Part 9

The advocates of bounties and of special legislation also ignore the fact that in this country, where mental energy is more nearly free in its action than in any other, manufactures and the mechanic arts develop in due proportion according to the age and the natural resources of the territory or state, nine-tenths or more of the occupations which are listed under these titles being free in the nature of things from any possibility of foreign competition through the import of a product of like kind.

There may be nothing new in this essay, but until my own observation had led me to the conclusion that land, labor and capital were alike inert and incapable without the cöordinating power of mental energy, the doubt continued to exist in my mind which is often expressed about the possibility of economic science having any real existence or right to the title. Also, until my own observation led me to the conclusion that the cost of a man to the community is what he consumes, and not what he secures in the way of income, the correlation of wealth and welfare had not been satisfactorily reconciled. I think that a very large part of what is written under the title of political economy would be greatly modified, and perhaps never have been written, had these concepts been derived by the writers from experience, as they have been in my own observation.

I have not much patience with abstract or _à priori_ theories, my own method being one of observation, then referring to the various authorities in order to find out whether my observations or their abstract theories have been shallow and superficial.

Again, I find in the ideal of the continuous miracle of creation in which man is a factor the solution of many intellectual difficulties. In the face of such a perception of the methods of the universe, the larger part of the dogmas that have been put forth under the name of religion take their place with much of the historic rubbish which passes under the name of history. When it becomes plain that every man has his place in the progress of continuous creation, and is a factor in it; that nothing is constant but change; that there is no such thing as fixed capital; all the doubts and fears regarding the future of humanity vanish in the light of sure progress.

What greater stimulus can there be than for every man each in his own way rendering service for service, his objective point being only the welfare of himself and his family, when he attains the conviction that by so much as his mental energy adds to the sum of the utilities by which mankind lives, so may that part which he consumes and which represents his cost to the community be fully justified, even though it is earned with more apparent ease and less physical exertion than are called for from his poorer neighbors.

Incomplete as his studies were, I have always found in the ‘Harmonies’ of Frederic Bastiat the greatest encouragement and the greatest incentive to the work which I have undertaken under the name of political economy, leading more and more to the conviction that war and warfare, whatever influence they may have had in developing progress in the past, are now due to ignorance and greed; the war of tariffs due to selfishness and stupidity; and the contest of labor and capital due to the errors of the ignorant workman and the ignorant capitalist alike. All interests are harmonious. The evolution of science and invention will surely bring them together on the lines of righteousness, peace and material abundance.

This essay has been condensed from a lecture prepared and given before a Clergymen’s Club some months ago. In it I tried to show the necessary connection of religion and life as developed by economic study, the law of mutual service being the rule by which commerce lives and moves and has its being. This lecture has since been read to several clubs of very different types of men, and from the great interest excited I am led to think there is something in it fit for the student of facts and figures to say.

I may, therefore, venture to repeat the statement of two principles which are presented in this treatise, which I think have been seldom if ever fully developed in any of the standard works upon political economy. To my own mind these are basic principles which when applied may profoundly modify many of the concepts of students of economic science. I join in the view that the family is the unit of society, the home the center. The end of all production is consumption. Nothing is constant but change, and there is no such thing as fixed material capital of any long duration in the progress of time. The two principles which I have endeavored to enforce are as follows:

First. The cost of each person or head of the family is what he and his immediate dependents consume. His income, whether measured in terms of money or in products, is, therefore, no measure of his cost; what he distributes in payment for service rendered being expended by those who receive it in procuring the commodities which constitute their cost to the community.

Second. No person who is occupied or is in the employment or service of others is paid for what he does. His work may occupy long hours and may be applied to arduous manual labor, or it may be done in a short number of hours per day, with but little physical effort. Neither the hours nor the effort constitute any measure on which payment can be based. The measure of payment is fixed by the measure of the work saved to him who makes the payment, consciously or unconsciously estimated.

These two precepts or principles, coupled with the theory that there is no conceivable limit to the power of mind over matter, or to the number of transformations of physical energy to which direction may be given in the material support of humanity, bring the visions of the Utopians within the scope of a law of progress in material welfare to which no limit can be put in time or space.

CHAPTERS ON THE STARS.

BY PROF. SIMON NEWCOMB, U. S. N.

VARIABLE STARS.

