Letters on Astronomy Part 3

This establishment, by the accuracy and extent of its observations, has contributed more than all other inst.i.tutions to perfect the science of astronomy.

To preside over and direct this great inst.i.tution, a man of the highest eminence in the science is appointed by the government, with the t.i.tle of _Astronomer Royal_. He is paid an ample salary, with the understanding that he is to devote himself exclusively to the business of the observatory. The astronomers royal of the Greenwich observatory, from the time of its first establishment, in 1676, to the present time, have const.i.tuted a series of the proudest names of which British science can boast. A more detailed sketch of their interesting history will be given towards the close of these Letters.

Six a.s.sistants, besides inferior laborers, are constantly in attendance; and the business of making and recording observations is conducted with the utmost system and order.

The great objects to be attained in the construction of an observatory are, a commanding and un.o.bstructed view of the heavens; freedom from causes that affect the transparency and uniform state of the atmosphere, such as fires, smoke, or marshy grounds; mechanical facilities for the management of instruments, and, especially, every precaution that is necessary to secure perfect steadiness. This last consideration is one of the greatest importance, particularly in the use of very large magnifiers; for we must recollect, that any motion in the instrument is magnified by the full power of the gla.s.s, and gives a proportional unsteadiness to the object. A situation is therefore selected as remote as possible from public roads, (for even the pa.s.sing of carriages would give a tremulous motion to the ground, which would be sensible in large instruments,) and structures of solid masonry are commenced deep enough in the ground to be unaffected by frost, and built up to the height required, without any connexion with the other parts of the building. Many observatories are furnished with a movable dome for a roof, capable of revolving on rollers, so that instruments penetrating through the roof may be easily brought to bear upon any point at or near the zenith.

You will not perhaps desire me to go into a minute description of all the various instruments that are used in a well-constructed observatory.

Nor is this necessary, since a very large proportion of all astronomical observations are taken on the meridian, by means of the transit instrument and clock. When a body, in its diurnal revolution, comes to the meridian, it is at its highest point above the horizon, and is then least affected by refraction and parallax. This, then, is the most favorable position for taking observations upon it. Moreover, it is peculiarly easy to take observations on a body when in this situation.

Hence the transit instrument and clock are the most important members of an astronomical observatory. You will, therefore, expect me to give you some account of these instruments.

[Ill.u.s.tration Fig. 7.]

The _transit instrument_ is a telescope which is fixed permanently in the meridian, and moves only in that plane. The accompanying diagram, Fig. 7, represents a side view of a portable transit instrument, exhibiting the telescope supported on a firm horizontal axis, on which it turns in the plane of the meridian, from the south point of the horizon through the zenith to the north point. It can therefore be so directed as to observe the pa.s.sage of a star across the meridian at any alt.i.tude. The accompanying graduated circle enables the observer to set the instrument at any required alt.i.tude, corresponding to the known alt.i.tude at which the body to be observed crosses the meridian. Or it may be used to measure the alt.i.tude of a body, or its zenith distance, at the time of its meridian pa.s.sage. Near the circle may be seen a spirit-level, which serves to show when the axis is exactly on a level with the horizon. The framework is made of solid metal, (usually bra.s.s,) every thing being arranged with reference to keeping the instrument perfectly steady. It stands on screws, which not only afford a steady support, but are useful for adjusting the instrument to a perfect level. The transit instrument is sometimes fixed immovably to a solid foundation, as a pillar of stone, which is built up from a depth in the ground below the reach of frost. When enclosed in a building, as in an observatory, the stone pillar is carried up separate from the walls and floors of the building, so as to be entirely free from the agitations to which they are liable.

The use of the transit instrument is to show the precise instant when a heavenly body is on the meridian, or to measure the time it occupies in crossing the meridian. The _astronomical clock_ is the constant companion of the transit instrument. This clock is so regulated as to keep exact pace with the stars, and of course with the revolution of the earth on its axis; that is, it is regulated to _sidereal_ time. It measures the progress of a star, indicating an hour for every fifteen degrees, and twenty-four hours for the whole period of the revolution of the star. Sidereal time commences when the vernal equinox is on the meridian, just as solar time commences when the sun is on the meridian.

Hence the hour by the sidereal clock has no correspondence with the hour of the day, but simply indicates how long it is since the equinoctial point crossed the meridian. For example, the clock of an observatory points to three hours and twenty minutes; this may be in the morning, at noon, or any other time of the day,--for it merely shows that it is three hours and twenty minutes since the equinox was on the meridian.

