UC-NRLF B M 527 UNIVERSITY OF CALIFORNIA SAN FRANCISCO LIBRARY The Contemporary Science Series. Edited by Havelock Ellis. Crown %vo, Cloth, y. 6d. per vol. ; Half Morocco, 6s. 6d. I. THE EVOLUTION OF SEX. By Prof. PATRICK GEDDES and J. ARTHUR THOMSON. With 90 Illustrations. Second Edition. " The authors have brought to the task as indeed their names guarantee a wealth of knowledge, a lucid and attractive method of treatment, and a rich vein of picturesque language." Nature. " A work which, for range and grace, mastery of material, originality, and incisiveness of style and treatment, is not readily to be matched in the long list of books designed more or less to popularise science." Scottish Leaier. II. ELECTRICITY IN MODERN LIFE. By G. W. DE TUNZELMANN. With 88 Illustrations. "A clearly- written and connected sketch of what is known about elec- tricity and magnetism, the more prominent modern applications, and the principles on which they are based." Saturday Review. III. THE ORIGIN OF THE ARYANS. By Dr. ISAAC TAYLOR. Illustrated. Second Edition. I' Canon Taylor is probably the most encyclopaedic all-round scholar now living. His new volume on the Origin of the Aryans is a first-rate example of the excellent account to which he can turn his exceptionally wide and varied information. . . . Masterly and exhaustive." Fall Mall Gazette. IV. PHYSIOGNOMY AND EXPRESSION. By P. MANTE- GAZZA. Illustrated. "Brings this highly interesting subject even with the latest researches. . . . Professor Mantegazza is a writer full of life and spirit, and the natural attractiveness of his subject is not destroyed by his scientific handling of it." Literary World ( Boston). V. EVOLUTION AND DISEASE. By J. B. SUTTON, F.R.C.S. With 135 Illustrations. "The work is of special value to professional men, yet educated persons generally will find much in it which it is both interesting and important to know." The Scottish Weekly. VI. THE VILLAGE COMMUNITY. By G. L. GOMME. . Illustrated. " His book will probably remain for some time the best work of reference for facts bearing on those traces of the village community which have not been effaced by conquest, encroachment, and the heavy hand of Roman law. " Scottish Leader. VII. THE CRIMINAL. By HAVELOCK ELLIS. Illustrated. "An ably written, an instructive, and a most entertaining book." Law Quarterly Review. "The sociologist, the philosopher, the philanthropist, the novelist all, indeed, for whom the study of human nature has any attraction will find Mr. Ellis full of interest and suggestiveness." Academy. VIII. SANITY AND INSANITY. By Dr. CHARLES MERCIER. Illustrated " He has laid down the institutes of insanity." Mind. " Taken as a whole, it is the brightest book on the physical side of mental science published in our time." Pall Mall Gazette. IX. HYPNOTISM. By Dr. ALBERT MOLL (Berlin). Second Edition. " Marks a step of some importance in the study of some difficult physio- logical and psychological problems which have not yet received much attention in the scientific world of England." Nature. X. MANUAL TRAINING. By Dr. C M. WOODWARD, Director of the Manual Training School, Washington University, St. Louis, Mo. Illustrated. " There is no greater authority on the subject than Professor Woodward." Manchester Guardian. XI. THE SCIENCE OF FAIRY TALES. By E. SIDNEY HARTLAND. " Mr. Hartland's book will win the sympathy of all earnest students, both by the knowledge it displays, and by a thorough love and appreciation of his subject, which is evident throughout." Spectator. XII. PRIMITIVE FOLK. By ELIE RECLUS. "An attractive and useful introduction to the study of some aspects of ethnograpy. " Nature. " For an introduction to the study of the questions of property, marriage, government, religion, in a word, to the evolution of society, this little volume will be found most convenient." Scottish Leader. XIII. THE EVOLUTION OF MARRIAGE. By Professor LETOURNEAU. "Among the distinguished French students of sociology, Professor Letour- neau has long stood in the first rank. He approaches the great study of man free from bias and shy of generalisations. To collect, scrutinise, and appraise facts is his chief business. In the volume before us he shows these qualities in an admirable degree. ... At the close of his attractive pages he ventures to forecast the future of the institution of marriage." Science. XIV. BACTERIA AND THEIR PRODUCTS. By Dr. G. SIMS WOODHEAD. Illustrated. "An excellent summary of the present state of knowledge of the subject." Lancet. XV. EDUCATION AND HEREDITY. By J. M. GUYAU. " It is a sign of the value of this book that the natural impulse on arriving at its last page is to turn again to the first, and try to gather up and co- ordinate some of the many admirable truths it presents." Anti-Jacobin. XVI. THE MAN OF GENIUS. By Prof. LOMBROSO. Illus- trated. " By far the most comprehensive and fascinating collection of facts and generalizations concerning genius which has yet been brought together." -Journal of Mental Science. London : WALTER SCOTT, 24 Warwick Lane, Paternoster Row. THE CONTEMPORARY SCIENCE SERIES. EDITED BY HAVELOCK ELLIS. THE GRAMMAR OF SCIENCE. THE GRAMMAR OF SCIENCE. BY KARL VPEARSON, M.A., Sir Thomas Greshatris Professor of Geometry, "La critique est la vie de la science." COUSIN, Q.MS WITH 25 FIGURES IN THE TEXT. LONDON: WALTER SCOTT, 24, WARWICK LANE, PATERNOSTER ROW, 1892. 911 M - . L! JL THE MEMORY OF SIR THOMAS GRESHAM, KNIGHT, WHILOM MERCHANT OF THE CITY OF LONDON. PREFACE. THERE are periods in the growth of science when it is well to turn our attention from its imposing superstructure and to carefullyexamine its foundations. The present book is primarily intended as a criticism of the fundamental concepts of modern science, and as such finds its justification in the motto placed upon its title-page. At the same time the author is so fully conscious of the ease of criticism and the difficulty of reconstruction, that he has attempted not to stop short at the lighter task. No one who knows the author's views, or who reads, indeed, this book, will believe that he holds the labour of the great scientists or the mission of modern science to be of small account. If the reader finds the opinions of physicists of world- wide reputation, and the current definitions of physical concepts called into question, he must not attribute this to a purely sceptical spirit in the author. He accepts almost without reserve the great results of modern physics ; it is the language in which these results are stated that he believes needs reconsider- ation. This reconsideration is the more urgent be- viii PREFACE. cause the language of physics is widely used in all branches of biological (including sociological) science. The obscurity which envelops the principia of science is not only due to an historical evolution marked by the authority of great names, but to the fact that science, as long as it had to carry on a difficult warfare with metaphysics arid dogma, like a skilful general conceived it best to hide its own deficient organiza- tion. There can be small doubt, however, that this deficient organization will not only in time be per- ceived by the enemy, but that it has already had a very discouraging influence both on scientific recruits and on intelligent laymen. ^Anything more hopelessly illogical than the statements with regard to force and matter current in elementary text-books of science, it is difficult to imagine ; and the author, as a result of some ten years' teaching and examining, has been forced to the conclusion that these works possess little, if any, educational value ; they do not encourage the growth of logical clearness or form any exercise in scientific method. One result of this obscurity we probably find in the ease with which the physicist, as compared with either the pure mathematician or the historian, is entangled in the meshes of such pseudo- sciences as natural theology and spiritualism. If the constructive portion of this work appears to the reader unnecessarily dogmatic or polemical, the author would beg him to remember that it is essentially intended to arouse and stimulate the reader's own thought, rather than to inculcate doctrine : this result is often best achieved by the assertion and contradiction which excite the reader to indepen- dent inquiry. The views expressed in this Grammar on the fun- PREFACE. IX damental concepts of science, especially on those of force and matter, have formed part of the author's teaching since he was first called upon to think how the elements of dynamical science could be presented free from metaphysics to young students. But the endeavour to put them into popular language only dates from the author's appointment last year to Sir Thomas Gresham's professorship in geometry. The substance of this work formed the topic of two intro- ductory courses on the Scope and Concepts of Modern Science. Gresham College is but the veriest shred of what its founder hoped and dreamt it would become a great teaching university for London but the author in writing this volume, whatever its failings, feels that so far as in him lies he is endeavouring to return to the precedent set by the earliest and most distinguished of his predecessors in the chair of geo- metry. To restore the chair and the college to its pristine importance is work worth doing, but it lies in other hands. This Grammar of Science, imperfect as it is, would have been still more wanting but for the continual help and sympathy of several kind friends. Mr. W. H. Macaulay, of King's College, Cambridge, has given aid in many ways, ever trying to keep the author's scientific radicalism within moderate and reasonable bounds. To his friend, Mr. R. J. Parker, of Lincoln's Inn, the author is indebted for a continuation of that careful and suggestive revision which he has for the last ten years given to nearly everything the author has written. Especially, however, his thanks are due to Dr. R. J. Ryle, of Barnet, whose logical mind and wide historical reading have produced a " betterment," which gives him almost a tenant-right in these pages. X PREFACE. Lastly, the author has to thank his friend and former pupil, Miss Alice Lee, Demonstrator in Physics at Bedford College, London, for the preparation of the index and for several important corrections. KARL PEARSON. GRESHAM COLLEGE, LONDON. January, 1892. CONTENTS. CHAPTER I. INTRODUCTORY. PAGE I. Science and the Present . . . . .1 2. Science and Citizenship .... 7 3. The First Claim of Science . . . .10 4. Essentials of Good Science . . . . n 5. The Scope of Science . . . . .14 6. Science and Metaphysics . . . . 18 7. The Ignorance of Science . . . . . 23 8. The Wide Domain of Science ... 29 9. The Second Claim of Science . . . .31 io. The Third Claim of Science .... 35 II. Science and the Imagination . . . . 36 12. The Method of Science Illustrated ... 39 13. Science and the ./Esthetic Judgment . . .42 14. The Fourth Claim of Science ... 44 Summary and Literature . . . ; 45 CHAPTER II. THE FACTS OF SCIENCE. I. The Reality of Things . . . . .47 2. Sense-Impressions and Consciousness ... 50 3. The Brain as a Central Telephone Exchange . . 53 4. The Nature of Thought . . . . 55 5. Other-Consciousness as an Eject . . . 59 6. Attitude of Science towards Ejects . . . 61 7. The Scientific Validity of a Conception . . .64 8. The Scientific Validity of an Inference . . 67 9. The Limits to Other-Consciousness . . .69 xil CONTENTS. 10. The Canons of Legitimate Inference . . . 71 n. The External Universe . . . . 73 12. Outside and Inside Myself .... 77 13. Sensations as the Ultimate Source of the Materials of Knowledge ...... 80 14. Shadow and Reality . . . . .83 15. Individuality ...... 86 16. The Futility of " Things-in-Themselves " . .87 17- The Term Knowledge is meaningless if applied to Unthinkable Things . . . . .89 Summary and Literature .... 90-1 CHAPTER III. THE SCIENTIFIC LAW. I. Foreword and Resume . . . . .92 2. Of the Word Law and its Meanings . . 94 3. Natural Law Relative to Man . . . 99 4. Man as the Maker of Natural Law . . . 102 5. The Two Senses of the Words " Natural Law " . 104 6. Confusion between the Two Senses of Natural Law 106 7. The Reason behind Nature . . . .109 8. True Relation of Civil and Natural Law . . in 9. Physical and Metaphysical Supersensuousness . .114 10. Progress in the Formulating of Natural Law . 116 n. The Universality of Scientific Law . . . 120 12. The Routine of Perceptions as possibly a Product of the Perceptive Faculty . . . . .122 13. The Mind as a Sorting-Machine . . . 128 14. Science, Natural Theology, and Metaphysics . .129 15. Conclusions . . . . . 13* Summary and Literature . . . . . 135 CHAPTER IV. CAUSE AND EFFECT. PROBABILITY. I. Mechanism ' . . J 3^ 2. Force as a Cause . . .140 3 ._Will as a Cause . 143 4. Secondary Causes Involve no Enforcement . 144 5. Is Will a First Cause? . . 147 6. Will as a Secondary Cause . . . .148 CONTENTS. xiil PAGE 7. First Causes have no Existence for Science . . 151 8. Cause and Effect as the Routine of Experience . 153 9. Width of the Term Cause . . .156 10. The Universe of Sense-Impressions as a Universe of Motions. ...... 157 ii. Necessity belongs to the World of Conceptions, not to that of Perceptions .... .160 12. Routine in Perception is a Necessary Condition of Knowledge . . . . . 162 13. Probable and Provable ..... 166 14. Probability as to Breaches in the Routine of Perceptions 170 15. The Basis of Laplace's Theory in an Experience of Ignorance ...... 171 16. Nature of Laplace's Investigations . . .176 17. The Permanency of Routine for the Future . . 177 Summary and. Literature .... 180 CHAPTER V. SPACE AND TIME. i. Space as a Mode of Perception . . . .181 2. The Infinite Bigness of Space . . . 187 3. The Infinite Divisibility of Space . . .190 4. The Space of Memoiy and Thought . . . 193 5. Conceptions and Perceptions .... 196 6. Sameness and Continuity .... 200 7. Conceptual Space, Geometrical Boundaries . . 203 8. Surfaces as Boundaries .... 206 9. Conceptual Discontinuity of Bodies. The Atom . 208 10. Conceptual Continuity. Ether . . . 213 n. On the General Nature of Scientific Conceptions . 214 12. Time as a Mode of Perception . . . 217 13. Conceptual Time and its Measurement . . . 222 14. Concluding Remarks on Space and Time . . 228 Summary and Literature ..... 229 CHAPTER VI. THE GEOMETRY OF MOTION. i. Motion as the Mixed Mode of Perception . .231 2. Conceptual Analysis of a Case of Perceptual Motion. Point-Motion . . . . . . 233 XIV CONTENTS. PAGE 3. Rigid Bodies as Geometrical Ideals . . . 237 4. On Change of Aspect, or Rotation . . . 239 5. On Change of Form, or Strain . . . 242 6. Factors of Conceptual Motion .... 246 7. Point-Motion. Relative Character of Position and Motion ....... 247 8. Position. The Map of the Path ... 250 9. The Time-Chart . . . . . .253 10. Steepness and Slope ..... 257 ii. Speed as a Slope. Velocity .... 260 12. The Velocity Diagram, or Hodograph. Acceleration 262 13. Acceleration as a Spurt and a Shunt . . . 265 14. Curvature ...... 268 15. The Relation between Curvature and Normal Acceleration 273 16. Fundamental Propositions in the Geometry of Motion . 276 17. The Relativity of Motion. Its Synthesis from Simple Components ...... 279 Summary and Literature ... * 284 CHAPTER VII. MATTER. i. "All Things Move" but only in Conception. . . 285 2. The Three Problems ..... 288 3. How the Physicists define Matter . . .291 4. Does Matter occupy Space? .... 296 5. The "Common-sense" View of Matter Impenetrable and Hard ...... 301 6. Individuality does not denote Sameness in Substratum 303 7. Hardness not characteristic of Matter . . 308 8. Matter as Non-Matter in Motion .... 310 9. The Ether as "Perfect Fluid" and "Perfect Jelly" 313 IO. The Vortex-Ring Atom and the Ether-Squirt Atom . 316 ii. A Material Loophole into the Supersensuous . 319 12. The Difficulties of a Perceptual Ether . . . 323 13. Why do Bodies move? .... 325 Summary and Literature ..... 330 CHAPTER VIII. THE LAWS OF MOTION. I. Corpuscles and their Structure . 332 2. The Limits to Mechanism . . . . 337 CONTENTS. XV PAGE 3. The First Law of Motion .... 340 4. The Second Law of Motion, or the Principle of Inertia 342 5. The Third Law of Motion. Acceleration is determined by Position ...... 345 6. Velocity as an Epitome of Past History. Mechanism and Materialism . . . . . 351 7. The Fourth Law of Motion . . . . 354 8. The Scientific Conception of Mass . . . 357 9. The Fifth Law of Motion. The Definition of Force 359 10. Equality of Masses tested by Weighing . . . 363 il. : How far does the Mechanism of the Fourth and Fifth Laws of Motion extend ? 367 12. Density as the Basis of the Kinetic Scale . . 370 13. The Influence of Aspect on the Corpuscular Dance . 374 14. The Hypothesis of Modified Action and the Synthesis of Motion ...... 376 15. Criticism of the Newtonian Laws of Motion . 380 Summary and Literature .... 386 CHAPTER IX. LIFE. i. The Relation of Biology to Physics . . .388 2. Mechanism and Life ..... 392 3. Mechanism and Metaphysics in Theories of Heredity . 395 4. The Definition of Living and Lifeless . . 400 5. Do the Laws of Motion apply to Life ? . . . 404 6. Life Defined by Secondary Characteristics . . 408 7. The Origin of Life ..... 410 8. The Perpetuity of Life, or Biogenesis . . 411 9. The Spontaneous Generation of Life, or Abiogenesis . 413 10. The Origin of Life in an "ultra-scientific" Cause . 417 ii. On the Relation of the Conceptual Description to the Phenomenal World ..... 420 12. Natural Selection in the Inorganic World . . 422 13. Natural Selection and the History of Man . . 425 14. Primitive History describable in terms of the Principles of Evolution ...... 428 15. Morality and Natural Selection . . . 430 16. Individualism, Socialism, and Humanism . . 434 Summary and Literature .... 439 xvi CONTENTS. CHAPTER X. THE CLASSIFICATION OF THE SCIENCES. PAGE I. Summary as to the Material of Science . . . 441 2. Bacon's " Intellectual Globe "... 443 3. Comte's "Hierarchy" . . . . .446 4. Spencer's Classification .... 448 5. Precise and Synoptic Sciences .... 452 6. Abstract and Concrete Sciences. Abstract Science . 454 7. Concrete Science. Inorganic Phenomena . . 459 8. Concrete Science. Organic Phenomena . . 465 9. Applied Mathematics and Bio-Physics as Cross Links . 469 10. Conclusion . . . . . .471 Summary and Literature ..... 475 APPENDIX. Note I. On the Principle of Inertia and Absolute Rotation . 477 Note II. On Newton's Third Law of Motion . . 480 Note III. William of Occam's Razor . . . .481 Note IV. On the Vitality of Seeds .... 482 Note V. A. R. Wallace on Matter . . . .483 Note VI. On the Sufficiency of Natural Selection to account for the History of Civilized Man . . . 484 INDEX. THE GRAMMAR OF SCIENCE. CHAPTER 1. INTRODUCTORY. THE SCOPE AND METHOD OF SCIENCE. i. Science and the Present. WITHIN the past forty years so revolutionary a change has taken place in our appreciation of the essential facts in the growth of human society, that it has become necessary not only to rewrite history, but to profoundly modify our theory of life and gradually, but none the less certainly, to adapt our conduct to the novel theory. The insight which the investigations of Darwin, seconded by the sugges- tive but far less permanent work of Spencer, have given us into the development of both individual and social life, has compelled us to remodel our historical ideas and is slowly widening and consoli- dating our moral standards. The slowness ought not to dishearten us, for one of the strongest factors of social stability is the inertness, nay, rather active hostility, with which human societies receive all new ideas. It is the crucible in which the dross is separated from the genuine metal, and which saves the body- social from a succession of unprofitable and possibly 2 2 THE GRAMMAR OF SCIENCE. injurious experimental variations. That the reformer should be also the martyr is, perhaps, a not over-great price to pay for the caution with which society as a whole must move ; to replace an individual man may require years, but a stable and efficient society is the outcome of centuries of development. If we have learnt, indirectly it may be, from the writings of Darwin that the means of production, the holding of property, the forms of marriage, and the organization of the family are the essential factors which the historian has to trace in the growth of Human society ; if in our history books we are ceasing to head periods with the names of monarchs and to devote whole paragraphs to their mistresses, still we are far indeed from clearly grasping the exact inter- action of the various factors of social evolution, or understanding why one becomes predominant at one or another epoch. We can indeed mark periods of great social activity and others of apparent quiescence, but it is probably only our ignorance of the exact stages of social evolution, which leads us to associate the fundamental variations in social institutions with re- formations and revolutions. We associate, it is true, the German Reformation with a replacement of collectivist by individualist standards, not only in religion but also in handicraft, art, and politics. The French Revolution in like manner is the epoch from which many are inclined to date the rebirth of those social ideas which have largely remoulded the mediaeval relations of class and caste, relations little affected by the sixteenth-century Reformation. Coming nearer to our own time indeed we can measure with some degree of accuracy the social influence of the great changes in the method of production, the INTRODUCTORY. 3 transition from home to capitalistic production, which transformed English life in the first half of this century, and has since made its way throughout the civilized world. But when we come to our own age, an age one of the most marked features of which is the startlingly rapid growth of the natural sciences and their far-reaching influence on the standards of both the comfort and conduct of human life, we find it impossible to compress its social history into the bald phrases by which we attempt to connote the characteristics of more distant historical epochs. It is very difficult for us who live in the last quarter of the nineteenth century to rightly measure the relative importance of our age in the history of civilization. In the first place we can look at it only from one standpoint that of the past. It needed at least an Erasmus to predict the outcome of the Reformation from all that preceded the Diet of Worms. Or, to adopt a metaphor, a blind man climbing a hill might have a considerable appreciation of the various degrees of steepness in the parts he had traversed, and he might even have a reasonable amount of certainty as to the slope whereon he was standing for the time being, but whether that slope led immediately to a steeper ascent, or was practically the top, it would be impossible for him to say. In the next place we are too close to our age, both in position and feeling, to appreciate without foreshortening and per- sonal prejudice the magnitude of the changes which are undoubtedly taking place. The contest of opinion in nearly every field of thought the struggle of old and new standards in every sphere of activity, in religion, in commerce, in social life touch the spiritual and physical needs of 4 THE GRAMMAR OF SCIENCE the individual far too nearly for us to be dispassionate judges of the age in which we live. That we live in an era of rapid social variation can scarcely be doubted by any one who regards attentively the marked contrasts presented by our modern society. It is an era alike of great self-assertion and of exces- sive altruism ; we see the highest intellectual power accompanied by the strangest recrudescence of super- stition ; there is a strong socialist drift and yet not a few remarkable individualist teachers ; the extremes of religious faith and of unequivocal freethought are found jostling each other. Nor do these opposing traits exist only in close social juxtaposition. The same individual mind, unconscious of its own want of logical consistency, will often exhibit our age in microcosm. It is little wonder that we have hitherto made small way towards a common estimate of what our time is really contributing to the history of human progress. The one man finds in our time a restlessness, a distrust of authority, a questioning of the basis of all social institutions and long-established methods characteristics which mark for him a decadence of social unity, a collapse of the only principles which he conceives capable of guiding conduct. The other with a different temperament pictures for us a golden age in the near future, when the new knowledge shall be diffused through the people, and when the new view of human relations, which he finds everywhere taking root, shall finally have supplanted worn-out customs. One teacher propounds what is flatly contradicted by a second. " We want more piety," cries one ; " We must have less," retorts another. u State inter- INTRODUCTORY. 5 ference in the hours of labour is absolutely needful," declares a third ; " It will destroy all individual initia- tion and self-dependence," rejoins a fourth. "The salvation of the country depends upon the technical education of its workpeople," is the shout of one party ; " Technical education is merely a trick by which the employer of labour thrusts upon the nation the expense of providing himself with better human machines," is the prompt answer of its opponents. " We need more private chanty," say some ; " All private charity is an anomaly, a waste of the nation's resources and a pauperizing of its members," reply others. " Endow scientific research and we shall know the truth, when and where it is possible to ascertain it ; " but the counterblast is at hand : " To endow research is merely to encourage the research for endowment ; the true man of science will not be held back by poverty, and if science is of use to us, it will pay for itself." Such are but a few samples of the conflict of opinion which we find raging around us. The prick of conscience and the prick of poverty have succeeded in arousing a wonderful restlessness in our generation and this at a time when the advance of positive knowledge has called in question many of the old customs and old authorities. It is true that there are but few remedies which have not a fair chance to-day of being put upon their trial. Vast sums of money are raised for every sort of charitable scheme, for popular entertainment, for technical instruction, and even for higher education in short, for religious, semi-religious, and anti-religious move- ments of all types. Out of this chaos ought at least to come some good ; but how shall we set the good against the evil which too often arises from ill-defined, 6 THE GRAMMAR OF SCIENCE. or even undefined, appropriation of those resources which the nation has spared by the hard labour of the past, or is drawing on the future's credit ? The responsibility of individuals, especially with regard to wealth, is great, so great that we see a growing tendency of the state to interfere in the administration of private charities and to regulate the great educa- tional institutions endowed by private or semi-public benefactions in the past. But this tendency to throw back the responsibility from the individual upon the state is really only throwing it back on the social conscience of the citizens as a body the " tribal conscience," as Professor Clifford was wont to call it The wide extension of the franchise in both local and central representation has cast a greatly increased responsibility on the individual citizen. He is brought face to face with the most conflicting opinions and with the most diverse party cries. The state has become in our day the largest employer of labour, the greatest dispenser of charity, and, above all, the school- master with the biggest school in the community. Directly or indirectly the individual citizen has to find some reply to the innumerable social and educational problems of the day. He requires some guide in the determination of his own action or in the choice of fitting representatives. He is thrust into an appalling maze of social and educational problems ; and if his tribal conscience has any stuff in it, he feels that these problems ought not to be settled, so far as he has the power of settling them, by his own personal interests, by his individual prospects of profit or loss. He is called upon to form a judgment apart from his own feelings and emotions if it possibly may be a judgment in what he conceives to be the interests of INTRODUCTORY. 7 society at large. It may be a difficult thing for the large employer of labour to form a right judgment in matters of factory legislation, or for the private school- master to see clearly in questions of state-aided education. None the less we should probably all agree that the tribal conscience ought for the sake of social welfare to be stronger than private interest, and that the ideal citizen, if he existed, would form a judgment free from personal bias. 2. Science and Citize?iship. How is such a judgment so necessary in our time with its hot conflict of personal opinion and its in- creased responsibility for the individual citizen how is such a judgment to be formed ? In the first place it is obvious that it can only be based on a clear knowledge of facts, an appreciation of their sequence and relative significance. The facts once classified, once understood, the judgment based upon them ought to be independent of the individual mind which examines them. Is there any other sphere, outside that of ideal citizenship, in which there is habitual use of this method of classifying facts and forming judgments upon them ? For if there be, it cannot fail to be suggestive as to methods of elimi- nating individual bias ; it ought to be one of the best training grounds for citizenship. The classifica- tion of facts and the formation of absolute judgments upon the basis of this classification judgments in- dependent of the idiosyncrasies of the individual mind is peculiarly the scope and metJiod of modern science. The scientific man has above all things to aim at self-elimination in his judgments, to provide an argument which is as true for each individual 8 THE GRAMMAR OF SCIENCE. mind as for his own. The classification of facts, the recognition of their sequence and relative significance is the function of science, and the habit of forming a judgment upon these facts unbiased by personal feeling is characteristic of what we shall term the scientific frame of mind. The scientific method of examining facts is not peculiar to one class of phenomena and to one class of workers ; it is applicable to social as well as to physical problems, and we must carefully guard ourselves against sup- posing that the scientific frame of mind is a peculiarity of the professional scientist. Now this frame of mind seems to me an essential of good citizenship, and of the several ways in which it can be acquired few surpass the careful study of some one branch of natural science. The insight into method and the habit of dispassionate investigation which follow from acquaintance with the scientific classification of even some small range of natural facts, give the mind an invaluable power of dealing with many other classes of facts as the occasion arises. 1 The patient and persistent study of some one branch of natural science is even at the present time within the reach of many. In some branches a few hours' study a week, if carried on earnestly for 1 To decry specialization in education is to misinterpret the purpose of education. The true aim of the teacher must be to impart an appreciation of method and not a knowledge of facts. This is far more readily achieved by concentrating the student's attention on a small range of phenomena, than by leading him in rapid and superficial survey over wide fields of knowledge. Personally I have no recollection of at least 90 per cent, of the facts that were taught to me at school, but the notions of method which I derived from my instructor in Greek Grammar (the contents of which I have long forgotten), remained in my mind as the really valuable part of my school equipment for life. INTRODUCTORY. 9 two or three years, would be not only sufficient to give a thorough insight into scientific method, but would also enable the student to become a careful observer and possibly an original investigator in his chosen field, thus adding a new delight and a new enthusiasm to his life. The importance of a just appreciation of scientific method is so great, that I think the state may be reasonably called upon to place instruction in pure science within the reach of all its citizens. Indeed, we ought to look with extreme distrust on the large expenditure of public money on polytechnics and similar institutions, if the manual instruction which it is proposed to give at these places be not accompanied by efficient teaching in pure science. The scientific habit of mind is one which may be acquired by all, and the readiest means of attaining to it ought to be placed within the reach of all. The reader must be careful to note that I am only praising the scientific habit of mind, and suggesting one of several methods by which it may be cultivated, No assertion has been made that the man of science is necessarily a good citizen, or that his judgment upon social or political questions will certainly be of weight. It by no means follows that, because a man has won a name for himself in the field oi natural science, his judgments on such problems as Socialism, Home Rule, or Biblical Theology will necessarily be sound. They will be sound or not according as he has carried his scientific method into these fields. He must properly have classified and appreciated his facts, and have been guided by them, and not by personal feeling or class bias in his judgments. It is the scientific habit of mind as an 16 THE GRAMMAR OF SCIENCE. essential for good citizenship and not the scientist as a sound politician that I wish to emphasize. 3. The First Claim of Modern Science. We have gone a rather roundabout way to reach our definition of science and scientific method. But it has been of purpose, for in the spirit and it is a healthy spirit of our age we have accustomed our- selves to question all things and to demand a reason for their existence. The sole reason that can be given for any social institution or form of human activity I mean not how they came to exist, which is a matter of history, but why we continue to encourage their existence lies in this : their existence tends to promote the welfare of human society, to increase social happiness, or to strengthen social stability. In the spirit of our age we are bound to question the value of science ; to ask in what way it increases the happiness of mankind or promotes social efficiency. We must justify the existence of modern science, or at least the large and growing demands which it makes upon the national exchequer. Apart from the increased physical comfort, apart from the intellectual enjoyment which modern science provides for the community points often and loudly insisted upon and to which I shall briefly refer later there is another and more fundamental justification for the time and material spent in scientific work. From the standpoint of morality, or from the relation of the individual unit to other members of the same social group, we have to judge each human activity by its outcome in conduct. How, then, does science justify itself in its influence on the conduct of men as citizens? I assert that the encouragement of INTRODUCTORY. 11 scientific investigation and the spread of scientific knowledge by largely inculcating scientific habits of mind will lead to more efficient citizenship and so to increased social stability. Minds trained to scientific methods are less likely to be led by mere appeal to the passions, by blind emotional excitement to sanction acts which in the end may lead to social disaster. In the first and foremost place, therefore, I lay stress upon the educational side of modern science, and state my proposition in some such words as these : Modern Science^ as training the mind to an exact and impartial analysis of facts is an edit cation specially fitted to promote sound citizenship. Our first conclusion, then, as to the value of science for practical life turns upon the efficient training it provides in method. The man who has accustomed himself to marshal facts, to examine their complex mutual relations, and predict upon the result of this examination their inevitable sequences sequences which we term natural laws and which are as valid for every normal mind as for that of the individual investigator such a man we may hope will carry his scientific method into the field of social problems. He will scarcely be content with mere superficial state- ment, with mere appeal to the imagination, to the emotions, to individual prejudices. He will demand a high standard of reasoning, a clear insight into facts and their results, and his demand cannot fail to be beneficial to the community at large. 4. Essentials of Good Science. I want the reader to appreciate clearly that science justifies itself in its methods, quite apart from any 12 THE GRAMMAR OF SCIENCE. serviceable knowledge it may convey. We are too apt to forget this purely educational side of science in the great value of its practical applications. We see too often the plea raised for science that it is useful knowledge, while grammar and philosophy are supposed to have small utilitarian or commercial value. Science, indeed, often teaches us facts of primary importance for practical life ; yet not on this account, but because it leads us to classifications and systems independent of the individual thinker, to sequences and laws admitting of no play-room for individual fancy, must we rate the training of science and its social value higher than those of grammar and philosophy. Herein lies the first, but of course not the sole, ground for the popularization of science. That form of popular science which merely recites the results of investigations, which merely communicates useful knowledge, is from this standpoint bad science, or no science at all. Let me recommend the reader to apply this test to every work professing to give a popular account of any branch of science. If any such work gives a description of phenomena that appeals to his ima- gination rather than to his reason, then it is bad science. The first aim of any genuine work of science, however popular, ought to be the presentation of such a classification of facts that the reader's mind is irresistibly led to acknowledge a logical sequence a law which appeals to the reason before it captivates the imagination. Let us be quite sure that whenever we come across a conclusion in a scientific work which does not flow from the classifi- cation of facts, or which is not directly stated by the author to be an assumption, then we are dealing with INTRODUCTORY. 13 bad science. Good science will always be intelligible to the logically trained mind, if that mind can read and translate the language in which science is written. The scientific method is one and the same in all branches, and that method is the method of all logically trained minds. In this respect the great classics of science are often the most intelligible of books, and if so, are far better worth reading than popularizations of them written by men with less insight into scientific method. Works like Darwin's Origin of Species and Descent of Man, Lyell's Principles of Geology, Helmholtz's Sensations of Tone, or Weismann's Essays on Heredity, can be profitably read and largely understood by those who are not specially trained in the several branches of science with which these works deal. 1 It may need some patience in the interpretation of scientific terms, in learning the language of science, but like most cases in which a new language has to be learnt, the com- parison of passages in which the same word or term recurs, will soon lead to a just appreciation of its true meaning. In the matter of language the de- scriptive natural sciences such as geology or biology are more easily accessible to the layman than the exact sciences such as algebra or mechanics, where the reasoning process must often be clothed in mathematical symbols, the right interpretation of which may require months, if not years, of study. To this distinction between the descriptive and exact sciences I propose to return later, when we are deal- ing with the classification of the sciences. 1 The list might be easily increased, for example by W. Harvey's Anatomical Dissertation on the Motion of the Heart and Blood, and by Faraday's Experimental Researches. 14 THE GRAMMAR OF SCIENCE. I would not have the reader suppose that the mere perusal of some standard scientific work will, in my opinion, produce a scientific habit of mind. I only suggest that it will give some insight into scientific method and some appreciation of its value. Those who can devote persistently some four or five hours a week to the conscientious study of any one limited branch of science will achieve in the space of a year or two much more than this. The busy layman is not bound to seek about for some branch which will give him useful facts for his profession or occupation in life. It does not indeed matter for the purpose we have now in view whether he seek to make himself proficient in geology, or biology, or geometry, or mechanics, or even history or folklore, if these be studied scientifically. What is necessary is the thorough knowledge of some small group of facts, the recognition of their relationship to each other, and of the formulae or laws which express scientifically their sequences. It is in this manner that the mind becomes imbued with the scientific method and freed from individual bias in the formation of its judg- ments one of the conditions, as we have seen, for ideally good citizenship. This first claim of scientific training, its education in method, is to my mind the most powerful claim it has to state support. I believe more will be achieved by placing instruction in pure science within the reach of all our citizens, than by any number of polytechnics devoting themselves to technical education, which does not rise above the level of manual instruction. 5. The Scope of Science. The reader may, perhaps, feel that I am laying all INTRODUCTORY. 1 5 stress upon method at the expense of solid contents. Now this is the peculiarity of scientific method, that when once it has become a habit of mind, that mind converts all facts whatsoever into science. The field of science is unlimited ; its solid contents are endless, every group of natural phenomena, every phase of social life, every stage of past or present development is material for science. The unity of all science con- sists alone in its method, not in its material The man who classifies facts of any kind whatever, who sees their mutual relation and describes their sequence, is applying the scientific method and is a man of science. The facts may belong to the past history of mankind, to the social statistics of our great cities, to the atmosphere of the most distant stars, to the digestive organs of a worm, or to the life of a scarcely visible bacillus. It is not the facts themselves which form science, but the method in which they are dealt with. The material of science is coextensive with the whole physical universe, not only that universe as it now exists, but with its past history and the past history of all life therein. When every fact, every present or past phenomenon of that universe, every phase of present or past life therein, has been examined, classified, and co-ordinated with the rest, then the mission of science will be completed. What is this but saying that the task of science can never end till man ceases to be, till history is no longer made, and development itself ceases ? It might be supposed that science has made such strides in the last two centuries, and notably in the last fifty years, that we might look forward to a day when its work would be practically ac- complished. At the beginning of this century it 16 THE GRAMMAR OF SCIENCE. was possible for an Alexander von Humboldt to take a survey of the entire domain of then extant science. Such a survey would be impossible for any scientist now, even if gifted with more than Humboldt's powers. Scarcely any specialist of to- day is really master of all the work which has been done in his own comparatively small field. Facts and their classification have been accumulating at such a rate, that nobody seems to have leisure to recognize the relations of sub-groups to the whole. It is as if both in Europe and America individual workers were bringing their stones to one great building and piling them on and fastening them down without regard to any general plan or to their individual neighbour's work; only where some one has placed a great corner-stone, is it regarded, and the building then rises on this firmer foundation more rapidly than at other points, till it reaches a height at which it is stopped for want of side support. Yet this great structure, the proportions of which are beyond the ken of any individual man, possesses a symmetry and unity of its own, notwithstanding its haphazard mode of construction. This symmetry and unity lies in scientific method. The smallest group of facts, if properly classified and logically dealt with, will form a stone which has its proper place in the great building of knowledge, wholly independent of the individual workman who has shaped it. Even when two men work unwittingly at the same stone they will but modify and correct each other's angles. In the face of all this enormous progress of modern science, when in all civilized lands men are applying the scientific method to natural, historical, and mental facts, we have yet to admit that the goal of science is and must be infinitely distant. INTRODUCTORY. 17 Here, too, we may note that when from a sufficient if partial classification of facts a simple principle has been discovered which describes the relationship and sequences of the group, then this principle or law itself generally leads to the discovery of a still wider range' of hitherto unregarded phenomena in the same or associated fields. Every great advance of science opens our eyes to facts which we had failed before to observe, and makes new demands on our powers of interpretation. This extension of the material of science into regions where our great-grandfathers could see nothing at all, or where they would have declared human knowledge impossible, is one of the most remarkable features of modern progress. Where they interpreted the motion of the planets of our own system, we discuss the chemical constitution of stars, many of which did not exist for them, for their telescopes could not reach them. Where they dis- covered the circulation of the blood, we see the physical conflict of living poisons within the blood, whose battles would have been absurdities for them. Where they found void and probably demonstrated to their own satisfaction that there was void, we conceive great systems in rapid motion capable of carrying energy through brick walls as light passes through glass. Great as the advance of scientific knowledge has been, it has not been greater than the growth of the material to be dealt with. The goal of science is clear it is nothing short of the complete interpre- tation of the universe. But the goal is an ideal one it marks the direction in which we move and strive, but never the point we shall actually reach. 1 8 THE GRAMMAR OF SCIENCE. 6. Science and Metaphysics. Now I want to draw the reader's attention to two results which flow from the above considerations, namely : that the material of science is coextensive with the whole life, physical and mental, of the universe, and furthermore that the limits to our perception of the universe are only apparent, not real. It is no exaggeration to say that the universe was not the same for our great-grandfathers as it is for us, and that in all probability it will be utterly different for our great-grandchildren. The universe is a variable quantity, which depends upon the keenness and struc- ture of our organs of sense, and upon the fineness of our powers and instruments of observation. We shall see more clearly the important bearing of this latter remark when we come to discuss more closely in another chapter how the universe is largely the construction of each individual mind. For the present we must briefly consider the former remark, which defines the unlimited scope of science. To say that there are certain fields for example metaphysics from which science is excluded, wherein its methods have no application, is merely to say that the rules of methodical observation and the laws of logical thought do not apply to the facts, if any, which lie within such fields. These fields, if indeed such exist, must lie outside any intelligible definition which can be given of the word knowledge. If there are facts, and sequences to be observed among those facts, then we have all the requisites of scientific classification and knowledge. If there are no facts, or no sequences to be observed among them, then the possibility of all knowledge disappears. The greatest assumption of everyday life the inference which the meta- INTRODUCTORY. 19 physicians tell us is wholly beyond science namely, that other beings have consciousness as well as ourselves, seems to have just as much or as little scientific validity as the statement that an earth-grown apple would fall to the ground if carried to the planet of another star. Both are beyond the range of ex- \ perimental demonstration, but to assume uniformity in : the characteristics of brain 'matter' under certain condi- tions seems as scientific as to assume uniformity in the characteristics of stellar * matter.' Both are only work- ing hypotheses and valuable in so far as they simplify our description of the universe. Yet the distinction between science and metaphysics is often insisted upon, and not unadvisedly, by the devotees of both. If we take any group of physical or biological facts say, for example, electrical phenomena or the develop- ment of the ovum we shall find that, though phy- sicists or biologists may differ to some extent in their measurements or in their hypotheses, yet in the fundamental principles and sequences the professors of each individual science are in practical agreement among themselves. A similar if not. yet so complete agreement is rapidly springing up in both mental and social science, where the facts are more difficult to classify and the bias of individual opinion is much stronger. Our more thorough classification, however, of the facts of human development, our more accurate knowledge of the early history of human societies, of primitive customs, laws, and religions, our application of the principle of natural selection to man and his communities, are converting anthropology, folklore, sociology, and psychology into true sciences. We begin to see indisputable sequences in groups of both mental and social facts, The causes which favour the 20 THE GRAMMAR OF SCIENCE. growth or decay of human societies become more obvious and more the subject of scientific investi- gation. Mental and social facts are thus not beyond the range of scientific treatment, but their classifi- cation has not been so complete, nor for obvious reasons so unprejudiced, as those of physical or biological phenomena. The case is quite different with metaphysics and those other supposed branches of human knowledge which claim exemption from scientific control. 1 Either they are based on an accurate classification of facts, or they are not. But if their classification of facts were accurate, the application of the scientific method ought to lead their professors to a practically identical system. Now one of the idiosyncrasies of meta- physicians lies in this : that each metaphysician has his own system, which to a large extent excludes that of his predecessors and colleagues. Hence we must conclude that metaphysics are either built on air or on quicksands either they start from no foundation in facts at all, or the superstructure has been raised before a basis has been found in the accurate classifica- tion of facts. I want to lay special stress on this point. There is no short cut to truth, no way to gain a know- ledge of the universe except through the gateway of scientific method. The hard and stony path of classify - 1 It is perhaps impossible to satisfactorily define the metaphysician, but the meaning attached by the present writer to the term will become clearer in the sequel. It is here used to denote a class of writers, of whom well-known examples are : Kant, in his later uncritical period (when he discovered that the universe was created in order that man might have a sphere for moral action !) ; the post-Kantians (notably Hegel and Schopenhauer), and their numerous English disciples, who " explain " the universe without having even an 3lementary knowledge of physical science. INTRODUCTORY. 21 ing facts and reasoning upon them is the only way to ascertain truth. It is the reason and not the imagina- tion which must ultimately be appealed to. The poet may give us in sublime language an account of the origin and purport of the universe, but in the end it will not satisfy our aesthetic judgment, our idea of harmony and beauty, like the few facts which the scientist may venture to tell us in the same field. The one will agree with all our experiences past and present, the other is sure, sooner or later, to contradict our observation because it is a dogma, where we are yet far from knowing the whole truth. Our aesthetic judgment demands harmony between the representa- tion and the represented, and in this sense science is often more artistic than modern art. The poet is a valued member of the community, for he is known to be a poet ; his value will increase as he grows to recognize the deeper insight into nature with which modern science provides him. The metaphy- sician is a poet, often a very great one, but unfor- tunately he is not known to be a poet, because he clothes his poetry in the language of apparent reason, and hence it follows that he is liable to be a dangerous member of the community. The danger at the present time that metaphysical dogmas may check scientific research is, perhaps, not very great. The day has gone by when the Hegelian philosophy threatened to strangle infant science in Germany ; that it begins to languish at Oxford is a proof that it is practically dead in the country of its birth. The day has gone by when philosophical or theological dogmas of any kind can throw back, even for generations, the progress of scientific investigation. There is no restriction now on research in any field, or on the publication of the 22 THE GRAMMAR OF SCIENCE. truth when it has been reached. But there is never- theless a danger which we cannot afford to disregard, a danger which retards the spread of scientific know- ledge among the unenlightened, and which flatters obscurantism by discrediting the scientific method. There is a certain school of thought which finds the laborious process by which science reaches truth too irksome ; the temperament of this school is such that it demands a short and easy cut to knowledge, where knowledge can only be gained, if at all, by the long and patient toiling of many groups of workers, perhaps through several centuries. There are various fields at the present day wherein mankind is ignorant, and the honest course for us is simply to confess our ignorance. This ignorance may arise from the want of any proper ' classification of facts, or because supposed facts are themselves inconsistent, unreal creations of man's un- trained mind. But because this ignorance is frankly admitted by science, an attempt is made to wall off these fields as ground whereon science has no business to trespass, where the scientific method is of no avail. Wherever science has succeeded in ascertaining the truth, there, according to the school we have re- ferred to, are the " legitimate problems of science." Wherever science is yet ignorant, there we are told its method is inapplicable ; there some other relation than cause and effect (than the same sequence recurring with the like grouping of phenomena), some new, but undefined relationship rules. In these fields we are told problems become philosophical and can only be treated by the method of philosophy. The philo- sophical method is opposed to the scientific method ; and here I think the danger I have referred to arises. We have defined the scientific method to consist in INTRODUCTORY. 23 the orderly classification of facts followed by the f recognition of their relationship and recurring se- quences. The scientific judgment is the judgment based upon this recognition and free from personal bias. If this were the philosophical method there would be no need of further discussion, but as we are told the subject-matter of philosophy is not the " legitimate problem of science," the two methods are presumably not identical. Indeed the philosophical method seems based upon an analysis which does not start with the classification of facts, but reaches its judgments by some process of internal cogitation. It is therefore dangerously liable to the influence of individual bias ; it results, as experience shows us, in an endless number of competing and contradictory systems. ' It is because the so-called philosophical method does not lead, like the scientific, to practical unanimity of judgments, when different individuals approach the same range of facts, 1 that science, rather than philosophy, offers the better training for modern citizenship. 7. The Ignorance of Science. It must not be supposed that science for a moment denies the existence of some of the problems which have hitherto been classed as philosophical or metaphysical On the contrary, it recognizes that a great variety of physical and biological phenomena lead directly to these problems. But it asserts that the methods 1 This statement by no means denies the existence of many moot points, unsettled problems in science ; but the genuine scientist admits that they are unsolved. As a rule they lie just on the frontier line between knowledge and ignorance, where the outposts of science are being pushed forward into unoccupied and difficult country. 24 THE GRAMMAR OF SCIENCE. hitherto applied to these problems have been futile, because they have been unscientific. The classifica- tions of facts hitherto made by the system-mongers have been hopelessly inadequate or hopelessly preju- diced. Until the scientific study of psychology, both by observation and experiment, has advanced im- mensely beyond its present limits and this may take generations of work science can only answer to the great majority of ' metaphysical ' problems, " I am ignorant." Meanwhile it is idle to be impatient or to indulge in system-making. The cautious and laborious classification of facts must have proceeded much further than at present, before the time will be ripe for drawing conclusions. Science stands now with regard to the problems of life and mind in much the same position as it stood with regard to cosmical problems in the seventeenth century. Then the system-mongers were the theo- logians, who declared that cosmical problems were not the " legitimate problems of science." It was vain for Galilei to assert that the theologians' classification of facts was hopelessly inadequate. In solemn congrega- tion assembled they settled that : " The doctrine that the earth is neither the centre of the universe nor immovable, but moves even with a daily rotation, is absurd, and both philosophically and theo- logically false ', and at the least an error of faith" * It took nearly two hundred years to convince the whole theological world that cosmical problems were the legitimate problems of science and science alone, 1 " Terram non esse centrum Mimdi, nee immobilem, sed moveri motu etiam diurno, est item propositio absurda, et falsa in Philosophia, et Theo- ligice considerata, ad minus erronea in fide" (Congregation of Prelates and Cardinals, June 22, 1633). INTRODUCTORY. 2$ for in 1819 the books of Galilei, Copernicus, and Keppler were still upon the index of forbidden books, and not till 1822 was a decree issued allowing books teaching the motion of the earth about the sun to be printed and published in Rome ! I have cited this memorable example of the absurdity which arises from trying to pen science into a limited field of thought, because it seems to me exceedingly suggestive of what must follow again, if any attempt, philosophical or theological, be made to define the " legitimate problems of science." Wherever there is the slightest possibility for the human mind to knoiv, there is a legitimate problem of science. Outside the field of actual knowledge can only lie a region of the vaguest opinion and imagination, to which un- fortunately men too often, but still with decreasing prevalence, pay higher respect than to knowledge. We must here investigate a little more closely what the man of science means when he says : " Here I am ignorant? In the first place he does not mean that the method of science is necessarily inapplicable, and accordingly that some other method is to be sought for. In the next place, if the ignorance really arises from the inadequacy of the scientific method, then we may be quite sure that no other method whatsoever will reach the truth. The ignorance of science means the enforced ignorance of mankind. I should be sorry myself to assert that there is any field of either mental or physical perceptions which science may not in the long course of centuries enlighten. Who can give us the assurance that the fields already occupied by science are alone those in which knowledge is possible? Who, in the words of Galilei, is willing to set limits to the human intellect ? Jt is true that this 26 THE GRAMMAR OF SCIENCE. view is not held by several leading scientists, both in this country and Germany. They are not content with saying, " We are ignorant," but they add, with regard to certain classes of facts, " Mankind must always be ignorant." Thus in England Professor Huxley has invented the term Agnostic, not so much for those who are ignorant as for those who limit the possibility of knowledge in certain fields. In Germany Professor E.duBois-Reymond has raised the cry: "Ignorabimus" "We shall be ignorant," and both his brother and he have undertaken the difficult task of demonstrating that with regard to certain problems human knowledge is impossible. 1 We must, however, note that in these cases we are not concerned with the limitation of the scientific method, but with the denial of the possibility that any method whatever can lead to knowledge. Now I venture to think that there is great danger in this cry: "We shall be ignorant." To cry "We are ignorant," is safe and healthy, but the attempt to demonstrate an endless futurity of ignorance appears a modesty which approaches despair. Conscious of the past great achievements and the present restless activity of science, may we not do better to accept as our watchword that of Galilei : "Who is willing to set limits to the human intellect?" interpreting it by what evolution has taught us of the continual growth of man's intellectual powers. Scientific ignorance may, as I have remarked (p. 22), either arise from an insufficient classification of facts, or be due to the unreality of the facts with which science has been called upon to deal. Let us take for example a number of fields of thought which 1 See especially Paul du Bois-Reymoncl : Ueber die Gnmdlagen der Erkenntniss in den exacten Wissenschaften. Tubingen, 1890. INTRODUCTORY. 2/ were very prominent in mediaeval times, such as alchemy, astrology, witchcraft. In the fifteenth cen- tury nobody doubted the " facts " of astrology and witchcraft. Men were ignorant as to how the stars exerted their influence for good or ill ; they did not know the exact mechanical process by which all the milk in a village was turned blue by a witch. But for them it was nevertheless a fact that the stars did influence human lives, and a fact that the witch had the power of turning the milk blue. Have we solved the problems of astrology and witchcraft to-day ? Do we now know how the stars influence human lives, or how witches turn milk blue? Not in the least. We have learnt to look upon the facts them- selves as unreal, as vain imaginings of the untrained human mind ; we have learnt that they could not be described scientifically because they involved notions which were in themselves contradictory and absurd. With alchemy the case was somewhat different. Here a false classification of real facts was combined with inconsistent sequences that is, sequences not deduced by a rational method. So soon as science entered the field of alchemy with a true classification and a true method, alchemy was converted into chemistry and became an important branch of human knowledge. Now it will, I think, be found that the fields of inquiry, where science has not yet penetrated and where the scientist still confesses ignorance, are very like the alchemy, astrology, and witchcraft of the Middle Ages. Either they involve facts which are in themselves unreal conceptions which are self-contradictory and absurd, and there- fore incapable of analysis by the scientific or any other method, or, on the other hand, our ignorance 28 THE GRAMMAR OF SCIENCE. arises from an inadequate classification and a neg- lect of scientific method. This is the actual state of the case with those mental and spiritual phenomena which are said to lie outside the proper scope of science, or which appear to be disregarded by scientific men. No better example can be taken than the range of pheno- mena which are entitled Spiritualism. Here science is asked to analyze a series of facts which are to a great extent unreal, which arise from the vain imaginings of untrained minds and from atavistic tendencies to superstition. So far as the facts are of this cha- racter, no account can be given of them, because, like the witch's supernatural capacity, their unreality will be found at bottom to make them self-contradictory. Combined, however, with the unreal series of facts are probably others, connected with hypnotic condi- tions, which are real and only incomprehensible be- cause there is as yet scarcely any intelligent classifica- tion or true application of scientific method. The former class of facts will, like astrology, never be reduced to law, but will one day be recognized as absurd ; the other, like alchemy, may grow step by step into an important branch of science. Whenever, there- fore, we are tempted to desert the scientific method of seeking truth, whenever the silence of science suggests that some other gateway must be sought to knowledge, let us inquire first whether the elements of the problem, of whose solution we are ignorant, may not after all, like the facts of witchcraft, arise from a superstition, and be self-contradictory and incomprehensible because they are unreal. If on inquiry we ascertain that the facts cannot possibly be of this class, we must then remember that INTRODUCTORY* 29 it may require long ages of increasing toil and in- vestigation before the classification of the facts can be so complete that science can express a definite judgment on their relationship. Let us suppose that the Emperor Karl V. had said to the learned of his day : " I want a method by which I can send a message in a few seconds to that new world, which my mariners take weeks in reaching. Put your heads together and solve the problem." Would they not undoubtedly have replied that the problem was im- possible ? To propose it would have seemed as ridiculous to them as the suggestion that science should straightway solve many problems of life and mind seems to the learned of to-day. It required centuries spent in the discovery and classification of new facts before the Atlantic cable became a possi- bility. It may require the like or even a longer time to unriddle those psychical and biological enigmas to which I have referred ; but he who declares that they can never be solved by the scientific method is to my mind as rash as the man .of the early sixteenth century would have been had he declared it utterly impossible that the problem of talking across the Atlantic Ocean should ever be solved. 8. The Wide Domain of Science. If I have put the case of science at all correctly, the reader will have recognized that modern science does much more than demand that it shall be left in undisturbed possession of what the theologian and metaphysician please to term its "legitimate field." It claims that the whole range of phenomena, mental as well as physical the entire universe is its field. It asserts that the scientific method is the sole gateway 36 tHE GRAMMAR OF SCIENCE. to the whole region of knowledge. The word science is here used in no narrow sense, but applies to all reasoning about facts which proceeds, from their accurate classification, to the appreciation of their relationship and sequence. The touchstone of science is the universal validity of its results for all normally constituted and duly instructed minds Because the glitter of the great metaphysical systems becomes dross when tried by this touchstone, we are compelled to classify them as interesting works of the imagination, and not as solid contributions to human" knowledge. Although science claims the whole universe as its field, it must not be supposed that it has reached, or ever can reach, complete knowledge in every department. Far from this, it confesses that its ignorance is more widely extended than its know- ledge. In this very confession of ignorance, however, it finds a safeguard for future progress. Science cannot give its consent to man's development being some day checked again by the barriers which dogma and myth would wish to erect round territory that science has not yet effectually occupied. It cannot allow theologian or philosopher, those Portu- guese of the intellect, to establish a right to the foreshore of ignorance, and so to hinder the settle- ment in due time of vast and yet unknown conti- nents of thought. In the like barriers erected in the past science finds some of the greatest difficulties in the way of intellectual progress and social advance at the present. It is the want of impersonal judg- ment, of scientific method, and of accurate insight into facts, due largely to a non-scientific training, which renders clear thinking so rare, and random and INTRODUCTORY. 31 irresponsible judgments so common, in the mass of our citizens to-day. Yet these citizens, owing to the growth of democracy, have graver problems to settle than probably any which have confronted their fore- fathers since the days of the Revolution. 9. The Second Claim of Science. Hitherto the sole ground on which we have con- sidered the appeal of modern science to the citizen is the indirect influence it has upon conduct owing to the more efficient mental training which it provides. But we have further to recognize that science can on occasion adduce facts having far more direct bearing on social problems than any theory of the state pro- pounded by the philosophers from the days of Plato to those of Hegel. I cannot bring home to the reader the possibility of this, better than by citing some of the conclusions to which the theory of heredity elabo- rated by the German biologist Weismann introduces us. Weismann's theory lies on the borderland of scientific knowledge; his results are still open to dis- cussion, his conclusions to modification. 1 But to indicate the manner in which science can directly influence conduct, we may assume for the time being Weismann's main conclusions to be correct. One of the chief features of his theory is the non-inheritance 1 His theory of the " continuity of the germ plasm " is in many respects open to question, but his conclusion as to acquired characteristics being uninherited stands on firmer ground. See Weismann : Essays on Heredity and Kindred Biological Problems, Oxford, 1889. A good criticism will be found in C. LI. Morgan's Animal Life and Intelli- gence, chap. v. A summary in W. P. Ball's Are the Effects of Use and Disuse Inherited? The reader should also consult P. Geddes and J. A. Thomson, The Evolution of Sex, and a long discussion in Nature, vols. xl. and xli. (mb indice, Weismann, Heredity). 32 THE GRAMMAR OF SCIENCE. by the offspring of characteristics acquired by the parents in the course of life. Thus good or bad habits acquired by the father or mother in their life- time are not inherited by their children. The effects of special training or of education on the parents have no direct influence on the child before birth. The parents are merely trustees who hand down their commingled stocks to their offspring. From a bad stock can come only bad offspring, and if a member of such a stock is, owing to special training and education, an exception to his family, his off- spring will still be born with the old taint. 1 Now this conclusion of Weismann's if it be valid, and all we can say at present is that the arguments in favour of it are remarkably strong radically affects our judg- ment on the moral conduct of the individual, and on the duties of the state and society towards their degenerate members. No degenerate and feeble stock will ever be converted into healthy and sound stock by the accumulated effects of education, good laws, and sanitary surroundings. Such means may render the individual members of the stock passable if not strong members of society, but the same process will have to be gone through again and again with their offspring, and this in ever-widening circles, if the stock, owing to the conditions in which society has placed it, is able to increase in numbers. The removal of that process of natural selection which in the struggle for existence crushed out feeble and degenerate stocks, may be a real danger to 1 Class, poverty, localization do much to approximately isolate stock, to aggregate the unfit even in modern civilization. The mingling of good and bad stock due to dispersion leads solely to panmixia^ it degenerates the good as much as it improves the bad. INTRODUCTORY. 33 society, if society relies solely on changed environment \ for converting its inherited bad into an inheritable good. If society is to shape its own future if we are to replace the stern processes of natural law, which have raised us to our present high standard of civilization, by milder methods of eliminating the unfit then we must be peculiarly cautious that in following our strong social instincts we do not at the same time weaken society by rendering the propa- gation of bad stock more and more easy. If this theory of Weismann's be correct if the bad man can by the influence of education and surround- ings be made good, but the bad stock can never be converted into good stock then we see how grave a responsibility is cast at the present day upon every citizen, who directly or indirectly has to consider pro- blems relating to the state endowment of education, the revision and administration of the Poor Law, and, above all, the conduct of public and private charities annually disposing of immense resources. In all problems of this kind the blind social instinct and the individual bias at present form extremely strong factors of our judgment. Yet these very problems are just those which, affecting the whole future of our society, its stability and its efficiency, require us, as good citizens, above all to understand and obey the laws of healthy social development. The example we have considered will not be futile, nor its lessons worthless, should Weismann's views after all be inaccurate. It is clear that in social problems of the kind I have referred to, the laws of heredity, whatever they may be, must profoundly influence our judgment. The conduct of parent to child, and of society to its anti-social members, can never be placed 4 34 THE GRAMMAR OF SCIENCE. on a sound and permanent basis without regard to what science has to tell us on the fundamental pro- blems of inheritance. The " philosophical " method can never lead to a real theory of morals. Strange as it may seem, the laboratory experiments of a biologist may have greater weight than all the theories of the state from Plato to Hegel ! The scientific classification of facts, biological or historical, the observation of their correlation and sequence, the resulting absolute, as opposed to the individual judgment these are the sole means by which we can reach truth in such a vital social question as that of heredity. In these con- siderations alone there appears to be sufficient justi- fication for the national endowment of science, and for the universal training of our citizens in scientific methods of thought. Each one of us is now called upon to give a judgment upon an immense variety of problems, crucial for our social gxistence. If that judgment confirms measures and conduct tending to the increased welfare of society, then it may be termed a moral, or, better, a social judgment. It follows, then, that to ensure a judgment's being moral, method and knowledge are essential to its formation. It cannot be too often insisted upon that the formation of a moral judgment that is, one which the individual is reasonably certain will tend to social welfare does not depend solely on the readiness to sacrifice individual gain or comfort, to act unselfishly : it depends in the first place on knowledge and method. The first de- mand of the state upon the individual is not for self- sacrifice, but for self-development. The man who gives a thousand pounds to a vast and vague scheme of charity, may or may not be acting socially ; his self- sacrifice, if it be such, proves nothing ; but the man INTRODUCTORY. 35 who gives a vote, either directly or even indirectly, in the choice of a representative, after forming a judgment based upon knoivledge is undoubtedly acting socially, and is fulfilling a higher standard of citizenship. lo.T/ie Third Claim of Science. Thus far I have been examining more particularly the action of science with regard to social problems. I have endeavoured to point out that it cannot legiti- mately be excluded from any field of investigation after truth, and that, further, not only is its method essential to good citizenship, but that its results bear closely on the practical treatment of many social difficulties. In this I have endeavoured to justify the state endowment and teaching of pure science as apart from its technical applications. If in this justi- fication I have laid most stress on the advantages of scientific method on the training which science gives us in the appreciation of evidence, in the classi- fication of facts, and in the elimination of personal bias, in all that may be termed exactness of mind we must still remember that ultimately the direct in- fluence of pure science on practical life is enormous. The observations of Newton on the relation between the motions of a falling stone and the moon, of Galvani on the convulsive movements of frogs' legs in contact with iron and copper, of Darwin on the adaptation of woodpeckers, of tree-frogs, and of seeds to their sur- roundings, of KirchhofT on certain lines which occur in the spectrum of sunlight, of other investigators on the life-history of bacteria these and kindred observations have not only revolutionized our conception of the universe, but they have revolutionized, or are revo- lutionizing, our practical life, our means of transit, 36 THE GRAMMAR OF SCIENCE. our social conduct, our treatment of disease. What at the instant of its discovery appears to be only a sequence of purely theoretical interest, becomes the basis of discoveries which in the end profoundly modify the conditions of human life. It is impossible to say of any result of pure science, that it will not some day be the starting-point of wide-reaching technical applications. The frog's legs of Galvani and the Atlantic cable seem wide enough apart, but the former was the starting-point of the series of investigations which ended in the latter. In the recent discovery of Hertz that the action of electro- magnetism is propagated in waves like light in his confirmation of Maxwell's theory that light is only a special phase of electro-magnetic action we have a result which, if of striking interest to pure science, seems yet to have no immediate practical application. But that man would indeed be a bold dogmatist who would venture to assert that the results which may ultimately flow from this discovery of Hertz's will not, in a generation or two, do more to revolutionize life than the frog's legs of Galvani had done when they had led to the perfection of the electric telegraph. 1 1 . Science and the Imagination, There is another aspect from which it is right that we should regard pure science one that makes no appeal to its utility in practical life, but touches a side of our nature which the reader may have thought that I have entirely neglected. There is an element in our being which is not satisfied by the formal pro- cesses of reasoning ; it is the imaginative or aesthetic side, the side to which the poets and philosophers appeal, and one which science cannot, to be scientific, INTRODUCTORY 3? disregard. We have seen that the imagination must not replace the reason in the deduction of relation and- law from classified facts. But, none the less, disciplined imagination has been at the bottom of all great scientific discoveries. All great scientists have, in a certain sense, been great artists ; the man with no imagination may collect facts, but he^cannot make great discoveries. If I were compelled to name the Englishmen who during our generation have had the widest imaginations and exercised them most bene- ficially, I think I should put the novelists and poets on one side and say Michael Faraday and Charles Darwin. Now it is very needful to understand the exact part imagination plays in pure science. We can, perhaps, best achieve this result by considering the following proposition : Pure science has a further strong claim upon us on account of the exercise it gives to the imaginative faculties and the gratification it provides for the aesthetic judgment. The exact meaning of the terms " scientific fact " and " scientific law " will be considered in later chapters, but for the present let us suppose an elaborate classification of such facts has been made, and their relationships and sequences carefully traced. What is the next stage in the process of scientific investigation ? Un- doubtedly it is the use of the imagination. The dis- covery of some single statement, some brief formula from which the whole group of facts is seen to flow, is the work not of the mere cataloguer, but of the man endowed with creative imagination. The single state- ment, the brief formula, the words of which replace in our minds a wide range of relationships between isolated phenomena, is what we term a scientific law. Such a law, relieving our memory from the burden of 38 THE GRAMMAk OF SCIENCE. individual sequences, enables us, with the minimum of intellectual fatigue, to grasp a vast complexity of natural or social phenomena. The discovery of law is therefore the pecul'ir function of the creative imagi- nation. But this imagination has to be a disciplined one. It has in the first place to appreciate the whole range of facts, which require to be resumed in a single statement ; and then when the law is reached often by what seems solely the inspired imagination of genius it must be tested and criticised by its dis- coverer in every conceivable way, till he is certain that the imagination has not played him false, and that his law is in real agreement with the whole group of phenomena which it resumes. Herein lies the key- note to the scientific use of the imagination. Hundreds of men have allowed their imagination to solve the universe, but the men who have contributed to our real understanding of natural phenomena have been those who were unstinting in their application of criticism to the product of their imaginations. It is such criticism which is the essence of the scientific use of the imagination, which is, indeed, the very life-blood of science. 1 No less an authority than Faraday writes : " The world little knows how many of the thoughts and theories which have passed through the mind of a scientific investigator have been crushed in silence and secrecy by his own severe criticism and adverse examination ; that in the most successful instances not a tenth of the suggestions, the hopes, the wishes, the preliminary conclusions have been realized." 1 " La critique est la vie de la science" says Victor Cousin. INTRODUCTORY. 39 12. The Method of Science Illustrated. The reader must not think that I am painting any ideal or purely theoretical method of scientific dis- covery. He will find the process described above accurately depicted by Darwin himself in the account he gives us of his discovery of the law of natural selection. After his return to England in 1837, he tells us, 1 it appeared to him that : " By collecting all facts which bore in any way on the variation of animals and plants under domestication and nature, some light might perhaps be thrown on the whole subject. My first note-book was opened in July, 1837. I worked on true Baconian principles, 2 and, without any theory, collected facts on a wholesale scale, more especially with respect to domesticated productions, by printed enquiries, by conversation with skilful breeders and gardeners, and by extensive reading. When I see the list of books of all kinds which I read and abstracted, including whole series 1 The Life and Letters of Charles Darwin, vol. i. p. 83. 