# Popular Science Monthly/Volume 57/September 1900/Chapters on the Stars III

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* CHAPTERS ON THE STARS.
By Professor SIMON NEWCOMB, U. S. N.
THE SPECTRA OF THE STARS.
THE principles on which spectrum analysis rests can be stated so concisely that I shall set them forth for the special use of such readers as may not be entirely familiar with the subject. Every one knows that when the rays of the sun pass through a triangular prism of glass or other transparent substance they are unequally refracted, and thus separated into rays of different colors. These colors are not distinct, but each runs into the other by insensible gradations, from deep red through orange, yellow, green and blue to a faint violet.
This result is due to the fact that the light of the sun is composed of rays of an infinite number of wave-lengths, or, as we might express it, of an infinite number of shades of color, since to every wave-length corresponds a definite shade. Such a spreading out of elementary colors in the form of a visible sheet is called a spectrum. By the spectrum of an incandescent object is meant the spectrum formed by the light emitted by the object when passed through a refracting prism, or otherwise separated into its elementary colors. The interest and value which attach to the study of spectra arise from the fact that different bodies give different kinds of spectra, according to their constitution, their temperature and the substances of which they are composed. In this manner it is possible, by a study of the spectrum of a body, to reach certain inferences respecting its constitution.
In order that such a study should lead to a definite conclusion, we must recall that to each special shade of color corresponds a definite position in the spectrum. That is to say, there is a special kind of light having a certain wave-length and therefore a certain shade which will be refracted through a certain fixed angle, and will therefore fall into a definite position in the spectrum. This position is, for every possible kind of light, expressed by a number indicating its wave-length.
If we form a spectrum with the light emitted by an ordinary incandescent body, a gaslight for example, we shall find the series of colors to be unbroken from one end of the spectrum to the other. That is to say, there will be light in every part of the spectrum. Such a spectrum is said to be continuous. But if we form the spectrum by means of sunlight, we shall find the spectrum to be crossed by a great number of more or less dark lines. This shows that in the spectrum of ​the sun light of certain definite wave-lengths is wholly or partly wanting. This fact has been observed for more than a century, but its true significance was not seen until a comparatively recent time.
If, instead of using the light of the sun, we form a spectrum with the light emitted by an incandescent gas, say hydrogen made luminous by the electric spark, we shall find that the spectrum consists only of a limited number of separate bright lines, of "various colors. This shows that such a gas, instead of emitting light of all wave-lengths, as an incandescent solid body does, principally emits light of certain definite wave-lengths.
It is also found that if we pass the light of a luminous solid through a sufficiently large mass of gas, cooler than the body, the spectrum, instead of being entirely continuous, will be crossed with dark lines like that of the sun. This shows that light of certain wave-lengths is absorbed by the gas. A comparison of these dark lines with the bright lines emitted by an incandescent gas led Kirchhoff to the discovery of the following fundamental principle:
Every gas, when cold, absorbs the same rays of light which it emits when incandescent.
An immediate inference from this law is that the dark lines seen in the spectrum of the sun are caused by the passage of the light through gases either existing on the sun or forming the atmosphere of the earth. A second inference is that we can determine what these gases are by comparing the position of the dark lines with that of the bright lines produced by different gases when they are made incandescent. Hence arose the possibility of spectrum analysis, a method which has been applied with such success to the study of the heavenly bodies.
So far as the general constitution of bodies is concerned, the canons of spectrum analysis are these:
Firstly, when a spectrum is formed of distinct bright lines, the light which forms it is emitted by a transparent mass of glowing gas.
Secondly, when a spectrum is entirely continuous the light emanates from an incandescent solid, from a body composed of solid particles, which may be ever so small, or from a mass of incandescent gas so large and dense as not to be transparent through and through.
Thirdly, when the spectrum is continuous, except that it is crossed by fine dark lines, the body emitting the light is surrounded by a gas cooler than itself. The chemical constitution of this gas can be determined by the position of the lines.
Fourthly, if, as is frequently the case, a spectrum is composed of an irregular row of bright and shaded portions, the body is a compound one, partly gaseous and partly solid.