Hence, when a star is on the meridian, the clock itself shows its right ascension, which you will recollect is the angular distance measured on the equinoctial, from the point of intersection of the ecliptic and equinoctial, called the vernal equinox, reckoning fifteen degrees for every hour, and a proportional number of degrees and minutes for a less period. I have before remarked, that a very large portion of all astronomical observations are taken when the bodies are on the meridian, by means of the transit instrument and clock.

Having now described these instruments, I will next explain the manner of using them for different observations. Any thing becomes a measure of time, which divides duration equally. The equinoctial, therefore, is peculiarly adapted to this purpose, since, in the daily revolution of the heavens, equal portions of the equinoctial pa.s.s under the meridian in equal times. The only difficulty is, to ascertain the amount of these portions for given intervals. Now, the clock shows us exactly this amount; for, when regulated to sidereal time, (as it easily may be,) the hour-hand keeps exact pace with the equator, revolving once on the dial-plate of the clock while the equator turns once by the revolution of the earth. The same is true, also, of all the small circles of diurnal revolution; they all turn exactly at the same rate as the equinoctial, and a star situated any where between the equator and the pole will move in its diurnal circle along with the clock, in the same manner as though it were in the equinoctial. Hence, if we note the interval of time between the pa.s.sage of any two stars, as shown by the clock, we have a measure of the number of degrees by which they are distant from each other in right ascension. Hence we see how easy it is to take arcs of right ascension: the transit instrument shows us when a body is on the meridian; the clock indicates how long it is since the vernal equinox pa.s.sed it, which is the right ascension itself; or it tells us the difference of right ascension between any two bodies, simply by indicating the difference in time between their periods of pa.s.sing the meridian. Again, it is easy to take the _declination_ of a body when on the meridian. By declination, you will recollect, is meant the distance of a heavenly body from the equinoctial; the same, indeed, as lat.i.tude on the earth. When a star is pa.s.sing the meridian, if, on the instant of crossing the meridian wire of the telescope, we take its distance from the north pole, (which may readily be done, because the position of the pole is always known, being equal to the lat.i.tude of the place,) and subtract this distance from ninety degrees, the remainder will be the distance from the equator, which is the declination. You will ask, why we take this indirect method of finding the declination?

Why we do not rather take the distance of the star from the equinoctial, at once? I answer, that it is easy to point an instrument to the north pole, and to ascertain its exact position, and of course to measure any distance from it on the meridian, while, as there is nothing to mark the exact situation of the equinoctial, it is not so easy to take direct measurements from it. When we have thus determined the situation of a heavenly body, with respect to two great circles at right angles with each other, as in the present case, the distance of a body from the equator and from the equinoctial colure, or that meridian which pa.s.ses though the vernal equinox, we know its relative position in the heavens; and when we have thus determined the relative positions of all the stars, we may lay them down on a map or a globe, exactly as we do places on the earth, by means of their lat.i.tude and longitude.

The foregoing is only a _specimen_ of the various uses of the transit instrument, in finding the relative places of the heavenly bodies.

Another use of this excellent instrument is, to regulate our clocks and watches. By an observation with the transit instrument, we find when the sun's centre is on the meridian. This is the exact time of _apparent_ noon. But watches and clocks usually keep _mean_ time, and therefore, in order to set our timepiece by the transit instrument, we must apply to the apparent time of noon the equation of time, as will be explained in my next Letter.

A _noon-mark_ may easily be made by the aid of the transit instrument. A window sill is frequently selected as a suitable place for the mark, advantage being taken of the shadow projected upon it by the perpendicular casing of the window. Let an a.s.sistant stand, with a rule laid on the line of shadow, and with a knife ready to make the mark, the instant when the observer at the transit instrument announces that the centre of the sun is on the meridian. By a concerted signal, as the stroke of a bell, the inhabitants of a town may all fix a noon-mark from the same observation. If the signal be given on one of the days when apparent time and mean time become equal to each other, as on the twenty-fourth of December, no equation of time is required.