It is a curious fact that the ancient astronomers, notwithstanding the care with which they observed the heavens, never noticed that any of the stars changed in brightness. The earliest record of such an observation dates from 1596, when the periodical disappearance of Omicron Ceti was noticed. After this, nearly two centuries elapsed before another case of variability in a star was recorded. During the first half of the nineteenth century Argelander so systematized the study of variable stars as to make it a new branch of astronomy. In recent years it has become of capital interest and importance through the application of the spectroscope.

Students who are interested in the subject will find the most complete information attainable in the catalogues of variable stars, published from time to time by Chandler in the ‘Astronomical Journal.’ His third catalogue, which appeared in 1896, comprises more than 300 stars whose variability has been well established, while there is always a long list of ‘suspected variables’--whose cases are still to be tried. The number to be included in the established list is continually increasing at such a rate that it is impossible to state it with any approximation to exactness. The possibility of such a statement has been yet further curtailed by the recent discovery at the Harvard Observatory that certain clusters of stars contain an extraordinary proportion of variables. Altogether at the time of the latest publication, 509 such stars were found in twenty-three clusters. The total number of these objects in clusters, therefore, exceeds the number known in the rest of the sky. They will be described more fully in a subsequent chapter. For the present we are obliged to leave this rich field out of consideration and confine our study to the isolated variable stars which are found in every region of the heavens.

Variable stars are of several classes, which, however, run into each other by gradations so slight that a sharp separation cannot always be made between them. Yet there are distinguishing features, each of which marks so considerable a number of these stars as to show some radical difference in the causes on which the variations depend.

We have first to distinguish the two great classes of irregular and periodic stars. The irregular ones increase and diminish in so fitful a way that no law of their change can be laid down. To this class belong the so-called ‘new stars’, which, at various periods in history, have blazed out in the heavens, and then in a few weeks or months have again faded away. It is a remarkable fact that no star of the latter class has ever been known to blaze out more than once. This fact distinguishes new stars from other irregularly variable ones.

Periodic stars are those which go through a regular cycle of changes in a definite interval of time, so that, after a certain number of days, sometimes of hours, the star returns to the same brightness. But even in the case of periodic stars, it is found that the period is more or less variable, and, in special cases, the amount of the variation is such that it cannot always be said whether we should call a star periodic or irregular.

The periodic stars show wide differences, both in the length of the period and in the character of the changes they undergo. In most cases they rapidly increase in brightness during a few days or weeks, and then slowly fade away, to go through the same changes again at the end of the period. In other cases they blaze up or fade out, from time to time, like the revolving light of a lighthouse. Some stars are distinguished more especially by their maximum, or period of greatest brightness, while others are more sharply marked by minima, or periods of least brightness. In some cases there are two unequal minima in the course of a period.

Chandler’s third catalogue of variable stars gives the periods of 280 of these objects, which seem to have been fairly well made out. A classification of these periods, as to their length, will be interesting. There are, of periods:

Less than 50 days 63 Stars. Between 50 and 100 days 6 ” ” 100 ” 150 ” 9 ” ” 150 ” 200 ” 18 ” ” 200 ” 250 ” 29 ” ” 250 ” 300 ” 40 ” ” 300 ” 350 ” 44 ” ” 350 ” 400 ” 44 ” ” 400 ” 450 ” 18 ” ” 450 ” 500 ” 6 ” ” 500 ” 550 ” 1 ” ” 550 ” 600 ” 1 ” ” 600 ” 650 ” 1 ”

It will be seen from this that, leaving out the cases of very short period, the greater number of the periods fall between 300 and 400 days. From this value the number falls off in both directions. Only three periods exceed 500 days, and of these the longest is 610 days. We infer from this that there is something in the constitution of these stars, or in the causes on which their variation depends, which limits the period. This limitation establishes a well-marked distinction between the periodic stars and the irregular variables to be hereafter described.

Returning to the upper end of the scale, the contrast between the great number of stars less than fifty days, and the small number between fifty and one hundred, seems to show that we have here a sharp line of distinction between stars of long and those of short period. But, when we examine the matter in detail, the statistics of the periods do not enable us to draw any such line. About eight periods are less than one day, and the number of this class known to us is continually increasing. About forty are between one and ten days, and from this point upwards they are scattered with a fair approach to equality up to a period of one hundred days. There is, however, a possible distinction, which we shall develop presently.

