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 conditions will be fulfilled at once if the tangent plane at this point be taken for the $xy$ -plane. If, further, the origin is placed at the point $A$  itself, the expression for the coordinate $z$ evidently takes the form

$$z = \frac{1}{2}T^{\circ}x^{2} + U^{\circ}xy + \tfrac{1}{2}V^{\circ}y^{2} + \Omega$$

where $\Omega$  will be of higher degree than the second. Turning now the axes of $x$  and $y$ through an angle $M$  such that

$$\tan 2M = \frac{2U^{\circ}}{T^{\circ} - V^{\circ}}$$

it is easily seen that there must result an equation of the form

$$z = \tfrac{1}{2}Tx^{2} + \tfrac{1}{2}Vy^{2} + \Omega$$

In this way the third condition is also satisfied. When this has been done, it is evident that

I. If the curved surface be cut by a plane passing through the normal itself and through the $x$ -axis, a plane curve will be obtained, the radius of curvature of which at the point $A$ will be equal to $\frac{1}{T},$  the positive or negative sign indicating that the curve is concave or convex toward that region toward which the coordinates $z$  are positive.

II. In like manner $\frac{1}{V}$  will be the radius of curvature at the point $A$ of the plane curve which is the intersection of the surface and the plane through the $y$ -axis and the $z$ -axis.

III. Setting $z = r \cos\phi,$ $y = r \sin \phi,$  the equation becomes

$$z = \tfrac{1}{2}(T\cos^{2}\phi + V\sin^{2}\phi) r^{2} + \Omega$$

from which we see that if the section is made by a plane through the normal at $A$ and making an angle $\phi$  with the $x$ -axis, we shall have a plane curve whose radius of curvature at the point $A$  will be

$$\frac{1}{T\cos^{2}\phi + V\sin^{2}\phi}$$

IV. Therefore, whenever we have $T = V,$ the radii of curvature in all the normal planes will be equal. But if $T$  and $V$ are not equal, it is evident that, since for any value whatever of the angle $\phi,$  $T\cos^{2}\phi + V\sin^{2}\phi$  falls between $T$  and $V,$  the radii of curvature in the principal sections considered in I. and II. refer to the extreme curvatures; that is to say, the one to the maximum curvature, the other to the minimum,


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 an autonomous district in respect of all areas within the district except those which are under the authority of Regional Councils, if any, within the district shall have power to make laws with respect to—
 * (a) the allotment, occupation or use, or the setting apart, of land, other than any land which is a reserved forest for the purposes of agriculture or grazing or for residential or other non-agricultural purposes or for any other purpose likely to promote the interests of the inhabitants of any village or town:

Provided that nothing in such laws shall prevent the compulsory acquisition of any land, whether occupied or unoccupied, for public purposes [by the Government of the State concerned] in accordance with the law for the time being in force authorising such acquisition;
 * (b) the management of any forest not being a reserved forest;
 * (c) the use of any canal or water-course for the purpose of agriculture;
 * (d) the regulation of the practice of jhum or other forms of shifting cultivation;
 * (e) the establishment of village or town committees or councils and their powers;
 * (f) any other matter relating to village or town administration, including village or town police and public health and sanitation;
 * (g) the appointment or succession of Chiefs or Headmen;
 * (h) the inheritance of property;
 * [(i) marriage and divorce;]
 * (j) social customs.

(2) In this paragraph, a “reserved forest” means any area which is a reserved forest under the Assam Forest Regulation, 1891, or under any other law for the time being in force in the area in question.

(3) All laws made under this paragraph shall be submitted forthwith to the Governor and, until assented to by him, shall have no effect.

4. Administration of justice in autonomous districts and autonomous regions.—(1) The Regional Council for an autonomous region in respect of areas within such region and the District Council for an autonomous district in respect of areas within the district other than those which are under the authority of the Regional Councils, if any, within the district may constitute village councils or courts for the trial of suits and cases between the parties all of whom belong to Scheduled Tribes within such areas, other than suits and cases to which the provisions of sub-paragraph (1) of paragraph 5 of this Schedule apply, to the exclusion of any court in the State, and may appoint suitable persons to be members of such village councils or presiding officers of such courts, and may also appoint such officers as may be necessary for the administration of the laws made under paragraph 3 of this Schedule.

(2) Notwithstanding anything in this Constitution, the Regional Council for an autonomous region or any court constituted in that behalf by the Regional Council or, if in respect of any area within an autonomous district there is no Regional Council, the District Council for such district, or any court constituted in that behalf by the District Council, shall exercise the powers of a court of appeal in respect of all suits and cases triable by a village council or court constituted under sub-paragraph (1) of this paragraph within such region or area, as the case may be, other than those to which the provisions of subparagraph (1) of paragraph 5 of this Schedule apply, and no other court except the High Court and the Supreme Court shall have jurisdiction over such suits or cases.

license: Creative Commons - Attribution Share-Alike - https://creativecommons.org/licenses/by-sa/4.0/


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Rh A wild and wondrous story, by the younger Mather penned, In that quaint Magnalia Christi, with all strange and marvellous things, Heaped up huge and undigested, like the chaos Ovid sings.

Dear to me these far, faint glimpses of the dual life of old, Inward, grand with awe and reverence; outward, mean and coarse and cold; Gleams of mystic beauty playing over dull and vulgar clay, Golden-threaded fancies weaving in a web of hodden gray.

The great eventful Present hides the Past; but through the din Of its loud life hints and echoes from the life behind steal in; And the lore of home and fireside, and the legendary rhyme, Make the task of duty lighter which the true man owes his time.

So, with something of the feeling which the Covenanter knew, When with pious chisel wandering Scotland’s moorland graveyards through, From the graves of old traditions I part the blackberry-vines, Wipe the moss from off the headstones, and retouch the faded lines.

Where the sea-waves back and forward, hoarse with rolling pebbles, ran, The garrison-house stood watching on the gray rocks of Cape Ann; On its windy site uplifting gabled roof and palisade, And rough walls of unhewn timber with the moonlight overlaid.

On his slow round walked the sentry, south and eastward looking forth O’er a rude and broken coast-line, white with breakers stretching north,— Wood and rock and gleaming sand-drift, jagged capes, with bush and tree, Leaning inland from the smiting of the wild and gusty sea.

Before the deep-mouthed chimney, dimly lit by dying brands, Twenty soldiers sat and waited, with their muskets in their hands; On the rough-hewn oaken table the venison haunch was shared, And the pewter tankard circled slowly round from beard to beard.

Long they sat and talked together,—talked of wizards Satan-sold; Of all ghostly sights and noises,—signs and wonders manifold; Of the spectre-ship of Salem, with the dead men in her shrouds, Sailing sheer above the water, in the loom of morning clouds;

Of the marvellous valley hidden in the depths of Gloucester woods, Full of plants that love the summer,—blooms of warmer latitudes; Where the Arctic birch is braided by the tropic’s flowery vines, And the white magnolia-blossoms star the twilight of the pines!

But their voices sank yet lower, sank to husky tones of fear, As they spake of present tokens of the powers of evil near;— Of a spectral host, defying stroke of steel and aim of gun; Never yet was ball to slay them in the mould of mortals run!

Thrice, with plumes and flowing scalp-locks, from the midnight wood they came,— Thrice around the block-house marching, met, unharmed, its volleyed flame; Then, with mocking laugh and gesture, sunk in earth or lost in air, All the ghostly wonder vanished, and the moonlit sands lay bare.

Midnight came; from out the forest moved a dusky mass that soon Grew to warriors, plumed and painted, grimly marching in the moon. “Ghosts or witches,” said the captain, “thus I foil the Evil One!” And he rammed a silver button, from his doublet, down his gun.


text: Adam's Reports on Vernacular Education in Bengal and Behar/Report 3/Chapter 1/Section 10


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54  Once again the spectral horror moved the guarded wall about; Once again the levelled muskets through the palisades flashed out, With that deadly aim the squirrel on his tree-top might not shun, Nor the beach-bird seaward flying with his slant wing to the sun.

Like the idle rain of summer sped the harmless shower of lead. With a laugh of fierce derision, once again the phantoms fled; Once again, without a shadow on the sands the moonlight lay, And the white smoke curling through it drifted slowly down the bay!

“God preserve us!” said the captain; “never mortal foes were there; They have vanished with their leader, Prince and Power of the air! Lay aside your useless weapons; skill and prowess naught avail; They who do the Devil’s service wear their master’s coat of mail!”

So the night grew near to cock-crow, when again a warning call Roused the score of weary soldiers watching round the dusky hall: And they looked to flint and priming, and they longed for break of day; But the captain closed his Bible: “Let us cease from man, and pray!”

To the men who went before us, all the unseen powers seemed near, And their steadfast strength of courage struck its roots in holy fear. Every hand forsook the musket, every head was bowed and bare, Every stout knee pressed the flag-stones, as the captain led in prayer.

Ceased thereat the mystic marching of the spectres round the wall, But a sound abhorred, unearthly, smote the ears and hearts of all,— Howls of rage and shrieks of anguish! Never after mortal man Saw the ghostly leaguers marching round the block-house of Cape Ann.

So to us who walk in summer through the cool and sea-blown town, From the childhood of its people comes the solemn legend down. Not in vain the ancient fiction, in whose moral lives the youth And the fitness and the freshness of an undecaying truth.

Soon or late to all our dwellings come the spectres of the mind, Doubts and fears and dread forebodings, in the darkness undefined; Round us throng the grim projections of the heart and of the brain, And our pride of strength is weakness, and the cunning hand is vain.

In the dark we cry like children; and no answer from on high Breaks the crystal spheres of silence, and no white wings downward fly; But the heavenly help we pray for comes to faith, and not to sight, And our prayers themselves drive backward all the spirits of the night!

of Herbipolis, one day, While kneeling at the altar’s foot to pray Alone with God, as was his pious choice, Heard from without a miserable voice, A sound which seemed of all sad things to tell, As of a lost soul crying out of hell.

Thereat the Abbot paused; the chain whereby His thoughts went upward broken by that cry; And, looking from the casement, saw below A wretched woman, with gray hair a-flow, And withered hands held up to him, who cried For alms as one who might not be denied.

She cried, “For the dear love of Him who gave His life for ours, my child from bondage save,— My beautiful, brave first-born, chained with slaves In the Moor’s galley, where the sun-smit waves Lap the white walls of Tunis!”—“What I can


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 if $T$  and $V$ have the same sign. On the other hand, one has the greatest convex curvature, the other the greatest concave curvature, if $T$  and $V$ have opposite signs. These conclusions contain almost all that the illustrious Euler was the first to prove on the curvature of curved surfaces.

V. The measure of curvature at the point $A$ on the curved surface takes the very simple form

$$k = TV,$$ whence we have the

The measure of curvature at any point whatever of the surface is equal to a fraction whose numerator is unity, and whose denominator is the product of the two extreme radii of curvature of the sections by normal planes.