2 It is from men like Laplace and Darwin, who have devoted their lives to natural science, rather than from workers in the pure field of conception, like Mill and Stanley Jevons, that we must seek for a true estimate of the Baconian method. Beside Darwin's words we may place those of Laplace on Bacon : " II a donne pour la recherche de la verite, le precepte et non 1'ex. emple. Mais en insistant avec toute la force de la raison et de 1'eloquence, sur la necessite d'abandonner les subtilites insignifiantes de 1'ecole, pour se livrer aux observations et aux experiences, et en indiquant la vraie methode de s'elever aux causes generates des phenomenes, ce grand philosophe a contribue aux progres immenses que 1'esprit humain a faits dans le beau siecle oil il a termine sa carriere " ( Theorie analytique des Probability's , QEuvres T. vii. p. clvi.). The carpenter who uses a tool is a better judge of its efficiency than the smith who forges it. For a good sketch of the estimation in which Bacon was held by his scientific contemporaries see the introduction to Prof. Fowler's edition of the Novum Organum. 40 THE GRAMMAR OF SCIENCE. of Journals and Transactions, I am surprised at my own industry. I soon perceived that selection was the keystone of man's success in making useful races of animals and plants. But how selection could be applied to organisms living in a state of nature re- mained for some time a mystery to me." Here we have Darwin's scientific classification of facts, what he himself terms his " systematic inquiry." Upon the basis of this systematic inquiry comes the search for a law. This is the work of the imagina- tion ; the inspiration in Darwin's case being ap- parently due to a perusal of Malthus' Essay on Popula- tion. But Darwin's imagination was of the disciplined scientific sort. Like Turgot, he knew that if the first thing is to invent a system, then the second is to be disgusted with it. Accordingly there followed the period of self-criticism, which lasted four or five years, and it was no less than nineteen years before he gave the world his discovery in its final form. Speaking of his inspiration that natural selection was the key to the mystery of the origin of species, he says : " Here, then, I had at last got a theory by which to work ; but I was so anxious to avoid prejudice, that I determined not for some time to write even the briefest sketch of it. In June, 1842 [z>, four years after the inspiration], I first allowed myself the satis- faction of writing a very brief abstract of my theory in pencil in 35 pages ; and this was enlarged during the summer of 1844 into one of 230 pages, which I had fairly copied out and still possess." Finally an abstract from Darwin's manuscript was published with Wallace's Essay in 1858, and the Origin of Species appeared in 1859. In like manner Newton's imagination was only INTRODUCTORY. 41 paralleled by that power of self-criticism which led him to lay aside a demonstration touching the gravi- tation of the moon for nearly eighteen years, until he had supplied a missing link in his reasoning. But our details of Newton's life and discoveries are too meagre for us to see his method as closely as we can Darwin's, and the account I have given of the latter is amply sufficient to show the actual application of scientific method, and the real part played in science by the disciplined use of the imagination. 1 1 That the classification of facts is often largely guided by the imagi- nation as well as the reason must be fully admitted. At the same time an accurate classification, either due to the scientist himself or to previous workers, must exist in the scientist's mind before he can proceed to the discovery of law. Here, as elsewhere, the reader will find that I differ very widely from Stanley Jevons' views as developed in his Principles of Science. I cannot but feel that Chapter xxvi. of that work would have been recast had the author been acquainted with Darwin's method of procedure. The account given by Jevons of the Newtonian method seems to me to lay insufficient stress upon the fact that Newton had a wide acquaintance with physics before he proceeded to use his imagination and test his theories by experiment that is, to a period of self-criticism. The reason that pseudo-scientists cumber the reviewer's table with idle theories, often showing great imaginative power and ingenuity, is not solely want of self-criticism. Their theories, as a rule, are not such as the scientist himself would ever propound and criticise. Their impossibility is obvious, because their propounders have neither formed for themselves, nor been acquainted with others' classifications of the groups of facts which their theories are intended to summarise. Newton and Faraday started with full knowledge of the classifications of physical facts which had been formed in their own days, and proceeded to further conjoint theorizing and classifying. Bacon, of whom Stanley Jevons is, I think, unreasonably contemptuous, lived at a time when but little had been done by way of classification, and he was wanting in the scientific imagination of a Newton or a Faraday. Hence the barrenness of his method in his own hands. The early history of the Royal Society's meetings shows how essentially the period of collection and classification of facts preceded that of valuable theory. With Stanley Jevons' last chapter on The Limits of Scientific Method the present writer can only express his complete disagreement ; many 42 THE GRAMMAR OF SCIENCE. 13. Science and the Esthetic Judgment. We are justified, I think, in concluding that science does not cripple the imagination, but rather tends to exercise and discipline its functions. We have still, however, to consider another phase of the relationship of the imaginative faculty to pure science. When we see a great work of the creative imagination, a striking picture or a powerful drama, what is the essence of the fascination it exercises over us ? Why does our aesthetic judgment pronounce it a true work of art ? Is it not because we find concentrated into a brief statement, into a simple formula or a few symbols, a wide range of human emotions and feelings ? Is it not because the poet or the artist has expressed for us in his representation the true relationship between a variety of emotions, which we, in a long course of experience, have been consciously or unconsciously classifying ? Does not the beauty of the artist's work lie for us in the accuracy with which his symbols resume innumerable facts of our past emotional ex- perience ? The aesthetic judgment pronounces for or against the interpretation of the creative imagination according as that interpretation embodies or contra- dicts the phenomena of life, which we ourselves have observed. 1 It is only satisfied when the artist's formula contradicts none of the emotional phenomena which it is intended to resume. If this account of the aesthetic judgment be at all a true one, the reader will have re- of its arguments appear to him unscientific, if it were not better to term them anti-scientific. 1 How important a part length and variety of emotional experience play in the determination of the aesthetic judgment is easily noted by investigating the favourite authors and pictures of a few friends of diverse ages and conditions. INTRODUCTORY 43 marked how .exactly parallel it is to the scientific judg- ment. 1 But there is really more than mere parallelism between the two. The laws of science are, as we have seen, products of the creative imagination. They are the mental interpretations the formulae under which we resume wide ranges of phenomena, the results of observation on the part of ourselves or of our fellow- men. The scientific interpretation of phenomena, the scientific account of the universe, is therefore the only one which can permanently satisfy the aesthetic judg- ment, for it is the only one which can never be con- tradicted by our observation and experience. It is necessary to strongly emphasise this side of science, for we are frequently told that the growth of science is destroying the beauty and poetry of life. It is undoubtedly rendering many of the old interpretations of life meaningless, because it demonstrates that they are false to the facts which they profess to describe. It does not follow from this, however, that the aesthetic and scientific judgments are opposed ; the fact is, that with the growth of our scientific know- ledge the basis of the aesthetic judgment is changing and must change. There is more real beauty in what science has to tell us of the chemistry of a distant star, or in the life-history of a protozoon, than in any cosmogony produced by the creative imagination of a pre-scientific age. By " more real beauty " we are to understand that the aesthetic judgment will find more satisfaction, more permanent delight in the former than in the latter. It is this continual gratifi- cation of the aesthetic judgment which is one of the chief delights of the pursuit of pure science. 1 The curious reader may be referred to Wordsworth's " General View of Poetry " in his preface to the Lyrical Ballads, 1815. 44 THE GRAMMAR OF SCIENCE. 14. The Fourth Claim of Science. There is an insatiable desire in the human breast to resume in some short formula, some brief state- ment, the facts of human experience. It leads the savage to " account " for all natural phenomena by deifying the wind and the stream and the tree. It leads civilized man, on the other hand, to express his emotional experience in works of art, and his physical and mental experience in the formulae or so-called laws of science. Both works of art and laws of science are the product of the creative imagination, both afford material for the gratification of the aesthetic judg- ment. It may seem at first sight strange to the reader that the laws of science should thus be asso- ciated with the creative imagination in man rather than with the physical world outside him. But as we shall see in the course of the following chapters the laws of science are products of the human mind rather than factors of the external world. Science endeavours to provide a mental r/sumt of the universe, and its last great claim to our support is the capacity it has for satisfying our cravings for a brief description of the history of the world. Such a brief description, a formula resuming all things, science has not yet found and may probably never find, but of this we may feel sure, that its method of seeking for one is the sole possible method, and that the truth it has reached is the only form of truth which can permanently satisfy the aesthetic judgment. For the present, then, it is better to be content with the fraction of a right solution, than to beguile ourselves with the whole of a wrong solution. The former is at least a step towards the truth, and shows us the direction in which other steps may be taken. INTRODUCTORY. 45 The latter cannot be in entire accordance with our past or future experience, and will therefore ulti- mately fail to satisfy the aesthetic judgment. Step by step that judgment, restless under the growth of positive knowledge, has discarded creed after creed, and philosophic system after philosophic system. Surely we might now be content to learn from the pages of history that only little by little, slowly line upon line, man, by the aid of organized observation and careful reasoning, can hope to reach knowledge of the truth, that science, in the broadest sense of the word, is the sole gateway to a knowledge which can harmonize with our past as well as with our possible future experience. As Clifford puts it : " Scientific thought is not an accompaniment or condition of human progress, but human progress itself." SUMMARY. 1. The scope of science is to ascertain truth in every possible branch of knowledge. There is no sphere of inquiry which lies outside the legitimate field of science. To draw a distinction between the scientific and philosophical methods is obscurantism. 2. The scientific method is marked by the following features : (a) Careful and accurate classification of facts and observation of their correlation and sequence ; (b) The discovery of scientific laws by aid of the creative imagination ; (c) Self-criticism and the final touchstone of equal validity for all normally constituted minds. 3. The claims of science to our support depend on : (a) The efficient mental training it provides for the citizen ; (b] The light it brings to bear on many important social problems ; (c) The increased comfort it adds to practical life ; (d) The permanent gratification it yields to the aesthetic judgment. LITERATURE. BACON, Francis. Novum Organum, London, 1620. A good edition by T. Fowler. Clarendon Press, 1878. 46 THE GRAMMAR OF SCIENCE. BOIS-REYMOND, E. du. Ueber die Grenzen des Naturerkennens. Veit & Co., Leipzig, 1876. BOIS-REYMOND, P. du. Ueber die Grundlagen der Erkenntniss in den exacten Wissenschaften. H. Laupp, Tubingen, 1890. CLIFFORD, W. K. Lectures and Essays. Macmillan, 1879. ("Aims and Instruments of Scientific Thought," " The Ethics of Belief," and " Virchow on the Teaching of Science.") HAECKEL, E. Freie Wissenschaft and freie Lehre. E. Schweizerbart, Stuttgart, 1878. HALDANE, J. S. " Life and Mechanism," Mind, ix. pp. 27-47 > a l so Nature, vol. xxvii., 1883, p. 561, vol. xxiv,, 1886, p. 73; and also Haldane, R. B., Proceedings of the Aristotolean Society, 1891, vol. i. no. 4, part i. pp. 22-27. HELMHOLTZ, H. On the Relation of the Natural Sciences to the Totality of the Sciences, translated by C. H. Schaible. London, 1869. This occurs also in the Popular Lectures, translated by Atkinson and others, First Series, p. i. Longmans, 1881. HERSCIIEL, Sir John. A Preliminary Dissertation on Natural Philosophy. London, 1830. JEVONS, W. Stanley. The Principles of Science : A Treatise on Logic and Scientific Method, 2nd ed. Macmillan, 1877. PEARSON, K. The Ethic of Freethought : A Selection of Essays and Lectures (" The Enthusiasm of the Market-place and of the Study"). Fisher Unwin, 1888. VIRCHOW, R. Die Freiheit der Wissenschaft im modernen Staat (Versammlung deutscher Naturforscher). Miinchen, 1877. CHAPTER II. THE FACTS OF SCIENCE. i. The Reality oj Things. IN our first chapter we have frequently spoken of the classification of facts as the basis of the scientific method ; we have also had occasion to use the words real and unreal, universe and phenomenon. It is proper, therefore, that before proceeding further we should endeavour to clear up our ideas as to what these terms signify. We must strive to define a little more closely in what the material of science consists. We have seen that the legitimate field of science embraces all the mental and physical facts of the universe. But what are these facts in themselves and what is for us the criterion of their reality ? Let us start our investigation with some " external object," and as apparent simplicity will be satisfied by takingafamiliarrequisiteoftheauthor'scalling,namely, a blackboard, let us take it. 1 We find an outer rectan- gular frame of brownish-yellow colour, which on closer inspection we presume to be wood, surrounding an inner fairly smooth surface painted black. We can measure a certain height, thickness, and breadth, we notice a certain degree of hardness, weight, resistance 1 The blackboard as an " object-lesson " is such a favourite instance with the writer, that the reader will perhaps pardon him the use of it here. Seine Mundart klebt jedem an. 48 THE GRAMMAR OF SCIENCE. to breaking, and, if we examine further, a certain temperature, for the board feels to us cold or warm. Now although the blackboard at first sight appears a very simple object, we see that it at once leads us up to a very complex group of properties. In common talk we attribute all these properties to the blackboard, but when we begin to think over the matter carefully we shall find that it is by no means so simple as it seems to be. To begin with, I receive certain im- pressions of size and shape and colour by means of my organs of sight, and these enable me to pronounce with very considerable certainty that the object is a blackboard made of wood and coated with paint, even before I have touched or measured it. I infer that I shall find it hard and heavy, that I could if I pleased saw it up, and that I should find it to possess various other properties which I have learnt to associate with wood and paint. These inferences and associations are something which I add to the sight-impressions, and which I myself contribute from my past experience and put into the object blackboard. I might have reached my conception of the blackboard by impres- sions of touch and not by those of sight. Blind- folded I might have judged of its size and shape, of its hardness and surface texture, and then have inferred its probable use and appearance, and associated with it all blackboard characteristics. In both cases it must be noted that a sine qua non of the existence of an actual blackboard is some immediate sense-impression to start with. The sense-impressions which determine the reality of the external object may be very few indeed, the object may be largely constructed by inferences and associations, but some sense-impressions there must be if I am to term the THE FACTS OF SCIENCE. 49 object real, and not a product merely of my imagina- tion. The existence of a certain number of sense- impressions leads me to infer the possibility of my receiving others, and this possibility I can, if I please, put to the test. I have heard of the Capitol at Washington, and although I have never been to America, I am convinced of the reality of America and the Capitol that is, I believe certain sense-impressions would be experienced by me if I put myself in the proper circumstances. In this case I have had indirect sense- impressions, contact with Americans, and with ships and chattels coming from America, which lead me to believe in the " reality " of America and of what my eyes or ears have told me of its contents. In constructing the Capitol it is clear that past expe- rience of a variety of kinds is largely drawn upon. But it must be noted that this past experience is itself based upon sense-impressions of one kind or another. These sense-impressions have been as it were stored in the memory. A sense-impression, if sufficiently strong, leaves in our brain some more or less permanent trace of itself, which is rendered manifest in the form of association whenever an immediate sense-impression of a like kind recurs. The stored effects of past sense-impressions form to a great extent what we are accustomed to speak of as an " external object." On this account such an object must be recognized as largely constructed by ourselves ; we add to a greater or less number of immediate sense- impressions an associated group of stored sense- impresses. The proportion of the two contributions will depend largely on the keenness of our organs of sense and on the length and variety of our experience* 5 v ; 5O THE GRAMMAR OF SCIENCE. Owing to the large amount we ourselves contribute to most external objects, Professor Lloyd Morgan, in the able discussion of this matter in his Animal Life and Intelligence (p. 3 1 2) proposes to use the term construct for the external object. What for our present purpose, then, it is very needful to bear in mind is this : an external object is in general a construct that is, a combination of immediate with past or stored sense- impressions. The reality of a thing depends upon the possibility of its occurring as a group of immediate sense-impressions. 1 2. Sense-Impressiotts and Consciousness. This conception of reality as based upon sense- ' impressions requires careful consideration and some reservations and modifications. Let us examine a little more closely what we are to understand by the word sense-impression. In turning round quickly in my chair, I knock my knee against a sharp edge of the table. Without any thought of what I am doing my hand moves down and rubs the bruised part, or the knee may cause me so much discomfort that I get up, think of what I shall do, and settle to apply some arnica. Now the two actions on my part appear of totally different character at least on first 1 The division between the real and unreal, and again between the real and ideal, is less distinct than many may think. For \ example, the planet Neptune passed from the ideal to the real, but the atom is still ideal. The ideal passes into the real when its perceptual equivalent is found, but the unreal can never become real. Thus the concepts of the metaphysicians, Kant's thing in itself or Clifford's mind stuff wto. in my sense of the words unreal (not ideal), they cannot become immediate sense-impressions, but the physical hypotheses as to * the nature of matter are ideal (not unreal) for they do not lie absolutely outside the field of possible sense-impressions. THE FACTS OF SCIENCE. $1 examination. In both cases physiologists tells . us that as a primary stage a message is carried from the affected part by what is termed a sensory nerve to the brain. The manner in which this nerve conveys its message is without doubt physical, although its exact modus operandt is still unknown. At the brain what we term the sense-impression is formed, and there most probably some physical change takes place which remains with a greater or less degree of per- sistence in the case of those stored sense-impresses which we term memories. Everything up to the receipt of the sense-impression by the brain is what we are accustomed to term physical or mechanical, it is a legitimate inference to suppose that what from the psychical aspect we term memory, has also a physical side, that the brain takes for every memory a permanent physical impress, whether by change in the molecular constitution or in the elementary motions of the brain-substance, and that such phy- sical impress is our stored sense-impress. 1 These physical impresses play an important part in the manner in which future sense-impressions of a like character are received. If these immediate sense- impressions be of sufficient strength, or amplitude as we might perhaps venture to say, they will call into some sort of activity a number of physical impresses due to past sense-impressions allied, or, to use a more suggestive word, attuned to the immediate sense-impression. The immediate sense-impression is conditioned by the physical impresses of the past, 1 The closest physical analogies to the "permanent impresses" termed memory are the set and after-strain of the elastician. To assert that they are more than analogies would be to usurp the function of the physiologist. 52 THE GRAMMAR OF SCIENCE. and the general result is what has been termed a " construct." Besides the sensory nerves which convey the mes- sages to the brain, there are other nerves which pro- ceed from the brain and control the muscles termed motor nerves. Through these motor nerves a message is sent to my arm bidding it rub my bruised knee. This message may be sent immediately or after my fingers have been dipped in arnica. In the latter case a very complex process has been gone through. I have realized that the sense-impression corresponds to a bruised knee, that arnica is good for a bruise, that a bottle of arnica is to be found in a certain cupboard, and so forth. Clearly the sense-impression has been conditioned by a number of past impresses before the motor nerve of the arm is called into play to rub the knee. The process is described as thinking, and as a variety of past experiences may come into play, the ultimate message to the motor nerves appears to us voluntary, and we call it an act of will, however f much it is really conditioned by the stored sense-im- i presses of the past. On the other hand, when, with- out apparently exciting any past sense-impresses, the message from the sensory nerve no sooner reaches the brain than a command is sent along the motor nerve for the hand to rub the knee, I am said to act involuntarily, from instinct or habit. The whole pro- cess may be so rapid, I may be so absorbed in my work, that I never realized the message from the sensory nerve at all. I do not even say to myself, " I have knocked my knee and rubbed it." Only a spectator, perhaps, has been conscious of the whole process of knee-knocking and rubbing. Now this is in many respects an important result. I can receive a sense- THE FACTS OF SCIENCE. 53 impression without recognizing it, or a sense-impres- sion does not involve consciousness. In this case there is no group of stored sense-impresses, no chain of what we term thoughts intervening between the immediate sense-impression and the message to the motor nerve. Thus what we term consciousness is largely, if not wholly, due to the stock of stored sense- impresses, and to the manner in which these condition the messages given to the motor nerves when a sen- sory nerve has conveyed a message to the brain. The measure of consciousness will thus largely depend on (i) the extent and variety of past sense-impressions, and (2) the degree to which the brain can perma- nently preserve the impress of these sense-impressions, or what might be termed the complexity and plasticity of the brain. 3. The Brain as a Central Telephone Exchange. The view of brain activity here discussed may per- haps be elucidated by comparing the brain to the central office of a telephone exchange, from which wires radiate to the subscribers A, B, C, D, E, F, &c., who are senders, and to W, X, Y, Z, &c., who are receivers of messages. A, having notified to the company that he never intends to correspond with anybody but W, his wire is joined to W's, and the clerk remains unconscious of the arrival of the mes- sage from A and its dispatch to W, although it passes through his office. 1 There is indeed no call-bell. This 1 If these wires were connected outside the office, we should have an analogy to certain possibilities of reflex action, which arise from sensory and motor nerves being linked before reaching the brain e.g., a frog's leg will be moved so as to rub an irritated point on its back even after the removal of the brain. 54 THE GRAMMAR OF SCIENCE. corresponds to an instinctive exertion following uncon- sciously on a sense-impression. Next the clerk finds by experience that B invariably desires to correspond with X, and consequently whenever he hears B's call- bell he links him mechanically to X, without stopping for a moment his perusal of Tit-Bits. This corre- sponds to a habitual exertion following unconsciously on a sense-impression. Lastly, C, D, E, and F may set their bells ringing for a variety of purposes ; the clerk has in each case to answer their demands, but this may require him to listen to the special com- munications of these subscribers, to examine his lists, his post-office directory, or any other source of infor- mation stored in his office. Finally, he shunts their wires so as to bring them in circuit with those of Y and Z, which seem to best suit the nature of the demands. This corresponds to an exertion following consciously on the receipt of a sense-impression. In all cases the activity of the exchange arises from the receipt of a message from one of a possibly great, but still finite number of senders, A, B, C, D, &c. ; the originality of the clerk is confined to immediately following their behests or to satisfying their demands to the best of his ability by the information stored in his office. The analogy of course must not be pressed too far in particular senders and receivers must be considered distinct, for sensory and motor nerves do not appear to interchange functions. But the conception of the brain as a central exchange certainly casts considerable light not only on the action of sensory and motor nerves, but also on thought and consciousness. With- out sense-impressions there would be nothing to store ; without the faculty of receiving permanent impress, without memory, there would be no possibility of THE FACTS OF SCIENCE. 55 thought ; and without this thought, this hesitation between sense-impression and exertion, there would be no consciousness. When an exertion follows immediately on a sense-impression we speak of the exertion as involuntary, our action as subject to the mechanical control of the "external object " to which we attribute the sense-impression. On the other hand, when the exertion is conditioned by stored sense- impresses we term our action voluntary. We speak of it as determined from " within ourselves," and assert the " freedom of our will." In the former case the exertion is conditioned solely by the immediate sense-impression ; in the latter it is conditioned by a complex of impressions partly immediate and partly stored. The past training, the past history and experi- ence which mould character and determine the will, are really based on sense-impressions received at one time or another, and hence we may say that exertion, whether immediate or deferred, is the product directly or indirectly of sense-impressions. 4. The Nature of Thought. There are still one or two points to be noted here. In the first place the immediate sense-impression is to be looked upon as the spark which kindles thought, which brings into play the stored impresses of past sense-impressions. But the complexity of the human brain is such, its stored sense-impresses are linked together in so many and diverse ways partly by continual thinking, partly by immediate sense-impres- sions occurring in proximity and so linking together apparently discordant groups of past impresses that we are not always able to recognize the relation be- 56 THE GRAMMAR OF SCIENCE. tween an immediate sense-impression and the result- ing train of thought. Nor, on the other hand, can we always trace back a train of thought to the immediate sense-impression from which it started. Yet we may take it for certain that elements of thought are ulti- mately the permanent impress of past sense-impres- sions, and that thought itself is started by immediate sense-impressions. 1 This statement must not be in any way supposed to narrow the material of thought to those combina- tions of " external objects " which we associate with immediate sense-impressions. Thought once excited, the mind passes with wonderful activity from one stored impress to another, it classifies these im- presses, analyzes or simplifies their characteristics, and forms general notions of properties and modes. It proceeds from the direct what might perhaps be termed the physical association of memory, to the indirect or mental association ; it passes from perceiv- ing to conceiving. The mental association, or recogni- tion of relation between the stored impresses of past sense-impressions has probably, if we could follow it, as definite a physical side as the physical association of immediate sense-impressions and past impresses- But the physical side of the impress is only a reasonable inference from the physical nature of the immediate sense-impression, and we must therefore content ourselves at present by considering it highly probable that every process of thought has a physical 1 The exact train of thought which follows an immediate sense-im- pression depends largely on the physical condition of the brain at the time of its receipt, and is further largely conditioned by the mode in which stored sense-impresses have been excited in the past, z. the impulses and hopes of men receive confirmation from science. Conscious- ness is found associated with matter ; we cannot demonstrate that consciousness is riot found with all forms of matter. Ergo t all matter is conscious, or matter and mind are never found except in con- junction, and we may legitimately speak of the " con- sciousness of society " and the " consciousness of the universe." These are but a few samples of the current method of fallacious inference usually, be it remarked, screened beneath an unlimited flow of words, and not thus exhibited in its naked absurdity. When we recognize how widely inferences of this 1 "That is a noteworthy fact which I have not fully appreciated before," remarks the untrained mind, and is already more than half- converted to thecsophy. THE FACTS OF SCIENCE. 69 character affect conduct in life, and yet grasp how unstable must be the basis of such conduct, how liable to be shaken to the foundations by the first stout logical breeze, then we understand how honest doubt is far healthier for the community, is more social, than unthinking inference, light-hearted and over-ready belief. Doubt is at least the first stage towards scientific inquiry ; and it is better by far to have reached that stage than to have made no intellectual progress whatever. 9. The Limits to Other-Consciousness. We cannot better illustrate the limits of legitimate inference than by considering the example we have last cited, and asking how far we may infer the existence of consciousness and of thought. We have seen (p. 52) that consciousness is associated with the process which may intervene in the brain between the receipt of a sense-impression from a sensory nerve and the dispatch of a stimulus to action through a motor nerve. Consciousness is thus associated with machinery of a certain cha- racter, which we term the brain and nerves. Further, it depends upon the lapse of an interval between sense-impression and exertion, this interval being filled, as it were, with the mutual resonance and cling- clang of stored sense-impresses and the conceptions drawn from them. Where no like machinery, no like interval can be observed, there we have no right to infer any consciousness. In our fellow- men we observe this same machinery and the like interval, and we infer consciousness, it may be as an eject, but as an eject which, as we have seen (p. 60), might not inconceivably, however improbably, become some day 76 THE GRAMMAR OF SCIENCE. an object. In the lower forms of life we observe machinery approximately like our own, and a shorter and shorter interval between sense-impression and exertion ; we may reasonably infer consciousness, if in reduced intensity. We cannot, indeed, put our finger on a definite type of life and say here con- sciousness ends, but it is completely illogical to infer its existence where we can find no interval between sense-impression and exertion, or where we can find no nervous system. Because we cannot point to the exact form of material life at which consciousness ceases, we have no more right to infer that conscious- ness is associated with all life, still less with all forms of matter, than we have to infer that there must always be wine mixed with water, because so little wine can be mixed with water that we are unable to detect its presence. Will, too, as we have seen, is closely connected with consciousness ; it is the feel- ing in our individual selves when exertion flows from the stored sense-impresses " within us," and not from the immediate sense-impression which we term " with- out us." We are justified, therefore, in inferring the feeling of will as well as consciousness in nervous systems more or less akin to our own ; we may throw them out from ourselves, eject them into certain forms of material life. But those who eject them into matter, where no nervous system can be found, or even into existences which they postulate as im- material, are not only exceeding enormously the bounds of scientific inference, but forming concep- tions which, like that of the centaur, are inconsistent in themselves. From will and consciousness associated with material machinery, we can infer nothing what- ever as to will and consciousness without that THE FACTS OF SCIENCE. 71 machinery. We are passing by the trick of a common-name to things of which we can postulate absolutely nothing, and of which we are only unable to deny the existence when we give to that term a meaning wholly opposed to the customary one. 1 10. The Canons of Legitimate Inference. We cannot here discuss more fully the limits of belief and legitimate inference. We shall, however, to some extent return to the subject when considering Causation and Probability in Chapter IV. But it may not be without service to state certain canons of legitimate inference with a few explanatory remarks, leaving the reader, if he so desire, to pursue the subject further in Stanley Jevons' Principles of Science, or in Clifford's essay on The EtJiics of Belief. We ought first to notice that the use of the word belief in our language is changing : formerly it denoted some- thing taken as definite and certain on the basis of some external authority ; now it has grown rather to denote credit given to a statement on a more or less sufficient balancing of probabilities. 2 The change in usage marks the gradual transition of the basis of conviction from uncriticizing faith to 1 Consciousness without a nervous system is like a horse without a belly a chimera, of which in customary language we deny the "existence." We cannot demonstrate that a horse without a belly may not exist " outside " the physical universe, only it would not be a horse and would exist " nowhere." The existence of something of which we can postulate nothing at nowhere can never be inferred from conceptions based on sense-impressions. Such a horse would be like Meister Eckehart's deity who was a non-god, a non-spirit, a non- person, a non-idea, and of whom, he says, any assertion must be more false than true. 2 Compare the older use in Biblical passages, such as "Jacob's heart 72 THE GRAMMAR OF SCIENCE. weighed probability. The canons we have referred to are the following : 1. Where it is impossible to apply man's reason, that is to criticize and investigate at all, there it is not only unprofitable, but antisocial to believe. Belief is thus to be looked upon as an adjunct to knowledge : as a guide to action where decision is needful, but the probability is not so overwhelming as to amount to knowledge. To believe in a sphere where we cannot reason is antisocial, for it is a matter of common experience that such belief prejudices action in spheres where we can reason. 2. We may infer what we cannot verify by direct sense-impression only when the inference is from known things to unknown things of the like nature in similar surroundings. Thus we may not infer an " infinite " consciousness outside the physical surroundings of finite conscious- ness ; we may not infer man in the moon, however like in nature to ourselves, because the physical sur- roundings in the moon are not such as we find man in here, &c., &c. 3. We may infer the truth of tradition when its contents are of like character and continuous with men's present experience, and when there is reason- able ground for supposing its source to lie in persons knowing the facts and reporting what they knew. The tradition that Wellington and Bliicher won the battle of Waterloo fulfils the necessary conditions, fainted for he believed them not," and "Except ye see signs and wonders ye will not believe," or in Locke's definition of belief as adherence to a proposition of which one is persuaded but does not know to be true, with such modern usage as : "I believe that you will find a Cab on the stand, and that the train starts at half-past eight." THE FACfS OF SCIENCE. ?$ while the miracle of Karl the Great and the adder fulfils neither condition. 4. While it is reasonable in the minor actions of life, where rapidity of decision is important, to infer on slight evidence and believe on small balances of probability, it is opposed to the true interests of society to take as a permanent standard of conduct a belief based on inadequate testimony. This canon suggests that the acceptance, as habitual guides to conduct, of beliefs based on insufficient evidence, must lead to the want of a proper sense of the individual's responsibility for the important deci- sions of life. I have no right to believe at seven o'clock that a cab will be on the stand at eight o'clock, if my catching the train at half-past is of vital impor- tance to others. ii. The External Universe. Before we draw from our present discussion any conclusions as to the facts of science we must return once more to the immediate sense-impression and examine its nature a little more closely. We are accustomed to talk of the "external world," of the " reality " outside us. We speak of individual objects having an existence independent of our own. Stored sense -impressions, our thoughts and memories, although most probably they have beside their psy- chical element a close correspondence with some phy- sical change or impress in the brain, are yet spoken of as inside ourselves. On the other hand, although if a sensory nerve be divided anywhere short of the brain we lose the corresponding sense-impression, we yet speak of many sense-impressions such as form ?4 THE GRAMMAR OF SCIENCE. and texture as existing outside ourselves. How close can we then actually get to this supposed world out- side ourselves? Just as near as but no nearer than the brain terminals of the sensory nerves. We are like the clerk in the central telephone exchange who cannot get nearer to his customers than his end of the telephone wires. We are, indeed, worse off than the clerk, for to carry out the analogy properly we must suppose him never to have been outside the telephone exchange, never to have seen a customer or any one like a customer in short, never, except through tfie telephone wire, to haie come in contact with the out- side universe. Of that " real " universe outside himself he would be able to form no direct impression ; the real universe for him would be the messages which flowed from the ends of the telephone wires in his office. About those messages and the ideas raised in his mind by them he might reason and draw his inferences ; and his conclusions would be correct for what ? For the world of telephonic messages, for the type of messages which go through the telephone. Something definite and valuable he might know with regard to the spheres of action and of thought of his telephonic subscribers, but outside those spheres he could have no experience. Pent up in his office he could never have seen or touched even a telephonic subscriber in himself. Very much in the position of such a telephonic clerk is the conscious ego of each one of us seated at the brain terminals of the sensory nerves. Not a step nearer than those terminals can the ego get to the " outer world," and what in and for themselves are the subscribers to its nerve ex- change it has no means of ascertaining. Messages in the form of sense-impressions come flowing in from THE FACTS OF SCIENCE. ?]> that " outside world " and these we analyze, classify, store up, and reason about. But of the nature of " things-in-themselves " of what may exist at the other end of our system of telephone wires we know nothing. But the reader, perhaps, remarks, " I not only see an object, but I can touch it. I can trace the nerve from the tip of my finger to the brain. I am not like the tele- phone clerk, I can follow my network of wires to their terminals and find what is at the other end of them." Can you, reader ? Think for a moment whether your ego has for one moment got away from his brain-exchange. The sense-impression that you call touch was just as much as sight felt only at the brain end of a sensory nerve. What has told you also of the nerve from the tip of your finger to your brain ? Why sense-impressions also, messages conveyed along optic or tactile sensory nerves. In truth, all you have been doing is to employ one subscriber to your telephone exchange to tell you about the wire that goes to a second, but you are just as far as ever from tracing out for yourself the telephone wires to the individual subscriber and ascertaining what his nature is in and for himself. The immediate sense-impression is just as far removed from what you term the " outside world " as the stored impress. If our telephone clerk had recorded by aid of a phonograph certain of the messages from the outside world on past occasions, then if any telephonic message on its receipt set several phonographs re- peating past messages, we have an image analogous to what goes on in the brain. Both telephone and phonograph are equally removed from what the clerk might call the " real outside world," but they enable him through their sounds to construct a universe ; he 76 THE GRAMMAR OF SCIENCE. projects those sounds, which are really inside his office, outside his office and speaks of them as the external universe. This outside world is constructed by him from the contents of the inside sounds, which differ as widely from things-in-themselves, as language, the symbol, must always differ from the thing it symbolizes. For our telephone clerk sounds would be the real world, and yet we can see how conditioned and limited it would be by the range of his particular telephone subscribers and by the contents of their messages. So it is with our brain ; the sounds from telephone and phonograph correspond to immediate and stored sense-impressions. These sense-impressions we pro- ject as it were outwards and term the real world outside ourselves. But the things-in-themselves which the sense-impressions symbolize, the "reality," as the metaphysicians wish .to call it, at the other end of the nerve remains unknown and is unknowable. Reality of the external world lies for science and for us in form 'and colour and touch sense-impressions as widely divergent from the thing " at the other end of the nerve " as the sound of the telephone from the sub- scriber at the other end of the wire. We are cribbed and confined in this world of sense-impressions like the exchange clerk in his world of sounds, and not a step beyond can we get. As his world is conditioned and limited by his particular network of wires, so ours is conditioned by our nervous system, by our organs of sense. Their peculiarities determine what is the nature of the outside world which we construct. It is the similarity in < the organs of sense and in the perceptive faculty of all normal human beings which makes the outside world the same, or practically the THE FACTS OF SCIENCE. . 77 same for them all. 1 To return to the old analogy, it is as if two telephone exchanges had very nearly identical groups of subscribers. In this case a wire between the two exchanges would soon convince the imprisoned clerks that they had something in common and peculiar to themselves. That conviction cor- responds in our comparison to the recognition of other- consciousness. 12. Outside and Inside Myself. We are now in a position to see clearly what is meant by " reality" and the " external world." Any group of immediate sense-impressions we project out- side ourselves and hold to be part of the external world. As such we call it a phenomenon, and in practical life term it real. Together with the immediate sense- impression we often include stored sense-impresses, which experience has taught us to associate with the immediate sense-impression. Thus we assume the blackboard to be hard, although we may only have seen its shape and colour. What we term the real world is thus partly based on immediate sense- impressions, partly on stored sense-impresses ; it is what has been called a construct. For an individual the distinction between the real world and his thought of it is the presence of some immediate sense-impres- sion. Thus the distinction of what is "outside" and what is " inside " myself at any instant depends entirely on the amount of immediate sense-impres- sion. This has been very cleverly represented by the well-known German scientist, Professor Ernst Mach, 1 Not exactly the same, for the range of the organs of sense and the powers of perception vary somewhat with different individual men, and probably enormously, if we take other life into account. ?S THE GRAMMAR OF SCIENCE. in the accompanying sketch. The professor is lying on his sofa, and having closed his right eye, the picture represents what is presented to his left eye : " In a frame formed by the ridge of my eyebrow, by FIG. T. my nose, and my moustache, appears a part of my body, so far as it is visible, and also the things and space about it. ... If I observe an element, A, within my field of vision, and investigate its connection with another element, B, within the same field, I go out of THE FACTS OF SCIENCE. 79 the domain of physics into that of physiology or psychology, if B, to use the apposite expression that a friend of mine employed upon seeing this drawing, passes through my skin." x From our standpoint, neglecting for simplicity the immediate contributions of any other senses than that of sight, the picture represents that part of the Pro- fessor's sense-impressions which for the instant forms his " outside world " ; the rest was " inside " existed for him only as stored sense-impresses. There is no better exercise for the mind than the endeavour to reduce the perception we have of " ex- ternal things " down to the simple sense-impressions by which we feel them. The arbitrary distinction between outside and inside ourselves is then clearly seen to be one merely of everyday practical con- venience. Take a needle ; we say it is thin, bright, pointed, and so forth. What are these properties but a group of sense-impressions relating to form and colour associated with conceptions drawn from past sense-impressions ? Their immediate source is the activity of certain optic nerves. These sense-impres- sions form for us the reality of the needle. Neverthe- less, they and the resulting construct are projected outside ourselves, and supposed to reside in an external thing, "the needle." Now by mischance we run the needle into our finger ; another nerve is excited and an unpleasant sense-impression, one which we term painful, arises. This, on the other hand, we term " in ourselves," and do not project into the needle. Yet the colour and form which constitute for us the needle are just as much sense-impressions within us as the 1 " The Analysis of the Sensations Anti-metaphysical," The Monist, vol. i. p. 59. 80 THE GRAMMAR OF SCIENCE. pain produced by its prick. The distinction between ourselves and the outside world is thus only an arbi- trary, if a practically convenient, division between one type of sense-impression and another. The group of sense-impressions forming what I term myself is only a small subdivision of the vast world of sense- impres- sions. My arm is paralyzed, I still term it part of me ; it mortifies, I am not quite so certain whether it is to be called part of me or not ; the surgeon cuts it off, it now ceases to be a part of that group of sense-impressions which I term " myself." Obviously the distinction between " outside " and " inside," be- tween one individuality and a second, is only a practical one. How many of the group of sense- impressions we term a tree are light and atmosphere effects ? What might be termed the limits of the group of sense-impressions which we term an indi- vidual cannot be scientifically drawn. But to this point we shall return later. 13. Sensations as the Ultimate Source of the Materials of Knoivledge. When we find that the mind is entirely limited to the one source, sense-impression, for its contents, that it can classify and analyze, associate and construct but always with this same material, either in its im- mediate or stored form, then it is not difficult to understand what, and what only, can be the facts of science, the subject-matter of knowledge. Science, we say at once, deals with conceptions drawn from sense-impressions, and its legitimate field is the whole content of the human mind. Those who assert that science deals with the world of external phenomena are only stating a half-truth. Science only appeals to THE FACTS OF SCIENCE. 8 1 the world of phenomena to immediate sense-impres- sions with the view of testing and verifying the accuracy of its conceptions and inferences, the ultimate basis of which lies as we have seen in such immediate sense-impressions. Science deals with the mental, the " inside " world, and the aim of its processes of classi- fication and inference is precisely that of instinctive or mechanical association, namely, to enable the exertion, best calculated to preserve the race and the individual, to follow on the sense-impression with the least expenditure of time and of intellectual energy. Science is in this respect an economy of thought a delicate tuning in the interests of the mind of the organs which receive sense-impressions and those which expedite activity. Turn the problem round and ponder over it as we will, beyond the sense- impression, beyond the brain terminals of the sensory nerves we cannot get. Of what is beyond them, of " things-in-themselves," as the metaphysicians term them, we can know but one characteristic, and this we can only de- scribe as a capacity for producing sense-impressions, for sending messages along the sensory nerves to the brain. This is the sole scientific state- ment which can be made with regard to what lies beyond sense-impressions. But even in this state- ment we must be careful to analyze our meaning. The methods of classification and inference, which hold for sense-impressions and for the conceptions based upon them, cannot be projected outside our minds, away from the sphere in which we know them to hold, into a sphere which we have recognized as unknown and unknowable. The laws, if we can speak of laws, of this sphere must be as unknown as 7 82 THE GRAMMAR Of SCIENCE. its contents, and therefore to talk of its contents as producing sense-impressions is an unwarranted in- ference, for we are asserting cause and effect a law of phenomena or sense-impressions to hold in a region beyond our experience. 1 We knoiv ourselves, and we know around us an impenetrable wall of sense-impres- sions. There is no necessity, nay, not even logic, in the statement that behind sense-impressions there are " things-in-themselves" producing sense-impressions. Of this supersensuous sphere we may philosophize and dogmatize unprofitably, but we can never know use- fully. It is indeed an unjustifiable extension of the term knowledge to apply it to something which can- not be part of the mind's contents. What is behind or beyond sense-impressions may or may not be of the same character as sense-impressions, we cannot say. We feel the surface of a body to be soft, but its core may be either hard or soft, we cannot say ; we can only legitimately call it a soft-surfaced body. So it is with sense-impressions and what may be behind them; we can only say sense-impression-stuff, or, as we shall term it, with a somewhat divergent meaning from the customary, sensation. By sensation we shall accordingly understand that of which the only know- able side is sense-impression. Our object in using the word sensation instead of sense-impression will be to express our ignorance, our absolute agnosticism, as to whether sense-impressions are " produced " by unknowable " things - in - themselves," or whether behind them may not be something of their own nature. 2 The outer world is for science a world of 1 This will appear clearer when we have discussed the scientific meaning of cause and effect. See Chapter IV. 2 Herein lies the arid field of metaphysical discussion. Behind THE FACTS OF SCIENCE. 83 sensations, and sensation is known to us only as sense-impression. 1 4. Shadow and Reality. The reader who comes to these problems for the first time may feel inclined to assert that if this world of sense-impressions is the world of scientific know- ledge, then science is dealing with a world of shadows and not of real substances. And yet, if such a reader will think over what happens when he knocks his elbow against the table, I think he will agree that it is the sense-impressions of hardness, and perhaps of pain, which are for him the realities, while the table, as a " source of these sense-impressions," is the shadow. Should he impatiently retort : " I see the table four-legged, brass-handled, with black oak top shining under the elbow-grease of a past generation there is the reality," let him stop for a moment to inquire whether his reality is not a construct from immediate and stored sense-impressions, of exactly the same character "as the previous sense-impression of hardness. He will soon convince himself that the real table lies for him in the permanent association of a certain group of sense-impressions, and that the shadow table is what might be left were this group abstracted. sense-impressions, and as their source, the materialists place Matter ; Berkeley placed God ; Kant, and after him Schopenhauer, placed Will; and Clifford placed Mind-stuff. Professor E. Mach in the paper referred to on p. 79 nas reduced the outer world to its known surface, sense- impression, which he terms sensation leaving no possible unknowable plus which we intend to signify by our use of the word sensation. Such a theory cannot lead to scientific error, but it does not seem a justifiable inference from sense-impression. The variety of inferences cited above shows the quagmire which has to be avoided, especially when the inferences are drawn with a view of influencing judgment in the world of sense. 84 THE GRAMMAR OF SCIENCE. Let us return for a moment to our old friend the blackboard, represented for us by a complex of properties (p. 48). In the first place we have size and shape, then colour and temperature, and, lastly, other properties like hardness, strength, weight, &c. Clearly the blackboard consists for us in the permanent association of these properties, in a construct from our sense-impressions. Take away the size and shape, leaving all the other pro- perties, and the group has ceased to be the black- board, whatever else it may be. Suppose the colour to go and again the blackboard has ceased to be. Finally, if the hardness and weight were to vanish, we might see the ghost of a blackboard, but we should soon convince ourselves that it was not the " reality " we had termed blackboard. Now, as the reader may be thinking that this blackboard has had too long an existence, at least in our pages, let us employ a carpenter to pull it to pieces and construct out of it a four-legged table. To cloak the obvious deficiences of such a table we will cause it to be coated with a thick layer of Aspinall's enamel. We have now a four-legged red table. It is no longer a blackboard, and any person not knowing its origin would think us quite mad if we termed it a black- board. We should probably, however, make our- selves intelligible to him by stating that the " same material " as was once in a blackboard is now in the red table. For practical purposes this is very proper and convenient, but will it help us to an accurate con- ception of individuality, if we say the blackboard and the table are the same thing ? New paint and pro- bably nails have been added ; the carpenter may have supplied some additional wood ; nay, more, if THE FACTS OF SCIENCE. 85 we begin to use our table a leg may come off and a new one be put on ; after a time a fresh top would be an advantage, thus even the " material " of the table may cease to be same as that of the blackboard. Or again, since our table is probably a bad one, we will break it up and burn it, and so the blackboard will be converted into various gases and some ashes. What has now become of it ? Size and shape, temperature and colour, hardness and strength have all gone. It is true that the chemist asserts that, if we could com- pletely collect the gases and ashes, one sense-impres- sion at least, that of weight, would remain the same in these and the original blackboard. But can we define sameness to consist in the permanence of some one sub-group of sense-impressions, notwith- standing the divergence of the majority? That permanence may be a link in the succession of our sense-impressions, but it can hardly be taken as a basis for defining individuality. If the gases and ashes could be collected ! They have, indeed, been scattered to the winds and in course of time may be absorbed by other vegetable life, ultimately, perhaps, to reappear as other blackboards, or even in legs of mutton. What has become of the " thing-in-itself" behind the group of sense-impressions we termed the original blackboard ? Surely there is less permanence in it than in our sense-impressions of the blackboard far less than in that purely mental conception of sameness of weight. Is it not clear that the reality of the blackboard consisted for us in the permanent grouping together of certain sense-impressions, and that that reality has disappeared for ever, except as a group of stored sense-impresses? 86 THE GRAMMAR OF SCIENCE. 15. Individuality. Let us look again at this matter from a slightly different standpoint. Let us consider a close friend, and then suppose his height, his figure, the familiar features of his face changed ; let his entire round of physical characteristics be profoundly modified, or vanish altogether. Next let us imagine his gifts, his prejudices, the little weaknesses which really endear him to us, his views on literature, politics, and social problems, all his conceptions of human life changed or removed entirely. In short, all the sense- impressions which constitute our friend gone. Clearly the friend would have ceased for us to be, his in- dividuality would have disappeared. The " reality " of the friend consists for us not in some shadowy "thing-in-itself," but in the persistency of the majority of the group of sense-impressions by which we identify him. We are accustomed to speak, for practical purposes, of the boy and the man as the same individual, but the body and mind have changed so enormously that the man would probably feel the boy a perfect stranger if he were brought into his presence. We experience an uncomfortable sense of strangeness in looking at portraits of ourselves taken twenty or thirty years ago. The properties of youth and man are, indeed, so widely different, that though for practical purposes we call them the same person, we suspect that they would cut each other if they chanced to meet in the street. Clearly an individual is not characterized by any sameness in the thing-in- itself, but by the permanency in certain groupings of sense-impressions; this is the basis of our identifica- tion. THE FACTS OF SCIENCE. 87 ib.The Futility of " Things-in-themselves." If at different times we meet with two groups of sense-impressions which differ very little from each other, we term them the same object or individual, and in practical life the test of identity is sameness in sense- impressions. The individuality of an object consists for us in the sameness of the great majority of our sense-impressions at two instants of time. In the case of growth, or rapid change in a group of sense- impressions, these instants must be taken closer and closer together as the rapidity increases. A stored impress of this sameness is then formed in the mind of the observer, and this constitutes in the case of the " external world " the recognition of individuality, in the case of the " internal world " the feeling of the continuity of the ego. The considerations of this section upon what we are to understand by an individual thing are more important than they may appear to the reader at first sight. Are we forced to assume a shadowy " thing-in- itself" behind a group of sense-impressions in order to account for the permanency of objects, their existence as individuals ? We have seen by the examples cited that the thing-in-itself would have to be supposed as transient as the sense-impressions, the permanency of which it is introduced to explain. 1 We are not, however, thrown back on any metaphysical inquiry as to things-in-themselves, in order to define for prac- tical and scientific purposes the sameness of objects. 1 Unless, indeed, we follow the crude materialism of Blichner, who takes the special sense-impressions which we term material to be the basis of all other sense-impressions, or to be the thing-in-itself. The individuality of the object is then thrown back on the sameness of the unknown elements of matter : see Chapter VII, 88 THE GRAMMAR OF SCIENCE. Looking out of my window I see in a certain corner of my garden an ash-tree, with boughs of a certain form and shape, the sun is playing upon it and a certain light and shade is visible, the wind is turning over the leaves of the western branches. All this forms a complex group of sense-impressions. I close my eyes, and on opening them I have again a complex group of sense-impressions, but slightly differing from the last, for the sun has left some leaves and fallen on others, and the wind is still ; but there is- a sameness in the great majority of the sense-impressions of the two groups, and accordingly I term them one and the same individual tree the ash-tree in my garden. If any one tells me that the sameness is due to some " thing-in-itself " which introduces the permanency into the group of sense-impressions, I can as little accept or deny his assertion as he forsooth can demonstrate anything about this shadowy thing-in- itself. He may call it Matter, or God, or Will, or Mind- stuff, but to do so serves no useful purpose, for it lies beyond the field of conception based on sense-impres- sions, beyond the sphere of logical inference or human knowledge. It is idle to postulate shadowy unknow- ables behind that real world of sense-impression in which we live. So far as they affect us and our conduct they are sense-impressions ; what they may be beyond is fantasy, not fact; if indeed it be wise to assume a beyond, to postulate that the surface of sense- impressions which shuts us in, must of necessity shut something beyond out. Such unknowables do not assist us in grasping why groups of sense-impressions remain more or less permanently linked together. Our experience is that they are so linked, and their association is at the present, and may ever remain, as. THE FACTS OF SCIENCE. 89 mysterious as is now the process by which stored impressions are involuntarily linked together in the brain. Why is the thought " garden " in my mind invariably followed by the thought "cats"? The psychical basis of the association is not what I mean. I recognize it in the repeated experience of the havoc which the feline race has wrought in my own garden. But what is the physical nexus between the two con- ceptions as impresses in my brain ? No one can say ; and yet this problem should be easier to answer than that of the nexus between the immediate sense- impressions we term objects. When physiological psychology has answered the former problem, then it will perhaps cease to be foolish for us to discuss the latter. Meanwhile let us confess our ignorance and work where a harvest may even at present be gathered. 17. The Term Knowledge is Meaningless if applied to Unthinkable Things. We are now, I think, in a position to clearly grasp what we mean by the facts of science ; we see that its field is ultimately based upon sensa- tions. The familiar side of sensations, sense- impressions, excite the mind to the formation of constructs and conceptions, and these again, by asso- ciation and generalization, furnish us with the whole range of material to which the scientific method applies. Shall we say that there are limits to the scientific method that our power of knowledge is imprisoned within the narrow bounds of sense-im- pression ? The question is an absurd one until it has been demonstrated that a definition can be found for knowledge, which shall include what does not lie in 90 THE GRAMMAR OF SCIENCE. the plane of men's thought. Our only experience of thought is associated with the brain of man ; no inference can possibly be legitimate which carries thought any further than nervous systems akin to his. But human thought has its ultimate source in sense-impressions, beyond which it cannot reach. We can therefore only show that our knowledge is of necessity limited by demonstrating that there are problems within the sphere of man's thought, the only sphere where thought can be legitimately said to exist, which can never be solved. Such a demonstration I, for one, have never met with, and I believe that it can never be given. We must one and all confess that within the sphere of thinkable things our knowledge is still the veriest thread. We may even go so far as to assert that unto complete knowledge we shall never attain in finite time ; but this admission differs widely from the assertion that knowledge is possible as to things outside thought, but yet, however possible, must be unattainable. Such an assertion must seem hopelessly absurd unless we use knowledge as a term for some relationship which exists between things outside thought. But even this strained use of the term, apart from its confusion, leads us no further than the statement that an un- meaning x exists among an unthinkable y and 2. SUMMARY. I. Immediate sense-impressions form permanent impresses in the brain which psychically correspond to memory. The union of im- mediate sense-impressions with associated stored impresses leads to the formation of "constructs," which we project " outside ourselves," and term phenomena. The real world lies for us in such constructs and not in shadowy things-in-themselves. " Outside " and "inside" one- self are alike ultimately based on sense-impressions ; but from these THE FACTS OF SCIENCE. 91 sense-impressions by association, mechanical and mental, we form conceptions and draw inferences. These are the facts of science, and its field is essentially the contents of the mind. 2. When an interval elapses between sense-impression and exertion filled by cerebral activity marking the revival and combination of stored impresses we are said to think or to be conscious. Other- consciousness is an inference, which, not yet having been verified by immediate sense-impression, we term an eject ; it is conceivable, how- ever, that it could become an object. Consciousness has no meaning beyond nervous systems akin to our own ; it is illogical to assert that all matter is conscious, still more that consciousness can exist outside matter. 3. The term knowledge is meaningless when extended beyond the sphere in which we may legitimately infer consciousness, or when applied to things outside the plane of thought, i.e., to metaphysical terms dignified by the name of conceptions although they do not ultimately flow from sense-impressions. LITERATURE. These notices being only intended to indicate easily readable matter for lay students, it would be idle to provide here a list of philosophical classics. I therefore refer with some hesitation to Kant's Kritik der reinen Vernunft (Eng. Trans, by Max Miiller). At the same time I know no elementary treatise on Kant's view of "things-in- themselves." As moderate in length and easily intelligible I cite: BERKELEY, G. An Essay towards a New Theory of Vision, 1709 ; A Treatise Concerning the Principles of Human Knowledge, 1710 ; and Three Dialogues Between Hylas and Philonous, 1713. (All to be found in vol. i. of Wright's edition of the Works of G. B., 1843-) CLIFFORD, W. K. Lectures and Essays ("Body and Mind" and "On the Nature of Things-in-themselves "). Further : Seeing and Thinking. Macmillan's " Nature " Series, 2nd ed., 1880. HUXLEY, T. H. Hume. Macmillan, 1879. MACH, E. Beitrage zur Analyse der Empfindungen, 1886. Further : '* The Analysis of the Sensations Anti-metaphysical," The Monist, vol. i. pp. 48-68 ; "Sensations and the Elements of Reality," Ibid. PP- 393-400. MORGAN, C. LL. Animal Life and Intelligence, chaps, viii. and ix. Arnold, 1891. PEARSON, K. The Ethic of Freethought (" Matter and Soul ") r CHAPTER III. THE SCIENTIFIC LAW. I. Resume and Foreword, THE discussions of our first two chapters have turned upon the nature of the method and material of modern science. The material of science corre- sponds, we have seen, to all the constructs and concepts of the mind. Certain of these constructs associated with immediate sense-impressions we pro- ject outwards and speak of as physical facts or phenomena ; others, which are obtained by the mental processes of isolation and co-ordination from stored sense-impresses, we are accustomed to speak of as mental facts. In the case of both these classes of facts, the scientific method is the sole path by which we can attain to knowledge. The very word know- ledge, indeed, only applies to the product of the scientific method in this field. Other methods, here or elsewhere, may lead to fantasy, as that of the poet or of the metaphysician, to belief or to superstition, but never to knowledge. As to the scientific method, we saw in our first chapter that it consists in the careful and often laborious classification I of facts, in the com- 1 The reader must be careful to recollect that classification is not identical with collection. It denotes the systematic association of kindred facts, the collection, not of all, but of relevant and crucial facts. THE SCIENTIFIC LAW. 93 parison of their relationships and sequences, and finally in the discovery by aid of the disciplined imagination of a brief statement or formula, which in a few words resumes the whole range of facts. Such a formula, we have, seen, is termed a scientific law. The object served by the discovery of such laws is the economy of thought ; the suitable asso- ciation of conceptions drawn from stored and corre- lated sense-impresses, permits the fitting exertion to follow with the minimum of thought upon the receipt of an immediate sense-impression. The knowledge of scientific law enables us to replace or supplement mechanical association, or instinct, by mental associa- tion, or thought. It is the forethought^ by aid of which man in a far higher degree than other animals is able to make the fitting exertion on the receipt of a novel group of sense-impressions. We are accustomed to speak of scientific law, or at any rate of one form of it termed "natural law," as some- thing universally valid ; we hold it to be as true for all men as for its original propounder. Nay, there are not wanting those who assert that natural law has a validity quite independent of the human minds which formulate, demonstrate, or accept it. We can easily observe that there is really something sui generis about the validity of natural law. The philosopher, who propounds a new system, or the prophet who pro- claims a new religion, may be absolutely convinced of the truth of his statement ; but it is the result of experience from time immemorial that he cannot demonstrate that truth so that conviction is produced in the mind of every rational being. A philosophic or a religious formula for example, the idealism of Berkeley, the scepticism of Hume, or the self-renun- 94 THE GRAMMAR OF SCIENCE. elation of the mediaeval mystics, however sure its teachers may be that it is capable of rational demon- stration, really appeals to the individual tempera- ment, and is accepted or rejected according to the emotional sympathies of the individual. On the other hand a formula, like that which Newton pro- pounded for the motion of the planetary system, will be accepted by every rational mind which has once understood its terms and clearly analyzed the facts which it resumes. 1 This is sufficient to indicate that there must be some wide difference between philoso- phic and scientific systems, between theological and scientific formulae. I shall endeavour in this chapter to ascertain wherein this difference lies, to discover what is the meaning of the word law when used scientifically, and in what sense we can say that scientific law has universal validity. 2. Of the Word Law and its Meanings. The term law probably recalls to the reader, in the first place, the rules of conduct proclaimed by the state and enforced under more or less heavy penalties against certain classes of its citizens. Austin, the most luminous English writer on jurisprudence, 2 who has devoted a very large portion of his well-known work to a discussion of the meaning of the word !aw, remarks : "A law, in the most general and comprehensive acceptation in which the term, in its literal meaning, 1 One system of planetary gravitation is accepted throughout the civi- lized world, but more than a dozen distinct theological systems and almost as many philosophical schools hardly suffice even for our own country. 8 Lectures on Jurisprudence, 4th ed. London, 1879. HE SCIENTIFIC LAW. 95 is employed, may be said to be a rule laid down for the guidance of an intelligent being by an intelligent being having power over him." He further goes on to observe that where there is such a rule there is a command, and where there is a command a corresponding duty. From this stand- point Austin proceeds to discuss the various types of law, such as civil, moral, and divine law. It will be at once seen that with Austin's definition of law there is no place left for law in the scientific sense. He himself recognizes this, for he writes : " Besides the various sorts of rules which are in- cluded in the literal acceptation of the term law, and those which are by a close and striking analogy, though improperly, termed laws, there are numerous applications of the term law, which rest upon a slender analogy and are merely metaphorical or figurative. Such is the case when we talk of laivs observed by the lower animals ; of laws regulating the growth or decay of vegetables ; of lazvs determining the move- ments of inanimate bodies or masses. For where intelligence is not, or where it is too bounded to take the name of reason, and therefore is too bounded to conceive the purpose of a law, there is not the will which law can work on, or which duty can incite or restrain. Yet through the misapplications of a name, flagrant as the metaphor is, has the field of jurispru- dence and morals been deluged with muddy specula- tion " (p. 90). Now Austin was absolutely in the right to empha- size the immense distinction between the use of the term law in science and its use in jurisprudence. There can be no doubt that the use of the same name for two totally different conceptions has led 96 THE GRAMMAR OF SCIENCE. to a great deal of confusion. But on the one hand, if the flagrant misapplication of the scien- tific meaning of the word law to the fields of jurisprudence and morals has deluged them with " muddy speculation," there is equal certainty on the other hand that the misapplication of the legal and moral sense of the term has been equally disadvan- tageous to clear thinking in the field of science. Austin probably had in his mind when he wrote the above passage, works like Hegel's Philosophy of Lazu, in which we find the conception of the permanent and absolute character of scientific law applied to build up a system of absolute civil and moral law which some- how realizes itself in human institutions. To the mind which has once thoroughly grasped the principle of evolution in its special factor of natural selection, the civil and moral laws of any given society at a particular time must appear as ultimate results of the struggle for existence between that society and its neighbours. The civil and moral codes of a com- munity at any time are those which are on the average best adapted to its current needs, and best calculated to preserve its stability. They are very plastic, and change in every age with the growth and variation of social conditions. What is lawful is what is not prohibited by the laws of a particular society at a particular time ; what is moral is what tends to the welfare of a particular society at a particular time. We are all well ac- quainted with the continual change of civil law ; in fact we keep up an important body, termed Parlia- ment, whose chief function it is to modify and adapt our laws, so that^they shall be best fitted at each period to assist the community in its struggle for THE SCIENTIFIC LAW. 97 existence. Of the changes in moral law we are, per- haps, less conscious, but they are none the less real. There are very few acts which have not been moral at some period in the growth of one or other society, and there are in fact many questions with regard to which our moral judgment is totally different from that of our grandfathers. It is the relativity, or variability with age and community, of civil and moral law, which led Austin, I think, to speak somewhat strongly of the speculation which confuses such law with law in the absolute sense of science. A law in the legal or moral sense holds only for individuals and individual com- munities, and is capable of modification or repeal. A law of science will be seen in the sequel to hold for all normal human beings so long as their perceptive and reasoning faculties remain without material modi- fication. The confusion of these two ideas is produc- tive of that "muddy speculation" which finds analogies between natural laws and those of the spiritual or moral world. Now if we find that two quite distinct ideas unfor- tunately bear the same name we ought, in order to avoid confusion, to re-name one of them, or failing this we ought on all occasions to be quite sure in which of the two senses we are using the name. Accordingly, in my first chapter, in order to keep clear of the double sense of the word law, I endeavoured to replace it, when spoken of scientifically, by some such phrase as the " brief statement or formula which resumes the relationship between a group of facts." Indeed it would be well, were it possible, to take the term formula, as already used by theologians and mathe- maticians, and use it in place of scientific or natural law. But the latter term has taken such root in our 3 98 THE GRAMMAR OF SCIENCE. language that it would be hard indeed to replace it now. Besides, if the word law is to be used in one sense only, we may ask why it is the scientist rather than the jurist who is to surrender his right to the word ? The jurists say that historically they have the older claim to the word that civil law existed long anterior to scientific law. This is perfectly true in a certain sense, 1 because the earliest attempts to codify laws for the conduct of men living in communities preceded any conscious recognition of scientific law. Now this leads us directly to a very important distinc- tion, which, if it be neglected, is the source of much con- fusion. Does law exist before it receives expression and recognition ? According to Austin, law in the juridical sense certainly does not, for such a law involves a " command," and a " corresponding duty " that is, expression and recognition. What are we to say, then, with regard to scientific law does it really exist before man has given expression to it ? Has the word any meaning when unassociated with the mind of man ? I hold that we must definitely answer " no " to both these questions, and I believe that the reader who has carefully followed my second chapter will see at once the grounds for this statement. A scientific law is related to the perceptions and conceptions formed by the perceptive and reasoning faculties in man ; it is meaningless except in association with these ; it is the resume or brief expression of the relationships and sequences of certain groups of these perceptions and conceptions, and exists only when formulated by man. 1 For our final conclusions as to the historical right to the word, see p. 114. THE SCIENTIFIC LAW. 99 3. Natural Law relative to Man. Let us take that branch of scientific law which deals with the so-called "outside world" natural law. We have seen that this outside world is a construct. It consists of objects constructed partly from imme- diate sense-impressions, and partly from stored im- presses. For this reason the " outside world " is essentially conditioned by the perceptive and reten- tive faculties in man. Even the metaphysicians, who postulate " things-in-themselves," admit that sense- impressions in nowise resemble them, and that man's sense-impressions so far from being the entire pro- duct of "things-in-themselves," are probably but the smallest portion of their " capacity for producing " sense -impression. Hence to talk about natural law as existing in "things-in-themselves" and apart from man's mind is again to assert an unmeaning x among an unthinkable y and z (p. 90). If nature for man is conditioned by his perceptive and re- tentive faculties, then natural law is conditioned by them also. It has no relation to something above and beyond man, but solely to the special pro- ducts of his perceptive faculty. We have no right to infer its existence for things without a perceptive faculty, or even for perceptive faculties not closely akin to man's. I believe that a great deal of the ob- scurity involved in popular ideas about " Nature " would have been avoided had this been borne in mind. A good instance of the relativity of natural law is to be found in the so-called Second Law of Thermo- dynamics. This law resumes a wide range of human experience, that is, of sequences observed in our sense- impressions, and embraces a great number of conclu- IOO THE GRAMMAR OF SCIENCE. sions not only bearing on practical life, but upon that dissipation of energy which is even supposed to fore- shadow the end of all life. The appreciation of the relativity of natural law is so important that the reader will, I trust, pardon me for citing the entire passage in which Clerk-Maxwell discusses this instance * : " One of the best-established facts in thermo-dyna- mics is that it is impossible in a system enclosed in an envelope which permits neither change of volume nor passage of heat, and in which both the temperature and pressure are everywhere the same, to produce any inequality of temperature or of pressure without the expenditure of work. This is the second law of thermo-dynamics, and it is undoubtedly true so long as we can deal with bodies only in mass, and have no power of perceiving or handling the separate mole- cules of which they are made up. But if we conceive a being whose faculties are so sharpened that he can follow every molecule in its course, such a being, whose attributes are still as essentially finite as our own, would be able to do what is at present impos- sible to us. For we have seen that the molecules in a vessel of air at uniform temperature are moving with velocities by no means uniform, though the mean velocity of any great number of them, arbitrarily selected, is almost exactly uniform. Now let us sup- pose that such a vessel is divided into two portions, A and B, by a division in which there is a small hole, and that a being, 2 who can see the individual mole- 1 Theory of Heat, 3rd ed. p. 308. Longmans, 1872. 