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THEODORE FABER'S "NEW LAW IN GEOMETRY."-CRITICISM. (Vol XIII, pp. 137, 169, 189, 229.) The foundation of his system on page 170 is a gross blunder, by giving to the words "inscribed square a meaning that the author never dreamed of. When the apexes of the inscribed square are in the middle of the sides of the circumscribed square, then "a circumscribed square is equal to twice the inscribed square," and then only; and that is the square which mathematicians mean when they speak of " the inscribed square."

In a square there may be inscribed any number of squares varying in area from one-half the square, to the smallest possible fraction less than the square itself according as the apex of the inscribed square travels from the middle of the side towards the corner.

On page 229, he says that "outside of 32+42=52, and its multiples, and some other numbers, all of which are coincidences, there are no two squares whose sum is a square."

When we know that "some other numbers" are really numbered by millions of millions, we must set down the author of the statement as either an ignoramus or a wilful falsifier.

In the expression (p-2)+(2pq)2=(p2+q) p and q may be any numbers whatever-whole numbers or fractions-and the expression gives two squares whose sum is equal to a square. We can have as many different results, not multiples, as the number of times that p and q can be taken prime to each other.

Why he should select 32+42-52 for special mention, I cannot understand, for what is true of that expression is equally true of these, 52+12=132, 82+152-172, and very many others without going beyond numbers of two figures.

If we define his "ideal root as an approximate but not precise root, we give him all the truth allows. For instance, he says that √21; if that is true and exact; then by squaring we have2 = 21. I will not enlarge further.

J. H. D.

We do not undertake to stand as an apologist for Theodore Faber deceased, but from a personal acquaintance with him, and several quite lengthy interviews and discussions on his new system, we will add a word. In several expressions in his writings, especially in his "Mathematical and Philosophical Manifesto " (p. 189), from which the "Deductions" (p. 229) were taken, he is somewhat obscure. His

system is the absolute harmony between arithmetic and geometry, in integral numbers. Hence, while he would admit that mathematicians make the circumscribed square to two equal inscribe squares, he denies this on the ground that it is impossible arithmetically, that is, for instance, that the square 64 is not equal to two equal squares, but is equal to four equal squares.

We suppose that Mr. Faber uses the words, "some other numbers," in a limited sense when compared with the infinite number of so called irrational squares, which are the sum of two squares.

On his theory of the "ideal root" we make no remark. We will send a copy of the reprinted pamphlet article to any interested reader who requests a copy, having held in reserve a few copies. pamphlet will briefly illustrate Mr. Faber's system of ideal roots.

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MOHAMMEDAN PARABLE. "Moses said to Adam, as they were disputing before God, Thou art Adam, whom God created and animated with the breath of life, and caused to be worshipped by the angels, and placed in Paradise, from whence mankind have been expelled for thy fault.' Whereto Adamn answered, Thou art Moses, whom God chose for his Apostle, and entrusted with his word, by giving thee the tables of the law, and whom he vouched to admit to discourse with himself. How many years dost thou find the law was written before I was created?' Moses says, 'forty.' Adam replied, and dost thou not find these words therein?" "And Adam rebelled against his Lord and transgressed," which Moses confessing, Dost thou therefore blame me,' continued he, 'for doing that which God wrote of me that I should do, forty years before I was created; nay, for what was decreed concerning me forty thousand years before the creation of heaven and earth?""

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GOD OF "SILENCE AND SECRECY." Harpocrates was the god of "silence and secrecy"; also Her pe-chrut, sometimes called Horus the child, among the Egyptians. There is a double symbolism here, Horus being the mystic son of Osiris and Isis, coming from the silent land in a state of helplessness and innocence, he presses his finger to his lip, and when grown to manhood becomes the representation of Osiris and enlightener of the world which light is mystical, and refers to the future life, and, therefore, should not be lightly spoken of by mortals. He was the god of the renewed year the son of Osiris, in the capacity of Creator; and peach blossoms were consecrated to him in the spring. His statues were erected at the porches of temples and other places of mystery.

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W. H. Lyttle did not write his famous poem the night before he died, though there is a superstition that he did so. A few years ago a friend sent me a copy of a Nashville paper of 1858, containing the complete poem. Appleton's "Cyclopædia of American Biography

says it was written in 1857.

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Since the time of Koener, if not from an earlier time, it has been customary to assume that any song written by a soldier, since dead, was composed the evening before he died. So we have Gen. Lyttle's

"I am dying, Egypt, dying," and Williamson's "Stonewall Jackson's Way," the latter wrongly ascribed to Major King. It is almost a wonder that we have not had history reconstructed to allow of General John A. Dix dying in battle the day after he finished his translation of "Dies Ira," but probably we shall have that yet.-E. T. C., in N. Y. Sun, October 10, 1895.

