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Rh eighteenth century it was, as proved by the sciences of organic life, the central point of theistic and idealistic philosophy.

The Darwinian principle of natural selection cut straight under this philosophy. If all organic adaptations are due simply to constant variation and the elimination of those variations that are harmful in the struggle for existence which is brought about by excessive reproduction, there is no call for a prior intelligent causal force to plan and preordain them. Hostile critics charged Darwin with materialism and with making chance the cause of the universe.

Some naturalists, like Asa Gray, favored the Darwinian principle and attempted to reconcile it with design. Gray held to what may be called design on the instalment plan. If we conceive the "stream of variations" to be itself intended, we may suppose that each successive variation was designed from the first to be selected. In that case, variation, struggle and selection simply define the mechanism of "secondary causes" through which the "first cause" acts; and the doctrine of design is none the worse off because we know more of its modus operandi.

Darwin could not accept this mediating proposal. He admits or rather he asserts that it is "impossible to conceive this immense and wonderful universe including man with his capacity of looking far backwards and far into futurity as the result of blind chance or necessity." But nevertheless he holds that since variations are in useless as well as useful directions, and since the latter are sifted out simply by the stress of the conditions of struggle for existence, the design argument as applied to living beings is unjustifiable; and its lack of support there deprives it of scientific value as applied to nature in general. If the variations of the pigeon, which under artificial selection give the pouter pigeon, are not preordained for the sake of the breeder, by what logic do we argue that variations resulting in natural species are pre-designed?

So much for some of the more obvious facts of the discussion of design versus chance as causal principles of nature and of life as a whole. We brought up this discussion, you recall, as a crucial instance. What does our touchstone indicate as to the bearing of Darwinian ideas upon philosophy? In the first place, the new logic outlaws, flanks, dismisses—what you will—one type of problems and substitutes for it another type. Philosophy forswears inquiry after absolute origins and absolute finalities in order to explore specific values and the specific conditions that generate them.


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96 Darwin concluded that the impossibility of assigning the world to chance as a whole and to design in its parts indicated the insolubility of the question. Two radically different reasons, however, may be given as to why a problem is insoluble. One reason is that the problem is too high for intelligence; the other is that the question in its very asking makes assumptions that render the question meaningless. The latter alternative is unerringly pointed to in the celebrated case of design versus chance. Once admit that the sole verifiable or fruitful object of knowledge is the particular set of changes that generate the object of study, together with the consequences that further flow from it, and no intelligible question can be asked about what, by assumption, lies outside. To assert—as is often asserted—that specific values of particular truths, social bonds and forms of beauty, if they can be shown to be generated by concretely knowable conditions, are meaningless and in vain; to assert that they are justified only when they and their particular causes and effects have all at once been gathered up into some inclusive first cause and some exhaustive final goal, is intellectual atavism. Such argumentation is reversion to the logic that explained the extinction of fire by water through the formal essence of aqueousness and the quenching of thirst by water through the final cause of aqueousness. Whether used in the case of the special event or in that of life as a whole, such logic only abstracts some aspect of the existing course of events in order to reduplicate it as a petrified eternal principle by which to explain the very changes of which it is the formalization.

When Henry Sidgwick casually remarked in a letter that as he grew older his interest in what or who made the world was altered into interest in what kind of a world it is anyway, his voicing of a common experience of our own day illustrates also the nature of that intellectual transformation effected by the Darwinian logic. Interest shifts from the wholesale essence back of special changes to the question of how these special changes serve and defeat concrete purposes; shifts from an intelligence that shaped things once for all to the particular intelligences which things are even now shaping; shifts from an ultimate goal of good to the direct increments of justice and happiness that intelligent administration of existent conditions may beget and that present carelessness or stupidity will destroy or forego.

In the second place, the classic type of logic inevitably set philosoophyphilosophy [sic] upon proving that life must really have certain qualities and values—no matter how experience presents the matter—because of some remote cause and eventual goal, while the logic of the new science frees philosophy from this apologetic habit and temper. The duty of wholesale justification inevitably accompanies all thinking that makes the meaning of special occurrences depend upon something that

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Rh Untang-anting, to swing, to wave to and fro. To return home the same day on which we go away.

Untung, fortune, good luck, also bad luck, chance, lot. Gain, profit, advantage. Untung nakěr, very profitable. Untung na ěun sakitu, his luck was only such, meaning that he was not very successful. Untung chapé, his gain was getting tired, as we should say, he got his trouble for his pains. Kumaha untung na bai, as chance may turn up.

Untung Jawa, name of the promontory made by the embouchures of the Chidani river, and opposite to the island of Onrust. It means the luck, the prosperity of Java.

Unun, to smoke, to kilndry. To put up over a fire-place so as to dry thoroughly and render durable.

Upah, hire, reward, recompense. Payment made in money or goods for any work done. To induce to do anything by a payment. Paid for. Upah nyusuk, to pay for making a canal, or water-course. Upah ngunjalan, to pay for taking away. Upah nyumpah, to pay for getting an oath.

Upahan, to recompense, to reward, to defray. Wages, payment.

Upama, for example, suppose, as if, quasi, like, resembling. Upama, C. 80, derived from Upa, like, Mā, to measure, likeness, resemblance, as a picture, an image, etc. Also a parable, a simile. Upama na kula datang isuk-isuk, měunang tah pulan rada běurang, suppose that I come very early in the morning, shall I be allowed to go away again rather early.

Upas, venom, poison. Any noxious juice either vegetable or animal. Upas orai, the poisonous spittle of a snake. The secretory matter which is contained in its poison-bag. Sirěum nu aya upasan, an ant which emits a virulent saliva. Sirěum upas, a variety of ant of the size of Tataman; it lives on trees, is black, and gives a very painful bite. Urut di gégél orai, upas na matih nakěr, having been bit by a snake, its secretory matter is very virulent.

Upěti, revenue, tribute, contribution.

Upih, the spatha which envelops the spadix of the unexpanded pinang-fruit. This, when carefully cut off and separated from the spadix, forms a broad, thin, leathery wrapper, which is much used for carrying about cooked rice, as when a man goes to a day's work, or on a journey. The green outer pellicle is stripped off, and then it is white on both sides. Běbĕd upih, an upih well filled with provisions for a journey. Buka upih, name of a swamp-bird, which is dark coloured whilst on the ground, but on rising in the air shows white like the upih, under the wings.

Ur, the idiomatic expression for rushing into the presence, of coming in a hurry upon any one, of a flock of birds or a herd of cattle starting off on their course. Ur bai mata-poi bijil, and the sun rushing on came out. Ur bai manuk hiběr sa loba-loba, the birds started on their flight in great numbers.

Urab, to mix eatables, as Bonteng or Iwung, etc. with the pulp of cocoa-nuts. See Orég.


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Rh lies once and for all behind them. The habit of derogating from present meanings and uses prevents our looking the facts of experience in the face; it prevents serious acknowledgment of the evils they present and serious concern with the goods they promise but do not yet fulfil. It turns thought to the business of finding a wholesale transcendent remedy for the one and guarantee for the other. One is reminded of the way many moralists and theologians greeted Herbert Spencer's recognition of an unknowable energy from which welled up the phenomenal physical processes without and the conscious operations without. Merely because Spencer labeled his unknowable energy "God," this faded piece of metaphysical goods was greeted as an important and grateful concession to the reality of the spiritual realm. Were it not for the deep hold of the habit of seeking justification for ideal values in the remote and transcendent, surely this reference of them to an unknowable absolute would be despised in behalf of the daily demonstrations of experience that knowable energies are daily generating about us precious values.

The displacing of this wholesale type of philosophy will doubtless not arrive by sheer logical disproof, but rather by growing recognition of its futility. Were it a thousand times true that opium produces sleep because of its dormitive energy, the inducing of sleep in the tired and the recovery to waking life of the poisoned, would not be thereby one least step forwarded. And were it a thousand times dialectically demonstrated that life as a whole is regulated by a transcendent principle to a final inclusive goal, truth and error, health and disease, good and evil, hope and fear in the concrete would remain none the less just what and where they now are. To improve our education, to ameliorate our manners, to advance our politics, we must have recourse to specific conditions of generation.

Finally, the new logic introduces responsibility into the intellectual life. To idealize and rationalize the universe at large is after all a confession of inability to master the courses of things that specifically concern us. As long as mankind suffered from this impotency, naturally it shifted a burden of responsibility which it could not carry over to the more competent shoulders of the transcendent cause. But if insight into specific conditions of value and into specific consequences of ideas is possible, philosophy must in time become a method of locating and interpreting the more serious of the conflicts that occur in life, and a method of projecting ways for dealing with them: a method of moral and political diagnosis and prognosis.

The claim to formulate a priori the legislative constitution of the universe is by its nature a claim that may lead into elaborate dialectic developments. But it is also one which removes these very conclusions from subjection to experimental test, for, by definition, these results


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98 make no differences in the detailed course of events. But a philosophy that humbles its pretensions to the work of projecting hypotheses for the education and conduct of mind, individual and social, is thereby subjected to test by the way in which the ideas it propounds work out in practise. In having modesty forced upon it, philosophy also acquires responsibility.