At the same time it is clear that the measure of curvature is positive for concavo-concave or convexo-convex surfaces (which distinction is not essential), but negative for concavo-convex surfaces. If the surface consists of parts of each kind, then on the lines separating the two kinds the measure of curvature ought to vanish. Later we shall make a detailed study of the nature of curved surfaces for which the measure of curvature everywhere vanishes.

9.

The general formula for the measure of curvature given at the end of Art. 7 is the most simple of all, since it involves only five elements. We shall arrive at a more complicated formula, indeed, one involving nine elements, if we wish to use the first method of representing a curved surface. Keeping the notation of Art. 4, let us set also

$$\begin{aligned} \frac{\partial^{2} W}{\partial x^{2}} &= P', & \frac{\partial^{2} W}{\partial y^{2}} &= Q', & \frac{\partial^{2} W}{\partial z^{2}} &= R' \\ \frac{\partial^{2} W}{\partial y. \partial z} &= P'', & \frac{\partial^{2} W}{\partial x. \partial z} &= Q'', & \frac{\partial^{2} W}{\partial x. \partial y} &= R'' \end{aligned}$$

so that

$$\begin{alignedat}{3}

dP &= P'\, &&dx + R\, &&dy + Q\, &&dz \\ dQ &= R\, &&dx + Q' \, &&dy + P\, &&dz \\ dR &= Q\, &&dx + P\, &&dy + R' \, &&dz \end{alignedat}$$

Now since $t = -\frac{P}{R},$ we find through differentiation

$$R^{2}\, dt = -R\, dP + P\, dR = (PQ - RP')\, dx + (PP - RR)\, dy + (PR' - RQ)\, dz$$


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text: Adam's Reports on Vernacular Education in Bengal and Behar/Report 3/Chapter 1/Section 12


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 Fire-fork, 256, n. 2.

Fish, speculations about, 182, n. 3.

Fisher, Jasper, 363; some account of, 363, n. 2.

Fisk, the astrologer, 228; particulars respecting; 228, n. 4.

Fit, playing a, 173 and n. 4.

Fitters, 272; moaning of the word, 272, n. 1.

Flagellants, amatorial, of Spain, 166, n. 2.

Flea, its long jump, 224, n. 5.

Fleetwood, the son-in-law of Cromwell, 337 and n. 2.

Flesh is grass, 60 and n. 3.

Flies, wasps, and hornets, 54, n. 3.

Florio, and Biancafiore, 168 and n. 5.

Fludd, Robert, 26, n. 1.

Foot, the right to be put foremost, 241, n. 3.

Fop-doodle, 254 and n. 1

Ford, Mr, sermons of, 61, n. 1.

Foulis, Mr, story told by, 183, n. 5.

Fowl-catching, 210 and n. 4.

Fox, cunning of the, 258 and n. 4; weighs geese, 291, n. 5.

Franc-pledge, view of, 185 and n. 4.

Freedom, conferred by a blow, 144 and n. 1.

French goods, 294 and n. 1.

Fulham's, 160; a cant word, 160, n. 1.

Gabardine, 104; a coarse robe, or mantle, J04, n. 1.

Galen and Paracelsus, 412 and n. 3.

Galileo, observations of, 242, n. 2.

Gallows, fear of the, 357 and n. 1.

Ganzas, or geese, 245 and n. 1.

Garters, new, 304 and n. 6.

Gascoign, Sir Bernard, respited, 84, n. 3.

Gath, men of, 334.

Gazettes, 405 and n. 1.

Generation on Faith, 289 and n. 1.

Genethliacks, or Chaldeans, 240 and n. 4.

Gentee, 163 and n. 4.

Geoffrey of Monmouth, 2, n. 1.

Geomancy, 308 and n. 1.

George-à-Green, 193 and n. 4.

Gill, or girl, 201 and n. 2.

Gizards, spiritual, 355 and n. 2.

Glass, the multiplying. 280 and n. 5.

Gleaves, or swords, 349 and n. 2.

Glory and shame, 145 and n. 2.

Glow-worm, its luminous tail, 230 and n. 4.

God, a child of, 312 and n. 1.

Godwin, afterwards Bishop of Hereford, his astronomical romance, 245, n. 1.

Godwyn, Dr Thomas, 199, n. 2.

Gold and silver, marked by the sun and moon in chemistry, 153, n. 1.

Gondibert, preferred a country lass, 58 and n. 3.

Goodwin, Thomas, a Calvinistic Independent, 199 and n. 2.

Gossip, tattling, 139 and n. 1, 3.

Government, not to be upheld without the aid of poetry, 58, n. 4.

Grace, introduced by sin, 375 and n. 1.

Grandier, the curate of Loudun, 217, n. 3.

Gratiæ Ludentes, an old book, 22, n. 1.

Great cry and little wool, 37, n. 1.

Green-hastings, 263 and n. 3.

Green-men, 293 and n. 3.

Gregory VII., Pope, his insolence and ambition, 127 and n. 1.

Gresham-carts, 323 and n. 2.

Grey, Dr, suppositions of, 98, n. 4; 164, n. 2; anecdote related by, 115, n. 2; stories told by, 190, n. 1; 192, n. 2; 316, n. 5; alluded to, 195, n. 1, 3; 202, n. 5.

Grey mare the better horse, 200 and n. 5.

Grizel, patient, 72 and n. 4.

Grosted, Bob, 220 and n. 2.

Groves, cutting down of, 338 and n. 4.

Guelphs and Gibellines, 355 and n. 7.

Gunpowder plot, 382, n. 2.

Guts in 's brains, 121 and n. 2.

Guy, Earl of Warwick, 54 and n. 1.


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 or, eliminating $dz$ by means of the equation

$$\begin{array}{c} P\, dx + Q\, dy + R\, dz = 0, \\ R^{3}\, dt = (-R^{2}P' + 2PRQ - P^{2}R')\, dx + (PRP + QRQ - PQR' - R^{2}R)\, dy. \end{array}$$

In like manner we obtain

$$R^{3}\, du = (PRP + QRQ - PQR' - R^{2}R)\, dx + (-R^{2}Q' + 2QRP - Q^{2}R')\, dy$$

From this we conclude that

$$\begin{aligned} R^{3}T &= -R^{2}P' + 2PRQ'' - P^{2}R' \\ R^{3}U &= PRP + QRQ - PQR' - R^{2}R'' \\ R^{3}V &= -R^{2}Q' + 2QRP'' - Q^{2}R' \end{aligned}$$

Substituting these values in the formula of Art. 7, we obtain for the measure of curvature $k$ the following symmetric expression:

$$\begin{array}{c} (P^{2} + Q^{2} + R^{2})^{2}k = P^{2}(Q'R' - P''^{2}) + Q^{2}(P'R' - Q''^{2}) + R^{2}(P'Q' - R''^{2}) \\ + 2QR(QR - P'P'') + 2PR(PR - Q'Q'') + 2PQ(PQ - R'R'') \end{array}$$

10.

We obtain a still more complicated formula, indeed, one involving fifteen elements, if we follow the second general method of defining the nature of a curved surface. It is, however, very important that we develop this formula also. Retaining the notations of Art. 4, let us put also

$$\begin{aligned} \frac{\partial^{2}x}{\partial p^{2}} &= \alpha, & \frac{\partial^{2}x}{\partial p. \partial q} &= \alpha', & \frac{\partial^{2}x}{\partial q^{2}} &= \alpha'' \\ \frac{\partial^{2}y}{\partial p^{2}} &= \beta, & \frac{\partial^{2}y}{\partial p. \partial q} &= \beta', & \frac{\partial^{2}y}{\partial q^{2}} &= \beta'' \\ \frac{\partial^{2}z}{\partial p^{2}} &= \gamma, & \frac{\partial^{2}z}{\partial p. \partial q} &= \gamma', & \frac{\partial^{2}z}{\partial q^{2}} &= \gamma'' \\ \end{aligned}$$

and let us put, for brevity,

$$\begin{aligned} bc' - cb' &= A \\ ca' - ac' &= B \\ ab' - ba' &= C \end{aligned}$$

First we see that

$$A\, dx + B\, dy + C\, dz = 0,$$

or

$$dz = -\frac{A}{C}\, dx - \frac{B}{C}\, dy.$$


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 ness in short, but a weakness not unamiable. The engraving seems to me very good. A certain not quite Christian expression—'not to put too fine a point upon it'—an expression of spite, most vividly marked in the original, is here softened, and perhaps a little—a very little—of the power has escaped in this ameliorating process. Did it strike you thus?"

Miss Brontë was in much better health during this winter of 1852–3, than she had been the year before.

"For my part," (she wrote to me in February) "I have thus far borne the cold weather well. I have taken long walks on the crackling snow, and felt the frosty air bracing. This winter has, for me, not been like last winter. December, January, February, '51–2, passed like a long stormy night, conscious of one painful dream, all solitary grief and sickness. The corresponding months in '52–3 have gone over my head quietly and not uncheerfully. Thank God for the change and the repose! How welcome it has been He only knows! My father too has borne the season well; and my book, and its reception thus far, have pleased and cheered him."

In March the quiet Parsonage had the honour of receiving a visit from the then Bishop of Ripon. He remained one night with Mr. Brontë. In the evening, some of the neighbouring clergy were invited to meet him at tea and supper; and during the latter meal, some of the "curates" began merrily to upbraid Miss


text: Adam's Reports on Vernacular Education in Bengal and Behar/Report 3/Chapter 1/Section 13


text: Twentieth Century Impressions of Hongkong, Shanghai, and other Treaty Ports of China/Finance


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 Brontë with "putting them into a book;" and she, shrinking from thus having her character as authoress thrust upon her at her own table, and in the presence of a stranger, pleasantly appealed to the bishop as to whether it was quite fair thus to drive her into a corner. His Lordship, I have been told, was agreeably impressed with the gentle unassuming manners of his hostess, and with the perfect propriety and consistency of the arrangements in the modest household. So much for the Bishop's recollection of his visit. Now we will turn to hers.