INRI. Whence have you derived most of your knowledge? India.
Who has been your best guide?
What has it produced in you?

Nature. Regeneration.

What have you combated?

Ignorance.

SOLAR PERIGEE AND VERNAL EQUINOX. In the year 4,089 B. C., or, singularly enough, near the supposed epoch of creation, the longitude of the Sun's perigee coincided with the spring equinox; so then the summer and autumn quarters were of equal length, but longer than the winter and spring quarters, which were also equal.

In the year 1,250 A. D., the perigee coincided with the winter solstice; the spring quarter was therefore equal to the summer quarter, and the autumn quarter to the winter, the former quarters being the longest.

In the year 6,589 A. D, the perigee will have completed half a revolution, and will then coincide with the autumnal equinox; summer will then be equal to autumn, and winter to spring; the former seasons, however, will be the shortest.

In the year 11,928 A. D., the perigee will have completed threefourths of a revolution, and will then coincide with the summer solstice; autumn will then be equal to winter, but longer than spring and summer, which will also be equal.

And finally, in the year 17,267 A. D., the cycle will be completed by the coincidence, for the first time since the creation of the world, and the solar perigee will correspond with the vernal equinox. -Chambers' Descriptive Astronomy, p. 67.

PLANETARY HARMONY. The key-note of the solar system must evidently be determined by its two primary nodes-the Sun, which is about 750 times as large as all the planets, and Jupiter, which is about 2 times as great as the aggregate mass of all the remaining planets. In order that the other planets may vibrate in unison with their great leader, and that there may be no discord in the continual hymn of our morning star, it is desirable that the elastic æthereal strings, being all of similar density, should be of harmonic lengths. Now Jupiter is so situated that it constitutes a node for each of the more remote planets, in the harmonical proportion,,. Its own. harpstring is so subdivided, as to form planetary nodes in the harmonical progression,,,,, etc.

This is in curious analogy with Bernoulli's law of organ pipes-that if the pipe is closed at the end opposite the mouthpiece, we can, by gradually increasing the force of the air current, obtain the uneven harmonics of the primary tone. The key-note is sounded at Jupiter's mean perhelion, or the point of its mean maximun vis viva. - Pliny Earle Chase.

Nature, while obeying with absolute precision the resultant of her efficient laws, such as Inertia, Attraction, etc., falls into forms which commonly both utility and taste, often independently of each other, would prescribe.-James Edward Oliver.

NUMBER OF GREEKS AT TROY.

Trollope remarks that the number has been variously given by different authors: Plutarch says there were 120,000 men; Thucydides gives about 102,000. Now if we take the whole number of ships, 1184, and multiply by 120, the number of men in each of the Boeotian vessels, we shall have 142,080 for the whole Grecian army. This is obviously too great ; and a much more probably way is to estimate it by taking the mean between 120 and 50, the smallest number mentioned for a vessel, which will give the average 85, and multiply this by 1184; then we shall have for the number 100,640. A chronologic mnemonic is that the figures of the date of the seige of Troy, 1184 B. C., are the same as the number of vessels, 1184. Protesilaus was the first hero slain in the war, being killed while leaping from his ship upon the Trojan shore.

PUZZLE. To discover the rule by which the following puzzle is worked. It is best exhibited in a dialogue :

A. Think of a number less than 90. B. I have done so.
A. Tack on to it any digit you like, from o to 9.

B. I have tacked on a 7.

What shall it be?

B. It is 2.

B. I tacked on 4.
It is 1.
B. It is 8.

A. Now divide by 3. What is the remainder?
A. Tack on to the quotient any digit you like.
A. Divide by 3. What is the remainder? B.
A. And what is the third figure from the end?
A. (Instantly rejoins) Then the number you thought of was 76.

POEMS ASCRIBED TO TWO AUTHORS. Some of our most prominent poems have been credited to different authors, for instance : "Burial of Sir John Moore," Charles Wolfe, and H. Marshall. "Blind Old Milton," John Milton, and Elizabeth Howell. "There is no Death," H. W. Longfellow, and E. Bulwer Lytton. "Janet's Hair," Charles G. Halpine, and Joaquin Miller. "I would not live alway," H. Muhlinburg, and

Ward.

"The Old Canoe," Gen. Albert Pike, and Emily R. Page.

"Oh! Why should the Spirit of Mortal be Proud?" William Knox, and Abraham Lincoln.

TRANCENDENTALISM sinks God and nature in man.

MATERIALISM sinks God and nature in the universe.

ATHEISM Sinks the will of God and man in the movement of destiny. PANTHEISM sinks man and nature in God.-Wm. B. Greene.

"The crucifixion of the human is the enthronement of the divine." - Christos.

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