demand a supply sufficient for the necessaries of life, though he may demand long enough before he will get them. It is true, there are the Union Workhouses, where, if bread is asked for, stones will be given; and when a man has broken these, he may break his fast afterwards. Next to personal security comes personal liberty, which consists in the power of moving from place to place,—a luxury often indulged in by debtors, occupants of furnished lodgings, and others, who prize liberty to such an extent, that the liberties they take are truly wonderful. Magna Charta says, that no freeman shall be imprisoned, except by his peers; and if this be true, every policeman who walks a man off to the station-house, must be considered as a peer for temporary purposes.

Besides the three great rights already touched on, there are a few auxiliary rights; the first of which is the right of demanding justicewhen you can afford to pay for it; and getting justice-when you are fortunate enough to obtain it.

The words of Magna Charta are these:"Nulli vendemus, nulli negabimus aut differemus, rectum vel justitiam,;" meaning literally— "We will sell, deny, or delay, justice to no man." Who the "we" may be that make this promise it is hard to say, for nobody thinks of keeping it. As to justice never being sold, let any man look at the bill of costs he gets from his attorney. As to its being denied, let him seek justice in a Court of Requests; and as to its being delayed, let him commence a suit in Chancery. Coke, who is the funniest fellow for a law writer that was ever known, says that any man "may have justice and right freely without sale, fully without any denial, and speedily without delay,"-a burst of humor such as old Coke very often favors us with.

The 16th of Charles the First gives to any one in prison the power of having his body brought before the Sovereign in council, that it may be determined if he is rightly in custody; but this glorious old privilege would give the Sovereign in council enough to do, if every gentleman who happened to have been "found The law cannot be altered, except by Parliadrunk in the streets" should take advantage of it. ment and the Court of Requests; the latter havOne of the great beauties of the Habeas Cor-ing, in fact, greater power than the former; for, pus Act is, that it prevents a Government from tyrannising, and yet as this would fetter the hands of Government, it may be suspended at the Government's will; and thus, says Fleta, "the subject is free, and yet not too free; while Government is strong, yet not too strong," from which it appears this magnificent Palladium of our liberties is neither one thing nor the other.

It now becomes a question, "What is imprisonment?" Unlawfully detaining a man in any way, is imprisonment; and semble that if you take your neighbor by the button, and cause him to listen to a long story, you are guilty of imprisonment. An Omnibus driver, who loiters on the road, and thus detains his passengers, is also guilty of imprisonment.

while the one only alters the law, the other utterly demolishes it. The sovereign may, it is true, erect new Courts, but they must proceed in the old way: or he may turn a garret into a Court, as in the case of Vice-Chancellor Wigram, who was thrust-with the sword of justice-into a three-pair back, where, to continue the figure, he had scarcely room to brandish the avenging weapon, with comfort to himself and satisfaction to the suitors.

The right of petitioning is another glorious privilege of Englishmen; but they do not often get much by it. Puffendorf, or somebody else, has said, "They who don't ask, don't want; but those who do ask, shan't have ;" and semble that this is the sort of view which Parliament takes of any wishes, expressed or not expressed, Every Englishman has a right to live in Eng-which do not happen to coincide with the wishes land; or at least, if he cannot live, he may have of the legislature. the glorious privilege of starving there. The The last right at present deserving of menSovereign may not send a subject even to Scot- tion is the right of having arms for one's deland, Guernsey, or Sark, though George the fence; and by the first of William and Mary, Fourth sent Brummel to Coventry; and our though it is the very last one would think of atpresent Queen has been heard to tell Sir Robert tending to, any man may walk about town with Peel to go to Bath, when he has proposed mea- a gun, for the purpose of self-preservation. sures contrary to the welfare and happiness of the people. The third right is the right of property, which the law peculiarly regards, and will not allow a man to be deprived of his property except by the law itself, "which often," says Fleta, "hath a' happie knacke of stryppinge him."

