space, up which the air is constantly passing from the outside into the house. At all times the air is finding its way, and, as the current is directed in an upward course, draught is not felt even when the air blows in freely. At the same time the sashes can be opened or closed, as may be desired, without altering the arrangement for ventilation.

I have recommended and employed Dr. Bird's costless ventilation so many years with such excellent practical results, I hardly like to venture on a shade of suggestion for its modification. There is, however, one change in it which, while it adheres entirely to the principle, is, I venture to think, an improvement in detail. This consists simply in letting the lower sash remain unchanged, and in bringing down the upper sash three inches, so as to let it by that distance overlap the lower. The space above on the upper part of the top sash has then to be filled up, and I recommend for this purpose a permanent bar of wood, against which the upper sash can close. The advantages of this detail are, that the window looks better; that light at the lower part is saved; that lower blinds are not interfered with; that the interposed piece of wood is out of the reach of the servants, so that it cannot be taken away without great trouble; and, that if there be a draught at the space where the sash touches the interposed portion of wood, it is at the top instead of the bottom sash, and is not felt by those who are passing the window on ascending the stairs.

The costless ventilation once effected, it should be in operation all the year round. It is true that in cold weather it causes a lower temperature on the landing than would exist if the window were absolutely closed; but this must be met by increasing the warmth within the house, not by the process of excluding the outer air.

It will be soon detected in windows in which the costless ventilation is set up, how large a quantity of dust there is in the air which finds its way into the dwelling-house of the great city. The space through which the air passes is very quickly charged with dust, some of which settles on the panes of the window and the framework, and requires removal at short regular intervals. It is raised by some as an objection to the system of costless ventilation that the dust enters so freely through the permanent opening as to become, in its turn, a nuisance. Hence, we often find the opening partly filled up with a sandbag, or else with a plate of perforated zinc, the openings of which are quite closed up with dust. Both these practices are bad; the open space should never be closed. In spite of the acknowledged inconvenience of dust, it is far better to have a free admission of air than to exclude the air. In practice, moreover, the dust nuisance is less than would be expected. It is only occasionally present, while bad air, if outer air be kept out, is always present.

The floor of the landing should be treated precisely in the same manner as the floor of the bedroom. In the course of the tread in the centre of the landing, for a width, say, of from eighteen inches to two feet, a line of carpet may be laid down, but the floor space on either side of the carpet should be uncovered, and if it be of wood it should be dry scrubbed and treated with wax and turpentine, when the boards will allow of it. Where the staircase and landing are of stone, nothing is more healthful than the stone itself duly cleaned and whitened. When the floor surface is of indifferent wood or stone, it may, with advantage, be covered with oilcloth, with the center carpet. In no case should the whole of a landing be carpet-covered so as to make the carpet hug the wall. A floor covered in that manner holds the dust, and keeps the air charged with dust, every step and every gust of air that moves the carpet from beneath tending to waft some particles of dust into the air above.

parts of bedroom floors, nothing can be said that is unfavorable, granting always that it is laid down with skill and care. As a rule it should be closely fitted to the floor, and well glued and nailed down at the edges, so that it can not become a coating for a thick layer of dust beneath it. Fixed firmly in its place in such a way as to form part of the floor itself, oilcloth can be cleaned with as much facility as can a boarded floor, and can be waxed as perfectly. It does not retain dust; it shows the presence of dust and dirt, and it is a good non-conductor of heat. The substance called linoleum is, in some particulars, an improvement on oilcloth, because it is a better non-conductor. Kamptulicon is more enduring than either, but it does not admit of such perfect cleaning; it catches the dust more, and it never looks so bright and cheery as the others do. We are told that it is so much more serviceable, and that is true; but then it is not good to have forever in view a structure that is unchangeable and practically indestructible. An occasional change of structure is a positive relief, and when it can be obtained at slight cost is a useful luxury.

The walls of the landing, like those of the bedroom, should be covered with a paint or paper that will readily admit of being washed. Failing this, they should be distempered.

ASCENDING VENTILATING SHAFT.