2 This "being" has become known to fame as "Clerk-Maxwell's demon," but it must be noted that Clerk-Maxwell supposes the being's attributes " essentially finite as our own " a peculiarity not usually associated with demons. THE SCIENTIFIC LAW. 10 1 cules, opens and closes this hole, so as to allow only the swifter molecules to pass from A to B, and only the slower ones to pass from B to A. He will thus, without expenditure of work, raise the temperature of B and lower that of A, in contradiction to the second law of thermo-dynamics." To render this passage clear to the lay reader, we have only to add that in this kinetic theory the tem- perature of a gas depends upon the mean speed of its molecules. Now the second law of thermo-dynamics resumes with undoubted correctness a wide range of human experience, and is, to that extent, as much a law of nature as that of gravitation. But the kinetic theory of gases, whether it be hypothetical or not,, enables us to conceive a demon having a percep- tive faculty differing rather in degree than quality from our own, for whom the second law of thermo- dynamics would not necessarily be a law of nature. Such a conception enables us to grasp how relative what we term nature is to the faculty which per- ceives it. Scientific law does not, any more than sense-impression, lie in a universe outside and unconditioned by ourselves. Clerk-Maxwell's demon would perceive nature as something totally different from our nature, and to a less extent this is in great probability true for the animal world, and even for man in different stages of growth and civilization. The worlds of the child and of the savage differ widely from that of normal civilized man. One half of the perceptions which the latter links together in a law of nature may be wanting to the former. Our law of the tides could have no meaning for a blind worm on the shore, for whom the moon had no exis- 1 This point is well brought out by Prof. Lloyd Morgan in his Animal 102 THE GRAMMAR OF tence. 1 By the contents and the manner of perception the law of nature is essentially conditioned for each perceptive faculty. To speak, therefore, of the uni- versal validity of a law of nature has only meaning in so far as we refer to a certain type of perceptive faculty, namely, that of a normal human being. 4.- Man as the Maker of Natural Law. The other problem with which we are concerned is the existence or non-existence of a scientific law before it has been postulated. Here the reader will feel inclined to remark: "Admitted that 'Nature' is conditioned by man's perceptive faculty, surely the sequences of man's perceptions follow the same law whether man has formulated that law in words or not? The law of gravitation ruled the motion of the planets ages before Newton was born." Yes and no, reader; the answer must depend on how we define our terms. The sequences involved in man's per- ception of the motion of the heavenly bodies were doubtless much the same to Ptolemy and Newton ; to primitive man and to ourselves the motion of the sun is a common perception, but a sequence of sense- impressions is not in itself a law. That planets Life and Intelligence. After pointing out the widvly different character of the sense organs in man and insects he continues : "Remember their compound eyes with mosaic vision, coarser by far than our retinal vision, and their ocelli of problematical value, and the complete absence of muscular adjustments in either one or the other. Can we conceive that, with organs so different, anything like a similar perceptual world can be elaborated in their insect mind ? I for one cannot. Admitting therefore that their perceptions may be fairly sur- mised to be analogous, that their world is the result of construction, I do not see how we can for one moment suppose that the perceptual world they construct can in any accurate sense be said to resemble ours " (pp. 298-9, 356-7, 361). THE SCIENTIFIC LAW. IO3 move, that a chick takes its origin from the egg, may be sequences of sense-impressions, they may be facts to be dealt with scientifically, but they are not laws in themselves, at least not in any useful interpretation of the word. The changes of the whole planetary system might be perceived, and even those percep- tions translated into words with a fulness surpassing that of our most accurate modern observer, and yet neither the sequence of perceptions in itself nor the description involve the existence of any law. The sequence of perceptions has to be compared with other sequences, classification and generalization have to follow ; conceptions and ideas, pure products of the mind, must be formed, before a description can be given of a range of sequences which, by its conciseness and comprehensiveness, is worthy of the name of scientific law. Let it be noted that in this it is not only the process of reaching scientific law which is mental, but that the law itself when reached involves an associa- tion of natural facts or phenomena with mental conceptions, lying quite outside the particular field of those phenomena. Without the mental concep- tions the law could not be, and it only comes into existence when these mental conceptions are first associated with the phenomena. The law of gravita- tion is not so much the discovery by Newton of a rule guiding the motion of the planets as his invention of a method of briefly describing the sequences of sense- impressions, which we term planetary motion. He did this in terms of a purely mental conception, namely, mutual acceleration. 1 Newton first brought the idea 1 The reader will find mutual acceleration fully defined and discussed in Chapter VIII. 104 THE GRAMMAR OF SCIENCE. of mutual acceleration of a certain type into associa- tion with a certain range of phenomena, and was thus enabled to state a formula, which, by what we may term mental shorthand, resumes a vast number of observed sequences. The statement of this formula was not so much the discovery as the creation of the law of gravitation. A natural law is thus seen to be a re'sumt in mental shorthand, which replaces for us a lengthy description of the sequences among our sense-impressions. Law in the scientific sense is thus essentially a product of the human mind and has no meaning apart from man. It owes its existence to the creative power of his intellect. There is more meaning in the statement that man gives laws to Nature than in its converse that Nature gives laws to man. $.The Two Senses of the Words " Natural Law." We have now traced at least one point of analogy between juridical and scientific law which I think escaped Austin, namely, both are the product of human intelligence. But we have at the same time seen the wide distinction between the two. The civil law involves a command and a duty ; the scientific law is a description, not a prescription. The civil law is valid only for a special community at a special time ; the scientific law is valid for all normal human beings, and is unchangeable so long as their perceptive faculties remain at their present stage of development. 1 For Austin, however, and 1 The perceptive faculty is probably, even on the average, varying slightly, however insensibly. Still, the perceptive faculty is now among men permanent in type, as compared with the changes it must have undergone during man's evolution from a lowly form of life. THE SCIENTIFIC LAW. 105 for many other philosophers too, the law of nature was not the mental formula, but the repeated sequence of perceptions. This repeated sequence of perceptions they projected out of themselves, and considered as part of an external world uncon- ditioned by and independent of man. In this sense of the word, a sense unfortunately far too common to-day, natural law could exist before it was recog- nized by man. In this sense natural law has a much older ancestry than civil law, of which it appears to be the parent. For tracing historically the growth of civil law, we find its origin in unwritten custom. The customs which the struggle for existence have gradually developed in a tribe become in course of time its earliest laws. Now, the farther we go back in the development of man, through more and more complete barbarism to a simply animal condition, the more nearly we find customs merging in instinctive habits. But the instinctive habit of a gregarious animal is very much akin to what Austin would have termed a natural law. The laws relating to property and marriage in the civilized states of to-day can be traced back with more or less continuity to the instinctive habits of gregarious animals. The his- torical origin, therefore, of civil law is to be sought in natural law in its older sense. Indeed this fact was recognized by the early Roman jurists, who refer to a lex natures as existing alongside the civil law. This law of nature they considered animals as well as men to have a knowledge of, and they made special reference to it in relation to marriage and the birth of children. Now it is clear that, however flagrant in Austin's opinion the metaphor may be when we speak of the laws observed by animals, still the use of 106 THE GRAMMAR OF SCIENCE. the word law in this sense is a very old one even among jurists themselves. 6. Confusion between the two Senses of Natural Law. But the Roman lawyers merely took the idea of natural law from the Greek philosophers, and it is specially to the Stoics that we owe a conception of law which is of value as illustrating the kind of obscurity which still attaches to the word natural law in many minds. The Stoics defined nature as the universe of things, and they declared this universe to be guided by reason. But reason, because it is a directive power, forbidding and enjoining, they called law. Now, the law of nature they considered to take in some manner its rise in nature itself there was no source of law to nature outside nature and they accordingly defined this law of nature as a force inherent in the universe. They further asserted that since reason cannot be twofold, and since man has reason as well as the universe, the reason in man and the universe must be the same, and therefore the law of nature must be the law by which men's actions ought to be guided. The string of dogma and unwarranted inference marking this argument which, however, has only reached us at second-hand 1 is characteristic enough. Yet the argument is noteworthy, for we find in it the three meanings of the term law with which we have been dealing hopelessly confused. The Stoics pass from the scientific law to the lex natures, the mere sequence of phenomena, and then to the civil or moral law without in the least observing the magni- 1 Marcus Aurelius, iv. 4, and Cicero, De legibus i. 6-7. Cf. T. C. Sandars, The Institutes of Justinian, p. xxii. Longmans, 1878. SCIENTIFIC LAW. 10? tude of their spring; and what these early philosophers accomplished in this way has been surpassed by the devotees of philosophy and natural theology in later ages. One example will, perhaps, suffice for our present investigation. Richard Hooker, a divine of the sixteenth century, who achieved a remarkable reputation for himself by stating paradoxes based on a confusion between natural and moral law, thus defines law in general : " That which doth assign unto each thing the kind, that which doth moderate the force and power, that which doth appoint the form and measure of working, the same we term a Law " (Ecclesiastical Polity ', bk. I. ii.). Hooker further considers that all things, including nature, have some operations " not violent or casual." This leads him to assert that such operations have "some fore-conceived end." Hence he holds that nature is guided by law, and that this law is a pro- duct of reason. Unlike the Stoics, Hooker placed this reason in a worker, God, outside and not inherent in Nature, otherwise his doctrine and the conclusions he draws from it closely resemble theirs. He was, however, aware of the elastic character of his defini- tion of law, for he writes : " They, who thus are accustomed to speak, apply the name Law unto that only rule of working which a superior authority imposeth ; whereas we, somewhat more enlarging the sense thereof, term any kind of rule or canon whereby actions are framed, a law " (bk. I. iii.). The views of Hooker and the Stoics thus briefly sketched deserve careful consideration by the reader, as they suggest the type of fallacy into which we fall IOS THE GRAMMAR OF SCIENCE. by ill-defined use of the term natural law. 1 In the first place these philosophers start from the concep- tion of natural law as the mere concatenation of phenomena, the succession or routine of sense-impres- sions. In the next place as materialists they project these sense-impressions into a real outside world, unconditioned by and independent of man's percep- tive faculty. Then they infer reason behind the concatenation of phenomena. Now, reason is known to us only in association with consciousness, and we find consciousness only with the accompaniment of a certain type of nervous organism. Thus to infer reason in what has been previously postulated as outside and independent of this type of nervous organism is unjustifiable ; it may be dogma, but it is not logic. It makes little difference whether, with the Stoic, we assert that reason is inherent in nature, or, like Hooker, place the lawgiver outside nature as at once its creator and director. Both assertions lie completely outside the field of knowledge, and, as we have said of the like statements before, they logically refer to an unmeaning x existing among an unthink- able y and z (i.e., " realities " unconditioned by man's perceptive faculty). 1 The study of fallacy in concrete examples ought to play a greater part in our educational curriculum. Certain works have a permanent value in this respect. I can conceive no better exercises for a student of logic or jurisprudence than an analysis of the paralogisms in Book I of Hooker's Ecclesiastical Polity ; for a student of physics, than a dis- covery of the fallacies in Mr. Grant Allen's Force and Energy ; or for both than a critical study of Drummond's A^/wra/Zaw in the Spiritual World ; while a more difficult study in pseudo-science will be found in the first part of J. G. Vogt's Das Wesen der Elektrizitdt und des Magnetismus. The power of criticism and the logical insight thus attainable are in many respects as advantageous as the appreciation of method which results from the perusal of genuine science. , THE SCIENTIFIC LAW. 1 09 7. The Reason behind Nature. But how, it may be asked, has the conception that reason exists behind phenomena become so wide- spead ? Why have so many philosophers and theolo- gians, nay, even scientists, 1 used the "argument from design"? The duty of science does not end with showing an argument to be fallacious ; it has to investigate the origin of the fallacy and show the nature of the process by which it has arisen. In the present case I do not think we have far to seek. Briefly stated, the " argument from design " consists in the production of evidence from the laws of nature, tending to exhibit those laws as the product of a rational being or of reason in one or another form. Now, although in the law of nature defined as a mere concatenation of phenomena, as a sequence of sense- impressions, there is, so far as I can perceive, no evidence of reason in any intelligible sense of the word, yet in the law of science, and in that branch of it which in this work we have termed natural law, there is every evidence of reason. So soon as man begins to form conceptions from his sense-impres- sions, to combine, to isolate, and to generalize, then he begins to project his own reason into phenomena, to replace in his mind the sense- impresses of past concatenations of phenomena by those brief resumes or formulae which describe the sequences of sense-impressions in mental short- hand. He begins to confuse the scientific law, the product of his own reason, with the mere con- catenation of phenomena, the natural law in the sense of Hooker and the Stoics. As he projects his 1 E.g., Sir G. G. Stokes, in his otherwise most suggestive and masterly Burnett Lectures on Light. IIO THE GRAMMAR OF SCIENCE. sense-impressions outside himself, and forgets that they are essentially conditioned by his own perceptive faculty, so he unconsciously severs himself from the products of his own reason, projects them into phenomena, only to refind them again and wonder what reason put them there. Here, in the double sense of the word natural law, lies the origin of much obscure speculation. The reason we find in natural phenomena is surely put there by the only reason of which we have any experience, namely, the human reason. The mind of man in the process of classifying phenomena and formulating natural law introduces the element of reason into nature, and the logic man finds in the universe is but the reflection of his own reasoning faculty. A dog, if able to recognize the instinct which guides his actions, might very naturally sup- pose instinct and not reason to be the basis of natural phenomena, reflecting his own source of action into all he observed around him. Indeed, it seems to me more logical to find instinct than reason behind the setting and rising of the sun, for instinct at least does not presuppose consciousness. Perhaps if our dog were a Stoic dog the instinct would seem to him inherent in the universe itself, while had he been reared at the parsonage he would certainly fancy his kennel the product of an instinct extramundane. But both dog and man, in thus arguing beyond the sphere of legitimate inference, are also breaking a funda- mental canon of the scientific method. This canon is practically due to Newton, and forbids us to seek superfluous causes for natural phenomena. 1 We ought 1 Causas rerum naturafaim non plures admittidebere, quam qua &vera sint & earwn Phanomenis explicandis sufficiunt. Natura enim simplex THE SCIENTIFIC LAW. Ill not to look for new causes to explain any group of phenomena until we have shown that no known cause is capable of explaining it. In our next chapter we shall see more clearly what is to be understood by the words " cause " and " explanation," but for the present Newton's canon suffices to show us that the Stoics were unscientific in seeking for unknown or unknow- able "reasons" inherent in nature, until they had demonstrated that the only rational faculty known to them namely, that of man was insufficient to account for the rational element they professed to observe in nature. What is reason ? Where may we infer its existence ? Can we proceed from this admis- sible reason to the rational element in natural law ? these are the questions the Stoics ought logically to have asked themselves. Our wonder ought not to be excited by the idea that so vast a range of phe- nomena are ruled (sic /) by so simple a law as that of gravitation, but we ought to express our astonishment that the human mind is able to express by so brief a description such wide sequences of sense-impressions. This capacity of itself suggests some harmony, some relation between the perceptive and reasoning faculties in man a matter to which I shall return later. 8. True Relation of Civil and Natural Law. Proceeding from Austin's definition of law, we have found it necessary to distinguish between two different ideas frequently confused under the term "natural law," namely, the mere concatenation of est <5r rerum causis stiperjlttis non luxuriat. Principia. (Editio Princeps, 1687, p. 402.) This "simplicity of nature" is, of course, a dogma, but the regula philosophandi which forbids us to revel in superfluous causes is fundamental to our view of science as an economy of thought. 112 THE GRAMMAR OF SCIENCE. phenomena and the mental formula which gives brief expression to their sequences. Before we devote our undivided attention to the latter as the scientific con- ception of natural law, it may be of interest to clear up one or two remaining points with regard to civil and scientific law. While Austin, thinking rather of natural law in the old sense, states that any relation between the two is merely metaphorical, both the Stoics and Hooker conceive that the reason, or the lawgiver to be recognized behind phenomena, ought to guide man's moral conduct. Now, if these philo- sophers were looking upon natural law as the product of the human reason there would be little to require further comment; but, as we have seen, this is far from the case. The Stoics tell us that reason cannot be twofold, that it must be the same reason in both man and the universe, and that therefore the civil law of man is identical with natural law. 1 The inference is of course unjustifiable, for the same reason may be at work in two quite distinct fields. It is important to notice, however, that in one sense civil and moral laws are natural products; they are products of par- ticular phases of human growth. This growth is itself capable of treatment by the scientific method, and the sequence of its stages can be expressed by scientific formulae, or, looking at civil and moral law as objective phenomena, by natural laws. Thus civil law is a natural product, and not identical with natural law any more than the particular configuration of the planetary system 1 Up to the " sameness of the reason " there is little exception to be taken to the argument, but few of us would agree with the dictum of that ancient and upright judge, Sir John Powell, that "nothing is law that is not reason." THE SCIENTIFIC LAW. 113 at this moment is identical with the law of gravitation. We are now, I think, in a position to draw a clear distinction between civil (or moral) law and natural law. Civil law takes its origin in natural Jaw in the old sense (p. 105), while its growth and variation can, in broad outline at least, be described in the brief formulae of science, or in natural laws in the scientific sense. Civil and moral laws are the natural product of societies, and of classes within society, struggling in the early days for self-preserva- tion, and in these later days for a maximum of indi- vidual comfort. A civil law, according to Austin, is a rule laid down for the guidance of an intelligent being by an intelli- gent being having power over him. Such a rule varies with every age and every society. On the other hand, a natural law is not laid down by one intelligent being for another ; it involves no command or corresponding duty, and it is valid for all normal human beings. It has taken centuries for men to arrive at a full appreciation of this distinction, and it would be well could the distinction be now em- phasized by the specialization of the word law in one or other of its senses. We sadly need separate terms for the routine of sense-impressions, for the brief description or formula of science and for the canon of social conduct, or, in other words, for the percep- tive order, the descriptive order, and the prescriptive order. Historically we cannot say that any of these orders has the higher claim to the title law, for the Roman ideas of law must at least be traced back to their Greek parentage. Here, in the Greek word 1/6/^09, law, the confusion centres, and at the same time the historical origin of the confusion becomes apparent 9 114 THE GRAMMAR OF SCIENCE. This word shows us that civil law originated in custom, and yet Plato derives it from "distribution of mind." 1 Anything from the harmony of nature to the strains of a song was for the Greek law. In the conception of order or sequence, therefore, we see the historical origin of law in all its senses, and thus no claim to priority on the part of either jurist or scientist can be historically proven. No individual writer can hope with success to remould such old-established usage as is associated with the word law, and all he can strive to do is to keep clearly distinct in the mind of his readers the sense in which the word on each occasion is used. 2 9. Physical and Metaphysical Supersenstiousness. Having now analyzed our ideas of law, and reached a definition of law in its scientific sense, it may be well, even at the cost of repetition, to discuss at greater length our conclusions and their application to our theory of life. From the material provided by the senses, either directly or in the form of stored sense-impresses, we draw conceptions. About these conceptions we reason, endeavouring to ascertain their relationships and to express their sequences in those brief statements or formulae which we have termed scientific laws. In this process we often analyze the material of sense-impressions into elements which are not in themselves capable of form- * The Laws, iv. 714, and see also iii. 700, and vii. 800. a For the remainder of this work I shall, for convenience, however speak of natural law in the old sense, or, as a mere routine of per- ceptions, as law in the nomic sense. Law in the nomic sense is thus no product of the reason, but a pure order of perceptions, while Bram- hall's coinage anomy may be conveniently used for a breach in the routine of perceptions. THE SCIENTIFIC LAW. 1 15 ing distinct sense-impressions ; we reach conceptions which are not capable of direct verification by the senses ; that is to say, we can never, or at least we cannot at present, assert that these elements have objective reality (see our p. 50). Thus physicists reduce the groups of sense-impressions which we term ma- terial substances to the elements molecule and atom y and discuss the motion of these elements, which have never been, and perhaps never can become, direct sense-impressions. No physicist ever saw or felt an individual atom. Atom and molecule are intellectual conceptions by aid of which physicists classify phe- nomena, and formulate the relationships between their sequences. From a certain standpoint, therefore, these conceptions of the physicist are super sensuous > that is, they do not at present represent direct sense- impressions ; but the reader must be careful not to confuse this kind of supersensuousness with that of the metaphysician. The physicist looks upon the atom in one or other of two different ways : either the atom is real, that is, capable of being a direct sense-impression, or else it is ideal, that is, a purely mental conception by aid of which we are enabled to formulate natural laws. 1 It is either a product of the perceptive faculty, or of the reflective or reasoning faculty in man. It may pass from the latter to the former, from the ideal stage to the real ; but till it does so, it remains merely a conceptual basis for classifying sense-impressions, it is not an actuality. On the other hand, the metaphysician asserts an existence for the supersensuous which is unconditioned by the per- ceptive or reflective faculties in man. His super- sensuous is at once incapable of being a sense- 1 That is, it is part of the physicist's mental shorthand. Il6 THE GRAMMAR OF SCIENCE. impression, and yet has a real existence apart from the imagination of men. It is needless to say that such an existence involves an unproven and un- demonstrable dogma. Nevertheless, the magnitude of the gulf between the supersensuous of the phy- sicist and that of the metaphysician is frequently neglected, and we are told that it is as logical to discuss " things-in-themselves " as molecules and atoms ! 10. Progress in the Formulating of Natural Law. By the formation of conceptions, which may or may not have perceptual equivalents in the sphere of sense-impression, the scientist is able to classify and compare phenomena. From their classification he passes to formulae or scientific laws describing their sequences and relationships. The wider the range of phenomena embraced, and the simpler the state- ment of the law, the more nearly we consider that he has reached a " fundamental law of nature." The progress of science lies in the continual discovery of more and more comprehensive formulae, by aid of which we can classify the relationships and sequences of more and more extensive groups of phenomena. The earlier formulae are not necessarily wrong, they are merely replaced by others which in briefer language describe more facts. We cannot do better than examine this process very briefly in a special case, namely, the motion of the planetary system. An easily observed part of this motion was the daily passage of the sun, its rising in the East and setting in the West. A primi- tive description of the motion consisted in the state- THE SCIENTIFIC LAW. 1 1/ ment that the same sun which set in the West passed, hidden by northern mountains, along the surface of the^to earth and rose again in the East The descrip- tion was clearly very insufficient, but it was a first attempt at a scientific formula. An obvious improve- ment was soon made by limiting the surface of the earth and supposing the sun to go below the solid earth. The motion of the sun taken in conjunction with the motion of the stars led early astronomers to con- clude that the earth was fixed in mid-space, and sun and stars were daily carried round it. The descrip- tion thus improved was still far from complete ; the sun was observed to vary its position with regard to the fixed stars. Gradually and laboriously facts were accumulated, and in time those early astronomers con- cluded that the sun went round yearly in the same circle, this circle itself being carried round with the starry heavens once in a day. This formula embraced a wider field of phenomena than the earlier ones, and probably was as exact a description as men's percep- tions of earth and sun allowed when it was invented. Hipparchus improved it by placing the earth not exactly in the centre of the sun's circle, and thus more accurately described certain apparent irregularities in the sun's motion. A still more complete description was adopted by Ptolemy (A.D. 140) nearly three hundred years after Hipparchus, who, fixing the spherical earth, considered sun and moon to move in circles yearly round the earth, and the other planets in circles, whose centres again described circles round the earth. The whole of this system revolved daily round the earth with the stars. This, the famous Ptolemaic system, remained for many centuries the current formula, and even to this day the eccentrics of Hipparchus and! Il8 THE GRAMMAR OF SCIENCE. epicycles of Ptolemy are not without service as ele- ments of the more modern description. It would be wrong, I think, to say that the Ptolemaic system was an erroneous explanation, it was simply an in- sufficient attempt to describe in brief and accurate language a too limited range of phenomena. Then at the end of the Middle Ages came Copernicus who got rid of the cumbersome sphere carrying the fixed stars by simply considering the earth to rotate round its axis and of the epicycles, if not of the eccentrics, by treating the sun, not the earth, as the central point of the system. Here was an im- mense advance in brevity and accuracy of description ; but still more facts remained to be included, more difficulties to be analyzed and overcome. This work was largely done by Keppler, who conceived the earth and planets to move in certain curves termed ellipses, of which the sun occupied a non-central point termed the focus. The formula of Keppler is one of the greatest achievements of the scientific method ; it was the work of a disciplined imagination analyzing a laborious and minute classification of facts. 1 A more wide-embracing statement than that of Keppler was not only possible, however, but required ; and this was provided by Newton in a single formula which embraces not only the motion of the planets, but that of their moons and of bodies at their surfaces. This formula is the well-known law of gravitation, but it is just as much a description of what takes place in planetary motion as Keppler's laws are a description it is simply a briefer, more accurate, and more wide-em- 1 The elaborate observations of Tycho Brahe. Keppler not only stated the form of the planetary path, but the mode of its description in his famous three laws. THE SCIENTIFIC LAW. 1 19 bracing statement. The one can just as fitly as the other be termed a natural law. The law of gravitation is a brief description of how every particle of matter in the universe is altering its motion with reference to every other particle. It does not tell us why particles thus move ; it does not tell us why the earth describes a certain curve round the sun. It simply resumes, in a few brief words, the relationships observed between a vast range of phe- nomena. It economizes thought by stating in mental shorthand that routine of our perceptions which forms for us the universe of gravitating matter. We have in the law of gravitation an excellent example of a scientific law. We see in its evolution the continual struggles of the human mind to reach a more and more comprehensive and exact formula, and at last Newton reaches one so simple and so wide- embracing that many have thought nothing further can be achieved in this direction. " Here," says Paul du Bois-Reymond, " is the limit to our possible know- ledge." If the reader once grasps the characteristics of this law of Newton's he will understand the nature of all scientific law. Men study a range of facts in the case of nature the material contents of their percep- tive faculty they classify and analyze, they discover relationships and sequences, and then they describe in the simplest possible terms the widest possible range of phenomena. How idle is it, then, to speak of the law of gravitation, or indeed of any scientific law, as ruling nature. Such laws simply describe, they never explain the routine of our perceptions, the sense-im- pressions we project into an " outside world." The scientific law, while thus the product of a rational analysis of facts, is always liable to be re- 120 THE GRAMMAR OF SCIENCE. placed by a wider generalization. Such replacement of one formula by another is indeed the regular course of scientific progress. The only final test we have of the truth of any law, of the sufficiency of its descrip- tion, the only proof that our intellect has been keen enough to reach a formula extending to the whole range of facts it professes to resume, is the actual comparison of the results of the formula with the facts themselves that is, historical observation or physical experiment. This test is all that marks the division between scientific hypothesis and scientific law, and the scientific law itself must, with every increase of our perceptive powers, return to the position of hypothesis and be anew put to the test of experience. Yet what philosophic system, what fantasy of the metaphysical mind in the region of the supersensuous has stood like Newton's formula of gravitation without the least change, the least variation in its statement, for more than two hundred years ? Assuredly none ; they have all shifted their ground with every advance of man's positive knowledge. They have not stood the test of experience ; they are phantasms, not truth ; for, as Sir John Herschel has said : " The grand, and indeed only, character of truth is its capability of enduring the test of universal expe- rience, and coming unchanged out of every possible form of fair dicussion." ii. The Universality of Scientific Law. The universality, the absolute character, which we attribute to scientific law is really relative to the human mind. It is conditioned : I. By the perceptive faculty. The outside world, THE SCIENTIFIC LAW. 121 the world of phenomena, must be practically the same for all normal human beings. 2. By the reflective faculty. The processes of association and logical inference, and the inner world of stored impresses and conceptions must be practi- cally the same for all normal human beings. Now, when we classify a number of things together and give them the same name, we can only mean to signify that they closely resemble each other in struc- ture and action. Hence when we speak of human beings we are referring to a class which in the normal civilized condition have perceptive and reflective faculties nearly akin. It is therefore not surprising that normal human beings perceive the same world of phenomena, and reflect upon it in much the same manner. The " universality " of natural law, the " absolute validity " of the scientific method, depends on the resemblance between the perceptive and reflec- tive faculties of one human mind and those of a second. Human minds are, within limits, all receiving and sift- ing-machines of one type. They accept only particular classes of sense-impressions being like automatic sweetmeat-boxes which if well constructed refuse to act for any coin but a penny and having received their material they arrange and analyze it, provided they are in working order, in practically the same manner. If they do not arrange and analyze it in this manner we say, that the mind is disordered, the reason wanting, the person mad. The sense-im- pressions of a madman may be as much reality for him as our sense-impressions are for us, but his mind does not sift them in the normal human fashion, and for him, therefore, our laws of nature are without meaning. 122 THE GRAMMAR OF SCIENCE. 12. The Routine of Perceptions is possibly a Product of the Perceptive Faculty. The idea of the human mind as a sorting-machine is not without suggestion with regard to another important matter, namely, the routine nature of our sense-impressions. How far does this routine of sense-impressions depend upon the perceptive faculty ? How far does it lie outside that faculty in the unknown and unknowable beyond of sensation (p. 82) ? The question is one to which at present no definite answer can be given, and perhaps one to which no answer can ever be found. If, with the materialists, we make matter the thing-in-itself, we throw the routine back on something behind sense- impressions, and, therefore, unknowable. Precisely the same happens if, with Berkeley, we attribute the routine to the immediate action of a deity. Ma- terialist and idealist are here at one in casting the routine of sense-impression into the unknowable. But the business of the scientist is to know, and therefore he will not lightly assent to throwing any- thing into the unknowable so long as known "causes" have not been shown to be insufficient. The scientific tendency would therefore be to consider the routine of our perceptions as due in some way to the structure of- our perceptive faculty before we appeal to any supersensuous aid. Far, indeed, as science at present stands from any definite solution of the problem, there are yet one or two points which it may not be unprofitable to consider. In the first place, have we any evidence that the perceptive faculty is a selective machine ? We have already seen that it is possible at times for us to be unconscious of sensations which on other occasions THE SCIENTIFIC LAW. 123 we may keenly appreciate (p. 53). We have seen that the outside world constructed by an insect in all probability differs widely from our own (p. 101). To assume, therefore, sensations which form no part of our consciousness, perhaps no part of any conscious- ness, is not an illogical inference, for we proceed only from the known to what is like the known (p. 72), to an eject which might have been, or may one day be, an object. x No better way of realizing the different selective powers of diverse perceptive faculties can be found than a walk with a dog. The man looks out upon a broad landscape, and the signs of life and activity he sees in the far distance may have deep meaning for him. The dog surveys the same land- scape indifferently, but his whole attention is devoted to matters in his more immediate neighbourhood, of which the man is only indirectly conscious through the activity of the dog. Many things may be going on in the distance, which, if at hand, would have considerable interest for the dog: some way off the man perceives the rabbits in the field skirting the copse, further off still a flock of sheep on the high-road, and behind them the shepherd with his collie all these remain unobserved by the dog, or if observed, un- reasoned on. Clearly the sense-impressions corre- sponding to the distant landscape are far less complex and intense in the dog than in the man. The per- ceptive faculty in the dog selects certain sense- impressions, and these form for it reality ; that of the man selects another and probably far more 1 " A feeling can exist by itself without forming part of a conscious- ness," writes Clifford in a paper, the main conclusion of which seems to me, however, quite unproven. (" On the Nature of Things-in-them- selves," Lectures and Essays, vol. i. p. 84). 124 THE GRAMMAR OF SCIENCE. complex range, which form in turn reality for him. Both may be again compared to automatic sweet- meat-boxes, which only work on the insertion oii coins of definite and different value. Objective reality does not consist of the same sense-impressions for man and dog. If we pass downwards from man to the lowest forms of life, we shall find the range of sensations perceived becoming less and less complex till they cease altogether as perceptions with the cessation of consciousness. Hence, if we accept the theory of the evolution of man from the lowliest types of life, we see a wide field of variation in the matter of the perceptive faculty open to him. Man will evolve a power of perceiving those sensations, the perception of which will on the whole help him in the struggle for existence. 1 Now, step by step with the perceptive faculty the reflective or reasoning faculty is developed ; the power of sifting and arranging perceptions, the power of rapidly passing from sense-impression to fitting exertion (p. 55), is seen to be a factor of paramount importance to man in the battle of life. Without our being able at present to clearly understand the relation between the perceptive and reflective faculties in man, the nature of their co-ordination, it is still reasonable to suppose a close relation between the two ; the one largely selects those perceptions which the other is capable of analyzing and resuming in brief formulae or laws. Within sufficiently wide limits the intensity of the perceptive faculty appears in all 1 Light and vision, sound and hearing, extension and touch, are known not to be identical in range. See Sir William Thomson's, Popular Lectures and Addresses^ vol. i. pp. 278-90. THE SCIENTIFIC LAW. 125 forms of life proportional to the reasoning faculty. x A world of sense-impressions in no way amenable to man's reason would be very prejudicial to man's preser- vation. In such plight a man, like an idiot or insane person, would be incapable of analysis, or would analyze wrongly; the fitting exertion would not follow on the sense-impression, and this man would have small chance of surviving among men whose perceptive and reasoning faculties were attuned. Possibly some sorts of idiocy and madness are a kind of atavism, a return to variations of the human mind in which perceptive and reflective faculties are not co-ordinatedvariations which on the whole have been eliminated in the struggle for existence. If this interpretation be at all a correct one if, namely, the perceptive faculty can be so moulded in the process of evolution as to accept some and reject other sense-impressions ; if, further, the perceptive and reflective faculties have been de- veloped in co-ordination, so that the former accepts what, in wide limits, can be analyzed by the latter then we have advanced some way towards under- standing why the routine of perceptions can be expressed in brief formulae by the human reason. The relation between natural law in the nomic (p. ^footnote] and the scientific senses becomes more intimate, when we thus attribute the routine of the perceptions to the machinery of the perceptive faculty. It will not, however, do to press this interpretation 1 That woman has greater perceptive, man greater reflective power, is one of those futilities which has been used as an excuse for hind* ranees to woman's development of both faculties. Exceptions of course there are, but the general rule seems to be that the deeper the intellectual power in both sexes, the wider is the range of perceptions, the more delicately sensitive is the nervous system. 126 THE GRAMMAR OF SCIENCE. too far; or at least we must be careful to remember that, while the perceptive faculty has developed the power of solely perceiving sense-impressions capable of being dealt with by the reflective faculty, it does not follow that they have already been dealt with by the latter faculty. Otherwise we shall be abruptly confuted by the fact that there are many sense-impressions which we perceive and yet have not classified and reduced to simple formulae. There are many phenomena of which we can at present only confess our ignorance. Compare, for example, what we know of the tides and the weather. Had Odysseus and his men been stranded high and dry by a spring tide on the Thrinacian Isle they would probably have offered a hecatomb to Poseidon praying him to send another spring tide on the morrow. A modern mariner, more wise and less pious than Odysseus, would have con- sumed the kine of Helios in peace for a fortnight, and then have taken his departure with comparative ease. On the other hand the modern manner, like Odysseus of old, might still pray for calm weather, thus projecting his inability to formulate a scientific law into want of routine and possible anomy (p. 1 14) in the sequence of his perceptions. If we believe in the capacity of the reflective faculty for ultimately reducing to a brief formula or law all types of phenomena, if we believe in the co-ordination of perception and reflection, then the weather will not probably appear a very strong argument against our hypothesis. It must at least be confessed that the discovery of a hundred or a five hundred years' period in the weather would sadly discomfort those who delight in assuming that some group of perceptions THE SCIENTIFIC LAW. 127 at least must be beyond the analysis of the reflective faculty. Yet such a discovery would not now be more remarkable than that of the Chaldean Saros or eclipse period, x must have been to those who looked upon eclipses as an arbitrary interference with their perceptions, and prayed vigorously for a restoration of the light of sun or moon. The coeval develop- ment of the perceptive and reflective faculties asso- ciated with a power of selecting sensations in the former is possibly an important, but it may not be the sole, factor in the marvellous power which the reason possesses of describing wide ranges of phe- nomena by simple laws. There is another point which undoubtedly deserves notice. Our sense- impressions are indeed complex in their grouping, but they come to us by very few and comparatively simple channels, namely, through the organs of sense. The simplicity of the scientific law may therefore be partly conditioned by the simplicity of the modes in which sense-impressions are received. The arguments of this section are, of course, very far from conclusive. They are only meant to suggest the possibility that the perceptive faculty in itself determines largely or entirely the routine of our perceptions. If this be true it will seem less of a marvel that the co-ordinated reflective faculty should be able to describe the "outside universe " by com- paratively simple formulae. On the whole this seems a more scientific hypothesis than those which make the routine depend on supersensuous entities, and which then to account for the power of the human reason 1 The Chaldeans had discovered that eclipses of the sun and moon recur in a cycle of eighteen years and eleven days, and were thus able to predict the dates of their occurrence. THE GRAMMAR OF SCIENCE. to analyze nature endow those entities with reason akin to man's, thus postulating thought and con- sciousness apart from that material machinery which alone justifies our inferring its existence. The hypo- thesis we have discussed, unproven as it may be, postulates reason no further than we may logically infer it, and at the same time attempts to account for the power of analyzing the routine of the percep- tions, which is undoubtedly possessed by the human reflective faculty. 13. The Mind as a Sorting-Machine. It is not hard to imagine by extension of existing machinery a great stone-sorting machine of such a character that, when a confused heap of stones was thrown in pell-mell at one end, some sizes would be rejected, while the remainder would come out at the other end of the machine sifted and sorted according to their sizes. Thus a person who solely regarded the final results of the machine might consider that only stones of certain sizes had any existence, and that such stones were always arranged according to their sizes. In some such way as this, perhaps, we may look upon that great sorting-machine the human perceptive faculty. Sensations of all kinds and magnitudes may flow into it, some to be rejected at once, others to be sorted all orderly, and arranged in place and time. It may be the perceptive faculty itself, which, without our being directly conscious of it, contributes the ordered sequence in time and space to our sense-impressions. The routine of perception may be due to the recipient, and not characteristic of the material. If anything like this be the case, then (granted a co-ordination of perceptive and reasoning THE SCIENTIFIC LAW. 1 29 faculties), it will be less surprising that, when the human mind comes to analyze phenomena in time and space, it should find itself capable of briefly describ- ing the past, and of predicting the future sequences of all manner of sense-impressions. From this standpoint the nomic natural law is an unconscious product of the machinery of the perceptive faculty, while natural law in the scientific sense is the con- scious product of the reflective faculty, analyzing the process of perception, the working of the sorting- machine. The whole of ordered nature is thus seen as the product of one mind the only mind with which we are acquainted and the fact that the routine of perceptions can be expressed in brief formulae ceases to be so mysterious as when we postulate a twofold reason, one type characteristic of "things-in-them- selves," beyond our sense-impressions, and another associated with the material machinery of nervous organization. 14. Science, Natural Theology, and Metaphysics, The reader, I trust, will treat these suggestions as suggestions and no more. What we are sure of is a certain routine of perceptions and a capacity in the mind to resume them in the mental shorthand of scientific law. What we have no right to infer is that order, mind, or reason all human characteristics or human conceptions falling on this side of sense- impressions exist on the other side of sense-impres- sions, in the unknown plus of sensations or in things- in-themselves. Whatever there may be on that outside, we cannot logically infer it to be like any- thing whatever on this side. Scientifically we must remain agnostic. If, however, it is possible to conceive 10 130 THE GRAMMAR OF SCIENCE. the order, the routine of perceptions as being due to anything on this side of sense-impression, we shall have withdrawn from the beyond the last anthropo- morphical element, and left it that chaos behind sense-impression, whereof to use the word knowledge would be the height of absurdity. To positive theology, to revelation, science has no rejoinder. It works in a totally different plane. Only when belief enters the sphere of possible knowledge, the plane of reality, must science sternly remonstrate ; only when belief replaces knowledge as a basis of conduct is science driven to criticize not the reality, but the morality of belief. Quite different, however, is the relation of science to natural theology and metaphysics, when they assert that reason can help us to some knowledge of the super- sensuous. Here science is perfectly definite and clear ; natural theology and metaphysics are pseudo- science. The mind is absolutely confined within its nerve-exchange; beyond the walls of sense-impression it can logically infer nothing. Order and reason, beauty and benevolence, are characteristics and con- ceptions which we find solely associated with the mind of man, with this side of sense-impressions. Into the chaos of sensations we cannot scientifically project them; we have no ground whatever for assert- ing that any human conception will suffice to describe what may exist there, for it lies outside the barrier of sense-impressions from which all human concep- tions are ultimately drawn. Briefly chaos is all that science can logically assert of the supersensuous the sphere outside knowledge, outside classification by mental concepts. If the Brahmins believe that the world arose from the instinct of an infinite spider, THE SCIENTIFIC LAW. 131 for so it has been revealed to them, we may wonder what the conceptions instinct and spider may be in their minds, and remark that their belief is without meaning for us. But if they assert that the phe- nomenal world gives in itself evidence of being spun from the bowels of this monster, then we pass from the plane of belief to that of reason and science, and promptly demolish their fantasy. 15. Conclusions. It may seem to the reader that we have been discussing at unjustifiable length the nature of scientific law. Yet therein we have reached a point of primary importance, a point over which the battles of system and creed have been long and bitter. Here the materialists have thrown down the gauntlet to the natural theologians, and the latter in their turn have endeavoured to deck dogma with the mantle of science. The world of phenomena for the materialists was an outside world unconditioned by man's perceptive faculty, a world of " dead " matter subjected for all time to unchangeable nomic laws (p. 1 14), whence flowed the routine of our percep- tions. The Stoics, with greater insight, found these laws replete with reason, but, dogmatic in turn, they postulated a reason akin to man's inherent in matter. The natural theologians, like the materialists, found " dead " matter, but, like the Stoics, they saw strong evidence of reason in its laws ; this reason they placed in an external lawgiver. Metaphysician and philosopher filled the measure of obscurity by hypotheses as to mind-stuff and will and conscious- ness, which had not become consciousness, existing behind the barrier of sense-impression. Science' 132 THE GRAMMAR OF SCIENCE. refusing to infer wildly where it cannot know, and unwilling to assume new causes where the old have not yet been shown insufficient treats the " dead matter " of the materialist as a world of sense-impres- sions. These sense-impressions appear to follow an unchanging routine capable of expression in the brief formulae of science because the perceptive and re- flective faculties are machines of practically the same type in all normal human beings. Like the Stoics, the scientist finds evidence of reason in his examination of natural phenomena, but he is content to think that this reason may be his own till he discovers evidence to the contrary. He recognizes that the so-called law of nature is but a simple resume, a brief descrip- tion of a wide range of his own perceptions, and that the harmony between his perceptive and reasoning faculties is not incapable of being traced to its origin. Natural law appears to him an intellectual product of man, and not a routine inherent in " dead matter." The progress of science is thus reduced to a more and more complete analysis of the perceptive faculty an analysis which unconsciously and not unnaturally we project into an analysis of something beyond sense-impression. Thus both the material and the laws of science are inherent in ourselves rather than in an outside world. Our groups of perceptions form for us reality, and the results of our reasoning on these perceptions and the conceptions deduced from them form our only genuine know- ledge. Here only we are able to reach truth to discover similarity and to describe sequence and we must remorselessly criticize every step we take beyond, if we would avoid the " muddy speculation " which will ever arise when we attempt to extend the THE SCIENTIFIC LAW. 133 field of knowledge by obscure definitions of natural law. If it should seem to the reader that I have too narrowly circumscribed, not the field of possible human knowledge, but the meaning of the word knowledge itself, he must remember the danger which arises when we employ terms without concise mean- ing and clearly defined limits. The right of science to deal with the beyond of sense-impressions is not the subject of contest, for science confessedly claims no such right. It is within the field of knowledge as we have defined it, especially at points where our know- ledge is only in the making, that the right of science has been questioned. It is easy to replace ignorance by hypothesis, and because only the attainment of real knowledge can in many cases demonstrate the false- ness of hypothesis, it has come about that many worthy and otherwise excellent persons assert an hypothesis to be true, because science has not yet by positive knowledge demonstrated its falsehood. Here, in the untilled part of the heritage of science, lies the playground of the undisciplined imagination. Mine, says science here, as it does not claim of the super- sensuous, and it hastens where it can to take effective occupation. Science, we are told, does not explain the origin of life ; science does not explain the development of man's higher faculties ; science does not explain the history of nations. If by explain 1 is meant "describe in a brief formula," let us admit that science has not yet fully analyzed 1 No objection can be raised to the words explain and explanation if they be used in the sense of the descriptive how, and not the deter- minative why. The former interpretation is the sole one given to them in this work. 134 THE GRAMMAR OF SCIENCE. these phenomena. What, then, must follow the ad- mission ? Why, an honest confession of our ignorance and not mistrust in our fundamental principles no meaningless hunt after unknown origins in the super- sensuous, until the known field of perceptions has been shown incapable of yielding the needful basis. To-day our churches still offer up prayers for the weather, and the mystery of Saturn's rings is hardly fully solved ; fifty years ago we could give no account of the origin of species. The mystery of the latter was used as striking evidence of the insufficiency of science and as a valid argument for an anomy, a separate creation of each type of life. Driven from one stronghold of ignorance, those who delight in the undisciplined imagination rather than in positive knowledge, only seek refuge in another. The part played years ago by our ignorance as to the origin of species is now played by our supposed ignorance as to the origin of the higher faculties in man. As well take refuge in the weather or in the mystery of Saturn's rings, for all alike belong to the world of sense-impressions and therefore are material with which the scientific method can and will ultimately cope. Does science leave no mystery ? On the contrary, it proclaims mystery where others profess knowledge. There is mystery enough in the chaos of sensations and in its capacity for containing those little corners of consciousness which project their own products, of order and law and reason, into an unknown and unknowable world. There is mystery enough here, only let us clearly distinguish it from ignorance within the field of possible knowledge. The one is impenetrable, the other we are daily subduing. THE SCIENTIFIC LAW. 135 SUMMARY. 1. Scientific law is of a totally different nature from civil law ; it does not involve an intelligent lawgiver, a command and a corresponding duty. It is a brief description in mental shorthand of as wide a range as possible of the sequences of our sense-impressions. 2. There are two distinct meanings to natural law : the mere routine of perception, and the scientific law in the field of nature. The " reason " in natural law is only obvious when we speak of law in the latter sense, and it is then really placed there by the human mind. Thus the sup- posed reason behind natural law does not enable us to pass from the routine of perceptions to anything of the nature of reason behind the world of sense-impression. 3. The fact that the human reflective faculty is able to express in mental formulae the routine of perceptions may be due to this routine being a product of the perceptive faculty itself. The perceptive faculty appears to be selective and to have developed in co-ordination with the reflective faculty. Of the world outside sense-impression science can only logically infer chaos, or the absence of the conditions of know- ledge ; no human concept, order, reason, or consciousness, can be logically projected into it. LITERATURE. AUSTIN, J. Lectures on Jurisprudence. London, 1879. (Especially Lectures I. to V.) HUME, D. Dialogues concerning Natural Religion (pp. 375-468 of vol. ii. of The Philosophical Works, edited by Green and Grose). STUART, J. A Chapter of Science ; or, What is a Law of Nature ? London, 1868. (A series of six lectures, of which the first five can still be read with some profit, if read cautiously, while the last forms for the student of logic a useful study in paralogisms. ) CHAPTER IV. CAUSE AND EFFECT. PROBABILITY. i. Mechanism. THE discussion of the previous chapter has led us to see that law in the scientific sense only describes in mental shorthand the sequences of our perceptions. It does not explain why those perceptions have a certain order, nor why that order repeats itself ; the law discovered by science introduces no element of necessity into the sequence of our sense-impressions ; it merely gives a concise statement of hoiv changes are taking place. That a certain sequence has occurred and recurred in the past is a matter of experience to which we give expression in the concept causation; that it will continue to recur in the future is a matter of belief to which we give expression in the concept probability. Science in no case can demonstrate any inherent necessity in a sequence, nor prove with ab- solute certainty that it must be repeated. Science for the past is a description, for the future a belief; it is not, and has never been, an explanation, if by this word is meant that science shows the necessity of any sequence of perceptions. Science cannot demonstrate that a cataclasm will not engulf the universe to-morrow, but it can prove that past experience, so far from providing a shred of evidence in favour of any such occur- CAUSE AND EFFECT. PROBABILITY. 137 rence, does, even in the light of our ignorance of any necessity in the sequence of our perceptions, give an overwhelming probability against such a cataclasm. If the reader has once fully grasped that science is an intellectual resumt of past experience and a mental balancing of the probability of future experience, he will be in no danger of contrasting the " mechanical explanation " of science with the " intellectual descrip- tion " of mythology. Some years ago (1885) Mr. Gladstone wrote a remarkable article in The Nineteenth Century in which he inveighed against the u dead mechanism " to which he asserted men of science reduced the universe. He contrasted the mechanical with the intellectual, and bravely defended what he termed the " majestic process of creation " described in the first chapter of Genesis against the Darwinian theory of evolution. He has recently repeated several of his arguments in a more elaborate work. 1 Now, when a man of Mr. Gladstone's ability states a paradox of this kind, we may be fairly certain that it arises from some popular confusion in the use of terms, and it befits us to inquire how popular and scientific usage differ as to the word mechanical. Unfortunately, some more or less super- ficial works on natural science give currency to the notion that mechanics is a code of rules which nature of inherent necessity obeys. We are told in books published even within the last few years that mechanics is the science of force, that force is the cause which produces or tends to produce change of motion, and that force is inherent in matter. Force thus appears to the popular mind as an agent inherent in unconscious matter producing change. This agent is very natu- 1 The Impregnabk Rock of Holy Scripture. London, 1890. 138 THE GRAMMAR OF SCIENCE. rally contrasted with the will of a living being, the consciousness of a capacity to produce motion. In matter this consciousness cannot be inferred, and thus force is contrasted as a " dead " agent with will as a "living" agent. The mind which has not probed beyond the surface of physics sympathizes with Mr. Gladstone's revolt against the "dead mechanism" to which, in the imagination of both, science reduces the universe. Now "matter" is for us a groupof sense-impressions and "matter in motion " is a sequence of sense-impressions. Hence that which causes change of motion * must be that which determines a sequence of sense-impressions, or, in other words, it is the source of a routine of per- ceptions. But the source of such routine, as we have seen, lies either in the field of the unthinkable beyond sense-impression or else in the nature of the perceptive faculty itself. The "cause of change in motion " thus either lies in the unthinkable or is a factor of percep- tion ; in neither case can it with any intelligible meaning of the words be spoken of as a " dead agent." In the former case the cause of change is unknowable, in the latter it is unknown, and may long remain so, for we are very far at present from understanding how the perceptive faculty can condition a routine of per- ceptions. Science does not deal with the unknowable, and if force be not unknowable, but unknown, then mechanics as the science of force would as yet have made no progress. The reality is indeed different from this. One of the greatest of German physicists, 1 We shall see reason in the sequel for asserting that " motion " is a conception, rather than a perception a scientific mode of representing change of sense-impressions, rather than a sense-impression itself. In this chapter, however, the term "motion " is used in its popular sense for a well-marked class of sequences of sense-impression. CAUSE AND EFFECT. PROBABILITY. 139 Kirchhoff, thus commences his classical treatise on mechanics x : " Mechanics is the science of motion ; we define as its object the complete description in the simplest possible manner of such motions as occur in nature." In this definition of KirchhofFs lies, I venture to think, the only consistent view of mechanism and the true conception of scientific law. Mechanics does not differ, as so often has been asserted, from biology or any other branch of science in its essential principles, The laws of motion no more account than the lawsof cell-development for the routine of perception ; both solely attempt to describe as completely and simply as possible the repeated sequences of our sense-im- pressions. Mechanical science no more explains or accounts for the motion of a molecule or a planet than biological science accounts for the growth of a cell. The difference between the two branches of science is rather quantitative than qualitative ; that is, the descriptions of mechanics are simpler and more general than those of biology. So wide-embracing and general are the laws of motion, so completely do they describe our past experience of many forms of change, that with a considerable degree of confidence we believe they will be found to describe all forms of change. It is not a question of reducing the universe to a " dead mechanism," but of measuring the amount of pro- bability that one description of change of a highly generalized and simple kind will ultimately be recog- nized as capable of replacing another description of a more specialized and complex character. It is not taking biology out of one branch of what might be 1 Vorlesungen uber mathematische Physik. Bd. I. Mechanik> S. I. Berlin, 1876. 146 THE GRAMMAR OF SCIENCE. termed descriptive science and removing it into another that of prescriptive science. Here by prescriptive science we denote an imaginary aspect of science, which mechanics are too frequently supposed to present, namely, that of deducing some inherent necessity in the routine of perceptions, instead of merely describing that routine in simple statements. When, therefore, we say that we have reached a " mechanical explana- tion " of any phenomenon, we only mean that we have described in the concise language of mechanics a certain routine of perceptions. We are neither able to explain why sense-impressions have a definite sequence, nor to assert that there is really an element of necessity in the phenomenon. Regarded from this standpoint the laws of mechanics are seen to be essentially an intellectual product, and it appears ab- solutely unreasonable to contrast the mechanical with the intellectual when once these words are grasped in their accurate scientific sense. 2. Force as a Cause. If force be looked upon as the cause of change in the sense that it necessitates a certain routine of percep- tions, then we have no means of dealing with force. It may be the structure of the perceptive faculty, or it may be any of the phantasms with which metaphy- sicians people the beyond of sense-impression. Force will not, therefore, aid us in our search for a scientific conception of cause. As we have seen that there are two or even three ideas conveyed by the one term law, so there are at least two ideas associated with the word cause, and their confusion has also led to as much " muddy speculation." Let us first investigate the popular idea of cause and then see how this is related CAUSE AND EFFECT. PROBABILITY. 141 to the scientific definition. A very slight amount of observation has shown men that certain sequences of change apparently arise from the voluntary action, the will of a living agent. I take up a stone ; no one can predict with certainty what I shall do with it. What follows my picking up the stone is to all appearances a new sequence quite independent of any which preceded it. I can let it fall again ; I can put it into my pocket, or I may throw it into the air in any direction and with any of a great variety of speeds. The result of my action may be a long sequence of physical phenomena to describe which mechanically would require the solution of complex problems in sound, heat, and elasticity. The sequence, however, appears to start in an act of mine, in my will, /appear to have called it into existence, and in ordinary language I am spoken of as the cause of the resulting pheno- mena. In this sense of the word cause I appear to differ qualitatively from any other stage in the sequence. Had the hand of a stronger man compelled mine to throw the stone, I should at once have sunk into a link in the chain of phenomena; he, not I, would have been the cause of the resulting motion. It is certainly true that even in popular usage inter- mediate stages in the sequence will occasionally be spoken of as causes. If the stone from my hand break a window, the cause of the broken window might very likely be spoken of as the moving stone. But al- though this usage, as we shall see afterwards, is an approach to the scientific usage of the word cause, it yet involves in the popular estimation an idea of en- forcement which is not in the latter. That the stone moving with a certain speed must produce the destruction of the window is, I think, the idea 142 THE GRAMMAR OF SCIENCE. involved in thus speaking of the moving stone as the cause of the breakage. Were our perceptive organs sufficiently powerful, what science conceives that we should see before the impact would be particles of window and particles of stone moving in a certain manner, and after the impact would be the same particles moving in a very different manner. We might carefully describe these motions, but we should be unable to say why one stage would follow another, just as we can describe how a stone falls to the earth, but not say why it does. Thus, scientifically the idea of necessity in the stages of the sequence stone in motion, broken window the idea of enforcement would disappear ; we should have a routine of experience, but an unexplained routine. Hence, when we speak of the stages of a sequence in ordinary life as causes, I do not think it is because we are approaching the scientific standpoint, but I fear it arises from our associating, through long usage, the idea of force with the stone. The stone is the cause of certain new motions, just as I am looked upon as the cause of certain motions in the stone that is, both stone and I are supposed to enforce subse- quent stages in the sequence. Now the reader who has once dismissed the notion of force as a cause, which I think he will probably be prepared to do, will perhaps admit that there is no element of enforcement, but merely a routine of experience in the motions of particles of stone and glass. Still he may say that the will of a living agent does seem to him a cause of motion in the necessarian sense. Nor would he be in this unreasonable, for I must confess that to attribute sequences of motion to will seems at first sight a more scientific hypothesis than to attribute CAUSE AND EFFECT. PROBABILITY. 143 them to an unknown and possibly unknowable source force. 3- Will as a Cause. It is not unnatural that human beings should be impressed at a very early stage of their mental growth with the real, or at any rate apparent, power which lies in their will of originating " motion." In this manner we find that most primitive peoples attribute all motions to some will behind the moving body ; for their first conception of the cause of motion lies in their own will. Thus they consider the sun as carried round by a sun-god, the moon by a moon-god, while rivers flow, trees grow, and winds blow owing to the will of a spirit which dwells within them. It is only in the long course of ages that mankind more or less clearly recognizes will as associated with consciousness and a definite physiological structure ; then the spiritualistic explanation of motion is gradually displaced by the scientific description ; we eliminate in one case after another the direct action of will in the motion of natural bodies. x The idea, however, of enforcement, of some necessity in the order of a sequence remains deeply rooted in men's minds, as a fossil from the spiritualistic explanation of will as the cause of motion. This idea is preserved in association with the scientific description of motion, and in the materialist's notion of force as that which necessitates certain changes or sequences of motion, we have the ghost of the old spiritualism. The force of the materialist is the will of the old spiritualist separated 1 The spiritualistic explanation still of course exists where the scientific analysis is incomplete. We continue to appeal to a spirit "at whose command the winds blow and lift up the waves of the sea and who stilleth the waves thereof," or who " sends a plague of rain and waters.'' 144 THE GRAMMAR OF SCIENCE. from consciousness. Both carry us into the region beyond our sense-impressions, both are therefore metaphysical ; but perhaps the inference of the old spiritualist was, if illegitimate, less absurdly so than that of the modern materialist, for the spiritualist did not infer will to exist beyond the sphere of conscious- ness with which he had always found will associated. Force as cause of motion r is exactly on the same footing as a tree-god as cause of growth both are but names which hide our ignorance of the why in the routine of our perceptions. 4. Secondary Causes involve no Enforcement. Let us endeavour to see a little more closely how the idea of any inherent necessity in the particular order taken by our perceptions disappears from the scientific conception of a sequence of motions at least from all but the first stage, if the sequence arise from an apparent act of will. Still speaking in the popular sense, we will term the act of will, if it exists, a first cause, and the successive stages of the sequence secondary causes. Our present proposition is that the scientific description of motion involves no idea of enforcement in the successive stages of motion. We shall see in the sequel that the whole tendency of modern physics has been to describe natural phenomena by reducing them to conceptual motions. From these motions we construct the more complex motions by aid of which we describe actual sequences of sense-impressions. But in no single case have we discovered why it is that these motions are 1 Force as a name used for a particular measure of motion will be found in our chapter on the " Laws of Motion" to involve no obscurity, and to be in itself a convenient term. CAUSE AND EFFECT. PROBABILITY. 145 taking place ; science describes how they take place, but the why remains a mystery. To term it force might not be so productive of .obscu- rity as it is, were there any suggestion in the ele- mentary text-books that the cause of motion, or of change in motion, may be the nature of the perceptive faculty, or will, or the deity, or any un- knowable x amid an unthinkable y and z. The glib transition from force as a cause to force as a measure of motion too often screens the ignorance which it is as much the duty of science to proclaim from the house-tops as it is its duty to assert knowledge on other points. Primitive man placed a sun-god behind the sun (as some of us still place a storm-god behind the storm), because he did not see how and why it moved. The physicist now proceeds to describe, how the sun moves, by describing how a particle of earth and a particle of sun move in each other's presence. The description of that motion is given by Newton's law of gravitation, but the why of that motion is just as mysterious to us as the motion of the sun to the barbarian. 1 No one knows why two ultimate particles influence each other's motion. Even if gravitation be analyzed and described by the motion of some 1 The reader will find it profitable to analyze what is meant by such statements as that the law of gravitation causes bodies to fall to the earth. This law really describes how bodies do fall according to our past experience. It tells us that a body at the surface of the earth falls about sixteen feet towards the earth in the first second, and at the dis- tance of the moon about -^rs^ part of this distance in the same time. The law of gravitation describes the rate at which a body falls, or, better, the rate at which its motion is changed at diverse distances, and the force of gravitation is really a certain measure of this change of motion, and no useful purpose can be served by defining it as the cause of change in motion. Other physical laws ought to be inter* prcted in the same anti-metaphysical manner. II 146 THE GRAMMAR OF SCIENCE. simpler particle or ether-element, the whole will still be a description, and not an explanation, of motion. Science would still have to content itself with recording the how. In what we have termed secondary causes, therefore, science finds no element of enforcement, solely the routine of experience- But the idea of will as a first cause has been over and over again associated with secondary causes. Aris- totle, noting the difficulty of explaining why motions take place, introduced not only God as a first cause, but, like primitive man, made God an immediate source of the enforcement in every secondary cause. God, Aristotle held, is continually imparting motion to all the bodies in the universe, and so producing phenomena. Aristotle's doctrine was accepted by the. mediaeval schoolmen, and for many centuries re- mained fundamental in philosophical and theological writings. Schopenhauer, the German metaphysician, perceiving that the only known apparent first cause of motion was will, placed will behind all the pheno- mena of the universe, much like the barbarian who postulates the will of a storm-god behind the storm. 1 But however little logical basis these metaphysical speculations possess all failing to satisfy our canons of legitimate inference (p. 72) they still suffice to mark the distinction between the popular or meta- physical conception of cause as enforcement, and the scientific conception of cause as the routine of experi- ence. Every association of inherent necessity with secondary causes is a passage from physics to meta- 1 Sir John Herschel went so far as to identify gravitation and will ! {Outlines of Astronomy -, arts. 439-40). Other samples of the same animistic tendency will be found in the writings of Dr. J. Martineau and the late Dr. W. B. Carpenter. CAUSE AND EFFECT. fROBABILITV. 147 physics, from knowledge to fantasy. Historically, I think, the whole association can be traced back through the old spiritualism to the sequences of motion which the will as a first cause can apparently enforce. Here, then, it befits us to ask two questions: Does the will in any way really account for motion ? Is there any ground for supposing the will to be an arbitrary first cause ? 5. Is Will a First Cause? Now, in attempting to answer these questions scientifically we must bear in mind that what we term will is only known to us in association with consciousness, and that we can only infer conscious- ness where we find a certain type of nervous system. Does will as an apparently spontaneous origin of motion throw any light on the mystery of motion ? Does it in any way explain the particular sequences motions take ? To be consistent we shall have to suppose, with Aristotle, that every phase of motion is the direct product of a conscious being. Let us return to the example of the stone. Apparently, by the arbitrary action of my will, I set the stone in motion. I appear in doing this as a first cause. But a complex sequence of motions now arises. Each stage of this sequence I can conceive myself mechani- cally describing, but I am quite unable to assert the necessity, the why of these stages. For example, the stone falls to the ground, and I can say approxi- mately how many feet it will fall in the first and in the following seconds. That is the result of past experi- ence used to predict the future, the result of the classification of phenomena resumed in the law of gravitation ; but this law does not explain the why 148 THE GRAMMAR OF SCIENCE. of the motion. If I grant that my will set the stone in motion, I cannot suppose it to continue in motion for the same reason, for any amount of willing after the stone has left my hand will not, in the majority of cases, be in the least able to influence its motion. Hence, even in motion started by a conscious being, we have at once a mystery. My will might explain the origin, it cannot explain the continuance of the motion. If will is to help us at all, we must postulate it as producing motion at every stage. But clearly this will is not my will ; it must be some other will. Here we are only restating the solutions of primitive man with his spiritualism behind nature, of Schopen- hauer with his undefined will behind all phenomena, of Aristotle when he says God moves all things. But this solution involves an extension of the notion of will beyond the sphere where we may legitimately infer its existence. Like the hypothesis of force it postulates an unthinkable x outside sense-impres- sions. It carries us no-whither. Will cannot, there- fore, be looked upon as necessitating a sequence of motion, any more than what we have termed a secondary cause, for in the great majority of cases, if will be supposed to start a motion, it cannot en- force its continuance in a particular sequence, and so far as the will is concerned the motion might cease at its birth. 