It is a beautiful fiction of the English law. that no man pays taxes without his own consent; and, from this assertion, it would naturally be supposed that the tax-gatherers were the very idols of the people, who flocked around them, tendering specie and asking receipts for it. By legal imagery, the people are declared to tax themselves; but Bracton, in a learned note, has added "Hookey" to this assertion; while Mr. Selden, by way of strengthening the comment, has subjoined "Walker," with his customary quaintness.

Such are the rights and liberties of Englishmen, which are less understood than talked about, and less practically experienced than either.

MELIORATION of Condition.-The melioration France has undergone during the last century, is which the physical condition of the people of thus noticed by the eminent statist M. Moreau de Jonnes :-In the year 1700, the number of persons who ate wheaten bread in France was 6,670,000, or 33 per cent. of the entire population of that period. In 1760, the proportion of the population who ate wheaten bread was as to that fed on inferior grain 40 per cent.; in 1815, 45 per cent.; and in 1840, no less than 60 per cent !-Chambers's Ed. Jour.

NEW VIEWS OF MATHEMATICS, WITH RE-
LATION TO MORALS AND SOCIETY.

From the New Monthly Magazine.

cedence, and etiquette, the majority of which are as unsubstantial as those of Euclid himself. There is also very little in the Hebrew points, and not much more in the Greek accents, or Dr. Bloomfield's points, which are members of the same small family. The sword's point is much the same as the point of death, and a sufficient number of such points form what is termed, in military science, a line of battle. This line is seldom a right one, and soldiers never trouble themselves with the question whether it is or not. Their sole care is not to allow their lines to be broken, or intersected by the lines of the enemy; and to prevent this, is one of the first points of generalship. Points, although the definition would represent them to be the merest nonentities (indeed the word is of French origin, and means nothing), have a great number of interesting features or properties. They are sometimes nice, often tender, frequently extremely delicate. Formerly, indeed, before the invention of buttons, all the propriety and delicacy extant, depended upon points. These were the points of the tailoring line, and the first tailor who dispensed with them was the celebrated Billy Button. The making of points, however, is still an extensive branch of British manufacture. Some men make it a point to pay their tradesmen's bills; but there are ten times the number who make it a point not to pay them. The debtor in this case is said to be disappointed. Points are also made at whist and ecarté; and there are many sensible people who make it a point to dine every day of their lives-provided they can get a dinner. A dinner is more a point in Ireland than it is even in England; for point is actually an important part of an Irishman's meal, and makes a single herring go as far (with a sufficient supply of potatoes), as a barrel of the same fish with us. Some mathematicians contend that this point is much the same as the point of starvation, which communicates to men the very property ascribed by Euclid to the right line, namely, length, without breadth or

AMONGST the various uses and applications of geometry, not the least curious and important (although they have hitherto been culpably neglected), are its applications in questions of morals, and in the concerns of society. Mathematics is not such a dry study as is commonly supposed. The "Loves of the triangles" are alone sufficient to demonstrate the subjection of geometrical figures to the laws of the passions and the influence of imagination. If an Isosceles can fall in love, why should it be thought incredible that a parallelogram should be liable to fanaticism, or a cirele be dissipated and profligate? We question very much if Euclid is not a more moral and sentimental writer than he is generally supposed to be; and we think we could trace in Apollonius and Archimedes evidence of a deeper meaning than one would conclude from the bare enunciation of their cold abstract propositions. Our belief is, that they were mathematicians "with ulterior designs," and that there was far more than is to be found on a first view, in the interior of their squares, and the centres of their circles. That mathematicians and poets are no very distant relations, is evident from both dealing so largely in lines and figures. A parallel and a simile are as like one another as two eggs. Besides, there is but the difference of a letter between the hyperbola, a conic section,* and the hyperbole, an equally favorite figure with the bards. Geometers and lawyers are closely connected also; both delight in points; and a point of law (although it is figuratively said to be handled), is just as difficult to grasp as the point of the mathematicians. Then law, or proceedings at law, are producible, and generally produced, ad infinitum, precisely in the same way that we read in Euclid of the infinite production of lines, or, in higher works on the same science, of the interminable windings of spirals. Law-substance. yers are proverbially called crooked, from their mathematical propensities to circuitous processes. The expression, a court of justice, resembles "lucus a non lucendo," inasmuch as the French word court signifies short and expeditious-which no legal proceeding is, or has ever been.