It is always good practice wherever it is practicable to make an opening from the stair-landing into, and out of, the roof of the house, or into the stack of the chimney. If the landing be just under the roof, then it is good to get a direct opening through the roof, or the cock-loft leading to it, so that there may be an immediate communication with the outer air above. In most houses this upper landingplace is connected by the staircase with the whole of the lower part of the house. The house from below ventilates into it, and if upon it there be no efficient outlet, it is in a bad position indeed. Should there be an intervening floor between the floor and the roof of the house, a small shaft should be carried up, and beneath that shaft a gas-burner may with much advantage be suspended, so as to make the haft a chimney for the conveyance of the products of the gas and of air, away from the interior of the house.

THE WATER-CLOSET ON THE STAIRCASE LANDING.

In the houses of crowded cities the worst sanitary difficulty of all lies in the arrangement of the water-closet on the landings of the staircases. Some sanitarians propose to meet these difficulties by introducing the dry earth-closet system, or by some other special system distinct from what is in general use. I do not object to such suggestions where they are practicable. [TO BE CONTINUED.]

RURAL MANNERS.

POLITENESS.

The first and most obvious reflections which arise in a man who changes the city for the country, are upon the different manners of the people whom he meets with in those two different scenes of life. By manners I do not mean inorals, but behavior and good breeding, as they show themselves in the town and in the country.

And here, in the first place, I must observe a very great revolution that has happened in this article of good breeding. Several obliging deferences, condescensions, and submissions, with many outward forms and ceremonies that accompany them, were first of all brought up among the politer part of mankind, who lived in courts and cities, and distinguished themselves from the rustic part of the species (who on all occasions acted bluntly and naturally) by such a mutual complaisance and intercourse of civilities. These forms of conversation by degrees multiplied, and grew

in them, and have therefore thrown most of them aside. Conversation, like the Romish religion, was so encumbered with show and ceremony, that it stood in need of a reformation to retrench its superfluities, and restore its natural good sense and beauty. At present, therefore, an unconstrained carriage, and a certain openness of behavior, are the height of good breeding. The fashionable world is grown free and easy; our manners sit more loose upon us: nothing is so modish* as an agreeable negligence. In a word, good breeding shows itself most, where to an ordinary eye it appears the least.

If after this we look on the people of mode in the country, we find in them the manners of the last age. They have no sooner fetched themselves up to the fashion of a polite world, but the town has dropped them, and are nearer to the first state of nature, than to those refinements which formerly reigned in the court, and still prevail in the country. One may now know a man that never conversed in the world by his excess of good breeding. A polite country squire shall make you as many bows in half an hour, as would serve a courtier for a week. There is infinitely more to do about place and precedency in a meeting of justices' wives, than in an assembly of duchesses.

This rural politeness is very troublesome to a man of my temper, who generally takes the chair that is next me, and walk first or last, in the front or in the rear, as chance directs. I have known my friend Sir Roger's dinner almost cold before the company could adjust the ceremonial, and be prevailed upon to sit down; and have heartily pitied my old friend, when I have seen him forced to pick and cull his guests, as they sat at the several parts of his table, that he might drink their healths according to their respective ranks and qualities. Honest Will. Wimble, who I should have thought had been altogether uninfected with ceremony, gives me abundance of trouble in this particular. Though he has been fishing all the morning, he will not help himself at dinner till I am served. When we are going out of the hall, he runs behind me; and last night, as we were walking in the fields, stopped short at a stile till I came up to it, and upon my making signs to him to get over, told me, with a serious smile, that sure I believed they had no manners in the country.

There has happened another revolution in the point of good breeding, which relates to the conversation among men of mode, and which I can not but look upon as very extraordinary. It was certainly one of the first distinctions of a well-bred man, to express everything that had the most remote appearance of being obscene in modest terms and distant phrases; whilst the clown, who had no such delicacy of conception and expression, clothed his ideas in those plain homely terms that are the most obvious and natural. This kind of good manners was, perhaps, carried to an excess, so as to make conversation too stiff, formal, and precise; for which reason (as hypocrisy in one age is generally succeeded by atheism in another) conversation is in a great measure relapsed into the first extreme; so that at present several of our men of the town, and particularly those who have been polished in France, make use of the most coarse, uncivilized words in our language, and utter themselves often in such a manner as a clown would blush to hear.

