I cubed. He returns again to the region below.

Now, there is scarcely a collection of folk-lore which does not

contain a story founded on this root. It appears in every branch of

the Aryan family, and examples might be quoted from Modern Greek,

Albanian, Neapolitan, French, German, Danish, Norwegian and Swedish,

Icelandic, Scotch, Welsh, and other collections of popular tales. I

have only space to mention some.

There is a Norse ThAittr of a certain Helgi Thorir's son, which is, in

its present form, a production of the fourteenth century. Helgi and

his brother Thorstein went on a cruise to Finnmark, or Lapland. They

reached a ness, and found the land covered with forest. Helgi explored

this forest, and lighted suddenly on a party of red-dressed women

riding upon red horses. These ladies were beautiful and of troll race.

One surpassed the others in beauty, and she was their mistress. They

erected a tent and prepared a feast. Helgi observed that all their

vessels were of silver and gold. The lady, who named herself

Ingibjorg, advanced towards the Norseman, and invited him to live with

her. He feasted and lived with the trolls for three days, and then

returned to his ship, bringing with him two chests of silver and gold,

which Ingibjorg had given him. He had been forbidden to mention where

he had been and with whom; so he told no one whence he had obtained

the chests. The ships sailed, and he returned home.

One winter's night Helgi was fetched away from home, in the midst of a

furious storm, by two mysterious horsemen, and no one was able to

ascertain for many years what had become of him, till the prayers of

the king, Olaf, obtained his release, and then he was restored to his

father and brother, but he was thenceforth blind. All the time of his

absence he had been with the red-vested lady in her mysterious abode

of GlA"sisvellir.

The Scotch story of Thomas of Ercildoune is the same story. Thomas met

with a strange lady, of elfin race, beneath Eildon Tree, who led him

into the underground land, where he remained with her for seven years.

He then returned to earth, still, however, remaining bound to come to

his royal mistress whenever she should summon him. Accordingly, while

Thomas was making merry with his friends in the Tower of Ercildoune, a

person came running in, and told, with marks of fear and astonishment,

that a hart and a hind had left the neighboring forest, and were

parading the street of the village. Thomas instantly arose, left his

house, and followed the animals into the forest, from which he never

returned. According to popular belief, he still "drees his weird" in

Fairy Land, and is one day expected to revisit earth. (Scott,

"Minstrelsy of the Scottish Border.") Compare with this the ancient

ballad of Tamlane.

Debes relates that "it happened a good while since, when the burghers

of Bergen had the commerce of the Faroe Isles, that there was a man in

Serraade, called Jonas Soideman, who was kept by the spirits in a

mountain during the space of seven years, and at length came out, but

lived afterwards in great distress and fear, lest they should again

take him away; wherefore people were obliged to watch him in the

night." The same author mentions another young man who had been

carried away, and after his return was removed a second time, upon the

eve of his marriage.

Gervase of Tilbury says that "in Catalonia there is a lofty mountain,

named Cavagum, at the foot of which runs a river with golden sands, in

the vicinity of which there are likewise silver mines. This mountain

is steep, and almost inaccessible. On its top, which is always covered

with ice and snow, is a black and bottomless lake, into which if a

stone be cast, a tempest suddenly arises; and near this lake is the

portal of the palace of demons." He then tells how a young damsel was

spirited in there, and spent seven years with the mountain spirits. On

her return to earth she was thin and withered, with wandering eyes,

and almost bereft of understanding.

A Swedish story is to this effect. A young man was on his way to his

bride, when he was allured into a mountain by a beautiful elfin woman.

With her he lived forty years, which passed as an hour; on his return

to earth all his old friends and relations were dead, or had forgotten

him, and finding no rest there, he returned to his mountain elf-land.

In Pomerania, a laborer's son, Jacob Dietrich of Rambin, was enticed

away in the same manner.

There is a curious story told by Fordun in his "Scotichronicon," which

has some interest in connection with the legend of the TanhA¤user. He

relates that in the year 1050, a youth of noble birth had been married

in Rome, and during the nuptial feast, being engaged in a game of

ball, he took off his wedding-ring, and placed it on the finger of a

statue of Venus. When he wished to resume it, he found that the stony

hand had become clinched, so that it was impossible to remove the

ring. Thenceforth he was haunted by the Goddess Venus, who constantly

whispered in his ear, "Embrace me; I am Venus, whom you have wedded; I

will never restore your ring." However, by the assistance of a

priest, she was at length forced to give it up to its rightful owner.

