Monday, 11 November 2013

Lecture 3: Observing and Cataloguing the Heavens

Lecture 3

Observing and Cataloguing the Heavens

            In my last lecture I described some of the instruments which are made use of by the practical astronomer. There are others which are sometimes employed, but as these are not absolutely necessary to our fictitious observer I shall defer their description untill we arrive at those parts in which they are more particularly concerned.

            Let us now pursue the path of our imaginary Astronomer. Let us suppose him placed in an elevated station having an uniterrupted prospect on every side to the horizon. He will naturally distinguish in the heavens three kinds of bodies marked by entirely different characters. The Sun, whose preserve is always indicated by the copious emission of light and heat, whose duration above the horizon constitutes that period called day. The Moon, whose rays never produce the least sensible heat, but illuminate in different degrees at various times. And the third kind of objects are the Stars, which yield no heat and but just sufficient light to render them visible. These are the less conspicuous and least splendid objects which attract his notice, but accordingly the laws of investigation to which we prescribed to him, he must for the present defer the consideration of the lunar and solar orbs which, though the most brilliant, are but solitary individuals and confine his attention to the examination of that numerous class called Stars.

The first question respecting them which will present itself to his mind will probably be this. What becomes of these objects during the day? is their light extinguished? have they themselves been removed? or what is the cause of their disappearance? By looking at their gradual appearance at sunset he will soon be convinced that they have not been removed from their places during the presence of this luminary, and it will soon occur to him that the probable cause of their being invisible is owing to the superior splendour of the Sun preventing their feeble rays from making any impression on our organs of sight. To put this explanation to the test he will make the following experiment.

            Having provided a long tube or a long telescope would be still better he makes the apertures at the ends extremely small, so that only a few rays shall enter at once. When this is directed to any part of the heavens at a distance from that in which the Sun is situated, the Stars will be visible by means of it. The reason is obvious. The rays from all other objects but that to which it is directed are excluded from the eye, and thus the faint rays proceeding from a star are rendered visible, even during the day.

After looking at them for a short time, he perceives that they appear all in motion, some moving but slowly, others with considerable velocity. He observes, in one quarter of the horizon, new stars appear, and at the opposite side those which were visible seem to sink below. The first conjecture he makes on these varied appearances is, that all the stars move in the same direction. To determine whether this is just he turns his eyes to that part of the heavens where the greater number appear to rise, and he examines whether there may not be some few which set in this part of the heavens. He will find that there are none. And on turning to that quarter where the stars appear to set he will likewise find that there is no exception. He is thus led to conclude that all the stars move in the same direction.

            This first result to which our observer arrives he is still anxious to confirm and continues to examine if there be no exception to it. Upon viewing some few, however, he finds to his disappointment that their apparent motion is in a contrary direction. On these stars he particularly fixes his attention, and after looking at them for some time, he finds that they never sink below the horizon, but appear to describe some curve, and when they get to the lowest point they reascend. This curve, it soon appears, is a circle, and the apparent exception is now explained. These stars move in their circles in the same direction as the others which he had observed, but  from the nature of this kind of motion, when they are in the lowest part of the circle, their motion appears contrary to the direction in which they move when they are in the upper half.

Thus then it is determined that this first law, namely that the stars all move in the same direction is confirmed without a single exception. Our fictitious astronomer has, however, made an important step by the doubt which at first assailed it: he has found that some of the stars continue above the horizon during the whole night, and that they describe circles round some imaginary point. For the sake of convenience he gives a name to this point which will frequently be referred to and calls it the Pole. No star is situated precisely in this point, but numbers move round it. One, however, is placed sufficiently near to mark its position, and is from this circumstance called the Pole Star. This will indicate in a rough manner the height of the Pole above the horizon. But our astronomer will devise a more accurate method. His attention, however, must for the present be turned to other objects.