Doubtless I may seem to have violated the implied promise of my earlier remarks and to have turned both prophet and partisan. But in anticipating the direction of the transformations in philosophy to be wrought by the Darwinian genetic and experimental logic, I do not profess to speak for any changes save those wrought in those who yield themselves consciously or unconsciously to this logic. No one can fairly deny that at present there are evident two effects of the Darwinian mode of thinking. On the one hand, there are making many sincere and vital efforts to revise our traditional philosophic conceptions in accordance with its demands. On the other hand, there is as definitely a recrudescence of absolutistic philosophies; an assertion of a type of philosophic knowing distinct from that of the sciences, which opens to us another kind of reality from that to which the sciences give access; an appeal through experience to something that radically transcends experiences. This reaction affects popular creeds and religious movements as well as technical philosophies. In other words, the very conquest of the biological sciences by the new ideas has led many to effect a more explicit and rigid separation of philosophy from science.

Old ideas give way slowly; for they are more than abstract logical forms and categories. They are habits, predispositions, deeply engrained attitudes of aversion and preference. Moreover, the conviction persists—though history shows it to be a hallucination—that all the questions that the human mind has asked are questions that can be answered in terms of the alternatives that the questions themselves present. But in fact intellectual progress usually occurs through sheer abandonment of such questions, together with both of the alternatives they assume—an abandonment that results from decreasing vitality and interest in their point of view. We do not solve them: we get over them. Old questions are solved by disappearing, evaporating, while new questions corresponding to the changed attitude of endeavor and preference take their place. Doubtless the greatest dissolvent of old questions, the greatest precipitant of new methods, new intentions, new problems, is the one effected by the scientific revolution completed in the "Origin of Species."


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Rh

this commencement season university presidents and others are likely to make addresses to academic audiences and the problems of the college and of the college student are likely to be subjects for comment in the daily papers and the monthly magazines. This year two addresses have attracted special attention. Some rather incidental remarks of President Wilson, of Princeton University, are of intrinsic interest, and the Phi Beta Kappa address of President Lowell, of Harvard University, preceding his inaugural address, gives the first indication of his attitude toward questions concerning which his influence and responsibility are very great.

It is somewhat curious that the president of Princeton appears to be more modern in his point of view than the president of Harvard. President Wilson is reported as saying:

A danger surrounding our modern education is the danger of wealth. I am sorry for the lad who is going to inherit money. I fear that the kind of men who are to share in shaping the future are not largely exemplified in schools and colleges.

So far as the colleges go, the sideshows have swallowed up the circus, and we in the main tent do not know what is going on. And I do not know that I want to continue under those conditions as ringmaster. There are. more honest occupations than teaching if you can not teach.

This is characteristically well put, but the point of view is unexpected. It was supposed that the officers of Princeton were comparatively well satisfied with their rich boys, their professional athletics and their preceptorial system. It seems that on this occasion the president of Princeton is too iconoclastic and too pessimistic. The rich boys and the college boys will surely do more than the average in "shaping the future," even though this may be accomplished by a kind of monopoly control. The boy need not cease to be an athlete when he leaves the preparatory school; the trouble in our colleges is not that there are too many athletes, but too few, and those few over-trained and over-exploited. The college boy can do athletic stunts better than any one else can and better than he can do anything else; so there is much to be said for letting him do them. Satan can find worse mischief for idle hands.

When Mr. Wilson says that the things which the modern world exacts are mostly intellectual, he presumably I refers to the kinds of things the Princeton preceptors try to teach. But what the world wants is men who will do the right thing at the right time. The boy i who is to be a scholar in after life i should be a scholar in college. But the average boy gains more from running the college paper or fraternity house than by writing Latin verses or even reading the innocuous literature prescribed by the College Entrance Examination Board. Certainly both college students and college teachers could be more usefully employed than they are at present; but it is odd that the president of Princeton should rub this in.

Mr. Lowell had undertaken to give the Phi Beta Kappa at Columbia before he was elected to the presidency of


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104 he did not attend a university. He became interested in science through the local scientific society and museum at Halifax, and received his training through them and through his own work. He accomplished scientific work of accuracy and importance, but was an amateur in the sense that he held no scientific position. Darwin is the most notable instance of the great contributions to science made in Great Britain by those having hereditary wealth and devoting their lives to scientific work, but he is only one of a large class, including men of great eminence, such as the two last presidents of the Royal Society, Lord Rayleigh and Sir William Huggins, and many others, such as Sladen, whose work may not be widely known, but is of a high class. It is to be hoped, though scarcely to be expected, that these traditions will be maintained in Great Britain and adopted here, as the number of our wealthy families increases.

Sladen concerned himself in the main with scientific work on the starfishes. In the course of twenty years he published thirty-five papers, the most extensive being the report on the Asteroidea collected by the Challenger which describes 184 new species. In an early paper he described an extraordinary form from a single specimen since lost which he placed in a new family intermediate between the Ophiurids and the Asterids. Another discovery of evolutionary interest was of certain "cribriform" organs in a family of starfishes. The function of these organs is not known; they appear in one family only with no indication as to how they may have been evolved, their number is fixed for each species, though it varies greatly within the family.

Though Sladen's scientific work was narrowly limited, he was a man of public spirit and wide accomplishments. He knew Persian as well as European literatures and was an expert collector and student of old books and manuscripts. He was zoological secretary of the Linnean Society and secretary of several committees of the British Association. His biographer says of him: "Cheerful, humorous and of a remarkably even temper, Sladen presented to his many friends a singularly lovable nature, in which unselfishness, sincerity and a generous appreciation of the work of others were some of the leading characteristics."

record with regret the deaths of Dr. Georg von Neumayer, the eminent German meteorologist; of Dr. Wilhelm Engelmann, professor of physiology at Berlin, and of Dr. F. G. Yeo, F.R.S., the physiologist.

those who will have received an honorary degree from Cambridge University on the occasion of the Darwin centenary are three Americans: Professor Jacques Loeb, of the University of California; Dr. Charles D. Walcott, secretary of the Smithsonian Institution, and Professor E. B. Wilson, of Columbia University.

president of the Johns Hopkins University, has been elected president of the Society for Chemical Industry.—Dr. E. F. Nichols, professor of experimental physics at Columbia University, has been elected president of Dartmouth College.—Mr. Lazarus Fletcher, F.R.S., the keeper of the department of mineralogy since 1880, has been appointed to the post of director of the natural history departments of the British Museum.


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T is claimed by astronomers that their science is not only the oldest, but that it is the most highly developed of the sciences. Indeed it should be so, since no other science has ever received such support from royalty, from the state and from the private individual. However this may be, there is no doubt that in recent years astronomers have had granted to them greater opportunities for carrying on large pieces of work than have been entrusted to men in any other department of pure science. One might expect that the practical results of a science like physics would appeal to the man who has made a vast fortune through some of its applications. The telephone, the electric transmission of power, wireless telegraphy and the submarine cable are instances of immense financial returns derived from the most abstruse principles of physics. Yet there are scarcely any physical laboratories devoted to research, or endowed with independent funds for this object, except those supported by the government. The endowment of astronomical observatories devoted to research, and not including that given for teaching, is estimated to amount to half a million dollars annually. Several of the larger observatories have an annual income of fifty thousand dollars.

I once asked the wisest man I know, what was the reason for this difference. He said that it was probably because astronomy appealed to the imagination. A practical man, who has spent all his life in his counting room or mill, is sometimes deeply impressed with the vast


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106 distances and grandeur of the problems of astronomy, and the very remoteness and difficulty of studying the stars attract him.

My object in calling your attention to this matter is the hope that what I have to say of the organization of astronomy may prove of use to those interested in other branches of science, and that it may lead to placing them on the footing they should hold. My arguments apply with almost equal force to physics, to chemistry, and in fact to almost every branch of physical or natural science, in which knowledge may be advanced by observation or experiment.

The practical value of astronomy in the past is easily established. Without it, international commerce on a large scale would have been impossible. Without the aid of astronomy, accurate boundaries of large tracts of land could not have been defined and standard time would have been impossible. The work of the early astronomers was eminently practical, and appealed at once to every one. This work has now been finished. We can compute the positions of the stars for years, almost for centuries, with all the accuracy needed for navigation, for determining time or for approximate boundaries of countries. The investigations now in progress at the greatest observatories have little, if any, value in dollars and cents. They appeal, however, to the far higher sense, the desire of the intellectual human being to determine the laws of nature, the construction of the material universe, and the properties of the heavenly bodies of which those known to exist far outnumber those that can be seen.

Three great advances have been made in astronomy. First, the invention of the telescope, with which we commonly associate the name of Galileo, from the wonderful results he obtained with it. At that time there was practically no science in America, and for more than two centuries we failed to add materially to this invention. Half a century ago the genius of the members of one family, Alvan Clark and his two sons, placed America in the front rank not only in the construction, but in the possession, of the largest and most perfect telescopes ever made. It is not easy to secure the world's record in any subject. The Clarks constructed successively, the 18-inch lens for Chicago, the 26-inch for Washington, the 30-inch for Pulkowa, the 36-inch for Lick and the 40-inch for Yerkes. Each in turn was the largest yet made, and each time the Clarks were called upon to surpass the world's record, which they themselves had already established. Have we at length reached the limit in size? If we include reflectors, no, since we have mirrors of 60 inches aperture at Mt. Wilson and Cambridge, and a still larger one of 100 inches has been undertaken. It is more than doubtful, however, whether a further increase in size is a great advantage. Much more depends on other conditions, especially those of climate, the kind of work to be done and, more than all,


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Rh the man behind the gun. The case is not unlike that of a battleship. Would a ship a thousand feet long always sink one of five hundred feet? It seems as if we had nearly reached the limit of size of telescopes, and as if we must hope for the next improvement in some other direction.