This infamous piece of good breeding, which reigns among the coxcombs of the town, has not yet made its way into the country; and as it is impossible for such an irrational way of conversation to last long among a people that makes any profession of religion, or show of modesty, if the country gentlemen get into it, they will certainly be left in the lurch. Their good breeding will come too late to them, and they will be thought a parcel of lewd clowns, while they fancy themselves talking together like men of wit and pleasure.

[End of Required Reading for January.]

*The vulgar use of this term has, I suppose, disgraced it. It would not now be endured in polite conversation, much less in polite writing.

A NIGHT WITH A COMET.*

On Thursday morning, June 23d, an employe of the Courier-Journal, of Louisville, was on his way to the office at the early hour of half-past three. Casting a look northward he saw a comet in the sky not far from a very bright star. That star was Capella, the most brilliant member of the constellation of Auriga, and the comet was the now famous No. 2 of 1881. A neighbor of mine in Richmond saw it at about the same time. The first news that I received of the presence of this unexpected celestial guest, came through the Courier-Journal of Friday, June 24th, and at 1:30 a. m. on Saturday, June 25th, I was busy getting out the University telescope for an observation. This instrument was made to our order by Alvan Clark & Sons, the noted telescope-makers of Cambridgeport, Mass. It has an aperture of six inches, a focal length of eight feet, magnifying power (as stated by Alvan Clark & Sons) from thirty-six to six hundred diameters, and is equatorially mounted on the largest tripod ever sent from the manufac1ory. Its power of definition may be estimated from the fact that it separates double stars whose centers are distant only one and one-half seconds.

While mounting this elegant instrument it was altogether natural to take a survey of the sky. Every part of the firmament has its own special glory, and one of the most glorious portions of it is found in the milky way running up through Perseus and Cassiopeia to Cygnus, near the zenith, and thence to the southern horizon by way of Sagittarius. Quite near this belt we see the lovely Vega in the Lyre, and Altair in the Eagle, two of the fairest gems of the northern celestial hemisphere. Then in Perseus and Sagittarius these are nebulæ, which, by the magic of the telescope start up into gorgeous cohorts with glittering helmets and spears. The nebular hypothesis imagines that the clouds of star-dust of millions of years ago were slowly fashioned into suns, planets and satellites. But the telescopic enchantress waves her wand over this long interval of ages, and the vapor so dim and vague to the naked eye of to-day flashes into a universe of worlds. When I first turned our instrument on one of Messier's nebulæ in Sagittarius, I was startled into an outcry; for a sudden wonder and joy smote upon my heart, as though God himself had spoken to me.

There is something unique in a night scene beheld by a solitary observer. If you are like the witty Frenchman, who said, "Yes, solitude is sweet; but how much sweeter to have some one by you to whom you can say, how sweet is solitude!"-if this be your temperament, I could hardly advise you to rise from balmy slumber at 1:30 a. m. to gaze at the heavens. But if there be in your spirit a touch of the mysticism of Hannah, in "Adam Bede;" if you at all resemble that gentle enthusiast who so loved to be alone with God, then you may find that to be alone with God's heavens is not a solitude, but a communion.

GROWTH OF A COMET.

You see there on the blackboard an egg which I have drawn. Just here is a bright point. Can those of you who are on the outskirts of the audience see it. Raise your hands. (Half a dozen hands went up.) Very well. That point represents the germ or nucleus, where life begins. Agassiz and others have described the very interesting process of its development.

This is intended for such an egg as the little boys and girls find under the barn floors or up in hay lofts. Remember, however, the old adage: "Omne vivum abovo”— every living thing comes from an egg.

* A lecture delivered in the Hall of Philosophy at Chautauqua, August 16, 1881, by Prof. L. G. Barb ur, Professor of Mathematics and Astronomy, Central University, Richmond, Kentucky.

Here I show you another egg, shaped much like the former, but not so solid looking. Older boys, and girls, too, as Miss Herschel and Miss Mitchell, find them in the sky. This is the way a comet looks when it is first seen in the far blue depths of heaven. And you see here also a germ. I do not say that all comets have germs. Perhaps some do not; at least in some no germ is detected, and such never come to much. I have chosen one with a germ. But what is it doing now? (The lecturer here began to develop the comet on the blackboard.) The comet and its germ seem to be expanding. Yet that may be owing to the fact that they

are coming nearer to us.

