tft of i@0Jmmmt Club CLASS ACC GIFT OF BOHEMIAN CLUB THE SOLAR ILLUMINATION OP THE . SOLAR SYSTEM. What shall you think, my dear Kepler, of the leading men of science here, when I tell you that, like the deaf adder that stoppeth her ears, they will not look at the Moon and Planets through my telescope, although I have had it offered to them for the purpose a thousand times ? They will not even look at the telescope itself. As the adder closes her ears so they close their eyes, to avoid the recognition of what is really going on. GALILEO'S LETTER TO KEPLER, FROM PADTJA, August, 19, 1610, [*** Quid dices [mi Keplere] de primariis hujus gymnasii philosophis qui,aspidis pertinacia repleti, nunquam, licet me ultro, deditS opera, millies offerente, nee Planetas, nee Lunam, nac perspicillum videre voluerunt ? Verum ut ille aures, sic isti oculos contra veritatis lucem obturarunt.] A TREATISE, IN POPULAR LANGUAGE, ON THE SOLAR ILLUMINATION OF THE SOLAR SYSTEM, OR, THE LAW AND THEORY OF THE INVERSE SQUARES 1 ; ' BEING AN ANALYSIS OF THE TWO RECEIVED LAWS EELATING TO THE DIMINUTION OF LIGHT BY DISTANCE, WHEEEIN IT IS SHOWN THAT, ACCOEDING TO UNDISPUTED FACTS OF NATUEE AND OF SCIENCE, THE SOLAE ILLUMINATION IS EQUAL THEOUaHOUT THE WHOLE SYSTEM, AND THE LAW OF THE INVEESE SQUAEES FOE LIGHT, PHYSICALLY IMPOSSIBLE. TO WHICH IS ADDED THE PEOSPECTUS FOE A PEIZE OF FIFTY GUINEAS OFFEEED FOE DISPEOOF OF THE SCIENTIFIC FACTS HEEE FOE THE FIRST TIME INDICATED. ALSO AN APPENDIX OF EXTEACTS FEOM THE WEITINGS OF PEOFESSIONAL MEN. BY COLLYNS SIMON, HON. LL.D., EDIN., n AUTHOR OP " SCIENTIFIC CERTAINTIES IN PLANETARY LIFE, OR NEPTUNE'S LIGHT AS GREAT AS OURS" (1855.) "THE NATURE AND ELEMENTS OF THE EXTERNAL WORLD," 'THE LOCALITIES CONNECTED WITH THE MISSION AND MARTYRDOM OF ST. PETER," &c., &c. WILLIAMS AND NORGATE, 14, HENRIETTA STEEET, COVENT GAEDEN, LONDON; AND 20, SOUTH FEEDEEICK STEEET, EDINBUEGH. 1879. Astron. Oopt. ASTRONOMY DEFT? TABLE OF CONTENTS. PAGE PREFACE xv PROSPECTUS OF THE PRIZE . 41 THE FOUR PARTS. PART I. Preliminary Information on the Question, and on the two ways in which Light is said to be diminished by Distance ; with explanation of the two Laws - 3 First Section. The Question stated ; more extensive than is commonly supposed. Proposed treatment of the subject - ibid Second Section. Light supposed to be diminished by distance in two ways at once, viz., through the action of the Medium and through enlarged space. The two Laws ----- 5 Third Section. Diminution by Medium, and its Law of Geo- metrical Progression explained. Two peculiarities of this Law - 14 Fourth Section. Diminution of Light by Expansion in enlarged Space, and its Law of the Inverse Squares explained. General meaning of the Law. Special remarks on the terms " spreading " and " distance." Difference which exists in the import of the term "distance " as used in this Law and in the Law for diminution in a Medium. The Square of the Distance in Geometry explained (1) by concentric spheres, and (2) by the pyramid or cone. Ap- plication of this geometrical principle to natural objects, Error 701072 Vlll CONTENTS. PAGB of supposing Light diminished in this Theory by distance from the Source. How Light is supposed to be diminished through enlargement of the area illuminated, shown by the concentric spheres and the parallel Screens. Precise definition of the Law and Theory. Distinction important between the geometrical Law and the alleged physical one, the one Law being the inverse or contrary of the other. Enlargement of the Area is, in this Theory of the Inverse Squares, a sine qua non of diminution. The seven propositions of which the Theory consists. Application of the Theory and its Law to the solar system ; (1) with regard to the size and position of the planets ; and (2) with regard to the varieties of relative area resulting from varieties of relative distance -----------16 Fifth Section. Concluding remarks on PART I. - - - 49 PART II. Physical Impossibility of the alleged diminution of Light by Expansion, Stretching, or Dilution, through Enlargement of the space illuminated, or, as com- monly expressed, by the Law of the Inverse Squares 55 First Section. The alleged fact of Nature - ibid. Second Section. The common fact of Nature and Experience - 61 Third Section. The consequence of the alleged fact and received Theory shown to be the increase of Light (as well as of Area) by the Square of the distance, instead of its decrease in that ratio- - "- \ ' - : '" 63 Fourth Section. Two main sources of the error : (1) The theory of multiplying the force which proceeds from a point or centre ; (2) The Divergence Theory . s .. .. r . .