The second great advance in astronomy originated in America, and was in an entirely different direction, the application of photography to the study of the stars. The first photographic image of a star was obtained in 1850, by George P. Bond, with the assistance of Mr. J. A. Whipple, at the Harvard College Observatory. A daguerreotype plate was placed at the focus of the 15-inch equatorial, at that time one of the two largest refracting telescopes in the world. An image of α Lyræ was thus obtained, and for this Mr. Bond received a gold medal at the first international exhibition, that at the Crystal Palace, in London, in 1851. In 1857, Mr. Bond, then Professor Bond, director of the Harvard Observatory, again took up the matter with collodion wet plates, and in three masterly papers showed the advantages of photography in many ways. The lack of sensitiveness of the wet plate was perhaps the only reason why its use progressed but slowly. Quarter of a century later, with the introduction of the dry plate and the gelatine film, a new start was made. These photographic plates were very sensitive, were easily handled, and indefinitely long exposures could be made with them. As a result, photography has superseded visual observations, in many departments of astronomy, and is now carrying them far beyond the limits that would have been deemed possible a few years ago.

The third great advance in astronomy is in photographing the spectra of the stars. The first photograph showing the lines in a stellar spectrum was obtained by Dr. Henry Draper, of New York, in 1872. Sir William Huggins in 1863 had obtained an image of the spectrum of Sirius, on a photographic plate, but no lines were visible in it. In 1876 he again took up the subject, and, by an early publication, preceded Dr. Draper. When we consider the attention the photography of stellar spectra is receiving at the present time, in nearly all the great observatories in the world, it may well be regarded as the third great advance in astronomy.

What will be the fourth advance, and how will it be brought about? To answer this question we must consider the various ways in which astronomy, and for that matter any other science, may be advanced.

First, by educating astronomers. There are many observatories where excellent instruction in astronomy is given, either to the general student or to one who wishes to make it his profession. At almost any active observatory a student would be received as a volunteer assistant. Unfortunately, few young men can afford to accept an unpaid position, and the establishment of a number of fellowships each offering a small salary sufficient to support the student would enable him to acquire the


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108 necessary knowledge to fill a permanent position. The number of these scholarships should not be large, lest more students should undertake the work than would be required to fill the permanent paying positions in astronomy, as they become vacant.

In Europe, a favorite method of aiding science is to offer a prize for the best memoir on a specified subject. On theoretical grounds this is extremely objectionable. Since the papers presented are anonymous and confidential, no one but the judges know how great is the effort wasted in duplication. The larger the prize, the greater the injury to science, since the greater will be the energy diverted from untried fields. It would be much wiser to invite applications, select the man most likely to produce a useful memoir, and award the prize to him if he achieved success.

The award of a medal, if of great intrinsic value, would be an unwise expenditure. The Victoria Cross is an example of a successful foundation, highly prized, but of small intrinsic value. If made of gold, it would carry no greater honor, and would be more liable to be stolen, melted down or pawned.

Honorary membership in a famous society, or honorary degrees, have great value if wisely awarded. Both are highly prized, form an excellent stimulus to continued work, and as they are both priceless, and without price, they in no way diminish the capacity for work. I recently had occasion to compare the progress in various sciences of different countries, and found that the number of persons elected as foreign associates of the seven great national societies of the world was an excellent test. Eighty-seven persons were members of two or more of these societies. Only six are residents of the United States, while an equal number come from Saxony, which has only a twentieth of the population. Of the six residents here, only three were born in the United States. Not a single mathematician, or doctor, from this country appears on the list. Only in astronomy are we well represented. Out of a total of ten astronomers, four come from England, and three from the United States. Comparing the results for the last one hundred and fifty years, we find an extraordinary growth for the German races, an equally surprising diminution for the French and other Latin races, while the proportion of Englishmen has remained unchanged.

A popular method of expending money, both by countries and by individuals, is in sending expeditions to observe solar eclipses. These appeal both to donors and recipients. The former believe that they are making a great contribution to science, while the latter enjoy a long voyage to a distant country, and in case of clouds they are not expected to make any scientific return. If the sky is clear at the time of the eclipse, the newspapers of the next day report that great results have


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The New International Encyclopædia/Munster

MUN'STER. The largest of the four provinces of Ireland, occupying the southwest part of that country and bounded north by Connaught, east by Leinster, and west and south by the Atlantic (Map: Ireland, C 4). It contains the six counties of Clare, Cork, Kerry, Limerick, Tipperary, and Waterford. Area, 9481 square miles. The population of the province in 1841 was 2,404,460; in 1891, 1,173,643; and in 1901, 1,075,075.


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Rh been secured, and after that nothing further is ever heard. Exceptions should be made of the English Eclipse Committee and the Lick Observatory, which, by long continued study and observation, are gradually solving the difficult problems which can be reached in this way only.

The gift of a large telescope to a university is of very doubtful value, unless it is accompanied, first, by a sum much greater than its cost, necessary to keep it employed in useful work, and secondly, to require that it shall be erected, not on the university grounds, but in some region, probably mountainous or desert, where results of real value can be obtained.

Having thus considered, among others, some of the ways in which astronomy is not likely to be much advanced, we proceed to those which will secure the greatest scientific return for the outlay. One of the best of these is to create a fund to be used in advancing research, subject only to the condition that results of the greatest possible value to science shall be secured. One advantage of this method is that excellent results may be obtained at once from a sum, either large or small. Whatever is at first given may later be increased indefinitely, if the results justify it. One of the wisest as well as the greatest of donors has said: "Find the particular man," but unfortunately, this plan has been actually tried only with some of the smaller funds. Any one who will read the list of researches aided by the Rumford Fund, the Elizabeth Thompson Fund or the Bruce Fund of 1890 will see that the returns are out of all proportion to the money expended. The trustees of such a fund as is here proposed should not regard themselves as patrons conferring a favor on those to whom grants are made, but as men seeking for the means of securing large scientific returns for the money entrusted to them. An astronomer who would aid them in this work, by properly expending a grant, would confer rather than receive a favor. They should search for astronomical bargains, and should try to purchase results where the money could be expended to the best advantage. They should make it their business to learn of the work of every astronomer engaged in original research. A young man who presented a paper of unusual importance at a scientific meeting, or published it in an astronomical journal, would receive a letter inviting him to submit plans to the trustees, if he desired aid in extending his work. In many cases, it would be found that, after working for years under most unfavorable conditions, he had developed a method of great value and had applied it to a few stars, but must now stop for want of means. A small appropriation would enable him to employ an assistant who, in a short time, could do equally good work. The application of this method to a hundred or a thousand stars would then be only a matter of time and money.

The American Astronomical Society met last August at a summer


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110 resort on Lake Erie. About thirty astronomers read papers, and in a large portion of the cases the appropriation of a few hundred dollars would have permitted a great extension in these researches. A sad case is that of a brilliant student who may graduate at a college, take a doctor's degree in astronomy, and perhaps pass a year or two in study at a foreign observatory. He then returns to this country, enthusiastic and full of ideas, and considers himself fortunate in securing a position as astronomer in a little country college. He now finds himself overwhelmed with work as a teacher, without time or appliances for original work. What is worse, no one sympathizes with him in his aspirations, and after a few years he abandons hope and settles down to the dull routine of lectures, recitations and examinations. A little encouragement at the right time, aid by offering to pay for an assistant, for a suitable instrument, or for publishing results, and perhaps a word to the president of his college if the man showed real genius, might make a great astronomer, instead of a poor teacher. For several years, a small fund, yielding a few hundred dollars annually, has been disbursed at Harvard in this way, with very encouraging results.

A second method of aiding astronomy is through the large observatories. These institutions, if properly managed, have after years of careful study and trial developed elaborate systems of solving the great problems of the celestial universe. They are like great factories, which by taking elaborate precautions to save waste at every point, and by improving in every detail both processes and products, are at length obtaining results on a large scale with a perfection and economy far greater than is possible by individuals, or smaller institutions. The expenses of such an observatory are very large, and it has no pecuniary return, since astronomical products are not salable. A great portion of the original endowment has been spent on the plant, expensive buildings and instruments. Current expenditures, like library expenses, heating, lighting, etc., are independent of the output. It is like a man swimming up stream. He may struggle desperately, and yet make no progress. Any gain in power effects a real advance. This is the condition of nearly all the larger observatories. Their income is mainly used for current expenses, which would be nearly the same whatever their output. A relatively small increase in income can thus be spent to great advantage. The principal instruments are rarely used to their full capacities, and the methods employed could be greatly extended without any addition to the executive or other similar expenses. A man superintending the work of several assistants can often have their number doubled, and his output increased in nearly the same proportion, with no additional expense except the moderate one of their salaries. A single observatory could thus easily do double the work that could be accomplished if its resources were divided between two of half the size.