But see again! A line of light leaps forth toward the sun. You will please understand that the sun is up yonder above the blackboard. Now another line nearly parallel on the left, and another here on the right, with a sound like "choo! choo! choo!" as we imitate to our little children the starting out of a train on the railroad. Now the intermediate space is filling up, and you see a very respectable white fan, just such a one as I saw carried by the comet of last June. The comets had fans long before the ladies used them. Our comet here perhaps needs one, as it is approaching the sun, and getting very warm.

See, now, streaming out on each side something like hair. It turns back in the general direction opposite to the sun. It reminds one of a little girl at play with her brothers: she runs so fast and gets so warm, and then with both hands brushes back the hair from her forehead.

The Greek word for comet (kometes) was originally an adjective, meaning hairy. Thus Aristotle, in his meteorology speaks of a hairy meteor. By a natural transition, the adjective has become a substantive; the termination has been lopped off, as we forever do with classical words; and hence we get our English designation for a comet.

The process of formation still goes on. The hair streams back, and thus the tail is produced. I extend it to the bottom of the board; but I cannot very well finish the job, as the tails are millions of miles long, and I have neither blackboard room nor time sufficient for the completion.

You observe a dark undefined strip down the middle of the tail. This is due to the fact that the tail is hollow Out toward the edges you look through a larger mass of the luminous matter, consequently the edges appear brighter than the middle. Something similar is seen when we examine a hair with a microscope. A hair is tubular, and down the middle of it you see a light colored stripe, reversing the colors of the comet's tail, but evidently caused in the same general way.

But there seems to be about as good reason for supposing a repulsive force also in the sun. Or, if I might suggest, there is a mutual repulsion between the sun and the matter of which the tails of comets are composed.

RAPID FORMATION OF THE TAILS.

"The tail of this comet (Donati's, 1858) increased in length at the rate of two millions of miles per day; that of the great comet of 1811, at the rate of nine millions of miles per day; while that of the great comet of 1843, soon after passing perihelion, increased at the rate of thirty-five millions of miles per day." * You may well imagine that the tails of some comets grow rather long. So they do. The comet of 1843 had a tail two hundred millions of miles long; enough to reach entirely across the orbit of the earth and lap over it some millions of miles. If a railroad train had started from the head of this comet to traverse the whole length of the tail at the speed of sixty miles per hour, day and night, Sundays included, the journey would have required three hundred and eighty years.

Comets have had more than one tail. One had as many as seven, all trending in different directions. These facts indicate that comets contain diverse kinds of matter, the tails being formed successively, and at different degrees of temperature.

DECLINE AND FALL.

The nucleus of a comet usually seems to diminish as it approaches very near the sun. One would have thought it would increase by the expansive power of heat; but the contrary is the observed fact. Look at the planet Jupiter, whose solid or possibly liquid body is surrounded by a dense cloud. If that cloud should be heated sufficiently, it would become transparent, and the body of the planet could be seen through it, so that Jupiter would appear smaller than it does at present. If the cloudy matter should cool down again and become opaque, the planet would seem to grow larger. Thus the coma of a comet diminishes, but the nucleus apparently increases in size when it first goes away from the sun. The tail, meanwhile, lessens, like a man who has passed the hot noon of life, and has less hair on his head, but more head and brains. Back, back, the poor comet goes, until it resumes its primeval state. Brave chanticleer becomes an egg again. This might be called an

instance of "reversion."

AN EXCEPTION.

This is the ordinary and periodic career of a comet; but there is a remarkable exception in the case of the one named after the Austrian captain, Biela. This comet was journey

You may be curious to know why the matter surrounding the nucleus thus streams out away from the sun. An old, but long ago abandoned theory was that it rose up as smoke and vapors rise from the earth; toward the sun being down, and away from the sun, up. This hardly merits a serious refutation. Neither can the tail be like the smoke

trailing cut behind a locomotive; for that has an alignment nearly parallel with the course of the locomotive itself, while the direction of a comet's tail is always nearly opposite to that of the sun.