The law of change in a variable star is represented to the eye by a curve in the following way. We draw a straight horizontal line _A X_ to represent the time. A series of equidistant points, _a_, _b_, _c_, _d_, etc., on this will represent moments of time. One of the spaces, _a_, _b_, _c_, etc., may represent an hour, a day, or a month, according to the rapidity of change. We take _a_ to represent the initial moment, and erect an ordinate _aa’_, of such length as to represent the brightness of the star on some convenient scale at this moment. At the second moment, _b_, which may be an hour or a day later, we erect another ordinate _bb’_, representing the brightness at this moment. We continue this process as long as may be required. Then we draw a curve, represented by the dotted line, through the ends of all the ordinates. In the case of a periodic star it is only necessary to draw the curve through a single period, since its continuation will be a repetition of its form for any one period.

We readily see that if a star does not vary, all the ordinates will be of equal length, and the curve will be a horizontal straight line. Moreover, the curve will take this form through any portion of time during which the light of the star is constant.

There are three of the periodic stars plainly visible to the naked eye at maximum, of which the variations are so wide that they may easily be noticed by any one who looks for them at the right times, and knows how to find the stars. These stars are:

Omicron Ceti, called also _Mira Ceti_. Beta Persei, or Algol. Beta Lyræ.

It happens that each of these stars exemplifies a certain type or law of variations.

_Omicron Ceti._ On August 13, 1596, David Fabricius noticed a star in the constellation Cetus, which was not found in any catalogue. Bayer, in his ‘Uranometria’, of which the first edition was published in 1601, marked the star Omicron, but said nothing about the fact that it was visible only at certain times. Fabricius observed the star from time to time, until 1609, but he does not appear to have fully and accurately recognized its periodicity. But so extraordinary an object could not fail to command the attention of astronomers, and the fact was soon established that the star appeared at intervals of about eleven months, gradually fading out of sight after a few weeks of visibility. Observations of more or less accuracy having been made for more than two centuries, the following facts respecting it have been brought to light:

Its variations are somewhat irregular. Sometimes, when at its brightest, it rises nearly or quite to the second magnitude. This was the case in October, 1898, when it was about as bright as Alpha Ceti. At other times its maximum brightness scarcely exceeds the fifth magnitude. No law has yet been discovered by which it can be predicted whether it shall attain one degree of brightness or another at maximum.

Its minima are also variable. Sometimes it sinks only to the eighth magnitude; at other times to the ninth or lower. In either case it is invisible to the naked eye.

As with other stars of this kind, it brightens up more rapidly than it fades away. It takes a few weeks from the time it becomes visible to reach its greatest brightness, whatever that may be. It generally retains this brightness for two or three weeks, then fades away, gradually at first, afterward more rapidly. The whole time of visibility will, therefore, be two or three months. Of course, it can be seen with a telescope at any time.

The period also is variable in a somewhat irregular way. If we calculate when the star ought to be at its greatest brightness on the supposition that the intervals between the maxima ought to be equal, we shall find that sometimes the maximum will be thirty or forty days early, and at other times thirty or forty days late. These early or late maxima follow each other year after year, with a certain amount of regularity as regards the progression, though no definable law can be laid down to govern them. Thus, during the period from 1782 to 1800 it was from thirteen to twenty-four days late. In 1812 it was thirty-nine days late. From 1845 to 1856 it was on the average about a month too early. Several recent maxima, notably those from 1895 to 1898, again occurred late. Formulæ have been constructed to show these changes, but there is no certainty that they express the actual law of the case. Indeed, the probability seems to be that there is no invariable law that we can discover to govern it.

Argelander fixed the length of the period at 331.9 days. More recently, Chandler fixed it at 331.6 days. It would seem, therefore, to have been somewhat shorter in recent times. It was at its maximum toward the end of October, 1898. We may, therefore, expect that future maxima will occur in July, 1901; June, 1902; May, 1903; April, 1904, and so on, about a month earlier each year. During the few years following 1903 the maxima will probably not be visible, owing to the star being near conjunction with the sun at the times of their occurrence. The most plausible view seems to be that changes of a periodic character, involving the eruption of heated matter from the interior, of the body to its surface, followed by the cooling of this matter by radiation, are going on in the star.