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Rh A third, and perhaps the best, method of making a real advance in astronomy is by securing the united work of the leading astronomers of the world. The best example of this is the work undertaken in 1870 by the Astronomische Gesellschaft, the great astronomical society of the world. The sky was divided into zones, and astronomers were invited to measure the positions of all the stars in these zones. The observation of two of the northern and two of the southern zones were undertaken by American observatories. The zone from +1° to +5° was undertaken by the Chicago Observatory, but was abandoned owing to the great fire of 1871, and the work was assumed and carried to completion by the Dudley Observatory at Albany. The zone from +50° to +55° was undertaken by Harvard. An observer and corps of assistants worked on this problem for a quarter of a century. The completed results now fill seven quarto volumes of our annals. Of the southern zones, that from −14° to −18° was undertaken by the Naval Observatory at Washington, and is now finished. The zone from −10° to −14° was undertaken at Harvard, and a second observer and corps of assistants have been working on it for twenty years. It is now nearly completed, and we hope to begin its publication this year. The other zones were taken by European astronomers. As a result of the whole, we have the precise positions of nearly a hundred and fifty thousand stars, which serve as a basis for the places of all the objects in the sky.

Another example of cooperative work is a plan proposed by the writer in 1906, at the celebration of the two-hundredth anniversary of the birth of Franklin. It was proposed, first to find the best place in the world for an astronomical observatory, which would probably be in South Africa, to erect there a telescope of the largest size, a reflector of seven feet aperture. This instrument should be kept at work throughout every clear night, taking photographs according to a plan recommended by an international committee of astronomers. The resulting plates should not be regarded as belonging to a single institution, but should be at the service of whoever could make the best use of them. Copies of any, or all, would be furnished at cost to any one who wished for them. As an example of their use, suppose that an astronomer at a little German University should discover a law regulating the stars in clusters. Perhaps he has only a small telescope, near the smoke and haze of a large city, and has no means of securing the photographs he needs. He would apply to the committee, and they would vote that ten photographs of twenty clusters, each with an exposure of an hour, should be taken with the large telescope. This would occupy about a tenth part of the time of the telescope for a year. After making copies, the photographs would be sent to the astronomer who would perhaps spend ten years in studying and measuring them. The committee


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112 would have funds at their disposal to furnish him, if necessary, with suitable measuring instruments, assistants for reducing the results, and means for publication. They would thus obtain the services of the most skilful living astronomers, each in his own special line of work, and the latter would obtain in their own homes material for study, the best that the world could supply. Undoubtedly, by such a combination if properly organized, results could be obtained far better than is now possible by the best individual work, and at a relatively small expense. Many years of preparation will evidently be needed to carry out such a plan, and to save time we have taken the first step and have sent a skilful and experienced observer to South Africa to study its climate and compare it with the experience he has gained during the last twenty years from a similar study of the climate of South America and the western portion of the United States.

The next question to be considered is in what direction we may expect the greatest advance in astronomy will be made. Fortunate indeed would be the astronomer who could answer this question correctly. When Ptolemy made the first catalogue of the stars, he little expected that his observations would have any value nearly two thousand years later. The alchemists had no reason to doubt that their results were as important as those of the chemists. The astrologers were respected as much as the astronomers. Although there is a certain amount of fashion in astronomy, yet perhaps the best test is the judgment of those who have devoted their lives to that science. Thirty years ago the field was narrow. It was the era of big telescopes. Every astronomer wanted a larger telescope than his neighbors, with which to measure double stars. If he could not get such an instrument, he measured the positions of the stars with a transit circle. Then came astrophysics, including photography, spectroscopy and photometry. The study of the motion of the stars along the line of sight, by means of photographs of their spectra, is now the favorite investigation at nearly all the great observatories of the world. The study of the surfaces of the planets, while the favorite subject with the public, next to the destruction of the earth by a comet, does not seem to appeal to astronomers. Undoubtedly, the only way to advance our knowledge in this direction is by the most powerful instruments, mounted in the best possible locations. Great astronomers are very conservative, and any sensational story in the newspapers is likely to have but little support from them. Instead of aiding, it greatly injures real progress in science.

There is no doubt that, during the next half century, much time and energy will be devoted to the study of the fixed stars. The study of their motions as indicated by their change in position was pursued with great care by the older astronomers. The apparent motions were so


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Rh small that a long series of years was required and, in general, for want of early observations of the precise positions of the faint stars, this work was confined mainly to the bright stars. Photography is yearly adding a vast amount of material available for this study, but the minuteness of the quantities to be measured renders an accurate determination of their laws very difficult. Moreover, we can thus only determine the motions at right angles to the line of sight, the motion towards us or from us being entirely insensible in this way. Then came the discovery of the change in the spectrum when a body was in motion, but still this change was so small that visual observations of it proved of but little value. Attaching a carefully constructed spectroscope to one of the great telescopes of the world, photographing the spectrum of a star, and measuring it with the greatest care, provided a tool of wonderful efficiency. The motion, which sometimes amounts to several hundreds of miles a second could thus be measured to within a fraction of a mile. The discovery that the motion was variable, owing to the star's revolving around a great dark planet sometimes larger than the star, added greatly not only to the interest of these researches, but also to the labor involved. Instead of a single measure for each star, in the case of the so-called spectroscopic binaries, we must make enough measures to determine the dimensions of the orbit, its form and the period of revolution.

What has been said of the motions of the stars applies also, in general, to the determination of their distances. A vast amount of labor has been expended on this problem. When at length the distance of a single star was finally determined, the quantity to be measured was so small as to be nearly concealed by the unavoidable errors of measurement. The parallax, or one half of the change in the apparent position of the stars as the earth moves around the sun, has its largest value for the nearest stars. No case has yet been found in which this quantity is as large as a foot rule seen at a distance of fifty miles, and for comparatively few stars is it certainly appreciable. An extraordinary degree of precision has been attained in recent measures of this quantity, but for a really satisfactory solution of this problem, we must probably devise some new method, like the use of the spectroscope for determining motions. Two or three illustrations of the kind of methods which might be used to solve this problem may be of interest. There are certain indications of the presence of a selective absorbing medium in space. That is, a medium like red glass, for instance, which would cut off the blue light more than the red light. Such a medium would render the blue end of the spectrum of a distant star much fainter, as compared with the red end, than in the case of a near star. A measure of the relative intensity of the two rays would serve to measure the distance, or thickness of the absorbing medium. The effect would be the


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114 same for all stars of the same class of spectrum. It could be tested by the stars forming a cluster, like the Pleiades, which are doubtless all at nearly the same distance from us. The spectra of stars of the tenth magnitude, or fainter, can be photographed well enough to be measured in this way, so that the relative distances of nearly a million stars could be thus determined.

Another method which would have a more limited application, would depend on the velocity of light. It has been maintained that the velocity of light in space is not the same for different colors. Certain stars, called Algol stars, vary in light at regular intervals when partially eclipsed by the interposition of a large dark satellite. Recent observations of these eclipses, through glass of different colors, show variations in the time of obscuration. Apparently, some of the rays reach the earth sooner than others, although all leave the star at the same time. As the entire time may amount to several centuries, an excessively small difference in velocity would be recognizable. A more delicate test would be to measure the intensity of different portions of the spectrum at a time when the light is changing most rapidly. The effect should be opposite according as the light is increasing or diminishing. It should also show itself in the measures of all spectroscopic binaries.

A third method of great promise depends on a remarkable investigation carried on in the physical laboratory of the Case School of Applied Science. According to the undulatory theory of light, all space is filled with a medium called ether, like air, but as much more tenuous than air as air is more tenuous than the densest metals. As the earth is moving through space at the rate of several miles a second, we should expect to feel a breeze as we rush through the ether, like that of the air when in an automobile we are moving with but one thousandth part of this velocity. The problem is one of the greatest delicacy, but a former officer of the Case School, one of the most eminent of living physicists, devised a method of solving it. The extraordinary result was reached that no breeze was perceptible. This result appeared to be so improbable that it has been tested again and again, but every time, the more delicate the instrument employed, the more certainly is the law established. If we could determine our motion with reference to the ether, we should have a fixed line of reference to which all other motions could be referred. This would give us a line of ever-increasing length from which to measure stellar distances.

Still another method depends on the motion of the sun in space. There is some evidence that this motion is not straight, but along a curved line. We see the stars, not as they are now, but as they were when the light left them. In the case of the distant stars this may have occurred centuries ago. Accordingly, if we measure the motion of the sun from them, and from near stars, a comparison with its actual


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Rh will give us a clue to their distances. Unfortunately, all the stars appear to have large motions whose law we do not know, and therefore we have no definite starting point unless we can refer all to the ether which may be assumed to be at rest.