1em

"The Bishop has been, and is gone. He is certainly a most charming Bishop; the most benignant gentleman that ever put on lawn sleeves; yet stately too, and quite competent to check encroachments. His visit passed capitally well; and at its close, as he was going away, he expressed himself thoroughly gratified with all he had seen. The Inspector has been also in the course of the past week; so that I have had a somewhat busy time of it. If you could have been at Haworth to share the pleasures of the company, without having been inconvenienced by the little bustle of the preparation, I should have been very glad. But the house was a good deal put out of its way, as you may suppose; all passed, however, orderly, quietly, and well. Martha waited very nicely, and I had a person to help her in the kitchen. Papa kept up, too, fully as well as I ex-


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 Thus, inasmuch as $z$  may be regarded as a function of $x,$  $y,$ we have

$$\begin{aligned} \frac{\partial z}{\partial x} &= t = -\frac{A}{C} \\ \frac{\partial z}{\partial y} &= u = -\frac{B}{C} \end{aligned}$$

Then from the formulæ

$$dx = a\, dp + a'\, dq,\quad dy = b\, dp + b'\, dq,$$

we have

$$\begin{alignedat}{4} &C\, dp = &&b'\, &&dx - a'\, &&dy \\ &C\, dq =-&&b\, &&dx + a\,  &&dy \end{alignedat}$$

Thence we obtain for the total differentials of $t,$  $u$

$$\begin{aligned} C^{3}\, dt &= \left(A\, \frac{\partial C}{\partial p} - C\, \frac{\partial A}{\partial p}\right)(b'\, dx - a'\, dy) + \left(C\, \frac{\partial A}{\partial q} - A\, \frac{\partial C}{\partial q}\right)(b \, dx - a \, dy) \\ C^{3}\, du &= \left(B\, \frac{\partial C}{\partial p} - C\, \frac{\partial B}{\partial p}\right)(b'\, dx - a'\, dy) + \left(C\, \frac{\partial B}{\partial q} - B\, \frac{\partial C}{\partial q}\right)(b \, dx - a \, dy) \end{aligned}$$

If now we substitute in these formulæ

$$\begin{alignedat}{4} \frac{\partial A}{\partial p} &= c'\beta &&+ b\gamma'  &&- c\beta'  &&- b'\gamma \\ \frac{\partial A}{\partial q} &= c'\beta' &&+ b\gamma &&- c\beta &&- b'\gamma' \\ \frac{\partial B}{\partial p} &= a'\gamma &&+ c\alpha'  &&- a\gamma'  &&- c'\alpha \\ \frac{\partial B}{\partial q} &= a'\gamma' &&+ c\alpha &&- a\gamma &&- c'\alpha' \\ \frac{\partial C}{\partial p} &= b'\alpha &&+ a\beta'  &&- b\alpha'  &&- a'\beta \\ \frac{\partial C}{\partial q} &= b'\alpha' &&+ a\beta &&- b\alpha &&- a'\beta' \end{alignedat}$$

and if we note that the values of the differentials $dt,$  $du$ thus obtained must be equal, independently of the differentials $dx,$  $dy,$  to the quantities $T\, dx + U\, dy,$  $U\, dx + V\, dy$  respectively, we shall find, after some sufficiently obvious transformations,

$$\begin{aligned} C^{3}T &= \alpha Ab'^{2} + \beta Bb'^{2} + \gamma Cb'^{2} \\ &\quad- 2\alpha' Abb' - 2\beta' Bbb' - 2\gamma' Cbb' \phantom{(ba'-a'b)(ba'-a'b} \\ &\quad+ \alpha Ab^{2} + \beta Bb^{2} + \gamma'' Cb^{2} \end{aligned}$$


text: Adam's Reports on Vernacular Education in Bengal and Behar/Report 3/Chapter 1/Section 14


text: Adam's Reports on Vernacular Education in Bengal and Behar/Report 3/Chapter 1/Section 15


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 pected, though I doubt whether he could have borne another day of it. My penalty came on in a strong headache as soon as the Bishop was gone: how thankful I was that it had patiently waited his departure. I continue stupid to-day: of course, it is the re-action consequent on several days of extra exertion and excitement. It is very well to talk of receiving a Bishop without trouble, but you must prepare for him."

By this time, some of the Reviews had begun to find fault with "Villette." Miss Brontë made her old request.

"My dear Sir,—Were a review to appear, inspired with treble their animus, pray do not withhold it from me. I like to see the satisfactory notices,—especially I like to carry them to my father; but I must see such as are unsatisfactory and hostile; these are for my own especial edification;—it is in these I best read public feeling and opinion. To shun examination into the dangerous and disagreeable seems to me cowardly. I long always to know what really is, and am only unnerved when kept in the dark

"As to the character of 'Lucy Snowe,' my intention from the first was that she should not occupy the pedestal to which 'Jane Eyre' was raised by some injudicious admirers. She is where I meant her to be, and where no charge of self-laudation can touch her.


text: Adam's Reports on Vernacular Education in Bengal and Behar/Report 3/Chapter 1/Section 16


text: The Strand Magazine/Volume 4/Index

title: The Strand Magazine/Volume 4/Index


text: Adam's Reports on Vernacular Education in Bengal and Behar/Report 3/Chapter 1/Section 17


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 $$\begin{aligned} C^{3}U &= -\alpha Aa'b' - \beta Ba'b' - \gamma Ca'b' \\ &\quad+ \alpha' A(ab' + ba') + \beta' B(ab' + ba') + \gamma' C(ab' + ba') \\ &\quad- \alpha Aab - \beta Bab - \gamma'' Cab \\ C^{3}V &= \alpha Aa'^{2} + \beta Ba'^{2} + \gamma Ca'^{2} \\ &\quad- 2\alpha' Aaa' - 2\beta' Baa' - 2\gamma' Caa' \\ &\quad+ \alpha Aa^{2} + \beta Ba^{2} + \gamma'' Ca^{2} \end{aligned}$$

Hence, if we put, for the sake of brevity,

$$\begin{alignedat}{4} &A\alpha  &&+ B\beta   &&+ C\gamma   &&= &D&\quad.\quad.\quad.\quad.\quad.\quad.\quad{(1)} \\ &A\alpha' &&+ B\beta'  &&+ C\gamma'  &&= &D'&\quad.\quad.\quad.\quad.\quad.\quad.\quad{(2)} \\ &A\alpha &&+ B\beta &&+ C\gamma &&= &D&\quad.\quad.\quad.\quad.\quad.\quad.\quad{(3)} \end{alignedat}$$

we shall have

$$\begin{aligned} C^{3}T &= Db'^{2} - 2D'bb' + D'' b^{2} \\ C^{3}U &= -Da'b' + D'(ab' + ba') - D''ab \\ C^{3}V &= Da'^{2} - 2D'aa' + D''a^{2} \end{aligned}$$

From this we find, after the reckoning has been carried out,

$$C^{6}(TV - U^{2}) = (DD - D'^{2}) (ab' - ba')^{2} = (DD - D'^{2}) C^{2}$$

and therefore the formula for the measure of curvature

$$k = \frac{DD'' - D'^{2}}{(A^{2} + B^{2} + C^{2})^{2}}$$

11.

By means of the formula just found we are going to establish another, which may be counted among the most productive theorems in the theory of curved surfaces. Let us introduce the following notation:

$$ \begin{aligned} &\begin{alignedat}{4} &a^{2} &&+ b^{2} &&+ c^{2} &&= E \\ &aa' &&+ bb' &&+ cc' &&= F \\ &a'^{2} &&+ b'^{2} &&+ c'^{2} &&= G \end{alignedat}\\ &\begin{alignedat}{7} &a &&\alpha &&+b &&\beta  &&+c &&\gamma  &&= m &\quad.\quad.\quad.\quad.\quad.\quad.\quad{(4)} \\ &a &&\alpha' &&+b &&\beta' &&+c &&\gamma' &&= m'&\quad.\quad.\quad.\quad.\quad.\quad.\quad{(5)} \\ &a &&\alpha&&+b &&\beta&&+c &&\gamma&&= m&\quad.\quad.\quad.\quad.\quad.\quad.\quad{(6)} \\ &a'\,&&\alpha &&+b'\,&&\beta  &&+c'\,&&\gamma  &&= n&\quad.\quad.\quad.\quad.\quad.\quad.\quad{(7)} \\ &a'&&\alpha' &&+b'&&\beta' &&+c'&&\gamma' &&= n'&\quad.\quad.\quad.\quad.\quad.\quad.\quad{(8)} \\ &a'&&\alpha&&+b'&&\beta&&+c'&&\gamma&&= n&\quad.\quad.\quad.\quad.\quad.\quad.\quad{(9)} \end{alignedat}\\ &A^{2} + B^{2} + C^{2} = EG - F^{2} = \Delta \end{aligned}$$


text: Adam's Reports on Vernacular Education in Bengal and Behar/Report 3/Chapter 1/Section 18


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 "The note you sent this morning from Lady Harriette St. Clair, is precisely to the same purport as Miss Muloch's request,—an application for exact and authentic information respecting the fate of M. Paul Emanuel! You see how much the ladies think of this little man, whom you none of you like. I had a letter the other day, announcing that a lady of some note, who had always determined that whenever she married, her husband should be the counterpart of 'Mr. Knightly' in Miss Austen's 'Emma,' had now changed her mind, and vowed that she would either find the duplicate of Professor Emanuel, or remain for ever single! I have sent Lady Harriette an answer so worded as to leave the matter pretty much where it was. Since the little puzzle amuses the ladies, it would be a pity to spoil their sport by giving them the key."

When Easter, with its duties arising out of sermons to be preached by strange clergymen who had afterwards to be entertained at the Parsonage,—with Mechanics' Institute Meetings, and school tea-drinkings, was over and gone, she came, at the close of April, to visit us in Manchester. We had a friend, a young lady, staying with us. Miss Brontë had expected to find us alone; and although our friend was gentle and sensible after Miss Brontë's own heart, yet her presence was enough to create a nervous tremour. I was aware that both of our guests were unusually silent; and I saw a little shiver run from time to time over Miss Brontë's frame. I could account for the modest reserve of the young lady; and the next day


text: Adam's Reports on Vernacular Education in Bengal and Behar/Report 3/Chapter 1/Section 19


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text:
Author:Louise Ahlén

Works

 * Du gamla, du fria, additional lyrics (1910)

title: Author:Louise Ahlén


text: Adam's Reports on Vernacular Education in Bengal and Behar/Report 3/Chapter 1/Section 20


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 Miss Brontë told me how the unexpected sight of a strange face had affected her.

It was now two or three years since I had witnessed a similar effect produced on her, in anticipation of a quiet evening at Fox-How; and since then she had seen many and various people in London: but the physical sensations produced by shyness were still the same; and on the following day she laboured under severe headache. I had several opportunities of perceiving how this nervousness was ingrained in her constitution, and how acutely she suffered in striving to overcome it. One evening we had, among other guests, two sisters who sang Scottish ballads exquisitely. Miss Brontë had been sitting quiet and constrained till they began "The Bonnie House of Airlie," but the effect of that and "Carlisle Yetts," which followed, was as irresistible as the playing of the Piper of Hamelin. The beautiful clear light came into her eyes; her lips quivered with emotion; she forgot herself, rose, and crossed the room to the piano, where she asked eagerly for song after song. The sisters begged her to come and see them the next morning, when they would sing as long as ever she liked; and she promised gladly and thankfully. But on reaching the house her courage failed. We walked some time up and down the street; she upbraiding herself all the while for folly, and trying to dwell on the sweet echoes in her memory rather than on the thought of a third sister who would have to be faced if we went in. But it was of no use; and dreading lest this struggle with


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 emotion to appear, and a close observer might have discovered a humane heart beating under that iron exterior.