It will be seen from the preceding statement that, in reality, a mass of gas so large as not to be transparent cannot be distinguished from a ​solid. It is therefore not strictly correct to say, as is sometimes done, that an incandescent gas always gives a spectrum of bright lines. It will give such a spectrum only when it is transparent through and through.
A gaseous mass, so large as to be opaque, would, if it were of the same temperature inside and out, give a continuous spectrum, without any dark lines. But the laws of temperature in such a mass show that it will be cooler at the surface than in the interior. This cooler envelope will absorb the rays emanating from the interior as in the case when the latter is solid. We conclude, therefore, that the fact that the great majority of stars show a spectrum like that of the sun, namely, a continuous one crossed by dark lines, does not throw any light on the question whether the matter composing the body of the star is in a solid, liquid or gaseous state. The fact is that the most plausible theories of the constitution of the sun lead to the conclusion that its interior mass is really gaseous. Only the photosphere may be to a greater or less extent solid or liquid. The dark lines that we see in the solar spectrum are produced by the absorption of a comparatively thin and cool layer of gas resting upon the photosphere. Analogy as well as the general similarity of the spectra lead us to believe that the constitution of most of the stars is similar to that of the sun.
CLASSIFICATION OF STELLAB SPECTRA.
When the spectra of thousands of stars were recorded for study, such a variety was found that some system of classification was necessary. The commencement of such a system was made by Secchi in 1863. It was based on the observed relation between the color of a star and the general character of its spectrum.
Arranging the stars in a regular series, from blue in tint through white to red, it was found that the number and character of the spectral lines varied in a corresponding way. The blue stars, like Sirius, Vega and α Aquilæ, though they had the F lines strong, as well as the two violet lines H, had otherwise only extremely fine lines. On the other hand, the red stars, like α Orionis and α Scorpii, show spectra with several broad bands. Secchi was thus led to recognize three types of spectra, as follows:
Fig. 1. Spectrum of Sirius.
Fig. 2. Spectra of α Asuræ and sun.
Fig. 3. Spectra of α Bootis and β Geminorum.
​red, one in the bluish green, and the two others in the violet. All four of these lines belong to hydrogen. Their marked peculiarity is their breadth, which tends to show that the absorbing layer is of considerable thickness or is subjected to a great pressure. Besides these broad rays, fine metallic rays are found in the brighter stars of this type. Secchi considers that this is the most numerous type of all, half the stars which he studied belonging to it.
The second type is that of the somewhat yellow stars, like Capella, Pollux, Arcturus, Procyon, etc. The most striking feature of the spectrum of these stars is its resemblance to that of our sun. Like the latter, it is crossed by very fine and close black rays. It would seem that the more the star inclines toward red, the broader these rays become and the easier it is to distinguish them. We give a figure showing the remarkable agreement between the spectrum of Capella, which may be taken as an example of the type, and that of the sun.
The spectra of the third type, belonging mostly to the red stars, are composed of a double system of nebulous bands and dark lines. The latter are fundamentally the same as in the second type, the broad nebulous bands being an addition to the spectrum, α Herculis may be taken as an example of this type.
It is to be remarked that, in these progressive types, the brilliancy
Fig. 7. Spectrum with both Bright and Dark Lines.
of the more refrangible end of the spectrum continually diminishes relatively to that of the red end. To this is due the gradations of color in the stars.
To these three types Secchi subsequently added a fourth, given by comparatively few stars of a deep red color. The spectra of this class consist principally of three bright bands, which are separated by dark intervals. The brightest is in the green; a very faint one is in the blue; the third is in the yellow and red, and is divided up into a number of others.
Fig. 4. Spectra of α Cygni and α Tauri.
Fig. 5. Spectrum of α Orionis.
Fig. 6. Spectrum of γ Cassiopeæ.
​shall discuss hereafter, is that they are nearly all situated very near the central line of the Milky Way.
Vogel proposed a modification of Secchi's classification, by subdividing each of his three types into two or three others, and including the Wolf-Rayet stars under the second type. His definitions are as follows:
Type I is distinguished by the intensity of the light in the more refrangible end of the spectrum, the blue and violet. The type may be divided into three subdivisions, designated a, b and c:
In Ia the metallic lines are very faint, while the hydrogen lines are distinguished by their breadth and strength.