- , . . - - - - 69 Fifth Section. Recapitulation of the received Theory and its physical impossibilities -------- 109 Sixth Section. Two popular efforts made by Professors to justify the Law, viz. (1) the effect of Perspective and the Medium employed to prove the natural expansion of Light or its CONTENTS. IX PAGE capability of spreading independently of all Medium ; and (2) the effect of the Medium alone in photometrical Experiments, em- ployed also to establish the same principle ; both which facts prove the contrary of what it is intended they should prove - 114 PART III. Logical Impossibility of the alleged Law in Optics, known as the "Law of the Inverse Squares ;" with four Illustrations of its incoherence - - - 125 First Section. Difference between the Theory and the Law. Two interpretations of the Law verbally possible. The ordinary one. Use of the term " inverse " in this place - - - - ibid. Second Section. Logical Impossibility here of the term "inverse." No data for it. (What yre do not know upon this subject ; What we should require to know in order to frame the Law; and What we do know) ------- 134 Third Section. Illustrations of the absurdity latent in the " Law of the Inverse Squares," and of the fact that " 900 times more reduced" does not mean "900 times less" - ..T-; - ; / - 143 Fourth Section. Recapitulation of PARTS II. and III. - - 149 PART IV. The Interplanetary Medium and its effect upon the Illumination of the Planets by the Sun - 155 First Section. Diminution by Absorption and Diffusion in a Medium the only diminution of Light in its passage from one point of space to another - - - - - - - - ibid. Second "Section. The professorial Law for this diminution in a Medium. Its two obvious errors - - > *. . - 156 Third Section. The ordinary, or unprofessional Law for this diminution in the Medium - - - - - - - -162 Fourth Section. Highly rarefied nature of the Interplanetary Medium ----------- 165 Fifth Section. Confusion made or tolerated by Professors, between the diminution from Absorption, and the other diminu- tion which they suppose to be independent of Absorption - - 167 X CONTENTS. PAGE Sixth Section. Two further errors tolerated and even en- couraged by the indifference of the Profession - 169 Seventh Section. General Conclusion ; -with a Recapitulation of the Propositions insisted upon in the Treatise - - - 170 THE APPENDIX. No. 1. Professor Hogg's "Elements of Natural Philosophy." Of the Spoke-Theory or Spoke-Form of Light. Of the jet-black spaces between the rays, and the relative (but not real) diminution of Light in consequence ; yet that every point of space has solar rays upon it. Of Con- vergence. Absorption very great in our Atmosphere and in Water - ..- - - - - 179 No. 2. Professor Lommel's " Nature of Light." Shows how the Law of Areas being true is supposed to prove that Light, when it has room, leaves the straight line and spreads, in the Spoke-Theory. Disputes this theory, denying the spoke-like isolation, and acknowledges that the Law of the Inverse Squares is an opinion or mere admission 181 No. 3. Professor Tyndall's "Notes on Light." Origin of the Divergence or Spoke-Theory. The Law of Areas in Geometry being true proves that Light deviates and spreads. Illustrations in a Medium of what happens without one. The Law, however, a mere opinion. Illustration of its truth from Perspective, Blocks of Light- . ..r;':- '.-- '.;. * ^^ 184 No. 4. Professor Kunzek's "Treatise on Light." Of partial Divergence or the Spoke-Theory as the origin of the Law of the Inverse Squares. The received Law for Absorption in a Medium - .'.>* 186 CONTENTS. XI PAGK No. 5. Professor Sir William Thomson's " Natural Philosophy." Of the Law of the Inverse Squares as an opinion only, and that in Science we should always be ready for future progress. Blocks of Light .... 187 No. 6. Professor Sir John Leslie, in the " Encyclopaedia Britannica." Of the Spoke-Theory, and of the Law as matters of opinion but very obvious - ibid. No. 7. Mr. Proctor, the Astronomer. Of the Illustration from Perspective, and of the Law as a mere opinion - - 188 No. 8. A President of the British Association. That the Optical Law is merely the Law of Areas in Geometry not the contrary of it- - - - - ... - ibid. No. 9. Sir David Brewster's " Optics." Of the Divergence-Theory or Spoke-Theory, and of Convergence. The Law for Absorption in a Medium -.,..._ 189 No. 10. Sir John Herschel's " Optics," in the Encyclopaedia Metro- politana. Of the dark cones radiating through out space, from the same source as the Light proceeds ; and of the distant Object more or less spotted with Light according to its distance from the Source ; also of the Law for Absorption in a Medium ------ 190 No. 11. Lambert, A.D, 1759.< Of the Superior importance and inexcusable neglect of Photometry as compared with the two other branches of Optics; and of the confusion made between what happens in a Medium and what happens aloof from Medium - 191 No. 12. Bouguer, A.D. 1729. That there are two totally distinct kinds of Diminution in Light supposed to be always going on in Nature at the same time. Of the Inverse Squares Theory, the Spatial Theory, or Diminution in empty Space. Of Diminution in a Medium. Of both Theories as mere suppositions or opinions - - 192 X CONTENTS. PAGE No. 13. Fischer's " Natural Philosophy" and Biot's Notes upon it. Of the two diminutions, one by the Medium, and one by Space alone, or the Spoke-Theory, both going on at the same time. The spots of Light farther from each other on the more distant objects. The Spoke- Theory the origin of the Law ----- 203 No. 14. An English Professor of the highest distinction. The Law and Theory of the Inverse Squares a mere opinion. The