6. Will as a Secondary Cause. Will thus appears, like the secondary cause, as a stage in the routine of perceptions. Our experience shows us that in the past an act of will occurred at a certain stage in a routine of perceptions, but we cannot assert that there was anything in the act CAUSE AND EFFECT. PROBABILITY. 149 itself which enforced the stages which followed. Does will, however, differ on closer analysis from other secondary causes in being the first stage of an observed routine ? This leads us to our second question (p. 147), and the answer to it is really in- volved in the views on consciousness which have been developed in our second chapter. We have seen that the difference between a volun- tary and involuntary exertion lies in the latter being conditioned only by the immediate sense-impression, while the former is conditioned by stored sense- impresses and the conceptions drawn from them. Where consciousness exists, there there may be an interval between sense-impression and exertion, this interval being filled with the " resonance," as it were, of associated but stored sense-impresses and their correlated conceptions. When the exertion is at once determined by the immediate sense-impression (which we associate with a construct projected outside ourselves), we do not speak of will, but of reflex action, habit, instinct, &c. In this case both sense- impression and exertion appear as stages in a routine of perceptions, and we do not speak of the exertion as a first cause, but as a direct effect of the sense- impression ; both are secondary causes in a routine of perceptions, and capable of mechanical description. On the other hand, when the exertion is conditioned by the stored sense-impresses, it appears to be con- ditioned by something within ourselves ; by the manner in which memory and past thought have linked together stored sense-impresses and the con- ceptions drawn from them. No other person can predict with absolute certainty what the exertion will be, for the contents of our mind are not objects 150 THE GRAMMAR OF SCIENCE. to him. None the less the inherited features of our brain, its present physical condition owing to past nurture, exercise, and general health, our past training and experience are all factors determining what sense-impresses will be stored, how they will be associated, and to what conceptions they will give rise. By this we are to understand that, if we could bring into the sphere of perception the processes that intervene in the brain between immediate sense- impression and conscious exertion, we should find them just as much routine changes as what precedes the sense-impression or follows the exertion. In other words, will, when we analyze it, does not appear as the first cause in a routine of perceptions, but merely as a secondary cause or intermediate link in the chain. The " freedom of the will " lies in the fact that exertion is conditioned by our own individuality, that the routine of mental processes which intervenes between sense-impression and exertion is perceived objectively neither by us nor by any one else, and psychically by us alone. Thus will as the first cause of a sequence of motions explains nothing at all ; it is only a limit at which very often our power of describing a sequence abruptly terminates. So much is this recognized by modern science, that special branches of it are entirely devoted to de- scribing the sequences of secondary causes, the routine which precedes special determinations of the will. Science tries to describe how will is influenced by desires and passions, and how these again flow from education, experience, inheritance, physique, disease, all of which are further associated with climate, class, race, or other great factors of evolution. Thus, with the advance of our positive knowledge, we come CAUSE AND EFFECT. PROBABILITY. !$! more and more to regard individual acts of will as secondary causes in a long sequence, as stages in a routine which can be described stages, however, at which the routine changes its at present knowable side from the psychical to the physical. An act of will thus appears as a secondary cause, and no longer as an arbitrary first cause. Evil acts flow indeed from an anti-social will, and as hostile to itself society endeavours to repress them ; but the anti-social will itself is seen as a heritage from a bad stock, or as arising from the conditions of past life and training. Society begins more and more to regard incorrigible criminals as insane, and slight offenders as uneducated children. 7. First Causes have no Existence for Science. We have now reached some very important con- clusions with regard to will as a cause. In the first place, the only will known to us (or the only like will that we can logically infer to exist) is seen not to be associated with an arbitrary power to originate, alter, or stop a motion. It appears merely as a secondary cause, as a stage in a routine, but one where the knowable side of the routine changes from the psychical to the physical. Further, there lies in this will no power of enforcing a sequence of motions. The will as first cause is merely a limit arising from some impossibility in our powers of further following the physical side of a routine, or of discovering its further psychical side ; it is merely another way of saying : At this point our ignorance begins. The moment the only will we know or infer ceases to appear as the arbitrary originator or enforcer of a sequence, so soon as it sinks to a stage if a re- 152 THE GRAMMAR OF SCIENCE. markable stage in a routine, then it becomes idle to suppose will as the backbone of natural phenomena. Will, as the creator and maintainer of nature, is either an old name used for some unknown and un- thinkable existence, or if used in the only sense now intelligible to us, that of a secondary cause or stage in a routine, it gives us no assistance in comprehending routine. We are just as wise if we drop this will behind phenomena, and content ourselves with ob- serving that there is a routine in perceptions. This, in fact, is what science does, not unnecessarily multi- plying causes, when no simplification of perceptions arises from postulating their existence. We have seen that the conception of will as an arbitrary source of motion arose historically, and not unnaturally, from a portion of the routine of which will is a stage being both physically and psychically screened from the observer, owing to its being buried in the individuality of another person. We have further noticed that as will and motion are more carefully analyzed, the conception that will originates motion ceases to have any consistency. But with will as first cause falls to the ground any possible experience of first causes on our part. We can no longer infer even the possibility of the existence of first causes, for there is nothing like them in our experience, and we cannot by the second canon of logical inference (p. 72) pass from the known to something totally unlike it in the unknown. Science knows nothing of first causes. They cannot, as Stanley Jevons has supposed, 1 be inferred from any branch of scientific investigation, and 1 In the remarkably unscientific chapter entitled, " Reflections on the Results and Limits of Scientific Method," with which his, in so many respects, excellent Principles of Science concludes. CAUSE AND EFFECT. PROBABILITY. 153 where we see them asserted we may be quite sure they mark a permanent or temporary limit to know- ledge. We are either inferring something in the beyond of sense-impression, where knowledge and inference are meaningless words, or we are implying ignorance within the sphere of knowledge, 1 in which case it is more honest to say : " Here, for the present, our ignorance begins," than, " Here is a first cause." 8. Cause and Effect as the Routine of Experience. We are now in a position, I think, to appreciate the scientific value of the word cause. Scientifically, cause, as originating or enforcing a particular se- quence of perceptions, is meaningless we have no experience of anything which originates or enforces something else. Cause, however, used to mark a stage in a routine, is a clear and valuable conception, which throws the idea of cause entirely into the field of sense-impressions, into the sphere where we can reason and reach knowledge. Cause, in this sense, is a stage in a routine of experience, and not one in a routine of inherent necessity. The distinction is, perhaps, a diffi- cult one, but it is all the more needful that the reader should fully grasp it. If I write down a hundred numbers at chance say by opening carelessly the 1 The latter alternative the temporary limit to ignorance has been the chief source of " first causes." So long as the routine of history cannot be traced back more than a few centuries, we find no difficulty in asserting that the world began 6,000 years ago. So long as we do not grasp the evolution of life from its most primitive types, we postulate a first cause creating each type (Paley). So long as we do not observe the various grades of animal intelligence and consciousness, we suppose a soul implanted in every human being at birth. So long as we do not see that the mutual motion of two atoms is as mysterious as the life changes of a cell, we postulate a total difference between the two kinds of motion and a separate creation of life. 154 THE GRAMMAR OF SCIENCE. pages of a book there results a sequence of numbers beginning, say 141, 253, 73, 477, !87> 5^5, 57, 353 &e., in which I cannot predict from any two or three or more numbers those which will follow. The number 477 does not enable me to say that 187 will follow it, the numbers which precede 187 in no way enforce or determine those which follow it. On the other hand, if I take the series i, 2, 3, 4, 5, 6, 7, 8 ... each individual number leads (by addition of i) to the immediately following number, or in a certain sense determines it. The first series can, however, be written down so often that we learn it by rote, that it becomes a routine of experience. The analogy must not, of course, be pressed far, but it may still be of service. There is nothing in any scientific cause which compels us of inherent necessity to predict the effect. The effect is associated with the caise simply as a result of past direct or indirect experience. Or again, perhaps the matter may be grasped more clearly from a geometrical analogy. If I form the conception of a circle, it follows of inherent necessity that the angle at the circumference on any diameter is a right-angle. The one conception flows not as a result of experience but as a logical necessity from the other. No sequence of sense-impressions involves in itself a logical necessity. The sequence might be chaotic like our first series of numbers ; it has become for us a routine by repeated experience. The noteworthy fact in a routine of perceptions lies not so much in the particular order of the stages in the sequence, as in the result of experience that this order can exactly repeat itself. CAUSE AND EFFECT. PROBABILITY. 155 The reader may perhaps wonder how, if the se- quences of sense-impressions are really of the chaotic nature represented by our first series of numbers, it is possible to describe such sequences apart from their repetition by those brief formulae we term scientific laws. As the perceptive faculty presents us, indeed, with the sequence, it is undeniably more like the second than the first series of numbers, for natural phenomena can without doubt be largely described by certain brief laws. We must rather put the actual case in the following form. We observe a person whose motives are quite unknown to us writing down the series I, 2, 4, 8, 16, 32, and at present he has reached the number 32. A law describing the series is obvious each number is twice the preceding one. With a great degree of probability we infer that he will now write down 64, especially if we have seen him write the series up to and beyond 32 before. But there is nothing of logical necessity about his writing 64 after the preceding numbers. Those numbers, when we know the law, suggest his doing so, but do not enforce it. We are now in a position to scientifically define cause. Whenever a sequence of perceptions D, E, F, G is invariably preceded by the perception C, or the perceptions C, D, E, F, G always occur in this order, that is, form a routine of experience, C is said to be a cause of D, E, F, G, which are then described as its effects. No phenomenon or stage in a sequence has only one cause, all antecedent stages are successive causes, and, as science has no reason to infer a first cause, the succession of causes can be carried back to the limit of existing know- 156 THE GRAMMAR OF SCIENCE. ledge, and beyond that ad infinitum in the field of conceivable knowledge. When we scientifically state causes we are really describing the successive stages of a routine of experience. Causation, says John Stuart Mill, is uniform x antecedence, and this defini- tion is perfectly in accord with the scientific concept, 9. Width of the Term Cause. The word cause, even in its scientific sense, is somewhat elastic. It has been used to mark uniform conjunction in space as well as uniform antecedence in time ; while if we take an actually existing group of perceptions, say the particular ash-tree in my garden, the causes of its growth might be widened out into a description of the various past stages of the universe. One of the causes of its growth is the existence of my garden, which is conditioned by the existence of the metropolis ; another cause is the nature of the soil, sand approaching the clay limit, which again is conditioned by the geological structure and past history of the earth. The causes of any individual thing thus widen out into the unmanageable history of the universe. The ash-tree is like Tenny- son's "flower in the crannied wall" : to know all its causes would be to know the universe. To trace causes in this sense is like tracing back all the lines of ancestry which converge in one individual ; we soon reach a point where we can go no further owing to the bulk of the material. Obviously science in tracing causes attempts no task of this character, but at the same time it is useful to remember how essentially the causes of any finite portions of the universe lead 1 " Uniformity " and " sameness" are, in the perceptual world, how- ever, only relative terms (see p. 200). CAtJSE AND EFFECT. PROBABILITY. 157 us irresistibly to the history of the universe as a whole. This thought suggests how closely knit together are in reality the most diverse branches of our positive knowledge. It shows us how difficult it is for the great building of science to advance rapidly and surely unless its various parts keep pace with each other (p. 16). Practically science has to content itself with tracing one line of ancestry, one range of causes at a time, and this not for a special and indi- vidual object like the ash-tree in my garden, but for ash-trees or even trees in general. It is because science for its descriptive purposes deals with general notions or conceptions, that the words cause and effect have been withdrawn from the sphere of sense- impressions, from phenomena to which they strictly belong, and applied to the world of conceptions and ideas, where, indeed, there is logical necessity but no true cause and effect. To this point I shall return under n. 10. The Universe of Sense-Impressions as a Universe of Motions. The reader can hardly fail to have been impressed in his past reading and experience with the great burden of explanation which is thrown on that un- fortunate metaphysical conception force. He will undoubtedly have heard of the " mechanical forces" ruling the universe, of the "vital forces" directing the development of life, and of the "social forces" govern- ing the growth of human societies. 1 He may perhaps 1 A good illustration of the obscurity attaching to the use of the words force and cause may be taken from the recently published History of ffitman Marriage, by E. Westermarck. The author writes : "Nothing exists without a cause, but this cause is not sought in an agglomeration of external or internal forces." He thus implies that a cause ought to be sought in this unintelligible ' ' agglomeration of 15$ THE GRAMMAR OF SCIENCE. have concluded, with the present writer, that the word is not infrequently a fetish which symbolizes more or less mental obscurity. But the reason for the repeated occurrence of the word is really not far to seek. Wherever motion, change, growth, were postulated, there in the old metaphysics force as the cause of motion was to be found. The frequent use of the word force was due to the almost invariable association of motion with our perceptions, or, in more accurate language, to the analysis of nearly all our sense-impressions by aid of conceptual motions. For example, a coal fire may be said to be a cause of warmth. Here we mean that the group of sense-impressions we term coal, followed by the group we term combustion, has invariably in our experience been accompanied by the sense-impression warmth. We may, if we are chemists, be able to describe the chemical processes, the atomic changes or motions to which the pheno- menon of combustion has been reduced ; we may, if we are physicists, describe the motion of the ethereal medium, to which the phenomenon of radiation of heat has been reduced ; we may, if we are physiologists, be able to describe the nerve- motions by aid of which the molecular motion of the finger-tips is interpreted as the sense-impression warmth at the brain. In all these cases we are dealing with the sequences of various types of motion, into which we analyze or reduce a variety of sense- external and internal forces." Now, what the author attempts to do is to describe the various stages through which marriage has passed, and then to express the sequence of these stages by brief formulae, such as those of natural selection. To use the \vordforce hopelessly obscures his method. CAUSE AND EFFECT. PROBABILITY. 159 impressions. Just as in the special case of gravi- tation, we can also describe these sequences and can frequently give a measure to the motions which we conceive to take place, but we are still wholly unable to state why these motions occur. We may talk, if we please, about the forces of combustion, the forces of radiation, or even the forces inherent in nerve substance ; we might indeed say that the warmth, of which combustion is the cause, is due to "an agglomeration of internal and ex- ternal forces," but in using these phrases we do not introduce an iota of new knowledge, but too often a mountain of obscurity. We hide the fact that all knowledge is concise description, all cause is routine. Now, it deserves special note that the sequences with which we are dealing are all reducible to de- scriptions of motion, -or of change. We need not start arbitrarily with the combustion of the coal ; its chemical constitution as an element in the sequence of causes can, for example, be carried back through a long past history in the evolution of coal, and we cannot logically infer (p. 151) any beginning or first cause in this sequence. Sequences of motion or of change in natural phenomena go backwards and forwards through an infinite range of causes, and to begin or end them anywhere with a first or last cause is simply to say that at such a point the sphere of knowledge ends with an unthinkable x. The universe thus appears to the scientist as a universe of motion, motion the why of which is unknown, but the sequences of which are, according to our experience, invariably repeating themselves. The cause of motion in the scientific sense lying in the sphere of sense- i6o THE GRAMMAR OF SCIENCE. impressions r cannot be the why of motions, we must seek it in some uniform antecedent of the motion such, for example, as the past history of the motion, the relative position of the moving bodies, and so forth. How such antecedents are true scientific causes of motion we shall see in our Chapter VIII. devoted to the " Laws of Motion." II. Necessity belongs to the World of Conceptions > not to that of Perceptions. At this point the reader may feel inclined to say : " But surely there is as much necessity that a planet describing its elliptic orbit should at a certain time be in a certain position, as that the angles on the diameter of a circle should be right-angles?" With this I entirely agree. The theory of planetary motion is in itself as logically necessary as the theory of the circle ; but in both cases the logic and necessity arise from the definitions and axioms with which we mentally start, and do not exist in the sequence of sense-impressions which we hope that they will, at any rate approximately, describe. The necessity lies in the world of conceptions, and is only unconsciously and illogically transferred to the world of perceptions. This difference may be well illustrated by an example due to Mr. James Stuart, formerly Professor of Mechanism in Cambridge. Suppose I were to put a stone on a piece of flat ground and walk round it in that particular curve termed an ellipse, which a planet describes about the sun. We will further suppose the stone to be at that particular point 1 That the frequently cited "muscular sensation of force" is really only a sense-impression interpreted as one of motion will be shown at a later stage of our work. CAUSE AND EFFECT. PROBABILITY. l6l termed the focus which in the case of an elliptic orbit is actually occupied by the sun ; and lastly, I will walk round so that a line drawn from the stone to me sweeps out equal areas in equal times, a funda- mental characteristic of the laws of planetary motion. Now my motion might be very fairly described by the law of gravitation, but it is quite clear that no force from the stone to me, no law of gravitation, could logically be said to cause my motion in the ellipse. We might in imagination conceive a point changing its motion according to the law of gravi- tation and tracing out my ellipse ; it might keep pace with me, and would, of logical necessity, cover equal areas in equal times. This logical necessity would flow from our definition, our con- ception, namely, that of a gravitating point. This point might be used to describe my elliptic motion, and to predict my positions in the future, but no observer would be logical in inferring that the necessary sequence of positions involved in the concept of a gravitating point could be transferred, or projected into a necessity in the sequence of his perceptions of my motion. I might go round the ellipse a hundred times in the same manner and then stop or go off in an entirely different path. The sole legitimate inference of the observer would then be that the law of gravitation was not a sufficiently wide- embracing formula to describe more than a portion of my motion. 1 This difference between necessity in 1 The example cited is given by Mr. Stuart on p. 168 of his A Chapter of Science. It is there used to support the argument of primitive man ; my will causes me to go round the ellipse, there- fore will causes the planets to go round in ellipses, and hence Mr. Stuart passes to Aristotle's God as continual mover of all things. That will is only found associated with certain types of material nervous 12 162 THE GRAMMAR OF SCIENCE. conception and routine in perception ought to be carefully borne in mind. The corpuscular, the elastic- solid, and the electro-magnetic theories of light all involve a series of conclusions of logical necessity, and we may use these conclusions as a means of testing our perceptions. So far as they are confirmed, the theory remains valid as a description ; if, on the other hand, our sense-impressions differ from these conclusions, the conclusions have just as much mental necessity, but the theory while valid for the mind is not valid as a description of the routine of perceptions. It is only the very great probability deduced from past experience of routine that enables us to speak of the " invariable order of the universe," or scientists to assert that facts which have hitherto proved obstinate will be ultimately embraced by well-established laws of nature. Not in the field of causation, but in that of conception do we deal with certainties. 12. Routine in Perception is a necessary condition of Knowledge. While in the nature of perceptions themselves there appears nothing tending to enforce an order D, E, F, G rather than F, G, D, E, there is still a real need, if thought is to be possible, that the perceptive systems is not used by Mr. Stuart, however, to logically infer the material nature of his first cause. He passes by the juggle of a common name from the known to the unthinkable outside the sphere of knowledge and science. The real truth which his Chapter of Science contains as to the characteristics of natural law is hopelessly vitiated by his theological standpoint. " I know," he says, "no result of science which could go to discredit any single thing in all the Bible" (p. 184). Mr. Stuart's ' science' is thus incomparably more retrograde than the modern Cambridge theology which discredits Noah's Ark. CAUSE AND EFFECT. PROBABILITY. 163 faculty should always repeat the sequence in the same order. In other words, repetition or routine is an essential condition of thought ; the actual order of the sequence is immaterial, but whatever it may be, it must repeat itself if knowledge is to be possible. We express this briefly in the law : That the same (p. 200) set of causes is always accompanied by the same effect. That the future will be like our ex- perience of the past is the sole condition under which we can predict what is about to happen and so guide our conduct. But thought has been evolved in the struggle for existence as a guide to conduct, and therefore could not have been evolved had this con- dition been absent. If after the sense-impressions D, E, F, G, the sense-impression H does not uniformly follow, but A, J, or even Z, occur equally often, then knowledge becomes impossible for us, and we must cease to think. The power of thinking, or of associating groups and sequences of sense- impressions, immediate or stored, vanishes if these groups and sequences have no permanent elements by which they can be classified and compared. In the struggle for existence man has won his dictatorship over other forms of life by his power of foreseeing the effects which flow from antecedent causes not only by his memory of past experience, but by his power of codifying natural law, that is, by his power of generalizing experience in scientific statements. It was not necessary for his success that he should know why phenomena take place, but only that he should know how they take place, that he should be able to observe in them a routine, a repeated sequence as a basis for his knowledge. We have only to consider in some simple case say that 164 THE GRAMMAR OF SCIENCE. of the combustion of coal what would follow for man if the resulting sense-impression were not uniform if it were, for example, either intense warmth or intense cold to appreciate that invariable order in the sequence of sense-impressions is an absolute con- dition for man's knowledge, and therefore for the foresight by aid of which he has won his dictatorship. In the chaos of sensations, in the " beyond " of sense- impressions, we cannot infer necessity, order or routine, for these are concepts formed by the mind of man on this side of sense-impressions. Yet if the supremacy of man is due to his reasoning faculty, so the condition for the existence of man as a reasoning being is routine in his perceptions, invariable order in the sequences of his sense -impressions. We can neither assert nor deny that this routine is due to something beyond sense-impression, for in that " beyond " the word routine is meaningless, and we can neither assert nor deny where we are dealing with a field to which the word knowledge cannot be applied. All we can assert is that the reasoning faculty in man connotes a perceptive faculty presenting sense-im- pressions in the same invariable order. That this routine is due to the nature of the perceptive faculty itself to factors, of which we are unconscious in its constitution, akin to the conscious association and memory of the reasoning faculty is a plausible if unproven hypothesis. It is one, however, as we have seen, suggested by the contemporaneous growth of perception and reason, and strengthened by the impossibility of any form of perceptive faculty, such as we find in the insane, surviving in the struggle for existence (p. 125). While invariable order in the sequence of sense- CAUSE AND EFFECT. PROBABILITY. 165 impressions is thus seen to be an essential character- istic of the perceptive faculty of a rational being, the power to understand the why and wherefore of any sequence is not so. It would undoubtedly be of great intellectual interest to know why bodies fall to the earth, but how they invariably fall is the practical knowledge, which now enables us to build machines and which enabled our forefathers to throw stones, and thus helped them as it helps us in the struggle for existence. Broadly speaking, here as elsewhere, the perceptive faculty has developed along lines which strengthen man's powers of self-preservation and not along those which would merely minister to his intellectual curiosity. Anything, be it noted, that tends to weaken our confidence in the uniform order of phenomena, in what we have termed the routine of perceptions, tends also to stultify our reasoning faculty by destroying the sole basis of knowledge. It decreases our power of foresight and lessens our strength in the battle of life. For this reason theosophists and spiritualists with their modern miracles contradicting the long-experienced routine of perceptions are very unlikely to form a society sufficiently stable to survive in the struggle for existence. Every ecstatic and mystical state weakens the whole intellectual character of those who experience it, for it impairs their belief in the normal routine of perceptions. The abnormal perceptive faculty, whether that of the madman or that of the mystic, must ever be a danger to human society, for it undermines the efficiency of the reason as a guide to conduct. Conviction, therefore, of the uniform order of phenomena is essential to social welfare. l66 HE GRAMMAR OF SCIENCE. But the reader may object that although this convic- tion be essential to social welfare, it does not follow that it is well based. Belief in a fetish may be essential to the welfare of a primitive tribe, and he who does not believe in it may be exterminated ; yet this does not demonstrate the rational character of the belief. It is right therefore that we should investigate whether our conviction is well based, and to this point we shall devote the remaining sections of this chapter. In concluding the present section we may resume the results reached as follows : In the order of perceptions (cause and effect) no inherent necessity can be demonstrated. In the uniformity with which sequences of percep- tions are repeated (the routine of perceptions) there is also no inherent necessity, but it is a necessary condition for the existence of thinking beings that there should be a routine in perceptions. The necessity thus lies in the nature of the thinking being and not in the perceptions themselves ; thus it is conceivably a product of the perceptive faculty. 1 3 . Probable and Provable. Stanley Jevons in his discussion of the theory of probability, which forms one of the most valuable and interesting portions of his Principles of Science, remarks that the etymology of the word probable does not help us to understand what probability is and where it exists : " For, curiously enough, probable is ultimately the same word as provable a good instance of one word CAUSE AND EFFECT. PROBABILITY. l6/ becoming differentiated to two opposite meanings " (p. 197).* Now we have seen that certainty belongs only to the sphere of conceptions ; that inherent necessity has a meaning in the mental field of logic, but that we can- not postulate it in the universe of perceptions ; that the " necessity of natural law " is really an unjustifi- able phrase. The word proof, therefore, used in the sense of a demonstrable certainty applies only to the sphere of conceptions. What are we then to understand when the word proof is applied to natural phenomena ? Shall we say that it is incorrect to use the word prove at all in such relationship ? Yet our leading men of science do use it. Here is a passage from Sir William Thomson's lecture on "The Six Gateways of Knowledge." 2 He is discussing the possibility of our having a " magnetic sense," and he writes : " I cannot think that that quality of matter in space magnetization which produces such a pro- digious effect upon a piece of metal, can be absolutely without any it is certainly not without any effect whatever on the matter of a living body ; and that it can be absolutely without any perceptible effect whatever on the matter of a living body placed there, seems to me not proved even yet, although nothing has been found." The word prove is here distinctly used of some- thing being demonstrable in the field of perception. 1 The source of both words must be sought, I think, in the mediaeval Latin proba, a sample, test, or trial. Thus probare is used in the sense of extracting a fact by torture, and probabilis is that which by aid of the proba has been attested and approved. 3 Popular Lectures and Addresses, vol. i. p. 261. London, 1889. 1 68 THE GRAMMAR OP^ SCIENCE. There is clearly an inference involved, and this inference is easily seen to be that of the routine of perceptions, namely, that if something has once been perceived, it will under precisely the same circum- stances be again perceived. Our conviction of this routine is not a certainty, but, as we have seen, a probability. Hence, when we are speaking of the sphere of perceptions we must remember that provable is ultimately the same word as probable. The association of the two words does not therefore seem without profit ; and the etymology may after all serve to remind us of the character of our knowledge in the field of perception. The problem before us is the following one : A certain order of perceptions has been experienced in the past, what is the probability that the perceptions will repeat themselves in the same order in the future? The probability is conditioned by two factors, namely: (i) In most cases the order has previously been very often repeated, and (2) past experience shows us that sequences of perceptions are things which have hitherto repeated themselves without fail. Thus there is past experience of repeti- tion in the class, as well as in the individual, strengthening the probability of a future recurrence of the same order. The probability that the sun will rise to-morrow is not only conditioned by men's past experience of the sun's motion, but by their past experience of the uniform order in natural pheno- mena. There is no need to repeat a cautiously conducted experiment a great number of times to prove that is, to establish an overwhelming pro- bability in favour of a certain sequence of percep- tions. The overwhelming probability drawn from CAUSE AND EFFECT. PROBABILITY. 169 past experience in favour of all sequences repeating themselves at once embraces the new sequence. Suppose the solidification of hydrogen to have been once accomplished by an experimenter of known probity and caution, and with a method in which criticism fails to detect any flaw. What is the probability that on repetition of the same process the solidification of hydrogen will follow? Now Laplace has asserted that the probability that an event which has occurred p times and has not hitherto failed, will occur again is represented by the fraction & Hence in the case of hydrogen, the probability of repetition would only be f , or, as we popularly say, the odds would be two to one in its favour. On the other hand, if the sun has risen without fail a million times, the odds in favour of its rising to-morrow would be 1,000,001 to i. It is clear that on this hypothesis there would be practical certainty with regard to the rising of the sun being repeated, but only some likelihood with regard to the solidification of hydrogen being repeated. The numbers, in fact, do not in the least represent the degrees of belief of the scientist regarding the repetition of the two phenomena. We ought rather to put the problem in this manner : / different sequences of perception have been found to follow the same routine however often repeated, and none have been found to fail, what is the probability that the (/)+i)th sequence of perceptions will have a routine? Laplace's theorem shows us that the odds are (p+i) to I in favour of the new sequence having a routine. In other words, since / represents here the infinite variety of phenomena in which men's past experience has shown that the same causes are on repetition followed THE GRAMMAR OF SCIENCE. by the same effect, there are overwhelming odds that any newly observed phenomena may be classified under this law of causation. 1 So great and, consider- ing the odds, reasonably great is our belief in this law of causation applying to new phenomena, that when a sequence of perceptions does not appear to repeat itself, we assert with the utmost confidence that the same causes have not been present in the original and in the repeated sequence. 14. Probability as to Breaches in the Routine of Perceptions. Laplace has even enabled us to take account of possible " miracles," anomies, or breaches of routine in the sequence of perceptions. He tells us that if an event has happened / times and failed q times, then the probability that it will happen the next time is or the odds in favour of its happening are o^+i. Now if we are as generous as we possibly can be to the reporters of the miraculous, we can hardly assert that a well-authenticated breach of the routine of perceptions has happened once in past experience for every 1,000 million cases of routine. In other words we must take p equal to 1,000 million times l8 7 2 - MORGAN, A. DE. The Theory of Probabilities. London, 1838. VENN, J. The Logic of Chance. London, 1866. The reader who wishes to study Laplace's labours at first-hand will find a guide to his memoirs and some account of the various editions of his Theorie analytique des Probabilites, in Todhunter's History of the Theory of Probability, chap. xx. He may also consult Arts. 841-857 of the same History. CHAPTER V. SPACE AND TIME. i. Space as a Mode of Perception. IN our second chapter (p. 77) we saw that the dis- tinction between " inside " and " outside " ourselves was not a very real or well-defined one. Certain of the vast complex of our sense-impressions we term inside, others again we term outside. To a savage the beginning of outside, the limit to self, is un- doubtedly his skin ; although on occasion he may extend the idea of self farther, and be peculiarly careful of what becomes of such outward-lying por- tions of self as nail-parings and hair-clippings. The skin seems to him to bound off self from an outside world of non-self. The group of sense-impressions which he calls skin, marks off a world which he can see and feel from one which in the normal condition is inaccessible to sight or touch. His first experiences of pain arise, or at least are perpetuated, from some- thing within this invisible and intangible world, and the nerve-vibrations, which he classifies as pain, he postulates as inside self; his indigestion does not seem immediately associated with the visible and tangible world outside his skin. Thus the sense- impression pain, even when associated later with a group of other sense-impressions classified as those of sight and touch, is still differentiated from them 1 82 THE GRAMMAR OF SCIENCE. as something especially internal. I receive for a moment, and then they vanish, the feelings of hard- ness and pain ; both may come to the seat of my consciousness as nerve-vibrations, or even by the same nerve-vibration ; both are associated with stored impresses of past hardnesses and pains, yet I project the sense-impression hardness into something out- side self, but the pain I consider as something peculiar to my inside. I spe,ak of my pain and your pain ; yet not of my hardness and your hardness, but of hardness as something peculiar to the table-leg. I thus give an objective reality to one group of sense-impressions, which I refuse to another. Now this distinction seems to me to have arisen from the historical fact that the stored sense-impresses with which we associate hardness have been drawn from the tangible and visible world " outside skin," while those with which we associate pain have been largely drawn from the intangible and invisible world "in- side skin." Even as our knowledge develops and "inside skin" becomes less intangible and invisible, even as we learn to associate pain with the stored impresses of various local organs " inside skin," we still feel it a somewhat doubtful use of language to talk of pain as " existing in space." Gradually, however, the skin has ceased to be a well-marked boundary between outside and inside. Self, like the soul of the metaphysicians, has disappeared from body and been concentrated in consciousness. Self, seated (metaphorically, not physically) in the telephonic brain exchange, receives an infinite variety of messages, which we can only assume to reach self in precisely the same manner. Yet self classes some groups of these messages together, and speaks of them SPACE AND TIME. 183 as objects existing in space, while to other groups it has denied in the past, or still denies, this spacial existence. How far is this distinction logical, how far historical ? J Now we shall find that the instant we associate a number of sense-impressions in a group, and separate them in perception from other groups, we consider them " to exist in space." Space is thus, in the first place, a mental expression for the fact that the per- ceptive faculty has separated coexisting sense-im- pressions into groups of associated impressions. This separation of immediate sense-impressions into groups, this discriminating power of the perceptive faculty is, at any rate in the early stages of man's development, most clearly recognized and closely associated with the senses of sight and touch. Hence it comes about that the invisible and intangible " inside skin " is at first not considered as in space. Later, for example, as we localize pain, or associate it with other sense-impressions classified as visible and tangible, we treat " inside skin " as belonging to space. Yet we still frequently consider the presence of visible and tangible members a condition for a spacial group of sense-impressions. Space, says Thomas Reid, is known directly by the senses of sight and touch. But probably a like, if less powerful, means of discriminating groups of sense-impressions lies in the senses of sound and smell. 2 We localize 1 By historical I mean that which arises in the natural history of man from imperfect knowledge and illogical inference. Thus the belief in ghosts, witches, and storm-spirits is a perfectly intelligible stage in the natural history of man, but not a logical inference from any natural phenomena in the light of more perfect knowledge. 2 My baby when three days old was able to distinguish between the snapping of the fingers of the right and left hands, and to follow with 1 84 THE GRAMMAR OF SCIENCE. sounds and smells without necessarily associating them with visible and tangible resounding and smell- ing bodies. It will, I think, be admitted on reflection that whenever we concentrate our attention on a limited group of associated sense-impressions, then we consider them as spacial, or " existing in space." We join together, owing to past experience, certain sense-impressions as a permanent group, and we then mentally separate this group from other groups. The actual boundary of the group, however, when we attempt to define it is found in reality to be vague (p. 80). The group, although in the main a per- manent association, has a continual flow in and out of junior partners ; while some of the partners belong, on closer examination, as much to one association as another. The separation is thus rather practical than real ; it arises, in the first place, from the fact that in our perception certain sense-impressions are more or less permanently grouped together, and, in the second place, from the mental habit of concen- trating our attention on one of these groups by placing about it in conception an arbitrary boundary separating it from other groups. Such arbitrary boundaries are conceptions drawn doubtless from sense-impressions of sight and touch, but they corre- spond, as we shall soon see, to nothing real in the world of sense-impression or in phenomena. The coexistence of more or less permanent and distinct groups of sense-impressions is a fundamental mode of our perception ; it is one of the ways in which we perceive things apart. There is nothing in the ear the direction of the sound. She would turn to a voice long before she paid any attention to bodies moving quite close to her eyes. Difference of position was thus associated with sound. SPACE AND TIME. 185 sense-impressions themselves which involves the notion of space, but whether space be " due " to something behind sense-impression or to the nature of the perceptive faculty itself we are unable at present to decide. Leibniz has defined space as the order of possible coexisting phenomena. This order may " arise " from something behind phenomena, or from the machinery of perception, but in either case the order itself is simply a mode or manner in which we perceive things. The reader must distinguish carefully between the groups of sense-impressions themselves and the order in which we perceive them to coexist. Perhaps the distinction will be best brought out by considering the letters of the alpha- bet : A, B, C, D, E, F, G, . . . The letters may be said to have a real existence like the groups of sense-impressions we term objects. The order of the letters is merely the mode in which we perceive them to coexist as an alphabet. The " existence " we attribute to the order is thus of a totally different character to the "existence" we attribute to the letters. The alphabet has in itself no existence except for the letters it contains, but the letters, on the other hand, could have a real existence if they had never been arranged in any order or alphabet. The alphabet has merely exis- tence as a manner of looking at all the letters to- gether. These results may all be interpreted of coexisting groups of sense-impressions and their order space. A single sense-impression might, indeed, exist for us without any coexisting groups being postulated, but space would have no meaning if there were not such coexisting groups. Space is an order 1 86 THE GRAMMAR OF SCIENCE. or mode of perceiving objects, but it has no existence if objects are withdrawn, no more than the alphabet could have an existence if there were no letters. If the reader has once grasped this point and it is undoubtedly a difficult and hard one (for our senses of sight and touch lead us imperceptibly to confuse the reality of sense-impressions with our mode of perceiving them), then he will cease to look upon space as an enormous void in which objects have been placed by an agency in nowise conditioned by his own perceptive faculty ; he will begin to consider space as an order of things, but not itself a thing. To say, therefore, that a thing " exists in space " is to assert that the perceptive faculty has distinguished it as a group of sense-impressions from other groups of sense-impressions, which actually or possibly coexist. We cannot dogmatically deny that the order of co- existing phenomena " arises " from something behind sense-impressions, 1 but we may feel pretty confident that space, our mode of perceiving these phenomena, is very different from anything in the unknowable world behind sense-impressions. Once recognize space as a mode of the perceptive faculty, and it appears as something peculiar to the individual per- ceptive faculty. Without any perceptive faculty it is conceivable that sensations might exist (see p. 123), but there could not be that mode of perception we term space. The remarkable fact is this : that the order of coexisting phenomena is apparently the same at any rate for the vast majority of human perceptive 1 Just as little ought we to assert that it does. The word arise suggests causation ; but the word causation is meaningless as a relation between the unknowable beyond of sense-impression and sense- impression itself (see pp. 82 and 151). SPACE AND TIME. 1 87 faculties. Why should this mode of perception be the same for all normal human faculties or, perhaps it would be better to say, very approximately the same ? We express the problem and the mystery wrongly when we ask "why space seems the same to you and me ; " we ought more precisely to ask " why your space and my space are alike." Because our perceptive faculties are of the normal type, may be the immediate answer ; but how similar organizing centres have come to exist in the chaos of sensations remains still to be described. Some light perhaps may be thrown on this difficult problem by considerations which will be more fully developed in our chapter on Life. Man has not reached his present high stage of development solely by individualistic tendencies, but also by socialistic or gregarious tendencies. The struggle of man against man might suffice to bring about a co-ordina- tion of the individual man's perceptive and reasoning faculties (p. 124), but in the struggle of group against group, and of group with its environment, it is clear that a great advantage would follow to any group from a close agreement of the perceptive faculties of its members, and great disadvantage to any group without this agreement. The survival of the former would be the natural result. 2. The Infinite Bigness of Space. " How big is space ? " is a meaningless question as it stands. " How big is space for me ? " admits, how- ever, of an answer. It is just so large as will suffice to separate all things which coexist for me. Let the reader try to imagine phenomenal space apart from groups of sense-impressions and he will quickly 1 88 THE GRAMMAR OF SCIENCE. discover how big space is for him. Space, he will at once recognize, has no meaning when we cease to perceive things apart to distinguish between groups of sense-impressions. We ought constantly to bear in mind that space is peculiar to ourselves, and that we ought not reasonably to be stirred to greater admiration by anyone descanting on the "magnitude of space," than we are wont to be when reflecting on the complex nature of our own perceptive faculty. The farthest star and the page of this book are both for us merely groups of sense-impressions, and the space which separates them is not in them, but is our mode of perceiving them. There is a cheap and, unfortunately, common form of emotional science which revels in contrasting the "infinities of space" with the "finite capacities of man." As instructive samples of this we may take the following passages from a popular writer on astronomy : " Can it be true that these countless orbs are really majestic suns, sunk to an appalling depth in the abyss of unfathomable space ? " " Yet, after all, how little is all we can see even with our greatest telescopes, when compared with the whole extent of infinite space ! No matter how vast may be the depth which our instruments have sounded, there is yet a beyond of infinite extent. Imagine a mighty globe described in space, a globe of such stupendous dimensions that it shall include the sun and his system, all the stars and nebulae, and even all the objects which our finite capacities can imagine. Yet, after all, what must be the relation of even this great globe to the whole extent of infinite space? The globe will bear to that a ratio infinitely SPACE AND TIME* 189 less than that which the water in a single drop of dew bears to the water in the whole Atlantic Ocean." 1 To speak of the mode in which we perceive co- existing phenomena as an abyss of appalling depth is perhaps rather meaningless phraseology ; but the statement that infinite space contains more than our finite capacity can imagine is hopelessly misleading. In the first place, the space of our perceptions, the space in which we discriminate phenomena, is not infinite : it is exactly commensurate with the contents of that finite capacity we term our per- ceptive faculty. In the second place, if by " all the objects which our finite capacities can imagine " the author means conceptions and not perceptions, he is confusing two different things space, as the order of real coexisting phenomena, what we may term real space, and the space of our thought, the conceptual space of geometry, what we may term ideal space. This latter, as we shall see in the sequel, may be conceived as either finite or infinite, although a limited portion of ideal infinite space describes most easily the real space of our perceptions. Thus the only infinite space we know of, so far from being a real immensity overwhelming our finite capacities, is a product of our own reasoning faculty. On the other hand cosmical space, the mode of our per- ception, is finite and limited by the range, not of what we imagine, but of what we perceive to co-exist. The mystery of space, whether it be the finite space of perception or the infinite space of conception, lies in, and not outside, each human consciousness. We must seek it either in our power of distinguishing (or of perceiving apart) so many and varied groups of 1 Ball's Story of the Heavens, pp. 2 and 538. THE GRAMMAR OF SCIENCE. sense-impressions or, in our power of drawing con- ceptions, which enables us to pass from the finite real to the infinite ideal. Only for us, as perceiving human beings, has space any meaning ; we cannot infer it where we do not find psychical machinery similar to our own. 3. The Infinite Divisibility of Space. The space of our perceptions, as we have seen, is finite and varies from individual to individual with the range and complexity of his perceptions. As it is just large enough for our perception of phenomena, so it is just small enough, by which we are to under- stand that it is not " infinitely divisible." The limit to its divisibility is the limit to our power of per- ceiving things apart. Our organs of sense are such that only sense-impressions of a certain intensity or amplitude fall within their cognizance. We may resolve phenomena into smaller and smaller groups of sense-impressions, but we ultimately reach a limit at which the sense-impression ceases. We may divide a piece of paper up into more and more minute fragments, but ultimately they cease to be sensible even by the aid of our most powerful microscopes. We have then reached a limit to our mode of per- ceiving apart, in ordinary parlance, to the divisibility of space. We may possibly conceive smaller divisions, but in doing this we have passed from the sphere of the real to the ideal from the space of perception to the space of geometry. It seems to me that this transition from perception to conception, often made quite unconsciously, is the basis of all the difficulties involved in the paradox as to the infinite divisibility SPACE AND TIM. tQl of space. The point has been referred to by Hume in his Essay concerning Human Understanding? where he writes as follows : " The chief objection against all abstract reasonings is derived from the ideas of space and time ideas which, in common life and to a careless view, are very clear and intelligible, but when they pass through the scrutiny of the profound sciences (and they are the chief object of those sciences) afford principles which seem full of absurdity and contradiction. No priestly dogmas, invented on purpose to tame and subdue the rebellious reason of mankind, ever shocked common sense more than the doctrine of the infinite divisibility of extension, with its con- sequences, as they are pompously displayed by all geometricians and metaphysicians with a kind of triumph and exultation. A real quantity, infinitely less than any finite quantity, containing quantities infinitely less than itself, and so on in infinitum ; this is an edifice so bold and prodigious that it is too weighty for any pretended demonstration to support, because it shocks the clearest and most natural prin- ciples of human reason. But what renders the matter most extraordinary is that these seemingly absurd opinions are supported by a chain of reasoning, the clearest and most natural ; nor is it possible for us to allow the premises without admitting the con- sequences." Now the reader should carefully note the uncon- scious transition in this passage from the ideas of space and time to the infinite divisibility of real quantities. The transition is even more marked in a 1 Section xii. part ii. Green and Grose : HumJs Works, vol. iv. > 128. 192 THE GRAMMAR OF SCIENCE. footnote which accompanies the passage, and which runs thus : " Whatever disputes there may be about mathe- matical points, we must allow that there are physical points that is, parts of extension, which cannot be divided or lessened either by the eye or imagination. These images, then, which are present to the fancy or senses, are absolutely indivisible, and consequently must be allowed by mathematicians to be infinitely less than any real part of extension ; and yet nothing appears more certain to reason than that an infinite number of them composes an infinite extension. How much more an infinite number of ' those infinitely small parts of extension, which are still supposed infinitely divisible." Here the transition from perception to conception and back again is made several times over. A point mathematically defined is a conception and has no real existence in the field of perception. It is true we base this conception on our perceptive experience of things which are not points, but the mathematical point is not a limit to any process which could be carried on in the field of perception ; it is the limit to a process which we imagine carried on in the field of thought, in the sphere of conceptions. If Hume means by a physical point the smallest possible groups of sense-impressions which we can perceive apart, then this cannot be divided or lessened by the eye. But this physical point transferred from the field of perception to that of conception can in the imagination be divided over and over again. This re- mark will be more clearly appreciated when we come to deal with the geometrical conception of space. It suffices for the present to note that Hume passes from SPACE AND TIME. 193 the eye to the imagination, from the mathematical to the physical, from the fancy to the senses, as if the geo- metrical theory of extension, that shorthand method of classifying and describing coexisting phenomena was itself the world of phenomena. Several types of geometry can be elaborated by our rational faculty, and the results, which flow from them, will depend upon the statement of their fundamental axioms. From these types we select that one which will enable us to describe the widest range of phenomena in the briefest possible formula, or which will enable us with the greatest accuracy to classify the differences between groups of sense-impressions. We have no more right to quarrel with the geometrician's con- ception of tiis infinite divisibility of space than with his conception of the circle, or with the physicist's conception of the atom. One and all are pure ideals beyond the range of perceptual experience. What we must ask is : How far are these conceptions of service in enabling us to briefly describe and classify our perceptions ; how far do they aid us in mentally storing up past experience as a guide for future action ? A point and an ellipse may be absolutely absurd in the world of perceptions, but they are none the less valid and useful conceptions, if they help us to describe and predict the motion of the earth about the sun. The paradoxes which Hume finds in the conclusions of geometry only exist so long as we assert that every conception has a precise counterpart in perception, and forget that science is only a shorthand descrip- tion of nature and not nature itself. 4. The Space of Memory and Thought. Before we pass from the subject of real or perceptual 194 THE GRAMMAR OF SCIENCE. space, we ought to note that this mode of perceiving phenomena appears not only in association with immediate sense-impressions, but also with the stored impresses of past experience. To be accurate, we ought perhaps to say that the mode of remembrance is akin to the mode of perception unless, indeed, we are using the word perception to refer to the con- sciousness alike of an " external " sense-impression and of an "internal" sense-impress. In all probability these processes of what Locke would term external and internal perception are much the same, only the sources from which they draw their material are different. In this case it is sufficient to say that space as a mode of perception applies as much to memory as to phenomena. We certainly gain by this method of regarding the matter new insight into the manner in which space may result from the nature of the psychical machinery. No one can look upon the space whereby the impresses of past experience are grouped and distinguished as a reality apart from internal perceptions ; it is too obviously a mode of the retentive faculty. But the distinction between the world of phenomena and the world of memories lies not in the order and relation of their contents, but in the intensity of the stimulus and the quality of the association in the two cases. The candles, the inkstand, the books and papers on my table have the same order and relation, whether I see and touch them or simply recall them as a memory, but there is a great difference in the vividness I of the external 1 Hume's definition of belief, slightly modified, well marks the difference : A group of immediate sense-impressions is a " more vivid, lively, forcible, firm, steady " perception of an object than a group of stored impresses alone is ever able to attain (Essay Concerning Human Understanding, sec. v. part ii.). SPACE AND TIME. 195 and internal perceptions, and a considerable change in the range of stored impresses with which the contents of perception are associated in the two cases. Once recognize space as the mode in which we perceive coexisting things apart, and we have either to multiply spaces or to consider that logically all separation denotes space. Thus our thoughts and conceptions will be found almost invariably to involve spacial relationship, while the psychical processes themselves are, like pain, being more and more localized or associated with individual centres of brain -activity. It may fairly be said that until the spacial relationship is recognized in any field, until we are able to perceive things apart, we have no basis for distinction, comparison, classification, and the resulting scientific knowledge. It is especially from the localization of psychical processes that we may hope for great results, for a true science of psychology in the future. This localization is not a " materialization " of thought, it is merely an asso- ciation of " internal " and " external " perceptions, both equally factors of consciousness. The asso- ciation is not an association of two totally diverse and opposed things matter and mind but of the two phases of perception. Groups of sense-im- pressions in space, being conditioned by the per- ceptive faculty, are as much a part of the sentient being as psychical processes themselves. Logically, then, it seems that whenever we clearly separate and distinguish coexisting things, we per- ceive them under the mode space ; and perception under this mode is what we ought to mean by " existence in space." Yet historically the notion of THE GRAMMAR OF SCIENCE. space has arisen from the separation and distinction of groups of sense-impressions, when some one or more members in each group were due to sight or touch ; for these senses are those by which groups have, in the natural history of man, been first perceived apart. Just as these groups of sense-impressions were pro- jected outward from our consciousness, and treated as things unconditioned by our perceptive faculty, as objects independent of the sentient being, so our mode of perception was treated as inherent in them, and given an objective existence, fossils of which are still to be found in the " primeval void " of myth- ology, and the " appalling abyss " of popular astro- nomers. Only gradually have we learnt to recognize that empty space is meaningless, that space is a mode of perception the order in which our perceptive faculty presents coexistence to us. We are not compelled to postulate a space outside self for pheno- mena, and spaces inside self for memory, thought, and the psychical processes, but rather we must hold that the mode in which we perceive in these different fields is essentially the same, and that this mode is what we term space. 5. Conceptions and Perceptions. If such be the space of perception, we have next to ask : How do we scientifically describe it ? What is conceptual space the space with which we deal in the science of geometry ? We have seen that our perceptive faculty presents sense-impressions to us as separated into groups, and further, that though this separation is most serviceable for practical purposes, it is not very exactly and clearly defined " at the limits " (p. 80). How do we represent in thought, StACE AND TIME. 197 in conception, this separation into groups which results from our mode of perception ? The answer is : We conceive groups of sense-impressions to be bounded by surfaces, to be limited by straight or curved lines. Thus our consideration of conceptual space leads us at once to a discussion of surfaces and lines to a study, in fact, of Geometry. Several important problems at once present them- selves for investigation. In the first place, have these surfaces and lines a real existence in the world of perception ? Are they phenomena ? Or, are they ideal modes whereby we analyze the manner in which we perceive phenomena ? In the second place, if they should be only ideals of conception, what is the historical process by which they have been reached ? what is their ultimate root in perception ? Now, there is at this stage an important remark to be made, namely, that what is imperceptible is not therefore inconceivable. This remark is all the more necessary, for it seems directly opposed to the healthy scepticism of Hume. 1 Yet unless it be true the whole fabric of exact science falls to the ground, neither the concepts of geometry, nor those of mechanics, would be of service ; for example, the circle and the motion of a point would be absurdities if, being imperceptible, they were really inconceivable. The basis of our conceptions doubtless lies in per- ceptions, but in imagination we can carry on per- ceptual processes to a limit which is itself not a perception ; we can further associate groups of stored sense-impresses, and form ideas which correspond to nothing in our perceptual experience. 1 See especially the Treatise of Human Nature^ part ii. Of the Ideas of Space and Time. Green and Grose's Hume's Works, vol. i. PP- 334-371- 198 THE GRAMMAR OF SCIENCE. Here a word of caution is, however, very necessary. Because we conceive a thing, we must not argue that it is either possible or probable as a perception. Indeed, the process or association by which we have reached our conception may in itself suffice to ex- hibit its perceptual impossibility or improbability. The appeal to experience can alone determine whether a conception is possible as a perception. For example, experience shows me that there is a sensible limit to the visible and tangible ; hence a point, valid as a conception, can never have a real existence as a perception. I reach this conception of a point by carrying to a limit in my imagination a process which cannot be so carried in perception. Exactly of the same character are my conceptions of infinite distance or infinite number ; they are the concep- tual limits to processes, which may be started in perception, but cannot be carried to a limit except in the imagination. Somewhat different from percep- tual impossibility is perceptual improbability. I can conceive Her Majesty Queen Victoria walking down Regent Street, but, tested by my experience of the past actions of royalty, this association of conceptions is hardly a perceptual probability. These instances may be sufficient to indicate that what is improbable or impossible in perception may be valid in concep- tion. But we must ever be careful to bear in mind that the reality of the conception, its existence out- side thought, can only be demonstrated by an appeal to perceptual experience. The geometrician even asserts the phenomenal impossibility of his points, lines, and surfaces ; the physicist by no means pos- tulates the existence of atoms and molecules as possible perceptions. Science is content for the SPACE AND TIME. 199 present to look upon these concepts as existing only in the sphere of thought, as purely the product of man's mind. It does not, like metaphysics or theology, demand any existence in or beyond sense- impression for its conceptions until experience has shown that the conceptual limit or association can become a perceptual reality. 1 The validity of scien- tific conceptions does not in the first place depend on their reality as perceptions, but on the means they provide of classifying and describing perceptions. If a circle and a rectangle have no real existence, they are still invaluable as enabling me to classify my per- ceptions of form, to describe, however imperfectly, the difference in shape between the faces of a page of this book and of my watch. They are symbols in that shorthand by means of which science describes the universe of phenomena. The atom, if a pure con- ception, still enables us, by codifying our past ex- perience, to economize thought ; it preserves within reasonable limits the material upon which we base our prediction of possible future experience. If any one tells us that the storm-god is to some minds as conceivable as the atom, we must, in the first place, reply that the conceivable is not the real ; and further, that the value to man of any ideal of conception depends upon the extent to which it subsumes the future in its resume of the past. The conception storm-god may, after all, be of some value as a striking monument to our meteorological ignorance, 2 Leverrier and Adams conceived a planet having a definite orbit as a method of accounting for the irregularities perceived in the motions of Uranus. Their conception might have been valid as a manner of describing these irregularities, if Neptune itself had never been perceived in other words, if their conception had not become a perceptual reality. 20O THE GRAMMAR OF SCIENCE. and as a useful reminder that we must " be prepared for all weathers." What we have at this stage to notice is that the mind is not limited to perceptual association, and that it can carry on in conception a process which may be begun, but cannot be indefinitely continued in the sphere of perception. The scientific value of such conceptions, whether reached by association or as a limit, must in every case be judged by the extent to which they enable us to classify, describe, and predict phenomena. 6. Sameness and Continuity. Now there are two ideas reached as conceptual limits to perceptual processes which have important bearings on the geometrical representation of space. These may be expressed by the words sameness and continuity. So far as our perceptual experience goes, probably no two groups of sense-impressions are exactly the same. The sameness in each depends upon the degree of our examination and observation. To a casual observer all the sheep in a flock appear the same, but the shepherd individualizes each. Two coins from one die, or two engravings from one block will always be found to possess some distinguishing marks. We may safely assert that absolute sameness has never occurred in our experience. Not even a " permanent " group of sense-impressions or an object is exactly the same at two different times. Various elements in the group have changed slightly with the time, the light, or the observer. Take a polished piece of metal and note two parts of its surface ; they appear exactly alike, but the microscope reveals their want of sameness. Thus sameness is never a SPACE AND TIME. real limit to our experience of phenomena ; the more closely we examine, the less is the sameness. Yet, as a conception, the sameness of two groups of sense- impressions is a very valid idea, and the basis of much of our scientific classification. In the sphere of perceptions sameness denotes the identity for certain practical purposes of two slightly different groups of sense- impressions. In the sphere of conceptions, however, sameness denotes absolute identity of all the members of either group; it is a limit to a process of comparison which cannot be reached in the per- ceptual world. The idea of continuity, in the sense in which we are now considering the word, involves that of sameness. If I take a vessel of water, I find a certain permanent group of sense-impressions which leads me to term the contents of the vessel water ; if I take a small quantity of the water out of the vessel I ftnd the " same " group, and this still remains true if I take a smaller and smaller quantity, even to a drop. I may continue to divide the drop, but apparently as long as the portion taken remains sensible at all, there is the same group of sense-impressions, and I term the fraction of the drop water. Now the question arises, if this division could be carried on indefinitely should we at last reach a limit at which the group of sense- impressions would change not only quantitatively, that is in intensity, but also qualitatively ? If we could magnify the sense-impressions due* to the infinitesimal fraction of a drop of water up to a sensible intensity, would they so differ from those characteristic of the contents of the original vessel that we should not give them the name water ? Now we cannot test the effects of an indefinitely continued 202 THE GRAMMAR OF SCIENCE. division in the phenomenal world, for we soon reach a stage at which we fail to get, by the means at our disposal, any sense-impressions at all from the divided substances. Our magnifiers of sense-impression have but a limited range. 1 But although in the sphere of perceptions there is no possibility of carrying division to its ultimate limit, we can yet in concep- tion repeat the process indefinitely. If after an infinite number of divisions we conceive that the same group of sense-impressions would be found, then we are said to conceive the substance as continuous. We have then to ask how far the conception of continuity applies to the real bodies of our percep- tual experience. From the finite process of division which is possible in perception, we might easily conclude that continuity was a property of real substances ; and there is small doubt that a slight amount.of observation is favourable to the notion that many real substances are continuous, although the infinite division necessary to the conception of con- tinuity fails as a perceptual equivalent. Further observation and wider insight, however, contradict this notion. The physicist and the chemist bring many arguments to show us that the finite process of division which suggests continuity would, if carried to an infinite limit, show bodies to be discontinuous. On a first and untrained inspection we find a continuity and a sameness in perceptions which disappear on closer and more critical examination. The ideas conveyed in these words are found to be no real limits to the actual, but ideal limits to processes which 1 E.g., the microscope, the microphone, the spectroscope, &c. From the spectroscope we obtain, perhaps, positive indications of a qualitative change in many substances as the quantity is diminished. SPACE AND TIME. 2O3 can only be carried out in the field of conception Bearing this in mind we may now return to the geometrical conceptions of space. 7. Conceptual Space. Geometrical Boundaries. It has been remarked (p. 197) that we conceive groups of sense-impressions to be limited by surfaces and lines. We speak of the surface of the table ; the fly-leaf of this book appears to be separated from the air above it by a plane surface and that plane to be bounded at its upper edge by a portion of a straight line. In the first place we have to ask whether our geometrical notions of line and plane correspond to the limits of anything we actually find in perception or whether they are purely ideal limits to processes begun in perception, but which it is impossible to carry to a limit in perception. The answer to these questions lies in the conceptions of sameness and con- tinuity. The geometrical ideas of line and plane involve absolute sameness in all their elements and absolute continuity. Every element of a straight line can in conception be made to fit every other element, and this however it be turned about its terminal points. Every element of a plane can be made to fit every other element, and this without regard to side. Further, every element of a straight line or a plane, however often divided up, is in conception, when magnified up, still an element of straight line or plane. The geometrical ideas correspond to absolute sameness and continuity, but do we experience any- thing like these in our perceptions ? The fly-leaf of this book appears at first sight a plane surface bounded by a straight line, but a very slight in- 2O4 THE GRAMMAR OF SCIENCE. spection with a magnifying lens shows that the surface has hollows and elevations in it, which quite defy all geometrical definition and scientific treat- ment. The straight line which seems to bound its edge becomes, under a powerful glass, so torn and jagged that its ups and downs are more like a saw edge than a straight line. The sameness and con- tinuity are seen to be wanting on more careful investigation. We take a glass cube skilfully cut and polished, and its faces appear at first as true planes. But we find that a small body placed upon one of its faces does not slide off when the cube is slightly tilted. The face of the cube must, after all, be rough, there are hollows and projections in it which catch those of the superposed body ; our plane again appears delusive. Or, we may take one of Whit- worth's wonderful metal planes obtained by rubbing the faces of three pieces of metal upon each other. Here again a powerful microscope reveals to us that we are still dealing with a surface having ridges and hollows. The fact remains, that however great the care we take in the preparation of a plane surface, either a microscope or other means can be found of sufficient power to show that it is not a plane surface. It is precisely the same with a straight line ; however accurate it appears at first to be, exact methods of investigation invariably show it to be widely removed from the conceptual straight line of geometry. It is a race between our power of representing a straight line or plane and our power of creating instruments which demonstrate that the sameness and continuity of the geometrical conceptions are wanting. Abso- lutely perfect instruments could probably only be SPACE AND TIME. 205 constructed if we were already in possession of a true geometrical line or plane, but the instruments we can make appear invariably to win the race. Our ex- perience gives us no reason to suppose that with any amount of care we could obtain a perceptual straight line or plane, the elements of which would on indefinite magnification satisfy the condition of ultimate sameness involved in the geometrical definitions. We are thus forced to conclude that the geometrical definitions are the results of processes which may be started, but the limits of which can never be reached in percep- tion ; they are pure conceptions having no corre- spondence with any possible perceptual experience What we have said of straight lines and planes holds equally of all geometrically defined curves and surfaces. The fundamental conceptions of geometry are only ideal symbols which enable us to form an approximate, but in no sense absolute, analysis of our sense-impressions. They are the scientific shorthand by which we describe, classify, and formulate the characteristics of that mode of perception which we term perceptual space. Their validity, like that of all other conceptions, lies in the power they give us of codifying past and predicting future experience. We speak of a spherical or cubical body, and say that it is of such and such a capacity. But no per- ceptual body is ever truly spherical or cubical, and the size we attribute to it is at best an approximate one. Further analysis of our sense-impressions leads us in each case to find variations from the geometrical definition and measurement. Yet the conceptions of sphere and cube are frequently sufficient to enable us to classify and identify various bodies and predict the different types of sense-impression to which these 206 THE GRAMMAR OF SCIENCE. bodies correspond. 1 Perhaps no better instance than geometry can be taken to show how science describes the world of phenomena by aid of conceptions corre- sponding to no reality in phenomena themselves. That our geometrical conceptions enable us on the whole to so effectually describe perceptual space is only a striking instance of the practically equal development of our perceptive and reasoning faculties (p. 125). 8. Surfaces as Boundaries. Although perceptual boundaries do not, on ultimate analysis, in any way correspond to any special geo- metrical definition such as that of plane or sphere, we have still to inquire whether they answer to our conception of surface at all. By surface in this sense we are to consider, not something of which it would be possible to analyze the properties by any of the known processes of geometry, but any continuous boundary between two groups of sense-impressions or bodies. 2 Is there a continuous boundary between the 1 Our whole system of measuring size will be found to be based on geometrical conceptions having no actuality in perception. 2 " That which has position, length and breadth but not thickness, is called surface. " The word surface in ordinary language conveys the idea of extension in two directions ; for instance, we speak of the surface of the earth, the surface of the sea, the surface of a sheet of paper. Although in some cases the idea of the thickness or the depth of the thing spoken of may be present in the speaker's mind, yet as a rule no stress is laid on depth or thickness. When we speak of a geometrical surface, we put aside the idea of depth and thickness altogether " (H. M. Taylor, Pitt Press Euclid, i.-ii. p. 3). It seems to me that in ordinary language there is something more than length and breadth involved there is an idea of continuous boundary. It is difficult to say how far this idea is really involved in the word extension. A veil may nave extension in two directions, but it fails to fulfil our idea of surface because ^ ''s not a continuous boundary. SPACE AND TIME. 2O/ open page of this book and the air above it ? Would it be possible to say at any distinct step of the passage from air to paper, here air ends and paper begins? At this point we reach one of the most important problems of science. Are we to consider the groups of sense-impressions which we term bodies continuous or not ? If bodies are not continuous, then it is clear that boundaries are only mental symbols of separation, and on deeper analysis correspond to no exact reality in the sphere of sense-impression. Would every element of the surface of a body still appear to us a continuous boundary, however small the element and however much we magnified it up ? If I could take the hundredth part of a square inch of this page and magnify it to a billion times its present size, would there still appear a continuous boundary between air and paper ? Consider the boundary of still water. It furnishes us with the impression of a continuous surface. On the other hand, examine a heap of sand closely, and it appears to have no continuous boundary at all. Are there any reasons which would lead us to suppose that, if we could sufficiently magnify a small element of this page of paper, it would produce in us sense- impressions not of continuity but of discontinuity ? Would it look, supposing it were still visible, like the surface of water, or rather like a heap of sand, a pile of small shot, or, better still, like a starry patch of the heavens on a clear night ? No group of stars is in perception separated from another by a line or surface. We can imagine such boundaries drawn across the heavens, but we do not perceive them. We have, then, to ask whether the boundary between paper and air, if immensely magnified, would look 208 THE GRAMMAR OF SCIENCE. sideways, not indeed like a geometrical line, but roughly like the first or second of these figures : FlGS. 2 AND 3. Now no direct answer can really be given to this question, because bodies cease to impress us sensibly long before we reach the point at which the appear- ance of continuity might be expected to disappear. We cannot predict what our sense-impressions would be, if we could magnify a drop of water up to the size of the earth. But we may put the question in a slightly different way. We may ask : Would it enable us to classify and describe phenomena better if we conceived bodies to be continuous as in Fig. 2, or discontinuous as in Fig. 3 ? The physicist promptly replies : I can only conceive bodies to be discon- tinuous. Discontinuity is essential to the methods by which I describe and formulate my sense-impressions of the phenomenal world. 