As a noon-mark is convenient for regulating timepieces, I will point out a method of making one, which may be practised without the aid of the telescope. Upon a smooth, level plane, freely exposed to the sun, with a pair of compa.s.ses describe a circle. In the centre, where the leg of the compa.s.ses stood, erect a perpendicular wire of such a length, that the termination of its shadow shall fall upon the circ.u.mference of the circle at some hour before noon, as about ten o'clock. Make a small dot at the point where the end of the shadow falls upon the circle, and do the same where it falls upon it again in the afternoon. Take a point half-way between these two points, and from it draw a line to the centre, and it will be a true meridian line. The direction of this line would be the same, whether it were made in the Summer or in the Winter; but it is expedient to draw it about the fifteenth of June, for then the shadow alters its length most rapidly, and the moment of its crossing the wire will be more definite, than in the Winter. At this time of year, also, the sun and clock agree, or are together, as will be more fully explained in my next Letter; whereas, at other times of the year, the time of noon, as indicated by a common clock, would not agree with that indicated by the sun. If the upper end of the wire is flattened, and a small hole is made in it, through which the sun may shine, the instant when this bright spot falls upon the circle will be better defined than the termination of the shadow.

Another important instrument of the observatory is the _mural circle_.

It is a graduated circle, usually of very large size, fixed permanently in the plane of the meridian, and attached firmly to a perpendicular wall; and on its centre is a telescope, which revolves along with it, and is easily brought to bear on any object in any point in the meridian. It is made of large size, sometimes twenty feet in diameter, in order that very small angles may be measured on its limb; for it is obvious that a small angle, as one second, will be a larger s.p.a.ce on the limb of an instrument, in proportion as the instrument itself is larger.

The vertical circle usually connected with the transit instrument, as in Fig. 7, may indeed be employed for the same purposes as the mural circle, namely, to measure arcs of the meridian, as meridian alt.i.tudes, zenith distances, north polar distances, and declinations; but as that circle must necessarily be small, and therefore incapable of measuring very minute angles, the mural circle is particularly useful in measuring these important arcs. It is very difficult to keep so large an instrument perfectly steady; and therefore it is attached to a ma.s.sive wall of solid masonry, and is hence called a _mural_ circle, from a Latin word, (_murus_,) which signifies a wall.

The diagram, Fig. 8, page 56, represents a mural circle fixed to its wall, and ready for observations. It will be seen, that every expedient is employed to give the instrument firmness of parts and steadiness of position. The circle is of solid metal, usually of bra.s.s, and it is strengthened by numerous radii, which keep it from warping or bending; and these are made in the form of hollow cones, because that is the figure which unites in the highest degree lightness and strength. On the rim of the instrument, at A, you may observe a microscope. This is attached to a micrometer,--a delicate piece of apparatus, used for reading the minute subdivisions of angles; for, after dividing the limb of the instrument as minutely as possible, it will then be necessary to magnify those divisions with the microscope, and subdivide each of these parts with the micrometer. Thus, if we have a mural circle twenty feet in diameter, and of course nearly sixty-three feet in circ.u.mference, since there are twenty-one thousand and six hundred minutes in the whole circle, we shall find, by calculation, that one minute would occupy, on the limb of such an instrument, only about one thirtieth of an inch, and a second, only one eighteen hundredth of an inch. We could not, therefore, hope to carry the actual divisions to a greater degree of minuteness than minutes; but each of these s.p.a.ces may again be subdivided into seconds by the micrometer.

[Ill.u.s.tration Fig. 8.]

From these statements, you will acquire some faint idea of the extreme difficulty of making perfect astronomical instruments, especially where they are intended to measure such minute angles as one second. Indeed, the art of constructing astronomical instruments is one which requires such refined mechanical genius,--so superior a mind to devise, and so delicate a hand to execute,--that the most celebrated instrument-makers take rank with the most distinguished astronomers; supplying, as they do, the means by which only the latter are enabled to make these great discoveries. Astronomers have sometimes made their own telescopes; but they have seldom, if ever, possessed the refined manual skill which is requisite for graduating delicate instruments.

The _s.e.xtant_ is also one of the most valuable instruments for taking celestial arcs, or the distance between any two points on the celestial sphere, being applicable to a much greater number of purposes than the instruments already described. It is particularly valuable for measuring celestial arcs at sea, because it is not, like most astronomical instruments, affected by the motion of the ship. The principle of the s.e.xtant may be briefly described, as follows: it gives the angular distance between any two bodies on the celestial sphere, by reflecting the image of one of the bodies so as to coincide with the other body, as seen directly. The arc through which the reflector is turned, to bring the reflected body to coincide with the other body, becomes a measure of the angular distance between them. By keeping this principle in view, you will be able to understand the use of the several parts of the instrument, as they are exhibited in the diagram, Fig. 9, page 58.