In Ib the hydrogen lines are wanting.
In Ic the lines of hydrogen and helium both show as bright lines. Stars showing this spectrum are now known as helium stars.
According to Vogel, the spectra of type II are distinguished by having the metallic lines well-marked and the more refrangible end of the spectrum much fainter than in the case of type I. He recognizes two subdivisions:
In IIa the metallic lines are very numerous, especially in the yellow and green. The hydrogen lines are strong, but not so striking as in Ia.
In IIb are found dark lines, bright lines and faint bands. In this subdivision he includes the Wolf-Eayet stars, more generally classified as of the fifth type.
The distinguishing mark of the third type is that, besides dark lines, there are numerous dark bands in all parts of the spectrum, and the more refrangible end of the latter is almost wanting. There are two subdivisions of this type:
In IIIa the broad bands nearest the violet end are sharp, dark and well-defined, while those near the red end are ill-defined and faint. In IIIb the bands near the red end are sharp and well-defined; those toward the violet faint and ill-defined. The character of the bands is therefore the reverse of that in subdivision a.
This classification of Vogel is still generally followed in Germany and elsewhere. It is found, however, that there are star spectra of types intermediate to all these defined. Moreover, in each type the individual differences are so considerable that there is no well-defined limit to the number of classes that may be recognized. At the Harvard Observatory a classification quite different from that of Vogel has been used, but it is too detailed for presentation here. The stars of type II are frequently termed Capellan stars, or Solar stars. Certain stars of type I are termed Orion stars, owing to the number of stars of the type found in that constellation. The stars which show the lines of helium are known as helium stars. We mention these designations because they frequently occur in literature. It would, however, be outside the object of the present work to describe all these classifications in detail. We therefore ​confine ourselves to a few illustrations of spectra of the familiar types described by Secchi and Vogel.
There are many star spectra which cannot be included in any of the classes we have described. Up to the present time these are generally described as stars of peculiar spectra.
As the present chapter is confined to the more general side of the subject, we shall not attempt any description of special spectra. These, especially the peculiar spectra of the nebulae, of new stars, of variable stars, etc., will be referred to, so far as necessary, in the chapters relating to those objects.
The most interesting conclusion drawn from observations with the spectroscope is that the stars are composed, in the main, of elements similar to those found in our sun. As the latter contains most of the elements found on the earth and few or none not found there, we may say that earth and stars seem to be all made out of like matter. It is, however, not yet easy to say that no elements unknown on the earth exist in the heavens. It would scarcely he safe to assume that, because the line of some terrestrial substance is found in the spectrum of a star, it is produced by that substance. It is quite possible that an unknown substance might show a line in appreciably the same position as that of some substance known to us. The evidence becomes conclusive only in the case of those elements of which the spectral lines are so numerous that when they all coincide with lines given by a star, there can be no doubt of the identity.
PROPER MOTIONS OF THE STARS.
We may assume that the stars are all in motion. It is true that only a comparatively small number of stars have been actually seen to be in motion; but as some motion exists in nearly every case where observations would permit of its being determined, we may assume the rule to be universal. Moreover, if a star were at rest at one time it would be set in motion by the attraction of other stars.
Statements of the motion from different points of view illustrate in a striking way the vast distance of the stars and the power of modern telescopic research. If Hipparchus or Ptolemy should rise from their sleep of 2,000 years—nay, if the earliest priests of Babylon should come to life again and view the heavens, they would not perceive any change to have taken place in the relative positions of the stars. The general configurations of the constellations would be exactly that to which they were accustomed. Had they been very exact observers they might notice a slight difference in the position of Arcturus; but as a general rule the unchangeability would have been manifest.
In dealing with the subject, the astronomer commonly expresses the ​motion in angular measurement as so many seconds per year or per century. The keenest eye would not, without telescopic aid, be able to distinguish between two stars whose apparent distance is less than 2' or 120" of arc. The pair of stars known as (ε) Lyræ are 3' apart; yet, to ordinary vision they appear simply as a single star. To appreciate what 1" of arc means we must conceive that the distance between these two stars is divided by 200. Yet this minute space is easily distinguished and accurately measured by the aid of a telescope of ordinary power.