            In order to discover the various motions of the stars, he considers a few of the principal and most luminous and measures with his sextant their relative distances from each other. For the purpose of distinguishing those which he observes he may perhaps represent their positions on a globe or a sheet of paper marking on it carefully their measured distances. This he puts aside in order to compare it with future observations. After making several of these drawings or maps of different parts of the heavens and comparing them on many successive evenings with the sky he will most probably find that they have always retained their respective distances, or that the figures which he had drawn of them will still represent their positions. It was doubtless by observing this constant regularity in the heavens that the idea of dividing them into Constellations first occurred, obviously for the purpose of distinguishing the various stars from each other and likewise for the convenience of describing their situation when they are not visible.

It may however possibly happen that a few of these observations indicate a relative motion in some of the stars. If this should be the case our astronomer will, for a short time, be puzzled: but on comparing a great variety of similar observations he will find that it is only two or three stars which have this motion, and he will therefore leave them out of his consideration at present.

            This discovery brings a new class of bodies to his notice. And the result of the observations he has now made is this: that the stars all move in one direction with considerable speed, and that the greater part of them never change their relative position, but that some few are exceptions to this rule and have a peculiar motion of their own. His principle of philosophising would now lead him to consider the general rule and omit for the present these exceptions. But before we leave the newly discovered bodies our astronomer must have some means of distinguishing them from other stars lest by this mistake he should be led into errors. After some trials he will probably find out this accurate and infallible method: by viewing these wanderers, which from this circumstance he calls planets, with a telescope possessing a tolerable magnifying power he will see them much increase in magnitude, but if he direct this same glass to any of the fixed stars he will see them exactly of the same size as they appear without its assistance, or indeed rather smaller.

The planets will appear small luminous circular bodies; the fixed stars will seem brilliant points. Whatever may be the magnifying power made use of the result will always be the same. The fixed stars viewed through the most powerful telescopes yet constructed always appear as mere luminous points. This then is a certain criterion by which they can always be distinguished from other bodies.

            Having now discovered that the stars all move in the same direction and always preserve their relative distances an important question will naturally suggest itself. What becomes of these stars which sink below the horizon? how does it happen that they reappear in the opposite part [of the sky]? An attentive consideration of the phenomena we have remarked will be sufficient for the solution to this question.

            It was observed that some of the stars described circles round an imaginary point called the Pole, and never disappeared below the horizon. These were situated at various distances from the Pole; some of them might in the lowest part of their circles almost touch the horizon. At a small distance beyond these other stars would sink below and be hid for a short time but  would soon reascend. Now those stars which remained but a short time below the horizon did while above it always continue at the same fixed distance from those which described circles. There is nothing which can induce us to suppose this distance changed while they are out of sight for they reappear with the same distance between them that there was when they parted from us. The conclusion is inevitable. They could not have altered that distance when out of our sight. From this it necessarily results that they likewise described circles around the same imaginary point or Pole.

The same train of reasoning may be applied to all other stars whether nearer or more distant from the Pole. -As important consequences result from it I will repeat the process- It is shortly this: certain stars which we see during the whole of their revolution move in circles round the Pole. Certain other stars which we see only in a part of their course, because they sink below the horizon, always preserve a fixed distance from the first mentioned ones, while we have the power of observing them. The consequence drawn from this is that they preserve the same distance when we have not the means of viewing them and therefore they also move in circles round the Pole. This law happily connects together a variety of appearances observed in the heavens. We see clearly from it why some stars appear to move fast [and] others more slowly. Those which move swiftly have larger circles to describe than those which have a slow motion. And therefore, that they may all finish their revolution in the same time, the velocity of the former must be proportionally larger than that of the latter.

Another very important result of this law is that the Earth is insulated in space; that it is not as was supposed by some of the ancients an immense place surrounded by an interminable ocean. It has limits for the stars move round it. But what may be its figure? or what is its magnitude? are enquiries which our imaginary observer must for the present postpone. Other investigations of more importance which present themselves in crowds at present demand his attention.