If the views expressed to you this morning are correct, we may expect that the future of astronomy will take the following form: There will be at least one very large observatory employing one or two hundred assistants, and maintaining three stations. Two of these will be observing stations, one in the western part of the United States, not far from latitude +30°, the other similarly situated in the southern hemisphere, probably in South Africa, in latitude −30°. The locations will be selected wholly from their climatic conditions. They will be moderately high, from five to ten thousand feet, and in desert regions. The altitude will prevent extreme heat, and clouds or rain will be rare. The range of temperature and unsteadiness of the air will be diminished by placing them on hills a few hundred feet above the surrounding country. The equipment and work of the two stations will be substantially the same. Each will have telescopes and other instruments of the largest size, which will be kept at work throughout the whole of every clear night. The observers will do but little work in the daytime, except perhaps on the sun, and will not undertake much of the computation or reductions. This last work will be carried on at a third station, which will be near a large city where the cost of living and of intellectual labor is low. The photographs will be measured and stored at this station, and all the results will be prepared for publication, and printed there. The work of all three stations will be carefully organized so as to obtain the greatest result for a given expenditure. Every inducement will be offered to visiting astronomers who wish to do serious work at either of the stations and also to students who intend to make astronomy their profession. In the case of photographic investigations it will be best to send the photographs so that astronomers desiring them can work at home. The work of the young astronomers throughout the world will be watched carefully and large appropriations made to them if it appears that they can spend them to advantage. Similar aid will be rendered to astronomers engaged in teaching, and to any one, professional or amateur, capable of doing work of the highest grade. As a fundamental condition for success, no restrictions will be made that will interfere with the greatest scientific efficiency, and no personal or local prejudices that will restrict the work.

These plans may seem to you visionary, and too Utopian for the twentieth century. But they may be nearer fulfilment than we anticipate. The true astronomer of to-day is eminently a practical man. He does not accept plans of a sensational character. The same qualities


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116 are needed in directing a great observatory successfully, as in managing a railroad, or factory. Any one can propose a gigantic expenditure, but to prove to a shrewd man of affairs that it is feasible and advisable is a very different matter. It is much more difficult to give away money wisely than to earn it. Many men have made great fortunes, but few have learned how to expend money wisely in advancing science, or to give it away judiciously. Many persons have given large sums to astronomy, and some day we shall find the man with broad views who will decide to have the advice and aid of the astronomers of the world, in his plans for promoting science, and who will thus expend his money, as he made it, taking the greatest care that not one dollar is wasted. Again, let us consider the next great advance, which perhaps will be a method of determining the distances of the stars. Many of us are working on this problem, the solution of which may come to some one any day. The present field is a wide one, the prospects are now very bright, and we may look forward to as great an advance in the twentieth century, as in the nineteenth. May a portion of this come to the Case School and, with your support, may its enviable record, in the past, be surpassed by its future achievements.


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 difference that after about 10 ℔ it takes a spinning-bait, usually a heavy spoon-bait, better than a fly.

Cat-fish.—None of the fresh-water cat-fishes (of which no example is found in England) are what may be called sporting fish, but several may be caught with rod and line. There are several kinds in North America, and some of them are as heavy as 150 ℔, but the most important is the wels (Silurus glanis) of the Danube and neighbouring waters. This is the largest European fresh-water fish, and it is credited with a weight of 300 ℔ or more. It is a bottom feeder and will take a fish-bait either alive or dead; it is said occasionally to run at a spinning bait when used very deep.

Burbot.—The burbot (Lota vulgaris) is the only fresh-water member of the cod family in Great Britain, and it is found only in a few slow-flowing rivers such as the Trent, and there not often, probably because it is a fish of sluggish habits which feeds only at night. It reaches a weight of 3 ℔ or more, and will take most flesh or fish baits on the bottom. The burbot of America has similar characteristics.

Sturgeon.—The sturgeons, of which there are a good many species in Europe and America, are of no use to the angler. They are anadromous fishes of which little more can be said than that a specimen might take a bottom bait once in a way. In Russia they are sometimes caught on long lines armed with baited hooks, and occasionally an angler hooks one. Such a case was reported from California in The Field of the 19th of August 1905.

Shad.—Two other anadromous fish deserve notice. The first is the shad, a herring-like fish of which two species, allice and twaite (Clupea alosa and C. finta), ascend one or two British and several continental rivers in the spring. The twaite is the more common, and in the Severn, Wye and Teme it sometimes gives very fair sport to anglers, taking worm and occasionally fly or small spinning bait. It is a good fighter, and reaches a weight of about 3 ℔. Its sheen when first caught is particularly beautiful. America also has its shads.

Flounder.—The other is the flounder (Pleuronectes flesus), the only flat-fish which ascends British rivers. It is common a long way up such rivers as the Severn, far above tidal influence, and it will take almost any flesh-bait used on the bottom. A flounder of 1 ℔ is, in a river, a large one, but heavier examples are sometimes caught.

Eel.—The eel (Anguilla vulgaris) is regarded by the angler more as a nuisance than a sporting fish, but when of considerable size (and it often reaches a weight of 8 ℔ or more) it is a splendid fighter and stronger than almost any fish that swims. Its life history has long been disputed, but it is now accepted that it breeds in the sea and ascends rivers in its youth. It is found practically everywhere, and its occurrence in isolated ponds to which it has never been introduced by human agency has given rise to a theory that it travels overland as well as by water. The best baits for eels are worms and small fish, and the best time to use them is at night or in thundery or very wet weather.

Sea Angling.

Sea angling is attended by almost as many refinements of tackle and method as fresh-water angling. The chief differences are differences of locality and the habits of the fish. To a certain extent sea angling may also be divided into three classes—fishing on the surface with the fly, at mid-water with spinning or other bait, and on the bottom; but the first method is only practicable at certain times and in certain places, and the others, from the great depths that often have to be sounded and the heavy weights that have to be used in searching them, necessitate shorter and stouter rods, larger reels and stronger tackle than fresh-water anglers employ. Also, of course, the sea-fisherman is liable to come into conflict with very large fish occasionally. In British waters the monster usually takes the form of a skate or halibut. A specimen of the former weighing 194 ℔ has been landed off the Irish coast with rod and line in recent years. In American waters there is a much greater opportunity of catching fish of this calibre.

Great Game Fishes.—There are several giants of the sea which are regularly pursued by American anglers, chief among them being the tarpon (Tarpon atlanticus) and the tuna or tunny (Thunnus thynnus), which have been taken on rod and line up to 223 ℔ and 251 ℔ respectively. Jew-fish and black sea-bass of over 400 ℔ have been taken on rod and line, and there are many other fine sporting fish of large size which give the angler exciting hours on the reefs of Florida, or the coasts of California, Texas or Mexico. Practically all of them are taken with a fish-bait either live or dead, and used stationary on the bottom or in mid-water trailed behind a boat.

British Game Fishes.—On a much smaller scale are the fishes most esteemed in British waters. The bass (Labrax lupus) heads the list as a plucky and rather difficult opponent. A fish of 10 ℔ is a large one, but fifteen-pounders have been taken. Small or “school” bass up to 3 ℔ or 4 ℔ may sometimes be caught with the fly (generally a roughly constructed thing with big wings), and when they are really taking the sport is magnificent. In some few localities it is possible to cast for them from rocks with a salmon rod, but usually a boat is required. In other places bass may be caught from the shore with fish bait used on the bottom in quite shallow water. They may again sometimes be caught in mid-water, and in fact there are few methods and few lures employed in sea angling which will not account for them at times. The pollack (Gadus pollachius) and coal-fish (Gadus virens) come next in esteem. Both in some places reach a weight of 20 ℔ or more, and both when young will take a fly. Usually, however, the best sport is obtained by trailing some spinning-bait, such as an artificial or natural sand-eel, behind a boat. Sometimes, and especially for pollack, the bait must be kept near the bottom and heavy weights on the line are necessary; the coal-fish are more prone to come to the surface for feeding. The larger grey mullet (Mugil capito) is a great favourite with many anglers, as it is extremely difficult to hook, and when hooked fights strongly. Fishing for mullet is more akin to fresh-water fishing than any branch of sea-angling, and indeed can be carried on in almost fresh water, for the fish frequent harbours, estuaries and tidal pools. They can be caught close to the surface, at mid-water and at the bottom, and as a rule vegetable baits, such as boiled macaroni, or ragworms are found to answer best. Usually ground-baiting is necessary, and the finer the tackle used the greater is the chance of sport. Not a few anglers fish with a float as if for river fish. The fish runs up to about 8 ℔ in weight. The cod (Gadus morhua) grows larger and fights less gamely than any of the fish already mentioned. It is generally caught with bait used on the bottom from a boat, but in places codling, or young cod, give some sport to anglers fishing from the shore. The mackerel (Scomber scomber) gives the best sport to a bait, usually a strip of fish skin, trailed behind a boat fairly close to the surface, but it will sometimes feed on the bottom. Mackerel on light tackle are game fighters, though they do not usually much exceed 2 ℔. Whiting and whiting-pout (Gadus merlangus and Gadus luscus) both feed on or near the bottom, do not grow to any great size, and are best sought with fine tackle, usually an arrangement of three or four hooks at intervals above a lead which is called a “paternoster.” If one or more of the hooks are on the bottom the tackle will do for different kinds of flat fish as well, flounders and dabs being the two species most often caught by anglers. The bream (Pagellus centrodontus) is another bottom-feeder which resembles the fresh-water bream both in appearance and habits. It is an early morning or rather a nocturnal fish, and grows to a weight of 3 ℔ or 4 ℔. Occasionally it will feed in mid-water or even close to the surface. The conger eel (Conger vulgaris) is another night-feeder, which gives fine sport, as it grows to a great size, and is very powerful. Strong tackle is essential for conger fishing, as so powerful an opponent in the darkness cannot be given any law. The bait must be on or near the bottom. There are, of course, many other fish which come to the angler’s rod at times, but the list given is fairly complete as representing the species which are especially sought. Beside them are occasional (in some waters too frequent) captures such as dog-fish and sharks, skates and rays. Many of them run to a great size and give

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Rh

ROFESSOR A. VOSS, of the University of Munich, recently made the following statement: "Our entire present civilization, as far as it depends upon the intellectual penetration and utilization of nature, has its real foundation in the mathematical sciences." He adds that this truth finds expression in the ever-increasing appreciation of the educational value of mathematics, notwithstanding the fact that it is the most unpopular of all the sciences. This unpopularity is natural since "unpopularity is an essential feature of a real science," because such a science can be comprehended only through tireless and continued efforts.