The thermometer fell still lower; the deck was quite deserted except by the Esquimaux dogs, who kept howling piteously. The 8th of December arrived, and the Doctor went out as usual to look at the thermometer. The mercury was frozen—completely frozen!

"Forty-four degrees below zero!" he exclaimed, in dismay. Yes! and on this very day the last atom of coal was thrown into the stove.

a moment despair gained the upper hand, and death seemed staring the unhappy crew in the face—death from cold. The fire got lower each moment, and the effect was soon felt on the temperature of the room. Johnson went to fetch some of his new combustible, and filled the stove with it, adding tow impregnated with frozen oil, which speedily gave out abundant heat. True, the stench was unbearable, and the boatswain was sufficiently convinced that his substitute for coal would find no favor in the middle-class houses of Liverpool. But what was to be done? It was this fat or nothing.

"And yet," said Johnson, "this stinking stuff may bring us some good after all."

"How's that?" asked the carpenter.

"It will be sure to attract the bears. They will think it a most savory odor."

"Well, but I don't see what we want with bears," replied Bell.

"Friend Bell," returned Johnson, "we can't reckon on any more seals; they have taken their departure for a long time, and if the bears don't furnish their share of combustible material, I don't see what is to become of us."

"You are right, Johnson. We are in a perilous situation—it is frightful to think of it. Only suppose our stock of this fat coming to an end! I see no way, I must confess!"

"Except one."

"And what is that?" asked Bell.


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 herself might bring on one of her trying headaches, I entered at last and made the best apology I could for her non-appearance. Much of this nervous dread of encountering strangers I ascribed to the idea of her personal ugliness, which had been strongly impressed upon her imagination early in life, and which she exaggerated to herself in a remarkable manner. "I notice," said she, "that after a stranger has once looked at my face, he is careful not to let his eyes wander to that part of the room again!" A more untrue idea never entered into anyone's head. Two gentlemen who saw her during this visit, without knowing at the time who she was, were singularly attracted by her appearance; and this feeling of attraction towards a pleasant countenance, sweet voice, and gentle timid manners, was so strong in one as to conquer a dislike he had previously entertained to her works.

There was another circumstance that came to my knowledge at this period which told secrets about the finely-strung frame. One night I was on the point of relating some dismal ghost story, just before bed-time. She shrank from hearing it, and confessed that she was superstitious, and prone at all times to the involuntary recurrence of any thoughts of ominous gloom which might have been suggested to her. She said that on first coming to us, she had found a letter on her dressing-table from a friend in Yorkshire, containing a story which had impressed her vividly ever since;—that it


text: Page:The Pharsalia of Lucan; (IA cu31924026485809).pdf/75


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 Let us eliminate from the equations 1, 4, 7 the quantities $\beta,$  $\gamma,$ which is done by multiplying them by $bc' - cb',$  $b'C - c'B,$  $cB - bC$  respectively and adding. In this way we obtain

$$\begin{array}{c} \mathbf{(}A(bc' - cb') + a(b'C - c'B) + a'(cB - bC)\mathbf{)}\alpha \\ = D(bc' - cb') + m(b'C - c'B) + n(cB - bC) \end{array}$$

an equation which is easily transformed into

$$AD = \alpha\Delta + a(nF - mG) + a'(mF - nE)$$

Likewise the elimination of $\alpha,$  $\gamma$ or $\alpha,$  $\beta$  from the same equations gives

$$\begin{alignedat}{4} &BD &&= \beta \Delta &&+ b(nF - mG) &&+ b'(mF - nE) \\ &CD &&= \gamma\Delta &&+ c(nF - mG) &&+ c'(mF - nE) \end{alignedat}$$

Multiplying these three equations by $\alpha,$  $\beta,$  $\gamma''$ respectively and adding, we obtain

$$DD = (\alpha\alpha+ \beta\beta + \gamma\gamma)\Delta + m(nF - mG) + n(mF - nE) \quad.\quad.\quad.{(10)}$$

If we treat the equations 2, 5, 8 in the same way, we obtain

$$\begin{alignedat}{4} {4} &AD' &&= \alpha'\Delta &&+ a (n'F - m'G) &&+ a'(m'F - n'E) \\ &BD' &&= \beta' \Delta &&+ b (n'F - m'G) &&+ b'(m'F - n'E) \\ &CD' &&= \gamma'\Delta &&+ c (n'F - m'G) &&+ c'(m'F - n'E) \end{alignedat}$$

and after these equations are multiplied by $\alpha',$  $\beta',$  $\gamma'$ respectively, addition gives

$$D'^{2} = (\alpha'^{2} + \beta'^{2} + \gamma'^{2})\Delta + m'(n'F - m'G) + n'(m'F - n'E)$$

A combination of this equation with equation (10) gives

$$\begin{alignedat}{1} DD - D'^{2} = (&\alpha\alpha + \beta\beta + \gamma\gamma - \alpha'^{2} - \beta'^{2} - \gamma'^{2})\Delta \\ &+ E(n'^{2} - nn) + F(nm - 2m'n' + mn) + G(m'^{2} - mm) \end{alignedat}$$

It is clear that we have

$$ \frac{\partial E}{\partial p} = 2m,\; \frac{\partial E}{\partial q} = 2m',\; \frac{\partial F}{\partial p} = m' + n,\; \frac{\partial F}{\partial q} = m'' + n',\; \frac{\partial G}{\partial p} = 2n',\; \frac{\partial G}{\partial q} = 2n'',$$

or

$$\begin{aligned} m  &= \tfrac{1}{2}\, \frac{\partial E}{\partial p}, & m' &= \tfrac{1}{2}\, \frac{\partial E}{\partial q}, & m'' &= \frac{\partial F}{\partial q} - \tfrac{1}{2}\, \frac{\partial G}{\partial p} \\ n  &= \frac{\partial F}{\partial p} - \tfrac{1}{2}\, \frac{\partial E}{\partial q}, & n' &= \tfrac{1}{2}\, \frac{\partial G}{\partial p}, & n'' &= \tfrac{1}{2}\, \frac{\partial G}{\partial q} \end{aligned}$$

Moreover, it is easily shown that we shall have

$$\begin{array}{c}\displaystyle \alpha\alpha + \beta\beta + \gamma\gamma'' - \alpha'^{2} - \beta'^{2} - \gamma'^{2} = \frac{\partial n}{\partial q} - \frac{\partial n'}{\partial p}  = \frac{\partial m''}{\partial p} - \frac{\partial m'}{\partial q} \\\displaystyle = -\tfrac{1}{2} \cdot \frac{\partial^{2}E}{\partial q^{2}} + \frac{\partial^{2}F}{\partial p. \partial q} - \tfrac{1}{2} \cdot \frac{\partial^{2}G}{\partial p^{2}} \end{array}$$


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 mingled with her dreams at night, and made her sleep restless and unrefreshing.

One day we asked two gentlemen to meet her at dinner, expecting that she and they would have a mutual pleasure in making each other's acquaintance. To our disappointment, she drew back with timid reserve from all their advances, replying to their questions and remarks in the briefest manner possible; till at last they gave up their efforts to draw her into conversation in despair, and talked to each other and my husband on subjects of recent local interest. Among these Thackeray's Lectures (which had lately been delivered in Manchester) were spoken of, and that on Fielding especially dwelt upon. One gentleman objected to it strongly, as calculated to do moral harm, and regretted that a man having so great an influence over the tone of thought of the day, as Thackeray, should not more carefully weigh his words. The other took the opposite view. He said that Thackeray described men from the inside, as it were; through his strong power of dramatic sympathy, he identified himself with certain characters, felt their temptations, entered into their pleasures, &c. This roused Miss Brontë, who threw herself warmly into the discussion; the ice of her reserve was broken, and from that time she showed her interest in all that was said, and contributed her share to any conversation that was going on in the course of the evening.

What she said, and which part she took, in the dis-


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 Standard Colors.—As used in this system of color nomemclature, the best pigmentary imitation of each of the six spectrum colors red, orange, yellow, green, blue and violet and black and white. These are more specifically called Pigmentary Standards in distinction from spectrum standards.

Spectrum Standards.—The six colors found in the solar spectrum and definitely located by their wave lengths, as follows in the ten millionths of a millimeter. Red, 6571; Orange, 6085; Yellow, 5793; Green, 5164; Blue, 4695; Violet, 4210.

Pigmentary Colors.—All colors used and produced in the arts and sciences. This is in distinction from colors seen in nature, as in flowers and the solar spectrum. The term refers not only to pigments in the strictest sense but to all surfaces coated, painted or dyed artificially.

Pure Colors.—A pure or full color, also called a saturated color, is the most intense expression of that color without the admixture of white or black or gray. All spectrum colors ire pure, while no pigmentary color is absolutely pure, but the pigmentary color which approaches most nearly to the corresponding color in the spectrum must be selected as the pigmentary type of purity of that color. For example, the standard for green must be the best possible pigmentary imitation of the spot in the spectrum which by general consent is called green, and so not only for the six standards but for all their combinations which produce the other colors in nature.

In pigmentary colors the term pure is entirely one of relative degree. As processes of manufacture are improved and new chemical discoveries made, there is good reason to believe that we shall have much more intense colors and hence much better imitations of spectrum colors than are at present possible. Therefore as our pigments become purer those now accepted as full colors will in time become tints or broken colors and new standards will be adopted.

Hue.—The hue of a given color is that color with the admixture of a smaller quantity of another color. An orange hue of


text: Adam's Reports on Vernacular Education in Bengal and Behar/Report 3/Chapter 2/Section 1


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 Rh them employment, and a sum of $600,000 has been appropriated for their relief.

The war in Cuba is of such a nature that short of subjugation or extermination a final military victory for either side seems impracticable. The alternative lies in the physical exhaustion of the one or the other party, or perhaps of both—a condition which in effect ended the ten years' war by the truce of Zanjon. The prospect of such a protraction and conclusion of the present strife is a contingency hardly to be contemplated with equanimity by the civilized world, and least of all by the United States, affected and injured as we are, deeply and intimately, by its very existence.

Realizing this, it appeared to be my duty, in a spirit of true friendliness, no Jess to Spain than to the Cubans who have so much to lose by the prolongation of the struggle, to seek to bring about an immediate termination of the war. To this end I submitted, on the 27th ultimo, as a result of much representation and correspondence, through the United States minister at Madrid, propositions to the Spanish Government looking to an armistice until October 1 for the negotiation of peace with the good offices of the President.

In addition, I asked the immediate revocation of the order of reconcentration, so as to permit the people to return to their farms and the needy to be relieved with provisions and supplies from the United States, cooperating with the Spanish authorities, so as to afford full relief.

