THE SEPTENARY.-A MATHEMATICAL DEMONSTRATION. Mathematicians tell us that even before the formula for the Binomial Theorem was known, the early writers on algebra had declared that the total number of ways of taking n things was 2"-1, or, in other words, the combination of n things taken 1 at a time, 2 at a time, 3 at a time, and so on. The proof is a simple example of mathematical induction, and it is easy to show empirically that if 1 be added to the total number of ways of taking n things, the result is invariably 2". Thus, if we take the two letters a, b, c, and form all the possible selections and prefix 1, we have: a, b, c, ab, ac, bc, abc. Here the total number of symbols is 8, that is 23. And 20-1 7. Thus we see that the sum total of the possible combinations of the three Hypostases, or Arasthâs, that are fouud in every religion, the Christian Trinity, the Hindu Trimûti, and the Triads of the other great religions, taken singly, in pairs, and altogether, or synthetically, must in the nature of things be neither more nor less than 7.-Lucifer, Vol. X, 55.

THE DIAPASON. According to the Pythagorean system, the world is a piece of harmony, and man the full chord, which consists of a fun damental or full tonic, its major third, its just fifth, and its octave. It will then be seen that the diapason (through all) means the complete chord, or, according to another system, a microsom of nature." Man touches Deity, passes through all the planets, and toubhes earth. It is because he touches Deity that he has an immortal soul, and it is because he runs through the planets that the planets influence nis nature.

FIGURES FINGERS. One explanation of "figures" is that it is a corruption of " fingers," the digits (Latin digiti). The primitive way of making the monads by the fingers. Thus the first four were simply i, ii, iii, iiii,; 5 was the outline of the hand simplified into a v probably; the next four fingers may have been the two combined, thus, vi, vii, viii, viiii; and 10 was a double v, thus, x. At a later period, iiii, and viiii were expressed by one less than, (i-v) for 5, and one less than ten, (i-x) for 9. Nineteen was ten plus nine, (x+i-x); etc.

PRONUNCIATION OF TALIAFERRO." (Vol. IX, p. 82.) In the answer to my question in the April No. of N. AND Q., you do not tell us how to pronounce "Taliaferro," the Christian name of Grand Representative Shaffner. And here I will ask, what is the pronunciation of the Christian name of that philosopher and mathematician, Blaise Pascal (1623-1662) ? O. F.

In England the name Taliaferro is pronounced as if spelled Tolliver, and we presume the same pronunciation obtains in this country.

LILITH. (Vol. IX, p. 84.) S. Baring-Gould, in his work "Legends of the Patriarchs and Prophets," gives an account of Lilith (pp. 17 and 34) according to the Rabbinical tradition, quoting as authorities Eisenmenger II, p. 416, aad the "History of Arabum," by Abraham Ecchellenus, p. 268. KET.

"After his fall, Satan took to himself four wives, Lilith, and Naama the daughter of Lamech and sister of Tubal-cain, Igereth, and Machalath. Each became the mother of a great host of devils, and each rules with her host over a season of the year; and at the change of seasons there is a great gathering of devils about their mothers. Lilith is followed by 478 legions of devils, for that number is comprised within her name. According to some, Lilith is identical with Eve. Lilith rules over Damascus, Naama over Tyre, Igereth over Malta and Rhodes, and Machalath over Crete."—Legends, p. 17.

"That Lilith was Adam's second wife was a common rabbinical speculation; certain ones of the commentators on Genesis having adopted this view to account for the double account of the creation of woman in the sacred text, first in Gen. 1, 27, and second in Gen. 11, 18. They say that Adam's first wife was named Lilith, but she was expelled from Eden, and after her expulsion Eve was created.

Abraham Ecchellensis gives the following account of Lilith and her doings: 'There are some who do not regard spectres as simply devils, but suppose them to be of a mixed nature, part demoniacal, part human, and to have had their origin from Lilith, Adam's first wife by Eblis, the prince of the devils. This has been transmitted to the Arabs from Jewish sources, by some converts of Mahomet from Cabbalism and Rabbinism, who have transferred the Jewish legends to the Arabs. They gave to Adam a wife, formed of clay, along with Adam, and called her Lilith; resting on the Scripture, male and female created he them: but when this woman, on account of her simultaneous creation with him, became proud and a vexation to her husband, God expelled her from Paradise, and then said: It is not good for that the man should be alone; I will make him a help meet for him. And this they confirm by the words of Adam when he saw the woman fashioned from his rib, This now bone of my bone, and flesh of my flesh, which is as much as to say, 'now God has given me a wife and companion, suitable to me, taken from my bone, and flesh, but the other wife he gave me was not of my bone, and flesh, and therefore was not a suitable companion and wife for me." "-Legends, p. 34.