            It is now obvious that somewhere beneath or on the other side of the Earth there must be another stationary point or Pole. One these two the whole heavens will appear to turn. This latter is called the South Pole, and the line which joins the two is called the Axis. At an equal distance from these two points will be a great circle extending round the heavens which is called the Equator. There are points and also a circle similarly situated on the surface of the Earth, which also possess the same name.

It will now be convenient for our astronomer to form some hypothesis to connect together the results he has arrived at. It is of little consequence whether that which for the present he assumes be true or false, provided only that it explains the few phenomena that he has observed. The ancient one of the crystalline sphere will answer his present object very well. Let him then suppose that at an immense distance from the Earth there is placed a transparent sphere in which the stars are fixed. Its revolution round the Earth will explain all the appearances he has yet observed.

            The next questions he would be solicitous to determine would be whether this starry sphere moves uniformly on its axis and whether its revolutions are always performed in the same time. To determine this point is not a matter of much difficulty, he places the transit instrument in any position he chooses and observes the passage of a star. He notes the time indicated by his clock, leaving the instrument and repeating this observation on the same star several successive evenings; and for the sake of greater accuracy he performs it on many different stars. From this he finds that the star always takes the same time to return to the instrument in whatever situation it is fixed, and consequently, he considers their motion as uniform.

Having now discovered that the time of the revolution of the stars is always invariable our astronomer may make a very advantageous use of it in future for the purpose of regulating his clock. Another point which will now be necessary to determine is the inclination of this sphere to the horizon, or in other words to find the height of the Pole. We have before observed that there is no star situated precisely in that point; how then is its altitude to be discovered? Indirect means must be made use of, and the following method will supply them. Those stars which never set are called Circumpolar Stars. Observe one of these when it arrives at its greatest height above the horizon. Measure its altitude by means of Hadley's Quadrant. And do the same when it arrives at its least height. The difference of these two altitudes will give the diameter of the circle which it describes round the Pole. Half this quantity added to the lowest of the two altitudes of the star will give the height of the Pole. When a star is at its greatest or least altitude above the horizon a perpendicular circle passing through it likewise passes through the Pole, and as this great circle is very frequently made use of a name is appropriated to it, and it is called the Meridian. All stars which are not circumpolar are, when they arrive at this line, at their greatest height above the horizon. And when a star passes it is said to "Transit the Meridian".

The purpose of finding a meridian line by which the transit instrument may be rectified, the equable revolution of the stars may be made use of: let the instrument be placed nearly in the plane of the meridian by means I have described at my last lecture and let some circumpolar star, that is one that never sets, be made choice of. This star revolves in a circle round the poles and as it moves equally it is obvious that it will take just as much time to descend from its highest elevation above the pole to its lowest depression below as it requires to ascend from this latter point to its greatest altitude. If now the transit instrument is placed nearly in the plane of the meridian, and if we note the time which elapses during its progress from its greatest to its least altitude, and again the interval of time which it occupies in returning to its greatest height, these two intervals will be equal if the instrument is accurately adjusted; but if they should be unequal the plane of its motion must be altered by moving the proper adjusting screws.

We may now suppose our astronomer to have determined accurately a meridian line and to have fixed his instrument in that plane. His next care will be to find some easy method of regulating his clock. This likewise will be readily afforded by the revolution of the heavens. He has observed that the same star always returns to the meridian after the same interval of time. If therefore he adjusts his clock by means of the pendulum so that when a circumpolar star comes to the meridian above the pole it shall point to twelve o'clock and the when this same star comes to the meridian below the pole it shall after having performed one revolution return to the same hour. It is obvious that if the clock goes correctly whenever this star is on the meridian the hands ought to point to the hour of 12. A clock regulated by these means is said to be adjusted to sidereal time. The difference between this and mean solar time will be explained when we consider the motions of the Sun. It has been observed that the great circle which divides the heavens into two equal parts and which is equally distant from both poles is called the Celestial Equator or the Equinoctial. It is by means of this circle and others called meridians which are perpendicular to it that the situation of a star is determined. If a great circle be drawn through any star and likewise through the pole it will cut the equinoctial line. And the distance of the point of intersection from some certain fixed point assumed in this line is called the Right Ascension [or R.A.] of a star. The point from which Right Ascension is generally measured is the intersection of the equinoctial line with another great circle called the Ecliptic. But as we must for the present suppose our observer unacquainted with this point he must employ some other means of reckoning it.