The reply of the Spanish cabinet was received on the night of the 31st ultimo. It offered, as the means to bring about peace in Cuba, to confide the preparation thereof to the Insular Parliament, inasmuch as the concurrence of that body would be necessary to reach a final result, it being, however, understood that the powers reserved by the constitution to the Central Government are not lessened or diminished. As the Cuban Parliament does not meet until the 4th of May next, the Spanish Government would not object, for its part, to accept at once a suspension of hostilities if asked for by the insurgents from the general in chief, to whom it would pertain, in such case, to determine the duration and conditions of the armistice.

The propositions submitted by General Woodford and the reply of the Spanish Government were both in the form of brief memoranda, the texts of which are before me, and are substantially in the language above given. The function of the Cuban Parliament in the matter of "preparing" peace and the manner of its doing so are not expressed in the Spanish memorandum; but from General Woodford's explanatory reports of preliminary discussions preceding the final conference it is understood that the Spanish Government stands ready to give the Insular Congress full powers to settle the terms of peace with the insurgents—whether by direct negotiation or indirectly by means of legislation does not appear.


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 If we substitute these different expressions in the formula for the measure of curvature derived at the end of the preceding article, we obtain the following formula, which involves only the quantities $E,$  $F,$  $G$ and their differential quotients of the first and second orders:

$$\begin{aligned}\displaystyle &\qquad 4(EG - F^{2})k = E\left(\frac{\partial E}{\partial q} . \frac{\partial G}{\partial q}      - 2 \frac{\partial F}{\partial p} . \frac{\partial G}{\partial q}  + \biggl(\frac{\partial G}{\partial p}\biggr)^{2}\right) \\ &+ F\left(\frac{\partial E}{\partial p} . \frac{\partial G}{\partial q}        - \frac{\partial E}{\partial q} . \frac{\partial G}{\partial p}       - 2 \frac{\partial E}{\partial q} . \frac{\partial F}{\partial q}       + 4 \frac{\partial F}{\partial p} . \frac{\partial F}{\partial q}       - 2 \frac{\partial F}{\partial p} . \frac{\partial G}{\partial p}\right) \\ &+ G\left(\frac{\partial E}{\partial p} . \frac{\partial G}{\partial p}      - 2 \frac{\partial E}{\partial p} . \frac{\partial F}{\partial q}  + \biggl(\frac{\partial E}{\partial q}\biggr)^{2}\right) - 2(EG - F^{2})\left(     \frac{\partial^{2}E}{\partial q^{2}}   - 2\frac{\partial^{2}F}{\partial p . \partial q}    + \frac{\partial^{2}G}{\partial p^{2}}  \right) \end{aligned}$$

12.

Since we always have

$$dx^{2} + dy^{2} + dz^{2} = E\, dp^{2} + 2F\, dp. dq + G\, dq^{2},$$

it is clear that

$$\sqrt{E\, dp^{2} + 2F\, dp. dq + G\, dq^{2}}$$

is the general expression for the linear element on the curved surface. The analysis developed in the preceding article thus shows us that for finding the measure of curvature there is no need of finite formulæ, which express the coordinates $x,$  $y,$  $z$ as functions of the indeterminates $p,$  $q;$  but that the general expression for the magnitude of any linear element is sufficient. Let us proceed to some applications of this very important theorem.

Suppose that our surface can be developed upon another surface, curved or plane, so that to each point of the former surface, determined by the coordinates $x,$  $y,$  $z,$ will correspond a definite point of the latter surface, whose coordinates are $x',$  $y',$  $z'.$  Evidently $x',$  $y',$  $z'$  can also be regarded as functions of the indeterminates $p,$  $q,$  and therefore for the element $\sqrt{dx'^{2} + dy'^{2} + dz'^{2}}$  we shall have an expression of the form

$$\sqrt{E'\, dp^{2} + 2F'\, dp. dq + G'\, dq^{2}}$$

where $E',$  $F',$  $G'$ also denote functions of $p,$  $q.$  But from the very notion of the development of one surface upon another it is clear that the elements corresponding to one another on the two surfaces are necessarily equal. Therefore we shall have identically

$$E = E',\quad F = F',\quad G = G'.$$

Thus the formula of the preceding article leads of itself to the remarkable

 If a curved surface is developed upon any other surface whatever, the measure of curvature in each point remains unchanged.


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 pute about Thackeray's lecture, may be gathered from the following letter, referring to the same subject:—

"The Lectures arrived safely; I have read them through twice. They must be studied to be appreciated. I thought well of them when I heard them delivered, but now I see their real power, and it is great. The lecture on Swift was new to me; I thought it almost matchless. Not that by any means I always agree with Mr. Thackeray's opinions, but his force, his penetration, his pithy simplicity, his eloquence,—his manly sonorous eloquence—command entire admiration Against his errors I protest, were it treason to do so. I was present at the Fielding lecture: the hour spent in listening to it was a painful hour. That Thackeray was wrong in his way of treating Fielding's character and vices, my conscience told me. After reading that lecture, I trebly felt that he was wrong—dangerously wrong. Had Thackeray owned a son, grown, or growing up, and a son, brilliant but reckless—would he have spoken in that light way of courses that lead to disgrace and the grave? He speaks of it all as if he theorised; as if he had never been called on, in the course of his life, to witness the actual consequences of such failings; as if he had never stood by and seen the issue, the final result of it all. I believe, if only once the prospect of a promising life blasted on the outset by wild ways had passed close under his eyes, he never could have spoken with such levity of what led to its piteous destruction.


text: Adam's Reports on Vernacular Education in Bengal and Behar/Report 3/Chapter 2/Section 2


text: Page:The Pharsalia of Lucan; (IA cu31924026485809).pdf/76


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 Also it is evident that any finite part whatever of the curved surface will retain the same integral curvature after development upon another surface.

Surfaces developable upon a plane constitute the particular case to which geometers have heretofore restricted their attention. Our theory shows at once that the measure of curvature at every point of such surfaces is equal to zero. Consequently, if the nature of these surfaces is defined according to the third method, we shall have at every point

$$\frac{\partial^{2} z}{\partial x^{2}}. \frac{\partial^{2} z}{\partial y^{2}} - \left(\frac{\partial^{2}z}{\partial x . \partial y}\right)^{2} = 0$$

a criterion which, though indeed known a short time ago, has not, at least to our knowledge, commonly been demonstrated with as much rigor as is desirable.

13.

What we have explained in the preceding article is connected with a particular method of studying surfaces, a very worthy method which may be thoroughly developed by geometers. When a surface is regarded, not as the boundary of a solid, but as a flexible, though not extensible solid, one dimension of which is supposed to vanish, then the properties of the surface depend in part upon the form to which we can suppose it reduced, and in part are absolute and remain invariable, whatever may be the form into which the surface is bent. To these latter properties, the study of which opens to geometry a new and fertile field, belong the measure of curvature and the integral curvature, in the sense which we have given to these expressions. To these belong also the theory of shortest lines, and a great part of what we reserve to be treated later. From this point of view, a plane surface and a surface developable on a plane, ''e. g. '', cylindrical surfaces, conical surfaces, etc., are to be regarded as essentially identical; and the generic method of defining in a general manner the nature of the surfaces thus considered is always based upon the formula

$$\sqrt{E\, dp^{2} + 2F\, dp. dq + G\, dq^{2}},$$

which connects the linear element with the two indeterminates $p,$  $q.$ But before following this study further, we must introduce the principles of the theory of shortest lines on a given curved surface.

14.

The nature of a curved line in space is generally given in such a way that the coordinates $x,$  $y,$  $z$ corresponding to the different points of it are given in the form of functions of a single variable, which we shall call $w.$  The length of such a line from


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 8 With this last overture in the direction of immediate peace, and its disappointing reception by Spain, the Executive is brought to the end of his effort.

In my annual message of December last I said:

Thereupon I reviewed these alternatives, in the light of President Grant's measured words, uttered in 1875, when after seven years of sanguinary, destructive, and cruel hostilities in Cuba he reached the conclusion that the recognition of the independence of Cuba was impracticable and indefensible; and that the recognition of belligerence was not warranted by the facts according to the tests of public law. I commented especially upon the latter aspect of the question, pointing out the inconveniences and positive dangers of a recognition of belligerence which, while adding to the already onerous burdens of neutrality within our own jurisdiction, could not in any way extend our influence or effective offices in the territory of hostilities.

Nothing has since occurred to change my view in this regard; and I recognize as fully now as then that the issuance of a proclamation of neutrality, by which process the so-called recognition of belligerents is published, could, of itself and unattended by other action, accomplish nothing toward the one end for which we labor—the instant pacification of Cuba and the cessation of the misery that afflicts the island.

Turning to the question of recognizing at this time the independence of the present insurgent government in Cuba, we find safe precedents in our history from an early day. They are well summed up in President Jackson's message to Congress, December 21, 1836, on the subject of the recognition of the independence of Texas. He said:

In all the contests that have arisen out of the revolutions of France, out of the disputes relating to the Crowns of Portugal and Spain, out of the separation of the American possessions of both from the European Governments, and out of the numerous and constantly occurring struggles for dominion in Spanish America, so wisely consistent with our just principles has been the action of our Government, that we have, under the most critical circumstances, avoided all censure, and encountered no other evil than that produced by a transient estrangement of good will in those against whom we have been by force of evidence compelled to decide.

It has thus made known to the world that the uniform policy and practice of the United States is to avoid all interference in disputes which merely relate to the internal government of other nations, and eventually to recognize the authority of the prevailing party without reference to our particular interests and views or to the merits of the original controversy.

But on this, as on every other trying occasion, safety is to be found in a rigid adherence to principle.

In the contest between Spain and the revolted colonies we stood aloof, and waited not only until the ability of the new States to protect themselves was fully established, but until the danger of their being again subjugated had entirely passed away. Then, and not until then, were they recognized.


text: Adam's Reports on Vernacular Education in Bengal and Behar/Report 3/Chapter 2/Section 3


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 Rh

Such was our course in regard to Mexico herself. It is true that with regard to Texas the civil authority of Mexico has been expelled, its invading army defeated, the chief of the Republic himself captured, and all present power to control the newly organized government of Texas annihilated within its confines; but, on the other hand, there is, in appearance at least, an immense disparity of physical force on the side of Texas. The Mexican Republic, under another Executive, is rallying its forces under a new leader and menacing a fresh invasion to recover its lost dominion.

Upon the issue of this threatened invasion the independence of Texas may be considered as suspended; and were there nothing peculiar in the relative situation of the United States and Texas, our acknowledgment of its independence at such a crisis could scarcely be regarded as consistent with that prudent reserve with which we have hitherto held ourselves bound to treat all similar questions.