Without pursuing these curious analogies further, let us see whether we cannot delineate, or lay the foundation of, a more comprehensive mathematical system than is to be found in the ordinary treatises upon this branch of human knowledge.

We believe a point (to begin with the beginning), is defined to be something having neither length, breadth, nor thickness. In fact, a point is nothing, and there is and can be nothing in a point. This definition evidently applies, not only to most points of law, to which we have already alluded, but to innumerable other points; such as points of honor, and points of ceremony, pre

It is a great point to get a place under government; whence places are called appointments, and men who are likely to have them, are said to be in the line of promotion;-not always a very straight one. Some make it a point with their friends to dine with them next week, or pass the next summer at their country-houses, and then they make it another point to be out of town, or on a continental tour, when the time for hospitality arrives.

We knew a gentleman of this hospitable nature who resided for many years in a foreign city, where business or pleasure frequently led us. His generous and established formula was

this:

"Now you must make it a point to dine with me the next time you come to

Euclid must needs be in error as to the invisi

bility and immateriality of points; for a point can be carried, and pushed, and turned, and twisted. You can be in a point;-as in the common case of one who is wrong in point of honor, Query, comic section ?—Printer's Devil. Comic-which is to be ungentlemanlike; or wrong in sections there are, however, as well as conic,-for point of taste,-which is to be a clown; or wrong example the cuts in "Punch," &c.

FEBRUARY, 1844. 14

in point of faith,-which is to be a heretic.

Their position is that a right line is the longest between two points, and consequently they detest all direct courses and proceedings. The problem with such philosophers is, to determine in any given combination of circumstances, which is the most oblique and circuitous mode of gaining the point aimed at.

Half-a-dozen lawyers are sometimes on a point | never take that road themselves, but invariably for an entire day, or three days together, and (as proceed by that particular species of line called we have before hinted), the point is sometimes a roundabout, and by some geometers a zigzag. as minute as the most beautiful mathematical one can be; so that lawyers have at least one accomplishment in common with angels, ten thousand of whom (it was held by Cardan or Paracelsus) can dance together on the point of a needle. For carrying points, the most adroit of all beings are those angels incarnate, vernacularly called women. Weak sex as they are, A great deal might be written on the properthe number of points that some of them will ties of the zigzag, and the method of progress carry is prodigious, and many of these points are by wriggling. Our own opinion is that the line weighty enough. Indeed, so kind are they, that of moral beauty is the right line, although that it is only with such points they encumber them- of physical is decidedly a curve. However, we selves; for when the point is slight and imma-advance this proposition timorously; for we terial, they allow their lovers or their lords to know what charms for certain eyes there are in carry it for them, as they do a parasol or a reti- spirals, and all manner of crookednesses. Diplo cule. However small, points are often carried macy in general revolts from the straight line. by both sexes with very disproportionate effort We owe the term serpentine to the first diploand labor; as, in one of O'Keefe's farces, three mate on record, who treated with Eve for the French valets come on the stage, toiling under surrender of Paradise.. Our fair first mother the load of a single bandbox. Often it happens would appear to have been so captivated by this that a point which looks great before it is gained, graceful and tortuous style of negotiation, that turns out then to be no point at all, or perhaps a she carefully transmitted to her lovely descendpoint against us, instead of a point in our favor. ants, all over the world, the preference for windMany a man has been ruined by carrying his ing ways which the old diplomatic dragon taught point. But who has not his point to carry? her. Hence is it the most difficult problem in The cardinal's grand point is to be made pope; practical mathematics to determine the locus of whence the expression cardinal points, figura- a woman's motions, or the laws of the female tively used by geographers to describe the great orbit. points of the compass. The curate's point is the The path of the pretty moon gives astronopoint of the church-steeple, of which he aspires mers more trouble than that of grizzly Mars, or to be the rector; and sometimes, to compass his thundering Jupiter; but the Cynthias of the object, he is thought (rane man!) to imitate over-earth are ten times more inexplicable than the much the gyrations of the weathercock on the top of it. The point of the dean is a bishopric, or the gilt points of the mitre. The attaché's point is to be secretary of legation, and the point of the secretary of legation is Constantinople, Paris, or Vienna. Points are not only carried, but they often carry other points. The author's point is carried by the point of the pen; the orator's and the woman's by the point of the tongue; the warrior's by the sword's point; the minister's by points of diplomacy, or sometimes, as well as the warrior's, by the point of the bayonet. But we make it a point to eschew politics.