The accepted conjecture now is that the sun has a repulsive force as well as a force of attraction, and the repulsion acts with prodigious power on at least a part of the cometic

matter. We do not know why the sun attracts the planets and the comets. We only account for the planetary and cometary motions by the supposed power of universal gravitation. Since Newton overthrew the vortices of Des Cartes, the scientific world has received the theory of attraction.

the garden of Eden, and as lonely. "Man the hermit sighed till woman smiled," after which he sighed far worse than he did before. Well, Eve was taken out of his side; and a fainter comet was made out of Biela's. Lo! there were two of them, companion comets, traveling the journey of space together. The Adam comet was the brighter and But the Eve comet the dimmer, just as it ought to be. soon the Eve comet began to brighten, and kept on getting brighter, until it outshone the Adam comet-just as it ought not to be! As you may well suppose trouble came of all this; but I can not stop to tell the rest of the story. WHAT BECOMES OF THE TAILS.

Amaryllis, at the age of twenty, had a fine suit of hair, four feet long. Amaryllis is now forty-five, and her hair is Yet it has been growing all the while only three feet long. at the rate of four to six inches per year. It ought to be one hundred or one hundred and fifty inches longer at the age of forty-five than at the age of twenty. Where are the chest

* Loomis.

nut, auburn, or raven locks that adorned her twenty-five years ago? Answer that, and perhaps I may be able to tell you whither the tails of the comets go.

The

You will at once see, however, that the matter of the tail lessens every time the comet whips around the sun. sun, like a cruel boy, hatchet in hand, cuts off their tails not by inches, but by millions of miles. When they grow out again, he cuts them off again, remorselessly; and so on, toties quoties. After a long, long time, all the cometic tadpoles will turn into frogs-another fact for Mr. Darwin, whereby to prove that tadpoles have been evolved from Comets.

PATHS OF THE COMETS.

In what sort of orbits do they move? Do all or most of them return to the neighborhood of our sun? These questions and their answers are more closely related than might appear at first. Understand in the outset that none of the heavenly bodies wander about, even though Byron did dream of earth's "wandering darkly through eternal space." Do you remember that grand saying of Goethe, in the Angel Song, prelude to Faust:

"The sun

Bounds his predestined course along."

All the orbits are exhibitions of inexorable law, and yet of most graceful motion. You have doubtless noticed the stern self-repression by which I have been restraining my steps from the flowing fields of mathematics. That ancient and honorable science measures a yard of tape, or the orbit of a eomet; weighs an eighth of a grain of morphine, or suns and systems. It is not, indeed, studied at Chautauqua, where languages, ancient and modern, Semitic and Indo-European, are investigated with such avidity. But this is because all good Chautauquans are supposed to have mastered mathematics before coming hither. You are not, then, like the excellent old lady out in Kentucky, who was very ill, and, in fact, was thought to be near her end. As she lay one day with her eyes closed, and apparently asleep, some friends sitting by began to discourse of the future state. The thought was advanced that the subjects of our liveliest interest here would engage our chief attention there; as, for instance, mathematics. "Mathematics!" said the invalid, opening her eyes, "if I have to study mathematics there, I don't want to go!" And she actually got well! [Laughter]. But I am not addressing a half-dead audience; and so, traveling along the dusty pathways of fact, fancy and fun, let us take a peep through the hedge into the violet sprinkled mead of geometry. When most people hear of geometry, they either stop their ears, or run away, or else begin to think painfully of an array of stiff, formal figures-of uninviting angles, and squares, and crooked things generally. But a curve is as geometrical as a straight line; I may say more so, for it is geometry on a higher key. There is no graceful line in existence that does not have its equation. In the structure of this wonderful universe, the All-wise Architect has used a great variety of lines, and you will find a fruitful theme of thought in the inquiry, What use does he make of them?

THE STRAIGHT LINE.

Ruskin says somewhere: "The fact is, the world is round, and all that is in it; except the works of man, and they are often very flat." Hogarth finds curves in clouds and hilltops; everywhere, except in crystals. Let us, however, use our own eyes a little; and here [exhibiting a large charcoal sketch] are two of the crystals, those flowers of the mineral kingdom. This is calespar, and that quartz crystal. Basalt may perhaps be classed among the crystals; and the layers of coal, limestones, and sandstones, may fairly be said to present flat surfaces.

dom we meet with a wonderful variety of curves, but the straight line does not disappear. May I say that since it measures the shortest distance from one point to another, it offers an economy of which even the august Creator avails himself. Here is a leaning, swaying plant; curves abound in it, but you see two straight lines in that opening bud. A German teacher once said to me, "The first thing is to have a good master; and who is the best master, if not God?" I accept the suggestion, and go to the fountain head of art.