An intelligent expression as regards the future of mathematics must be based not only upon the past and present state of this science, but also upon its real essence. One of those elements which mathematics has in common with some of the other sciences, but which are more prominent in mathematics than in any of the others, is the tendency to use thought in the most economical manner. When one considers the extent to which efforts to simplify methods, theorems and formulas direct mathematical endeavor, one must admit that the statement "Mathematics is the science of saving thought" expresses a great truth, even if it is too sweeping to serve as a definition.

That mathematics is the science which is preeminently devoted to the discovery and mapping of routes along which thought may ascend securely and with the greatest ease, is supported by the fact that it has the oldest and the most extensive symbolical language. In the introduction to his classic history of mathematics, Moritz Cantor asks, "Why has mathematics, since the remotest times, found support, simplification and advancement by means of word symbols, whether these are number symbols or other mathematical symbols?" Although the oldest of these word symbols are probably relics of a very ancient picture language, yet it is of great interest that in mathematics the picture language was retained and used side by side with an alphabetic and syllabic language, while the latter displaced the former elsewhere. Even those who have mastered only the elements of algebra and the


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Rh differential calculus are in position to appreciate the value of mathematical symbols for the purpose of centralizing and intensifying thought.

It is true that some of the roads which mathematical thought has made through great difficulties have been practically abandoned and that the popularity of many of the others has changed from time to time. Among the former we may class the results of investigations recorded at the beginning of the oldest extensive mathematical work that has been deciphered, viz., the formulas relating to unit fractions which are found in the nearly four thousand-years-old work of Ahmes. A subject which appears to have been placed at the very beginning of advanced mathematical instruction four thousand years ago is now entirely abandoned in our courses, except when the history of the development of the science is under consideration. While mathematics presents a number of other roads which are now of interest only to the historian, yet there are also many which have been known for centuries and which have been pursued with profit and pleasure by great minds in all the civilized nations. The latter class includes all the longer ones leading gradually to points of view from which the connection between many natural phenomena may be clearly discerned.

The intellectual heights reached by means of a long series of connected mathematical theorems do not always reveal their greatest lesson to the first explorers. For instance, the large body of facts relating to conic sections, developed by Apollonius and other Greek geometers, became a much greater glory to the human mind through the discovery, nearly two thousand years later, that the bodies of the solar system describe conic sections. Such experiences in the past tend to justify the fact that a large number of men are devoting their lives to the discovery of abstract results irrespective of applications, and they tend to explain why the largest prize (about twenty-five thousand dollars) ever offered for a mathematical theorem is being offered for a theorem in number theory, which is not expected to have any application to subjects outside of pure mathematics.

There seems to be a general impression abroad to the effect that mathematics and the ancient languages constituted the main parts of the curriculum of our colleges and universities a century or two ago. As regards mathematics this is quite contrary to fact, as may be seen from a few historical data. Less than two centuries ago the students in Harvard College began the study of arithmetic in their senior year. In fact, no knowledge of any mathematics was required to enter Harvard before 1803, and it was not until 1816 that the whole of arithmetic was required for entrance. In other American institutions the mathematical situation was generally worse, and in Europe the improvements were not very much earlier. It is during


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Rh recent years that mathematics has made most of its gains towards being recognized as a fundamental science, and the study of advanced mathematics in our universities had a still later origin.

The rapid recent advances in various fields of mathematics have given rise to a very optimistic spirit as to the future. Although we still hold in high esteem the brilliant discoveries of the Greeks, we are inclined to give much more thought and attention to recent work, as may be seen from the references in the extensive German and French mathematical encyclopedias which are in the process of being published. The history of mathematics furnishes many instances of the vanishing of apparently insurmountable barriers. We need only recall the barrier created by the Greek custom of confining oneself to the rule and circle in the most acceptable geometric constructions, and the very formidable barrier furnished by the imaginary, and even by the negative and the irrational roots of a quadratic equation.

Those who fixed their attention upon these barriers in the past have naturally been led to think that the days of important advances in mathematics were about ended and that it only remained to fill in details. Such predictions had few supporters when new methods led over these barrier and turned them into steps to richer mathematical domains. As this process has been repeated so often it has gradually reduced the number of those to whom the future of mathematics looked dark. In fact, Poincaré, in his address before the Fourth International Congress of Mathematicians, which was held at Rome, in April, 1908, said that all those who held these views are dead.

These facts seem to justify a very hopeful spirit as regards future progress, but it is necessary to examine them with great care in order to deduce from them any helpful suggestions as to the probable nature of this progress. Such prognostications clearly demand a mind that can deal with big problems as well as a thorough acquaintance with the past and the present developments in mathematics, to insure that the results obtained by a kind of extrapolation may be worthy of confidence. It is doubtful whether any living mathematician would be more generally regarded as qualified to make reliable predictions along this line than Poincaré, of Paris. The address to which we referred in the preceding paragraph was devoted to this subject and we proceed to give some of the main results.

The objects of mathematical thought are so numerous that we cannot expect to exhaust them. This appears the more evident since the mathematician creates new concepts from the elements which are presented to him by nature. Hence there must be a choice of subject matter, but who is to do the choosing? Some are inclined to think that the mathematician should confine himself to those problems which


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120 may be set for him by the physicist or the engineer. If he had done this in the past he would not have created the instruments necessary to solve such problems, and hence it is unreasonable to make such restrictions as to the future.

If the physicists of the eighteenth century had abandoned the study of electricity because it seemed to serve no useful end, we should not have had the many useful applications of electricity during the nineteenth century. Similarly, if the mathematician had abandoned the study of negative and imaginary numbers because they seemed to point only to impossibilities, we should not have had the many powerful instruments of thought which enable us to cope more successfully with many problems of nature. Just as the physicist is largely guided in his work by those facts which seem to point to general laws, so the mathematician is guided in his work by the desire to discover extensive relations and laws having a wide range of application. Millions of isolated facts present themselves to the investigator, some of which are of striking interest to the initiated, but they are of practically no value in the development of mathematics except that they may sometimes serve as an exercise in secondary instruction.

At a first thought the statement that "Mathematics is the art of giving the same name to different things" may appear to be entirely contrary to fact, but from a certain standpoint this statement conveys a very fundamental truth. It should be borne in mind that these different things must have in common the property to which this common name refers, and that it is the duty of the mathematician to discover and exhibit this common property. By way of illustration we may recall the use of x for various unknowns in algebra and the (1,1) correspondence between the two series of operators. When the language has been properly chosen it is often surprising to find that the demonstrations, as regards a known object, apply immediately to a large number of new objects without even a change of name.

Just as the boundaries between the elementary subjects of mathematics—arithmetic, algebra and geometry—vanish when the knowledge of these subjects is sufficiently extended, so the boundaries between subjects in pure and applied mathematics are disappearing, and it is exactly in these bordered lands, or in this common territory of two or more subjects, where the greatest recent progress has been made and where the greatest future activity may be expected. The work in this common territory is made possible by observing similarity of form where there is dissimilarity of matter, or by observing some other common properties which admit mathematical treatment.

In Poincaré's address some of these general observations were illustrated by numerous examples chosen from various fields of higher mathematics. On the contrary, we shall confine our illustrative


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122 general, to eight distinct numbers. Starting with 5, these eight numbers are

No new number is obtained by dividing 2 by any of these numbers or by subtracting any of them from 2. The proof of the fact that the eight operations by means of which each one of these eight numbers may be derived from any one of them have the same properties in relation to each other as the eight movements of the square is not difficult, but it involves details which may be omitted in a popular exposition.

An instance where the octic group plays an important role in algebra is furnished by the three-valued function xy + zw, which is fundamental in the theory of the general equation of the fourth degree. On account of the existence of this function the solution of the general equation of the fourth degree may be made to depend upon the solution of the general equation of the third degree. This function is transformed into itself by eight substitutions, and we may arrange its letters separately on the vertices of a square in such a way that the eight substitutions transforming the function into itself correspond to the eight movements which transform the square into itself. Such an arrangement exhibits the intimate relations between this function and the movements of a square, and the preceding examples illustrate the fact that the octic group finds application in each of the elementary subjects—arithmetic, algebra, geometry and trigonometry, and that it forms a part of the domain common to all of these disciplines.