For this purpose he chooses any remarkable star and measures the R.A. of all other stars by their distance from this when referred to the equinoctial. If, on this supposition, he determines the R.A. of a multitude of stars and should afterward, from any discovery, wish to alter the point from which it is reckoned, it may be readily effected. Thus suppose the difference of R.A. between the new point  from which he proposes to commence his reckoning and the point from which it was counted to be 10 degrees then the R.A. of each star he has observed must be increased or diminished by these 10 degrees according as the new point is situated to the east or west of the point from which it was originally reckoned.

            For the convenience of calculations it is usual to divide the circle into a number of equal parts called degrees: there were generally 360, a number probably selected from its being nearly equal to that of the number of days in the year. Each degree was again subdivided into sixty equal parts called minutes, and these were also subdivided into 60 parts called seconds. This is the oldest method of division. Another has lately been substituted by the French. It consists in dividing the quadrant in 100 degrees and each degree into 100 minutes. This is called the decimal division of the circle. The former or sexagesimal division is usually adopted in this country.

To return however to the determination of the positions of the stars, each star during about 24 hours appears to describe a circle round the earth or to move through 360 degrees. It will therefore during a less space of time move over a proportionally less arc of the circle. From this circumstance we may measure the difference of R.A. between two objects. If a star is observed to transit the meridian at a given hour and another star passes it 2 hours after we know that the difference in R.A. is 30 degrees for 2 hours is the 12th part of 24, the time in which a star moves through 360 degrees. Therefore we must allow 30 degrees which is the twelfth part of 360 degrees for its motion in two hours. Another method will however answer this purpose with much less trouble. Let the pendulum clock be so adjusted that the hour hand may move round the dial once in 24 hours. Instead of marking the face of the dial with the hours let it be divided into 360 parts or degrees. From this arrangement it is evident that the heavens and the clock will make one revolution or pass over 360 degrees in the same time. Suppose now that when a particular star transits the meridian the hands of this timekeeper be set to the commencement of the divisions, it is obvious that after any interval of time the star and the index of the clock will have passed over the same angle. And consequently we may know exactly how far this star is from the meridian. If therefore at the moment we observe the transit of a star over the meridian the number of degrees indicated by the clock be observed, this is the R.A.

Our astronomer has now an easy and expeditious method of determining one of the elements which fix the place of stars. He observes in his transit instrument the moment a star is bisected by the middle wire and makes a signal to an assistant who immediately observes the degrees indicated by the timekeeper. By this means he may determine the R.A. of some hundred in the course of a night.

            An observation of a different nature will be necessary for ascertaining the other element which determines the position of a fixed star. This is called its Declination. Declination is the distance of a star from the equinoctial measured on a great circle which passes through the object and the pole. If therefore we can find its distance from the pole the declination may be easily found by subtracting this from 90 degrees or the quarter of a circle. But the polar distance may be readily found by means of the astronomical quadrant. Its altitude must be observed when it comes to the meridian. Let us suppose it a circumpolar star, and that we have observed its altitude when it transits the meridian below the pole. As our observer has already found the elevation of the pole, he has only to subtract from it the altitude of the object and the remainder will be its polar distance.

These two quantities R.A. and declination determine the position of a star. Our astronomer for the purpose of discovering whether there exist any minute motions among them may be supposed to form a catalogue of an immense number and to have ascertained accurately their R.A. and Declination.