Thereupon Andrew Jackson proceeded to consider the risk that there might be imputed to the United States motives of selfish interest in view of the former claim on our part to the territory of Texas, and of the avowed purpose of the Texans in seeking recognition of independence as an incident to the incorporation of Texas in the Union, concluding thus:

These are the words of the resolute and patriotic Jackson. They are evidence that the United States, in addition to the test imposed by public law as the condition of the recognition of independence by a neutral state (to wit, that the revolted state shall "constitute in fact a body politic, having a government in substance as well as in name, possessed of the elements of stability," and forming de facto, "if left to itself, a state among the nations, reasonably capable of discharging the duties of a state"), has imposed for its own governance in dealing with cases like these the further condition that recognition of independent statehood is not due to a revolted dependency until the danger of its being again subjugated by the parent state has entirely passed away.

This extreme test was, in fact, applied in the case of Texas. The Congress to whom President Jackson referred the question as one "probably leading to war," and therefore a proper subject for "a previous understanding with that body by whom war can alone be declared and by whom all the provisions for sustaining its perils must be furnished," left the matter of the recognition of Texas to the discretion of the Executive, providing merely for the sending of a diplomatic agent when the President should be satisfied that the Republic of Texas bad become "an independent State." It was so recognized by President Van Buren, who commissioned a chargé d'affaires March 7, 1837, after


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Page:Batman upon Bartolome.djvu/84

 For in ſléeping the pulſe is wont to bée little and ſlow: and after ſléepe ſtrong & great. For then the kind heat is comforted: but yet if the ſléepe be too long, the pulſe waxeth thin and féeble. Wherfore if a man be ſodeinly awaked of his ſléep, otherwiſe then kinde will, anone pulſe is found ſwift and thicke, quaking, and inordinate. And if he take his reſt after ſuch fright, againe the pulſe turneth to his former eſtate. Alſo through trauaile and buſineſſe of the bodie, if it bée temporate, it maketh the pulſe ſtrong, great, ſwift, and thicke. For by temporate trauaile the kinde heate is ſtirred. But if the trauaile paſſeth temporaunce, the contrary happeneth, the pulſe is lyttle, hard, ſlowe, and thin. For in them that trauaile ſo, the vertue faileth, and kinde heate is diſſolued, and then the pulſe is féebled. Alſo through vſe of often bathing. For they bath temporatly in hot water, they haue the pulſe ſtrong, great, and thicke, and that is through the comfort of kinde, and of deſtroieng of ſuperfluitie of moiſture. But in them that abide too long in the water, the pulſe is made féeble: But yet the ſwiftneſſe and thicknes abideth as it was afore hand. Alſo likewiſe they bath them temporatly in cold water, haue  pulſe ſtrong and ſwifte, and that chaunceth through ioyning togethers of kindly heat & comfort of the vertue that commeth of temporance of the vtter keeling. But to long abiding in ſuch a bath, feebleth the pulſe and the vertue. And that happeneth more in leane men then in fat, through coldneſſe that commeth to the vtter partes to ſodeinly. And as it were without let, pearcing in, and as it were conſtraining the partes about the heart more then inough. Alſo through diuerſe taking of meate and drinke. For too much meal & vndigeſted féebleth the pulſe. But meat moderatly taken and digeſted, & ſpread into the limmes, by ſtirring vp the vertue, augmenteth the pulſe. Alſo moderate drinke, and digeſted, maketh the pulſe ſtrong, great, and ſwift. Hot drinke maketh the pulſe ſwift and thicke, but cold drinke maketh the pulſe thin & ſlow. Alſo through diuerſe paſſions of the ſoule. For wrath maketh pulſe ſwift, ſtrong, and thicke: & gladneſſe maketh it meane. Alſo dreade or feare maketh the pulſe ſwift, inordinate in quaking: and ſo doth ſorrow. And ſo of other paſſions it happeneth. And this that is ſaid of the properties, vertues, effects, and working of the might and ſtrength of the ſoule, touching this treatiſe is inough at this time. Now ſomewhat ſhall be ſaid, by the help and grace of God, of the properties of mans bodie Of the which body the ſoule is act and perfection.

FINIS LIBRI TERTII. '''¶INCIPIT LIBER QVARTVS.'''

¶Of the properties of the corporall ſubſtaunce.
treate of the properties of mans body, and of the parts therof, we ſhall firſt begin to treate of the qualities of the elements and of the humors, of the which the body is made.

¶Of the foure qualities Elementarie. Chap. 1.
ements there are foure, & ſo there be foure qualities of Elements, of the which euery bodie that hath a ſoule, is compoſed and made, as of matter. And namely mans bodie, that is nobleſt among all the Elements, and moſt nobly ordeined among all things, that be compoſed

title: Page:Batman upon Bartolome.djvu/84


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Page:General Investigations of Curved Surfaces, by Carl Friedrich Gauss, translated into English by Adam Miller Hiltebeitel and James Caddall Morehead.djvu/36

 an arbitrary initial point to the point whose coordinates are $x,$  $y,$  $z,$ is expressed by the integral

$$ \int dw. \sqrt{ \left(\frac{dx}{dw}\right)^{2} + \left(\frac{dy}{dw}\right)^{2} + \left(\frac{dz}{dw}\right)^{2}}$$

If we suppose that the position of the line undergoes an infinitely small variation, so that the coordinates of the different points receive the variations $\delta x,$  $\delta y,$  $\delta z,$ the variation of the whole length becomes

$$\int \frac{dx. d\, \delta x + dy. d\, \delta y + dz. d\, \delta z}{\sqrt{dx^{2} + dy^{2} + dz^{2}}}$$

which expression we can change into the form

$$\begin{array}{c}\displaystyle \frac{dx. \delta x + dy. \delta y + dz. \delta z}    {\sqrt{dx^{2} + dy^{2} + dz^{2}}} \\ \displaystyle -\int \Biggl(   \delta x . d\frac{dx}{\sqrt{dx^{2} + dy^{2} + dz^{2}}}  + \delta y . d\frac{dy}{\sqrt{dx^{2} + dy^{2} + dz^{2}}}  + \delta z . d\frac{dz}{\sqrt{dx^{2} + dy^{2} + dz^{2}}}  \Biggr) \end{array}$$

We know that, in case the line is to be the shortest between its end points, all that stands under the integral sign must vanish. Since the line must lie on the given surface, whose nature is defined by the equation

$$P\, dx + Q\, dy + R\, dz = 0,$$

the variations $\delta x,$  $\delta y,$  $\delta z$ also must satisfy the equation

$$P\, \delta x + Q\, \delta y + R\, \delta z = 0,$$

and from this it follows at once, according to well-known rules, that the differentials

$$d\frac{dx}{\sqrt{dx^{2} + dy^{2} + dz^{2}}},\quad d\frac{dy}{\sqrt{dx^{2} + dy^{2} + dz^{2}}},\quad d\frac{dz}{\sqrt{dx^{2} + dy^{2} + dz^{2}}}$$

must be proportional to the quantities $P,$  $Q,$  $R$ respectively. Let $dr$  be the element of the curved line; $\lambda$  the point on the sphere representing the direction of this element; $L$  the point on the sphere representing the direction of the normal to the curved surface; finally, let $\xi,$  $\eta,$  $\zeta$ be the coordinates of the point $\lambda,$  and $X,$  $Y,$  $Z$  be those of the point $L$  with reference to the centre of the sphere. We shall then have

$$dx = \xi\, dr,\quad dy = \eta\, dr,\quad dz = \zeta\, dr$$

from which we see that the above differentials become $d\xi,$  $d\eta,$  $d\zeta.$ And since the quantities $P,$  $Q,$  $R$  are proportional to $X,$  $Y,$  $Z,$  the character of shortest lines is expressed by the equations

$$\frac{d\xi}{X} = \frac{d\eta}{Y} = \frac{d\zeta}{Z}$$


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Page:The life of Charlotte Brontë (IA lifeofcharlotteb02gaskrich).pdf/311

 Had I a brother yet living, I should tremble to let him read Thackeray's lecture on Fielding. I should hide it away from him. If, in spite of precaution, it should fall into his hands, I should earnestly pray him not to be misled by the voice of the charmer, let him charm never so wisely. Not that for a moment I would have had Thackeray to abuse Fielding, or even Pharisaically to condemn his life; but I do most deeply grieve that it never entered into his heart sadly and nearly to feel the peril of such a career, that he might have dedicated some of his great strength to a potent warning against its adoption by any young man. I believe temptation often assails the finest manly natures; as the pecking sparrow or destructive wasp attacks the sweetest and mellowest fruit, eschewing what is sour and crude. The true lover of his race ought to devote his vigour to guard and protect; he should sweep away every lure with a kind of rage at its treachery. You will think this far too serious, I dare say; but the subject is serious, and one cannot help feeling upon it earnestly."


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 10 Mexico had abandoned an attempt to reconquer the Texan territory, and when there was at the time no bona fide contest going on between the insurgent Province and its former Sovereign.

I said in my message of December last, "It is to be seriously considered whether the Cuban insurrection possesses beyond dispute the attributes of statehood which alone can demand the recognition of belligerency in its favor." The same requirement must certainly be no less seriously considered when the graver issue of recognizing independence is in question, for no less positive test can be applied to the greater act than to the lesser; while, on the other hand, the influences and consequences of the struggle upon the internal policy of the recognizing State, which form important factors when the recognition of belligerency is concerned, are secondary, if not rightly eliminable, factors when the real question is whether the community claiming recognition is or is not independent beyond peradventure.

Nor from the standpoint of expediency do I think it would be wise or prudent for this Government to recognize at the present time the independence of the so-called Cuban Republic. Such recognition is not necessary in order to enable the United States to intervene and pacify the island. To commit this country now to the recognition of any particular government in Cuba might subject us to embarrassing conditions of international obligation toward the organization so recognized, In case of intervention our conduct would be subject to the approval or disapproval of such government. We would be required to submit to its direction and to assume to it the mere relation of a friendly ally.

When it shall appear hereafter that there is within the island a government capable of performing the duties and discharging the functions of a separate nation, and having, as a matter of fact, the proper forms and attributes of nationality, such government can be promptly and readily recognized and the relations and interests of the United States with such nation adjusted.

There remain the alternative forms of intervention to end the war, either as an impartial neutral by imposing a rational compromise between the contestants, or as the active ally of the one party or the other.

As to the first, it is not to be forgotten that during the last few months the relation of the United States has virtually been one of friendly intervention in many ways, each not of itself conclusive, but all tending to the exertion of a potential influence toward an ultimate pacific result, just and honorable to all interests concerned. The spirit of all our acts hitherto has been an earnest, unselfish desire for peace and prosperity in Cuba, untarnished by differences between us and Spain, and unstained by the blood of American citizens.

The forcible intervention of the United States as a neutral to stop the war, according to the large dictates of humanity and following


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Page:Life and Works of Abraham Lincoln, v6.djvu/102

80 SPEECHES [May 19

Reply to the Committee Informing Him of His Nomination for President by the Chicago Convention.

May 19, i860.