Here is an enlarged copy of a leaf by the Great Master: a beech leaf which I picked up the other day here at Chautauqua. What do we see? A curved periphery, or bounding line, and that again used as a foundation for a frill, scollop, serration, or whatever you may please to call it. But, also, we see a straight axis running down the centre, and a score of straight lines branching off right and left in parallels. In the next drawing you see a fuchsia, taken from a specimen in a rustic flower box in front of Brother Lewis Miller's cottage. In the pistils and stamens the straight line appears. In this outline of a maple leaf, copied from nature, the straight line almost disappears, but not quite.

Now for the animal kingdom. The straight line is hardly seen at all. These are two shells copied from specimens on sale at the stand near the Point. The Great Artist has lavished an infinite variety of curves even on the mollusks, and the vertebrates of land and water abound in elegant forms. These curves are of very high order, geometrically considered; yet while we are sure that they ail have their equations, those equations are not known. This is a department into which some coming mathematician may enter. It is a virgin soil. I take special interest in the thought that man's spiritual life manifests itself by the help of curves. They are its language, and therewith we smile, we bless, we worship; we give outward expression to our hope, our trust, our love. This is visible in the works of all the great artists; perhaps most of all in Raphael. It has been said that Raphael himself could not draw a straight line; perhaps not without a straight-edge. Examine the photograph of his Sistine Madonna, in Newton Hall. I have found, amid an opulence of curves, a half dozen straight lines obscurely introduced on one side of the picture. Probably they are meant to give us the true up and down of the picture, without attracting attention to themselves. In Titian's "Assumption of the Virgin," and Murillo's "Immaculate Conception," scarcely a vestige of a straight line is seen.

That

is, seen on the surface. You must look below the surface if you would behold them; you must look back into the artist's mind. When the sign painter, or ornamental type cutter, gives us a very elaborate letter, with ever so many flourishes to it, the trained observer requires that underneath all there shall lie the simple, severe lines, curved or straight, which would make a good plain letter. Then, also, a young artist friend of mine said to me lately: "In drawing the mouth, we have a straight line in our mind; so with the eyes." "Just so," I replied, "and God, the chief artist, had the straight line in his mind when he made our features. We have in our mind what he first had in his; we interpret his thoughts."

WHERE THE COMET ORBITS COME IN.

C

The Almighty might have selected some other law of attraction by which the orbits would have been far more complicated. In fact, the old Greek astronomers thought they were so. They invented cycles and epicycles in bewildering confusion. But one trait of the All-wise Intelligence is a disposition to effect his ends by the simplest means possible.

Mankind have only at last, after fifty-five centuries, come to understand the mechanism of the heavens. If the laws of orbital motion had been much more intricate, man must have been built on a larger intellectual scale, or else have been forever confounded by the celestial maze. Suppose the equations had been of the fifth or tenth degree, instead of the second! Again, one undying attraction of the Pythagorean system, revived by Copernicus, and now triumphant in christendom over the Ptolemaic, is this very simplicity. We are made in the image of God. The skies unroll their illuminated missal before us, as the mother of Alfred the Great did to her children. The text is not too difficult for strenuous endeavor to decipher; we persevere, and the volume is ours.

ART AND SCIENCE

I do not know how it will strike you, but to my own mind one of the most interesting features of this whole subject is the explanation of the fact that art has so outstripped science in the realm of form. The curves of planetary and cometary motion, while shapely enough, are specially commendable for simplicity and utility. It is mainly in the higher curves that grace and beauty shine forth. In the study of these man has copied, not originated. Leonardo da Vinci advises the artist to be forever observing and forever copying. The lines were too high for us to invent. Happy is he who can detect them, understand them, love them, and make them his own. They are ours when we can reproduce them at will, and employ them fittingly. But remember, they are God-given; if they had not been given, high art would have been impossible.