It is, you observe, of a triangular shape, and it is made strong and firm by metallic cross-bars. It has two reflectors, I and H, called, respectively, the index gla.s.s and the horizon gla.s.s, both of which are firmly fixed perpendicular to the plane of the instrument. The index gla.s.s is attached to the movable arm, ID, and turns as this is moved along the graduated limb, EF. This arm also carries a _vernier_, at D, a contrivance which, like the micrometer, enables us to take off minute parts of the s.p.a.ces into which the limb is divided. The horizon gla.s.s, H, consists of two parts; the upper part being transparent or open, so that the eye, looking through the telescope, T, can see through it a distant body, as a star at S, while the lower part is a reflector.

[Ill.u.s.tration Fig. 9.]

Suppose it were required to measure the angular distance between the moon and a certain star,--the moon being at M, and the star at S. The instrument is held firmly in the hand, so that the eye, looking through the telescope, sees the star, S, through the transparent part of the horizon gla.s.s. Then the movable arm, ID, is moved from F towards E, until the image of M is reflected down to S, when the number of degrees and parts of a degree reckoned on the limb, from F to the index at D, will show the angular distance between the two bodies.

FOOTNOTE:

[3] Brewster's Life of Newton

LETTER VI.

TIME AND THE CALENDAR.

"From old Eternity's mysterious...o...b..Was Time cut off, and cast beneath the skies."--_Young._

HAVING hitherto been conversant only with the many fine and sentimental things which the poets have sung respecting Old Time, perhaps you will find some difficulty in bringing down your mind to the calmer consideration of what time really is, and according to what different standards it is measured for different purposes. You will not, however, I think, find the subject even in our matter-of-fact and unpoetical way of treating it, altogether uninteresting. What, then, is time? _Time is a measured portion of indefinite duration._ It consists of equal portions cut off from eternity, as a line on the surface of the earth is separated from its contiguous portions that const.i.tute a great circle of the sphere, by applying to it a two-foot scale; or as a few yards of cloth are measured off from a piece of unknown or indefinite extent.

Any thing, or any event which takes place at equal intervals, may become a measure of time. Thus, the pulsations of the wrist, the flowing of a given quant.i.ty of sand from one vessel to another, as in the hourgla.s.s, the beating of a pendulum, and the revolution of a star, have been severally employed as measures of time. But the great standard of time is the period of the revolution of the earth on its axis, which, by the most exact observations, is found to be always the same. I have antic.i.p.ated a little of this subject, in giving an account of the transit instrument and clock, but I propose, in this letter, to enter into it more at large.

The time of the earth's revolution on its axis, as already explained, is called a sidereal day, and is determined by the revolution of a star in the heavens. This interval is divided into twenty-four _sidereal_ hours. Observations taken on numerous stars, in different ages of the world, show that they all perform their diurnal revolution in the same time, and that their motion, during any part of the revolution, is always uniform. Here, then, we have an exact measure of time, probably more exact than any thing which can be devised by art. _Solar time_ is reckoned by the apparent revolution of the sun from the meridian round to the meridian again. Were the sun stationary in the heavens, like a fixed star, the time of its apparent revolution would be equal to the revolution of the earth on its axis, and the solar and the sidereal days would be equal. But, since the sun pa.s.ses from west to east, through three hundred and sixty degrees, in three hundred and sixty-five and one fourth days, it moves eastward nearly one degree a day. While, therefore, the earth is turning round on its axis, the sun is moving in the same direction, so that, when we have come round under the same celestial meridian from which we started, we do not find the sun there, but he has moved eastward nearly a degree, and the earth must perform so much more than one complete revolution, before we come under the sun again. Now, since we move, in the diurnal revolution, fifteen degrees in sixty minutes, we must pa.s.s over one degree in four minutes. It takes, therefore, four minutes for us to _catch up_ with the sun, after we have made one complete revolution. Hence the solar day is about four minutes longer than the sidereal; and if we were to reckon the sidereal day twenty-four hours, we should reckon the solar day twenty-four hours four minutes. To suit the purposes of society at large, however, it is found more convenient to reckon the solar days twenty-four hours, and throw the fraction into the sidereal day. Then,

24h. 4m. : 24h. :: 24h. : 23h. 56m. 4s.