On the other hand, if we measure the motions by terrestrial standards they are swift indeed. Arcturus has been moving ever since the time of Job at the rate of probably more than 200 miles per second—possibly 300 miles. Generally, however, the motion is much smaller, ranging from an imperceptible quantity up to 5, 10 or 20 miles a second. Slow as the angular motion is, our telescopic power is such that the motion in the course of a very few years (with Arcturus the motion in a few days) can be detected. As accurate determinations of positions of the stars have been made only during a century and a half, no motions can be positively determined except those which would become evident to telescopic vision in that period. Only about 3,000 stars have been accurately observed so long as this. In the large majority of cases the interval of observation is so short or the motion so slow that nothing can be asserted respecting the law of the motion.
The great mass of stars seem to move only a few seconds per century, but there are some whose motions are exceptionally rapid. The general rule is that the brighter stars have the largest proper motions. This is what we should expect, because in the general average they are nearer to us, and therefore their motion will subtend the greatest angle to the eye. But this rule is only one of majorities. As a matter of fact, the stars of largest proper motion happen to be low in the scale of magnitude. It happens thus because the number of stars of smaller magnitudes is so much greater than that of the brighter ones that the very small proportion of large proper motions which they offer over-balances those of the brighter stars.
The discovery of the star of greatest known proper motion was made by Kapteyn, of Groningen, in 1897, coöperating with Gill and Innes, of the Cape Observatory. While examining the photographs of the stars made at this institution, Kapteyn was surprised to notice the impression of a star of the eighth magnitude which at first could not be found in any catalogue. But on comparing different star lists and different photographs it soon became evident that the star had been previously seen or photographed, but always in slightly varying positions. An examination of the observed positions at various times showed that the star had a more rapid proper motion than any other yet known. Yet, great ​though this motion is, it would require nearly 150,000 years for the star to. make a complete circuit of the heavens if it moved round the sun uniformly at its present rate.
The fact that the stars move suggests a very natural analogy to the solar system. In the latter a number of planets revolve round the sun as their center, each planet continually describing the same orbit, while the various planets have different velocities. Around several of the planets revolve one or more satellites. Were civilized men ephemeral, observing the planets and satellites only for a few minutes, these bodies would be described as having proper motions of their own, as we find the stars to have. May it not then be that the stars also form a system; that each star is moving in a fixed orbit performing a revolution around some far-distant center in a period which may be hundreds of thousands or hundreds of millions of years? May it not be that there are systems of stars in which each star revolves around a center of its own while all these systems are in revolution around a single center?
This thought has been entertained by more than one contemplative astronomer. Lambert's magnificent conception of system upon system will be described hereafter. Mädler thought that he had obtained evidence of the revolution of the stars around Alcyone, the brightest of the Pleiades, as a center. But, as the proper motions of the stars are more carefully studied and their motion and direction more exactly ascertained, it becomes very clear that when considered on a large scale these conceptions are never realized in the actual universe as a whole. But there are isolated cases of systems of stars which are shown to be in some way connected by their having a common proper motion. We shall mention some of the more notable cases.
The Pleiades are found to move together with such exactness that up to the present time no difference in their proper motions has been detected. This is true not only of the six stars which we readily see with the naked eye, but of a much larger number of fainter ones made known by the telescope. It is an interesting fact, however, that a few stars apparently within the group do not partake of this motion, from which it may be inferred that they do not belong to the system. But there must be some motion among themselves, else the stars would ultimately fall together by their mutual attraction. The amount and nature of this motion cannot, however, be ascertained except by centuries of observation.
Another example of the same sort is seen in five out of the seven stars of Ursæ Major, or The Dipper. The stars are those lettered β, γ, δ, ε and ζ. All five have a proper motion in R. A. of nearly 8" per century, while in declination the movements are sometimes positive and sometimes negative: that is to say, some of the stars are apparently lessening their distance from the pole, while ​others are increasing it. But when we project the motions on a map we find that the actual direction is very nearly the same for all five stars, and the reason why some move slightly to the north and others slightly to the south is due to the divergence of the circles of right ascension. It is worthy of remark that the community of motion is also shown by spectroscopic observations of the radial motions described below.