In a similar manner other groups could be traced through these elementary subjects of mathematics and it could be shown that the theory of these groups may be used to clarify many fundamental points and to exhibit deep-seated contact. If the common domains will furnish the most active fields of future investigations in accord with the predictions of Poincaré, and if we may expect the greatest future progress to be based upon the modeling of the less advanced science upon the one which has made the more progress, it is reasonable to expect that a subject like group theory will grow in favor, and that some of the elements of this subject will become a part of the ordinary courses in secondary mathematics. In support of this view we may quote a recent statement by Professor Bryan, President of the Mathematical Association, which is as follows: "I believe Professor Perry will get some very good material for applications out of the theory of groups, when explorers have first made their discoveries, and when the colonists have been over it and surveyed it, and discovered means for cultivating it. We do not know anything about its practical applications now."


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Rh The future of mathematics appears bright, both for the investigator and for the teacher. When a country which has such an enlightened educational system as France increased the amount of time devoted to secondary mathematics so recently as 1902 and again in 1906, it furnishes one of the strongest possible encouragements to the teacher who may have been troubled by the thought that the educational value of mathematics was not being as fully appreciated as in earlier years. Naturally we may expect that there will be local changes of view as regards the value of mathematics as an educational subject, and these changes will not always be for the better, but the civilized world, as a whole, is learning to appreciate more and more the fundamental importance of early mathematical training, so that we should not be too much perturbed by local steps backwards, but we should move ahead with the assurance that we are engaged in a work of the highest pedagogical importance.

The boundless confidence in the importance of early and extensive mathematical training should, however, not blind us to the need of changes and new adaptations. As an important function of mathematical training is the furnishing of the most useful and the most powerful tools of thought, it is evident that the choice of these tools will vary with the advancement of general knowledge. All admit that the concept of a derivative is one of the most useful elementary tools of thought, and in a number of countries this concept has been introduced into secondary mathematics and used with success. At the last International Mathematical Congress, held at Rome, M. Borel, of Paris, reported that the notion of derivative had been introduced into French secondary education in 1902 and that it had led to satisfactory results. At the same meeting M. Beke, of Budapest, stated that this notion, together with the notion of function and graph, had been introduced into the courses of secondary education in Hungary.

At the recent joint conference of the Mathematical Association and the Federated Association of London Non-Primary Teachers, the chairman remarked: "I have always thought that a mathematician was a man who when he wants to find anything out, uses his brains for that purpose, whereas a physicist, when he wants to find out anything, resorts to experiment." Although this statement is not to be construed literally, yet it does involve a great partial truth and it calls attention to elements which insure mathematical appreciation as long as there is scientific thought. "It is the mind that sees as well as the eye," and the mind sees some of the greatest truths most clearly by means of mathematical symbolism. In fact, mathematical symbols serve both as a telescope and also as a microscope for mental vision, and as long as such vision is demanded the teacher of mathematics will be appreciated.


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124

HE writer makes no pretense of being an archeologist, but finding few accounts of the wonderful megalithic monuments of Brittany in English, he has written this account of his visit to them as thread on which to string a few pictures. Those huge stones erected by human hands—no one knows by whom or why or when—which are called megalithic monuments, occur throughout western Europe, from the "Huns' beds" east of the Zuider Zee, through Britain, France and Spain and into northern Africa, across the Strait of Gibraltar, but nowhere are they as numerous or striking as in Brittany. The tourist is familiar with that strange circle of standing stones at Stonehenge and, to a less extent with "Kit's Coty House" in Kent and the circle at Avebury, but Morbihan is far out of the usual track and hence is seen by comparatively few of our people.

The department of Morbihan lies on the southern shore of Brittany, three hundred miles in a straight line west of Paris, and considerably farther as the trains run. The part of it where these megaliths abound is, perhaps, twenty miles, east and west, and ten north and south. It contains no large cities—Vannes, the capital, has not twenty-five thousand inhabitants—it has no churches or art galleries starred in Badeker; its sole attractions are its delightful inhabitants who still adhere to their ancient costumes, and the monuments.

Archeologists divide these standing stones into different categories, according to the way they are arranged, and each kind has its name derived from either the Keltic or the French. There are menhirs (Keltic, long stones) which stand upright in the soil, usually upon the smaller end. Menhirs may be isolated, scattered here and there through the region, or they may be arranged in lines or rows (alignments) stretching across the fields. In certain places the menhirs form square or semicircular enclosures called cromlechs (Keltic, curved stones). Again, the megaliths have been built into chambers, the walls composed of upright stones placed close together, and roofed in by one or more large blocks of stone. These are the dolmens (table stones), the enlarged chamber being usually reached by a narrower passage, though occasionally the entrance is in one side of the chamber. In some cases


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Rh to elementary subjects. Our first effort will be directed towards exhibiting some territory which is common to each of the four subjects—arithemtic, geometry, algebra and trigonometry. By observing common properties we shall not only see a bond connecting these fund a* mental subjects, but we shall also be led to general methods which make it unnecessary to study the same properties in different forms. The thing to be emphasized is that these four elementary subjects have in common fundamental notions which not only connect them, but also establish contact between them and many other subjects. Such a fundamental notion is a group of order 8, known as the octic group. Some of the properties of this group may be easily seen by considering the possible movements of space which transform a square into itself.

The period or order of a movement represents the number of times the movement must be made in order to arrive at the identity, or at the original position. It is clear that the eight movements of the square include two of period four, five of period two, and the identity A profound study of these eight movements would disclose many interesting facts. For instance, it would be seen that only two of them (the square of these of period four and the identity) are commutative with each one of others, while each one of the remaining six is commutative with only four of the possible eight movements. Although a profound study of this group of eight movements would be necessary to exhibit the fundamental role which it plays in the various subjects, it is not necessary to enter deeply into its properties in order to see that it is common to the four subjects mentioned above.

At a first thought it might appear as if these eight movements had nothing in common with trigonometry, but a very fundamental connection may be seen as follows: If the vertex of the angle A is the center of a square and the initial line of A coincides with a line of symmetry of the square, the operations of taking the complement and the supplement of A correspond to movements transforming the square into itself. Hence the eight angles which may be obtained from a given angle by a repetition of finding supplement and complement may be placed in a (1, 1) correspondence with the eight movements of the square. As these eight angles play such a fundamental role in elementary trigonometry, it has been suggested that our ordinary school trigonometry might appropriately be called the trigonometry of the octic group, or the trigonometry of the group of movements of the square.

Although the eight operations of the octic group do not occupy such an important place in elementary arithmetic as in geometry and trigonometry, yet these operations serve to explain some facts which present themselves in the most elementary arithmetic processes. For instance, the operations of subtracting from 2 and dividing 2 lead, in


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Rh instead of a true dolmen there is a narrow passage alone, an allée couaverte. Various subdivisions of these types are recognized, but they may be ignored here.

It was to see these megaliths that we took the all-day journey (really only 148 miles) across Brittany. It was early morning when we left the wonderful rock of St. Michel's Mount and the omelettes of the now reconciled Poulards, with whose quarrels all travelers are familiar. Half an hour by tram took us to Pontorson. Why do places like Pontorson exist? Our two hours were one continual struggle with station agent, hack drivers and porters, all of whom were insistent that we should drive out to Mt. St. Michel. "One franc a person" but we knew their ways; half way there would be a demand for a pourboire which would make the original fare look like twenty cents. Besides, we had just come from the Mount, and why should we go back? At Dol another wait, this time long enough to get an early lunch, before we could get a cross-country train for Rennes. Up to that day Rennes had been associated in our minds with the Dreyfus trial of a few years ago. Two hours here were sufficient to assure us that Bädeker did not slander the town when he wrote that with its 75,000 inhabitants, "its spacious modern streets are generally dull, lifeless and deserted."

Next a wait of an hour at Redon before taking the last train of the day—the Nantes-l'Orient express for Auray, which we reached just in time for dinner at the most comfortable and hospitable Pavilion hotel.

One may go in various ways from the railway to the monuments, but there is a best way—by carriage. There is the route from Vannes, taking a boat down through the sea of Morbihan to Locmariaquer. It is a picturesque route through a land-locked arm of the sea, studded with islands, like a miniature Casco Bay. But it is not to be depended upon, as the sailing of the steamers varies with the tides. It is cheaper to take the train from Auray to Carnac station on the little road to Quiberon, and then the little tram to Carnac village and to Erdeven. This brings one within easy walking distance of the principal alignments; but to reach the other monuments a carriage is convenient; even necessary, if one is to see the important menhirs, dolmens, etc., of Locmariaquer. Besides, the foot traveler will have to have a guide, otherwise he will waste much time and probably will miss much that he ought to see. Bädeker's map is on too small a scale to be of much assistance. The total drive from Auray to all of the standing stones is about thirty-five miles, but by cutting out some which apparently were repetitions of others, we made our round trip about twenty-five miles. The country traversed is best described in the terms of physical geography as a peneplain and the shore to the south as a drowned coast. It is nearly level, with no hills rising markedly above the rest of the country. We saw the first of the monuments about six miles out of Auray and


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126 our first glimpse was rather disappointing. A couple of hundred feet to the left of the road was the first dolmen, a dozen stones, about five feet high, standing upright in a pasture, and roofed in by two large stones lying across them. It recalled a child's house on a large scale, built out of the lichen-covered stones of the field. By its side stood a square stone monument announcing that this dolmen of Keriaval is the property of the French Republic, and that any one injuring it in any way will be prosecuted. It may be said that by each group in the entire district is a similar stone. On the other side of the road are three dolmens, close together, standing scarcely above the surrounding soil but excavated inside so that one may stand upright in the interior.