That is, when we reduce twenty-four hours and four minutes to twenty-four hours, the same proportion will require that we reduce the sidereal day from twenty-four hours to twenty-three hours fifty-six minutes four seconds; or, in other words, a sidereal day is such a part of a solar day. The solar days, however, do not always differ from the sidereal by precisely the same fraction, since they are not constantly of the same length. Time, as measured by the sun, is called _apparent time_, and a clock so regulated as always to keep exactly with the sun, is said to keep apparent time. _Mean time_ is time reckoned by the _average_ length of all the solar days throughout the year. This is the period which const.i.tutes the _civil_ day of twenty-four hours, beginning when the sun is on the lower meridian, namely, at twelve o'clock at night, and counted by twelve hours from the lower to the upper meridian, and from the upper to the lower. The _astronomical_ day is the apparent solar day counted through the whole twenty-four hours, (instead of by periods of twelve hours each, as in the civil day,) and begins at noon.

Thus it is now the tenth of June, at nine o'clock, A.M., according to civil time; but we have not yet reached the tenth of June by astronomical time, nor shall we, until noon to-day; consequently, it is now June ninth, twenty-first hour of astronomical time. Astronomers, since so many of their observations are taken on the meridian, are always supposed to look towards the south. Geographers, having formerly been conversant only with the northern hemisphere, are always understood to be looking towards the north. Hence, left and right, when applied to the astronomer, mean east and west, respectively; but to the geographer the right is east, and the left, west.

Clocks are usually regulated so as to indicate mean solar time; yet, as this is an artificial period not marked off, like the sidereal day, by any natural event, it is necessary to know how much is to be added to, or subtracted from, the apparent solar time, in order to give the corresponding mean time. The interval, by which apparent time differs from mean time, is called the _equation of time_. If one clock is so constructed as to keep exactly with the sun, going faster or slower, according as the lengths of the solar days vary, and another clock is regulated to mean time, then the difference of the two clocks, at any period, would be the equation of time for that moment. If the apparent clock were _faster_ than the mean, then the equation of time must be subtracted; but if the apparent clock were slower than the mean, then the equation of time must be added, to give the mean time. The two clocks would differ most about the third of November, when the apparent time is sixteen and one fourth minutes greater than the mean. But since apparent time is sometimes greater and sometimes less than mean time, the two must obviously be sometimes equal to each other. This is, in fact, the case four times a year, namely, April fifteenth, June fifteenth, September first, and December twenty-fourth.

Astronomical clocks are made of the best workmanship, with every advantage that can promote their regularity. Although they are brought to an astonishing degree of accuracy, yet they are not as regular in their movements as the stars are, and their accuracy requires to be frequently tested. The transit instrument itself, when once accurately placed in the meridian, affords the means of testing the correctness of the clock, since one revolution of a star, from the meridian to the meridian again, ought to correspond exactly to twenty-four hours by the clock, and to continue the same, from day to day; and the right ascensions of various stars, as they cross the meridian, ought to be such by the clock, as they are given in the tables, where they are stated according to the accurate determinations of astronomers. Or, by taking the difference of any two stars, on successive days, it will be seen whether the going of the clock is uniform for that part of the day; and by taking the right ascensions of different pairs of stars, we may learn the rate of the clock at various parts of the day. We thus learn, not only whether the clock accurately measures the length of the sidereal day, but also whether it goes uniformly from hour to hour.

Although astronomical clocks have been brought to a great degree of perfection, so as hardly to vary a second for many months, yet none are absolutely perfect, and most are so far from it, as to require to be corrected by means of the transit instrument, every few days. Indeed, for the nicest observations, it is usual not to attempt to bring the clock to a state of absolute correctness, but, after bringing it as near to such a state as can conveniently be done, to ascertain how much it gains or loses in a day; that is, to ascertain the _rate_ of its going, and to make allowance accordingly.

Having considered the manner in which the smaller divisions of time are measured, let us now take a hasty glance at the larger periods which compose the calendar.

As a _day_ is the period of the revolution of the earth on its axis, so a _year_ is the period of the revolution of the earth around the sun.

This time, which const.i.tutes the _astronomical year_, has been ascertained with great exactness, and found to be three hundred and sixty-five days five hours forty-eight minutes and fifty-one seconds.