The five stars in question are all of the second magnitude except δ, which is of the third. It is a curious fact that no fainter stars than these five have been found to belong to the system.
From a study of these motions Höffler has concluded that the five stars lie nearly in the same plane and have an equal motion in one and the same direction. From this hypothesis he has attempted to make a determination of their relative and actual distances. The result reached in this way cannot yet, however, be regarded as conclusive.
There are three stars in Cassiopeia, β, η and μ, each having a large proper motion in so nearly the same direction that it is difficult to avoid at least a suspicion of some relation between them. The angular motions are, however, so far from equal that we cannot regard the relation as established.
In the constellation Taurus, between Aldebaran and the Pleiades, most of the stars which have been accurately determined seem to have a common motion. But these motions are not yet so well ascertained that we can base anything definite upon them. They show a phenomenon which Proctor very aptly designated as star-drift.
The systems we have just described comprise stars situated so far apart that, but for their common motion, we should not have suspected any relation between them. The community of origin which their connection indicates is of great interest and importance, but the question belongs to a later chapter.
MOTIONS IN THE LINE OF SIGHT, OR RADIAL MOTIONS.
No achievement of modern science is more remarkable than the measurement of the velocity with which stars are moving to or from us. This is effected by means of the spectroscope through a comparison of the position of the spectral lines produced by the absorption of any substance in the atmosphere of the star with the corresponding lines produced by the same substance on the earth. The principle on which the method depends may be illustrated by the analogous case of sound. It is a familiar fact that if we stand alongside a railway while a locomotive is passing us at full speed, and at the same time blowing a whistle, the pitch of the note which we hear from the whistle is higher as the engine is approaching than after it passes. The reason is that the pitch of a sound depends upon the number of sound beats per second.
​Now, we may consider the waves which form light when they strike our apparatus as beats in the ethereal medium which follow each other with extraordinary rapidity, millions of millions in a second, moving forward with a definite velocity of more than 186,000 miles a second. Each spectral line produced by a chemical element shows that that element, when incandescent, beats the ether a certain number of times in a second. These beats are transmitted as waves. Since the velocity is the same whether the number of beats per second is less or greater, it follows that, if the body is in motion in the direction in which it emits the light, the beats will be closer together than if it is at rest; if moving away they will be further apart. The fundamental fact on which this result depends is that the velocity of the light-beat through the ether is independent of the motion of the body causing the beat. To show
the result, let A be a luminous body at rest; let the seven dots to the right of A be the crests of seven waves or beats, the first of which, at the end of a certain time, has reached X. The wave-length will then be one seventh the distance A X. Now, suppose A in motion toward X with such speed that, when the first beat has reached X, A has reached the point B. Then the seven beats made by A while the first beat is traveling from A to X, and A traveling from A to B, will be crowded into the space B X, so that each wave will be one seventh shorter than before. In other words, the wave-lengths of the light emitted by any substance will be less or greater than their normal length, according to the motion of the substance in the direction in which its light is transmitted, or in the opposite direction.
The position of a ray in the spectrum depends solely on the wave-length of the light. It follows that the rays produced by any substance will be displaced toward the blue or red end of the spectrum, according as the body emitting or absorbing the rays is moving towards or from us. This method of determining the motions of stars to or from us, or their velocity in the line of sight from us to the star, was first put into practice by Mr.—now Sir William—Huggins, of London. The method has since been perfected by photographing the spectrum of a star, or other heavenly body, side by side with that of a terrestrial substance, rendered incandescent in the tube of a telescope. The rays of this substance pass through the same spectroscope as those from the star, so that, if the wave-lengths of the lines produced by the substance were the same as those found in the star spectrum, the two lines would correspond in position. The minute difference found on the photographic plate is the measure of the velocity of the star in the line of sight.
It will be seen that the conclusion depends on the hypothesis that ​the position of any ray produced by a substance is affected by no cause but the motion of the substance. How and when this hypothesis may fail is a very important question. It is found, for example, that the position of a spectral ray may be altered by compressing the gas emitting or absorbing the ray, and it may be inquired whether the results for motion in the line of sight may not be vitiated by the absorbing atmosphere of the star being under heavy pressure, thus displacing the absorption line.