            We have seen that the first labour of this kind was undertaken by Hipparchus. But the number in his catalogue as extended by Ptolemy only amounted to 1022. Succeeding observers devoted much attention to this subject. Flamsteed the first who made use of a telescope for this purpose gave a catalogue of 3000 stars.

            Dr. Maskelyne published a catalogue of 36 of the most brilliant fixed stars. The situation of each was determined by the mean of several hundred observation, and this list though small in number was the result of several years labour.

            The catalogue of greatest extent in point of number is that began in 1789 by Jerome Lalande and continued by his nephew. By their joint labours they had in less than 6 months observed 3,000 stars, a number equal to that which had occupied Flamsteed during twenty eight years.

About the end of 1790 the number observed amounted to 8,000 when the elder Lalande was unable to support the fatigue it required and gave up the completion of the task to his nephew which occupied him without intermission until 1799 when he had determined the position of 50,000 stars.

            Our fictitious astronomer having now ascertained that the motion of the stars is uniform and having determined their situations may readily find by calculation the time at which they ought to rise and set. He will therefore wish to put his theory to the test by observing if these times correspond with those he has calculated. Upon trying various stars he finds that they all appear to rise sooner and set later than they ought from theory and that this happens indifferently to every star in whatever part of the heavens it may be situated. This will induce him to try whether their observed altitudes at different times correspond with those derived from calculation. He will find that they do not accurately agree but that this disagreement is always greatest near the horizon and diminish up to the zenith where it disappears.

On considering what may be the cause of this difference he will observe that it seems to have some connection with the Earth because it is much the greatest when near the horizon. He will then be naturally led to enquire whether it may not be owing to the air with which the Earth is surrounded. When an object is in the zenith its rays will pass through but a small part of the atmosphere, whereas when it is situated in the horizon they must traverse a large portion of dense vapours. Analogy will confirm the conjecture. It is an established principle in Optics that as soon as rays of light enter obliquely into a medium the density of which differs from that of the medium from which thay came they are bent from their rectilineal direction. If the medium into which the rays enter is equally dense throughout they are only bent at their entrance, but if its density increases in proportion to its depth the rays of light will be more and more curved their curvature following a law that is correspondent to that proportion.

This takes place in the rays of light passing from the heavenly bodies to the eye, for the atmosphere through which they must pass before they arrive at the eye being unequally dense causes the rays to be bent and arrive at they eye in a different direction from that in which they would come to it were it not for the effect of the intervening medium. The difference between the real and apparent place of the heavenly bodies as affected by the passage of the rays of light through the atmosphere is by astronomers called Refraction. When rays of light pass from air into a fluid or vice versa this refraction is very evident.

            The appearance of a stick or an oar partly immersed in water is familiar to everyone it appears broken. This is owing to the part within the fluid appearing raised by refraction. It is from the same cause that the real depth of water is always one third more than it appears to be. The practical application of this property is well known to fishermen who when they wish to destroy a salmon by the spear or by shooting it always aim considerably below its apparent place. These are strong arguments from analogy that refraction exists in the atmosphere, but if it does it might perhaps be expected that distant land objects should appear elevated above their real situation. This in fact does take place in particular states of the atmosphere. It is called Terrestial Refraction and as the circumstances which sometimes accompany it are very remarkable some account of them may not be uninteresting.

A singular phenomenon of this kind is related to have been discovered at the town of Modbury in Devonshire which is situated at 12 miles distance in a straight line from Plymouth. On the 4th December 1793 a gentleman viewing the surrounding country with an acromatic telescope descried an object like a perpendicular pole standing up in the chasm of a hedge which bounded his view at about 9 miles distance which from its direction was conjectured to be the flagstaff on Maker near Plymouth. Directing the glass the next morning to the same part of the horizon a flag was perceived on the pole which corroborated the conjecture of the preceding day. This day's view also discovered the pinnacles and part of the shaft of the tower. Viewing the same spot at 8 am in the morning on the 9th January 1794 the whole tower and part of the roof of the church with other remote objects not before noticed became visible.