Cynthias of the sky herself. Their intricacies would perplex Kepler, and even the starry Galileo himself; nay, we question if Newton or La Place could reduce their orbits to any system, or ascertain a lady's right ascension and declination for any given moment of her life.

There ought to be female tables constructed, if possible, on the plan of the lunar tables; but the difficulty of the task would be enormous. Such a planet as Rabelais's "Queen Whims," would puzzle South, or Arago, "pretty considerably." We venture to say they would take many thousand observations, before they would know more of any given heavenly body in the galaxy of their own country women than they knew of the late comet.

Speaking of points of oratory, we have a theorem to announce respecting them, which, if not our own discovery, is not of the less value on that account. The best point in nine speeches The eccentricities of the planets of earth are out of ten is the full stop at the end of them;-infinite, and aberrations have been occasionally from which it may be deduced as a corollary that the earlier in the harangue this point is introduced, the more popular the orator is likely to prove.

detected to an extent unknown amongst the lights of the firmament. It is indeed a question whether they are planets at all, for they certainly often want that particular planetary moIn discussing points we have incidentally tion which astronomers call direct; and they treated on the properties of lines, but there is are rarely, if ever, stationary. Besides, they something more to be added upon this branch of shine with a lustre of their own, and give light, the subject. A right line is not always the short- instead of borrowing it; for the old opinion, that est between two points, let Philosopher Square light is of both sexes, is untenable, although say what he will. Indeed, the proverb that cuts sanctioned by the authority of Milton; science at what are called short-cuts demonstrates the having long since demonstrated that the only falsity of Euclid's proposition, at least in prac-genuine light in the world is that of the terrestice. The shortest way across a river, is to go trial fires which revolve about the focus of the round by the bridge, no matter how far the latter household, be their motions complex as they may be distant. Nay, there are mathematicians may,

who insist that the right line is in no case the shortest way to any given object; at least they

Cycle in epicycle, orb in orb,

beyond the solution of Copernicus, and only to be expounded by the mazes of the Ptolemæic system, or the vortices of Des Cartes.

Another class of lines which perplex scientific men not a little, are boundary lines. The fundamental theorem is, that a boundary line must run somewhere; but, this being admitted, the question arises, where and how to run them; a problem now and then worked philosophically, but which has most frequently been solved with the sword, according to formulas laid down by such formidable geometricians as Alexander and Cæsar.

On the subject of parallels, Plutarch has written, to our taste, more agreeably than Euclid. All lines are not susceptible of parallelism. People often take a line which has no parallel. What parallel is there for the line of business in which the singing mouse," for instance, has lately set up? We could easily multiply such examples; but parallels are often as odious as comparisons, and therefore we leave this branch of our subject for the present.

There is a vast deal of curious doctrine about angles, which is not to be found in any of the elementary treatises. An angle is nothing more or less than a corner, and the secret history of corners would be the most entertaining and piquant that was ever written. The theory of corners is closely connected with that of holes. When we see men addicted to the transaction of business in holes and corners, we know at once that they are descended from the Angles. A full development of the uses of corners would lead us much too far for our present purpose; but we may just remark that some persons are as fond of corners, as of crooked lines. They are particularly convenient to that branch of the Horner family, who not only like to have their fingers in a pie, but prefer another man's pie to their own.

O si angulus ille!