To this it may be replied that, in any case, the outer layers of the atmosphere, through which the light must last pass, are not under pressure. How far inner portions may produce an absorption spectrum we cannot discuss at present, but it does not seem likely that serious errors are thus introduced in many cases.
These measures require apparatus and manipulation of extraordinary delicacy, in order to avoid every possible source of error. The displacement of the lines produced by motion is in fact so minute that great skill is required to make it evident, unless in exceptional cases. The Mills spectrograph of the Lick Observatory in the hands of Professor Campbell has, notwithstanding these difficulties, yielded results of extraordinary precision. Quite a number of investigators at some leading observatories of Europe and America are pursuing the work of determining these motions. The determinations have almost necessarily been limited to the brighter stars, because, owing to the light of the star being spread over so broad a space in the spectrum, instead of being concentrated on a point, a far longer exposure is necessary to photograph the spectrum of a star than to photograph the star itself. The larger the telescope the fainter the star whose spectrum can be photographed. Vogel, of Potsdam, who has made the most systematic sets of these measures that have yet appeared, included few stars fainter than the second magnitude. With the largest telescopes the spectro of stars down to about the fifth magnitude may be photographed; beyond this it is extremely difficult to go. The limit will probably be reached by the spectrograph of the Yerkes Observatory, which is now being put into operation by Professors Hale and Frost.
THE MOTION OF THE SUN.
When a star is found to be seemingly in motion, as described in the last section, we may ascribe the phenomenon to a motion either of the star itself or of the observer. In fact no motion can be determined or defined except by reference to some body supposed to be at rest. In the case of any one star, we may equally well suppose the star to be at rest and the observer in motion, or the contrary. Or we may suppose both to have such motions that the difference of the two shall represent the ​apparent movement of the star. Hence our actual result in the case of each separate star is a relation between the motion of the star and the motion of the sun.
I say the motion of the sun and not of the earth, because although the observer is actually on the earth, yet the latter never leaves the neighborhood of the sun, and, as a matter of fact, the ultimate result in the long run must be a motion relative to the sun itself as if we made our observations from that body. The question then arises whether there is any criterion for determining how much of the apparent motion of any given star should be attributed to the star itself and how much to a motion of the sun in the opposite direction.
If we should find that the stars, in consequence of their proper motions, all appeared to move in the same direction, we would naturally assume that they were at rest and the sun in motion. A conclusion of this sort was first reached by Herschel, who observed that among the stars having notable proper motions there was a general tendency to move from the direction of the constellation Hercules, which is in the northern hemisphere, towards the opposite constellation Argo, in the southern hemisphere.
Acting on this suggestion, subsequent astronomers have adopted the practice of considering the general average of all the stars, or a position which we may regard as their common center of gravity, to be at rest, and then determining the motion of the sun with respect to this center. Here we encounter the difficulty that we cannot make any absolute determination of the position of any such center. The latter will vary according to what particular stars we are able to include in our estimate. What we can do is to take all the stars which appear to have a proper motion, and determine the general direction of that motion. This gives us a certain point in the heavens toward which the solar system is traveling, and which is now called the solar apex, or the apex of the solar way.
The apparent motion of the stars due to this motion of the solar system is now called their parallactic motion, to distinguish it from the actual motion of the star itself.
The interest which attaches to the determination of the solar apex has led a great number of investigators to attempt it. Owing to the rather indefinite character of the material of investigation, the uncertainty of the proper motions, and the additions constantly made to the number of stars which are available for the purpose in view, different investigators have reached different results. Until quite recently, the general conclusionn was that the solar apex was situated somewhere in the constellation Hercules. But the general trend of recent research has been to place it in or near the adjoining constellation Lyra. This ​change has arisen mainly from including a larger number of stars, whose motions were determined with greater accuracy.
Former investigators based their conclusions entirely on stars having considerable proper motions, these being, in general, the nearer to us. The fact is, however, that it is better to include stars having a small proper motion, because the advantage of their great number more than counterbalances the disadvantage of their distance.
The conclusions reached by some recent investigators of the position of the solar apex will now be given. We call A the right ascension of the apex; D its declination.
Prof. Lewis Boss, from 273 stars of large proper motion found
A = 283°.3; D = 44°.l.