9. Conceptual Discontinuity of Bodies. The Atom. Foremost among the physicist's reasons for postu- lating the discontinuity of bodies is the elasticity which we notice in all of them. Air can be placed SPACE AND TIME. under a piston in a cylinder and compressed ; a bar of wood can be bent in other words, a portion of it squeezed and another portion stretched. Even the amounts by which we can squeeze iron or granite are capable of measurement. Now, it is very hard, I think impossible, to conceive how we can alter the size of bodies if we suppose them continuous. We feel ourselves compelled to assert that, if the parts of a body move closer together, they must have some- thing free of body into which they can move. If a body were continuous and yet compressible, there appears to be no reason why it should not be indefi- nitely compressible, or indefinitely extensible, both results repugnant to our experience. Further, our sense-impressions of temperature in both gaseous and solid bodies, and of colour in solid bodies, the phenomena of pressure in gases, and those of the absorption and emission of light, are easily analyzed and described, if we conceive the ultimate parts of bodies to have a capacity for relative motion ; but there is no possibility of conceiving such a motion if all the parts of a body are continuous. A crowd of human beings seen from a great height may look like a turbulent fluid in motion at every point. But we know from experience that this motion is only possible, because there is some void in the crowd. It may become so densely packed that motion is no longer practicable. Thus it is with that relative motion of the parts of bodies upon which so much of modern physics depends ; absolutely close pack- ing, that is continuity, seems to render it impos- sible. It is only by reducing in conception the complex groups of sense-impressions, which we term bodies, into simple elements directly depending on IS 2IO THE GRAMMAR OF SCIENCE. the motion of discontinuous systems, of what we may term granular or starlike systems, that we have been able to resume phenomena in the wide-reaching laws of physics and chemistry. The relative motion of the ultimate parts of bodies, involving the idea of discontinuity is one of the fundamental concep- tions of modern science (p. 159). These ultimate parts of bodies we are accustomed to speak of as atoms ; groups of atoms which apparently repeat themselves over and over again in the same body, something like planetary systems in the starry universe, we term molecules. The generally accepted atomic or molecular theory of bodies postulates essentially their discontinuity. Take, for example, a spherical drop of water to follow Sir William Thomson- suppose it to be as big as a football, then if we could magnify the whole drop up to the size of the earth, the structure, he tells us, would be more coarse- grained than a heap of small shot, but probably less coarse-grained than a heap of footballs. x Now I propose later to return to the atomic hy- pothesis. At present I will only ask the reader to look upon atom and molecule as conceptions which very greatly reduce the complexity of our description of phenomena. But what it is necessary to notice at this stage is : that the conception atom, when applied to our perceptions, is opposed to the conception of surface as the continuous boundary of a body. We have here an important example of wJiat is not an uncommon occurrence in science, namely, two con- ceptions which cannot both correspond to realities in the perceptual world. Either perceptual bodies have 1 Popular Lectures and Addresses^ vol. i., " The Size of Atoms," p, 217. SPACE AND TIME. 211 continuous boundaries, and the atomic theory has no perceptual validity ; or, conversely, bodies have an atomic structure, and geometrical surfaces are per- ceptually impossible. At first sight this result might appear to the reader to involve a contradiction be- tween geometry and physics ; it might seem that either physical or geometrical conceptions must be false. But the whole difficulty really lies in the habit we have formed of considering bodies as objective realities unconditioned by our perceptive faculty. We cannot too often recall the fact that bodies are for us more or less permanent, more or less clearly defined groups of sense-irnpressions, and that the correlations and sequences among the sense-impres- sions are largely conditioned by the perceptive faculty. At the present time we have no sense-impressions corresponding to geometrical surface or to atom ; we may legitimately doubt whether our perceptive faculty is of such a nature that it could present impressions in any way corresponding to these con- ceptions. It is impossible, therefore, to say that one of these conceptions must be real and the other unreal, for neither at present has perceptual validity that is, exists in the world of real things. As con- ceptions both are equally valid ; both are equally ideals, not involved in our sense-impressions them- selves, but which the reasoning faculty has dis- covered and developed as a means of classifying different types of sense-impressions and of resuming in brief formulae their correlations and sequences. Thus geometrical truths apply with absolute ac- curacy to no group whatever of our sense-impres- sions ; but they enable us to classify very wide ranges of phenomena by aid of the notions of 212 THE GRAMMAR OF SCIENCE. position, size, and shape. Geometry enables us to predict with absolute certainty a variety of relations between sense-impressions, when these impressions do not involve more than a certain keenness in our senses, more than a certain degree of exactness in our measuring instruments. The absolute sameness and continuity demanded by geometrical conceptions do not exist as limits in the world of perceptual expe- rience, but only as approximations or averages. 1 In precisely the same way the theory of atoms treats of ideal conceptions ; it enables us to classify another and different range of sense-impressions, and to formulate their mutual relations to a certain degree of keenness again in our senses, or of exactness in our scientific apparatus. Should the atom become a perception as well as a conception, this would not invalidate the usefulness of geometry. Very pro- bably, however, if we could magnify a football up to the size of the earth, so that the perceptual atom, if it existed, would have a size between small shot and a football, we should find that the sense-impressions which the atom was conceived to distinguish and resume, had themselves disappeared under the new conditions. 2 In other words, our scientific concep- tions are valid for the world as we know it, but we cannot in the least predict how they would be related to a world which is at present beyond perception. 1 Geometry might almost be termed a branch of statistics, and the definition of the circle has much the same character as that of Quetelet's rhomnie moyen. 2 The visibility and tangibility of bodies may possibly be described by the motion of atoms, but we cannot predict that a single atom would be either visible or tangible, still less " bounded by a surface." SPACE AND TIME. 213 10. Conceptual Continuity. Ether. The reader will now be prepared to appreciate scientific conceptions, which, if they corresponded to realities of the phenomenal world, would contradict each other. Having destroyed the continuity of bodies by the idea of atom, it might at first sight appear as if our conceptual space were fundamentally different from perceptual space. The latter, as we have seen, is our mode of distinguishing groups of sense-impressions, and where there is nothing to distinguish, there there is no space. The perceptive faculty rather than nature may be said "to abhor a vacuum." On the other hand, having destroyed the continuity of bodies by the atomic hypothesis, we seem at first sight to be postulating a void in conceptual space. But here the physicist compels us to introduce a new continuity. This new continuity is that of the ether, a medium which physicists conceive to fill up the interstices between bodies and between the atoms of bodies. By aid of this concept, the ether (to which we shall return later), we are able to classify and resume other wide groups of sense -impressions. With regard to the perceptual existence of the ether, it now stands, some physicists would assert, on a rather different footing from that of the atom. By the real existence of anything we mean (p. 85) that it forms a more or less permanent group of sense-impressions. Now this can hardly be asserted of the ether ; we conceive it rather as a conduit for the motions by which we interpret sense-impression. The nerves seem to us conduits of the like kind, but then the nerves also appear to us as permanent groups of sense-impressions apart from their function of con- ductivity. There are no sense-impressions which we 214 THE GRAMMAR OF SCIENCE. class together and term ether, and on this account it still seems better to consider the ether as a concep- tion rather than a perception. It is true that to some minds the ether may appear as real a perception as the air, and the matter is, perhaps, largely one of definition. Still Hertz's experiments, 1 for example, do not seem to me to have logically demonstrated the perceptual existence of the ether, but to have immensely increased the validity of the scientific concept, ether, by showing that a wider range of perceptual experience may be described in terms of it, than had hitherto been demonstrated by experiment. Further, many of the properties which we associate with the ether are not such as our past experience shows us are likely to become matter for direct sense-impression. I shall therefore continue to speak of the ether as a scientific concept on the same footing as geometrical surface and atom. n. On the General Nature of Scientific Conceptions. Our discussion of these special conceptions will the better have enabled the reader to appreciate the nature of scientific conceptions in general. Geo- metrical surface, atom, ether, exist only in the human mind, and they are " shorthand " methods of dis- tinguishing, classifying, and resuming phases of sense- impression. They do not exist in or beyond the world of sense-impressions, but are the pure product of our reasoning faculty. The universe is not to be 1 Annalen der Physik, 1887-9. See also Nature, vol. xxxix. pp. 402, 45> 547- -A- n interesting account of Hertz's researches by von Tunzel- vnann will be found in The Electrician for 1888, vol. xxi., pp. 587, 625, 663, 696, 725, 757, 788, and vol. xxii., pp. 16, 41. SPACE AND TIME. 21$ thought of as a real complex of atoms floating in ether, both atom and ether being to us unknowable " things-in-themselves," producing or enforcing upon us the world of sense-impressions. This would indeed be for science to repeat the dogmas of the meta- physicians, the crassest paradoxes of a short-sighted materialism. On the contrary, the scientist postulates nothing of the world beyond sense ; for him the atom andtheether are, like the geometrical surface, modes by aid of which he resumes the world of sense. The ghostly world of " things-in-themselves" behind sense he leaves as a playground to the metaphysician and the materialist. There these gymnasts, released from the dreary bondage of space and time, can play all sorts of tricks with the unknowable, and explain to the few who can comprehend them how the universe is " created " out of will, or out of atom and ether, how a knowledge of things beyond perception, beyond the knowable, may be attained by the favoured few. The scientist bravely asserts that it is impossible to know what there is behind sense-impression, if indeed there can " be " anything ; * he therefore refuses to project his conceptions, atom and ether, into the real world of perception until he has perceived them there. They remain for him valid ideals so long as they con- tinue to economize his thought. That the conceptions of geometry and physics immensely economize thought is an instance of that wonderful power to which I have previously referred in this work (p. 125), namely, the power the reason- ing faculty possesses of resuming in conceptions and 1 Our notion of " being " is essentially associated with space and time, and it may well be questioned whether it is intelligible to use the word except in association with these modes of perception. 2l6 THE GRAMMAR OF SCIENCE. brief formulae the correlations and sequences it finds in the material presented to it by the perceptive faculty. As our knowledge grows, as our sense becomes keener under the action of evolution and with the guidance of science, so we are compelled to widen our concepts, or to add additional ones. This process does not as a rule signify that the original concepts are invalid, but merely that they form a basis, which is only sufficient for classifying and describing certain phases of sense-impression, certain sides of phenomena. As we grow cognizant of other phases and sides, we are forced to adopt new concepts, or to modify and extend the old. We may ultimately reach perceptions of space which cannot be described by the geometry of Euclid, but none the less that geometry will remain perfectly valid as an analysis and classification of the wide range of perceptions to which it at present applies. If the reader will bear in mind the views here expressed with regard to the concepts of science, he will never consider that science reduces the universe to a " dead mechanism " by asserting a reality for atom or ether or force as the basis of sense-impression. Science, as I have so often reiterated, takes the universe of perceptions as it finds it, and endeavours briefly to describe it. It asserts no perceptual reality for its own shorthand. One word more before we leave this space of con- ception, separated by continuous boundaries in the eye of the geometrician, peopled with atoms and ether by the mind of the physicist. How, if geometrical surface, if atom and ether have no perceptual reality, has the mind of man historically reached them ? I believe by carrying to a limit in SPACE AND TIME. 21 7 conception processes which have no such limit in per- ception. Preliminary stages in comparison show apparent sameness and continuity, where more exact and final stages show no such limit ; hence arises the conception of continuous boundaries. The atom again is a conceptual limit to the moving bodies of per- ception ; while the ether possesses an elasticity, which we have never met with in the elastic bodies of our perceptual experience, but which is a purely concep- tual limit to the type of elastic substances with which we are directly acquainted. These concepts them- selves are a product of the imagination, but they are suggested, almost insensibly suggested, by what we perceive in the world of phenomena. 12. Time as a Mode of Perception. I have dealt at greater length with space than it will be necessary to deal with time, for much that has been said in the former case as to perception and conception will directly apply to the latter. Space and time are so similar in character, that if space be termed the breadth, time may be termed the length of the field of perception. As space is one mode in which the perceptive faculty distinguishes objects, so time is a second mode. As space marks the co- existence of perceptions at an epoch of time we measure the breadth of our field so time marks the progression of perceptions at a position in space we measure the length of our field. The combination of the two modes, or change of position with change of time, is motion, the fundamental manner in which phenomena are in conception presented to us. If we had solely the power of perceiving coexist- ing things, our perception might be wide, but it would 2l8 THE GRAMMAR OF SCIENCE. fall far short of its actuality. The power of " per- ceiving things apart" by progression or sequence is an essential feature of conscious life, if not of existence. Without this time-mode of perception the only sciences possible would be those which deal with the order or correlation of coexisting things, with number, position, and measurement in other words, the sciences of Arithmetic, Algebra, and Geometry. Bodies might have size and shape and locality, but science would be unable to deal with colour, warmth, weight, hardness, &c., all of which sense-impressions we conceive to depend upon our appreciation of sequence. In short, the physical, biological, and his- torical sciences, which have for their essential topics change, or sequence in perception, would be im- possible. I have spoken of certain branches of science being possible or impossible without the time-mode of per- ception. I ought rather to say that the material for these branches of science can or cannot be con- ceived to exist without time. For in truth all scientific knowledge would be impossible without time ; thought undoubtedly involves an association of immediate and stored sense-impressions (p. 55); every conception, geometrical as well as physical, is ultimately based on perceptual experience, and the very word experience connotes the time-mode of perceiving things. This leads us to what at first sight appears a fundamental distinction between the modes space and time. Space as our method of per- ceiving coexisting things, of distinguishing groups of immediate sense-impressions, is associated with the world of actual phenomena which we project outside ourselves (p. 73). For this reason it has been SPACE AND TIME. 219 termed an external mode of perception. On the other hand, time is the perception of sequence in stored sense-impresses the correlation of past per- ceptions with the immediate perception. Thus time involves in its essence memory and thought in other words, consciousness? Consciousness might indeed be defined as the power of perceiving things apart by succession. It may perhaps be possible to conceive consciousness as existing without the space-mode of perception, but we cannot conceive it to exist with- out the time-mode. On this account, time has been termed an internal mode of perception. A little con- sideration, however, soon shows us that this distinc- tion is not a very valid one as, indeed, no distinction based on the words external and internal can ever be (p. 80). Perception in space is, as a matter of fact, as largely dependent on the association of immediate and stored sense-impressions as perception in time. As we have seen, every object is for us largely a con- struct (p. 50), and the coexisting objects which we can perceive apart are indeed very limited. I dis- tinguish the papers, the books, the inkstand, the candlesticks on my table as separate objects by the mode space ; but at any instant of time, it is only a very small element of this complex of sense-impressions which is immediate, the rest are stored sense-impresses, capable of becoming immediate sense-impressions in the next instant, but not so in actuality. Thus in the case of both time and space the " perceiving apart " 1 For a new-born infant time cannot be said to exist it is without consciousness (p. 53). Only as stored sense-impresses result from immediate sense-impression does the faculty of memory, and so the time-mode of perception become developed. The rest is reflex action, the product of inherited and unconscious association. 22O THE GRAMMAR OF SCIENCE. is the perception of an order existing between a very small element of sense-impression and a much larger range of stored sense-impresses. We do not therefore gain by terming space and time external and internal modes of perception. Both modes of perception are so habitual and yet so difficult of analysis, so commonplace and yet so mysterious, that, although we recognize a distinction between the two, we are often hardly certain whether we are distinguishing things by time or by space. Why we perceive things under these modes, the scientist is content to classify with all other whys as an idle and irrational question ; but clearer views as to the how of these modes of perception will undoubtedly come with the growth of physiological psychology, and with increased observa- tion of the manner in which the lower forms of life and young children discriminate perceptions. Of time as of space we cannot assert a real exis- tence; it is not in things, but is our mode of perceiving them. As we cannot postulate anything of the beyond of sense-impression, so we cannot attribute time directly or indirectly to the supersensuous. Like space, it appears to us as one of the plans on which that great sorting-machine, the human perceptive faculty, arranges its material. Through the doorways of perception, through the senses of man, crowd, in our waking state, sense-impression upon sense-impres- sion ; sound and taste, colour and warmth, hardness and weight all the various elements of an infinite variety of phenomena, all that forms for us reality crush through the open gateways. The perceptive faculty, sharpened by long centuries of natural selection, 1 sorts 1 We cannot infer the time and space-modes of perception except for perceptive faculties, more or less similar to our own. The order of SPACE AND TIME. 221 and sifts all this mass of sense-impressions, giving to each a place and an instant. Thus the magnitude of space and time depends upon no external world independent of ourselves, but on the complexity of our sense-impressions, immediate and stored. Infinity of space or eternity of time have no meaning in the field of perception, because the correlation and sequence of our perceptions, wide as both un- doubtedly are, do not require these enormous frames to exhibit them. Where the senses perceive no object, there there is no space, for there no groups of sense-impressions are to be distinguished. Where I can no longer carry back the sequence of phenomena, there time ceases for me because I no longer require it to distinguish an order of events. Let the reader endeavour to realize empty time, or time with no sequence of events, and he will soon be ready to grant that time is a mode of his own perception and is limited by the contents of his experience. 1 Thus the moments devoted to wonder over the eternities of time are as ill-spent as those consumed in ponder- ing on the immensities of space (p. 188). They are like moments employed in examining the frame of a picture and not its contents, in admiring the constitu- tion of the artist's canvas and not his genius. The phenomena in both space and time is essentially conditioned by the intensity and quality of the consciousness (p. 101). 1 It may well be questioned whether anything that falls outside human experience can be said to have existed in perceptual time. Such time is essentially the mode by which we distinguish an immediate sense-impression from a succession of stored sense-impresses (p. 49). That the world has existed for 60,000,000 years is a conception, and the period referred to a conceptual rather than a perceptual one. The future also is a notion attaching rather to conceptual than to perceptual time. The full discussion of these points cannot, however, be entered upon at this stage. 222 THE GRAMMAR OF SCIENCE. frame is just large and strong enough to support the picture, the canvas is just wide and stout enough to sustain the artist's colours. But frame and canvas are only modes by which the artist brings home his idea to us, and our wonder should not be for them, but for the contents of the picture and its author. So it is with time and space these are but the frame and the canvas by aid of which the perceptive faculty dis- plays our experience. Our admiration is due not to them, but to the complex contents of perception, to the extraordinary discriminating power of the human perceptive faculty. The complexity of nature is conditioned by our perceptive faculty ; the compre- hensive character of natural law is due to the ingenuity of the human mind. Here, in the human powers of perception and reason, lies the mystery and the grandeur of nature and its laws. Those, whether poets or materialists, who do homage to nature as the sovereign of man, too often forget that the order and complexity they admire are at least as much a pro- duct of man's perceptive and reasoning faculties as are their own memories and thoughts. 13. Conceptual Time audits Measurement. Time as a mode of perception is limited, we have seen, to the extent to which sequences of stored sense-impresses can be carried back ; it marks that order of perceptions which is the history of our consciousness. From this it is clear that perceptual time has no future and no eternity in the past. That consciousness in the future will continue as it has done in the past is a conception, but not a perception. We perceive the past, but we only conceive the future. How, then, we may ask, do we pass from SPACE AND TIME. 223 perceptual to conceptual time, from our actual sequences of sense-impressions to a scientific mode of describing and measuring them ? Clearly it would he extremely cumbersome to measure time by a detailed account of the changes in our sense- impressions. Imagine the labour of describing all the stages of consciousness between breakfast and dinner as a means of determining the period which has elapsed between the two meals ! Yet this method of considering time brings out clearly how time is a relative order of sense-impressions, and how there is no such thing as absolute time. Every stage in sense-impression marks in itself an epoch of time, and may form the basis of a measurement of time for an individual. " I am sleepy, it is time to go to bed," says the child ; " I am hungry, it is time to eat," says the savage, and both without thinking of the clock or the sun. Fortunately for us we are not compelled to measure time by a description of the sequence of states of consciousness. There are certain sense- impressions which experience has shown us repeat themselves, and which, on the average, correspond to the same routine of consciousness. In the first place, the recurrence of night and day are observed very early in the natural history of man to mark off approximately like sequences of sense-impressions ; a day and night becomes a measure of a certain interval of consciousness. That the same amount of con- sciousness can, at any rate approximately, be got into each day and night by the normal human being is a matter rather of experience than of demonstration ; it cannot be proved, it can only be felt. Very much the same holds for the smaller intervals of time. When we say it is four hours since break- 224 THE GRAMMAR OF SCIENCE. fast, we mean in the first place that the large hand of our clock or watch has gone round the dial-face four times a repeated sense-impression which we could, if we please, have observed. But how shall we decide whether each of those four hours represents equal amounts of consciousness, and the same amount to-day as yesterday? It may possibly be that our time-keeper has been compared with a standard clock, regulated perhaps from Greenwich Observatory. But what regulates the Greenwich clock? Briefly, without entering into details, it is ultimately regulated by the motion of the earth round its axis, and the motion of the earth round the sun. Assuming, however, as a result of astronomical experience, that the intervals day and year have a constant relation, we can throw back the regulation of our clock on the motion of the earth about its axis. We may regulate what is termed the " mean solar time " of an ordinary clock by " astronomical time " of which the day corresponds to a complete turn of the earth on its axis. Now, if an observer watches a so-called circumpolar star, or one that remains all day and night above the horizon, it will appear, like the end of his astronomical clock- hand, to describe a circle ; the star ought to appear to the observer to describe equal parts of its circle in equal times by his clock, or while the end of the clock-hand describes equal parts of its circle. In this manner the hours on the Greenwich astronomical cloch, and ultimately on all ordinary watches and clocks regulated by it, will correspond to the earth turning through equal angles on its axis. We thus throw back our measurement of time on the earth as a time-keeper ; we assume that equal turns of the earth on its axis correspond to equal intervals of SPACE AND TIME. 225 consciousness. But, all clocks being set by the earth, how shall we be certain that the earth itself is a regular time-keeper? If the earth were gradually to turn more slowly upon its axis, how should we know it was losing time, and how measure the amount ? It might be replied that we should find that the year had fewer days in it ; but then how could we settle that it was the day that was growing longer and not tlie year that was growing shorter ? Again, it may be objected that we know a great, number of astronomical periods relating to the motion of the planets expressed in terms of days, and that we should be able to tell by comparison with these periods. To this we must answer that the relation of these periods expressed in days, and in terms of each other, appears now indeed invariable ; but what if all these relations are found to have slightly changed a thousand or five thousand years hence ? Which body shall we say has been moving uniformly, which bodies have been gaining or losing ? Or, what if, the ratios of their periods remaining the same, they were all to have lost or gained? How shall we, with such a possibility in view, assert that the hour to-day is the " same " interval as it was a thousand, or better perhaps a million, years back ? Now certain investigations with regard to the frictional action of the tides make it highly probable that the earth is not a perfect time- keeper, nor are we able to postulate that regularity of motion, by which alone we could reach absolute time, of any body in our perceptual experience. Astronomy says it is not in me, nor do we get a more definite answer from physics. Suppose an observer to measure the distance traversed by light in one second ; can this be for all time a permanent record of the length 16 226 THE GRAMMAR OF SCIENCE. of a second? Another observer a thousand years after measures again the distance for one of his seconds, and finds it differs from the old determina- tion. What shall he infer ? Is the speed of light really variable, has the planetary system reached a denser portion of the ether, has the second changed its value, or does the fault lie with one or other observer ? * No more than the astronomer can the physicist provide us with an absolute measure of time. So soon as we grasp this we appear to lose our hold on time. The earth, the sole clock by which we can measure millions of years, fails us when we once doubt its regularity. Why should a year now represent the same amount of consciousness as it might have done a few million years back? The absolutely uniform motion by which alone we could reach an absolute measurement of time fails us in perceptual experience. It is, like the geometrical surface, reached in conception, and in conception only, by carrying to a limit there the approximate same- ness and uniformity which we observe in certain perceptual motions. Absolute intervals of time are the conceptual means by which we describe the sequence of our sense-impressions, the frame into which we fit the successive stages of the sequence, but in the world of sense-impression itself they have no existence. Newton, defining what we term here conceptual time, tells us : " That absolute, true, and mathematical time is conceived as flowing at a constant rate, unaffected by the speed or slowness of the motions of material things. 33 Clearly such time is a pure ideal, for how can we SPACE AND TIME. 22/ measure it if there be nothing in the sphere of per- ception which we are certain flows at a constant rate ? " Uniform flow," like any other scientific concept, is a limit drawn in imagination in this case, from the actual " speed or slowness of the motions of material things." But, like other scientific concepts, it is invaluable as a shorthand method of description. Perceptual time is the pure order in succession of our sense-impressions and involves no idea of absolute interval. Conceptual time is like a piece of blank paper ruled with lines at equal distances, upon which we may inscribe the sequence of our perceptions, both the known sequence of the past and the predicted sequence of the future. The fact that upon the ruled lines we have inscribed some standard recurring sense-impression (as the daily transit of a heavenly body over the meridian of Greenwich), must not be taken as signifying that states of consciousness succeed each other uniformly, or that a "uniform flow " of consciousness is in some way a measure of absolute time. It denotes no more than this : that from noon to noon the average human being experi- ences much the same sequence of sense-impressions, and thus the same space in our conceptual time-log may be conveniently allotted for their inscription. Above all, it must not lead us to project the absolute time of conception into a reality of perception ; the blank divisions at the top and bottom of our con- ceptual time-log are no justification for rhapsodies on the past or future eternities of time, for rhapso- dies which, confusing conception and perception claim for these eternities a real meaning in the world of phenomena, in the field of sense-impression. 228 THE GRAMMAR OF SCIENCE. 1 4. Concluding Remarks on Space and Time. The reader who has recognized in perceptual space and time the modes in which we distinguish groups of sense-impressions, who has grasped that infinities and eternities are products of conception, not actualities of the real world of phenomena, will be prepared to admit the important conclusions which flow from these views for both practical and mental life. If the individual carries space and time about with him as his modes of perception, we see that the field of miracle is transferred from an external mechanical world of phenomena to the individual perceptive faculty. The knowledge of this in itself is no small gain to clearing up our ideas with regard to such recrudescences of superstition as spiritualism and theosophy. If space and time are to be annihilated, it cannot be done once for all, but it must be done for each individual perceptive faculty. When, for example, theosophists tell us that, putting aside the bondages of space and time, they can communicate with adepts from Central Asia in London drawing- rooms, they are really saying that their own percep- tive faculties can distinguish groups of sense-im- pressions in other than those modes of space and time which are characteristic of the normal perceptive faculty. They have not abrogated our space and time, only their own. They are merely declaring that their modes of perception are different from ours. If we find from long experience that there is in man a normal perceptive faculty which co-ordinates sense- impressions in space and time in the same uniform manner, then we are justified in classifying the infinitesimal minority who suffer from abnormal modes of perception with the ecstatic and the insane. SPACE AND TIME. 229 Through sickness they have lost, or through atavistic tendencies they have failed to develop, the normal perceptive faculty of a healthy man the mens sana in corpore sano. No less valuable is the conclusion that it is idle to speak of anything as existing in space or as happening in time which cannot be the material of perception. Whatever by its nature lies beyond sense-impression, beyond the sphere of perception, can neither exist in space nor happen in time. Thus the scientific con- ception of causation, or that of uniform antecedence, cannot with any meaning be postulated of it a result we have already reached from a slightly different standpoint (pp. 152 and 186). Indeed, it seems to me that, with a clear appreciation of space and time as modes of perception, most phases of superstition and obscurity fade into nothingness, while the field to which the category of knowledge applies is seen to be sharply defined. SUMMARY. 1. Space and Time are not realities of the phenomenal world, but the modes under which we perceive things apart. They are not infinitely large nor infinitely divisible, but are essentially limited by the contents of our perception. 2. Scientific concepts are, as a rule, limits drawn in conception to processes which can be started but not carried to a conclusion in perception. The historical origin of the concepts of geometry and physics can thus be traced. Concepts such as geometrical surface, atom, and ether, are not asserted by science to have a real existence in or behind phenomena, but are valid as shorthand methods of describing the correlation and sequence of phenomena. From this standpoint conceptual space and time can be easily appreciated, and the danger avoided of projecting their ideal infinities and eternities into the real world of perceptions. 230 THE GRAMMAR OF SCIENCE. LITERATURE. HUME, DAVID. A Treatise on Human Nature (1739), book i. part ii. Of the Ideas of Space and Time. Green and Grose : Works of Hume, vol. i. pp. 334-371. KANT, IMMANUEL. Kritik der reinen Vernunft (1781). Elementar- lehre, i. Theil. Sammtliche Werke, Ausgabe v. Hartenstein, Bd. iii. S. 58-80. A good account of Kant's views will be found in Kuno Fischer's Geschichte der Philosophic, Bd. iii. S. 312-349. A brief description is given on pp. 218-20 of Schwegler's Handbook of the History of Philo- sophy, translated by J. H. Stirling, Edinburgh, 1879. None of the geometrical or physical text-book writers have hitherto ventured to discuss how the conceptual space and time which are at the basis of their investigations are related to perceptual experience. The reader will, however, find much that is valuable in Clifford's Philosophy of the Pure Sciences (1873), Lectures and Essays, vol. i. pp. 254-340, and in his "Of Boundaries in General," Seeing and Thinking (1880), pp. 127-156. A criticism of Hume's views will be found on pp. 230-254 of Green's " General Introduction " to Hume's Works, vol. i., while Kant's doc- trines have been attacked by both Trendelenburg and Uebervveg. References are given in vol. ii. pp. 158, 330, and 525 of the latter writer's History of Philosophy, London, 1874. A good deal that is suggestive with regard not only to space and time, but position and motion, may still with caution be extracted from the Physics of Aristotle. See especially E. Zeller, Die Philosophie der Griechen ii. Theil, 2 Abth. S. 384-408, and Ueberweg loc. '/., vol. i. pp. 163-6. The reader must not be discouraged by the contempt expressed for Aristotle's ideas of space and motion in George Henry Lewes's Aristotle : a Chapter from the History of Science, London, 1864 (p. 128 et seq,}. CHAPTER VI. THE GEOMETRY OF MOTION. i . Motion as the Mixed Mode of Perception. WE have seen in the previous chapter that there are two modes under which the perceptive faculty dis- criminates between groups of perceptions, namely, those of space and time. The combination of these two modes, to which we give the various names of change, motion, growth, evolution, may be said to be the mixed mode under which all perception takes place. 1 Science, accordingly, if we except special branches treating of the modes under which we perceive and think, is essentially, as a description of the contents of perception, a description of change or variation. In order to draw a mental picture of the universe, to map out in broad outline its character- istics, science has introduced the conception of geometrical forms ; in order to describe the sequence of perceptions, to form a sort of historical atlas of the universe, science has introduced the conception of geometrical forms changing with absolute time. The 1 Trendelenburg sees in real or constructive motion the basis of all perception and conception. He tries to show that the conception of motion does not require the notions of space and time, which he asserts flow from the conception of motion itself. I do not think he is successful in this, but his attempt is instructive as showing how essentially per- ception and conception involve motion. (See his Logische Untersuch- ungen" 2nd edition, Bd. i., chaps, v.-viii., Leipzig, 1862.) 232 THE GRAMMAR OF SCIENCE. analysis of this conception is what we term the Geometry of Motion. The geometry of motion is thus the conceptual mode in which we classify and describe perceptual change. Its validity depends not upon its corresponding absolutely to anything in the real world a correspondence at once rebutted by the ideal character of geometrical forms but upon the power it gives us of briefly resuming the facts of perception or of economizing thought. 1 The geo- metry of motion has been technically termed kine- matics^ from the Greek word /clvi^a, signifying a movement. It teaches us how to represent and measure motion in the abstract, without reference to those particular types of motion which a long series of experiments, and much careful observation of the world of phenomena, have shown us are best fitted to exhibit the special changes in the sphere of percep- tion. When we apply what we have learnt in the 1 The term economy of thought, originally due, I think, to Professor Mach, of Prague, embraces in itself a very important series of ideas. Its value is much more significant, if we remember how thought depends on stored sense-impresses, and that it is difficult to deny to these and to their nexus association a physical or kinetic aspect (p. 51). The economy of thought thus becomes closely associated with an economy of energy. The range of perceptions is so wide, their sequences so varied and complex, that no single brain could retain a clear picture of the relationship of the smallest group but for the short- hand descriptions provided by the conceptions of science. Dr. Wallace, in his Darwinism, declares that he can find no origin for the existence of pure scientists, especially mathematicians, on the hypothesis of natural selection. If we put aside the fact that great power in theoretical science is correlated with other developments of increasing brain-activity, we may, I think, still account for the existence of pure scientists as Mr. Wallace would himself account for that of worker-bees. Their functions may not fit them individually to survive in the struggle for existence, but they are a source of strength and efficiency to the society which produces them. The solution of Mr. Wallace's difficulty lies, I think, in the social advantage of science as an economy of intellectual energy. THE GEOMETRY OF MOTION. 233 geometry of motion to those particular types of motion natural types as they may be conveniently called and investigate how they are correlated, then we are led to the so-called Laws of Motion and to those conceptions of Mass and Force * upon which our physical description of the universe depends. These will form the topics of succeeding chapters, but, in order to see our way more clearly through that maze of metaphysics which at present obstructs the entry to physics, we must devote some space to a discussion of the elementary notions of kinematics. 2. Conceptual Analysis of a Case of Perceptual Motion. Point-Motion. We shall, I think, best obtain clear ideas of motion by examining some familiar case of physical change of position and endeavouring to analyze it into simple types which may be easily discussed by the aid of geometrical ideals. Let us take, for instance, the case of a man ascending a staircase which may have several landings and turns in its course. The changes in our sense-impressions during the man's ascent are of an extremely complex character, and we see at once how difficult, if not impossible, it would be to describe all that we perceive. Not only the position of the man on the staircase changes, but his hands and his legs are perpetually varying their position with regard to his trunk, while his trunk itself turns and oscillates, bends and alters its shape. For simplification let us> in the first place, fix our attention on some small element of his person ; let us follow with our eye, for example, the top button of his waistcoat. Now, the 1 Not force as the cause of motion, but force as a measure of motion. 234 THE GRAMMAR OF SCIENCE. first observation that we make is that this button takes up a series of positions which are perfectly continuous from the start to the finish of the ascent. There can be no break in this series of positions anywhere throughout the whole extent of the stair- case ; for, if there were any, the button must, in accurate language, have ceased to be a permanent group of sense-impressions, and to be distinguished from other groups under the mode space. In ordinary parlance, it must " have left our space and come back to it again " a phenomenon totally contrary to the experience of the normal human perceptive faculty. If we cut the button off the waistcoat, we could still conceive it to move up the staircase in precisely the same manner as when the man wore it, carried up, let us suppose, by an invisible spirit hand. It will be obvious that this motion of the button, if fully known to us, would tell us a good deal about the motion of the man. It would not describe, of course, how he moved his legs and arms about, but it would indicate very fairly how long the man took to go from one landing to another, and when he was going quickly, when slowly. But it is still far from clear how we are to describe the motion of the button, so that we could conceive its motion repeated by aid of our descrip- tion. The button, like the man, has many elements, and the question again arises how we are to describe the motions of them all. Let us now stretch our imaginations a little further ; let us suppose the staircase to be imbedded in a great mass of soft wax, and suppose the button, guided still by the spirit hand, to move up the staircase precisely as it did on the man's waistcoat, but now pushing its way through the wax. The passage of the button THE GEOMETRY OF MOTION. 235 would now form a long tube-like hollow in our mass of wax extending from the bottom to the top of the staircase. This tube would not necessarily be of equal bore throughout, because, owing to the motion of the man, the button might occasionally move more or less sideways. Still, the smaller the button the smaller would be the bore of the tube cut through the wax. We will now suppose a long piece of stiff wire passed through the tube and firmly fixed at its ends. The wax, and even the staircase, may now be removed, and then, if a small bead be slung on the wire and move up the wire in the same manner as the button moved up the tube, we shall be able to describe a good deal of the motion of the button from that of the bead. Now in conception we may suppose the wire to get thinner and thinner, and the bead smaller and smaller, till in conception the wire ends in a geometrical line or curve, and the bead in a geo- metrical point. The motion of the ideal point along the ideal curve will represent with a great degree of accuracy the motion of an extremely small button up a tube through the wax of an extremely small bore. The reader may feel inclined to ask why we did not commence by saying : " Consider a point of the man ; its motion must give a curve passing from top to bottom of the staircase." The answer lies in this : that we cannot perceive a point. In conception we reach a point by carrying to a limit the perceptual process of taking a smaller and smaller element of the man, and the stages we have indicated from man to button, bead and geometrical point, indicate how certain elements of the perceptual motion are dropped at each stage, till in conception we reach as a limit an ideal motion capable of being fairly easily described. 236 THE GRAMMAR OF SCIENCE. The motion of a point along a curve is the simplest ideal motion we can discuss. Obviously, however, it will enable us to classify and describe with consider- able exactness a number of our perceptions with regard to the man's motion. Harness the button to the point, and the man to the button ; then if the point move along its path, carrying button and man with it, we shall have a means of describing a good deal of the real motion of the man. When he starts, when he stops, when he goes fast, when he goes slowly, what time he takes from one landing to another will be deducible from the motion of the point. Of course this point-motion does not enable us to fully describe the motion of the man. For instance, it is conceivable that he may have turned several somersaults in going upstairs. About such eccentricities in the man's motion the motion of the point may tell us nothing at all. Even had the man been incapable of moving his arms, legs, head, &c., had he been a rigid body the point-motion would have been incapable of fully describing his motion. As a rigid body the man might have been turned round and about the point without changing its motion. Did he go upstairs backwards or forwards, head or feet uppermost, or partly in one, partly in another of these modes ? Clearly the motion of the point can tell us nothing of all this. The motion of the point can tell us nothing of how the man as a rigid body might have turned about the point ; we should want to know at each instant of the motion which way the man was facing, what was his aspect, and further how he was changing his aspect or rotating about the point. The description of the ideal point-motion would have to be supplemented THE GEOMETRY OF MOTION. 237 by a description of the rotating or spinning motion, even if the man were supposed to be a rigid body. The first type of motion, corresponding to change of position, is termed motion of translation ; the second type, corresponding to the change of aspect of a rigid body, is termed motion of rotation. 3. Rigid Bodies as Geometrical Ideals. Just as the former motion is described by the purely ideal conception of a point moving along a curve, so the latter is also made to depend on geometrical notions, namely, those of a rigid body turning about a line passing through a point. What, in the first place, do we mean by using the term rigid body ? The real man is moving his limbs and bending his body, and generally changing his form at each in- stant of the motion. Now the reader may feel inclined to say : Replace the man by a wooden table or chair, and we shall have a rigid body. But this is only popular language, and what we are seeking is an accurate or scientific definition of rigidity. Such a definition is usually given in the following words: A body is said to remain rigid during any given motion when the distances between all pairs of its points remain unaltered throughout the whole dura- tion of the motion. But we see at once from this definition that we have replaced the real body, the group of sense- im- pressions which forms part of the picture constructed by our perceptive faculty, by an ideal geometrical body possessing " points," and that it is a property of this body existing only on the ideal map on which conception plots out perception that we are de- fining. It is quite true that the geometrical ideal of 238 THE GRAMMAR OF SCIENCE, a rigid body is a better description of a wooden chair than of the flexible body of a man ; yet what is a " point " on the chair, and what is the " distance " between a pair of points ? How, again, am I to ascertain accurately that such distances remain unaltered during the motion ? The very idea of distance, when clearly appreciated, involves the geo- metrical conception of points and does not corre- spond to anything in our perceptual experience. * Rigidity is thus seen to be a conceptual limit, which by concentrating our attention on a special group of perceptions forms a valuable method of classification. Although for the description of some types of motion it may be useful to replace the wooden chair by a body of ideal rigidity in our conceptual map, still the physicist tells us that for the purpose of classifying other phases of sense-impression, he is bound to consider that the chair is not rigid, and that he is perceptually able to measure changes in the relative position of its parts. He cannot describe the mechanical action between different parts of the chair without supposing it elastic, and this elasticity in- volves changes of form in its parts. For example, 1 We speak, for example, of the " distance " from London to Cambridge being fifty-five miles, and this is a practical method of de- scribing the sense-impressions of a journey from one place to the other, and distinguishing it from a journey of fifty-six or fifty-seven miles. But what do we exactly mean? From Stepney Church to St. Mary's? If so, from which part of one church to which part of the other ? Or, again, is it from the stone near the gateway of Stepney Church to the last milestone by St. Mary's? If so, from which side of the one stone to which side of the other ? In the end we find ourselves driven to the conception of a point on either stone no perceptual mark gets over the difficulty of the where to the where. We are forced to conclude that the idea of distance is a conception, invaluable for classifying our experience but not accurately corresponding to a perceptual reality. THE GEOMETRY OF MOTION. 239 the action between the parts of the chair changes, when it is supported on its back instead of its legs, and thus the chair changes its form in these two positions. A like change of form will take place even if the chair be only rotating. Nor does this variation in shape merely result from the chair being of wood it would be equally true if the chair were of iron, or any other material. Change of form is in many cases perceptually appreciable, and in most cases we can determine its conceptual value. Thus, so far from the rigid body being a limit which might be reached in perception, our whole perceptual experience seems to indicate that the conception rigidity corresponds to nothing in the real world of phenomena. We perceive that most bodies do change their form, and where we do not perceive it physics compel us to conceive it. Thus rigidity is very much like the spherical surfaces of geometry. The latter correspond accurately to nothing in our perceptual experience, and we cannot even conceive a continuous surface as a limit to be reached in per- ception. Both, however, are alike valuable bases of classification. By replacing real bodies by ideal rigid bodies we are able, although neglecting their changes of form, to classify and describe a wide range of our perceptions of motion. To classify other perceptions, however, we conceive the same bodies not to be rigid, but varying in form ; we actually measure the very changes in shape, which we purposely neglected in another branch of our survey of the physical universe. 4. On Change of Aspect or Rotation. Even when we have transferred our moving body from the perceptual to the conceptual sphere by 240 THE GRAMMAR OF SCIENCE. postulating its rigidity, we shall still find the notions of aspect and spin involve further geometrical con- ceptions. Let us consider our rigid body capable of turning about a point, the question then arises, How can we distinguish one aspect from a second? Clearly, the notion of direction involves that of a line, but the change in direction in one line will not be sufficient to describe change of aspect. For if C (Fig. 4) repre- sent the fixed point about which the body rotates, and A be another definite point of the body, the line CA may take up a new position CA' ; but the change in position of CA to C A' does not fully determine the aspect of the body, for there is nothing to fix how much the body may have been turned about the line CA while it was moving into the position CA'. We are compelled, therefore, to take a second point B, and a second direction CB ; then if we state the new position CB' taken by CB as well as the new position CA f of CA, we shall have absolutely determined the change of aspect of the body. The reader will very easily convince him- self that in giving the new positions of two definite points A and B of the rigid body, we have absolutely fixed its position. It is easy to show that this turn- ing of two lines CA and CB into new positions CA' and CB' may also be described as a turning of the body about a certain line of direction CO through a certain angle. 1 Thus the manner in which we conceive 1 This may be proved by the aid of elementary geometry in the following manner : Let the triangle CBA be displaced into the position CB'A'. Join the points A, A' and B, B', and let the mid-points of AA' and BB be M and N respectively. Through C and M draw a plane perpendicular to AA' and through C and N a plane perpendicular to BB'. These two planes meet in a line passing through C, since C is common to THE GEOMETRY OF MOTION. 241 change of aspect to be described and measured is essen- tially geometrical, or ideal. It depends on the con- ception of a straight line fixed in the body and fixed in space about which the body turns. It further them both. Let O be any point in this line, and join it to M and N, then OM and ON are respectively perpendicular to AA' and BB/ In the triangles AOM, A'OM, AM and A'M are equal, OM is common, and the angles at M are right, hence it follows by Euclid i. 4 that the third sides OA and OA' are equal. For precisely similar reasons it FIG 4. follows that OB and OB' are equal. Hence the three distances of O from the angles of the triangle ABC are equal to its distances from the three angles of the triangle A'B'C respectively. Thus the two tetra- hedrons with summits at O and having bases ABC and A'B'C respectively are equal in every respect, for all their edges are equal each to each. One of them may thus be looked upon as the other in a changed position. They have, however, the same edge OC. Hence one tetrahedron may be moved into the position of the other by rotating it through a certain angle about the edge OC. That is to say, the triangle CBA may be turned into the position CB'A' by rotating it through a certain angle the angle between the planes BOC and B'OC about the line OC. 17 242 THE GRAMMAR OF SCIENCE. involves the conception of the body turning through a certain angle, but an angle Euclid tells us is the inclination of two lines. Thus our description of change of aspect depends upon the conception of lines existing in the rigid body. It is entirely a conceptual description, but like the idea of point- motion, it again serves as a powerful means of dis- criminating and classifying our experiences of per- ceptual motion. 5. On Change of Form, or Strain. Thus far we have analyzed the motion of our man ascending the staircase by considering the motion of an ideal point of him, and then treating him as a rigid body turning about this point, or changing its aspect. It only remains for us to consider how, when the point is in any given position and the man has any given aspect, we may remove the condition of rigidity, and describe how he can move his limbs about, change his form, or alter the relative distances of his parts. This change of form is technically termed strain, and its description and measurement forms the third great division in the conceptual motion of bodies. Now we cannot in this work enter into a technical discussion- of how strain is scienti- fically described and measured, but for our present purposes we must ascertain whether the theory of strains deals, like that of the translation of a point and that of the rotation of a rigid body, with con- ceptual ideals. There are two fundamental aspects of strain which most of us consciously or unconsciously recognize. These are change of size without change of shape, and change of shape without THE GEOMETRY OF MOTION. 243 change of size. Take a thin hollow india-rubber ball and blow more air into its interior. This will in- crease its size without necessarily changing its shape. It was spherical in shape and remains spherical in shape, only it is larger. We conceive the ball represented by a sphere, and the change in size will depend upon the change in diameter. The ratio of the extension to the original length of the diameter may be taken as a proper basis for the measurement of the strain. Such a ratio is termed a stretch^ and it may be shown that for a small increase of size the ratio of the increase of volume to the original volume is very nearly three times the stretch of the diameter. 1 This ratio is termed the dilatation^ and is a proper measure of the change in size. Now it is clear that in order to measure this change of size, we require to measure the diameters in the two conditions of the body. But a diameter, although in the conceptual body definite enough as a straight line terminated by two points, is, in this accurate sense of the word, a meaningless term when we are dealing with a perceptual body. If the body has no continuous boundary, but, according to the physicist, is a mass of discrete atoms (Fig. 5), none 01 which we can individually feel, and the mutual dis- 1 The volumes of bodies of similar shape are as the cubes of corre- sponding lengths. Hence if V and V be the old and new volumes, d and (? the old and new lengths, F'/J 7 ^ 3 /^ 3 , but if s be the stretch (c? d)/d=s, or (T = d(i+s). A little elementary algebra gives us for the dilatation d : ^ = -^^=^^=(l+^) 3 -i = 3^+3^+^ 3 = 3^ nearly, if s, as in most practical cases, be very small. For example, in metal s = unny would be a rather large value ; but taking S = 3*, we should only be neglecting about T&S& f ^ e va l ue of & 244 THE GRAMMAR OF SCIENCE. tances of which we cannot measure, it is clear that the only diameter we can be talking about is that of *.vt '.V'.V. a conceptual sphere by which we have replaced the perceptual ball. As it is with change of size, so it is with change of shape : we are really basing our system of measure- ment upon conceptions, which enable us to describe and classify perceptions, but are not real limits to perception. Change of shape without change of size can be realized in the following manner : Take a piece of woven silk or other slightly elastic material, and draw a rectangle upon it with sides a few inches long FIG 6 . f/G . 7 parallel to the warp and woof. Then if such a rectangle be held firmly top and bottom between two pairs of parallel pieces of wood, or even between the THE GEOMETRY OF MOTION. 245 two thumbs and their respective forefingers, a slide of the holders parallel to each other will produce a change of form without change of size. Now the extent of such a strain will depend on the amount by which the warp and woof have changed their inclina- tion to each other, that is to say, on the amount after strain by which the angle between them differs from a right-angle. But this change in angle only becomes of meaning if we suppose the warp and woof to be straight lines. In other words, to get a measure of the strain we replace the perceptual warp and woof by a geometrical network. Such a type of strain is termed a slide or shearing strain, and all changes of shape without change of size can in con- ception be analyzed into slides. 1 Further, it may be shown that all changes of form whatever can be analyzed into stretches and slides, 2 or into changes of length and changes of angle. But in the cases of both slide and stretch we are thrown back on geometrical notions, when we come to consider their measurement ; in both cases we replace the percep- tual body by a conceptual body built up of points, lines, and angles. Thus the whole theory of strain deals with a conceptual means of distinguishing and describing perceptions, and not with something abso- lutely inherent in the perceptions themselves. 1 Technically the slide is not measured by the change in angle or by the angle bac in Fig. 7, but by the trigonometrical tangent of this angle, or by the ratio of the length be to the length ba in other words, by the ratio of the amount the woof has been slid to the length of the warp. 3 An elementary discussion of strain will be found in Clifford's Elements of Dynamic, part i. pp. 158-90; or in Macgregor's Kinematics and Dynamic s> pp. 166-84. The reader may also consult 8 and 13, contributed by the present writer to Chapter iii. of Clifford's Common Sense of the Exact Sciences. 246 THE GRAMMAR OF SCIENCE. 6. Factors of Conceptual Motion. We started with a man ascending a staircase, and we have seen by our analysis that the conceptual descrip- tion of his motion requires us to discuss : (a) The Motion of a Point, (b) the Motion of a Rigid Body about a Fixed Point, (c) the Relative Motion of the Parts of a Body or its Strain. These are the three great divisions of Kinematics, or the Geometry of Motion. But in the case of all these divisions we find that we are thrown back on the ideal conceptions of geometry ; we measure distances between points and angles between lines, which are not true limits to our perceptual experience. Thus our ideas of motion appear as ideal modes, in terms of which we describe and classify the sequences of our sense-impressions : they are purely symbols by aid of which we resume and index the various and continual changes under- gone by the picture our perceptive faculty presents to us. The more fully and clearly the reader grasps this fact, the more readily will he admit that science is a conceptual description and classification of our perceptions, a theory of symbols which economizes thought. It is not a final explanation of anything. Tt is not z.plan which lies in phenomena themselves. Science may be described as a classified index to the successive pages of sense-impression, but it in nowise accounts for the peculiar structure of that strange book of life. 1 1 The extremely complex results which flow from the simple basis of the planetary theory have often been taken as an evidence of " design " in the universe. The universe has been with much confusion spoken of as the conception of an infinite mind. But the conceptual basis of the planetary theory lies in geometrical notions, no ultimate evidence of which can be discovered in the perceptual world. Thus, while the THE GEOMETRY OF MOTION. 247 Of the three types of motion just introduced to the notice of the reader, the first, or point-motion, is that which for our present purposes is most important. The remainder of the present chapter will therefore be devoted to its discussion. The reader will, I trust, pardon its somewhat technical character, for without this investigation of point-motion it would be impossible to analyze the fundamental notions of Matter and Force, or to rightly interpret the Laws of Motion. 7. Point-Motion. Relative Character of Position and Motion. Motion has been looked upon as change of position, but if we try to represent the position of a point we must do so with regard to something else. If space be a mode of distinguishing things, we must have at least two things to distinguish before we can talk about position in space. Position of a point is there- fore relative, relative to. something else, which for our present purposes we will suppose to be a second point. Absolute position in space, just as absolute space itself (p. 186), is meaningless. Let the letter P (Fig. 8) represent a point, and the letter O a point from which we are to measure P's relative position. Now the distance from O to P would indicate for us planetary theory answers our purposes of description, it could never have been the conception upon which the univeise was " designed," for the conception is nowhere found perceptually realized. Starting with his material endowed with all its peculiar properties, the carpenter makes for us a box according to our geometrical description, but in reality not ultimately geometrical. Starting with nothing but the power of realizing conception in perception, he would have produced from our geometrical plan a geometrical box. Geometrical notions could flow from the material universe, but the latter could not flow from the former. 248 THE GRAMMAR OF SCIENCE. the position of P relative to O, but in our conceptual space we have in general a variety of other points or geometrical bodies besides O which we wish to dis- tinguish from P, and to do this we must give what is termed direction to the distance OP, we must deter- mine, as it were, whether it runs north and south, south-west and north-east, or upwards and down- wards. 1 But even this is not enough. We must be also told the sense of this direction, whether, for example, it be op or op' (Fig. 8), or, say, runs from south-west to north-east or north-east to south-west. Thus, if we want to plot out position in space about FIG. 8. a point O, we must do this by measuring distances from O in given directions and with given senses. 1 In the conceptual space which corresponds most closely to percep- tual space so-called space of three dimensions we require, in order to mark the relative position of all possible bodies, to start from three standard points (which must not be in the same straight line) in order to fix direction. Throughout this chapter we shall understand by the position of a point P relative to another point O, the directed step OP, and by the motion of P relative to O change in this directed step. A fuller account of Position will be found in the chapter under that title contributed by the author to Clifford's Common Sense of the Exact Sciences. THE GEOMETRY OF MOTION. 249 We must know distance and bearing* from O to determine fully a point P. To represent geometrically the position of P with regard to O, we may draw a piece of a straight line (of) having as many units of length on our scale as there are units of distance from O to P, the line having the same direction as this distance, and having an arrow-head upon it to mark the sense. Such a line marking the magnitude, di- rection, and sense of P's position relative to O is termed a step. Such a step tells us how to shift our position from O to P. Step so many feet with such and such a bearing, and we shall pass from O to P. If P be in motion and we know what is the step from O to P at each instant of the motion, we shall have a complete picture of the sequences of positions, the motion of P relative to O. The reader must be careful to notice the relativity of the motion ; abso- lute motion, like absolute position, is inconceivable: a point P is conceived as describing a path relatively to something else. Thus the button on the man's waistcoat moved relatively to the staircase, but the staircase is rushing perhaps 1,000 miles an hour round the axis of the earth, while the earth itself may be bowling 66,000 miles an hour round the sun. The sun itself is moving towards the con- stellation of Lyra at some 20,000 miles an hour, while Lyra itself is doubtless in rapid motion with regard to other stars, which, so far from being " fixed," may be travelling thousands of % miles an hour relatively to each other. Clearly it is not only impossible to tell how many thousand miles an 1 With the signification in which the words are here used, a line has direction but not bearing. We must add to direction the conception of sense before we form the idea of bearing. 2$0 THE GRAMMAR OF SCIENCE. hour we are each one of us to be conceived as speed- ing through space, but the expression itself is mean- ingless. We can only say how fast one thing is moving relatively to another, since all things whatsoever are in motion, and no one can be taken as the standard thing, which is definitely " at rest." Is it correct to say that the earth actually goes round the sun, or that the sun goes round the earth ? Either or neither ; both are conceptions which de- scribe phases of our perception. Relatively to the earth the sun describes approximately an ellipse round the earth in a focus, relatively to the sun the earth describes approximately an ellipse about the sun in a focus. Relatively to Jupiter neither state- ment is correct. Why, then, do we say that it is more scientific to suppose the earth to go round the sun? Simply for this reason : the sun as centre of the planetary system enables us to describe in conception the routine of our perceptions far more clearly and briefly than the earth as centre. Neither of these systems is the description of an absolute motion actually occurring in the world of phenomena. Once realize the relativity of motion and the symmetry of the planetary system is seen to depend largely on the standpoint from which we perceive it : the planetary theory can thus be easily recognized as a mode of description peculiar to an inhabitant of a solar system. 8. Position. The Map of the Path. Relatively to O, then, our point P describes a con- tinuous curve or path, and its position at any instant of the motion is given by the step OP. In order that the reader may have a clearer conception of what we are considering, we will suppose the motion THE GEOMETRY OF MOTION. 251 to take place in one plane, and conceptualize certain everyday perceptions. We will suppose O to be a point taken as the conceptual limit of Charing Cross, P to be the point which marks the conceptual motion of translation of a train on the Metropolitan Railway, and the curve in the above Fig. 9 to be a conceptual map of the same railway to the scale of about one furlong to the T^th f an inch. The points P I} P 2 , P 3 , . . . P l6 , mark the successive stations between Aldgate and South Kensington. Any step like OP 6 will accurately determine a certain position of the train relative to Charing Cross. The reader must notice an important result about these steps. Suppose we had been determining the position of P 6 relative to O r say St. Paul's instead of O. We see at once that there are two ways of describing the position of P 6 relative to O'. We might either say, step the directed step O'P 6 , or, again, step first from O' to O, and then step from O to P 6 . These two latter steps lead to exactly the same final position as the former single step. Now science is not only an economy of thought, but, what is almost the same thing, an economy of 252 THE GRAMMAR OF SCIENCE. language. Hence we require a shorthand mode of expressing this equivalence in final result of two stepping operations. This is done as follows : which, put into words, reads : Step from O' the directed step O'O, and then take the directed step O'P 6 , and the spot finally reached will be the same as if the directed step O'P 6 had been taken from O'. The reader must be careful not to confuse this geo- metrical addition with ordinary arithmetical addition. For example, if OO' were eight furlongs, O'P 6 ten furlongs, and OP 6 twelve furlongs, then we appear at first sight to have : 8+12=10, and this is deemed absurd. But it is only absurd to the arithmetician. For the geometrician 8, 12, and 10 may be the lengths of directed steps, and he knows that, if he follows a directed step of 8 furlongs by one of 12, he may really have got only ten furlongs from his original position. How, then, is the arithmetician limited ? Why, obviously we must suppose him incapable of stepping out in all direc- tions in space, we must tie him down to motion along one and the same straight line. In this case a step of 8 followed by one of 12 will always make a step of 20, as arithmetic teaches us it should do. Briefly, the freedom of the geometrician consists in his power of turning corners. Let us now go back a little and note that the geometrical addition of steps, O'O + OP 6 = O'P 6 , may be represented in a slightly different manner. Let us draw the line O'A parallel to OP 6 and P 6 A parallel to OO', then we are said to complete the parallelogram on O'O and OP 6 , the line O'P 6 THE GEOMETRY OF MOTION. 253 joining two opposite angles is termed a diagonal, and we have the following rule : Complete the parallelo- gram on two steps, and its diagonal will measure a single step equivalent to the sum of the other two. This rule is termed addition by the parallelogram law, and we see that the steps by which we measure relative position, or displacements, obey this law. In itself it is the same thing as geometrical addition. Its importance lies in the fact that all the concep- tions of the geometry of motion, displacements, velocities, spins, and accelerations may be represented as steps and can be shown to obey the parallelogram law : that is to say, we add together velocities, spins, or accelerations geometrically and not arith- metically. Although our space may not admit of our demonstrating this result for all the conceptions of kinematics, 1 the reader will do well to bear it in mind, as it is an important principle to which we shall have occasion again to refer. 9 The Time-Chart. Hitherto we have been considering how the position of the point P relative to O might be determined at each instant of time. We want, however, to know how the position changes, and how this change is to be described and measured. In order to do this we must consider how the displacement OP 6 , for example, changes to the displacement OP 7 . In our geometrical shorthand: OP 7 =-OP 6 + P 6 P 7 , and the step P 6 P 7 measures the change of position. We want, then, to ascertain a fitting measure of the 1 For proofs see Clifford's Elements of Dynamic, " Velocities, "p. 59, " Spins," pp. 123-4. 254 THE GRAMMAR OF SCIENCE. manner in which this change varies with the time. To enable the reader better to conceive our purpose we will try to turn into geometry a column of Bradshaw, or, more definitely, a portion of a time-table of the Metropolitan Railway, corresponding to the stations marked in Fig. 9. Down the left-hand side of Fig. 10 are placed the names of the stations represented in Fig. 9 by the points P T , P 2 , P 3 , P 4 , . . . P l6 . These are placed, as in Bradshaw, against a vertical line, but we will somewhat improve on his arrangement. He puts the stations at equal distances below each other, and gives no hint as to the distance between each pair of them. Now we will place them at such distances along the vertical from each other that every ^th of an inch represents a furlong, or fths of an inch represents a mile, so that an inch-scale applied to the vertical ought theoretically to determine the par- liamentary fare between any two stations. In the next place, we will place off (or plot off, as it is termed) on the horizontal line through P z the number of minutes that the train takes from Aldgate to each of the other stations. Thus the times of a vertical column of Bradshaw are in our case arranged hori- zontally. But we will place these times at such distances that ^th of an inch shall represent a minute, or the minutes between any pair of stations may be at once read off by aid of an inch-scale. To connect each station with its corresponding time we will draw a horizontal line PQ through the station, and vertical line tQ through the corresponding time. These meet in a point Q, and we obtain a series of points Qx, Q 2 , . . . Q I6 , in our diagram, corresponding to the sixteen stations. Now at first sight it may seem rather an inconvenient form of Bradshaw^ when <4 -*. i t * i ! 1 N | 1 ,J % i 256 THE GRAMMAR OF SCIENCE. each train takes up an entire page. 1 The reader, however, must wait till we have seen whether our page may not be made to convey a great deal more information as to the motion of the train than Bradshavfs single column. Now it is clear that what we have done for the stations may be done for every signal-box, Si, S 2 , S 3 , &c., on the line, and not only for every signal-box, but for every position along the whole line at which we choose to observe the time at which the train passes. We thus obtain a series of points : Q x , Q 2 , Qs> Q 4 > Qs> Si, Q 6 , Q 7 , Q 8 , Q 9 , S a , &c., which are seen to take more and more the form of a curve as we increase their number. We will join this series of points by a continuous line, and to simplify matters we will suppose our train to run from Aldgate to South Ken- sington without stopping, otherwise our curve would have a small straight horizontal piece at each station. This curve must be carefully distinguished from the map of the path in Fig. 9 ; it tells us nothing about the direction in which the train is moving at a given time that is to say, whether it is going north- wards, or southwards, or what. But with the help of Fig. 9 it tells us the exact time the train takes to reach, not only every station, but every position whatever between either terminus ; or, on the other hand, it tells us the exact position for every time up to 38 minutes after leaving Aldgate. How far has the train got in 26 minutes, for example? To 1 Such geometrical Bradshaws with, however, many train-curves on a page, are used by the traffic managers of several French railways. I possess a fac-simile of that for the Paris-Lyons route containing between 30 and 40 train-curves, and showing the passing places, stoppages and speeds of the corresponding trains. THE GEOMETRY OF MOTION. 257 answer this we must scale off along the horizontal line, or time-axis^ 26 eighths of an inch ; we must then draw a vertical line, striking our curve in the point M ; a horizontal through M strikes the vertical line of stations, or distance-axis ', at the point N between Praed Street and Bayswater, and a scale divided into f ths of an inch applied to PuN tells us how many furlongs the train is beyond Praed Street. An inverse process will show us the time to any chosen position on the distance-axis. Our geometrical time-table, or time- chart, as we shall call it, thus gives us a good deal more information than Bradshaw. It is further clear that such a time-chart can be drawn in conception for every point-motion, and that, taken in conjunction with a map of the path, it fully describes the most com- plex point-motion. Hence the fundamental problem in such motions is to ascertain the map and the time- chart. 1 10. Steepness and Slope. If we examine the time-chart we see that there is a considerable difference in its steepness at different points, and other motions would give us curves with still greater variations in this respect. We observe that if we lessen the time between two stations, say P IO and PU, we must shift the line QII^H towards Q I( / IO and the result is that the curve becomes steeper between Q IO and Q II On the other hand, if we lessen the space traversed in a given time the curve becomes less steep and ultim- ately quite horizontal if the train stops at a station. Thus the steepness of the time-chart curve 1 The time-chart has been generally attributed to Galilei ; I do not know on what authority. A speed-chart occurs in his Discorsi but I do not think there is anything that could be called a time-chart. 18 258 THE GRAMMAR OF SCIENCE. corresponds in some manner to the speed of the train. We thus reach two new conceptions which need defini- tion and measurement, namely, those of steepness and speed. In Fig. 1 1 we have a horizontal straight line AB, and a sloping line AC. Clearly the greater the angle BAC the steeper AC will be, and the greater will be the height we shall ascend for the horizontal distance AB. If AB be 100 feet and CB the vertical through B be 20 feet, we shall have ascended 20 feet for a horizontal 100, or since the steepness of AC is the same at all points, we shall ascend 2 feet in 10 feet, or 200 feet in 2,000 feet, or -J- of a foot in I foot. 1 Now, by elementary arithmetic the ratios of 20 to 100, 2 to 10, 200 to 2,000, and -J- to I are all equal and may be expressed by the fraction \. This is termed the slope of the straight line AC, and is a fitting measure of its steepness. The slope is clearly the number of units or the fraction of a unit we have risen vertically for a unit of horizontal distance. If slope be a fit measure of steepness for a straight line, we have next to inquire how we can measure the steepness of a curved line. Let A and C in Fig. 12 be two points on a curved line, the curve showing no abrupt change of direction at the point A. 2 Now draw the line, or so-called chord, AC ; then, whether we go up 1 This statement depends on the proportionality of the corresponding sides of similar triangles (see Euclid, vi. 4). 2 A must be in the " middle of continuous curvature," as Newton expresses it. This condition is important) but for a full discussion of the steepness of curves we must refer the reader to pp. 44-7 of Clifford's Elements of Dynamic, part i. THE GEOMETRY OF MOTION. 