Mr. Chairman and Gentlemen of the Com- mittee: I tender to you, and through you to the RepubHcan National Convention, and all the people represented in it, my profoundc-.t thanks for tlie high honor done me, which you now formally announce. Deeply and even painfully sensible of the great responsibility which is in- separable from this high honor — a responsibility which I could almost wish had fallen upon some one of the far more eminent men and experi- enced statesmen whose distinguished names were before the convention — I shall, by your leave, consider more fully the resolutions of the convention, denominated the platform,* and without any unnecessary or unreasonable delay respond to you, jIr. Chairman, in writing, not doubting that the platform will be found satis- factory, and the nomination gratefully accepted.

And now I will not longer defer the pleasure of taking you, and each of you, by the hand.

Acceptance of Nomination as President.

Letter to George Ashmun and Others.

Springfield, III. May 23, i860. Hon. George Ashmun,

President of the Republican National Con- vention. Sir : I accept the nomination tendered irio. by

 * See succeeding pages.


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Page:General Investigations of Curved Surfaces, by Carl Friedrich Gauss, translated into English by Adam Miller Hiltebeitel and James Caddall Morehead.djvu/37

 Moreover, it is easily seen that

$$\sqrt{d\xi^{2} + d\eta^{2} + d\zeta^{2}}$$ is equal to the small arc on the sphere which measures the angle between the directions of the tangents at the beginning and at the end of the element $dr,$ and is thus equal to $\frac{dr}{\rho},$  if $\rho$  denotes the radius of curvature of the shortest line at this point. Thus we shall have

$$\rho\, d\xi = X\, dr,\quad \rho\, d\eta = Y\, dr,\quad \rho\, d\zeta = Z\, dr$$

15.

Suppose that an infinite number of shortest lines go out from a given point $A$ on the curved surface, and suppose that we distinguish these lines from one another by the angle that the first element of each of them makes with the first element of one of them which we take for the first. Let $\phi$  be that angle, or, more generally, a function of that angle, and $r$  the length of such a shortest line from the point $A$ to the point whose coordinates are $x,$  $y,$  $z.$  Since to definite values of the variables $r,$  $\phi$  there correspond definite points of the surface, the coordinates $x,$  $y,$  $z$  can be regarded as functions of $r,$  $\phi.$  We shall retain for the notation $\lambda,$  $L,$  $\xi,$  $\eta,$  $\zeta,$  $X,$  $Y,$  $Z$  the same meaning as in the preceding article, this notation referring to any point whatever on any one of the shortest lines.

All the shortest lines that are of the same length $r$ will end on another line whose length, measured from an arbitrary initial point, we shall denote by $v.$  Thus $v$  can be regarded as a function of the indeterminates $r,$  $\phi,$  and if $\lambda'$  denotes the point on the sphere corresponding to the direction of the element $dv,$  and also $\xi',$  $\eta',$  $\zeta'$  denote the coordinates of this point with reference to the centre of the sphere, we shall have

$$\frac{\partial x}{\partial \phi} = \xi' \cdot \frac{\partial v}{\partial \phi},\quad \frac{\partial y}{\partial \phi} = \eta' \cdot \frac{\partial v}{\partial \phi},\quad \frac{\partial z}{\partial \phi} = \zeta' \cdot \frac{\partial v}{\partial \phi}$$

From these equations and from the equations

$$\frac{\partial x}{\partial r} = \xi,\quad \frac{\partial y}{\partial r} = \eta,\quad \frac{\partial z}{\partial r} = \zeta$$

we have

$$\frac{\partial x}{\partial r} \cdot \frac{\partial x}{\partial \phi} + \frac{\partial y}{\partial r} \cdot \frac{\partial y}{\partial \phi} + \frac{\partial z}{\partial r} \cdot \frac{\partial z}{\partial \phi} = (\xi\xi' + \eta\eta' + \zeta\zeta') \cdot \frac{\partial v}{\partial \phi} = \cos \lambda\lambda' \cdot \frac{\partial v}{\partial \phi}$$


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her visit to Manchester, she had to return to a re-opening of the painful circumstances of the previous winter, as the time drew near for Mr. Nicholls' departure from Haworth. A testimonial of respect from the parishioners was presented, at a public meeting, to one who had faithfully served them for eight years: and he left the place, and she saw no chance of hearing a word about him in the future, unless it was some second-hand scrap of intelligence, dropped out accidentally by one of the neighbouring clergymen.

I had promised to pay her a visit on my return from London in June; but, after the day was fixed, a letter came from Mr. Brontë, saying that she was suffering from so severe an attack of influenza, accompanied with such excruciating pain in the head, that he must request me to defer my visit until she was better. While sorry for the cause, I did not regret that my going was delayed till the season when the moors would be all glorious with the purple bloom of the heather; and thus present a scene about which she had often spoken to me. So we agreed that I should not come to her before August or September. Meanwhile, I received a letter from which I am tempted to take an


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 always violent and sanguinary; whereas, till the time of the Gracchi, no blood had ever been shed in any Roman faction; and from the time of the Gracchi the Roman republic may be considered as in reality dissolved. Notwithstanding, therefore, the very respectable authority of Plato, Aristotle, and Polybius, and notwithstanding the very ingenious reasons by which Mr. Montesquieu endeavors to support that authority, it seems probable that the musical education of the Greeks had no great effect in mending their morals, since, without any such education, those of the Romans were upon the whole superior. The respect of those ancient sages for the institutions of their ancestors, had probably disposed them to find much political wisdom in what was, perhaps, merely an ancient custom, continued, without interruption, from the earliest period of those societies, to the times in which they had arrived at a considerable degree of refinement. Music and dancing are the great amusements of almost all barbarous nations, and the great accomplishments which are supposed to fit any man for entertaining his society. It is so at this day among the negroes on the coast of Africa. It was so among the ancient Celts, among the ancient Scandinavians, and, as we may learn from Homer, among the ancient Greeks in the times preceding the Trojan war. When the Greek tribes had formed themselves into little republics, it was natural that the study of those accomplishments should, for a long time, make a part of the public and common education of the people.

The masters who instructed the young people either in music or in military exercises, do not seem to have been paid, or even appointed by the State, either in Rome or even in Athens, the Greek republic of whose laws and


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 Rh many historical precedents where neighboring States have interfered to check the hopeless sacrifices of life by internecine conflicts beyond their borders, is justifiable on rational grounds. It involves, however, hostile constraint upon both the parties to the contest as well to enforce a truce as to guide the eventual settlement.

The grounds for such intervention may be briefly summarized as follows:

First. In the cause of humanity and to put an end to the barbarities, bloodshed, starvation, and horrible miseries now existing there, and which the parties to the conflict are either unable or unwilling to stop or mitigate. It is no answer to say this is all in another country, belonging to another nation, and is therefore none of our business. It is specially our duty, for it is right at our door.

Second. We owe it to our citizens in Cuba to afford them that protection and indemnity for life and property which no government there can or will afford, and to that end to terminate the conditions that deprive them of legal protection.

Third. The right to intervene may be justified by the very serious injury to the commerce, trade, and business of our people, and by the wanton destruction of property and devastation of the island.

Fourth. and which is of the utmost importance. The present condition of affairs in Cuba is a constant menace to our peace, and entails upon this Government an enormous expense. With such a conflict waged for years in an island so near us and with which our people have such trade and business relations—when the lives and liberty of our citizens are in constant danger and their property destroyed and themselves ruined—where our trading vessels are liable to seizure and are seized at our very door by war ships of a foreign nation, the expeditions of filibustering that we are powerless to prevent altogether, and the irritating questions and entanglements thus arising—all these and others that I need not mention, with the resulting strained relations, are a constant menace to our peace, and compel us to keep on a semiwar footing with a nation with which we are at peace.

These elements of danger and disorder already pointed out have been strikingly illustrated by a tragic event which has deeply and justly moved the American people. I have already transmitted to Congress the report of the naval court of inquiry on the destruction of the battle ship Maine in the harbor of Havana during the night of the 15th of February. The destruction of that noble vessel has filled the national heart with inexpressible horror. Two hundred and fifty-eight brave sailors and marines and two officers of our Navy, reposing in the fancied security of a friendly harbor, have been hurled to death, grief and want brought to their homes and sorrow to the nation.

The naval court of inquiry, which, it is needless to say, commands the unqualified confidence of the Government, was unanimous in its conclusion that the destruction of the Maine was caused by an exte-


text: Adam's Reports on Vernacular Education in Bengal and Behar/Report 3/Chapter 2/Section 4


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24  At midnight spanning with a bridge of silver The Merrimac by Uncanoonuc’s falls.

There were five souls of us whom travel’s chance Had thrown together in these wild north hills: A city lawyer, for a month escaping From his dull office, where the weary eye Saw only hot brick walls and close thronged streets; Briefless as yet, but with an eye to see Life’s sunniest side, and with a heart to take Its chances all as godsends; and his brother, Pale from long pulpit studies, yet retaining The warmth and freshness of a genial heart, Whose mirror of the beautiful and true, In Man and Nature, was as yet undimmed By dust of theologic strife, or breath Of sect, or cobwebs of scholastic lore; Like a clear crystal calm of water, taking The hue and image of o’erleaning flowers, Sweet human faces, white clouds of the noon, Slant starlight glimpses through the dewy leaves, And tenderest moonrise. ’T was, in truth, a study, To mark his spirit, alternating between A decent and professional gravity And an irreverent mirthfulness, which often Laughed in the face of his divinity, Plucked off the sacred ephod, quite unshrined The oracle, and for the pattern priest Left us the man. A shrewd, sagacious merchant, To whom the soiled sheet found in Crawford’s inn, Giving the latest news of city stocks And sales of cotton, had a deeper meaning Than the great presence of the awful mountains Glorified by the sunset; and his daughter, A delicate flower on whom had blown too long Those evil winds, which, sweeping from the ice And winnowing the fogs of Labrador, Shed their cold blight round Massachusetts Bay, With the same breath which stirs Spring’s opening leaves And lifts her half-formed flower-bell on its stem, Poisoning our seaside atmosphere.

It chanced That as we turned upon our homeward way, A drear northeastern storm came howling up The valley of the Saco; and that girl Who had stood with us upon Mount Washington, Her brown locks ruffled by the wind which whirled In gusts around its sharp, cold pinnacle, Who had joined our gay trout-fishing in the streams Which lave that giant’s feet; whose laugh was heard Like a bird’s carol on the sunrise breeze Which swelled our sail amidst the lake’s green islands, Shrank from its harsh, chill breath, and visibly drooped Like a flower in the frost. So, in that quiet inn Which looks from Conway on the mountains piled Heavily against the horizon of the north, Like summer thunder-clouds, we made our home: And while the mist hung over dripping hills, And the cold wind-driven rain-drops all day long Beat their sad music upon roof and pane, We strove to cheer our gentle invalid.