"But Lilith, afher she was expelled from Paradise, is said to have married the devil, by whome she had children, who are called Jins, Thene were endued with six qualities, of which they share three with men, and three with devils."-History of Arabum, b. 268.

The word Lilith occurs once in the Hebrew Bible (Isaiah XXXVI, 14)

and translated "screech-owl," while the maruinal reading is " nightmonster." (See McClintock & Strong's "Cyclopædia, "Vol. IX, p. 462.) "Lilith the Legend of the First Woman," by Ada Langworthy Collier, is a poem which tells the whole legendary history of this subject. Boston, 1885; pp. 104.

PARALLEL LINES (=) FOR EQUALITY. The origin of two parallel lines for equality has been attributed to "Roberte Recorde, Physicion." In his mathematical work, the "Whetsone of Witte" (sig. Ff. 1'), published in 1557, he giving his reason for the use of parallels in the following quaint words :

"And to avoide the tediouse repetition of these woordes, is equalle to, I will sette as I doe often in woorke use, a paire of paralleles, or Gemowe lines of one lengthe, thus: =, bicause noe 2 thynges can be more equalle."

Yet, for a long time afterwards, the continental mathematicians employed the symbol a, which some suppose was a rapid formation of the diphthong æ, the initial of the phrase æquale est, "it is equal to."

FIVE-THE EVIL NUMBER. (Vol. IX, p. 24.) The number 5 was currently regarded as an evil number by the Egyptians because it was a disturbing element added to the perfect number 4. It was however not necessarily an evil number, but rather bore the power of good and evil. KET.

THE DIGAMMA. (Vol. IX, p. 24.) The digamma was a consonant sound in the oldest Greek. Hadley's "Greek Grammar," (p. 8, Section 23) says:

"The oldest Greek had another consonant sound represented by the sixth letter of the primitive alphabet. This was the semi-vowel F named (Faŭ) Vau, named also from it form Digamma (dígamma) i. e. double gamma, one placed upon another. It corresponds in place and form to the Latin f, but in power to Latin w consonant (r) being sounded much like the English w." KET.

This name

THE "FATHER OF CHRONOLOGY." (Vol. IX, p. 23.) was applied to Eratosthenes, keeper of the Alexandrian Library (apud 130 B. C.). He was the first person, in his "Chronographia, to use vears, the natural division of time, instead of generations, as a method of computing dates and events. (See "Encyclopædia Britannica," Art. Chronology.) KET,

Ye Tragical Tale of Ye Ancient Hiram.

"Old Hiram Abiff"-so the histories run-
Was a jolly old chap, a lone "Widow's Son."
His father a Tyrian-and as to his mother,
Genealogists make up a deuce of a bother,
Some going for one and somefor another.
Some say she belonged to the Nathan clan,
And some called her one of "the daughters of Dan."
This Hiram he came to Jerusalem,

And made that famed city his own happy home;
He helped wise King Sol his temple to build,
For in all works of brass he was mightily skilled.
But alas! his sad fate we must now bewail,
Come, all ye bright Masons, now list to my tale!
This tragical tale, which they say is a true one,
Is old, but the manner is wholly a new one ;

For Bill Drew-who's a writer of some reputation !
Has told it before in a tedious narration.

In a style of such melo-dramatic fullness,
To which nobody listens, because of its dullness.
At high twelve-his usual custom they say,
Old Hiram went into the temple to pray.
(A very remarkable event, by-the way.)
And while he was praying in his great hearted mood,
Three rascally, scoundrelly Fellow Crafts stood

At the gates of the temple, on murder intent,
And waited for Hiram, when outward he went.
When Hiram had finished, he straightway arose,
And most enegetically blew his red nose;

But when he arrived at the gate of the south,
Then one of the ruffans opened his mouth,
And asked him to give him the word and the grip,
Saying, "Now, then, my Tyrian, I've thee on the hip."

Says Hiram, "Mein Gott! was it dese dings? Ha! Ha!
Oh yaw! I furstay, and dats you, Ja!"
"Dry up, you Dutchman ; " then the villian said:
Give me them secrets, or I'll punch your head!"