259 the curve from A to C or along the chord from A to C, we shall have ascended the same vertical piece CB for the same hori- zontal distance AB. The slope of the chord AC is then termed the mean slope of the portion AC of the curve, be- cause, however the steepness may vary , x ' from A to C, the final result CB in AB could have been attained by the uniform average slope of AC. But this idea of mean slope does not settle the actual steepness of the curve, say, at the point A. Now let the reader imagine that the curve AC is a bent piece of wire, and the chord AC a straight piece of wire ; further, he must suppose small rings placed about both wires at A and C. In conception we will suppose the wires to be indefinitely thin, so that they approach as closely as we please to the geometrical ideals of curve and line. Then the ring A, being held firmly at A on the curved wire, let the ring C be moved along the curved wire towards A. As it moves the straight wire slips first into the position AC' and ultimately, when the ring C reaches A, takes up the position AT. In this position the straight line is termed the tangent to the curved line at the point A. As the slope of AC or AC' measures the mean steepness of the curve from A to C, or from A to C', so does the slope of the chord in its limiting position of touching line, or tangent, measure the mean steepness of an indefinitely 260 THE GRAMMAR OF SCIENCE. small part of the curve about A. The slope of the tangent is then said to measure the steepness of the curve at A. It is clear that in this notion of mea- suring the mean for a vanishingly small length of curve we are dealing with a conception which is invaluable as a method of description. It represents, however, a limit which, no more than a curve or line, can be attained in perceptual experience. n. Speed as a Slope. Velocity. Having now reached a conception by aid of which we can measure the steepness of a curve at any point namely, by the slope of the tangent at that point we may return to the curve of our time-chart and ask what we are to understand by its slope. Turning to Fig. 10, we observe that the mean slope of the portion Q 6 Q 7 of the curve corresponding to the transit from King's Cross to Gower Srteet is Q 7 m in Q 6 m, or since Q 7 m is equal to P 6 P 7 , and Q 6 m to t e t 7 , it is P 6 P 7 in t e t T But P 6 P 7 is, in a certain scale, the number of miles between the two stations, and t 6 t 7 is, in another scale, the number of minutes between the two stations. Thus the slope, which with one interpretation is a cer- tain rise in a certain horizontal length, is with another interpretation a certain number of miles in a certain number of minutes. Now a certain number of miles in a certain number of minutes is exactly what we understand by the mean or average speed of the train between King's Cross and Gower Street ; the train has increased its distance from Aldgate by so many miles in so many minutes. The manner in which change of distance is taking place during any finite time is thus determined by the slope of the corresponding chord of the time-chart. The average THE GEOMETRY OF MOTION. 261 rate of change of distance, or the mean speed fa* any given interval is thus recorded by the slopes of these chords. It is clear, however, that by varying the length of the chord Q 6 Q 7 by bringing Q 7 nearer to Q 6 for example we shall obtain different mean speeds for different lengths of the journey after passing King's Cross. The shorter .we take the time the steeper becomes in this case the chord, the greater the mean speed. The conception of a limit to this mean speed is then formed ; namely, the mean speed for a vanish- ingly small time after leaving King's Cross, and this mean speed is defined as the actual speed of passing King's Cross. We see at once that the actual speed will be measured by the slope of the tangent to the time-chart at O 6 , for this tangent is, according to our definition, the limit to the chord. Thus the actual speed at each instant of the motion is determined by the steepness at the corresponding point of the time- chart, and it is measured in miles per minute by the slope of the tangent at that point. We thus find that our time-chart is not only like Bradshaw, a time-table, but is also a diagram of the varying speed of the train throughout its journey. There are one or two points about speed which the reader will find it useful to bear in mind. In the first place speed is a numerical quantity, it is equal to a slope, the unit of which is one vertical unit in or per one horizontal unit ; thus the speed unit is one space unit in or per one time unit for example, one mile per minute. Secondly, unless the time-chart has a straight line for its curve, the speed must continually change its magnitude from one point to another of the path. If the curve of the time-chart be a straight line 262 THE GRAMMAR OF SCIENCE. the speed is said to be uniform, otherwise it is calle variable. Lastly, looking back at the map of the path (Fig. 9, p. 251), we see that, the bearing of the motion as well as the speed varies from point to point of the path. Remembering our definition of tangent we see that the direction of the motion at P is along the tangent at P, and further it has a sense for example, the motion is from P 6 to P 7 and not from P 7 to P 6 . Now we see that the change in the motion is of two kinds : change in magnitude, or change in speed, and change in bearing. In order to trace this change still more clearly we form a new conception, namely, that of speed with a certain bearing, and this combi- nation of speed and bearing we term velocity. To fully describe the velocity, say at the position P 6 we must therefore combine speed and bearing ; the speed is the slope of the tangent at Q 6 (Fig. 10, p. 255), and, when the units of time and space have been chosen, it is solely a number ; the bearing is the direction of the tangent to the path at P 6 (Fig. 9) together with the sense, namely, from P 6 to P 7 . Like displacement velocity can accordingly be represented by a step, the magnitude of the step measures the speed, the direc- tion of the step shows the direction of the motion, and the arrow-head gives the sense of the motion. 12. The Velocity Diagram or Hodograph. Acceleration. Now, as it is awkward to have to turn to two dif- ferent figures the map of the path and the time- chart in order to determine velocity, we construct a new figure in the following manner : From any point I we draw a series of rays, IV I} IV 2) IV 3> IV 4> . . . IV I6) parallel to the tangents at the successive points P lf P 2 , P 3 , . . . P 16 , and we measure off along THE GEOMETRY OF MOTION. 263 these rays in the sense of the motion as many units of length as there are units of speed in the motion at these points. Each of these rays will, by what precedes, be a step representing the velocity at the corresponding point of the path. If this be done for a very great number of positions the points V X| V 2| V 3( &c., will be a series approaching more and more closely to a curve. This curve is termed the hodo- graph, from two Greek words signifying a " descrip- 15 FIG 13 tiori of the path." The name has been somewhat unfortunately chosen as the curve is not a " descrip- tion of the path," but a " description of the motion in the path," rather a kinesigraph than a hodograph. Fig. 13 is supposed to represent the hodograph of the motion dealt with in our Figs. 9 and IO. 1 Thus while 1 The true hodograph would require a great number of points, such as V, to determine its shape at all accurately. The constant changes in 264 THE GRAMMAR OF SCIENCE. the rays of the map of the path (Fig. 9, p. 251) give the position of P relative to O, the rays of the hodo- graph give the velocities of P relative to O. So soon as we are in possession of the time-chart and the map of the path we can construct this diagram of the velocities. When constructed it forms an accurate picture of how the motion is changing in both mag- nitude and direction. Let us now examine this hodograph a little more closely. It consists of a point or pole I and rays IV drawn from this pole to a curve V t V 2 V 3 . . . V l6 . Now this is exactly what the map in Fig. 9 consists of. In that figure we have a pole O and rays OP drawn from this pole to a curve Pj P 2 P 3 . . . P l6 . In the course of the motion P passes along the whole length of this curve, and in just the same manner we may look upon V as moving along the whole length of the hodograph-curve. The ray IV would in each position be the displacement of V rela- tive to I. The question now arises : Has the motion of V round its curve any meaning for the motion of P in the path ? Suppose we were now to treat the hodograph as the map of a new motion, and to con- struct first the time-chart and then the hodograph of this motion, what would the rays of this second hodo- graph represent ? Now a sort of logical rule-of-three sum will give us the answer to this question. As the rays of the first hodograph are to the map of the path, so are the rays of the second hodograph to the map of V's motion. But we have seen that the rays of the first hodograph measure the velocities of P in its the direction of the railway (see Fig. 9, p. 251) cause the hodograph curve to bend backwards and forwards, while the slight variations of the speed produce the tangles in the curve. THE GEOMETRY OF MOTION. 265 path, and that these velocities are a fitting measure of how the ray OP, or the position of P relative to O, is changing. Hence it follows that the rays of the second hodograph would measure the velocities of V in the first hodograph, and that these velocities are a fitting measure of how the ray IV or the velocity of P relative to O is changing. Thus the velocity of V along the hodograph is the measure of how the velocity of P relative to O is changing. This velocity of V, or change in the velocity of P, is termed accelera- tion^ and we see that a diagram of accelerations may be obtained by drawing the hodograph of the velocity- diagram, treated as if it were itself the map of an independent motion. Acceleration therefore stands in just the same relation to velocity as velocity stands to the position-step. As change of position is repre- sented by the steps drawn as rays of the velocity- diagram or first hodograph, so change of velocity is represented by the steps drawn as rays of the acceleration-diagram or second hodograph. 1 What- ever may be demonstrated of the position-step and velocity will still hold good if the words position-step and velocity be replaced by the words velocity and acceleration respectively. 13. Acceleration as a Spurt and a Shunt. We must now investigate somewhat more closely this notion of acceleration as a proper measure of the change in velocity. In a certain interval of time the speed of the point P (Fig. 9, p. 251) changes from a number 1 We might proceed in the same manner to measure the change in acceleration by drawing a third hodograph. Fortunately this third hodograph is rarely, if ever, wanted. The concepts which practically suffice to describe our perceptual experiences of change are position, velocity, and acceleration. 266 THE GRAMMAR OF SCIENCE. of miles per minute represented by the number of linear units in IV 4 to the number of miles per minute represented by the linear units in IV 5( the speed has in this case (see Fig. 13) quickened, or there has been what we may term a spurt in the speed. Further, the bearing of the motion has changed ; instead of the point P moving in the direction IV 4 , it now moves in the direction IV 5 , that is to say, the direction of the motion has received a shunt. Thus the total change in the velocity of P as it moves from P 4 to P s consists of a spurt and a shunt. When a train quickens its speed from 40 to 60 miles an hour, and instead of running due north runs north-east, we may describe its motion as spurted and shunted ; technically, we say that its velocity has been accelerated. Acceleration has thus two fundamental factors the spurt and the shunt. 1 If we consider the perceptual world around us, it is clear that the spurting and shunting of motion are conceptions as important for describing our everyday experience as those of the speed and direction of motion itself. We have seen that the speed changes from the length IV 4 to the length IV 5 in a certain time that represented by the length t^t^ of our time-chart (Fig. 10). The increase of speed per unit of time (or the ratio of the difference of I V 5 and IV 4 to / 4 s ) is termed the mean speed-acceleration or the mean spurt between P 4 and P s . Further, the ray IV has been turned from IV 4 to IV 5 , or through the angle V 4 IV 5 in time 4 s . This increase of angle per unit time (or the ratio of the angle V 4 IV 5 to t 4 t 5 ) is termed the mean shunt^ or mean spin of direction between 1 Spurt in scientific language includes a retardation or slackening of speed as a negative spurt. THE GEOMETRY OF MOTION. 267 the positions P 4 and P 5 . The two combined, or the mean rate of spurting and shunting, form what is termed the mean acceleration during the given change of position, or for the given time (/4/s). What we measure, therefore, in acceleration is the rate at which spurting and shunting take place. Turning to Fig. 13 the reader must notice that there are two processes by aid of which we can conceive the velocity IV 4 converted into IV 5 . In the first process we follow the method just discussed : we stretch IV 4 till it is as long as IVs, that is, we increase the speed from its value in the position P 4 to its value in the position P s ; then we spin this stretched length round I till it takes up the position IV S . This is the spurt and shunt conception of acceleration. In the second process we say add the step V 4 V 5 to the step IV 4 and we shall reach the step IV 5 (pp. 252-3) that is to say, we can consider the new velocity IV 5 obtained from the old velocity IV 4 by adding the step or velocity V 4 V S by the parallelo- gram law. The mean acceleration is in this case expressed by the step V 4 V 5 added in the given interval t 4 t$. But if we compare Figs. 9 and 13 as maps for the motions of P and V we shall see that adding V 4 V S in time t 4 t s corresponds to adding P 4 P S in time ^ 5 . The latter operation, however, led us, by aid of the time-chart, from the idea of mean speed or mean change in OP to the idea of actual speed or instantaneous change in OP at P 4 ; the instantaneous change in OP 4 was in the direction of the tangent at P 4) and was measured by the slope of the time-chart at Q 4 (see Fig. 10). In precisely the same manner the instantaneous change in IV 4 will be along the tangent at V 4 , and will be measured by the THE GRAMMAR OF SCIENCE. slope of the time-chart for V*s motion at the corre- sponding point. Thus actual acceleration appears, as in our first discussion of the matter, as the velocity of V along the hodograph. Now, however close V 5 is to V 4) whether we give a stretch and a spin or add the small step V 4 V 5( the final result of the two processes will be the same. Hence we can either look upon actual acceleration as the velocity of V along the hodograph, or as the combined mode in which IV is being actually stretched and spun. 1 Either method of treating acceleration leads to the same result, and both possess special advantages for describing various phases of motion. In the first case actual acceleration is represented by a step; the bearing of this step denotes the direc- tion and sense in which V is moving, or the velocity with which IV is changing ; the number of units of length in this step denote the number of units of speed with which V is moving, or the number of units of speed being actually added per unit of time in the given direction to the velocity IV of P. By " added in the given direction " we are to understand that the incre- ments of velocity are to be added geometrically or by the parallelogram law (e.g., IV S =IV 4 +V 4 V 5 and this however small conception V 4 V 5 may be in). 14. Curvature. In the spurt and shunt method of regarding accelera- tion, on the other hand, actual acceleration will be specified by two factors : (i.) the rate at which velocity is being spurted or IV being stretched ; (ii.) the 1 What we have here stated of acceleration applies just as much to change of position. Turning to Fig. 9, we may look upon the change of position of OP as measured by the velocity of P along its path or by the manner in which OP is being actually stretched and spun. THE GEOMETRY OF MOTION. 269 rate at which velocity is being shunted, or IV being spun about I (Fig. 13, p. 263). As in the first case the direction of actual acceleration at V 4 is that of V 4 T or the tangent at V 4 , it is clear that as a rule accelera- tion will not be in the direction of velocity, 1 but will act partly in the direction of velocity and partly at right-angles to it. This result is so important that the reader will, I hope, pardon me for considering it from a slightly different standpoint. Let us imagine the ac- celeration to be always such that it never stretches IV, and let us try to analyze this case a little more closely. Obviously if IV is never stretched, if the speed is never spurted, the point V can only describe a circle, for IV remains uniform in length. Uniform speed can, how- ever, be conceived associated with a point moving in any curved path whatever. Let Fig. 14 represent this path, and let Fig. 1 5 be the circular hodograph, corre- sponding points of both curves being denoted by the same subscript numerals attached to the letters Pand V. 1 At V 3 , for example, IV 3 appears to coincide with the direction of the tangent at V 3 . In this case the whole effect of acceleration is instantaneously to spurt without shunting. 2/O THE GRAMMAR OF SCIENCE. Now, since all the acceleration in this case depends upon the change in the direction of motion, or the change in the direction of the tangent to the path, we must stay for a moment to consider how this change in direction, or \htbendingtfihz path, may be scientifically described and measured. Now if we pass, for example, from the point P 4 to P 5 on the path, and P 4 L 4 , PsL- be the tangents (p. 259) at P 4 , P s respectively, then the direction of the curve has continuously altered from P 4 L 4 to PsL 5 as we traverse the length P 4 P 5 of the curve. The angle between these directions is L 4 NL 5 , and clearly the greater this angle for a given length of curve P 4 ?5, the greater will be the amount of bending. 1 The amount of angle through which the tangent has been turned for a given length of curve forms a fit measure of the total amount of bending in that length. Accordingly we define the mean bending or mean curvature of the element of curve P 4 P 5 as the ratio of the number of units of angle in L 4 NL 5 to the number of units of length in the element of curve P 4 Ps- Thus the mean curvature of any por- tion of a curve is the average turn of its tangent per unit length of the curve. From the mean curvature we can reach a conception of actual curvature as a limit when the element of arc P 4 P S is very small in just the same manner as from mean speed we reached a con- ception of actual speed. This process of reaching a limit in conception, which cannot be really attained in perception, is so important that we will again repeat it for this special case, in order that the reader may have ' We are supposing here that the direction of bending between P 4 and P 5 does not change, that the curve is not like this : CO. We can always insure that no such change takes place by taking a sufficiently small length of arc- THE GEOMETRY OF MOTION. 271 little difficulty henceforth in discovering and discussing such limits for himself. Let us accordingly suppose the distances between the points P x , P 2 , P 3 , , . . P 6 plotted off (Fig. 16) down a vertical line as in the time-chart of Fig. 10 (p. 255). Along the horizontal line PjM 6 instead of assuming units of length to represent units of time, let them represent units of angle, 1 and let the FIC.I6. number of units taken from P T represent successively the number of units of angle between the tangents P 2 L 2 , P 3 L 3) P 4 L 4 , &c., in Fig. I4(p. 269), and the tangent 1 According to Euclid iii. 29, and vi. 33, the angles at the centre of a circle which stand on equal arcs are themselves equal j if we double or treble the arc we must double or treble the angle ; the arc is thus seen to be a fit measure of the angle. Further (Clifford's Common Sense of the Exact Sciences, pp. 123-5), the arcs of different circles subtending equal angles at their respective centres are easily shown to be in the 272 THE GRAMMAR OF SCIENCE. to the curve at P x . Thus let P Z M 4 represent the angle between the tangents at P t and at P 4 ; PiM 5 that between the tangents at P x and at P s and so on. Now draw in Fig. 16 vertical lines through the points M 2 > M 3 , &c., and horizontal lines through the points P 2 , P 3 , &c., and suppose these lines pair and pair to meet in the points Q 2 , Q 3 , &c. We have then a series of points Q, which increase in number as we increase the points P in Fig. 14, and in conception ultimately give us the curve marked in Fig. 16 by the continuous line. The diagram thus obtained is a chart of the bending or curvature in Fig. 14. For, the mean curvature in the length P 4 ?5 is the ratio of the angle L 4 NL S to the length P 4 ?5 in Fig. 14, or, what is the same thing, the ratio of the number of units in M 4 M 5 to the number in P 4 ?5 in Fig. 16. But if Q 4 K be drawn parallel to M 5 Q S to meet P$Q$ in K, this ratio is that of KQ 5 to Q 4 K, or is the slope of the chord Q 4 Q S to the vertical line P X P 6 . Thus the slope of any chord of the curvative-chart to the ver- tical measures the mean curvature of the corresponding portion of the curve in Fig. 14. When we make the chord Q 4 Q 5 smaller and smaller by causing Q s to move towards Q 4 , the mean curvature becomes more and more nearly the mean curvature at and about P 4 ; ratio of their radii. If, therefore, we take as our standard circle for measuring angles the circle whose radius is the unit of length, its arc c for any given angle will be to the arc a of a circle of radius r sub- tending the same angle in the ratio of I to r, or in the form of a propor- tion, c : a : : I : r, whence it follows that c = a/r, or the circular measttre c of any angle is the ratio of the arc a subtended by this angle at the centre of any circle to the radius r of this circle. The unit of angle in circular measure will therefore be one for which a equals r, or which subtends an arc equal to the radius. This unit is termed a radian, and is generally used in theoretical investigations. THE GEOMETRY OF MOTION. 273 but as on p. 259 the chord becomes more and more nearly the tangent at Q 4 . As we have defined actual curvature to be the limit to the mean curvature in a vanishingly small length of curve beyond P 4 (see Fig. 14), we see that the actual curvature at P 4 is the slope to the vertical of the tangent Q 4 S at the corre- sponding point O 4 of the curvature-chart. This slope, and accordingly the actual curvature, is therefore a measurable quantity at each point of any curve. 1 15. The Relation between Curvature and Normal Acceleration. Returning again to Figs. 14 and 15, we note that the mean curvature over the length P 4 ?5 is the ratio of the number of angle units in L 4 NL 5 to the number of length units in the element of curve P 4 ?5. Now the speed in the length P 4 ?5 is constant and equal to IV 4 ; hence if the point P traverse this length in 1 The mean curvature over any arc ab of a circle centre O is the ratio of the angle between the tangents at its extremities, or what is the same thing, since the tangents are perpendicular to the radii Qa and Ob of the angle aQb at the centre to the arc ab. But we have seen in the footnote, p. 271, that the measure of this angle in radians is the ratio of the arc ab to the radius. Hence it follows that the mean curva- ture of a circle is equal to the inverse of the radius (or unity divided by the radius). As this mean curvature is therefore independent F I CM 17 of the length of the arc, it follows that the actual curvature at each point must be the same and be equal to the in- verse of the radius. Since the radius of a circle can take every value from aero to infinity, a circle can always be found which has the same amount of bending as a curve at a given point, and thus fits it more closely at that point than a circle of any other radius. The radius of this circle is termed the radius of curvature of the curve at the given point. Hence the curvature of a curve is the inverse of its radius of curva- ture. 19 THE GRAMMAR OF SCIENCE. a number of minutes, which we will represent by the letter t, we must have, since speed is the num- ber of units of length per minute, the length P 4 P 5 equal to the product of IV 4 and t (or in symbols P 4 P 5 =IV 4 x/). Further, since the angle L 4 NL 5 is turned through by the tangent also in time /, the ratio of the angle L 4 NL 5 to t is the mean rate at which the tangent is turning round in the time t, or is the mean spin of the tangent (or, if the mean spin be denoted by the letter S, we have in symbols L 4 NL 5 ^=Sx/). From these results it follows at once that the mean curvature which is the ratio of L 4 NL 5 to P 4 P S must be equally the ratio of the mean spin, S, to the mean speed IV 4 . Thus we have di- rectly connected motion with curvature. Proceeding in conception to the limit we have the important kinematic result that : If a point moves along a curve the ratio of the spin of the tangent to the speed of the point is the actual curvature at each situation of the point. It remains to connect this result with the accelera- tion. The acceleration in the case we are dealing with is the velocity of V along its circle (Fig. 15). This acceleration at V 4 , for example, is along the tangent V 4 T 4 to the circle, or at right-angles to I V 4 the direction of the velocity of P (Fig. 14) ; it has thus, as we have seen, purely a shunting and no spurting effect. Now, since IV 4 and IV 5 were drawn parallel to the directions of motion L 4 P 4 , L 5 P 5 at P 4 and P 5 respectively, it follows that the angles L 4 NL 5 and V 4 IV 5 between two pairs of parallel lines must be equal. Hence the mean spin of the tangent from P 4 to P 5 must be the ratio of the angle V 4 IV 5 to the time / in which P passes from P 4 to P 5 , or, what is THE GEOMETRY OF MOTION. 2/5 the same thing, in which V passes from V 4 to V s . But the magnitude of the angle V 4 IV S is (see the footnote, p. 271) the ratio of the arc V 4 V S to the radius IV 4 . Further, the ratio of the arc V 4 V 5 to the time t is the mean speed of V from V 4 to V 5 (p. 260). Thus it follows that the mean spin of the tangent (Fig. 14) is the ratio of the mean speed of V to the radius IV 4 . Taking P 5 closer and closer to P 4 , and therefore V 5 to V 4 , mean values become the actual values at P 4 and V 4 ; we therefore conclude that the actual spin of the tangent at P 4 is the ratio of the actual speed of V at V 4 to IV 4 , or, in other words, to the speed of P. Thus the spin of the tangent is the ratio of the speed of V to the speed of P. But the speed of V is the magnitude of the acceleration, which in this case is all shunt. Hence we conclude that the rate of shunting at P is properly measured by the product of the spin of the tangent and the speed of P (or in symbols, shunt acceleration's X U, U being the speed of P). But we have seen above that the curva- ture is the ratio of the spin of the tangent to the speed of P (or in symbols curvature=S/U). Combining, accordingly, these two results we see that the shunt acceleration in this case is properly measured by the product of curvature and the square of the speed. 1 This acceleration takes place in the direction V 4 T 4 , or is perpendicular to the direction of motion at P. A little consideration will show the reader that the expression we have deduced for the acceleration per- 1 If r be the radius of curvature (see the footnote, p. 273), then i/r will be the curvature, and if we term this element of acceleration normal acceleration, we have, by the above results, the three equivalent values : U 2 normal acceleration = - =S X U =/ S 3 . 2/6 THE GRAMMAR OF SCIENCE. pendicular to the motion would not be altered were the speed to vary between P 4 and P 5 . For, returning to Fig. 13, we note that IV 4 is to be changed to IV 5 . This can be conceived as accomplished in the follow- ing two stages (p. -267) : (i.) rotate IV 4 round I without changing its length into the position IV 5 ; (ii.) stretch IV 4 in its new position into IV 5 . The first stage corresponds to the type of motion we have just dealt with, or shunt acceleration without spurt ; the second stage to the case of spurt acceleration without shunt. In the limit when IV 5 is indefinitely close to IV 4 , the first stage gives us the element of acceleration perpen- dicular to the direction of motion, and the second stage the element of acceleration in the direction of motion. By the above reasoning the former is seen to be measured by the product of the square of the speed and the curvature. 1 6. Fundamental Propositions in the Geometry of Motion. We are now in a position, after restating our results, to draw one or two important conclusions. Acceleration has spurt and shunt components. The spurt acceleration takes place in the direction of motion, and is measured by the rate at which speed is being increased (or, it may be, decreased). The shunt acceleration takes place perpendicular to the direction of motion, and is measured by the pro- duct of the curvature and the square of the speed. These two kinds of acceleration are usually spoken of as speed acceleration and normal acceleration. From these results we conclude that : i. If a point be not accelerated it will describe a straight line with uniform speed. For there will be no spurt, and therefore the speed must be uniform, THE GEOMETRY OF MOTION. 277 and there will be no shunt, and therefore the path must have zero curvature, but the only path without bending is a straight line. Neither uniform speed nor zero curvature alone denote an absence of ac- celeration. 2. When a point is constrained to move in a given path the normal acceleration may be determined in each position from the speed and the form of the path, i.e., from its curvature or bending. In this case the problem is to find the speed from the speed acceleration. 3. When a point is free to move in a given plane, then its motion can be theoretically determined, if we know its velocity in any one position, and its accelera- tion for all positions. For from the normal acceleration and the speed we can calculate the initial amount of bending of the path; thus the initial form of the path is known. For a closely adjacent position on this initial form, we can determine from the speed acceleration the change in speed due to this change of position. Hence we obtain the speed in the new position. From the speed in the new position and the normal acceleration in this position, the bending in the next little element of path may be deduced- This process may be repeated as often as we please, till the whole path of the motion is constructed. The succession of positions may be taken so close together that we obtain the form of the path to any degree of accuracy required. Knowing the path and the speed at each point of it we are able to construct a time-chart like that of our Fig. 10 (p. 255). For we know from the speeds the slope at each point of the Q-curve. Hence we commence by drawing a little element, say PiQ 2 , at the slope given by the initial speed ; this element by aid of the horizontal Q 2 P 2 , 278 THE GRAMMAR OF SCIENCE. through its terminal Q 2 , gives a new position at distance P 1 P 2 from the initial position ; the speed in this new position determines the slope of the next little element Q 2 Qs of the curve ; Q 3 by aid of the horizontal Q 3 P 3 gives a third position with a third speed a id so a slope for the third element, and this process can be continued till we have constructed the time-chart by a succession of little elements. By taking these elements sufficiently small, we make the resulting polygonal line differ as little from the true curve of the time-chart as we please. Now we have seen that when the map of the path and the time- chart are known, the motion has been fully described. Thus we conclude that : Given the velocity of a point in any position and the acceleration of the point in all positions, the motion of the point is fully deter- mined.' 1 This proposition is the basis of the whole of our mechanical description of the universe. Rightly interpreted, it contains all that we can assert of the " mechanical determinism " of nature ; wrongly inter- preted, it is the basis of that crude materialism which pictures the universe as an aggregate of objective material bodies, enforcing for all eternity certain motions on each other, and a perception of those motions upon us. What the proposition exactly tells us is this : that a motion is fully determined, that is, can be described, either by giving the path and the 1 The methods by which we have shown that the initial velocity and position, together with the acceleration in all positions, determine the map of the path and the time-chart, are only theoretical methods of construction. The practical methods of constructing these curves involve the highest refinement of mathematical analysis. Our object here is only to show that the motion is theoretically determined by a knowledge of the above quantities. THE GEOMETRY OF MOTION. 279 time to each position of the path, or by giving the velocity in any one position and the acceleration in all positions. We are really dealing with two different modes of describing motion, either of which can be deduced from the other, but neither of which explains why the motion takes place, or can be said to " deter- mine " it in the sense of the materialists. 17, The Relativity of Motion. Its Synthesis from Simple Components. There still remains a point to which it is needful to draw the reader's attention. The whole motion of our point P (Fig. 9, p. 25 1) has been considered relative to a point O. We started with a position relative to O, and it follows that the velocity and acceleration we have been discussing describe changes of motion relative to O also. Thus absohite velocity and absolute acceleration are seen to be as meaningless as absolute position. If the points O and P were both to have their motions accelerated in the same manner the relative path would not be changed any more than the map (Fig. 9) is changed by our moving about, in any manner we please, the page on which it is printed. But the fact that all motion is relative leads us at once to the very natural question : How are we to pass from the motion of a point relative to one pole O to motion relative to a second pole O' ? We must look at this point somewhat closely, for it involves some important consequences. Let us suppose the motion of P relative to O known, and the motion of O' relative to O known, we require to find the motion of P relative to O'. Let PI, P 2 (Fig. 1 8) be two successive positions of P relative to O, and O',, O' a the corresponding positions 28O THE GRAMMAR OF SCIENCE. of O'. Then O'tPj is the first and O' 2 P 2 is the second step, measuring the position of P relative to O'. From O'j draw O' T P' 2 parallel and equal to O' 2 P 2 , then O'xPx and O' r P' 2 give the relative motion of P with regard to O z , and the relative displacement in the given interval is P X P' 2 . Now draw O\O 2 parallel and equal to O' 2 O, then O^O, and O' 2 O, or O'xO 2 , give the relative positions of O with regard to O. But by the equality of opposite sides of parallelo- grams OO 2 equals O' a O'i, equals P 2 P' 2 . Hence A P. P 2 P' 2 is equal to the displacement of O relative to O'. But in the geometry of steps (p. 252) : PT>' T> T> j T> T)f i A 2^1* 2 + ^ 2 r 2 , or in words : the displacement of P relative to O' is equal to the displacement of P relative to O added geometrically to the displacement of O relative to O'. Now this result is true, however large or small these displacements may be, and these displacements divided by the number of units in the interval of time which is the same for all of them, represent the mean velocities in this interval. Hence we conclude that : the mean velocity of P relative to O' is equal THE GEOMETRY OF MOTION. 28 1 to the mean velocity of P relative to O added geo- metrically to the mean velocity of O relative to O'. If we take the interval of time, and consequently the displacements smaller and smaller, mean velocities become in the limit the actual velocities. These actual velocities have always the direction of the displacements P^, PjP 2 and OO 2 which ulti- mately from chords become tangents to the corre- sponding paths ; further, since the interval of time is the same for all the displacements, the magnitudes or speeds of these velocities are always proportional to the sides P X P' 2 , P X P 2 , and P 2 P' 2 , (or OO 2 ) of the triangle P^'aPa. Hence the mean velocities and ultimately the actual velocities always form the three sides of a triangle which has its sides parallel and proportional to the sides of the triangle P^'aPa, and this however small the latter triangle becomes. The actual velocity of P relative to O' thus forms one side of a triangle of which the actual velocities of P relative to O and of O relative to O' form the other two sides. In other words, the actual velocity of P relative to O' is obtained from the actual velocities of P relative to O, and of O relative to O' by adding them geometrically, or by the parallelogram law. Just as the position of P relative to O' was found by applying the parallelogram law to the steps O'O and OP (p. 253), so we obtain the velocity of P relative to O' by applying the same law to the velocities of P relative to O, and of O relative to O'. A very similar proof shows us that the accelera- tion of P relative to O' may be obtained in the same way from the accelerations of P relative to O and O relative to O f . We thus obtain an easy rule that of the parallelogram law for passing from 282 THE GRAMMAR OF SCIENCE. the motion of P relative to O to that of P relative toO'. The whole of this discussion may be looked at from a somewhat different standpoint. We may suppose the plane of the paper in which the motion of P about O takes place to be always moved as a whole so that the point O' remains stationary. In order to do this we must always be shifting the paper so that O' 2 falls back on O' r , and O' 2 O'i will measure the fitting shift of the paper. This carries P 2 clearly forward to P' 2 and O to O 2 . Thus the motion of P relative to O' may be looked at as the motion of P due to two sources a movement of P about O, and a movement of the plane containing P and O ; this later motion is the motion of O about O', or is equal and opposite to the perfectly arbitrary motion of O' about O. Thus we conclude that if a point P has two inde- pendent velocities (corresponding to the limits of the displacements P t P 2 and P 2 P' 2 ) then the actual velocity of P will be found by adding these velocities geometrically. This statement is usually termed the parallelogram of velocities. A precisely similar state- ment holds for independent accelerations (p. 253), and is called the parallelogram of accelerations. To these important results we shall have occasion again to refer. We conclude, therefore, with the general statement that the independent displacements, the independent velocities, and the independent accelera- tions of a moving point are respectively added geo- metrically as we add steps, or by the so-called parallelogram law. The value of this rule of combination lies in the power it gives us of building up complex cases of motion from simple cases. If we find as a result of THE GEOMETRY OF MOTION. 283 experience that the perceptual antecedents 1 of one acceleration may be superposed on the perceptual antecedents of a second acceleration without these accelerations altering their value to our degree of re- finement in measuring them, then the parallelogram of accelerations will be invaluable as a mode of synthesis^ or of constructing the complex from the simple. The law of gravitation applied to the planetary theory is a striking example of the value of such a synthesis. In this chapter we have seen how the relative position, velocity, and acceleration of points may be defined, described, and measured. We have been gleaning wholly in the conceptual field of geometrical ideals. We have next to ask how these conceptions may be applied to describe our perceptual experi- ence of change in the world of phenomena. How are these three factors, position, velocity, and accelera- tion, related to each other in that ideal dance of cor- puscles to which we reduce the physical universe, in that atomic gallop by aid of which we describe and resume our sense-impressions? How do we conceive the relative position of these corpuscles to change ? How are their speeds and directions of motion varying? Does experience show us that relative position produces a definite speed, or a definite spurt and shunt ? The answer to these questions lies in the so-called properties of matter and in the laws of motion which will be the topics of our two following chapters. 1 By "perceptual antecedents" we are to understand cause in the scientific sense, but the word has not been used in the above paragraph, because the reader might have supposed the cause of acceleration to be the metaphysical (and imperceptible) entity force, whereas it really lies in perceptible relative position (p. 345). 284 THE GRAMMAR OF SCIENCE. SUMMARY. 1. All the notions by aid of which we describe and measure change are geometrical^ and thus are not real perceptual limits. They are forms distinguishing and classifying the contents of our perceptual experience under the mixed mode of motion. The principal of these forms are point-motion, spin of a rigid body and strain. Motion is found to be relative, never absolute ; for example, it is meaningless to speak of the motion of a point without reference to what system the motion of the point is considered with regard to. 2. An analysis of point-motion leads us to the conceptions of velocity and acceleration, the first as a proper measure of the manner in which position is instantaneous changing, the second as a proper measure of how velocity itself is changing. It is found that a motion is fully determined, or theoretically a complete description of its path and position at each instant of time may be deduced, when the velocity in any one position and the acceleration for all positions are given. 3. The parallelogram law as the general rule for combining motions is the foundation of the synthesis by which complex motions are con- structed out of simple motions. LITERATURE. CLERK-MAXWELL, J. Matter and Motion, chaps, i. and ii. London, 1876. CLIFFORD, W. K. The Common Sense of the Exact Sciences, chap, iv. "Position," and chap. v. "Motion",* London, 1885. Also for a more advanced treatment the same writer's Elements of Dynamic, part i., book i. chaps, i. and ii. ; bcok ii. chaps, i. and ii. ; book iii. chap. i. ; London, 1878. MACGREGOR, J. G. An Elementary Treatise on Kinematics and Dynamics, part i., "Kinematics," chaps, i.-iii., v. and vii. Lon- don, 1887. CHAPTER VII. MATTER. i. "All things move " but only in Conception. AN old Greek philosopher, who lived perhaps some five hundred years B.C., chose as the dictum in which he summed up his teaching the phrase : " All things floiu." After ages, not understanding what Heraclitus meant it is doubtful whether he understood himself dubbed him " Heraclitus the Obscure." But to-day we find modern science almost repeating Heraclitus' dictum when it says : "All things are in motion'' Like all dicta which briefly resume wide truths, this dictum of modern science requires expanding and explaining if it is not to be misinterpreted. By the words " All things are in motion " we are to understand that, step by step, science has found it possible to describe our experience of perceptual changes by types of relative motion : this motion being that of the ideal points, the ideal rigid bodies or the ideal strainable media which stand for us as the signs or symbols of the real world of sense-impressions. We interpret, describe, and resume the sequences of this real world of sense- impressions by discussing the relative positions, velocities, accelerations, rotations, spins, and strains of an ideal geometrical world which stands for us as a conceptual representation of the perceptual world. In our Chapter V. we saw that space and time did 286 THE GRAMMAR OF SCIENCE. not themselves correspond to actual perceptions, but were modes under which we perceived, and by which we discriminated, groups of sense-impressions. So motion as the combination of space with time is essentially a mode of perception, and not in itself a perception (p. 231). The more clearly this is realized the better able the reader will be to appreciate that the " motion of bodies " is not a reality of perception, but is the conceptual manner in which we represent this mode of perception and by aid of which we describe changes in groups of sense-impressions ; the perceptual reality is the complexity and variety of the sense- impressions which crowd into the telephonic brain- exchange. That the results which flow from the conceptual world of geometrical motions agree so closely with our perceptual experience of the outside world of phenomena (p. 77) is a phase of that ac- cordance between the perceptive and reasoning facul- ties upon which we have laid stress in an earlier part of this volume (p. 124). Wherein lies the advance from Heraclitus to the modern scientist ? Why was the dictum of one not unjustly termed obscure, while the other claims and rightly claims to find in the development of his dictum the sole basis for our knowledge of the physical universe ? The difference lies in this : Hera- clitus left his flow undescribed and unmeasured, while modern science devotes its best energies to the accurate investigation and analysis of each and every type of motion which can possibly be used as a means of describing and resuming any sequence of sense- impressions. The whole object of physical science is the discovery of ideal elementary motions which will enable us to describe in the simplest language the MATTER. 287 widest ranges of phenomena ; it lies in the symboli- zation of the physical universe by aid of the geometrical motions of a group of geometrical forms. To do this is to construct the world mechanically T ; but this mechanism, be it noted, is a product of concep- tion, and does not lie in our perceptions themselves (p. 139). Startling as it may, when first stated, appear to the reader, it is nevertheless true that the mind struggles in vain to clearly realize the motion of any- thing which is neither a geometrical point nor a body bounded by continuous surfaces; the mind absolutely rebels against the notion of anything moving but these conceptual creations, which are limits, unrealizable, as we have seen, in the field of perception. If the world of phenomena be, as the materialists would have us to believe, a world of moving bodies like the conceptual world by which science symbolizes it, if we are to assert the perceptual existence of atom and ether, then in both cases we are incapable of con- sidering the ultimate element which moves as any- thing but a perceptual realization of geometrical ideals. Yet so far as our sensible experience goes these geometrical ideals have no phenomenal existence ! We have clearly, then, no right to infer as a basis of perception things which our whole experience up to the present shows us exist solely in the field of conception. It is absolutely illogical to fill up a void in our perceptual experience by pro- jecting into it a load of conceptions utterly unlike the adjacent perceptual strata. It is " a profound psychological mistake," says George Henry Lewes, " to assert that whenever we can form clear ideas, not 1 This word is here used in the scientific sense of Kirchhoff, and not in the popular sense of Mr. Gladstone : see pp. 137 and 139. 288 THE GRAMMAR OF SCIENCE. in themselves contradictory, these ideas must of necessity represent truths of nature." * The reader will, we feel certain, find it impossible to conceive anything other than geometrical ideals as the moving element at the basis of phenomena. The attempt, however, to conceive something else is worth the making for it inevitably leads us to the con- clusion that the term " moving body " is not scientific when applied to perceptual experience. In external perception (p. 219) we have sense-impressions and more or less permanent groups of sense-impressions. These sense-impressions vary, dissolve, form new groups that is, they change. Of these messages re- ceived at the brain telephonic exchange, or of groups of them, we cannot say they move they appear, disappear, and reappear. Change is the right word to apply to them rather than motion. It is in the field of conception solely that we can properly talk of the motion of bodies ; it is there, and there only, that geometrical forms change their position in absolute time that is, move. In the field of perception motion is but a popular expression to describe the mixed mode in which we discriminate and distinguish groups of sense-impressions. 2. The Three Problems. That we speak of the motion of bodies as a fact of perceptual experience is largely due to the con- structive elements associated with immediate sense- impression 2 (p. 49). These constructive elements are * See especially 69, 6Qa, and 108 of his Aristotle: a Chapter from the History of Science. London, 1864. 2 The writer is not objecting to the current use of such expressions as " the sun moves," or "the train moves." Both do move in concep- MATTER. 289 drawn from our conceptual notions of change, which again flow very naturally from a limited perception ; a deeper perceptual experience is required to demonstrate their purely ideal character (p. 203). But the reader will, perhaps, hardly be prepared to accept the conclusion that change is perceptual, motion con- ceptual, without closer analysis. This analysis may be summed up in the three questions : What is it that moves ? WJiy does it move ? How does it move ? In the first place we must settle whether we are asking these questions of the conceptual or percep- tual spheres. If it be of the former, the world of symbolic motions by aid of which science describes the sequences of our sense-impressions, then these questions are easy to answer. The things which move are points, rigid bodies and strainable media, geometrical concepts one and all. To ask why they move is to ask why we form conceptions at all, and ultimately to question why science exists. Finally, the manner in which they move is that which enables us most effectually to describe the results of our per- ceptual experience. If we turn to the perceptual sphere and ask what it is that moves and why it moves, we are compelled to confess ourselves utterly incapable of finding any answers whatever. Ignorabimus^ we shall always be ignorant, say some scientists. That we are really ignorant will be the theme of the present chapter, but I believe that this ignorance does not arise from the limitation of our perceptive or reasoning faculties. It is rather due to our having asked unanswerable tion ; in perception there is a change of sense-impressions. So soon as space is recognized as a mode of perception, and not itself a phenomenon, this conclusion cannot be avoided. 20 290 THE GRAMMAR OF SCIENCE. questions. We may legitimately ask why the com- plex of our sense-impressions changes, but, according to the views expressed above, motion is not a reality of perception, and it is therefore, for the sphere of per- ception, idle to ask what moves and why it moves. With the growth of more accurate insight into the conceptual nature of motion these questions will, I believe, be dismissed like the older questions as to the blue milk of the witches and the influence of the stars (p. 27). With their dismissal, however, physical science will be for ever relieved of the metaphysical difficulties as to matter and force which it has inherited from scholastic traditions. Ignorabimus, therefore, does not seem the true answer to the first two questions ; it may be a true answer to the problem of changes in sense-impression (see our pp. 129 and 288). The third question How do things move ? also wants re- stating to be of any real value, and when restated it merges in the same question asked of the conceptual sphere. What, we must ask, are the conceptual types of motion best suited to describe the stages of our perceptual experience ? The answer to this question forms the subject-matter of our next chapter. Some of my readers may feel inclined to consider that in this discussion we are entirely deserting the plane of common sense. What moves ? Why, natural bodies move, they will say, is the common-sense answer. But common-sense is often a name for in- tellectual apathy. Being inquisitive, we naturally ask what these bodies consist in, and probably shall be told that they are quantities of matter. Still persisting with our questions we ask : What, then, is matter ? It will not do to put us off with the reply that matter is that which moves. All we should, then, have done MATTER* 291 would be to give a name to the moving thing, but in doing so we should not have succeeded in defining or describing it. The reader may, perhaps, imagine that insight into the nature of matter will be gained by consulting the accepted text-books of science. Let us accordingly examine the statements of one or two. 3. How the Physicists define Matter. A first writer says : "Matter is a primary conception of the human mind" and more than one elementary text-book provides us with practically the same definition. Now, the obscurity and paralogism of this statement could only be equalled by the perversities of metaphysics. 1 Matter, we are told, is what moves in the phenomenal world, and if it were asserted that matter is a primary perception of the human mind we might be no wiser, but at any rate the statement would not be without sense. But perhaps the phrase is not to be taken literally as signifying that a primary conception actually moves among perceptions, but only that we can form intuitively a conception of what moves perceptually that the perceptual actually corresponds to the conceptual. In this case 1 " Matter," says Hegel, " is the mere abstract or indeterminate reflection-intosomething-else, or reflection-into-self at the same time as determinate; it is consequently Thinghood which then and there is, the subsistence or substratum of the thing. By this means the thing finds in the matters its reflection-into-self ; it subsists not in its own self, but in the matters, and is only a superficial association between them, or an external bond over them" (The Logic of Hegel, translated by W. Wallace, Oxford, 1874, p. 202). We may smile over such absurdities, but that they should be taught in the last decade of the nineteenth century in our universities, and this to immature minds, and largely at the public expense, is a cause for sorrow rather than amusement. The much-abused schoolmen never rivalled these Hegelian quagmires even before they were transferred to English soil. 292 THE GRAMMAR OF SCIENCE. we are again thrown back on the fact that conceptual motion is a motion of geometrical ideals, and that these correspond in no accurate sense to our percep- tions. Indeed, if matter be a conception at all, like the conception of a circle it ought to be a clear and definite idea, whereas the reader who will honestly ask himself what he conceives by matter will find that an answer is impossible, or that in attempting one he is sinking deeper and deeper into the metaphysical quagmire. Proceeding further, we naturally turn to the little work termed Matter and Motion, by Clerk-Maxwell, one of the greatest British physicists of our genera- tion. This is what he writes of matter : " We are acquainted with matter only as that which may have energy communicated to it from other matter, and which may in its turn communicate energy to other matter:' Now this appears something definite ; the only way in which we can understand matter is through the energy which it transfers. What, then, is energy ? Here is Clerk-Maxwell's answer : "Energy, on the other hand, we know only as that which in all natural phenomena is continually passing from one portion of matter to another" All our hopes are shattered ! The only way to understand energy is through matter. Matter has been defined in terms of energy, and energy again in terms of matter. Now Clerk-Maxwell's statements are extremely valuable as expressing concisely the nature of certain conceptual processes, by aid of which we describe certain phases of our perceptual experience, but as defining matter they carry us no further than the statement that matter is that which moves. MATTER. 293 We will now turn to the famous Treatise on Natural Philosophy of Sir William Thomson and Professor Tait the standard work in the English language on its own branches of physical science. These writers, in 207, tell us : " We cannot, of course, give a definition of matter which will satisfy the metaphysician, but the naturalist may be content to know matter as that which can be perceived by the senses, or as that which can be acted upon by, or can exert, force. The latter, and indeed the former also, of these definitions involves the idea of force, which, in point of fact, is a direct object of sense ; probably of all our senses, and certainly of the ' muscular sense.' To our chapter on * Properties of Matter ' we must refer for further discussion of the question, What is matter ? " That the naturalist nowadays is not bound to satisfy the metaphysician any more than he is bound to satisfy the theologian will be admitted at once by the sympathetic reader of our own volume. But the naturalist is bound in the spirit of science to probe and question every statement, however high the authority on which it is made ; and he is further bound to inquire whether a statement as to a physical fact is also in accord with his psychological ex- perience. Science cannot be separated into com- partments which have no mutual relationship, no mutual dependence, and no intercommunication. Science and its method form a whole, and if a physical definition be not psychologically true, it is not physically true. Now we have seen that the contents of perception are sense-impressions and stored sense-impresses, and that which can be per- ceived by the senses are these and these only. Do 294 THE GRAMMAR OF SCIENCE. our authors mean to define all sense-impressions as matter ? Would they call colour, hardness, pain, matter ? We think this is hardly likely ; they would probably tell us that the source of certain groups of sense-impressions is what they term matter; but this is not what they say. Had they said it they must themselves have recognized that they were passing beyond the veil of sense-impression and postulating a "thing-in-itself" (p. 87) behind the world of phenomena. They would then have seen that they were unconsciously endeavouring to satisfy the meta- physician, whom they had so properly disowned. This unconscious attempt to satisfy the " meta- physician within themselves " is further evidenced by their second statement, which throws back matter upon force. But force for these authors is the cause of motion ( 217), not in the import of an ante- cedent or accompanying sense-impression as, for example, relative position but in the metaphysical sense of a moving agent. They do not, indeed, place this moving agent behind sense-impression ; they even describe it as a " direct object of sense/' but from the psychological standpoint force must either be a sense- impression or a group of sense-impressions, for as source or object of sense-impressions it would be purely metaphysical. But as a group of sense- impressions in us, force cannot be that which causes motion in an objective world. As to our muscular appreciation of force, that is a point to which we shall find occasion to return later. We ought not, however, to lay much stress on these authors' remarks as to matter, for they expressly tell us that what matter is will be further discussed in another chapter of their work. Unfortunately, this portion of their MATTER. 295 great treatise has never been published, although they wrote the above remarks more than twenty years ago. Perhaps, had they returned to the subject, they would have recognized that, if the word matter had not appeared more frequently in their text than it does in their index, their volumes would have lost not an iota of their inestimable value to the physicist. One of the two authors of the Treatise on Natural Philosophy has, however, published a separate work, entitled, The Properties of Matter. On pp. 12-13 of this work we have no less than nine, and on pp. 287-91 we have no less than twenty-five definitions or descriptions of matter, yet so far from matter being rendered intelligible by all these statements with regard to it, Professor Tait himself writes : " We do not knozv, and are probably incapable of dis- covering, what matter is" And again : " The discovery of the ultimate nature of matter is probably beyond the range of human intelligence? Now these statements mark a considerable ad- vance on the standpoint of the Treatise on Natural Philosophy. They will at least suggest to the reader that it is no mere whim on my part to question the right of matter to appear at all in scientific treatises. When one author tells us it is a primary conception of the human mind, and another that it is probably beyond the range of human intelligence, we feel an uncomfortable sense of the metaphysician smiling somewhere round the corner. If our leading scientists either fail to tell us what matter is, or even go as far as to assert that we are probably incapable of know- ing, it is surely time to question whether this fetish of the metaphysicians need be preserved in the temple of science. 296 THE GRAMMAR OF SCIENCE. 4. Does Matter occupy Space ? But to return to Professor Tait ; he has called his book The Properties of Matter, and this the reader will say means something, and something very definite. Now, for the purposes of classifying our sense-impressions, it is undoubtedly useful to term particular groups of them which have certain dis- tinguishing characteristics " material sense-impres- sions," and these material sense-impressions are what Professor Tait deals with under the properties of matter. It is Professor Tait, the unconscious meta- physician, who groups this class of sense-impressions together and supposes them to flow as properties from something beyond the sphere of perception, namely, matter. 1 As a working definition of matter, Professor Tait considers that we may say : "Matter is whatever can occupy space? Now this definition will lead us to a number of ideas which it is instructive to follow up. In the first place, is it perceptual or con- ceptual space to which the definition applies ? If the latter, then matter must be a geometrical form a result which we think our author does not intend. We think it more probable that Professor Tait looks upon space as itself objective, although he avoids any definite statement on this really important issue (p. 47). From the standpoint of our present volume, however, space is the mode by which we distinguish 1 The unconscious metaphysics of Professor Tait occur on nearly every page of his treatment of the fundamental concepts of physical science. Thus he asserts the "objectivity of matter," while force is not objective, we are told, but subjective. Notwithstanding this assertion, "matter is, as it were, the plaything of force." How this nothing, this "mere phantom suggestion of our muscular sense," this force, can have an objective plaything it would puzzle a metaphysician to explain. MATTER. 297 coexisting groups of sense-impressions, and therefore only groups of sense-impressions can be said to " occupy " space. This definition would therefore lead us to identify matter with groups of sense- impressions, and in practical everyday life the things which we term matter are certainly more or less permanent groups of sense-impressions, not unknow- able "things-in-themselves" beyond sense-impression. Now there can be no scientific objection to our classi- fying certain more or less permanent groups of sense- impressions together and terming them matter, to do so indeed leads us very near to John Stuart Mill's definition of matter as a "permanent possibility of sensation " T but this definition of matter then leads us entirely away from matter as the thing which moves. It can hardly be said that weight, hardness, impenetrability move ; these are sense-impressions in the brain telephonic exchange ; their grouping, their variation and succession may lead us to the conception of motion, but a sense-impression in itself cannot be said to move ; it is there at the brain terminal or not there. In order to bring motion into the sphere of sense-impression, we are compelled to associate colour, hardness, weight, &c., with geometrical forms, and in making such constructs (p. 49) we pass from the plane of perception to that of conception. I move my hand ; my power to realize this motion depends on my conceiving my hand bounded by a continuous surface. If the physicist tells me that my hand is an 1 System of Logic, bk. i. chap. iii. That groups of sense-impressions recur in a more or less permanent state is an experience we have every moment of our lives. There is a " permanent possibility of sense- impressions." We are not forced to assert anything about this possi- bility residing in a supersensuous entity matter. 298 THE GRAMMAR OF SCIENCE. aggregation of discrete molecules, then my idea of the motion of the hand is thrown back on the motion of the swarm of molecules. But the same difficulty arises about the individual molecule. I may surmount it by supposing the molecule to be in itself a corpora- tion of atoms, but I cannot conceive the atom's motion unless it be bounded by a continuous surface or else be a point The only other way out of the difficulty is to construct the atom of still smaller atoms (and there are certain phenomena presented by the spectrum analysis of the gaseous elements that might well induce us to believe that the atom cannot be con- ceived as the ultimate or " prime element of matter ") but what about these smaller atoms, are they geometrical ideals or are they built up of tinier atoms still, and if so where are we to stop ? The process reminds us of the lines of Swift : " So naturalists observe, a flea Has smaller fleas that on him prey ; And these have smaller still to bite 'em, And so proceed ad injinitum." I am unable to verify Swift's statement as to the fleas, but I feel quite sure that to assert the real existence in the world of phenomena of all the concepts by aid of which we scientifically describe phenomena molecule, atom, prime-atom even if it be ad infinitum, will not save us from having ultimately to consider the moving thing to be a geometrical ideal, from having to postulate the phenomenal existence of what is contrary to our perceptual experience. This point brings out very clearly what the present writer holds to be a fundamental canon of scientific method, namely : To no concept^ however invaluable it may be MATTER. 299 as a means of describing the routine of perceptions > ought phenomenal existence to be ascribed until its perceptual equivalent has been actually disclosed. Whenever we disregard this canon, when, for ex- ample, we assert reality for the mechanisms by aid of which we describe our physical experience, then we are more likely than not to conclude with an antinomy, or a conflict of rules. For such mechanisms are con- structs largely based on conceptual limits, which are unattainable in the field of perception. When we consider space as objective and matter as that which occupies it, we are forming a construct largely based on the geometrical symbols by aid of which we analyze motion conceptually. We are projecting the form and volume of conception into perception, and so accustomed have we got to this conceptual element in the construct that we confuse it with a reality of perception itself. When we go a stage further in the phenomenalizing of conceptions, and postulate the reality of atoms, the antinomy becomes clear. If bodies are made up of swarms of atoms, how can they have a real volume or form ? What is the volume or form of a swarm of bees or a cloud of dust? Obviously we can only give them shape and size by enclosing them conceptually in an ideal geometrical surface. Just as in a swarm of bees or a cloud of dust odd members of the community near this imagi- nary surface are continually passing in and out, so if we phenomenalize conception we must assert that at the surface of water or of iron odd molecules or atoms are perpetually leaving or, it may be, re-entering the swarm. Condensation and evaporation go on at the surface of the water and iron has a metallic smell. Now if the swarm be in this continual state of flow 3OO THE GRAMMAR OF SCIENCE. at the surface we can only speak of it as having volume or form ideally^ or as a mode of conceptually distinguishing one group of sense-impressions from another (p. 197). It is the conceptual volume or form which occupies space, and it is this form, and not the sense-impressions, which we conceive to move. If we throw back the occupancy of space on the individual members of the swarm, it is certainly not the volumes or forms of the individuals, which we con- sider as the volume or form of the material body, for the former we treat as imperceptible and the latter as perceptible. Further, we must then infer that the unknown is ultimately unlike the known, that geo- metrical ideals can be realized in the imperceptible. This, however, is a distinct breach of the canon of logical inference (p. 72). So far, then, our analysis of the physicist's defini- tions of matter irresistibly forces upon us the following conclusions : That matter as the unknowable cause of sense-impression is a metaphysical entity x as meaningless for science as any other postulating of causation in the beyond of sense-impression ; it is as idle as any other thing-in-itself, as any other projection into the supersensuous, be it the force of the mate- rialists, or the infinite mind of the philosophers. The classification of certain groups of sense-impressions as material groups is, on the other hand, scientifically of value ; it throws no light, however, on matter as that which perceptually moves. Conceptually all motion is the motion of geometrical ideals, which are so chosen as best to describe those 1 The scientific reader must for the present have at least sufficient confidence in the author not to believe that mass is thrown overboard with the fetish matter. MATTER. 301 changes of sense-impression which in ordinary lan- guage we term perceptual motion. 5 . The " Common-sense" View of Matter as Impenetrable and Hard. Now the reader may feel inclined, on the basis of his daily experience, to assert that both the physicists above referred to and the author are really quibbling about words, and that we can sufficiently describe matter by saying that it is impenetrable and hard. Now these terms describe important classes of sense- impressions, and the sense-impressions of impenetra- bility and hardness are very frequently factors of what we have called material groups of sense-impressions. But it is very doubtful whether we can consider them as invariably associated with these material groups. At any rate if we do we shall find ourselves again involved in the antinomies which result when we pass incautiously to and fro from the field of perception to that of conception. When we say a thing is impene- trable, we can only mean that something else will not pass through it, or that there are two groups of sense-impressions which, in our perceptual experience, we have always been able to distinguish under the mode space. Impenetrability, therefore, can only be a relative term ; one thing is .impenetrable for a second. When we say that matter is impenetrable we cannot mean that nothing whatever can pass through it. A bird cannot fly through a sheet of plate glass, but a ray of light does penetrate it per- fectly easily. A ray of light cannot pass through a brick wall, but a wave of electric oscillations can. In order to describe the motion of these luminous and electric waves the physicist conceives ether to pene- 302 THE GRAMMAR OF SCIENCE trate all bodies and to act as a medium for the transit of energy through them. Matter cannot therefore be looked upon as the thing which is absohitely impene- trable. Or, are we missing the point of what is meant, when it is asserted that matter is that which is impenetrable ? Are we to postulate the real existence of atoms and then to suppose the individual members of the swarm impenetrable ? Here again a difficulty arises. There is much that tends to convince physicists that the atom cannot be conceived as the simplest element of the conceptual analysis of material groups. Just as a bell when struck sets the air in motion and gives a note, so we conceive an atom capable of being struck, and of setting not the air but the ether in motion, of giving, as we might express it, an ether note. These notes produce in us certain optical sense-impressions for example, the bright lines of the spectrum of an attenuated gas. As without seeing two bells we might, and indeed often do, distinguish them by their notes, 1 so the physicist distinguishes an atom of hydrogen from an atom of oxygen, although he has never seen either, by the different light notes which he conceives to arise from them. But as the bell to give a note must be considered as vibrating changing its shape or undergoing strain so the physicist prac- tically finds himself compelled to conceive the atom as undergoing strain, or changing its shape. This conception forces us to suppose the atom built up of distinct parts capable of changing their relative 1 The householder is generally able to distinguish the sound of the back-door from that of the front-door bell, although, probably, in ninety-nine cases out of a hundred he may never have seen the bells in his house. MATTER. 303 position. What are these ultimate parts of the atom, by the relative motion of which we describe our sense- impressions of the bright lines in the spectrum ? We have as yet formed no conception. Does the ether or anything else penetrate between these ultimate parts of the atom ? We cannot say. In the present state of our knowledge it is impossible to tell whether it would or would not simplify things to conceive the atom as penetrable or impenetrable. Hence, even if we go so far as to give the concept atom a phenomenal existence, it will not help us to understand what is meant by the assertion that matter is impenetrable. 6. Individuality does not denote Sameness in Substratum. Shall we, however, be more dogmatic still, and, denying that ether is matter, assert that matter is impenetrable relative to matter ? In order to give any definite answer to this question we have again to pass from the perceptible material group to its supposed elementary basis, the atom, and to ask whether we have any reason for conceiving atoms as incapable of penetrating each other. In the first place the physicist, although he has never caught an atom, yet conceives it as something which is incapable of disappearing it continues to be. In the next place, if we conceive it as entering into combination with a second atom, although we have no reason for asserting that the two atoms do not mutually penetrate, we are still compelled, in order to describe by aid of atoms our perceptual experience, to conceive that, out of the combination, two separate atoms can again be obtained with the same individual characteristics as the original two possessed. What right have we to postulate these laws with regard to atoms when atoms are, even 304 THE GRAMMAR OF SCIENCE. if real, still absolutely imperceptible to us, when we are absolutely unable to observe their mutual action ? We have exactly the same logical right as we have to lay down any scientific law whatever. Namely, we find that these laws as to the action of single atoms, when applied to large groups of atoms, enable us to describe with very great accuracy what occurs in those phenomenal bodies, which we scientifically symbolize by groups of atoms ; they enable us to construct without contradiction by perceptual experience, those routines of sense-impression which we term chemical reactions. The hypotheses that the individual atom is both indestructible and impenetrable suffice to elucidate certain physical and chemical properties of the bodies we construct from atoms. But the continued existence of atoms under physical changes and the reproduction of their individuality on the dissolution of chemical combination might possibly be deduced from other hypotheses than those of the indestructibility and impenetrability of the individual atom. It does not follow of logical necessity that because we experience the same group of sense-impressions at different times and in different places, or even continuously, that there must be one and the same thing at the basis of these sense-impressions. An example will clearly show the reader what we mean and at the same time demonstrate that however useful as hypotheses the indestructibility and impenetrability of the atom may be, they are still not absolutely necessary conceptions ; so that even if we do project our atom into an imper- ceptible of the phenomenal world, it will not follow that there must be an unchangeable individual some- thing at all times and in all positions as the basal MATTER. 305 element of a permanent group of sense-impressions. The permanency and sameness of the phenomenal body may lie in the individual grouping of the sense-impressions and not in the sameness of an imperceptible something projected from conception into phenomena. The example we will take is that of a wave on the WAVE FIG. 19. surface of the sea. The wave forms for us a group of sense-impressions, and we look upon it, and speak of it, as if it were an individual thing. But we are compelled to conceive the wave when it is fifty yards off as consisting of quite different moving things to what it does when it reaches our feet the substratum of the wave has changed. Throw a cork in ; it rises 21 306 THE GRAMMAR OF SCIENCE. and falls as the wave passes it, but is not carried along by it. The wave may retain its form and be for us exactly the same group of sense-impressions in different positions and at different times, and yet its substratum may be continually changing. We might even push the illustration further ; we might send two waves of different individual shapes (Ffg. 19) along the surface of still water in opposite directions (a), or in the same direction if the pursuing wave had the greater speed. One of these waves would meet or overtake the other (&) ; they would coalesce or combine (<:), pro- ducing in us for a time (which depends entirely on their relative speeds), a new group of sense-impressions dif- fering totally from either individual group ; but they would ultimately pass each other (d) and emerge with their distinct individualities the same as of old (e). Throughout the whole of this sequence the substrata of the two individual waves are changing and for the time of the combination their substratum is identical, and yet the waves are able to preserve their individual characteristics, so far as reappearing with them after combination is concerned. 1 Thus sameness of sense- impressions before and after a combination is seen from a perceptual example not to involve of necessity a sameness of substratum. Now we have cited this example of the wave for two reasons. In the first place it shows us that it is possible to conceive atoms as penetrable by atoms, and as varying from moment to moment 1 If analogy were to be sought to the sameness of total weight before, during, and after combination, it might be found in the sameness of the volume of fluid raised above the sea-level, before, during, and after coalition. Thus sameness of weight does not in conception necessarily involve sameness of substratum. MATTER. 307 in their substratum, without at the same time denying the possibility of their physical perma- nency and individual reproduction after chemical combination. To consider an atom as consisting always of the same substratum, and as impenetrable by other atoms, may help us to describe easily certain physical and chemical phenomena ; but it is quite conceivable that other hypotheses may equally well account for these phenomena, and this being so we have clearly no right first to project special conceptions into the world of real phenomena, and then to assert on the strength of this that matter, penetrable in itself, is impenetrable in its ultimate element, the atom. Clearly impenetrability is neither in perception nor conception a necessary factor of material groups of sense-impressions. Further, the permanence and sameness of such a group do not necessarily involve the conception of a permanent and same substratum for the group. My second reason for citing this wave example lies in the light it throws on the possibilities involved in the statement : "Matter is that ivhich moves" The wave consists of a particular form of motion in the sub- stratum which for the time constitutes the wave. This form of motion itself moves along the surface of the water. Hence we see that besides the substratum something else can be conceived as moving, namely, forms of motion. What if, after all, matter as the moving thing could be best expressed in conception by a form of motion moving, and this whether the substratum remain the same or not ? To this sugges- tion we shall return later, as it is one extremely fruitful in its results. 308 THE GRAMMAR OF SCIENCE. 7. Hardness" not Characteristic of Matter. It remains for us now to deal with the other cha- racteristic, hardness, which is popularly attributed to matter. There are certain persons who, when men's ignorance as to the nature of matter is suggested to them, are content to remark that one has only to knock one's head against a stone wall in order to have a valid demonstration of the existence and the nature of matter. Now if this statement be of any value, it can only mean that the sense-impression of hardness is the essential test of the presence of matter in these persons' opinion. But none of us doubt the existence of the sense-impression hardness associated with other sense- impressions in certain permanent groups ; we have been aware of it from childhood's days, and do not require its existence to be experimentally demon- strated now. It is one of those muscular sense- impressions which we shall see are conceived by science to be describable in terms of the relative acceleration of certain parts of our body and of external bodies. But it is difficult to grasp how the sense-impression of hardness can tell us more of the nature of matter than the sense-impression of soft- ness might be supposed to do. There are clearly many things which are popularly termed matter and are certainly not hard. Further, there are things which satisfy the definitions of matter as that which moves or as that which fills space, but which are very far indeed from producing any sense-impression of the nature of hardness or softness ; nor would they even satisfy our definition if we said that matter is that which is heavy, heaviness being certainly a more widely- spread factor of material groups of sense-impressions than hardness. Between the sun and planets, between MATTER. 