The simpler lines our Maker has left us to work out for ourselves, and it is certainly remarkable that the four curves mentioned were discovered by the ancient Greeks before the Christian era. The history of human thought scarcely affords a parallel instance of the ardent study of apparent abstractions which afterwards were found to be embodied in most concrete realities. A few singular curves, kept as a precious thought-treasure by Greek and Saracen, and transmitted to the Christians. Why? Because it is seen at last that they were the principles of the handicraft of him who built the universe. He has made us so that what interests him shall also interest us.

The æsthetic element in our nature is like the bird that flies upon easy pinion over mountain height; the mathematical like the locomotive that climbs slowly up their sides. The former learns directly from the Great Teacher; the latter creates for itself. In the former the Heavenly Teacher gives us theorems to believe; in the latter, problems to solve, and withal, hints for their solution.

HINTS.

An infinitely curious subject is that of nature's hints. Nature whispers to us. See this drawing in which the whisper comes to us through the lips of a flower. First it tells us of the circle hidden in its corolla. But this is not the whole of its lesson.

If I had the preternatural hand-cunning of a Frank Beard, I would sketch in a sweet little girl here. A thousand ringlets should fall adown her shoulders; a thousand graceful curves cling about her; and the flower-if that might beshould wave in the wind and say, "Do you see my ellipse, little maid? See, see, here it is, here it is!"

Some misguided individuals would rather think of youthan of the ellipse.

So the planets whispered to our race; how patiently, too, through the long centuries,

"From the sky serene and far,

Their voice fell like a falling star,"

until at last a God-fearing German gazed steadfastly into the heavens and said, "I see!" Yet again the comets said, "Look at us; do not be afraid; we will not hurt you. We will move slowly, quietly through the sky, tracing our ellipses through space." And a God-fearing Englishman saw at last, and now he who wills may see.

PARABOLAS.

Bear in mind that only four curves are possible to comets under our present law of gravitation; that two of these, the circle and the ellipse, are closed curves; that no circular orbit has ever been discovered, but many elliptical ones; and that any true and independent American citizen who has no flowers to wave in the wind, but who has a silver dollar in his pocket, may, by turning that dollar slowly over, see before him in succession the orbits of all the planets, all the satellites, and very many of the comets.

Now for the two curves that are closed at one end and widen out forever in their two branches. All good Chautauquans are familiar with parabolas. Some of you have made hundreds, and even thousands of them. I will describe one for you with a piece of chalk. Look sharp! Here goes! [Tossing a bit of chalk in the air.] Except the deviation caused by passing through the atmosphere, that may be considered a very respectable parabola. Our base ball players make countless such curves. Their "bee-lines" are parabolas with large parameters, and their "flies" are ditto with small parameters. When an astronomer has found a comet in the sky, the first thing is to see if he can "catch it on the fly," or, in more scientific language, fit a parabolic curve to its observed path. At least three good observations are necessary.

For most purposes a parabolic orbit fits well enough in many instances. But while we may not be able just yet to get a better fit, be it said that in all likelihood, as there is no circular orbit known, so there is no parabolic orbit, strictly speaking, in all the solar system.

"THE RIGOR OF THE GAME."

"A bright fire, a clean hearth," said Sarah Battle, the champion whist player, "and the rigor of the game!"

Bad life-occupation; good apothegm. Bad thing to do; good thing to say-at least in the exact sciences, where you ought to be exact, one would think.

All the text-books in mechanics say that the curve described in the air by the piece of chalk I tossed up a moment since, is a parabola. Every year I prove it to my classes in relation to projectiles. But in utmost rigor it is not true. It would be true if the center of the earth were at an infinite distance beneath us; or still more precisely, if a plumb-line here were accurately parallel to a plumb-line yonder. In fact, this parallelism is assumed in the demonstrations of the books. But since the plumb-lines converge, the curve was after all a very elongated ellipse,-such as you see in the dollar just before the ellipse turns into a straight line.

A sufficient reason why there are no circular orbits is that at a given point of its path the velocity of a revolving body would have to be exactly so much, and not the least bit more or less. A trifle more or less would throw it into an ellipse. For instance the attraction of Venus or Mars would pull the earth out of a circular orbit; and once out, it could never get back.