The star _Algol_, or _Beta Persei_, as it is commonly called in astronomical language, may, in northern latitudes, be seen on almost any night of the year. In the early summer we should probably see it only after midnight, in the northeast. In late winter it would be seen in the northwest. From August until January one can find it at some time in the evening by becoming acquainted with the constellations. It is nearly of the second magnitude. One might look at it a score of times without seeing that it varied in brilliancy. But at certain stated intervals, somewhat less than three days, it fades away to nearly the fourth magnitude for a few hours, and then slowly recovers its light. This fact was first discovered by Goodrick in 1783, since which time the variations have been carefully followed. The law of variation thus defined is expressed by a curve of the following form:

The idea that what we see in the star is a partial eclipse caused by a dark body revolving round it, was naturally suggested even to the earliest observers. But it was impossible to test this theory until recent times. Careful observation showed changes in the period between the eclipses, which, although not conclusive against the theory, might have seemed to make it somewhat unlikely. The application of the spectroscope to the determination of radial motions, enabled Vogel, of Potsdam, in 1889, to set the question at rest. His method of reasoning and proceeding was this:

If the fading out which we see is really due to an eclipse by a dark body, that body must be nearly or quite as large as the star itself, else it could not cut off so much of its light. In this case, it is probably nearly as massive as the star itself, and therefore would affect the motion of the star. Both bodies would, in fact, revolve around their common center of gravity. Therefore, when after the dark body has passed in front of the star, it has made one-fourth of a revolution, which would require about seventeen hours, the star would be moving towards us. Again, seventeen hours before the eclipse, it ought to be moving away from us.

The measurement of six photographs of the spectrum, of which four were taken before the eclipses and two afterward, gives the following results:

Before eclipses: Velocity _from_ the sun equals 39 km. per second.

After eclipses: Velocity _toward_ the sun equals 47 km. per second.

These results show that the hypothesis in question is a true one, and afforded the first conclusive evidence of a dark body revolving around a distant star. A study of the law of diminution and recovery of the light during the eclipse, combined with the preceding motions, enabled Vogel to make an approximate estimate of the size of the orbit and of the two bodies. The star itself is somewhat more than a million of miles in diameter; the dark companion a little less. The latter is about the size of our sun. Their distance apart is somewhat more than three millions of miles; the respective masses are about one-half and one-fourth that of the sun. These results, though numerically rather uncertain, are probably near enough to the truth to show us what an interesting system we here have to deal with. We can say with entire certainty that the size and mass of the dark body exceed those of any planet of our system, even Jupiter, several hundred fold.

The period of the star is also subject to variations of a somewhat singular character. These have been attributed by Chandler to a motion of the whole system around a third body, itself invisible. This theory is, however, still to be proved. Quite likely the planet which causes the eclipse is not the only one which revolves around this star. The latter may be the center of a system like our solar system, and the other planets may, by their action, cause changes in the motion of the body that produces the eclipses. The most singular feature of the change is that it seems to have taken place quite rapidly, about 1840. The motion was nearly uniform up to near this date; then it changed, and again remained nearly uniform until 1890. Since then no available observations have been published.

It is found that several other stars vary in the same way as Algol; that is to say, they are invariable in brightness during the greater part of the time, but fade away for a few days at regular intervals. This is a kind of variation which it is most difficult to discover, because it will be overlooked unless the observer happens to notice the star during the time when an eclipse is in progress, and is thoroughly aware of its previous brightness. One might observe a star of this kind very accurately a score of times, without hitting upon a moment when the partial eclipse was in progress. On the principle that like effects are due to like causes, we are justified in concluding that in the cases of all stars of this type, the eclipses are caused by the revolution of a dark body, now called ‘Algol variables,’ round the principal star.

A feature of all the Algol variables is the shortness of the periods. The longest period is less than five days, while three are less than one day. This is a result that we might expect from the nature of the case. The nearer a dark planet is to the star, the more likely it will be to hide its light from an observer at a great distance. If, for example, the planet Jupiter were nearly as large as the sun, the chances would be hundreds to one against the plane of the orbit being so nearly in the line of a distant observer that the latter would ever see an eclipse of the sun by the planet. But if the planet were close to the sun, the chances might increase to one in ten, and yet farther to almost any extent, according to the nearness of the two bodies.

Still, we cannot set any definite limit to the period of stars of this type; all we can say is that, as the period we seek for increases, the number of stars varying in that period must diminish. This follows not only from the reason just given, but from the fact that the longer the interval that separates the partial eclipses of a star of the Algol type, the less likely they are to be detected.

STARS OF THE BETA LYRÆ TYPE.

The star Beta Lyræ shows variations quite different in their nature from those of Algol, yet having a certain analogy to them. Anyone who looks at the constellation Lyræ a few nights in succession and compares Beta with Gamma, a star of nearly the same brightness in its neighborhood, will see that while on some evenings the stars are of equal brightness, on others Beta will be fainter by perhaps an entire magnitude.