309 the atoms of bodies, physicists conceive the ether to exist, a medium whose vibrations constitute the channel by means of which electro-magnetic and optical energy is transferred from one body to another- In the first place, the ether is a pure conception by aid of which we correlate in conceptual space various motions. These motions are the symbols by which we briefly describe the sequences and relationships we perceive between various groups of phenomena. The ether is thus a mode of resuming our perceptual experience ; but like a good many other conceptions of which we have no direct perception, physicists project it into the phenomenal world and assert its real existence. There seems to be just as much, or little, logic in this assertion as in the postulate that there is a real substratum, matter, at the back of groups of sense-impressions ; both at present are metaphysical statements. Now there is no evidence forthcoming that the ether must be conceived as either hard or heavy, 1 and yet it can be strained or its parts put in relative motion. Further, from Professor Tait's standpoint, it occupies space. Hence those who associate matter with hardness and weight must be prepared to deny that the ether is matter, or be content to call it non- matter. It is worth noting, at the same time, that the metaphysicians whether they be materialists asserting the phenomenal existence both of space and of a permanent substratum of sense-impression, or " com- mon-sense " philosophers asking us to knock our 1 I venture to think Sir William Thomson's attempt to weigh ether a retrograde step (see his Lectures on Molecular Dynamics, pp. 206-8, Baltimore, 1884). If the ether be a sufficiently wide-embracing con- ception, gravitation should flow from it, and this certainly was Sir William's view when he propounded the vortex atom. 316 THE GRAMMAR OF SCIENCE. heads against stone walls reach hopelessly divergent results when they say that matter is that which moves, that matter occupies space, and that matter is that which is heavy and hard. 8. Matter as non- Matter in Motion. There is, however, a still greater dilemma in store for the " common-sense " philosophers. We have not yet reached a clear conception of what the ether, the non-matter of our philosophers, consists in. There are in fact two, at first sight, completely divergent ways in which the ether is reached as a conceptual limit to our perceptual experience (see p. 217), but it is the great hope of science at the present day that "hard and heavy matter " will be shown to be ether in motion. In other words, it is well within the range of possibility that during the next quarter of a century science will have discovered that our symbolic description of the phenomenal universe will be immensely simplified, if we take as our symbolic basis for material groups of sense-impressions a type of motion of the conceptual ether ; in other, more expressive if less accurate, language, if we treat our friends' matter as their non- matter in motion. We shall then find that our sense- impressions of hardness, Weight, colour, temperature, cohesion, and chemical constitution, may all be described by aid of the motions of a single medium, which itself is conceived to have no hardness, weight, colour, temperature, nor indeed elasticity of the ordinary perceptual type. This would mean an immeasurably great advance in our scientific power of description. Yet if physicists even then persist in projecting the conceptual into the sphere of sense- impression, and in asserting a phenomenal existence MATTER. 311 for the ether, we should still be ignorant of what it is that moves, of what ether-matter may really consist in. Our analysis, therefore, of the various statements made by physicists and common-sense philosophers with regard to the nature of matter, shows us that they are one and "^metaphysical- that is, they attempt to de- scribe something beyond sense-impression,beyond per- ception, and appear, therefore, at best as dogmas, at worst as inconsistencies. If we confine ourselves to the field of logical inference, we see in the phenomenal uni- verse not matter in motion, but sense-impressions and changes of sense-impressions, coexistence and sequence, correlation and routine. This world of sense-impression science symbolizes in conception by an infinitely ex- tended medium, whose various types of motion corre- spond to diverse groups of sense-impressions, and enable us to describe the correlations and sequences of these groups. The moving elements of this medium can in thought be conceived of only as geometrical ideals, as points or continuous surfaces. To make our symbolic chart or picture agree the better with perceptual experi- ence, we find it necessary to endow these geometrical ideals with certain relative positions, velocities, and ac- celerations, the correlations of which are expressible in certain simple laws termed the laws of motion (see the following Chapter). If we choose to term the moving things of the conceptual chart matter, there can be no objection to the term, provided we carefully distinguish this conceptual matter from any meta- physical ideas of matter as the substratum of sense- impression, as that which perceptually moves, as that which fills space, or as that which can be defined as heavy, hard, and impenetrable. Conceptual matter is 312 THE GRAMMAR OF SCIENCE. thus merely a name for the geometrical ideals endowed with certain correlated motions by aid of which we describe the routine of our external perceptions. It is in this sense that we shall use the term matter for the remainder of this work, unless we are expressly referring to the matter of the metaphysicians. " Heavy " matter will be a name for the conceptual symbol by which we represent what we have termed material groups of sense-impressions, while ether- matter will be a name for the symbol by which we describe other phases of sense-impression, especially the correlation in space and time of sense-impressions belonging to diverse material groups. We shall not project our conceptions into imperceptibles in the field of perception (!) T -except in so far as it may be necessary in order to criticize current physical notions. We shall try and preserve throughout the standpoint that science is a description of perceptual experience by aid of conceptual shorthand, the symbols of this shorthand being in general ideal limits to perceptual processes, and as such having no exact perceptual equivalents. The reduction of " matter to non-matter in motion," of heavy-matter to ether-matter in motion, is so im- portant as a possible simplification of our scientific analysis of phenomena that we must devote a few pages to its discussion. We will term the fundamental element of heavy matter, the element out of which, 1 The reader may perhaps expect the words "unperceived things" father than " imperceptibles." But as every external perception is a group of sense-impressions, and as our senses are limited, the atom, if a real phenomena, could only appear sensible by colour, hardness, tem- perature, &c., the very sense-impressions it is conceived to describe. Hence, if the atom is to be not these things but their source, it may be truly termed imperceptible. MATTER, 313 perhaps, chemical atoms themselves are to be con- ceived as built up, the prime-atom. We have, them to ask what types of motion in the ether have been suggested as possible forms for the prime-atom. There are two suggestions to which reference may be made, both of which depend upon our postulating the same constitution for the ether. We must here make a brief digression in order to throw some light on this constitution of the ether. g. TAe Ether as Perfect Fluid" and " Perfect Jelly." The reader is certainly acquainted with two types of perceptual bodies which may be roughly described as liquid and elastic. As specimens of these two types we will take water and jelly. As substances water and jelly have a remarkable agreement in one respect and a remarkable divergence in another. If we put either water or jelly into a cylinder closed at the bottom and attempt to compress them by aid of a heavily-loaded piston, we shall find that the compres- sion is either insensible or of very small amount indeed. Careful experiments with elaborate apparatus show that these substances are compressible, but the amount of compression, although measurable, is exceedingly minute as compared, for example, with the amount that air would be compressed by the same load. We express this result by saying that both water and jelly, offer great resistance to one form of strain, namely, change of size (p. 243). But this resistance is only relative, relative to other substances, such as gases, and to the machinery of compression at our disposal. So far as our perceptive experience goes there is no substance which resists absolutely all change of size, and for which change of size is impossible. Hence 314 THE GRAMMAR OF SCIENCE. an incompressible substance is merely a conceptual limit which has not its equivalent in the world of phenomena, but which is reached in conception by carrying on indefinitely a process (or a classification of compressible bodies) starting in perception. Turning from this agreement to the divergence between water and jelly, we remark that if a lath of wood or even a knife-blade be pressed downwards on a jelly it requires considerable effort to shear or separate the jelly into two parts ; on the other hand, the water is separated by the lath without any sensible resistance. Now the change of shape we are in this case concerned with is of the nature of a slide (p. 245), and we say that the water offers little and the jelly considerable resistance to sliding strain. Here, again, the question of the amount of resistance is relative. So far as our perceptual experience goes, all fluids offer some, however small, resistance to the sliding of their parts over each other. The fluid which offers absolute resistance to compression and no resistance at all to slide of its parts, or the parts of which slip over each other without anything of the nature of frictional action, is only a conceptual limit. Such a fluid is termed a perfect fluid. On the other hand; by proceeding to the opposite limit in the case of an incompressible jelly, that is, by supposing it to resist absolutely change of shape by sliding, we should obtain a body incapable of changing its form by either compression or slide, and thus reach that conceptual limit, the rigid body. If we suppose absolute resistance to compression and partial resistance to slide, we have in conception a medium which might perhaps be de- scribed as a perfect jelly. Returning now to our ether, we note that physicists MATTER. 315 conceive it incompressible, but that for some purposes they appear to treat it as a perfect fluid, for other purposes as a perfect jelly .* This might at first sight appear a contradiction or conflict of conceptions, and it does undoubtedly involve difficulties which physicists are at present far from having thoroughly mastered. If we consider the ether as purely conceptual, then, in order to describe different phases of phenomena, we are certainly at liberty to first consider it as of one nature and then as of another. But in doing so it is evident that we are leaving room for a wider concep- tion which will resume both phases of phenomena at once, and will not lead us into logical contradictions if both phases have to be dealt with in the same in- vestigation. Thus, if the ether as a perfect fluid enables us to describe atoms by its types of motion, and the ether as a perfect jelly enables us to describe the radiation of light, it is clear that when we treat the atom as a source of light-radiations, we may get into serious confusion by the conception that the ether is at the same time a perfect fluid and a perfect jelly. We are compelled, indeed, to try and find some reconciliation between these two conceptions. If we turn to perceptual experience for a suggestion, we may note that water is the principal component of jelly, and may, by the addition of more or less gelatinous material, be stiffened to a jelly of any con- sistency. In the like manner we can conceive a series of perfect jellies formed, ranging in their resistance to slide, from the perfect fluid, through all stages of viscosity, up to the perfectly rigid body. We might, then, out of this series of jellies choose one which, for slid ing strains of a certain magnitude, was sensibly 1 For further purposes again scarcely as either. 316 THE GRAMMAR OF SCIENCE. a perfect fluid, while for smaller strains, such as are involved in the theory of light-radiation, it would act as a perfect jelly. This is the solution propounded in 1845 by Sir George G. Stokes, 1 and it may be termed the jelly-theory of the ether. The jelly- theory of the ether has undoubtedly been of value in simplifying many of our conceptions of physical phenomena, but how far it can be reconciled with any system of ether- motion as a basis for the prime-atom yet awaits investigation. 2 There is another possibility to which I can only briefly refer here namely, that the ether is to be conceived as a perfect fluid, but that just as a certain type of motion of this ether corresponds to the atom, so types of motion may be used to stiffen the ether, or to give it elastic rigidity. The ether may be a perfect fluid, but, owing to the turbulence of its motion, it may act for certain purposes as a perfect jelly. This hypothesis will be better appreciated when I have said a few words as to the ether-motions which may constitute the prime-atom. 10. The Vortex-Ring Atom and the Ether- Squirt Atom. In constructing an atom out of an ether-motion we have first to gain some idea of how it is possible that ether, not being itself hard or resisting change 1 Mathematical and Physical Papers, vol. i. pp. 125-29, and vol. ii. pp. 12-13. The present writer considers, however, that there is a difference in quality as well as in degree between a viscous fluid and an elastic medium. The complete difference in type between the equations of a plastic solid and a viscous fluid is sufficient evidence of this. In the former case, any shear above a certain magnitude produces set ; in the latter any shear whatever, if continued long enough. 2 For example, Sir William Thomson's vortex atom would hardly be a possibility. MATTER. 317 of shape, can yet be conceived to produce the sen- sations of hardness and resistance by its motion. Some general idea can easily be got of the sort of resistance produced by particular types of motion in the following manner : Take an ordinary spinning- top, and suppose we succeed by great care in balancing it on its peg. Clearly the least touch of the hand will upset it ; it offers no resistance to the motion of the hand. The same remark applies if the peg of the top were fixed by a ball-and-socket joint to the table. But, on the other hand, if the top be set spinning, we shall find the case entirely altered ; it will now present considerable resistance to being upset, and, if partially turned round its ball-and-socket joint, will tend to return to the old vertical position. A con- siderable number of such spinning-tops would offer a large amount of resistance to a hand passed over the table at a less distance than their height. This example may perhaps bring home to the reader how a certain type of motion may suffice to stiffen a body not otherwise stiff. Another example of motion stiffening a body is the smoke-ring, with which most devotees of tobacco are well acquainted. Two such smoke-rings will not coalesce ; they pass through or wriggle round each other, and round solid corners which come in their way, and, furthermore, their relative motion is easily seen to closely depend upon their relative position. Now we see smoke-rings because the moist particles in the smoke render the gaseous mixture visible, as similar particles render steam visible ; but we might blow air-rings in air, which would act precisely as the smoke-rings do, only they would be invisible. Such rings are termed vortex-rings ; and if we study the action of such 3l8 THE GRAMMAR OF SCIENCE. rings not in air or water but in our conceptual per- fect fluid, we shall find that, like atoms, they retain their own individuality ; they enter into combination, but cannot be created or destroyed. This is the basis of Sir William Thomson's vortex-ring theory of matter a prime atom, according to his theory, is an ether vortex-ring. 1 By the aid of vortex-motion, or spin- ning elements of liquid in a liquid, we are also able to conceive a liquid stiffened up to a required degree of resistance to sliding strain, and thus to replace the ether as a perfect jelly by the ether as a perfect fluid in a turbulent condition. 2 We can then dispense with Sir George Stokes' hypothesis of slight viscosity. But however suggestive these ideas may be for the lines upon which we may in future work out our concep- tions of ether and atom, they are very far indeed from being at present worked out, and there are many difficulties in the vortex-atom theory notably that of deducing gravitation which the present writer is not very hopeful will ever be surmounted. While Sir William Thomson's theory supposes that the substratum of an atom always consists of the same elements of moving ether, the author has ven- tured to put forward a theory in which, while the ether is still looked upon as a perfect fluid, the indi- vidual atom does not always consist of the same ele- ments of ether. In this theory an atom is conceived to be a point at which ether flows in all directions 1 For a fuller account of this theory see Clerk-Maxwell's article " Atom," in the Encyclopedia Britannica, or his Scientific Papers, vol. ii. pp. 445-84. See also as to spin producing elastic resistance Sir William Thomson's Popular Lectures and Addresses, vol. i. pp. 142-46 and 235-52. 2 See G. F. Fitzgerald : " On an Electro-magnetic Interpretation of Turbulent Fluid Motion," Nature, vol. xl. pp. 32-4. MATTER. 319 into space ; such a point is termed an ether-squirt. An ether-squirt in the ether is thus something like a tap turned on under water, except that the machinery of the tap is dispensed with in the case of the squirt. Two such squirts, if placed in ether, move rela- tively to each other, exactly like two gravitating particles, the mass of either corresponding to the mean 'rate at which ether is poured in at the squirt. From periodic variations of the rate of squirting, as influenced by the mutual action of groups of squirts, we are able to deduce many of the phenomena of chemical action, cohesion, light, and electro-magnetism. Indeed the ether-squirt seems a conceptual mechanism capable of describing a very considerable range of phenomena. It involves, of course, the conception of negative matter, or ether- sinks ; for the amount squirted into an incompressible fluid must be at least equalled by the amount which passes out. As, however, an ether-squirt and an ether-sink must be conceived to repel each other, there need be no surprise that we are compelled to consider our portion of the universe as built up of positive matter ; the negative matter, or ether-sinks, would long ago have passed out of the range of ether- squirts. 1 ii. A Material Loophole into the Super sensuous. Now the reader may naturally ask : Where can we 1 Carnelley, however, demanded an element of negative atomic weight, and a substance of negative weight is by no means incon- ceivable. Should the reader be interested in a mathematical account of this theory he may consult : " Ether-squirts; Being an Attempt to Specialize the Form of Ether-Motion which forms an Atom in a Theory propounded in former Papers," American Journal of Mathematics ; vol. xiii. pp. 309-62. See also Camb. Phil. Trans, vol. xiv. p. 71 ; London Math. Society, vol. xx. pp. 38 and 297. 32O THE GRAMMAR OF SCIENCE. conceive the ether to come from when it pours in at the squirt or prime-atom ? In taking the ether-squirt as a model dynamical system for the atom, we are not bound to answer this question in order to demon- strate its validity, any more than we are bound to explain why ether and atom themselves come to be. From our standpoint, they are justified as conceptions if they enable us to resume our perceptual experi- ence. But as there are many who will insist on project- ing the conceptual into the phenomenal field, I will endeavour to answer the question by suggestion. Suppose we had two opaque horizontal plane sur- faces placed close together, and containing between them water in which lived a flat fish, say a flounder. Now it is clear that the perceptions of our fish would be limited to motion forwards or backwards, to right or to left, but vertically upwards or downwards would be an imperceptible, and therefore probably inconceivable, motion for him. Now let us pass in conception to a limit unrealizable in perception ; let us suppose our flounder to get flatter and flatter, and the film of water thinner and thinner, as the planes are pressed closer together. The motion of the flounder and the motion of the water may then, for conceptual purposes, be supposed to take place in one horizontal plane. Now if we were to make a hole in one of the planes and squirt water in, it is clear that our flounder would experience new sense- impressions when he came into the neighbourhood of the squirt. Indeed the pressure produced by the flow of water might compel the flounder to circum- navigate the squirt that is, the squirt might be for him hard and impenetrable. Such squirts, although only water in motion, might form very material groups MATTER. 321 of sense-impressions for our fish. If, however, he were told that matter was formed of squirts, he would be quite unable to conceive where the squirt came from. It could be from neither forwards nor back- wards, neither from right nor left, for. it flows in in all these directions. The flounder would presume we were quite mad did we suggest that the water came vertically upwards or downwards ; that there was another direction in space " upward and outward in the direction of his stomach," as the author of Flat- land^- felicitously expresses it. Could the flounder get out of his space through the squirt through and out in the direction of matter he would reach a new FIG. 20. world, wherein he would perceive what squirts were, what his matter really consisted in. Through the eye of the needle, out through the matter of flatland, the flounder would reach the heaven of our three- dimensioned space, where we go up and down, as well as forward and backward, and to right and left. But for the flounder this " out through matter " would remain inconceivable, not to say ridiculous ; it would be to penetrate behind the surface of sense- impressions. Now this parable of the flounder is specially in- 1 Flatland: a Rotnance of Many Dimensions, by A Square. London, 1884. 22 322 THE GRAMMAR OF SCIENCE. tended for those minds which, strive as they will, cannot wholly repress their metaphysical tendencies, which must project their conceptions into realities beyond perception. The danger of this meta- physical speculation lies in the frequency with which it contradicts our perceptual experience when it passes from the " beyond " of sense-impression to the world of phenomena. Now a happy conception as to how the prime-atom is to be constructed, fitting in with all our perceptual experience (that is, enabling us to describe it symbolically with great accuracy), might leave a loophole for the metaphysical mind to pass to something which does not symbolize the per- ceptual, and therefore might dogmatically be assumed to belong to the supersensuous. Out from our space through the ether-squirt, out through matter we in conception pass, like the flounder, to another dimen- sioned space. This space has for a number of years past formed the subject of elaborate investigations by some of our best mathematicians, 1 and it possesses this great advantage : that when we pass from the conclusions drawn for this higher space to the space of our perceptual experience, then we are not involved in the contradictions which abound in the transition from the older metaphysics to our physical experi- ence. Here in this new playroom, entered, perhaps, by the doorway of matter, metaphysician and theologian can for the present safely spin beyond the sensible the cobwebs, which have been swept away by the scientific broom whenever they encumbered the habitable apartments of knowledge. The necessary mathematical equipment required for genuine re- search in the field of higher-dimensioned space will 1 Riemann, Helmholtz, Beltrami, and Clifford. MATTER. 323 at any rate act as a safeguard against over light- hearted expeditions "beyond the sensible"! Should a time ever come, which may, perhaps, be doubted, when a happy conception as to the structure of the prime- atom is discovered to be a perceptual fact, then if such a conception involves the existence of four-dimen- sioned space, 1 our friends will have done yeoman service in preparing a way for a scientific theory of the supersensuous out through the doorway of matter ! 1 2. The Difficulties of a Perceptual Ether. But we have romanced enough for the sake of the metaphysically-minded. Returning to the solid ground of fact, we have to remember that no hypothesis as to the structure of the prime-atom from ether in motion is at present scientifically accepted ; no model dynamical system for the atom has as yet been shown to have such a wide-reaching power of describing our perceptual experience that it has passed from the field of imagination and become a current symbol of scientific shorthand. Nor is the reason far to seek ; we desire to construct, if pos- sible, the prime-atom from an ether-motion, but our conceptions of the ether are at present very ill-defined. 1 The ether-squirt is not the only atomic theory which suggests a space beyond our own. Clifford imagined matter to be a wrinkle in our space, which suggests the idea of another space to bend it in. This notion of Clifford's may, perhaps, be brought home to our reader by imagining the flounder rigidly flat and a crumple or wrinkle in his plane of motion. The wrinkle would, like matter, be impenetrable to the fish ; he could not fit it ; either the wrinkle or he would have to get out of the way. This non-fitting of two kinds of space has not hitherto, however, been developed as a mode of describing any of our fundamental physical experiences. 324 THE GRAMMAR OF SCIENCE. We are agreed that it must be conceived as a medium which resists strain, but we are not certain how to represent best the relative motions that follow on relative change in the position of the ether-ele- ments. We are not yet satisfied with a perfect fluid, a perfect jelly, or even a turbulent perfect fluid con- ception of the ether. Treating the ether not as a conception but as a phenomenon, we find it difficult to realize how a con- tinuous and same medium could offer any resistance to a sliding motion of its parts, for the continuity and sameness would involve, after any displacement, every- thing being the same as before displacement The idea of a perfect jelly appears to involve some change in structure as we magnify smaller and smaller elements larger and larger. Finally, any relative motion of translation as distinct from one of rotation seems excluded by the idea of absolute incom- pressibility. 1 It is not a metaphysical quibble when we demand that two things shall not occupy the same space, but that when motion begins there shall be somewhere unoccupied for something to move into. The obvious fact is that while in conception we can represent the moving parts of the ether as points, and we can endow these points with such relative velocities and accelerations as will best describe our perceptual experience, yet when we project the ether into the phenomenal world it is at once recognized as a concep- tual limit unparalleled in perceptual experience, and we do not feel at home with it. The old problems as to " heavy matter " recur. What is the ultimate element of the ether which moves ? and why does it * For absolutely incompressible elements (other than points) motion round any closed curve other than a circle seems inconceivable. MATTER. 325 move ? Build a perceptual matter out of a pheno- menal ether, and we have again thrust upon us the question as to ether-matter's nature. Is it also to be a terra incognita mine et in ceternum ? The mind again fails to rest in peace until it reaches somewhere the motion of a point, the sizeless ultimate element of matter postulated by Boscovich. We find our- selves again involved in the contradictions which flow from asserting a reality for motion in the phe- nomenal field. We are again forced to the conclusion that motion is a pure conception, which may describe perceptual changes, but cannot be projected into the phenomenal world without involving us in inexpli- cable difficulties. 13. Why do Bodies Move ? We have left but little space for the discussion of our second question : Why do bodies move ? But the answer to this question must be clear after what precedes. If we mean : Why do sense-impressions change in a certain manner ? then we have already seen what are the possibilities of knowledge on this point when considering consciousness, the nature of the perceptive faculty and the routine of perceptions (pp. 122-9). If we mean: Why do the geometrical symbols by which we conceptualize material groups of sense-impressions move in a certain fashion ? then the answer is, that after many guesses we have found these types of motion to be best capable of describing the past and predicting the future routine of our perceptions. If, however, any one persists in phenomenalizing our conceptual symbols of motion, then science can only reply to this question : Why does matter move ? We don't know. Let us suppose 326 THE GRAMMAR OF SCIENCE. that the earth actually moves in an ellipse round the sun in a focus, and then let us attempt to analyze the why of it. Well, conceptually we construct this motion out of a certain relative motion of the ele- mentary parts of sun and earth. We say that if these elementary parts have certain relative accelerations when in each other's presence, then the earth will describe an ellipse about the sun. These elementary parts may be looked upon as atoms or groups of atoms, but to save any hypothesis let us simply term them particles of matter. Now, why do two particles when in each other's presence move relative to each other in a certain fashion ? It will not do to answer : Owing to the law of gravitation. That merely de- scribes how they move. Nor can we say : Owing to the force of gravitation. That is merely throwing the answer on the beyond of sense-impression it is the metaphysical method of avoiding saying : We don't know. When we see two persons dancing round each other we assume that they do it because they wish to, because they will to. They cannot be said, if one is not holding the other, to enforce each other's motion. To attribute the dance to their common will is the sole explanation we can give of it. 1 When we find the ulti- mate particles of matter dancing about each other, we can hardly, like Schopenhauer, attribute it to their common will to dance thus, because will denotes the presence of consciousness, and consciousness we can- not logically infer unless there be certain types of material sense-impressions associated with it. Thus will, if it had any meaning as a cause of motion which we have seen it has not (p. 150) could not 1 See Appendix, Note V, MATTER. 327 help us with regard to our dance of material particles. All we can scientifically say is, that the cause of their motion is their relative position ; but this is no expla- nation of why they move when in that position. The difficulty cannot be surmounted by appealing to the notion of force. Of the metaphysical conception of force we have said enough (pp. 140 et seq.\ and we need not reconsider it here. But force is sometimes said to be a sense-impression we are said to have a " muscular sensation " of force. I will to push a thing with my hand, and on the will becoming action a " muscular sensation " occurs which is termed the exertion of force. But why is this more a sense-im- pression of force than a sense-impression of changes in the motion, or of relative accelerations in the particles of my finger-tips ? Add to this that the so-called " muscular sensation " of force is associated with a conscious being, or is a subjective side of some changes of motion in his person, and we see that it can throw absolutely no light on the reason why material particles move. " Force is a direct object of sense," write Sir William Thomson and Professor Tait 1 Force " is not a term for anything objective," writes Professor Tait. 2 In the face of such contra- dictions, is it not better to cease supposing that any lucid explanation of the why of motion can be abstracted from the idea of force ? But may not our particles, like two dancers, hold hands, and so the one " enforce " the other's motion ? We must not say that this holding hands is impossible, although they be 90,000,000 miles apart. We conceive 1 A Treatise on Natural Philosophy, part i. p. 220. Cambridge, 1879- 2 The Properties of Matter. Edinburgh, 1885. 328 THE GRAMMAR OF SCIENCE. light as easily traversing those 90,000,000 miles by aid of the ether, and may not our particles hold hands by means of the ether? All scientists hope that this may be so, at any rate conceptually, although they have not yet conceived how it can be so. But if we phenomenalized the ether and were able to describe by aid of it action at a distance of millions of miles, we should still be left with the problem : Why does the relative position of two adjacent parts of ether influence the motion of those parts ? It might seem at first sight easier to explain why two adjacent ether elements " move each other " than why two distant particles of matter do. The common-sense philosopher is ready at once with an explanation : They pull or push each other. But what do we mean by these words? A tendency when a body is strained to resume its original form ; a tendency in a certain relative position of its parts to a certain relative motion of its parts. But why does this motion follow on a particular position ? It is the old problem over again, with the difference that rela- tive position now involves small instead of large distances. It will not do to attribute it to the elas- ticity of the medium ; this is merely giving the fact a name. We do indeed try to describe the phe- nomenon of elasticity conceptually, but this is solely by constructing elastic bodies out of non-adjacent particles, the changes of position of which we associate with certain relative motions. In other words, to appeal to the conception of elasticity is only to "explain" one "action at a distance" by a second " action at a distance." If the ether-elements owe their elasticity to such an arrangement, we shall want another ether to " explain " the motion of the MATTER. 329 first, and the process will have to be continued ad infinitum. Clearly the phenomenalization of the ether is absolutely useless as a means of explaining why matter moves. It still leaves us with the same problem in another form : Why does ether-matter move ? And here no answer can be given. We can- not proceed for ever " explaining " mechanism by mechanism. Those, who insist on phenomenalizing mechanism must ultimately say : " Here we are ignorant" or, what is the same thing, must take refuge in matter and force. According to Paul du Bois-Reymond, the problem of action at a distance is the third Ignorabimus* but the problem is really identical with that of Emil du Bois-Reymond's first IgnorabimuSy the nature of matter and force. It seems to me that we are ignorant and shall be ignorant just as long as we project our conceptual chart, which symbolizes but is not the world of phenomena, into that world ; just as long as we try to find realities corresponding to geometrical ideals and other purely conceptual limits.. So long as we do this we mistake the object of science, which is not to explain but to describe by conceptual shorthand our perceptual experience. When we once clearly recog- nize that change of sense-impression is the reality, motion and mechanism the descriptive ideal, then the Brothers du Bois-Reymonds' first and third problems, and their cry of Ignorabimus become meaning- less. Matter and force and " action at a distance " are witch - and - blue - milk problems (p. 27), if mechanism be purely a conceptual description. What moves in conception is a geometrical ideal, and it moves because we conceive it to move. How it 1 See the work cited on our p. 46. 33O THE GRAMMAR OF SCIENCE. moves becomes the all-important question, for it is the means by which we regulate our mechanism so as to describe our past and predict our future experience. This how of motion is the point to which we must next turn. The laws of motion in the widest sense embrace all physical science perhaps it were not too much to say all science whatever. All laws, von Helm- holtz tells us, must ultimately be merged in laws of motion. Even such a complex phenomenon as that of heredity is at bottom, Haeckel holds, a transference of motion. Strong in her power of describing how changes take place, Science can well afford to neglect the why. She may not go so far as to fully accept even Emil du Bois-Reymond's second Ignorabimus, so long at least as psychology stands where it does ; but as to what consciousness is and why there is a routine of sense-impressions she is content for the present to say, " Ignoramus" SUMMARY. The notion of matter is found to be equally obscure whether we seek for definition in the writings of physicists or of " common-sense " philosophers. The difficulties with regard to it appear to arise from assert- ing the phenomenal but imperceptible existence of conceptual symbols. Change of sense-impression is the proper term for external perception, motion for our conceptual symbolization of this change. Of perception the questions " what moves " and "why it moves " are seen to be idle. In the field of conception the moving bodies are geometrical ideals. Of the du Bois-Reymonds' three cries of Ignorabimus, only the second in a modified sense is scientifically valuable, the others are un- intelligible, because we find that matter, force, and "action at a dis- tance " are not terms which express real problems of the phenomenal world. MATTER. 331 LITERATURE. BOIS-REYMOND, EMIL DU. Ueber die Grenzen des Naturerkennens. Leipzig, 1876. CLERK-MAXWELL, J. Articles " Atom " and " Ether " in the Encyclo- paedia Britannica, reprinted in the Scientific Papers, vol. ii. pp. 445 and 763. The article on the " Constitution of Bodies " may also be consulted with advantage. CLIFFORD, W. K. Lectures and Essays, vol. i. (" Atoms " and " The Unseen Universe "). London, 1879. TAIT, P. G. Properties of Matter (especially chaps, i.-v.). Edin- burgh, 1885. THOMSON, SIR WILLIAM. Popular Lectures and Addresses, vol. i. (especially pp. 142-52). London, 1889. CHAPTER VIII. THE LAWS OF MOTION. i. Corpuscles and their Structure. IN the last chapter we have seen how the physicist conceptually constructs the universe by aid of a vast atomic dance. I use the word atom although it is very probably the ultimate element of the ether, which we ought to talk about as the fundamental unit of the dance. Let us term this latter unit the ether- element, without intending to assert by the use of this word that the ether is necessarily discontinuous. 1 Two adjacent ether-elements will be the symbols, necessarily geometrical, by which we represent the relative motion of the parts of the ether. On the basis of the ether-element let us try and conceive how the physicist imagines his mechanical model of the universe constructed. Perceptual experience gives us no hint as to what we ought to conceive the ether-element to consist of, or how we ought to imagine it to act, if it could be isolated. But we are compelled to consider ether-elements when in each other's presence as moving in certain definite modes, as taking part in a regulated dance. Perceptually 1 If we suppose the ether to be a conceptual limit to a perceptual fluid or jelly (pp. 313 and 328), then to conceptualize at all its trans- mission of stress or its elasticity we are, I think, compelled to suppose it discontinuous. THE LAWS OF MOTION. 333 there is no reason for this dance, conceptually it enables us to describe the world of sense-impres- sions. Probably, although this point is far from being definitely settled, one type of motion among the ether-elements may be conceived as constituting the prime-atom. These prime-atoms, the protyle of Crookes, are to be taken as symbols of the ultimate basis of material groups of sense-impressions, or, in ordinary language, of gross or sensible " matter." Prime-atoms in themselves, or, what is more likely, in groups, form the atom of the chemist, the con- ceptual substratum of the so-called simple elements such as hydrogen, oxygen, iron, carbon, &c., by aid of which the chemist classifies all the known heavy matter of the physical universe. If the prime-atom of the physicist is really the atom of the chemist, then the prime-atom must be conceived as having variations either in its structure or in its type of motion corresponding to the different chemical ele- ments. There are certain perceptual facts, however, which suggest that we should describe phenomena best by conceiving the atom of the simple chemical element to be constructed from groups of prime-atoms, the disassociation of which corresponds to no defi- nite perceptual results which the chemist has hitherto succeeded in attaining. Out of the atoms of the simple elements the chemist constructs compounds ; that is, by combining conceptually these atoms in certain groupings he forms the molecule of the com- pound. Thus two atoms of hydrogen and one of oxygen are united to form the molecule of water. Any portion of the compound substance itself is conceived as composed of an immense number of 334 THE GRAMMAR OF SCIENCE. molecules. In order to describe the sense-impres- sions which we physically associate with a " piece of a given substance " we are bound to postulate that the smallest physical element of it is to be con- sidered as containing millions of molecules. 1 If we take a piece of any substance, say a bit of chalk, and divide it into small fragments, these still possess the properties of chalk. Divide any frag- ment again and again, and so long as a divided fragment is perceptible by aid of the microscope it still appears chalk. Now the physicist is in the habit of defining the smallest portion of a substance which, he conceives, could possess the physical properties of the original substance as a particle. The par- 1 The reasons for this statement are chiefly drawn from the Kinetic Theory of Gases. Clerk-Maxwell in his article "Atom" {Encyclopedia Britannicd) considers that the minitmtm visibile of the present day may be conceived as containing sixty to one hundred million atoms of oxygen or nitrogen. He proceeds to draw from this result conclusions, which I think quite unwarranted, as to our power of describing by aid of molecular structure the physiological facts of heredity. He remarks that : " Since the molecules of organised substances contain on an average fifty of the more elementary atoms, we may assume that the smallest particle visible under the microscope contains about two million molecules of organic matter. At least half of every living organism consists of water, so that the smallest living being visible under the microscope does not contain more than about a million organic molecules. Some exceedingly simple organism may be supposed built up of not more than a million similar molecules. It is impossible, however, to conceive so small a number sufficient to form a being furnished with a whole system of specialized organs." This reasoning is simply a form of special pleading based on the assump- tion that variations in physiological organs depend solely on chemical constitution and not on physical structure. Why are we to put on one side the facts that there are upwards of fifty atoms in the organic molecule, that there is a certain proportion of water, and that these organic molecules must be conceived as closely packed into a scarce visible germ ? Why are these one hundred million atoms not to be conceived as physically influencing each other's motion ? If this be so, THE LAWS OF MOTION. 335 ticle is thus a purely conceptual notion, for we cannot say when we should reach the exact limit of subdivision at which the physical properties of the substance would cease to be. But the particle is of great value in our conceptual model of the universe, for we represent its motion by the motion of a geometrical point. In other words, we suppose it to have solely a motion of translation (pp. 237 and 246) ; we neglect its motions of rotation and of strain. The physicist has here reached a purely conceptual limit to perceptual experience ; he takes a smaller and smaller element of gross " matter," and supposing it always to be of the same substance (i.e., to produce the same sense- impressions although it becomes imperceptible), he deals with it as a moving point. What right has the physicist to invent this ideal particle ? He has never perceived the limiting quantity, the minimum esse of a substance, and therefore cannot assert that it would not produce in him sense-impressions which could only be described by aid of the concepts spin and strain. The logical right of the physicist is, however, exactly that on which all scientific conceptions are based. We have to ask whether postulating an ideal then their relative position, the structure of the germ as a dynamical system, may be shown to involve no less than 10,000 million million periodic motions, having various relative positions in space, and apart from this relative position having in amplitude, phase, and " note," three hundred million variables at the disposal of the physiologist ! Whether heredity can or cannot be described by the influence of such a molecular structure on other molecules is quite beyond our present scientific knowledge to determine ; but we certainly cannot dogmatically assert with Maxwell that : " Molecular science sets us face to face with physiological theories. It forbids the physiologist from imagining that structural details of infinitely small dimensions can furnish an explana- tion of the infinite variety which exists in the properties and functions of the most minute organism ." 336 THE GRAMMAR OF SCIENCE. of this sort enables us to construct out of the motion of groups of particles those more complex motions by aid of which we describe the physical universe. Is the particle a symbol by aid of which we can describe our past and predict our future sequences of sense- impressions with a great and uniform degree of accuracy ? If it be, then its use is justified as a scientific method of simplifying our ideas and econo- mizing thought. The reader must note that this hypothesis of the particle is made use of by Newton in the statement of his law of gravitation : " Every particle of matter in the universe attracts every other particle" he tells us, in such and such a manner. Yet Newton is here dealing with conceptual notions, for he never saw, nor has any physicist since his time ever seen, individual particles, or been able to examine how the motion of two such particles is related to their position. The justification of the law of gravitation lies in the power it gives us of constructing the motion of the groups of particles by aid of which we symbolize physical bodies and ultimately describe and predict the routine of our sense-impressions. The particle, therefore, as the symbolic unit of physical substance with its simple motion of translation is as valid as the law of gravita- tion, in the statement of which it is indeed involved. Lastly, groups of particles bounded in conception by continuous surfaces are the symbols by which we represent those material groups of sense-impressions that are currently spoken of as physical bodies or objects. To find the simplest possible types of relative motion for these various concepts, and thence to con- struct the motion of the geometrical forms by which we symbolize physical bodies, so that the motion de- THE LAWS OF MOTION. 337 scribes to any required degree of accuracy our routine of sense-impressions, is the scope of physical science. We find that by assuming certain laws for the relative motion of these conceptual symbols the laws of motion in their widest sense we are able to construct. a world of geometrical forms moving in conceptual space and time, which describe with wonderful exact- ness the complex phases of our perceptual experience. 2. The Limits to Mechanism. Let us now resume the elements of our conceptual model of the physical universe in a purely diagram- matic manner. 1 An asterisk shall represent the ether- QD * ., *;.** \,t **' ETHER-UNITS PRIME ATOM CHEMICAL ATOM MOLECULE (-;) PARTJCLU-V) BODY FIG. 21. element, a ring of asterisks will suggest the prime-atom probably constructed from a special ether-element motion for example, a vortex- ring. One, two, or more-prime atoms form the chemical atom, and for its symbol we will take three interlaced rings. Com- binations of chemical atoms form the molecule, in our diagram represented by two chemical atoms of three and one of two prime atoms. Millions of these mole- cules, of which we can only represent a few by the shorthand symbol /, would form the particle (short- hand symbol i/), while millions of particles, here 1 The diagram is only to suggest the physical relationships to the reader, and has no meaning from the standpoint of relathe size or form. 23 338 THE GRAMMAR OF SCIENCE. merely suggested, conceptually enclosed by a con- tinuous surface, symbolize the physical bodies of our perceptual experience. These concepts, it must be borne in mind, from ether-element to particle, have no perceptual equivalents, and it is only by experiments on the perceptual equivalent of the last of the series, the conceptual body, that the physicist is able to test the truth of the laws of motion he propounds. In the first place he postulated these laws for par- ticles, and demonstrated their validity by showing that they enabled him to describe the routine of his sense-impressions with regard to physical " bodies." But with the growth of our ideas as to the nature of ether and gross " matter," we naturally begin to question whether the laws which describe the relative motion of two particles are to be conceived as holding for two molecules, two chemical atoms, two prime-atoms, and ultimately for two ether-elements. Or, what may possibly be still more important, are they to hold for the relative motion of a prime-atom and adjacent ether-elements ? How far are we to consider the laws of motion as applied to particles of gross " matter " to result from the manner in which particles are built up from molecules, molecules from atoms, and ultimately atoms probably from ether-elements ? Now this is a very important issue, and one which does not appear to have always been sufficiently regarded. If we assume that the particle is ultimately based on a certain type of ether-motion, then we must admit the existence of other types of ether-motion which do not constitute gross " matter." In this case it will by no means follow that the relative motion of two particles, or of two prime-atoms, will follow the same laws as the relative motion of two ether-elements. It is quite THE LAWS OF MOTION. 339 clear, of course, that modes of motion peculiar to gross " matter " must arise from its special structure, and not be assumed to flow from laws applying to all moving things. For example, gravitation, magnetization, electrification, the absorption and emission of heat and light are all phases of sense-impression which we associate with gross " matter," and therefore they must be described by modes of motion characteristic of gross " matter," or modes which flow from its peculiar constitution. As kinetic formulae or special laws of motion they cannot be extended to the ether in general. But there are still more general laws of motion, which we may describe as the Newtonian laws, and which certainly when applied to particles are confirmed by our perceptual experience of bodies. Ought we to assert that these laws hold in their entirety for all the scale from particle to ether- element ? Shall we find our conceptual description of the universe simplified, or the reverse, by sup- posing complete mechanism to extend from particle to ether-element ? Or will it be more advantageous to postulate that mechanism in whole or part flows from the ascending complexity of our structures, that the ether-element is largely the source of mechanism, but is not completely mechanical J in the sense of obeying the laws of motion as given in dynamical text-books ? The question is undoubtedly an important one, but one which cannot be answered offhand. Nor, indeed, till we have much clearer con- ceptions of the structure of the prime-atom than we have at present reached, will it be possible to say how 1 For example, as will be shown in the sequel, the "mass "of a particle must be considered as in all probability very different from the " mass " of an ether-element (p. 368). 340 THE GRAMMAR OF SCIENCE. far the mechanism we postulate of particles may be conceived to flow from its structure. In order to remind the reader that the general laws of motion we are about to discuss may either entirely or only in part hold for the whole series of physical con- cepts from particle to ether-element, we will class the whole series together as corpuscles^ a word simply signi- fying little elementary bodies. We shall then have to ask in each case to which of the ideal corpuscles we are to suppose our laws to apply. The test will always be the same, namely : How far is the assumption neces- sary in order to obtain a model which will enable us to describe briefly the routine of perception ? 3. The First Law of Motion. Let us now return to our conception of the universe as the regulated dance of the elemental groups which we have termed prime-atoms, chemical atoms, mole- cules, and particles. Individual corpuscles dance in groups, groups dance round groups, and groups of groups dance relatively to each other. How, we have next to ask, do two corpuscles dance with regard to each other ? In the first place we must observe that, at least in the case of gross " matter ", a corpuscle which is conceived as forming part of the sun must be considered as regulating its dance with due regard to a corpuscle forming part of the earth. We cannot assert that it would not be best to con- ceive this as really done through a chain of part- ners, namely, ether-elements intervening between the sun and earth corpuscles, but as we have not yet settled how this chain of partners is to act, we must content ourselves at present by the statement that sun and earth corpuscles do regard each other's THE LAWS OF MOTION. 341 presence. But if they can do this at 90 million miles, there is every reason for inferring no breach in continuity and supposing they would also do it at 90 billion miles. We note, however, at once that it is necessary to conceive a particle at the surface of the earth paying more attention in its dance to an earth particle than to a sun particle, and again the phenomenon of cohesion tells us that two adjacent particles of the same piece of substance pay more heed to each other than particles of different pieces. Hence we conclude that : (i) in general terms corpuscles must be conceived as moving with greater regard to their immediate partners in the dance than to their near neighbours, and with greater regard to near neighbours than to still more distant corpuscles ; but, (2) there is no limit to the distance at which we conceive corpuscles can influence each other's motion. This influence may, however, be so small that even when summed for the bodies that we construct from corpuscles, there is no perceptual equivalent to be found for it by aid of any instrument at our disposal. We can now state a first general law of motion : Every corpuscle in the conceptual model of the universe must be conceived as moving with due regard to the presence of every other corpuscle, although for very distant corpuscles the regard paid is extremely small as compared with that paid to immediate neigh- bours. If the reader once grasps that every corpuscle in the universe must be conceived as influencing the motion of every other corpuscle, he will then fully appreciate the complexity of the corpuscular dance by aid of which we symbolize the world of sense-impres- 342 THE GRAMMAR OF SCIENCE. sions. The law of motion just stated probably applies to prime-atoms, and through them to chemical atoms, molecules, and particles. Possibly it does not apply to distant ether-elements directly, but these, perhaps, influence each other's motion only indirectly by directly influencing the motion of their immediate neighbours. In this case the " action at a distance " generally asserted of corpuscles of gross " matter," may very probably be conceived as due to the action between adjacent ether-elements. We should then have to state the first law as follows : Every corpuscle, whether of ether or gross " matter" influences the motion of the adjacent ether corpuscles, and through them of every other corpuscle, however dis- tant ; the influence thus spread is nevertheless very insignificant at great as compared with small distances. 4. The Second Law of Motion, or the Principle of Inertia. Now, in constructing the universe conceptually from our corpuscles, it is impossible to take into account the influence of all the corpuscles upon each other at one and the same time. Accordingly we neglect at once influences which even in the aggregate are beyond our powers of measurement. Further, we purposely exclude from consideration slight, if measurable, variations of motion due to more distant groups. We isolate a particular group of corpuscles, and this group which we deal with conceptually apart from the rest we term, for the purposes of some particular discussion, The most limited field that we can conceive is that of a single corpuscle. If we could isolate such a corpuscle from the rest of the conceptual universe, how would it move ? At first sight the question is absurd, because THE LAWS OF MOTION. 343 in Chapter VI. (p. 247) we saw that motion is mean- ingless if it be not relative to something. The moment, however, we introduce a second corpuscle into the field in order to measure the motion of the first, they begin to pay regard to each other's presence, and we are no longer dealing with the motion of an isolated corpuscle. But we have seen that the greater the distance between the corpuscles, the less this influ- ence must be conceived to be ; hence we may take the conceptual limit by supposing that the corpuscles are so far off that their mutual influence is negligible, while their mutual presence will still suffice to mark a relative motion. 1 Now in order that the laws which govern the motion of corpuscles shall lead to the con- struction of complex motions, fully describing the phases of our perceptual experience, we are compelled to suppose that the more and more completely we separate one corpuscle from the influence of a second corpuscle, the more and more nearly does its motion relative to the second corpuscle cease to vary. The first corpuscle either remains at rest relatively to the second or continues to move with the same speed the same number of miles per minute in the same direction. But this is what we term uniform motion, or motion without acceleration (pp. 276-7), and we are thus endowing our corpuscles with a very important property, namely, we assert that they will not dance, that is, alter their motion, unless they have partners to dance with. This characteristic of cor- 1 The reader must remember that relative position is conceptualized by a directed step and that it is a series of directed steps which form the path of the relative motion (p. 250). Each directed step is to be con- ceived as " fixed " in direction, *. This definition leads us to two important points. We see, namely, that the mass of a corpuscle has relation to some standard corpuscle, or mass is always a relative quantity ; and, further, mass is a mere number representing a ratio of accelerations. We have here, then, a perfectly clear and intelligible definition ; we can grasp what velocity means, and we can under- stand how its change is measured by acceleration. Mass, accordingly, as the ratio of the numbers of units in two accelerations, is a conception which can easily be appreciated. It is in this manner that mass is invariably determined scientifically, yet neverthe- less the reader will frequently find mass defined in text-books of physics as " the quantity of matter in a body." After our discussion of matter in Chapter VII. the reader will easily appreciate how idle is a definition of mass in terms of matter. 1 1 Quantity belongs essentially to the sphere of sense-impression. We cannot consider it to have any meaning when projected beyond that sphere. It seems, therefore, illogical to apply the word quantity to the metaphysical "source" of sense-impressions. THE LAWS OF MOTION. 3 59 9. The Fifth Law of Motion. The Definition of Force. We can now pass to the next stage in our investi- gation of the corpuscular dance. Having selected a standard corpuscle Q, we conceive the masses rela- tive to it of many other corpuscles A, B, C, &c. measured. If we tabulated these masses and then compared them with the ratio of the mutual accelera- tions of A and B, B and C, C and A, &c., with a view of ascertaining whether there were any relation between the mutual accelerations of each pair and their masses, we should very soon discover a fifth important law of motion, namely, that the ratio of the acceleration of A due to B to the acceleration of B due to A is exactly equal to the ratio of the mass of B to the mass of A, or in simple algebraical notation : Acceleration of A due to B Mass of B , x L- = , , (y) Acceleration of B due to A Mass of A This is expressed briefly by the statement that mutual accelerations are inversely as masses. The validity of this statement is demonstrated in precisely the same manner as the fourth law of motion. We note that if 'unity be taken as representing the mass of the standard corpuscle, 1 Q, the definition of mass on p. 358 may be replaced by the formula :>- Acceleration of Q due to A _ Mass of A , Acceleration of A due to Q Mass of Q a result in perfect accordance with the law just stated. Now this law may be put into a slightly different form. By a well-known proposition 2 the product of 1 That is, the ratio of the mutual accelerations of Q and an absolutely identical corpuscle. These accelerations must by symmetry be exactly equal, and hence their ratio, the mass of Q, must be taken as unity. 2 Euclid, vi. 1 6, interpreted arithmetically. 360 THE GRAMMAR OF SCIENCE. the means in any proportion is equal to that of the" extremes. Hence it follows that : Mass of A X Acceleration of A due to B is equal to Mass of B X Acceleration of B due to A; We will, then, give a name to this product of mass into acceleration ; we will term the product of the mass of A into the acceleration of A due to the presence of B, the force of B on A. This force will be considered to have the direction and sense of the acceleration of A due to B, while its magnitude will be obtained by multiplying the number of units in the acceleration of A due to B by the number of units in the mass of A. Thus the proper measure of a force will be its number of units of mass-acceleration. Remembering that the accelerations of A and B are of opposite sense, we can now restate our fifth law in new language, thus : The force 0/B on A is equal and opposite to the force of A on B ; Or, as it was originally stated by Newton himself: " 'Action and Reaction are equal and opposite " I . . (t). Now it is clear that with our definition force is a certain measure of how a corpuscle is dancing relative to a second corpuscle, this measure depend- ing partly on the individual character of the first corpuscle (its mass) and partly on the attention it is paying to the presence of a second corpuscle (its acceleration due to the second corpuscle). That this measure is scientifically a convenient one is proven by its general use, and may be almost fore- seen by comparing the simplicity of the statement 1 " Actioni contrariam semper et aquaUm esse reactiondn" THE LA\VS OF MOTION. 361 (e) with the complexity of (7). The definition of force we have reached is a perfectly intelligible one ; it is completely freed from any notion of matter as " the moving thing," or from any notion of a meta- physical " cause of motion." We have only to take the step which represents the acceleration of A due to B's presence and to stretch or magnify its length in the ratio of A's mass to the mass of the standard body Q, and we have a new step which represents B's force on A. Force is accordingly an arbitrary con- ceptual measure of motion without any perceptual equivalent. The distinction between the definition of force thus given and that to be found in the ordinary text- books * may at first sight seem slight to the reader, but the writer ventures to think that the distinction makes all the difference between an intelligible and an unintelligible theory of life, between sound physical science and crude metaphysical materialism. Causa- tion, as we have had occasion more than once to point out, is only intelligible in the perceptual sphere as antecedence in a routine of sense-impressions. In the conceptual sphere, on the other hand, the cause of change in the motion of our corpuscles lies solely in our desire to form an accurate mechanical model of the world of phenomena. For every definite con- figuration of the corpuscles we postulate certain mutual accelerations as a mode of bringing our mechanism into tune with our sense-impressions of 1 "Force is any cause which tends to alter a body's natural (sic!) state of rest, or of uniform motion in a straight line " (Tait's Dynamics of a Particle, art. 53). It is perhaps unnecessary to remark that we cannot conceive any body to be naturally at rest or moving in a straight line, unless the word natural be re-defined in some artificial sense. 362 THE GRAMMAR OF SCIENCE. change. Force as an arbitrary measure of these conceptual changes in motion is intelligible. On the other hand, to project the cause of motion into something behind sense-impression is to dogmatically assert causation where we cannot know, to illogically infer from the like to the unlike (pp. 72, 1 86). The only alternative is to consider force as an antecedent group of sense-impressions ; this, however, is not only to project our purely conceptual notions of motion into the perceptual field, but it throws upon us the duty of defining the particular group of sense-impressions to which force corresponds. We have already spoken of the " muscular sensation of force " (p. 327), which, if we project conceptions into the perceptual field, is more accurately to be described as a sense-impression of mutual acceleration indissolubly linked to the fact of consciousness. It throws absolutely no light on the cause of motion in such " automata without consciousness," as we must conceive " phenomenal corpuscles " to be. Hence, whichever way we turn, the current definitions of both mass and force lead us only into metaphysical obscurity. Mass as the quantity of matter in a body, matter as that which perceptually moves, force as that which changes its motion, are solely and purely names which serve to cloak human ignorance. This ignorance is at bottom the ignorance of why there is routine in our sense- impressions, and with this question of routine we have already fully dealt (pp. 122-8). But science answers no why it simply provides a shorthand description of the how of our sense-impressions ; and it therefore follows that if mass and force are to be used as scientific terms they must be symbols by aid of which we describe this how. It is thus that THE LAWS OF MOTION. 363 I have dealt with them ; we have seen that to briefly describe the corpuscular dance, which forms our con- ceptual model of the universe, the notions of mass and force as based on mutual accelerations arise naturally and with intelligible definitions. 10. Equality of Masses Tested by Weighing. Although it is impossible for us to review the whole field of mechanics, it is still necessary to in- dicate to the reader that our definitions of mass and force would ultimately lead us to the same conclu- sions as he will find in current physical text-books. In the first place we will investigate an elementary problem which will lead us to a mode of testing the equality of masses. Suppose we had two particles A and B of masses m & and m\> in the same field, and we will suppose them placed in a horizontal line, A to the left and B to the right. Now, owing to the presence of some system to the left of A, which we need not definitely describe, we will suppose A to have an acceleration represented by g units horizon- tally to the left. Similarly B, owing to some other system, shall have a horizontal acceleration of g units to the right. Further, A and B will mutually accele- rate each other, and we will represent B's acceleration of A from left to right by the symbol f\^ and A's of B by./ab> which will be in the opposite sense. We are going to choose a particular " physical field " for the acceleration of A and B ; they shall be linked together so that their distance cannot change, but the link itself shall be conceived as producing no accelera- tions in either A or B. We might conceptualize this link by aid of a limit to actual perception, namely, by a fine weightless and inextensiblc string. Such a 3^4 THE GRAMMAR OF SCIENCE. string would not in itself produce sensible accelera- tions in A or B. Since the string is inextensible, the whole system must move in the same direction, say from right to left. Then clearly the velocity of A must be at all times equal to the velocity of B, or the string would be stretched. But if the velocities of A and B are always equal, their accelerations must also FIG. 23. be equal, or their velocities, being differently spurted, would begin to differ. Hence we conclude that the total acceleration of A towards the left must be equal to the total acceleration of B in the same direction, or in symbols : /ba=/ab (f.). But by the fifth law of motion (i.e. (y), p. 359) - a = (ii) /ab m a 1 1L ' THE LAWS OF MOTION. 365 Thus (i.) and (ii.) are two simple relations to find f^ and /ab- By elementary algebra we have : = 2 Hence we deduce : Acceleration of A or B to the left = g / ba = " /a ~ ;;/b ^ . . (iii. ) ;//a + ;/Zb Further : Force of B on A = mass of A X acceleration of A due to B. = /a X / ba , P, = Wb X j^b, or Force of A on B. Now this force of B on A is what we usually term the tension in the string. Hence we have : Tension in the string = 2 -^ a -^- ..... (iv.). Wa. + ^b A further important point has now to be noticed. In order that A and B should be at rest relative to the field which produces the acceleration g t it will be necessary that their velocities should always be zero, and this involves that the changes in their velocities, or their accelerations, should always be zero. But the only way in which these accelerations can be zero is seen at once from (iii.) to arise from m & and m\> or the masses of A and B, being equal, for then the dif- ference, m & m\> is zero. Thus rest will depend on the equality of the masses of A and B. A further conceptual notion can now be introduced, namely, that the terminal physical effects consequent sense-impressions are not altered in magnitude, only in direction, by carrying a weightless inextensible 366 THE GRAMMAR OF SCIENCE. string round any " perfectly smooth " body. This again is a purely conceptual limit to a very real per- ceptual experience. Now we will suppose our string placed round a perfectly smooth horizontal cylinder or peg inserted under it at its mid-point C, so that the portions eA, e'E of the string hang vertically downwards. We can further suppose that the par- ticular systems, which produce the acceleration g in both A and B, are now replaced by the single system of the earth, for Galilei has demonstrated that all particles at the same place on the surface of the earth are to be conceived as having the same vertical acceleration (g) towards the surface. We conclude, therefore, that if two particles be connected by a weightless inextensible string placed over a perfectly smooth cylinder, the acceleration of one downwards and the other upwards is given by the relation (iii.) and the tension in the string by (iv.). Hence, if the particles are to be at rest, or to " balance each other," their masses must be equal. In this case, since m & = ;;/ b , the tension in the string equals m & X g, or equals the product of the mass of A into the acceleration of A due to the earth ; that is, equals the force of the earth on A. This force is termed the iveight of A, and since m & ~ m^ it follows that the weight of A is equal to the weight of B. In this investigation, therefore, we have reached the simplest conceptual notion of a weighing-machine an inextensible string, with the particles suspended from its extremities, placed over a smooth cylinder. If the weights of the particles are equal, their masses will also be equal, and they will balance. Thus equality of masses may be tested by weighing. Another important result also flows from this dis- THE LAWS OF MOTION. 367 cussion. If a particle suspended by a string be at rest relative to the earth, then its weight will be equal to the tension in the string. Hence, if the earth-acceleration g at any place be known, we have a means of measuring mass in terms of tension. A further development of this principle forms the basis of important methods of determining the equality of masses by the equality of strains (p. 242) due to equal tensions. 1 1 . How far does the Mechanism of the Fourth and Fifth Laws of Motion extend? Before we conclude this discussion of mass, there are still several points with regard to it which must be elucidated even in an elementary work like the present. We have first to ask whether our fourth and fifth laws of motion, with the definitions of mass and force involved in them, must be conceived as holding for the whole range of corpuscles from ether- element to particle. The same difficulty, of course, arises with regard to force as arose with regard to acceleration, if we conceive prime-atoms as pos- sibly, and chemical atoms and molecules as almost certainly, extended bodies. There cease to be defi- nite points between which the mutual accelerations, and accordingly the forces, act. We are thrown back on the conception that if these laws are to be applied to atoms and molecules, it must be to the action and re- action between the elementary parts of those corpuscles and to the masses of the elementary parts that our laws refer. From the action of these elementary parts on each other we must, then, deduce by aid of the above laws the total action between two atoms or two molecules. This will not necessarily be mea- 368 THE GRAMMAR OF SCIENCE. surable by a single force acting between two definite points. Further difficulties, however, arise with regard to our conception of mass. Is the mass of an ether- element of the same character as the mass of an atom, or a molecule, or a particle ? This seems very doubtful indeed. If the ratios of the mutual accelera- tions of two ether-elements, of two atoms and of two particles be each in themselves constant and capable of leading us to a clear definition of mass for each type, it is still by no means certain whether the ratio of the mutual accelerations of an ether-element and a particle are inversely as the ratio of the ether- element mass to the particle mass. Possibly we cannot conceive these masses measurable by the same standard. If the prime-atom consist of ether in motion, then its mass would certainly vanish with this motion ; but the ether-elements which formed the prime-atom would still retain their ether-mass. Hence it seems likely that the possibility of a velocity entering into the mass of gross " matter " may hinder us from asserting that the ratio of the mutual accelerations of ether-element and particle is "inversely as their masses." Thus the idea of mechanical action and reaction between ether and gross " matter " becomes very obscure. Of the validity of postulating these laws for particles there can be small doubt ; 'they may pos- sibly suffice to describe the relation of ether-elements to each other, but they cannot be dogmatically asserted of the action between ether and gross " matter." I have purposely led the reader to these difficult and still unsettled points, because physicists finding that certain laws of motion applied to par- LAWS OF MOTION; 369 tides will suffice to describe our perceptual experience of physical bodies, are, I venture to think, too apt to assert that these same laws hold throughout the whole of the conceptual model by which they describe the universe. They would admit that special modes of acceleration like gravitation, magnetiza- tion, &c., &c., probably flow from the manner in which the prime-atom and the particle are to be conceived as constituted. But there may be more than this to be admitted the greater part of the laws of motion as we state them for particles may also flow from the peculiar structure of the particle. They may largely result from the nature we postu- late for the ether and from the particular types of ether-motion by aid of which we construct the various phases of gross " matter." It is not, therefore, questioning the well-established results of modern physics when we ask whether to conceive the ether as a pure mechanism x is, after all, scientific. The object of science is to describe in the fewest words the widest range of phenomena, and it is quite possible that a conception of the ether may one day be formed in which the mechanism of gross " matter " itself may, to a great extent, be re- sumed. Indeed, it is on these points of the constitu- tion of the ether and the structure of the prime-atom that physical theory is at present chiefly at fault, There is plenty of opportunity for careful experi- ments to define more narrowly the perceptual facts we want to describe scientifically ; but there is still more need for a brilliant use of the scientific imagina- 1 By a pure mechanism the writer means the reader to understand a system which is conceived to obey (t!t the fundamental laws of moticfl as stated in mechanical treatises. 25 THE GRAMMAR OF SCIENCE. tion (p. 36). There are greater conceptions yet to bd formed than the law of gravitation or the evolution of species by natural selection. It is not problems that are wanting, but the inspiration to solve them ; and those who shall unravel them will stand the compeers of Newton and Darwin. 12. Density as the Basis of the Kinetic Scale. If our mechanism as it is formulated in the above laws of motion can only be definitely asserted as true for particles, we have still to ask how the geometri- cal forms by which we symbolize perceptual bodies are to be conceived as constructed from particles, and how many different families of particles we are to postulate. Now in order to appreciate the answer to this question, we must define what we mean by same- ness of substance. Suppose we take two portions of different bodies, or of the same body, and suppose we find these portions, however we test them, present to us the same groupings of physical and chemical sense-impressions, then we shall term these portions of the same substance. Further, if portions of a body, taken from any part of it whatever, always appear of the same substance, so that, if we could postulate exactly the same perceptions of shape, any one por- tion might be mistaken for any other, then we shall say that the body is homogeneous. Now although we cannot realize a particle in perception, still we conceive that if particles were to be formed by taking smaller and smaller elements from every part of such a homogeneous substance, all these particles would be of equal mass. We thus come to look upon oui conceptual symbol for a homogeneous body as a fHE LAWS OF MOTiON. 37 1 Uniform distribution of particles of equal mass throughout a geometrical surface. Applying our laws as to the motion of particles to such a uniform distribution of particles, we construct a motion for the geometrical form which closely describes our routine of sense-impressions in the case of those per- ceptual bodies which approximate to the conceptual ideal of homogeneity. We then define the sum of the masses of the particles contained in any portion of our geometrical form as the mass of this portion. From this it follows at once that : the masses of any tivo portions of the same homogeneous substance are proportional to their volumes. This result is not a truism x ; it flows only from the uniform distribution of particles which we postulate for a homogeneous substance, and this distribution is a conception only justified, like the law of gravita- tion, by the results which it describes being in accord- ance with our perceptual experience. If we take two small and equal volumes of a homogeneous substance, then the smaller they are the more nearly we can describe our perceptual experience of them by the conceptual symbols, " particles of equal mass." If we take two small and equal volumes of two different homogeneous substances, then, the smaller they are, the more nearly we can describe our perceptual experience of them by the conceptual symbols of " particles of different mass." Thus in conception each independent substance must be looked upon as individualized for the purposes of our mechanical model of the universe by a special mass for its fundamental particle. If we take any homogeneous substance as a standard substance, then if we take 1 It might well be described as the sixth fundamental law of motion. 372 THE GRAMMAR OF SCIENCE. small and equal volumes of any given homogeneous substance and of the standard substance, the ratio of the masses of the particles by which we represent conceptually these volumes as they become smaller and smaller is termed the density of the given homo- geneous substance. 1 It follows, from the above state- ment as to the masses of two portions of the same homogeneous substance being proportional to their volumes, that : the density of a given homogeneous sub- stance is the ratio of the masses of equal volumes of it and of tJie standard substance. If a body be not such that its portions, anywhere taken, present to us the same groupings of physical and chemical sense-impressions, then the body is said to be heterogeneous. If we take small and equal volumes of this body from different parts, then the smaller we take them the more nearly we find that our perceptual experience of them can be described by particles of different masses. If we take small and equal volumes " from a given point " of a heterogeneous body and from the standard homogeneous substance, then the smaller We take them the more nearly our perceptual ex- perience can be described by the mutual action of two particles. The ratio of the mass of this particle of the heterogeneous substance to that of the particle of the standard substance is termed the density of the heterogeneous substance at the given point. The density of such a substance is therefore not, as in the case of a homogeneous substance, the ratio of the masses of finite volumes of the given and of the 1 The name adopted in the text-books is "specific gravity," but I think this term unfortunately chosen and I prefer to use the word density in this sense* THE LAWS OF MOTION. 373 standard substances, it is a quantity which varies from point to point of the heterogeneous body. Clearly the notion of density thus discussed affords a key to the manner in which we are to conceive the symbols for physical bodies constructed from aggre- gates of particles. By means of density we indi- vidualize substances and kinetically classify the particles which are the conceptual elements of bodies. Density forms the kinetic scale we have been in search of (p. 355) ; it is the fundamental means by which we measure the relative magnitude of the accelerations which we conceive the ideal elements of bodies to experience in each other's presence. It throws life into the geometrical forms by means of which we conceptualize the phenomenal universe. The reader must, however, be careful to note that the whole of this discussion of density abounds in purely ideal notions. I have defined homogeneity ; but homogeneity thus defined is a limit drawn purely in conception to a process of comparison which can be begun but not completed perceptually. No perceptual substance is accurately homogeneous. Further, I have spoken about taking " equal volumes," a process which is a geometrical concep- tion, and never exactly realizable in perception, where continuous boundaries cannot be postulated (p. 205). Then, again, I have spoken of taking a " volume at a point," and of the "density of a hetero- geneous body at a point," conceptual limits again having no exact perceptual equivalents. Lastly, I have spoken of density as equal to the ratio of the masses of " certain volumes," and of aggregates of particles as filling " geometrical forms." These indi- cations will be sufficient to show the reader that 374 THE GRAMMAR OF SCIENCE. density, like mass, is a conceptual notion, an ideal means of classifying the symbols of our conceptual model of the universe. We do, indeed, choose these densities so that our model shall describe as accu- rately as possible our perceptual experience, but the density itself belongs to the conceptual sphere, and is defined with regard to the geometrical forms by which we symbolize physical bodies. It is a con- ceptual link between those geometrical forms and the accelerations with which we endow them. The im- portance of this point must be insisted upon, for it is this relation between geometrical volume and mass in the case of homogeneous substances which led physicists to the definition of mass as the " quantity of matter in a body" (p. 358). The geometrical form was first projected into the phenomenal world, and then this form filled with the metaphysical source of sense-impressions matter. Mass as proportional to volume thus became mass as a measure of matter, and the sluice-gate was opened for that flood of meta- physics which has threatened to undermine the solid basis of physical science. 