If he excluded the motions of 26 stars which exceeded 40" per century the result was
A = 288°.7; D = 51°.5.
A comparison of these numbers shows how much the result depends on the special stars selected. By leaving out 26 stars the apex is changed by 5° in R. A., and 7° in declination.
It is to be remarked that the stars used by Boss are all contained in a belt four degrees wide, extending from 1° to 5° north of the equator.
Dr. Oscar Stumpe, of Berlin, made a list of 996 stars having proper motions between 16" and 128" per century. He divided them into three groups, the first including those between 16" and 32"; the second between 32" and 64"; the third between 64" and 128". The number of stars in each group and the position of the apex derived from them are as follows:
Gr. I, 551 stars; A = 287°.4; D = x45°.0 II, 339 282°.2 43°.5 III, 106 280°.2 33°.5
Porter, of Cincinnati, made a determination from a yet larger list of stars with results of the same general character.
These determinations have the advantage that the stars are scattered over the entire heavens, the southern as well as the northern ones. The difference of more than 10° between the position derived from stars with the largest proper motions, and from the other stars, is remarkable.
The present writer, in a determination of the precessional motion, incidentally determined the solar motion from 2,527 stars contained in Bradley's Catalogue which had small proper motions, and from about 600 more having larger proper motions. Of the latter the declinations only were used. The results were:
From small motions: A = 274°.2; D = x31°.2 From large motions: 276°.9 31°.4
​From all these results it would seem that the most likely apex of the solar motion is toward the point in
Right Ascension, 280° Declination, 38° north.
This point is situated in the constellation Lyra, about 2° from the first magnitude star Vega. The uncertainty of the result is more than this difference, four or five degrees at least. We may therefore state the conclusion in this form:
The apex of the solar motion is in the general direction of the constellation Lyra, and probably very near the star Vega, the brightest of that constellation.
It must be admitted that the wide difference between the position of the apex from large and from small proper motions, as found by Porter, Boss and Stumpe, require explanation. Since the apparent motions of the stars are less the greater their distance, these results, if accepted as real, would lead to the conclusion that the position of the solar apex derived from stars near to us was much further south than when derived from more distant stars. This again would indicate that our sun is one of a cluster or group of stars, having, in the general average, a different proper motion from the more distant stars. But this conclusion is not to be accepted as real until the subject has been more exhaustively investigated. The result may depend on the selection of the stars; and there is, as yet, no general agreement among investigators as to the best way of making the determination.
The next question which arises is that of the velocity of the solar motion. The data for this determination are more meagre and doubtful than those for the direction of the motion. The most obvious and direct method is to determine the parallactic motion of the stars of known parallax. Regarding any star 90° from the apex of the solar motion as in a state of absolute rest, we have the obvious rule that the quotient of its parallactic motion during any period, say a century, divided by its parallax, gives the solar motion during that period, in units of the earth's distance from the sun. In fact, by a motion of the sun through one such unit, the star would have an apparent motion in the opposite direction equal to its annual parallax. If the star were not 90° from the apex we can easily reduce its observed parallactic motion by dividing it by the sign of its actual distance from the apex.
Since every star has, presumably, a proper motion of its own, we can draw no conclusion from the apparent motion of any one star, owing to the impossibility of distinguishing its actual from its parallactic motion. We should, therefore, base our conclusion on the mean result from a great number of stars, whose average position or center of mass we might assume to be at rest. Here we meet the difficulty that there are ​only about 60 stars whose parallaxes can be said to be determined; and one-half of these are too near the apex, or have too small a parallax, to permit of any conclusion being drawn from them.
A second method is based on the spectroscopic measures of the motion of stars in the line of sight, or the line from the earth to the star. A star at rest in the direction of the solar apex would be apparently moving toward us with a velocity equal to that of the solar motion. Assuming the center of mass of all the stars observed to be at rest, we should get the solar motion from the mean of all.
Thus far, however, there are only about 50 stars whose motions in the line of sight have been used for the determination, so that the data are yet more meagre than in the case of the proper motions. From them, however, using a statistical method Kapteyn has derived results which seem to show that the actual velocity of the solar system through space is about 16 kilometres, or 10 statute miles, per second.