The lawyer in the pauses of the storm Went angling down the Saco, and, returning, Recounted his adventures and mishaps; Gave us the history of his scaly clients, Mingling with ludicrous yet apt citations Of barbarous law Latin, passages From Izaak Walton’s Angler, sweet and fresh As the flower-skirted streams of Staffordshire, Where, under aged trees, the southwest wind Of soft June mornings fanned the thin, white hair Of the sage fisher. And, if truth be told, Our youthful candidate forsook his sermons,


text: Adam's Reports on Vernacular Education in Bengal and Behar/Report 3/Chapter 2/Section 5


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Page:General Investigations of Curved Surfaces, by Carl Friedrich Gauss, translated into English by Adam Miller Hiltebeitel and James Caddall Morehead.djvu/38

 Let $S$  denote the first member of this equation, which will also be a function of $r,$  $\phi.$ Differentiation of $S$  with respect to $r$  gives

$$\begin{aligned} \frac{\partial S}{\partial r} &= \frac{\partial^{2} x}{\partial r^{2}}. \frac{\partial x}{\partial \phi} + \frac{\partial^{2} y}{\partial r^{2}}. \frac{\partial y}{\partial \phi} + \frac{\partial^{2} z}{\partial r^{2}}. \frac{\partial z}{\partial \phi} + \tfrac{1}{2}. \frac{\partial \left(      \left(\tfrac{\partial x}{\partial r}\right)^{2}     + \left(\tfrac{\partial y}{\partial r}\right)^{2}     + \left(\tfrac{\partial z}{\partial r}\right)^{2}   \right)}{\partial \phi} \\ &= \frac{\partial \xi}{\partial r}. \frac{\partial x}{\partial \phi} + \frac{\partial \eta}{\partial r}. \frac{\partial y}{\partial \phi} + \frac{\partial \zeta}{\partial r}. \frac{\partial z}{\partial \phi} + \tfrac{1}{2}. \frac{\partial(\xi^{2} + \eta^{2} + \zeta^{2})}{\partial \phi} \end{aligned}$$

But

$$\xi^{2} + \eta^{2} + \zeta^{2} = 1,$$

and therefore its differential is equal to zero; and by the preceding article we have, if $\rho$  denotes the radius of curvature of the line $r,$

$$\frac{\partial \xi}{\partial r} = \frac{X}{\rho},\quad \frac{\partial \eta}{\partial r} = \frac{Y}{\rho},\quad \frac{\partial \zeta}{\partial r} = \frac{Z}{\rho}$$

Thus we have

$$\frac{\partial S}{\partial r} = \frac{1}{\rho}. (X\xi' + Y\eta' + Z\zeta'). \frac{\partial v}{\partial \phi} = \frac{1}{\rho}. \cos L\lambda'. \frac{\partial v}{\partial \phi} = 0$$

since $\lambda'$  evidently lies on the great circle whose pole is $L.$ From this we see that $S$  is independent of $r,$  and is, therefore, a function of $\phi$  alone. But for $r = 0$ we evidently have $v = 0,$  consequently $\frac{\partial v}{\partial \phi} = 0,$  and $S = 0$  independently of $\phi.$  Thus, in general, we have necessarily $S = 0,$  and so $\cos\lambda\lambda' = 0,$  ''i. e. '', $\lambda\lambda' = 90^{\circ}.$ From this follows the

If on a curved surface an infinite number of shortest lines of equal length be drawn from the same initial point, the lines joining their extremities will be normal to each of the lines.

We have thought it worth while to deduce this theorem from the fundamental property of shortest lines; but the truth of the theorem can be made apparent without any calculation by means of the following reasoning. Let $AB,$  $AB'$ be two shortest lines of the same length including at $A$  an infinitely small angle, and let us suppose that one of the angles made by the element $BB'$  with the lines $BA,$  $B'A$  differs from a right angle by a finite quantity. Then, by the law of continuity, one will be greater and the other less than a right angle. Suppose the angle at $B$ is equal to $90^{\circ} - \omega,$  and take on the line $AB$  a point $C,$  such that

$$BC = BB'. \operatorname{cosec} \omega.$$

Then, since the infinitely small triangle $BB'C$ may be regarded as plane, we shall have

$$CB' = BC. \cos \omega,$$


text: Adam's Reports on Vernacular Education in Bengal and Behar/Report 3/Chapter 2/Section 6


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 12 rior explosion, that of a submarine mine. It did not assume to place the responsibility. That remains to be fixed.

In any event the destruction of the Maine, by whatever exterior cause, is a patent and impressive proof of a state of things in Cuba that is intolerable. That condition is thus shown to be such that the Spanish Government can not assure safety and security to a vessel of the American Navy in the harbor of Havana on a mission of peace, and rightfully there.

Further referring in this connection to recent diplomatic correspondence, a dispatch from our minister to Spain, of the 26th ultimo, contained the statement that the Spanish minister for foreign affairs assured him positively that Spain will do all that the highest honor and justice require in the matter of the Maine. The reply above referred to of the 31st ultimo also contained an expression of the readiness of Spain to submit to an arbitration all the differences which can arise in this matter, which is subsequently explained by the note of the Spanish minister at Washington of the 10th instant, as follows:

To this I have made no reply.

President Grant, in 1875, after discussing the phases of the contest as it then appeared, and its hopeless and apparent indefinite prolongation, said:

In the last annual message of my immediate predecessor during the pending struggle, it was said:

When the inability of Spain to deal successfully with the insurrection has become manifest, and it is demonstrated that her sovereignty is extinct in Cuba for all pur-


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text: Adam's Reports on Vernacular Education in Bengal and Behar/Report 3/Chapter 2/Section 7


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 Rh poses of its rightful existence, and when a hopeless struggle for its reestablishment has degenerated into a strife which means nothing more than the useless sacrifice of human life and the utter destruction of the very subject-matter of the conflict, a situation will be presented in which our obligations to the sovereignty of Spain will be superseded by higher obligations, which we can hardly hesitate to recognize and discharge.

In my annual message to Congress, December last, speaking to this question, I said:

The long trial has proved that the object for which Spain has waged the war can not be attained. The fire of insurrection may flame or may smolder with varying seasons, but it has not been and it is plain that it can not be extinguished by present methods. The only hope of relief and repose from a condition which can no longer be endured is the enforced pacification of Cuba. In the name of humanity, in the name of civilization, in behalf of endangered American interests which give us the right and the duty to speak and to act, the war in Cuba must stop.

In view of these facts and of these considerations, I ask the Congress to authorize and empower the President to take measures to secure a full and final termination of hostilities between the Government of Spain and the people of Cuba, and to secure in the island the establishment of a stable government, capable of maintaining order and observing its international obligations, insuring peace and tranquillity and the security of its citizens as well as our own, and to use the military and naval forces of the United States as may be necessary for these purposes.

And in the interest of humanity and to aid in preserving the lives of the starving people of the island I recommend that the distribution of food and supplies be continued, and that an appropriation be made out of the public Treasury to supplement the charity of our citizens.

The issue is now with the Congress. It is a solemn responsibility. I have exhausted every effort to relieve the intolerable condition of affairs which is at our doors. Prepared to execute every obligation imposed upon me by the Constitution and the law, I await your action.


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 14 Yesterday, and since the preparation of the foregoing message, official information was received by me that the latest decree of the Queen Regent of Spain directs General Blanco, in order to prepare and facilitate peace, to proclaim a suspension of hostilities, the duration and details of which have not yet been communicated to me.

This fact with every other pertinent consideration will, I am sure, have your just and careful attention in the solemn deliberations upon which you are about to enter. If this measure attains a successful result, then our aspirations as a Christian, peace-loving people will be realized. If it fails, it will be only another justification for our contemplated action.

2em

April 11, 1898.


text: Adam's Reports on Vernacular Education in Bengal and Behar/Report 3/Chapter 2/Section 9


text: Adam's Reports on Vernacular Education in Bengal and Behar/Report 3/Chapter 2/Section 8


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Rh His commentaries, articles and creeds, For the fair page of human loveliness, The missal of young hearts, whose sacred text Is music, its illumining, sweet smiles. He sang the songs she loved; and in his low, Deep, earnest voice, recited many a page Of poetry, the holiest, tenderest lines Of the sad bard of Olney, the sweet songs, Simple and beautiful as Truth and Nature, Of him whose whitened locks on Rydal Mount Are lifted yet by morning breezes blowing From the green hills, immortal in his lays. And for myself, obedient to her wish, I searched our landlord’s proffered library: A well-thumbed Bunyan, with its nice wood pictures Of scaly fiends and angels not unlike them; Watts’ unmelodious psalms; Astrology’s Last home, a musty pile of almanacs, And an old chronicle of border wars And Indian history. And, as I read A story of the marriage of the Chief Of Saugus to the dusky Weetamoo, Daughter of Passaconaway, who dwelt In the old time upon the Merrimac, Our fair one, in the playful exercise Of her prerogative,—the right divine Of youth and beauty,—bade us versify The legend, and with ready pencil sketched Its plan and outlines, laughingly assigning To each his part, and barring our excuses With absolute will. So, like the cavaliers Whose voices still are heard in the Romance Of silver-tongued Boccaccio, on the banks Of Arno, with soft tales of love beguiling The ear of languid beauty, plague-exiled From stately Florence, we rehearsed our rhymes To their fair auditor, and shared by turns Her kind approval and her playful censure.

It may be that these fragments owe alone To the fair setting of their circumstances,— The associations of time, scene, and audience,— Their place amid the pictures which fill up The chambers of my memory. Yet I trust That some, who sigh, while wandering in thought, Pilgrims of Romance o’er the olden world, That our broad land,—our sea-like lakes and mountains Piled to the clouds, our rivers overhung By forests which have known no other change For ages than the budding and the fall Of leaves, our valleys lovelier than those Which the old poets sang of,—should but figure On the apocryphal chart of speculation As pastures, wood-lots, mill-sites, with the privileges, Rights, and appurtenances, which make up A Yankee Paradise, unsung, unknown, To beautiful tradition; even their names, Whose melody yet lingers like the last Vibration of the red man’s requiem, Exchanged for syllables significant, Of cotton-mill and rail-car, will look kindly Upon this effort to call up the ghost Of our dim Past, and listen with pleased ear To the responses of the questioned Shade.

O child of that white-crested mountain whose springs Gush forth in the shade of the cliff-eagle’s wings, Down whose slopes to the lowlands thy wild waters shine, Leaping gray walls of rock, flashing through the dwarf pine;

From that cloud-curtained cradle so cold and so lone, From the arms of that wintry-locked mother of stone, By hills hung with forests, through vales wide and free, Thy mountain-born brightness glanced down to the sea!

No bridge arched thy waters save that where the trees Stretched their long arms above thee and kissed in the breeze: No sound save the lapse of the waves on thy shores, The plunging of otters, the light dip of oars.

Green-tufted, oak-shaded, by Amoskeag’s fall Thy twin Uncanoonucs rose stately and tall,