The most ancient nations determined the number of days in the year by means of the _stylus_, a perpendicular rod which casts its shadow on a smooth plane bearing a meridian line. The time when the shadow was shortest, would indicate the day of the Summer solstice; and the number of days which elapsed, until the shadow returned to the same length again, would show the number of days in the year. This was found to be three hundred and sixty-five whole days, and accordingly, this period was adopted for the civil year. Such a difference, however, between the civil and astronomical years, at length threw all dates into confusion.

For if, at first, the Summer solstice happened on the twenty-first of June, at the end of four years, the sun would not have reached the solstice until the twenty-second of June; that is, it would have been behind its time. At the end of the next four years, the solstice would fall on the twenty-third; and in process of time, it would fall successively on every day of the year. The same would be true of any other fixed date.

Julius Caesar, who was distinguished alike for the variety and extent of his knowledge, and his skill in arms, first attempted to make the calendar conform to the motions of the sun.

"Amidst the hurry of tumultuous war, The stars, the G.o.ds, the heavens, were still his care."

Aided by Sosigenes, an Egyptian astronomer, he made the first correction of the calendar, by introducing an additional day every fourth year, making February to consist of twenty-nine instead of twenty-eight days, and of course the whole year to consist of three hundred and sixty-six days. This fourth year was denominated _Biss.e.xtile_, because the sixth day before the Kalends of March was reckoned twice. It is also called Leap Year.

The Julian year was introduced into all the civilized nations that submitted to the Roman power, and continued in general use until the year 1582. But the true correction was not six hours, but five hours forty-nine minutes; hence the addition was too great by eleven minutes.

This small fraction would amount in one hundred years to three fourths of a day, and in one thousand years to more than seven days. From the year 325 to the year 1582, it had, in fact, amounted to more than ten days; for it was known that, in 325, the vernal equinox fell on the twenty-first of March, whereas, in 1582, it fell on the eleventh. It was ordered by the Council of Nice, a celebrated ecclesiastical council, held in the year 325, that Easter should be celebrated upon the first Sunday after the first full moon, next following the vernal equinox; and as certain other festivals of the Romish Church were appointed at particular seasons of the year, confusion would result from such a want of constancy between any fixed date and a particular season of the year.

Suppose, for example, a festival accompanied by numerous religious ceremonies, was decreed by the Church to be held at the time when the sun crossed the equator in the Spring, (an event hailed with great joy, as the harbinger of the return of Summer,) and that, in the year 325, March twenty-first was designated as the time for holding the festival, since, at that period, it was on the twenty-first of March when the sun reached the equinox; the next year, the sun would reach the equinox a little sooner than the twenty-first of March, only eleven minutes, indeed, but still amounting in twelve hundred years to ten days; that is, in 1582, the sun reached the equinox on the eleventh of March. If, therefore, they should continue to observe the twenty-first as a religious festival in honor of this event, they would commit the absurdity of celebrating it ten days after it had pa.s.sed by. Pope Gregory the Thirteenth, who was then at the head of the Roman See, was a man of science, and undertook to reform the calendar, so that fixed dates would always correspond to the same seasons of the year. He first decreed, that the year should be brought forward ten days, by reckoning the fifth of October the fifteenth; and, in order to prevent the calendar from falling into confusion afterwards, he prescribed the following rule: _Every year whose number is not divisible by four, without a remainder, consists of three hundred and sixty-five days; every year which is so divisible, but is not divisible by one hundred, of three hundred and sixty-six; every year divisible by one hundred, but not by four hundred, again, of three hundred and sixty-five; and every year divisible by four hundred, of three hundred and sixty-six._

Thus the year 1838, not being divisible by four, contains three hundred and sixty-five days, while 1836 and 1840 are leap years. Yet, to make every fourth year consist of three hundred and sixty-six days would increase it too much, by about three fourths of a day in a century; therefore every hundredth year has only three hundred and sixty-five days. Thus 1800, although divisible by four, was not a leap year, but a common year. But we have allowed a _whole_ day in a hundred years, whereas we ought to have allowed only _three fourths_ of a day. Hence, in four hundred years, we should allow a day too much, and therefore, we let the four hundredth remain a leap year. This rule involves an error of less than a day in four thousand two hundred and thirty-seven years.

The Pope, who, you will recollect, at that age a.s.sumed authority over all secular princes, issued his decree to the reigning sovereigns of Christendom, commanding the observance of the calendar as reformed by him. The decree met with great opposition among the Protestant States, as they recognised in it a new exercise of ecclesiastical tyranny; and some of them, when they received it, made it expressly understood, that their acquiescence should not be construed as a submission to the Papal authority.