The singularity of this phenomenon has occasioned repeated observations of it. From all which it appears that the summer season and wet windy weather are unfavourable to this refracted elevation, but that calm frosty weather with the absence of the Sun are favourable to it.

            Another curious effect of refraction is the appearance of two or three images of the same object. Sometimes the additional images appear above sometimes below the real one. At one time it is erect; at another it is inverted. An instance of this nature was mentioned in the Philosophical Transactions for 1795 by Mr Dalby who relates that he observed the top of a hill on the horizon to appear detached and the sky to be seen under it. Another instance was observed at Malta. There appeared rising out of the sea at the distance of about 8 miles an island in the shape of a conical mountain. It excited the surprise of hundreds collected to view it and several fishwomen put off to take possession of this newly risen island. But long before they could arrive at the spot it was imagined to have occupied the illusion had vanished and no traces remained. This appearance was seen from the observatory, but the telescope through which it was viewed followed the stranger home again and discovered at an immense distance in the same direction the lofty summit of Mount Etna, which in clear weather is just visible to the inhabitants of Malta. These and various similar phenomena have been explained by Dr. Wollaston in Phil. Trans. 1801. He refers them all to two causes. The first is a considerable difference of density between different strata of air in contact with each other. The other cause is rapid evaporation which increases the refractive power of the lower strata of the atmosphere. To the first of these causes may be attributed the appearances of double images and the inversion of objects; to the second may be ascribed  their extraordinary elevation. This latter is illustrated by the appearances of Maker tower.

I shall only mention one other phenomenon which has been accounted for by the refractive power of the atmosphere. It is well known that the caravans which travel through the deserts of Egypt are obliged to carry water with them as they meet with no supply of this very necessary article during their journey. it sometimes happens that their stock is exhausted and they are compelled to search for one of the wells of brackish water which are thinly scattered through the desert while thirsty travellers are thus employed it sometimes occurs that they perceive at a short distance the appearance of a lake. If unacquainted with the deception they rush forward to cool their burning lips the tempting beverage like the rainbow flies their pursuit.

            It is in vain they accelerate their pace. However they advance it still preserves the same provoking distance thus realising to them the fictitious sufferings of Tantalus. Sometimes though more rarely a city appears at a small distance and gradually removes as they advance. Both these phenomena were observed by the French army in Egypt and both are explained by refraction. The following solution was given by Monge, a member of the Egyptian Institute. The sand with which the desert is covered is heated by the rays of the Sun to a very considerable degree. This causes the lower strata of the air close to the surface of the sand to be much rarified. If now a ray of light proceeds from a town a great distance it will enter the lower strata very obliquely and the effect of refraction being here very strong will turn the ray into a direction nearly parallel with the surface; but still continuing to suffer the refractive influence it will be bent slightly upwards and then reach the eye of a spectator still more distant instead of being lost by striking against the earth. If there is no city at a distance the rays proceeding from the clouds will suffer the same operation and in that serenity of an eastern sky might be readily mistaken for water. This phenomenon is from the resemblance of the operation of the heated air to the effect of a looking glass called the Mirage.

This explanation is an ingenious one, but there are some circumstances which it does not explain. I am inclined to believe that the theory of Dr. Wollaston is more applicable to it and that it arises from the evaporation during the day of the copious dew which falls in the night. One strong reason against the hypothesis of Monge is that, if it were true, there ought to be a city at about 6 to 8 times the distance of the apparent one. This however is not the case for similar appearances are asserted to have taken place at many days' journey from any town. Dr. Wollaston's theory will account for this. He has shown that if the evaporation from the surface of water be sufficient to cause a refraction of about one minute of a degree in every mile the ray of light will have an equal curvature with the surface of the Earth and consequently an object may become visible at any distance.