13. The Influence of Aspect on the Corpuscular Dance. Hitherto I have only been dealing with the value of the ratio of the mutual accelerations of two cor- puscles. The discussion of the absolute values of these mutual accelerations for each individual field would carry us through the whole range of modern physics ; we should have to deal with those special laws of motion which describe the phenomena we class under the heads of cohesion, gravitation, capil- larity, electrification, magnetization, &c., &c. To discuss these does qot fall within the scope of oijr THE LAWS OF MOTION. 375 present work, but there are one or two general points I must notice here. I proceed, in the first place, to state in accurate terms the second problem suggested on p. 354. I ask : Are the absolute magni- tudes of the mutual accelerations of two corpuscles influenced by the aspect they present to each other ? Now no very decisive answer can yet be given to this very important question of aspect influence. If we discriminate between the various types of cor- puscles, there seem no facts of our perceptual ex- perience that would lead us to suppose that aspect plays any part in the mutual action of ether-elements. With regard to the prime-atom, we can only leave the matter unsettled ; if this atom were a vortex- ring aspect would be of importance, but if it were an ether-squirt it would not. On the other hand, in both cases, and probably in most other conceivable mechanisms, aspect would play a great role in the mutual actions between chemical atoms and between molecules. These groups, built up of comparatively few prime-atoms, can hardly accelerate each other's motion in the same manner however they turn towards each other. It is to this change of mutual acceleration with change of aspect that we have pro- bably to look for aid in our conceptual attempts to describe such phenomena as crystallization and magnetization. As to the particle, aspect has pro- bably little influence when we are dealing with particles at distances great compared with their vanishingly small size ; but it is still conceivable that if all the molecules in a particle had a similar aspect, aspect might be important in determining the action of this particle on an adjacent particle. In the phenomenon of gravitation aspect does not, however, 3/6 THE GRAMMAR OF SCIENCE. play any part that we can perceptually appreciate. On the whole we conclude that aspect must be con- sidered as a significant factor in determining the absolute magnitudes of mutual accelerations, but the exact influence which the " posture " of our dancers has upon the mode in which they dance remains still one of the obscure points of physics (see pp. 369, 386), 14. The Hypothesis of Modified Action and the Synthesis oj Motion. The next problem that we have to consider is one that is of extreme importance when we are dealing with the synthesis of motion, or the construction of the motion of complex from simple groups of cor- puscles (p. 283). It is the problem of modified action. I may state it thus : If we have found the acceleration of A in the pre- sence of B, will the magnitude r of this acceleration be altered when C is introduced into the presence of A and B ? This problem may be put a little differently, thus : Suppose we find when A and B are alone in the field that the acceleration of A due to B is represented by the step b, and that when A and C are alone in the field the acceleration of A due to C is represented by the step c, then when both B and C are in the field will these accele- rations remain the same, and consequently will the total accelerating effect of B and C be represented, owing to the law we have stated for combining accelerations (p. 282), by the diagonal step d of the 1 We have already seen that the ratio of the mutual accelerations, or of the masses of A and B, is not to be conceived as altered by the presence of other corpuscles in the field ; but this leaves the question of absolute magnitudes unsettled. THE LAWS OF MOTION. 377 parallelogram, whose sides are b and c? Or, on the other hand, are we to conceive that when B and C are both in the field the former acceleration b due to B is altered to b' and the acceleration c due to C to c\ so that the total acceleration of A is now the diagonal is m tirnes the step d. This force is termed the 3/8 THE GRAMMAR OF SCIENCE. resultant force ; and we see that, since the resultant and component forces are respectively m times the diagonal and the sides of the acceleration-parallelo- gram, these forces must themselves form the diagonal and sides of a parallelogram A ft S y which is a mag- nified picture of the acceleration-parallelogram. This is the famous parallelogram of forces, and we notice that it follows at once from the parallelogram of accelerations when we assume that B and C do not modify each other's action. 1 If they do modify each other's action there will still be a parallelogram (A ft' &' 7') of forces, namely, the resultant force m X d' will be the diagonal of the parallelogram on the sides m X b* and m x c'. But if we mean, as physicists generally do, by the force of B on A, the force when A and B are alone in the field, and similarly by the force of C on A the force when A and C are alone in the field, then we must assert that on the hypothesis of modified action : the parallelogram of forces is not a synthesis by which we can .truly combine forces. This conclusion may appear to the reader so entirely .opposed to all that he has read of mechanics, that he may be led at once to reject the hypothesis of modi- fied action. One of Newton's laws of motion dis- tinctly excludes indeed this hypothesis, and a great simplification in our process of constructing complex from simple mechanical systems undoubtedly arises when we exclude it ; we have not to deal with every new field afresh, and to re-measure accelerations for each variation of its constituent elements : we simply 1 This, for the purposes of the physics of the particle, might be spoken of as the seventh law of motion. THE LAWS OF MOTION. 379 analyze it, break it up into simple fields the indivi- dual motions of which have been previously discussed. Yet it is not scientific to assert that the simplest hypo- thesis is necessarily correct (Appendix, Note III.) ; we must ask, when we proceed to extend it beyond the range where it has been found to describe experience, whether it still suffices to simplify our conceptions, or leaves undescribed certain recognized phases of perception. Newton's law appears perfectly sufficient, and may therefore be said to be verified, when we are dealing with particles of gross " matter." The mutual accelerations, for example, of two gravitating particles seem to be uninfluenced by the presence of a third particle ; there is nothing, to take a still more concrete example, yet observed which would compel us to conceive that the mutual accelerations, by which we describe the mutual dance of sun and earth, are in the least influenced by the presence of the moon. Yet when we come to extend this law of Newton's, invaluable as it is for dealing with particles of gross " matter," to the mutual action of molecules, atoms, and ether- elements, there appears to be considerable reason for doubting its accuracy. We can conceive atomic structures for example, the ether-squirt for which modified action is essentially true. There are phenomena of cohesion which can hardly be described without supposing the action of two molecules A and B to be modified by the presence of a third molecule C. 1 There are chemical facts which suggest that the introduction of a third 1 A fuller discussion of "aspect" and "modified action" by the author will be found in Todhunter's History of Elasticity, vol. i. arts. 921-31, 1527, and vol. ii. arts. 276, 304-6. See also the American Journal of Mathematics j vol. xiii. pp. 321-2, 345, 353, 36,1, 380 THE GRAMMAR OF SCIENCE. atom C may even reverse the sense of the mutual accelerations of two atoms A and B. Nay, those who, in order to describe the radiation of light, treat the ether as an elastic jelly (p. 315), will find that it is very difficult to conceptualize its elastic structure, with- out asserting that the hypothesis of modified action is true of the ether-elements. The parallelogram of forces, then, as a synthesis of motion must be considered as applying in the first place to particles of gross " matter " ; its extension to other corpuscles can only be made cautiously and with continual reservation. Like so many other features of me- chanism it cannot be dogmatically asserted to hold for all corpuscles, but it may in itself flow from the constitution we postulate for the ether and the struc- tures we assume for the various types of gross " matter." 15. Criticism of the Newtonian Laws of Motion. Before we close our discussion of the laws of motion it is only just to the reader to state that the method adopted differs widely from the customary physical treatment ; and in deference to the authority on which that treatment is based some comparison and criticism seems called for. We have already dealt with the cur- rent definitions of force, matter, and mass, and shown reasons for rejecting them as involving metaphysical obscurity. When, therefore, we come across these terms in the statement of the laws of motion we must endeavour to interpret them in our own sense. To the reader on first examination the Newtonian state- ment of the laws of motion may seem simpler than that of the present chapter. They are stated generally of bodies^ and appear to describe the mechanism THE LAWS OF MOTION. 381 under which all bodies move, and therefore pre- sumably describe the motion of the whole range of corpuscles from ether-element to particle. Now this loses sight of what the present writer thinks a very important possibility, namely, that not only special modes of motion, but much of the mechanism which describes the action of sensible bodies, will be found ultimately to be involved in some wide-reaching con- ception of ether and atom. It is not logically satis- factory to describe one mechanism by another of equal complexity; and we must hope to ultimately concep- tualize an ether from the simple structure of which several of the laws of motion postulated for particles of gross " matter " may directly flow. Remembering these points we now turn to the version of the New- tonian laws given by Thomson and Tait. 1 Law I. Every body continues in its state of rest or of uniform motion in a straight line, except in so far as it may be compelled by force to change that state. Now the reader who is acquainted with treatises on dynamics will remember that one of the most difficult chapters is frequently entitled, Motion of a Body under the Action of no Forces. The motion described is of an extremely complex kind. For example, the body may not only be spinning about an axis, but may be, and as a general rule is, conceived as con- tinually changing the axis about which it spins. 1 A Treatise on Natural Philosophy, part ii. pp. 241-7. The writer will not admit that he is second to any one in his admiration for the genius of Newton, or in his respect for the authors of the above classical Treatise. Yet he cannot believe that the two centuries which have elapsed since Newton stated his Leges Motiis " have not shown a necessity for any addition or modification " ! Old words grow as men are compelled to express new ideas in terms of them, and few definitions have a virile life of even a score years. 32 THE GRAMMAR OF SCIENCE. The " state of rest or of uniform motion in a straight line " is thus not that which the physicist postulates to describe the motion of a body under the action of no forces. It is quite true that we conceive a certain point termed the centre of mass of such a body to be either at rest or moving uniformly in a straight line; this, however, is not a conception which is itself axiomatic, but arises from an application of the principle of the equality of action and reaction to the particles by which we conceptually construct the body. In the first place, therefore, the use of the word body does not really give generality to the law, but introduces obscurity ; we ought at least to replace it by the word particle. In the next place the law is very wanting in explicitness as to what we are to understand by state of rest or of uniform motion in a straight line. All motion must be relative to something, but Newton does not indicate with regard to what, for example, the relative path is a straight line. Force is also a relative term (p. 360), but Newton nowhere tells us what the force on the body is related to. Thus, until a second body (or other particles) be introduced (p. 343), the law remains meaningless. In the last place, what are we to understand by the words, " compelled by force to change that state " ? We take force to be a certain measure of motion, namely, the product of mass into acceleration ; then to assert the absence of force is to assert the absence of acceleration, or the law would merely contain the platitude that without change of motion a particle moves uniformly. But Newton certainly meant something more than this, for he was thinking of force in the sense of mediaeval metaphysics as " a cause of change in motion." Now the nearest THE LAWS OF MOTION. 383 approach we can get to his idea is that position relative to surrounding particles determines a given particle's acceleration, and thus the first law is seen, liberally interpreted, to amount to the statement that surrounding circumstances determine acceleration - that without the presence of other particles there is no acceleration. This is the important principle of inertia to which we have already referred (p. 342), but it certainly appears to be stated with great obscurity in Newton's first law of motion. Further, even in this law, as I have restated it, no hint is given as to what application the principle may have to other corpuscles than particles of gross " matter " (p. 344). Law II. Change of motion is proportional to force applied^ and takes place in the direction of the straight line in which force acts. This is a veritable metaphysical somersault. How the imperceptible cause of change in motion can be applied in a straight line surpasses comprehension ; the only straight line that can be conceived, or, as some physicists would have it, perceived, is the direc- tion of change of motion. We may assert that the imperceptible has this direction, but to postulate that the imperceptible will determine this direction for us seems to be pure metaphysics. We come down on our feet again, however, when we interpret this law as simply indicating that physically force is going to be taken as a measure for some change in motion (p. 360). As to the exact meaning of change of motion taking place in a straight line, all the real difficulties as to what thing we are to suppose changing its motion, and what is the presence associated with this change of motion, i.e., the difficulties about the line joining two corpuscles (p. 367), are concealed by talking vaguely 384 THE GRAMMAR OF SCIENCE. about force as an entity " acting in a straight line. 5 ' Furthermore, if the " change of motion " is to be that of a body, not a particle, then we naturally ask which point of the body will have its motion changed in the direction of a straight line. We are thus again brought face to face with the fact that the motion of " bodies " is far more complex than is in the least indicated by this law. Sir William Thomson and Professor Tait have restated the Second Laiv in the following form : When any forces whatever act on a body, then, ^vhether the body be originally at rest or moving zvith any velocity and in any direction, each force produces in the body the exact change of motion which it would have produced had it acted singly on the body originally at rest. These conclusions they consider really involved in Newton's Second Law. The same difficulty repeats itself here with regard to the interpretation of the term " body." Further, the law thus expressed denies the possibility of " modified action " (pp. 376-80), and the likelihood that in certain cases the velocity of corpuscles may help to determine their mutual acce- lerations (p. 349). It thus asserts the absolute vali- dity of that synthesis, which we have termed the parallelogram of forces, and which we have ventured to suggest cannot be dogmatically asserted of cor- puscles of all types. Law III. To every action there is always an equal and contrary reaction, or the mutual actions of any two bodies are always equal and oppositely directed. If we replace " bodies " by " particles " for the mutual action of two bodies is more complex than a reader just starting his study of mechanism would THE LAWS OF MOTION. 385 imagine, if he naturally interpreted mutual action as corresponding to mutual acceleration in some one line the above law is identical with our Fifth Law (p. 359), and therefore we need not repeat the quali- fying discussion of our 11. See Appendix, Note II. The Newtonian laws of motion form the starting- point of most modern treatises on dynamics, and it seems to me that physical science, thus started, resem- bles the mighty genius of an Arabian tale emerging amid metaphysical exhalations from the bottle in which for long centuries it has been corked down. When the mists have quite cleared off we shall see more clearly its proportions, and there is special need for a strong breeze to clear away our confused notions as to matter, mass, and force. The writer is far from imagining that he can accomplish this clearance, but he is convinced that a firm basis for physics will only be found when scientists recognize that mechanism is no reality of the phenomenal world that it is solely the mode by which we conceptually mimic the routine of our perceptions. The semblance is, indeed, so striking that we are able with astonishing accuracy to predict in vast ranges of phenomena what will be the exact sequence of our future sense-impressions. If, however, the scientist projects the whole of his conceptual machinery into the perceptual world he throws himself open to the charge of being as dogmatic as either theologian or metaphysician. On the other hand, when he simply postulates the conceptual value of his symbols as a mode of describing past and predicting future percep- tual experience, then his position is unassailable, for he asserts nothing as to the why of phenomena. But as soon as he does this, matter as that which moves, and force as the cause of change in motion, disappear into 26 386 THE GRAMMAR OF SCIENCE. the limbo of self-contradictory notions. What moves is only a geometrical ideal, and it moves only in con- ception. Why things move thus becomes an idle question, and how things are to be conceived as moving the true problem of physical science. 1 In this field we know much, but our account of the laws of motion has been specially intended to empha- size how great is the room both for further investigation and for the exercise of disciplined imagination. In the vagueness of our conceptions of ether and atom lies the ill-explored continent which, by clearer defini- tion, the Galilei and Newton of the future will annex. But before this annexation there is work for the unpretending pioneer in helping to clear away the jungle of metaphysical notions which impedes the progress of physical science. SUMMARY. The physicist forms a conceptual model of the universe by aid of corpuscles. These corpuscles are only symbols for the component parts of perceptual bodies and are not to be considered as resembling definite perceptual equivalents. The corpuscles with which we have to deal are ether-element, prime-atom, atom, molecule, and particle. We conceive them to move in the manner which enables us most accurately to describe the sequences of our sense-impressions. This manner of motion is summed up in the so-called laws of motion. These laws hold in the first place for particles, but they have been frequently assumed to be true for all corpuscles. It is more reasonable, however, to conceive that a great part of mechanism flows from the structure of gross "matter." The proper measure of mass is found to be a ratio of mutual acceler- 1 " Such demonstrations, however, only show how all these things may be ingeniously made out and disentangled, not how they may truly subsist in nature ; and indicate the apparent motions only, and a system of machinery arbitrarily devised and arranged to produce them not the very causes and truth of things " (Bacon, De Augmentis, bk. iii. chap. iv.). THE LAWS OF MOTION. 387 ations, and force is seen as a certain measure of motion, and not its cause. The customary definitions of mass and force, as well as the Newtonian statement of the laws of motion, are shown to abound in metaphysical obscurities. It is also questionable whether the principles involved in the current statements as to the superposition and combination of forces are scientifically correct when applied to atoms and molecules. The hope for future progress lies in clearer conceptions of the nature of ether and of the structure of gross " matter." LITERATURE. The views put forward in this chapter were reached when the author was studying the laws of motion for teaching purposes in 1882, and were developed for the purpose of college lectures in 1884 and subsequent years. A brief account of them was published in 1885, on pp. 267-71 of Clifford's Common Sense of the Exact Sciences, but the only pub- lished work in which the author has found any indication of similar opinions, or from the perusal of which he has received any help or encouragement, and the only work he can therefore heartily recommend to the reader is : MACH, E. Die Mechanik in ihrer Entwicklung, S. 174-228. Leip- zig, 1883. The customary physical view of the Laws of Motion will be found in : CLERK-MAXWELL, J. Matter and Motion, pp. 33-48. London, 1876. THOMSON, Sir W., and TAIT, P. G. Treatise on Natural Philosophy, part i. pp. 219-24, 240-49. Cambridge, 1879. CHAPTER IX. LIFE. i. The Relation of Biology to Physics. IT does not fall within the range of the present work, still less within the power of its author, to discuss at any length the fundamental principles of biological science. The object of our Grammar has been to investigate the radical concepts of physics, the basis of that " dead " mechanism to which science is popularly supposed to reduce the universe. In the course of this investigation we have had occasion to call in question several of the notions commonly associated with these physical concepts ; we have seen that in speaking of matter and force much of our current language requires to be remodelled for scientific purposes Now physics is a much older branch of science than biology, and biologists have been so wont to look with something of awe and a little of envy to the presumed exactness both in language and in conclusions of mechanical science, that it may come with rather a shock to them when they hear that physics, like biology, is solely a description and not a fundamental explanation. While on the one hand, however, phy- sicists can get on very well without biology, at any rate within a certain limited field of observation, biologists, on the other, have not only adopted many of the physicist's notions as to matter, force^ and eternity, LIFE. 389 as modes of describing biological facts, but they are further, whether they wish it or not, inevitably bound to physics by the fact that life is never found apart from physical associations. Mechanism, on its side does not as a theory involve a discussion of biological phenomena, but biology without a discussion of mechanism is necessarily incomplete. 1 " The elements of living matter are identical with those of mineral bodies ; and the fundamental laws of matter and motion apply as much to living matter as to mineral matter ; but every living body is, as it were, a complicated piece of mechanism which 'goes,' or lives only under certain conditions." So wrote Professor Huxley in 1880. The use of physical terms abound- in biology, often, I fear, with scarcely accurate definition. Nageli talks of the " known forces of the organism, heredity and variability " ; Weismann speaks of the impossi- bility of the egg being " controlled by two forces of different kinds in the same manner as it would have been by one of them alone " ; he further talks of " forces residing in the organism " influencing the germ-plasm, which imperceptible entity he halves and divides as if it were a physical quantity. 2 Lan- kester speaks of " that first protoplasm which was 1 From the author's standpoint, of course, conceptions as representing the products of the perceptive faculty are largely conditioned by the perceptive faculty of an individual genus, man (pp. 99-104, 211), and therefore their nature may be ultimately elucidated by biological, in particular pyschological, inquiry. 2 If Spencer can be included in the list of biologists, it will be found that he uses force without special definition in the following senses: (i.) As cause of change in motion ; (ii. ) as a biological process ; (iii.) as a name for kinetic energy; (iv.) as a name for potential energy; (v.) as a general name for physical sense-impressions, such as light and heat, &c. 390 THE GRAMMAR OF SCIENCE the result of a long and gradual evolution of chemical structure and the starting-point of the development of organic form." Biologists lay the greatest weight on the " chemical structure " of protoplasm and the chemical processes which are or accompany physio- logical functions, while free use is made of such terms as " unit-mass of living matter," " resultant of organic forces," "molecular stimuli," "continuity of organic substance," "conditions of tension and movement," " physical constitution necessary for immortality," &c., &c. Now either these terms are used figuratively, in which case we ought to find them re-defined, or else biologists have adopted them from physics and intend to use them in the sense of the latter science. But there is small doubt that the latter alternative represents the true state of the case. The biologist considers his organic matter to be inexorably united to the " matter " of the physicist, and he uses, or considers he uses, such terms as matter, force, me- chanism, &c, in the sense of the sister science. This dependence of biology on physics is so well brought out in the following passage that the reader must pardon our quoting it at this stage of our investiga- tions : Experience cannot help us to decide this question ; we do not know whether spontaneous generation was the commencement of life on the earth, nor have we any direct evidence for the idea that the process of development of the living world carries the end within itself, or for the converse idea that the end can only be brought about by means of some external force. I admit that spontaneous generation, in spite of ail vain efforts to demonstrate it, remains for me a logical necessity. We cannot regard organic and inorganic matter as independent of each other and both eternal, for organic matter is continually passing without residuum, into the inorganic. If the eternal and indestructible are alone without beginning, then the non-eternal and destructible must have had a beginning. But the organic world is certainly not eternal LIFE. 391 and indestructible in that absolute sense in which we apply these terms to matter itself. We can, indeed, kill all organic beings and thus render them inorganic at will. But these changes are not the same as those which we induce in a piece of chalk by pouring sulphuric acid upon it ; in this case we only change the form, and the inorganic matter remains. But when we pour sulphuric acid upon a worm, or when we burn an oak-tree, these organisms are not changed into some other animal and tree, but they disappear entirely as organized beings and are resolved into inorganic elements. But that which can be com- pletely resolved into inorganic matter must have also arisen from it, and must owe its ultimate foundation to it. The organic might be con- sidered eternal if we could only destroy its form, but not its nature. It therefore follows that the organic world must once have arisen, and further, that it will some time come to an end. 1 Now this passage is extremely instructive, for we have the notion of the " eternal and indestructible " character of inorganic " matter " used to demonstrate the " logical necessity " of spontaneous generation. The reader who is in sympathy with the results of our discussion on "matter" and has recognized: (i) that " matter" as a substratum of our sense-impressions is a metaphysical dogma, not a scientific concept (p. 3 1 1) ; (2) that eternity is an idle phrase in the field of nomena (pp. 221, 227) ; and (3) that indestructibility relates to certain groupings of sense-impressions and not to an undefinable something behind them (p. 304), will be inclined to admit that the physicist is not wholly free from responsibility for the intrusion of metaphysics into biology. The physicist is therefore hardly warranted in demanding that the biologist shall accurately define his use of such terms as matter and force, for the physicist himself is not above reproach. At the same time the author is free to confess that the concepts of physics as defined, and he believes logically defined, in the present work 1 Weismann : Essays on Heredity, p. 33. Oxford, 1889 392 THE GRAMMAR OF SCIENCE. scarcely lend themselves to the reasoning of the above passage. Nor can he think that, when physics has impressed upon biology that force is only a certain measure of motion, and not an explanation of anything whatever, biologists will be so ready to ascribe the phenomena of life to " forces residing in the organism." It is with the intention of suggesting how the view of mechanism, discussed in this work, can be conceived as applying to life rather than of dealing with the fundamental principles of biology, that the present chapter has been included in our volume. . 2. Mechanism and Life. In previous chapters we have seen how the phe- nomenal world is a world of groups of sense-impressions distinguished by the perceptive faculty under the two modes of space and time, or the mixed mode of change. This change or shifting of sense-impressions occurs in repeated sequences, or what we have charac- terized as routine. In the sense-impression itself there is nothing to suggest or enforce a routine, nor have we sufficient grounds as yet to definitely attribute this routine to the perceptive faculty. It remains for the present the fundamental mystery of perception, but it is the basis upon which all scientific knowledge is built. Science is the description in conceptual shorthand (never the explanation) of the routine of our perceptual experience. If this be true, it follows that the task of the biologist is to describe in conceptual shorthand (not to explain) the sequences of certain classes of sense-impressions. The problem of whether life is or is not a mechanism is thus not a question of whether the same things, " matter " and " force," are or are not at the back of organic and inorganic phenomena LIFE. 393 of what is at the back of either class of sense- impressions we know absolutely nothing but of whether the conceptual shorthand of the physicist, his ideal world of ether, atom, and molecule, will, or will not, also suffice to describe the biologist's percep- tions of life. The mystery in the routine of sense-impressions is precisely the same whether those sense-impressions belong to the class of living or to that of lifeless groups. Life as a mechanism would be purely an economy of thought ; it would provide the great advantages which flow from the use of one instead of two conceptual shorthands, but it would not " explain " life any more than the law of gravitation explains the elliptic path of a planet (p. 160). As we have to speak paradoxically no sense which can reach any- thing behind sense-impressions, no " metaphysical sense" which enables us to perceive that supposed entity " matter," so we have no special sense which enables us to perceive another supposed entity, " life." * Life and lifeless are merely class names for special groups of sense-impressions. When, therefore, we assert " matter " as the substratum of one group of sense- impressions and " life " as the substratum of another, and " explain " life by aid of matter and its attribute "force," we are simply, albeit often unconsciously, wallowing in the Stygian creek of metaphysic dogma. If the biologist gives us an accurate account of the development of the ovum and then remarks that the changes are due to " forces resident in the egg," he certainly cannot mean that the chemist and physicist are capable of explaining what has taken place. He 1 The " sense of consciousness," if so it can be called, is hardly a special sense of life, for consciousness and life are not equivalent terms. 394 THE GRAMMAR OF SCIENCE. probably considers that the conceptual shorthand of chemistry and physics would suffice to describe what he has himself described in other language. If we always remember that the physicist's fundamental conception of change of motion is that the change of motion of one particle is associated with its position relative to other particles, and that force is a certain convenient measure of this change, then, I think, we shall be in a safer position to interpret clearly the numerous biological statements which involve an appeal to the conception of force. We must in each case ask what individual thing it is which is con- ceptualized as moving, what is the field with regard to which it is considered as moving, and how its motion is conceived to be measured. When we have com- pleted this investigation then we shall be better able to appreciate the real substance which lies beneath the metaphysical clothing with which biological, like physical, statements are too often draped. 1 Admitting, therefore, that our object in biology is identical with that in physics, namely, to describe the widest ranges of phenomena in the briefest possible formulae (p. 1 1 6), we see that the biologist cannot throw back life for an explanation on physics. Whether he 1 We are told, for example, that "force is always bound up with matter," that too small an "amount of matter" may be present to exercise a "controlling agency" over the development of the embryo, and when we seek to associate this "amount of matter" with some definite group of sense-impressions we find that no perceptual equivalent has been found for it. What the biologist is clearly striving to do is to form a conceptual model of the embryo by aid of the relative motions of the parts of a geometrical or rather kinetic structure (p. 373), but it is difficult to reach his ideas beneath the metaphysical language in which he projects matter, force, and germ-plasm into real substrata of sense- impression (see Weismann : Essays en Heredity, pp. 226-7). LIFE. 395 can hope to describe life in physical shorthand is a point to which we shall return a little later. If we look upon biology as a conceptual description of organic phenomena, then nearly all the statements we have made with regard to physics will serve as canons for determining the validity of biological ideas. In particular, any biological concept will be scientifically valid if it enables us to briefly summarize without internal contradiction any range of our perceptual experience. But the moment the biologist goes a step further, and asserts on the ground of the validity of his concept that it is a reality of the phenomenal world, although no perceptual equivalent has yet been found for it, then he at once passes from the solid ground of science to the quicksands of metaphysics. He takes his stand with the physicist who asserts the phenomenal existence of the concepts atom and molecule. 3. Mechanism and Metaphysics in Theories of Heredity. I cannot bring home to the reader the difficulties with which the projection of conceptions into the phenomenal world is attended better than by briefly referring to two well-known biological theories of heredity. Of the change in those groups of sense- impressions which the biologist sets himself to describe there are two prominent features which at first sight might seem to correspond to nomic and anomic changes (p. 1 i^, footnote], to routine and to breaches of routine. These features are the recurrence in our ex- perience of the offspring of sense-impressions associated with the parental organism, and the occurrence in our experience of the offspring of sense-impressions not associated with the parental organism. These features 396* THE GRAMMAR OF SCIENCE. are termed inheritance and variation. The apparent anomy, involved in variation is very probably like the anomy of the weather, a result of our not yet having formed a sufficiently wide or fundamental classi- fication of facts. Be this as it may, inheritance and variation form the basis upon which biologists construct the evolution of life. Theories which endeavour to resume inheritance and variation under a single and simple formula are termed theories of heredity, and two of the most important of these theories are due respectively to Darwin and Weismann. On Darwin's hypothesis of pangenesis every cell of the body throws off particles or gemmules which collect in the reproductive cells. These gemmules, or " undeveloped atoms," are transmitted by the parent to the offspring, they multiply by self-division, they may remain undeveloped during early life, or even during several generations, but when under the influence of suitable environment they do develop, they become cells like those from which they were derived. By aid of this hypothesis Darwin was able to resume a great many of the facts of heredity. Inheritance was simply the development of the parental gemmules in the offspring ; variation could be described partly by a commingling of the gemmules of two parents, partly by a modification of the gemmules of the parental cells due to their use or disuse. 1 Now it is quite clear that no biologist would have propounded this hypothesis, but for the currency of corpuscular theories in physics. Indeed, Weismann actually re- states Darwin's hypothesis in terms of molecules, and speaks of unknown forces drawing these molecules 1 Variation of Animals and Plants under Domestication, vol. ii. chap, xxviii. LIFE. 397 to the reproductive cells and marshalling them there. 1 But as no physicist ever caught an atom, so no biolo- gist ever caught an "undeveloped atom," or gemmule. The validity of the conception can only be tested by the power it gives us of resuming the facts of heredity, and it is no more disproved by the statement that " gemmules have not been found in the blood," than the atomic theory is disproved by the fact that no atoms have been found in the air. If the biologist has once grasped that the physicist is making a meta- physical statement when he asserts the phenomenal existence of corpuscles, then he will be the more ready to admit that the non-finding of gemmules and the " unknown forces necessary to control them " are not arguments against a conceptual description of heredity, but against a metaphysical projection of its concepts into the phenomenal world. Weismann, who I think projects Darwin's gemmules into the phenomenal world, and then rather oddly states that they compel us to suspend all physical conceptions, has, on the other hand, shown good reason for Darwin's theory not being valid as a full description of the phenomena of heredity, notably because the transmission of acquired characteristics receives sup- port from that theory, but hardly from our perceptual experience. He has in his turn endeavoured to formulate a theory which shall more accurately describe the facts of heredity, especially those relating to the non-transmission of characters acquired by parents, owing either to use or accident during their lives. This theory is summed up in the formula of the "continuity of the germ-plasm." According to this theory there exists a substance of a definite 1 Essays on Heredity, pp. 75-8. THE GRAMMAR OF SCIENCE. chemical and molecular structure termed germ-plasm, which resides somewhere in the germ-cells, from which reproduction takes place. In each reproduction a part of the germ-plasm " contained in the parent egg- cell is not used up in the construction of the body of the offspring, but is reserved unchanged for the for- mation of the germ-cells of the following generation." This constitutes the continuity of the germ-plasm. 1 Variation arises from the mixture of parental germ-plasms ; similarity of characteristics in parent and offspring inheritance from their both being developed under the control of the same germ-plasm. The " immortal " part of the organism which descends from generation to generation is the germ-plasm. 2 Now this hypothesis of Weismann as a conceptual mode of describing our perceptual experience seems to be of considerable value, but the author weakens his position throughout by projecting his conceptions into the phenomenal world, where up to the present nothing has been identified as the perceptual equivalent of germ-plasm. It is this transition from science as a conceptual description of the sequences of sense- impressions to metaphysics as a discussion of the imperceptible substrata of sense-impressions, which mars biological as well as physical literature. But the physicist is here to blame, for he has projected without perceptual evidence his molecule and atom into the phenomenal world, and the biologist only 1 The reader must be careful to note that it is not a continuity of the germ-cells, but of a hitherto unidentified substance contained in these cells. Cells, we know, nuclei we know, with complicated networks of nucleoli ; but what is germ-plasm ? Not to be seen and not to be caught by aniline stain or acetic acid. 2 The Continuity of the Germ-plasm as the Foundation of a Theory of Heredity, 1885. Essays on Heredity, pp. 165-248. LIFE. 399 follows the physicist's example when he asserts the reality of gemmule or germ-plasm. Finding the ground behind sense-impressions already occupied by molecule and atom, by matter and force, he not un- naturally gives his metaphysical products molecular or atomic structure ; he endows them with force and " explains " life by mechanism. In both the theories of Darwin and Weismann a metaphysical element seems to enter owing to a misinterpretation of the concepts of physics. 1 Only when we have fully recognized that physical science is solely a conceptual description, that matter as that which moves, and force as the why of its motion are meaningless, will this recognition begin to react on the fundamental conceptions of biology. Our object hitherto has been to suggest that if the physicist withdraws, as we trust he may do, from the metaphysical limbo beyond sense-impression, then the biologist who has followed him there will retreat also. The problem as to whether life is or is not a mechanism will then have to be restated. We shall then have to ask whether organic and inorganic phenomena are capable of being described by the same conceptual shorthand. In order to understand more clearly the exact nature of this question we must stay for a moment to consider what we mean when we speak of organic and inorganic phenomena. What 1 There are still stronger metaphysical aspects in Weismann's doctrine. That a substance which possesses continuity and sameness should in- definitely reproduce itself, or if it increases by absorption of foreign substances should remain the same, and this owing to a definite molecular structure, can hardly be looked upon even as a conceptual limit to any perceptual experience. We may ask, as Weismann does of Darwin's gemmule, whether it does not compel us "to suspend all known physical and physiological conceptions" ? 400 THE GRAMMAR OF SCIENCE. groups of sense-impressions do we classify as living, what groups as lifeless ? 4. The Definition of Living and Lifeless. Now the first point to be noted is that there is no single sense-impression which can be said to be that of life. We do, indeed, seem in our own individual cases to have in consciousness a direct sense of life. But in the first place we have not at present any per- ception of consciousness except in our own individual case (p. 58), and in the next place we cannot even infer that consciousness is associated with all types of life (p. 69). We still find it reasonable to speak of human beings as living when they are asleep, or as living when they are completely paralyzed ; we speak of organisms as living when there is none of that hesitation between immediate sense-impression and exertion which constitutes thought and is the essential factor in human consciousness (p. 51). We cannot, indeed, say where consciousness must be taken to cease in the scale of life, but it would be ridiculous to question whether fungus spores had consciousness or not as a means of settling whether they were to be classified as living or dead substance. The less we find exertion conditioned by stored sense-impresses, the less degree of consciousness can we infer. The lowliest organisms appear to respond directly to their environment, and in this they resemble very closely the ideal corpuscle of the physicist, which dances in response to its surroundings. Seeds which have been preserved for fifty or a hundred years with- out losing their power of germination (see Appen- dix, Note IV.) are organic substance and contain life, at least in a dormant form, yet it is idle here to LIFE. 401 postulate consciousness as a means of classifying living and lifeless organisms. The moment we accept without reservation the theory that all life has been evolved from some simple organism, then we are bound to recognize that con- sciousness has gradually become part of life, as forms of life grow more and more complex. This does not explain consciousness, but it is the only consistent description we can give of its evolution. The corre- lation of thought and consciousness seems to indicate that this complexity of the organism is to be sought in the inception and development of its capacity for storing sense-impressions. We can mark where this storage fails, we can mark where it exists ; but where it exactly begins we can hardly assert. This apparent continuity has led to some rather metaphysical reasoning on the part of biologists seeking for a distinguishing characteristic between living and lifeless groups. As in some types of life consciousness may be evolved, it is argued that there must be in life " something-which-is-not-yet-conscious- ness-but-which-may-develop-into-consciousness," and to this something Professor Lloyd Morgan has given the name of metakinesis}- This metakinesis does not appear to be more than a metaphysical name for non- conscious life, for there is no sense-impression that we have of such life that we can describe as metakinetic. Metakinesis is as intangible as the germ-plasm of the biologist or the molecule of the physicist, but less conceptually valuable as it describes no phenomenal side of life except the fact that it may or may not be associated with consciousness. Those who believe that the organic has been developed from inorganic, 1 See in particular his letter to Nature, vol. xliv. p. 319. 27 402 THE GRAMMAR OF SCIENCE. that living has proceeded from dead " matter," may then assert that there must be in matter " something- which-is-not-yet-life-but-which-may-develop-into-life," and may fitly term this side of matter supermateriality. It is quite true that we have no direct series of sense- impressions to which this supermateriality corresponds, but as we mark some forms of matter associated with life (just as we mark some forms of life associated with consciousness), so we have the same reason for postu- lating its existence as we have in the case of meta- kinesis. How metakinesis develops from super- materiality will of course be the next stage in metaphysical investigation ! Now, I hope that Professor Lloyd Morgan will not think I am laughing at him, for this is far from being the case. I believe that no biologist is so patient with the physicist, even when the latter waxes paradoxical ; and I recognize that to look upon the mechanical and the conscious as two aspects of one and the same process may be a distinct simplification of our descrip- tion of life, and therefore scientifically valid. But I want to point out, and this very earnestly, how the physicist too often entices the biologist into a meta- physical slough by postulating mechanism as the substratum and not as the conceptual description of certain groups of sense-impressions. Had the physicist asserted that the reality of the external world lies for him in the sphere of sense-impressions, and that of the beyond of sense-impression physics knows nothing had he said : " What I term mechanism and Professor Lloyd Morgan kinesis (see our p. 355) is purely a mode of describing conceptually the sequences of my sense-impressions," then the door would not have been opened for the metaphysician to parody LIFE. 403 metakinesis by supermateriality. So long as the biologist is taught to look upon mechanism as a series of imperceptible motions undertaken by imperceptible bodies under the guidance of imperceptible " mole- cular forces," he cannot be criticized for introducing another imperceptible element " metakinesis " into this process. But when the physicist ceases to postu- late any of these imperceptibles and boldly states that mechanism is a conceptual process, by aid of which he is able to describe at any rate certain phases in those sequences of sense-impressions which we classify as unconscious life, then he may fairly ask what sense- impressions of unconscious life the biologist classifies by aid of metakinesis. If the biologist replies it is the potentiality of consciousness, then this is not the equivalent of the mechanism of primitive forms of life, The latter corresponds not only to the poten- tiality of all the complex nervous system of a con- scious organism, but it actually describes some of our perceptual experience of primitive life. It thus does more than describe a potentiality, it describes a reality, and thus cannot be classed like metakinesis with supermateriality as a metaphysical "being," " essence," or " aspect." The biologist therefore may describe for us the various stages in the evolution of consciousness, reducing them to scientific formulae or laws, but he cannot postulate metakinesis, still less consciousness, as that which separates living from lifeless groups. All types of life do not appear capable of developing into conscious types ; and a potentiality not bearing any outward " recognition marks " will not lead us to a definition of life any more than the potentiality of becoming a bishop would lead us to a definition of man. 404 THE GRAMMAR OF SCIENCE. 5.- 720 the Laws of Motion apply to Life ? If we seek for the characteristics of life apart from the possibility of consciousness, we can only seek them in some special features of those sequences of sense- impressions which we associate with living organisms. Now we have seen that groups of sense-impressions are all distinguished under the two modes of space and time, and we are thus able to conceptualize all change as a motion of ideal corpuscles. Now " currents/' " vibrations of filaments," " moving masses of proto- plasm," " contraction/' " change of form," " strain," &c., &c., are all terms in current biological use adopted to describe sequences or changes in sense-impressions. As to what are the symbolic bodies to which these motions are attributed and how they are to be built up from the most elementary organic corpuscles " unit-masses of living matter " as one biologist terms them there appears to be some diversity of opinion. But there is practical agreement among biologists that the organic corpuscles the "physiological units " of Spencer or the " plastidules " of Haeckel must be conceived as con- structed from the atom and molecule, the inorganic corpuscles of the physicist. Hence, if all we are to understand by mechanism, is something which we conceive as being constructed of atom and molecule and in motion, then life can only be conceived as mechanical. How, therefore, we must ask, is it possible for us to distinguish the living from the lifeless, if we can describe both conceptually by the motion of inorganic corpuscles ? The only answer that can be given to this must be that the nature of the motions by which we conceptualize organic and inorganic phenomena are very different We mean by mechanism some- LIFE. 405 thing more than the conceptual description of change by aid of the motion of physical corpuscles ; we mean that this motion is itself summed up in the laws of motion discussed in the preceding chapter. Herein lies the apparent kernel of the problem. Before we assert that life can be described mechanically, we must determine whether the motion by which we concep- tualize organic phenomena can be resumed in the same laws as the motion by which we conceptualize inorganic phenomena. But we soon find that we are only at the beginning of our investigation. In Chapter VIII. we have seen that the complex laws of motion which hold for particles of gross "matter" do not necessarily hold throughout the whole range of physical corpuscles ; they vary in character and probably increase in com- plexity from ether-element up to particle. We cannot therefore, without further consideration, determine what are the laws of motion which are to be postu- lated of the organic corpuscle, if life is to be dealt with as a mechanism. The laws which describe the motion of two groups of molecules are not necessarily the same as those which describe the motion of two isolated molecules, or of two atoms. If the laws by aid of which we might describe the motion of ideal organic corpuscles were found to differ from those which describe the motion of particles of heavy " matter," it would not settle the problem as to whether we could describe life mechanically or not. The atomic system by which we conceptualize even the simplest unit of life is far too complex to allow, in the present state of mathematical analysis, of any synthesis of its motions in the presence of other 406 THE GRAMMAR OF SCIENCE. systems by which we conceptualize either living or lifeless " matter." We cannot at present assert that the peculiar atomic structure of the life-germ and its environment, or field (p. 342), would not be sufficient to enable us on. the basis of the laws of atomic motion to describe our perceptual experience of life. Such a broad generalization as that of the conservation of energy does not appear to be contradicted by our ex- perience of the action of living organisms ; but then the conservation of energy is not the sole factor of mechanism, as some fetish-worshippers nowadays imagine it to be. For example, there is the principle of inertia, the statement that no physical corpuscle need be con- ceived as changing its motion except in the presence of other corpuscles, that there is no need of attribut- ing to it any power of self-determination (p. 343). There are probably those who think some power of self-determination must be ascribed to the elemen- tary organic corpuscle, but this seems very doubtful. Placed in a certain field, environed with other organic or inorganic corpuscles, the life-germ moves relatively to them in a certain manner, but there seems no reason to assert (indeed there are facts pointing in the exactly opposite direction) that any change of movement need be postulated were the life-germ entirely removed from this environment. Indeed the whole notion of self-determination as an attribute of living organisms seems to have arisen from those ex- tremely complex systems of organic corpuscles, where the environment in the form of immediate sense-im- pressions determines change through a chain of stored sense-impresses peculiar to the individual or self (p. 149). But if this be self-determination we can LIFE. 407 hardly consider it to have any bearing on the simplest forms of life. We see, then, that biological change can probably be conceptually described by the change of motion of certain organic corpuscles in the presence of other corpuscles, either organic or inorganic. The structure of these organic corpuscles can further, to a great ex- tent, be described in terms of physical corpuscles. But whether the laws of this motion can be deduced from the laws of motion of physical corpuscles remains at present, and may long remain, an unsolved problem. If the one set of laws could be deduced from the other, it would greatly simplify scientific description, but it would not lessen the mystery of life. Those who project their conceptions into the phenomenal sphere would still be puzzled to know why corpuscles dance in each other's presence, and the mystery would be no less or no greater because a dance of organic corpuscles is at bottom a dance of inorganic atoms. Those who treat all motion as conceptual (p. 329) would still have the mystery of why sense-impressions change and change with routine as insoluble as ever. Clearly those who say mechanism cannot explain life are perfectly correct, but then mechanism does not explain anything. Those, on the other hand, who say mechanism cannot describe life are going far beyond what is justifiable in the present state of our know- ledge. We must content ourselves for the time being by saying that organic phenomena may be described by aid of organic corpuscles constructed out of in- organic corpuscles, and that the organic corpuscles move in certain characteristic manners, but that whether this motion follows or does not follow laws deducible from those dealt with in Chapter VIII. we have not at present the means of determining. 408 THE GRAMMAR OF SCIENCE. 6. Life Defined by Secondary Characteristics. Thedistinction,therefore, between the inorganic and the organic cannot be defined by saying that the one is mechanical and the other is not. We are ultimately obliged, in order to define life, to take secondary characteristics to describe the structure by which we conceptualize the organic corpuscle, the motions which are peculiar to it, and the environment in which alone we perceive life to exist. Thus we note that its atomic structure is based upon complex compounds (p. 333) of carbon, hydrogen, nitrogen, and oxygen, a substance termed protein peculiar to organic bodies, together with water. The combination is termed protoplasm, but although its chemical constitution has in some measure been investigated, it has not been, and there at present appears no probability of its being, obtained except from organic substances. Turning to the characteristic movements of life, we note that organic substance is conceived as growing differently from inorganic substance. When crystals increase in size we conceive them to set molecule to molecule, building up from the outside. Organisms, on the other hand, we suppose to grow by an inner growth or the addition of new organic corpuscles in between and not on the surface of the old ones. Life further undergoes cyclical changes or movements in which some process of reproduction or division renews the individual. Lastly, a peculiar environment, certain conditions of moisture and temperature are necessary to maintain life. All these characteristics suffice to mark off the organic from the inorganic, and the dis- tinction thus drawn appears to be absolutely rigid. 1 1 These are the distinctions of biology (see, for example, the article Biology in the Encyclopedia Britannica}. Of course a physical state- LIFE. 409 There is at the present time, so far as we know, no generation of living from lifeless substance. Thus our endeavour to define life has led, through some per- haps not unprofitable byways, to the consideration that the distinction between organic and inorganic is not so marked that we can separate the one from the other by anything but a lengthy statement of secondary characteristics. The axiom omne vivum e vivo is one which deserves the reader's special attention, for it is closely associated with many important problems on the borderland of biology and physics. In the language of this Grammar^ living and lifeless are class names for certain groups of sense-impressions, fundamentally distinguished from each other by requiring for their conceptual description different atomic structures and different types of motion. So far as our present ex- perience goes there is no routine of sense-impressions which, starting from the lifeless class, concludes with the living class. On the other hand the converse tran- sition from the living to the lifeless is an everyday routine. 1 We have seen (p. 390) that the latter fact has been used by Weismann as an argument in favour of the spontaneous generation of life "that which can be completely resolved into inorganic matter must also have arisen from it and must owe its ultimate foundation to it," he writes. This passage seems to be rather too dogmatic and to ment as to the laws under which organic corpuscles are to be conceived as moving in each other's presence and in that of inorganic corpuscles, might, could it be found, resume many of these characteristics in a simple formula. 1 For example, in the boiling of impure water or in the pouring of acid on vegetable matter, but hardly in the ordinary " death " of a complex animal organism. 4IO THE GRAMMAR OF SCIENCE. suggest a metaphysical subtratum to sense-impres- sion which is " completely resolved." The argument would only be a valid one if we could assert that all sequences of sense-impressions are reversible, but this is too wide a statement to be laid down unrestrictedly in the present state of scientific knowledge. Physicists will recall processes like the degradation of energy, of which they are unable to at present conceive any reversion. It may be that their perceptual experience is not wide enough, and that their geometrical and mechanical laws are only applicable to a certain portion of the universe, or it may be, after all, that sequences are irreversible. Hence the spontaneous generation of life does not follow as a " logical necessity " from the transition of living into lifeless substance, at least as long as we cannot reasonably infer the reversibility of all sequences of sense-impres- sions. 7. The Origin of Life. Those who accept the evolution of all forms of life from some simple unit, a protoplasmic drop or grain and this scientific formula is so powerful as a means of classification and description that no rational mind is likely to discard it will hardly feel satisfied to stop at this stage. They will demand some still more wide-embracing formula, which will bring under one statement their perceptual experience of both the living and the lifeless. Here the physicist comes in with some very definite conclusions. He tells us that in order to classify his perceptions with regard to the earth he is compelled to postulate a period, distant, it is true, many millions of years back, in which, owing to conditions of fluidity and temperature, no life, such as we now know life, not even the protoplasmic grain, LIFE. 41 1 could have existed on the earth. This period has been termed the azoic or lifeless period, but we must be careful to note that we mean by lifeless only " with- out life as we now know it" Bearing these facts in mind there are three hypotheses by which we can con- ceptually describe and classify our present experiences of the living and the lifeless. They are as follows : (a) Life may be conceived as based upon an organic corpuscle which is immortal that is to say, it will, with suitable environment, continue to exist for ever. This hypothesis may be termed \h.t perpetuity of life. (b) Life may be conceived as generated from a special union of inorganic corpuscles, which union may take place under favourable environment. This hypothesis is termed the spontaneous generation of life.^ (c) Life may have arisen from the " operation in time of some ultra-scientific cause." This is the hypothesis of a special creation of life. We will briefly consider these hypotheses in succes- sion. 8. The Perpetuity of Life, or Biogenesis. The perpetuity of life at first sight appears to con- tradict what physicists tell us of the azoic condition of the earth. A reconciliation of the two hypotheses has, however, been found by Von Helmholtz and Sir William Thomson, who suggest that a meteorite like an ethereal gondola might have brought in a crevice the protoplasmic drop to our earth when the azoic stage was passed. But our experience of meteorites especially the intense cold they are subjected to in 1 In more technical language the hypotheses (a) and (If), are spoken of as biogenesis and abiogenesis respectively. In using the popular term " spontaneous generation " I must not be supposed to suggest that life (any more than consciousness) can be suddenly generated. 412 THE GRAMMAR OF SCIENCE. space and the intense heat they undergo in passing through our atmosphere, together with the proba- bility that they are fragments of azoic rather than zoic bodies does not allow of much significance being attributed to this pleasant conceit. The perpetuity of life seems to involve the conception of forms of life anterior to the protoplasmic grain and capable of withstanding an environment totally unlike what protoplasm as we know it can endure. Now it is highly probable that protoplasm itself must be con- ceived as having had a long development anterior to any stage in which we now find it. These stages may have been eliminated in the struggle for existence, or they may have been peculiar to conditions of moisture and temperature which have long passed away on our earth. We might indeed be forced to conceive them as imperceptible like the atom, or, indeed, as indis- tinguishable from inorganic substance, which would lead us remarkably close to the second hypothesis of spontaneous generation. This theory of the perpetuity of life, we must remember, is stated in purely conceptual language. As " eternity " is a meaningless term in the perceptual universe of physical phenomena, so it must be in the perceptual universe of biological phenomena. Time is a mode of distinguishing our sense-impressions, and it extends only so far as we have sense-impressions to distinguish (p. 221). The perpetuity of some primitive life unit is therefore a pure conception which, like that of the indestructibility of the atom (p. 304), helps us to classify and describe our perceptual ex- perience, but for which it is meaningless to assert any phenomenal reality. The perpetuity of life, however, involves some LIFE. 413 rather extensive inferences in particular, that life in its earliest protoplasmic forms (which we must con- ceive to have resembled in many respects existing pro- toplasm), was yet capable of subsisting under a totally unlike environment, 1 an environment in which only what we term inorganic substances have hitherto been perceived to exist. Such an hypothesis must accord- ingly be less adequate than any other which without greater inference, brings under a single formula our perceptual experience of both the living and the lifeless. 9. The Spontaneous Generation of Life, or Abiogenesis. Such a formula is that of the spontaneous genera- tion of life. In the first place, this formula involves the conception of forms of protoplasm anterior to those with which we are at present acquainted, but it does not suppose these like forms to have existed in unlike conditions. It postulates that if we were to go backwards the organic would have disappeared into the inorganic before we reached the azoic age. After the azoic age the physical conditions must be con- ceived as such that the various chemical compounds were evolved which ultimately culminated in the first protoplasmic unit. 2 But if this be so, it may be asked : 1 Compare the Second Canon of Logical Inference (p. 72). 2 Lankester (Article "Protozoa "), remarking on the steps which brought the earliest type of protoplasm into existence, writes : " A conceivable state of things is that a vast amount of albuminoids and other such compounds had been brought into existence by those processes which culminated in the development of the first protoplasm, and it seems therefore likely enough that the first protoplasm fed upon these ante- cedent steps in its own evolution just as animals feed on organic compounds at the present day, more especially as the large creeping plasmodia of some Mycetozoa feed on vegetable refuse." These words suffice to indicate the long stages of development that probably lie behind protoplasm as we know it. 4H THE GRAMMAR OF SCIENCE. Why cannot we find this sequence of sense-impressions in our present experience, why cannot we repeat the spontaneous generation of life in our laboratories? The reply probably lies in the statement that we seek to reverse a process which is irreversible (p. 410). In five or ten minutes we convert living into lifeless substance, but there is no reason for asserting that the reverse process can be gone through even in the lifetime of a man. On the contrary, it probably took millions of years, with complex and varying conditions of temperature, to pass from the chemical substance of life to that complex structure which may have been the first stage of organic being. Let us for a moment consider that there is possibly as long an evolution from the chemical substance to the protoplasm we now know, as from protoplasm to conscious animal life. Let us suppose that all the existing links between protoplasmic life, and that of the highest mammals had disappeared, and then let us set the biologist to demonstrate in his laboratory the spontaneous generation of consciousness by experi- ments on protoplasm ! We cannot assert where consciousness begins or ends, but we can trace back in continuous series the conscious to the unconscious, and it is no argument against the truth of the hypothesis that consciousness is spontaneously gene- rated to say that we cannot repeat the process at our will. In precisely the same manner spontaneous generation of life could only be perceptually demon- strated by filling in the long terms of a series between the complex forms of inorganic and the simplest forms of organic substance. Were this done, it is quite possible that we should be unable to say (es- pecially considering the vagueness of our definitions LIFE. 415 of life) where life began or ended. The failure to reproduce the spontaneous generation of life in a laboratory has thrown some discredit on the hypo- thesis ; but we ought to wonder that any one should have hoped for an experimental demonstration of such an hypothesis rather than be surprised at its absence. At the very best, physicists will have to give us far more definite information than we have at present, both with regard to the physical changes at the close of the azoic period, and with regard not only to the chemical constitution but the physical structure of protoplasm, before it would be advisable even to think of further experiments on the spontaneous generation of life. Even in the face of laboratory failure this second hypothesis seems far more satisfactory than that of the perpetuity of life. For in the latter case we carry back life through a continuous evolution to a stage where change seems to cease and we are left with a primordial life-germ and no antecedent state. Yet our whole perception of the phenomenal universe is continuous change. It cannot be said that this prim- ordial germ is comparable with the physicist's prime- atom. The latter is a pure concept by aid of which the physicist constructs his symbols for phenomenal bodies, but he does not assert that these bodies have been evolved from prime-atoms. Bodies, he considers, may at any time be formed by aggregates of atoms, or again dissolved, but he does not postulate that the whole physical universe was ever in such a condition that it would have to be conceived of as resolved into simple disaggregated prime-atoms. Indeed it is clear if he did so, that the primordial life-germ, if anything akin to protoplasm, would be non-extant, and the 4l6 THE GRAMMAR OF SCIENCE. perpetuity of life be contrary to physical theory. In order to compare at all the primordial germ with the atom, we ought to take the former as the basis of the most complex extant organisms and suppose that on their dissolution they were resolved again into germs. But this would practically involve the indestructibility of the unit of life an hypothesis which appears to be at once confuted by our perceptual experience. The physical history of the universe does not lead us back to an evolution from a prime-atom and then stop at that point. The hypothesis of the perpetuity of life does lead us back to a primordial germ and then stop there. What is more, this germ appears placed in surroundings where it is destructible, while no environ- ment, so far as our experience goes, need be conceived to have this effect on the atom. The two hypotheses, of the perpetuity of life and of the indestructibility of the atom, are therefore, if superficially alike, in reality far from comparable. It is an inference from the like to the unlike when we assert an evolution up to the primordial germ, and then a cessation of that evolution. On the other hand, it is no argument against spontaneous generation to assert that it, in its turn, leads us back to the prime-atom, at which we must again stop. For this is not the fact. It only leads us back to bodies conceptually constituted of prime-atoms, but which in physical evolution may be continually passing from one condition of aggregation to another. On the hypothesis of spontaneous gene- ration we must conceive life as reappearing and again disappearing when and wherever the physical condi- tions are suitable. The hypothesis does not in the least explain the appearance of life ; it merely formu- lates its appearance as a routine on the occurrence LIFE. 417 of certain phenomena. Whenever a planet passing through the azoic stage begins to consolidate and cool, then begins the chemical evolution which ends in the first stage of life ; but why this succession of stages takes place is no more a subject of knowledge than why the sun rises daily. As we describe the latter so we could describe the former, were we capable of closely watching for millions of years the physical history of a planet. 10. The Origin of Life in an "ultra-scientific" Cause. As to the hypothesis of a " special creation," science could not accept it as a contribution to knowledge had it even been able to cross-examine the only witness to the proceeding. The object of science is to classify and resume in brief formulae the phases of our perceptual experience. It has to knit together all our sense-impressions by conceptual links, and thus to enable us to take a wide survey of the universe with the least possible expenditure of thought. Since time is a mode under which we perceive things, we cannot accurately assert of the earth that such and such changes occurred " between one and two hundred million years ago." What we really mean is this : that in order to resume and classify our perceptual experience of the earth, we form a conceptual model of it, and such a model we conceive to have passed through certain changes one or two hundred million years ago in absolute time (p. 226). Such a statement is ultimately involved in the formulae by which we resume our immediate sense-impressions, and its scientific validity does not depend upon its describing something . which took place beyond the 28 41 8 THE GRAMMAR OF SCIENCE. sphere of our perceptions, but upon its flowing from laws which accurately describe the whole of our present perceptual experience in the same field. Now the hypothesis of a " special creation " cannot be accepted as part of a conceptual model of the uni- verse ; it cannot serve like the formula of evolution for example as a means of linking together phases of our perceptual experience : it would not bring unity into the phenomena of life nor enable us to economize thought. Had the universe been created, just as it is, yesterday, the scientific mind would describe and classify its immediate sense-impressions and its stored sense-impresses far better by aid of the theory of evolution than by aid of a "special creation," and in this sense science cannot accept the hypothesis of a special creation as any contribution to knowledge at all. Knowledge is the description in conceptual shorthand of the various phases of our perceptual experience, and the very statement of the hypothesis as " the operation in time of some ultra-scientific cause MI shows us that we have gone beyond know- ledge, and are metaphysically separating time from perception and projecting causation beyond the sphere of sense-impression (p. 186). The history of human thought shows us that at whatever stage men's power of describing the sequence of phenomena fails, that is, wherever their knowledge ends and their ignorance begins, there, to fill the place of the unknown antecedent, they call in a " special creation " or an " ultra-scientific cause." To the untrained minds of earlier ages this cloak to 1 This form of the statement is due to Sir G. G. Stokes : On the Beneficial Effects of Light, p. 85. (Third Course of Burnett Lectures.) London, 1887. LIFE. 419 ignorance seemed natural enough, but in a scientific age it is only an excuse for intellectual inertia; it shows that we have given up trying to know, where to strive to know is the first duty of science. For many centuries a seven days' creation of the world sufficed to screen our ignorance of the physical history of the earth, and of organic evolution, or the origin of species. On these points science is now perfectly definite, but it has had a hard struggle to get rid of the obstacles across the path of knowledge. The slight plantation by which mythology sought to screen human ignorance had become a forest, the special preserve of a caste, which it was sacrilege to hew down. Whether the battle will be now transferred to a " special creation " of the ultimate element of life remains to be seen, but in saying that science is at present ignorant as to the ultimate origin of life, we must be careful to allow no metaphysical hypothesis of an " ultra-scientific cause " to take root. We trust that light will come to science here, as it has come in equally difficult problems in the past ; and not im- possibly this light will come in the direction of the spontaneous generation of life. It is not before or behind in the sequence of cause and effect that we must insert the supernatural full stop. There is no need to cloak ignorance at distant stages with mystery ; the mystery lies at hand in every change of sense-impression, in the fact that knowledge is at all times a description, but never an explanation of that change. The spontaneous generations of life and of consciousness are not conceptions which reduce the mystery of being ; they but knit more closely together the veil of sense-impressions which bounds the field of knowledge and enshrouds the fundamental 42O THE GRAMMAR OF SCIENCE. mysteries of why we perceive at all and why we perceive by routine. ii. On the Relation of the Conceptual Description to the Phenomenal World. The reader will have noticed that the standpoint which the author of this volume has reached through an analysis of physical conceptions is largely con- firmed when we turn to biological science. Hypotheses of heredity, of the generation of life, and of the origin of consciousness, are clearly formulae which attempt to describe the routine of our percep- Past - FIG. 25. tual experience ; and they do this by aid of a conceptual model which not only resumes our present perceptions, but enables us to carry back into the past, or forward into the future, the sequence of scientific causation (p. 153). That the conceptual model and our perceptual experience agree at all points where we can compare them, forms the sole basis of our assertion that the model can be used to describe the non- perceptible past and future. If two curves were to be in contact along the whole of that portion of the arc which we were capable of examining, it would be valid to replace one curve by the other ; and to calcu- LIFE. 42 1 late the probability that the curves would continue to touch, would be to measure the belief we ought to put in our scientific predictions as to the future (p. 177). The capacity of the conceptual curve for representing the phenomenal curve within the sphere of our perceptions would not be in the least invalidated, if the phenomenal curve came to a full stop beyond the sphere of perception. 1 It is only when the symbols of our conceptual description are treated as the substrata of perception, or converted into what may truly be described as " ultra-scientific causes " of the routine of phenomena, it is only when the scientist becomes metaphysical, that difficulty arises. In biology this projection seems invariably to occur through the channel of physics ; the biologist looks to force, chemical constitution, molecular structure, for an explanation, where at best they can merely provide conceptual shorthand for descriptive purposes. It seems all the more necessary to emphasize and repeat this important distinction, because the failure to grasp it has been made the ground for what is really a metaphysical attack on the Darwinian theory of evolution. As I interpret that theory it is truly scientific, for the very reason that it does not attempt to explain anything. It takes the facts of life as we perceive them, and attempts to describe them in a brief formula involving such con- ceptions as "variation," " inheritance," "natural selection," and " sexual selection." But no more than 1 The analogy to the laws of science may be still better brought home, at least to the mathematician, by supposing the equation to the conceptual curve known, but not that to the fragment of a curve AB (Fig. 25). The points A and B would not lend themselves to scientific description, they would fall outside the field of knowledge. 422 THE GRAMMAR OF SCIENCE. the law of gravitation explains our routine of percep- tions with regard to the sun, does Darwin's theory of the origin of species explain our perceptions of change in living forms. Perhaps some of the modern critics of Darwin will be less ready to con- sider adaptations as " not explicable " by natural selection, but due to the " precise chemical nature of protoplasmic metabolism," or to " an internal fate, expressible in terms of dominant chemical constitu- tion," if they once grasp that physics and chemistry in their turn render nothing " explicable," but merely, like natural selection itself, are shorthand descriptions of changes in our sense-impressions. 12. Natural Selection in the Inorganic World. There is a problem, however, with regard to natural selection which deserves special attention from both physicist and biologist, namely : Within what limits is the Darwinian formula a valid description ? As- suming the spontaneous generation of life as a plausible, if yet unproven, hypothesis, where are we to consider that selection as a result of the struggle for existence began ? Again, for what, if any, forms of life are we to consider it as ceasing to be an essential factor in descriptive history ? We may not be able to answer these questions definitely, but some few words at least must be said with regard to their purport. In the first place we notice that as soon as we con- ceive a perfectly gradual and continuous change from inorganic to organic substance, then we must either call upon the physicist to admit that natural selection applies to inorganic substances, or else we must seek from the biologist a description of how it came to be a LIFE. 423 factor in organic evolution. Now there are two elements in natural selection environment, which may be either organic or inorganic, and death, as a process of eliminating those less fitted to this environment. In the case of purely inorganic substances we can con- ceive that, under the physical conditions which follow the azoic period of a planet, all sorts of chemical products with varying physical structures might appear. Scientifically we might describe these pro- ducts as the complex dances of corpuscular groups. In the meeting of group and group some groups would retain their individuality, others would lose it or be dissolved and possibly re-combined in new forms. Any group which retained its individuality would be spoken of physically as a stable product; and in the early history of a planet, although we are far from being able to describe accurately what might actually take place, it is not unreasonable to suppose that a physical selection of stable and destruction of unstable products might go on. We do not know why one element is more stable than a second, why it is better suited to its environment (we might describe the stability by aid of atomic accelerations, but this would not explain^ only resume it) ; we can only suggest a selection of certain compounds which, because they are selected, we describe as more stable. Now this selection of stable compounds is a very possible feature of physical evolution, 1 but it must be noted that it is not precisely the same as natural selection. The environment is in this case purely 1 It has been applied with remarkable power by Crookes (British Association Address, Section B, l8