean our fingers.  Every thing inclines us to think, that these were the first instruments used by men to assist them in the practice of numeration.  We may observe in Homer, that Proteus counts his sea-calves by fives and fives, that is, by his fingers.  Several nations in America have no other instruments of calculation.  It was probably the same in the primitive ages.  It is another strong presumption of the truth of what I now advance, that all civilized nations count by