The classic legend of Ulysses, held captive for eight years by the

nymph Calypso in the Island of Ogygia, and again for one year by the

enchantress Circe, contains the root of the same story of the

TanhA¤user.

What may have been the significance of the primeval story-radical it

is impossible for us now to ascertain; but the legend, as it shaped

itself in the middle ages, is certainly indicative of the struggle

between the new and the old faith.

We see thinly veiled in TanhA¤user the story of a man, Christian in

name, but heathen at heart, allured by the attractions of paganism,

which seems to satisfy his poetic instincts, and which gives full rein

to his passions. But these excesses pall on him after a while, and the

religion of sensuality leaves a great void in his breast.

He turns to Christianity, and at first it seems to promise all that he

requires. But alas! he is repelled by its ministers. On all sides he

is met by practice widely at variance with profession. Pride,

worldliness, want of sympathy exist among those who should be the

foremost to guide, sustain, and receive him. All the warm springs

which gushed up in his broken heart are choked, his softened spirit is

hardened again, and he returns in despair to bury his sorrows and

drown his anxieties in the debauchery of his former creed.

A sad picture, but doubtless one very true.

Fatality of Numbers.

The laws governing numbers are so perplexing to the uncultivated mind,

and the results arrived at by calculation are so astonishing, that it

cannot be matter of surprise if superstition has attached itself to

numbers.

But even to those who are instructed in numeration, there is much that

is mysterious and unaccountable, much that only an advanced

mathematician can explain to his own satisfaction. The neophyte sees

the numbers obedient to certain laws; but _why_ they obey these laws

he cannot understand; and the fact of his not being able so to do,

tends to give to numbers an atmosphere of mystery which impresses him

with awe.

For instance, the property of the number 9, discovered, I believe, by

W. Green, who died in 1794, is inexplicable to any one but a

mathematician. The property to which I allude is this, that when 9 is

multiplied by 2, by 3, by 4, by 5, by 6, &c., it will be found that

the digits composing the product, when added together, give 9. Thus:--

2 A-- 9 = 18, and 1 + 8 = 9

3 A-- 9 = 27, " 2 + 7 = 9

4 A-- 9 = 36, " 3 + 6 = 9

5 A-- 9 = 45, " 4 + 5 = 9

6 A-- 9 = 54, " 5 + 4 = 9

7 A-- 9 = 63, " 6 + 3 = 9

8 A-- 9 = 72, " 7 + 2 = 9

9 A-- 9 = 81, " 8 + 1 = 9

10 A-- 9 = 90, " 9 + 0 = 9

It will be noticed that 9 A-- 11 makes 99, the sum of the digits of

which is 18 and not 9, but the sum of the digits 1 + 8 equals 9.

9 A-- 12 = 108, and 1 + 0 + 8 = 9

9 A-- 13 = 117, " 1 + 1 + 7 = 9

9 A-- 14 = 126, " 1 + 2 + 6 = 9

And so on to any extent.

M. de Maivan discovered another singular property of the same number.

If the order of the digits expressing a number be changed, and this

number be subtracted from the former, the remainder will be 9 or a

multiple of 9, and, being a multiple, the sum of its digits will be 9.

For instance, take the number 21, reverse the digits, and you have

12; subtract 12 from 21, and the remainder is 9. Take 63, reverse the

digits, and subtract 36 from 63; you have 27, a multiple of 9, and 2 +

7 = 9. Once more, the number 13 is the reverse of 31; the difference

between these numbers is 18, or twice 9.

Again, the same property found in two numbers thus changed, is

discovered in the same numbers raised to any power.

Take 21 and 12 again. The square of 21 is 441, and the square of 12 is

144; subtract 144 from 441, and the remainder is 297, a multiple of 9;

besides, the digits expressing these powers added together give 9. The

cube of 21 is 9261, and that of 12 is 1728; their difference is 7533,

also a multiple of 9.

The number 37 has also somewhat remarkable properties; when multiplied

by 3 or a multiple of 3 up to 27, it gives in the product three digits

exactly similar. From the knowledge of this the multiplication of 37

is greatly facilitated, the method to be adopted being to multiply

merely the first cipher of the multiplicand by the first multiplier;

it is then unnecessary to proceed with the multiplication, it being

sufficient to write twice to the right hand the cipher obtained, so

that the same digit will stand in the unit, tens, and hundreds places.

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