It would serve no useful purpose to give our itinerary in detail, but a clearer idea of these strange structures may be given by a general description of the monuments as a whole, specifying here and there those of more particular interest from size or other features.

Possibly the most striking of all are the alignments. Certainly they are the most difficult to explain. Of these there are several groups, each distinct from its fellows, and yet the whole series being in the same belt. Many of the stones have tumbled down and some have been utilized in building walls and houses. Thus the little church of St. Cornély at Carnac is built entirely of menhirs, broken up into blocks of convenient size, while the curious crown that surmounts its west portal was carved out of a single menhir. Le Rouzic, whom I shall often quote, says that the series of alignments once extended from a point to the west of the village of Carnac, five miles east to the Crac'h River, while other series occur further west, near Erdeven.


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 Edwin Sandys, Nichols Ferrar and the Earl of Southampton—worthy successors of Gilbert and Raleigh—undertook the solution of the problem. Raleigh, confined in the Tower, could not take an active part at this time, but his friends and relations were the chief actors and workers in the new colonization schemes.

Two large associations were formed—one composed of lords, knights and merchants of the city of London, and the other of residents in the cities of Bristol, Exeter and Plymouth,—and they obtained from King James I., April 10, 1606, a joint charter which defined Virginia as the portion of North America lying between the 34th and 45th parallel of north latitude, practically the present United States. In this vast extent of territory the first Company, called the Virginia Company of London, was permitted to establish a settlement anywhere between 34 and 41 degrees; and the second, called the Plymouth Company, anywhere between 38 and 45 degrees. The actual jurisdiction of each Company was represented by a rectangle extending fifty miles north of the settlement and fifty miles south, and east and west 100 miles from the coast seaward, and 100 miles from the coast inland. The Plymouth Company was singularly unfortunate in its attempts, but the efforts of the Virginia Company were crowned with success; and by two new charters, 1609 and 1612, its jurisdiction was extended over the entire limit of its original sphere of possible settlement, and from sea to sea.

The subsequent history of Virginia affairs under the Company for nearly twenty years is one of stupendous self-sacrifice both in England and America. The men in England who had the supreme control gave freely of their money and time, and received no return except the satisfaction of having founded in America a fifth kingdom under the Crown. The men in Virginia incurred hardships without parallel in the world's history, and most of them went to the martyrdom of cruel death by climatic disease, starvation and Indian attack. It was but natural that, in those unprecedented conditions, those in England should try to shield themselves from the blame and throw upon the settlers the responsibility. But discriminating history has seen the light at last, and while the motives of the directors of the enterprise were always high and honorable, it is now recognized that in the government of the colony they made many and serious blunders. For fear of making the enterprise unpopular they refused to tell the English public the real truth as to the dangerous climate and the other natural conditions making for evil. Virginia, as a country, had to be "boomed," at all events. Thus the poor settlers, who, for the most part, consisted of the best materials in England—old sailors under Hawkins and Drake, or old soldiers of the Netherlands—were abused and shamelessly villified. The appalling mortality which overwhelmed them for a great number of years is itself a pathetic and passionate vindication. Never did any martyr suffer so patiently, so patriotically, as these devoted settlers did—a prey to Indian attack,


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390 Rabi-ul-Awal,— Awal, first , — the third month of the Mahomedan year called also Mulud. Rabia, Arabic, the spring, vernal, Crawfurd. This spring could not last long as applicable to the month, as the Mahomedan year retrocedes every year 11 days.

Rabul, coming in numbers, coming tumultuously. Coming frequently. Rabul bai datang, they came in a crowd.

Rabut and Rabutan, to pull up, to pull out; to pluck out of the ground. See Chabut.

Rachĕlék, here and there, scantily. Few and far between.

Rachělok, not even, not alike; where some are long and others short; where some have done and others are still busy.

Rachik, a noose, a running knot. A noose, or string with a running knot set to catch birds or animals, which by stepping into the noose and walking on pull the knot tight about the leg.

Rad, Dutch Raad, council, board of council; the lower court of Justice, called Raad van Justitie. Rad Sambang, the Circuit court. This name is also given to the Circuit Judge.

 * Rada, rather, somewhat. Rada hadé, rather good. Rada panjang, rather long.

Radang, a disease in the skin of man, called in the West Indies the Yaws. In Malay it is called Rarang. Blotches of ulcers break out on various parts of the body, and remain long festering and ulcerating. When of long duration, it affects the bones, which become much weakened, and recovery is then very difficult.

Radén, a title of birth, of descent. Prefixed to a mans name shows him to be of good family. Rada, Clough 585, a king, a sovereign, from Rāja, blood. Rah in Javanese, both in Kawi and in the Basa Krama, means blood, and Hadé, good, and with the addition of the constructive an, we should have Rah-hadé-an, contracted into Rahdén. Or in place of Hadé, it may be Adhi, C. 24, chief, above, and thus Rah-adhi-an = Rahdén, chief or noble blood.

[[wikt:radén adipati|Radén Adipati, title of the prime Minister or Ryksbestierder, ruler of the kingdom, under the Javanese Government.

Radén Adipati, a title of high rank given to some native Regents on Java.

Radén Ayu, a Queen, a Princess; a woman of the highest rank. Ayu, C. 64, age, duration of life. Probably denoting that she is no longer a girl.

Radin, clean, purified, said of women who are washed after child birth. Di radinan, to purify or wash after child birth. Io suka to radin, not with my pleasure, or clean free will; a common expression of dissent.

Ra-éh, to sell on credit. Mĕunchit kěbo di ra-éh bai, having killed a buffaloe, I gave out the flesh on credit, (which is usually done at extravagant prices). Barang di ra-éh, goods on credit.

Ragap, and Ragapan, to lay hold of and feel. To take in the hand to examine. To handle an animal to ascertain the state of its body.

Ragĕdĕd, to tie tight, to secure by tying. Ragĕdĕd bai di bawa, having bound him, they led him away.


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Rh Ogoan, proud, vain, boasting.

Ogong, a largish shell fish resembling the Tulut, found in the rivers of the South coast of Bantam. Ogong bĕurĕum bĕungĕut, Ogong with red face, is another variety.

Ohol, one of the numerous names for a wild pig.

Ojoi, feeling inclined for, disposed to grant or concede. Having an inward disposition towards.

Ojol, to change, to give or take any one thing for another; to swap, to exchange. Ojol kuda, to swap horses. Wang pérak di ojolkĕn, to exchange, or get change for, silver money.

Okol, energetic, doing work by oneself. Persevering without assistance.

Olah, to cook meat or vegetables—not rice.

Olé-oléan, a child's trumpet made of paddy straw, something after the fashion of a clarionette, and blown by sticking one end into the mouth. Called also Ĕmpét-ĕmpétan.

Oliah, Arabic, the most High; Saints. See Aulia.

Olok, using profusely, using without thrift or economy. Squandering away especially either money or household stuff. Said also of other matters.

Olongan, to make love to — as chowéné éta di olongan ku aing, that young maid is courted by me. See Ngolong.

Omar, the second Caliph in Arabia — same as Umar, a common name for a native. (عمر)

Omas, a small variety of rattan, of no particular use.

Ombak, a wave, surf, surge, swell on water.

Ombol, said of planting out paddy on sawahs, where the binih is stuck in by handfulls at a time, and thus carelessly, whereas only four or six stumps ought to be put in at one place.

Omé, to repair, to put in order, to take of; to interfere with, to molest. Ulah di omé d'ontdon't [sic] molest it.

Oméan, to repair, to put in order. Molesting. Imah kudu di oméan, the house must be repaired. Oméan chukang, to repair a bridge. Oméanan tĕuyn, d'ont meddle with it, literally, meddling too much.

Oméanĕun, something which has to be repaired.

Omong, to talk, to converse. Conversation. Omong kosong, empty talk, said of conversation which is only fishing for information; Gĕdé omong, a great talker, a chatter box. (Jav. Batav. idem).

Omongan, to talk over, to persuade by talk.

Ompong, toothless, said when the whole or a great part of the teeth are wanting.

Ondang and Ondangan, to invite to a feast, or any other occasion of ceremony. When a native wants to hold a feast, he either goes himself, or sends a friend to the neighbours or such persons as he wishes to see, and over a quid of sĕurĕuh makes his communication. (Batav. Kondangan, a person called to a feast. Jav. Undang to call, to invite).


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The New International Encyclopædia/Münster, Sebastian

MÜNSTER,, (1489-1552). A German theologian and geographer. He was born at Ingelheim, studied at Heidelberg and Tübingen, and in 1529 left the Catholic Church for the Reformed. He was professor of theology and Hebrew at Heidelberg until 1536, when he became professor of mathematics at Basel. He edited in 1534 the first Hebrew Bible to appear under the care of a German. But his chief work was his Cosmographia (1544), a

which was translated into Italian, French, and Latin, and passed through twenty-four editions in a hundred years.