"Have patience, J. -a," Old Hiram replied,

"Wait till the cruel war is over, and you'll be satisfied"
"Talk not to me of patience! Again, I charge thee, stay!
And give me them ere secrets, or you I'll surely slay!"
But Hiram was steadfast, and bold as a lion,
And told him his dodge it was no use to try on;
So Ja was wrathy, and boiling with rage,
And immediately picked up his two-foot gauge,

And with it hit Hiram right over the crocker,
And knocked him almost stiff as a poker.
To the west with a flash did Old Hiram then flee,
Thus changing his base with a flank march, do you see?
A critical movement in tactics we know,
For there stood the other fellow called J-
The villian tried hard to pump our Grand Master,
Yet Hiram had stuck to his purpose the faster.

And finding his solicitations no go,
The scoundrel hit him a thundering blow

Upon his left breast with a wrought-iron square,

Not the square thing to do, all Masons declare.

With the weight of the onslaught was Hiram so addled,

By strategic movement to the east he skedaddled.

But alas in that place " Oriental" he found

No "beautiful waiter girls," not "zwei lager " around

And mindful only to escape of course ;

"A horse!" he hoarsely bawled, "my kingdom for a horse!"

"Do you take me for an ass?" and almost stricken dumb,

Poor Hiram recognized the voice of far-famed J.

This fellow was naught, if you'll believe, then
A sort of Tyrian "Ticket-of-Leave Man,"

Who makes his debut in this panorama,

As the murderous villian in this thrilling drama.

-m.

"Jim Dalton," says he, " you were always my ruin,"
(Meaning Hiram of course), "so up now and be doing;

Give me those secrets that you keep so close,
Or by the famed River Styx I'll split your nose!
But Hiram undaunted, just struck a posish,'
Like Lester in Rosedale, that delectable dish;
And the villain, not posted in acts pugilistic,
Nor daring to try on a combat so fistic,

Hit Hiram so telling a crack with his gavel,
That he sent him to grass, or rather to gravel.
Thus did this ruffian-this foul J- -m,
Knock our Grand Master into Kingdom come.
"Not a drum was heard, nor a funeral note,

As his corse "in the rubbish they buried,
But a fearful remorse their conscience smote,
As away from the spot the three hurried.
At midnight hour, when, as I h've heard said,
When grave-yards yawn and give up their dead,

These villainous traitors, who had till now deferred,
The body of poor Hiram had next now disinterred,

And toting it out of the temple due West,

On the brow of the hill they laid him to rest.

A sprig of Shillelah-or Acacia, a branch,

Was planted near by and they-vamosed the ranch.
When Solomon came to the temple next day,
He wondered very much where Hiram did stay,

And fearing that Hiram might have got into a fuss,
Sent out detectives to see if there had been a muss.
Just at this time twelve fellows did appear,
All clad in clean shirts-much needed I fear-

A Loyal League affair, in vogue at that day,
But loyal in nothing but the name I say;
King Sol, that wise and mighty potentate,
Then ordered them at once to separate

And traveled East, and West, and North. and South,
In search of Hiram's carcass, and so forth.
Away they went, and those who traveled West,
Met a way-faring man, whom they addressed.

A sort of Connie Soogah, who reported

Three men he'd seen who wished to be transported.

But having nary a pass, nor any other tickets,

They could'nt make out to pass the outer pickets.

The three returned, and to the King they told the story o'er, Who cried aloud, Again depart, and travel as before." One of the three who raveled West, becoming taint and weary, Sat down to rest, at brow of the hill, so lonely and so dreary While thus he sat, he heard three shock

ing exclamations from a rock;

And peeping in-what should he see,
Bnt J-a and company!

They seized them all and bound them tight
And brought them to King Sol that night,
Who ordered them out of the western gate,
Their horrible crime to expiate.

A full account of the affair you will get,

In a former number of the "Jerusalem Gazette."

King Solomon then got up a procession,

Of Craftsmen and Masters in regular succession.

With Gideon's Brass Band on the right of the column,
Playing a Solomon song in a manner quite solemn.

When arrived at the grave they all gathered around,
And with eyes full of sorrow, they gazed at the ground.
Their noses turned up in a style quite imperious,

For they smelled nothing like a "Night Blooming Cereus ! '

And King Solomon then-though weak in his joints,

Raised his dead rabbit up, "a la mode de Five Points."
Then back to the temple they all of them went,
And o'er his remains built a fine monument :
With a column all broken and a virgin a crying,
While Chronos stands behind her, her ringlets dyeing
With Adam's Ambrosia, or Invigorator,

Of which Cross or Morris was the originator.

And then-but here we'll draw the mystic vail,

Of Hiram Abiff, and the tragical tale.-Masonic Review.