Oh, for a corner of my neighbor's pasty, or for
a slice off his estate, or a snug little official nook,
with one's thumbs in the national plum-pudding!
When men are so happy as to slip themselves
into an angle like this, they ought to keep as quiet
as possible, eat their pudding and hold their
tongues. The greedy, however, often betray
themselves, like lovers, by their giggling,

Nunc et latentis proditor intimo
Gratus puellæ risus ab angulo,

one of those formidable chef d'œuvres of cutlery which seem made for cutting one's hand in as many different directions. Your angular man has as many salient, sharp, offensive points as he has notions, sentiments, or feelings. He is a sort of intellectual porcupine, or a hybrid between the mimosa and the thistle, every weapon of offence being also an organ of sensibility. To understand a character like this is as arduous as a trigonometrical survey, the angles to be calcu lated are so numerous. A mental theodolite would be an instrument of the greatest value for the measurement of angular men. We have some notion of fitting up a moral and intellectual observatory, where, in addition to our theodolite, we mean to have an instrument for taking the altitude of the human understanding, and a circle with a micrometer screw, for measuring the minute and horary variations of the mutables of both sexes. There would also be a thermometer for the passions, on the principle of the thermometer in the "Tatler," for the fluctuations of religious zeal. This, with a telescope for seeing future events, and a microscope for the study of little minds, and the innumerable pettinesses of human conduct, would make a very useful addition to our present stock of philosophical instru· ments.

From angles we have only to turn the corner to arrive at triangles, whose amorous propensities have been the subject of a treatise very superior in its way to the dissertations of dry geometers. As love and harmony go hand in hand, it is not surprising to find the triangle playing its part in the production of that particular description of noise and hubbub called a concert of instrumental music. We should write the bass of a triangle, not its base.

But

Triangles, being so addicted to the tender passion, ought not to be introduced into boardingschools for young ladies, who may be very well accomplished, and make excellent wives and mothers, without a tincture of either Euclid or algebra; although a little arithmetic is highly commendable, subtraction being better than detraction, and accounts of household expenses preferable to the accounts of backbiters. a lady has to do with no roots but vegetable ones, which are never either squares or cubes; and the only cone she has any affair with is the sugarloaf. When she gets into surds she becomes absurd, and the less she meddles with ratios the more rational she will be thought. In her proportions, however, she cannot be too perfect, and if she happens to have a portion besides, it is no harm. Without the slightest acquaintance with equations, she may possess an equal temper; as Besides hole-and-corner men, there are also she may be straight as a wand without a notion angular men; and the property of angularity in on the subject of perpendiculars, and the delight character is as well worth the attention of the of all circles, without knowing the difference be student as any part of moral mathematics. A tween centre and circumference. In her figure person of this peculiar constitution is like the she ought to be rounded, without being round; post at the corner of the street, which you are angles are as fatal to her person as their study is sure to knock your shins against on a dark night. unnecessary for her mind. If she squares she Conversation with him is perpetual collision. must be a termagant. Sufficient for her are the His understanding is like a polygon with a thou-work-box, the opera-box, and the dressing-box. sand acute angles; which Euclid would tell you A tangent she may be, but never a secant, and is a mathematical impossibility, but which is a she must not be too familiar with projectiles, lest moral phenomenon only too often met with. Or she should throw herself away. An oval face is he may be likened to a hundred-bladed penknife a beauty, and the curve of a female lip may

to quote Horace again, one of the ablest writers of antiquity, on the principles and practices of

corners.

sometimes osculate without reproach. A pretty | dozens of claret, and Madeira that has gone woman may have an arched brow, an arched the rounds; then come rounds of healths and nose, nay, she may be a little arch herself, with- toasts, until with the rotations of the glass the out the slightest impropriety. Let her be radiant without talking of radii, and let her only chords be those of the piano and the harp.

The truly social figure is the circle in fact there is not a jollier personage in all the com-Or they are waken'd by its mighty pow'r, monwealth of mathematics. We make gay par- And in their spirit's dreadful agony, ties in round numbers, and have rounds of din- They leave this world on Death's dread wings to ners at round tables, where jokes go round and bumpers, and there are rounds of beef, round