readiness of all, to have disproof of this Law and Theory when disproof can be discovered - - - ibid. No. 15. Arnott's " Elements of Physics." Of the rays splitting up, or dissolving, and thus deviating from the straight line in empty space (called "the Spreading of Light.") That whatever proves the Geometrical Law of areas proves that Light spreads. He nevertheless supposes the Law to be independent of enlarged area, and merely, as in a medium, dependent upon distance from the Source. Absorption very great in Air and Water. Two kinds of Diminution, that by mere Space and that by mere Absorption, going on, at the same time - - 204 No. 16. Ganot's "Natural Philosophy." Of Air and Water as powerful Absorbents. Of invisible Light. Radiation of Light, universal, extending to every point of Space, from every point of the central Source ; i.e., convergent cones from the disc, universal. The Spatial Diminu- tion, or Spoke-Theory of Light, is the origin of the Theory respecting the Inverse Squares _ - - 207 No. 17. Faraday's " Various Forces of Nature." The Law " a sad jumble of words," and " a curious expression." He explains what is meant by the Law, and says it is found true of Gravitation; but does not here vouch for its truth with regard to Light. When, at the end, he says " this screen is the brightest because it is the CONTENTS. Xlli PAGE nearest," no one supposes the sagacious Faraday to mean that this is not the result of Absorption - - 208 No. 18. Professor Helmholtz. The two diminutions supposed to be always going on together. The solar light not diminished by mere distance from the source; being equal at all distances, unless we suppose its rectili- near course to be stopped, and that each ray dissolves and becomes scattered, when it gets room, by some inherent explosive or expansive nature. That Bougiier's experiments on the Inverse Squares apply only to our atmosphere ---___ 209 No. 19. Schiaparelli. The Law a mere matter of opinion, and attended with much difficulty - ibid. No. 20. Dr. Thomas Young. If we suppose rays, we must suppose a space black as jet on each side of each. The absorption of Light in our Atmosphere, immense, also in Water. The same amount of Light falls on surfaces of all sizes equally exposed to a central source. He, like so many others, represents the Law as a mere " supposition " or matter of opinion, which, however, many things render probable. In opposition to the Spoke-Theory and the dark cones, be insists that the " ray " or atom of Light is the cone which consists of the whole light of the disc, converging on each point of space, and therefore on each point of each surface presented to the disc. That the Law is not applied to Gravitation for the same reasons as it has been applied to Light ; and has both applications, as being in itself the simplest law for rectilinear action where the lines of action have cones of space between them, exempt from action ; but without saying why any one supposes these cones or intervals - 210 PKEFACE. HAVING endeavoured, in short statements, without success, for nearly five-and-twenty years, to induce professional men to study the subject in Physical Optics here mainly treated of, viz., the Theory and Law of the Inverse Squares, and the Illumination of the Solar System by the Sun, I now propose to lay the facts more in detail before a more extended class of readers, before the scientific who, not being Professors, may therefore have more time to attend to what is new, and before the more thoughtful of the community, even though these may hitherto have made no special scientific studies. In the interests of this latter class of readers, every statement here made will be found entirely divested of Technicalities, those Technicalities which, however useful as stenography for Professors among themselves, I cannot but regard as the closed doors of Science, by which public discussion is consciously and care- fully excluded, and by which, no doubt most unconsciously, scientific progress is impeded, as all progress is, and must be, in the dark corners of Monopoly and Protection. It was in 1855, in reply to the Essay on the " Plurality of Worlds," by a writer of great distinction, that I published a small volume on some facts of Science connected with Life upon the Planets, for the express purpose of drawing attention to this equal distribution of the solar Light, as well as to some few other points of planetary science which xvi PREFACE. also seemed to me to have been hitherto unaccountably neglected. That little work was examined, with their usual liberality, by our two highest authorities in the science of Optics, Sir David Brewster and Sir John Herschel. They had the kindness to point out in the work an error respect ing the exhausted receiver, but neither of them found any error to point out in what was there stated respecting the distribution of the Sun's Light throughout the system, both merely saying, in kind and candid letters, that my general conclusion was so extensive, and involved so many con- siderations, that they could not, with their large amount of daily work, examine it sufficiently, but that they saw no reason to doubt that the ordinary opinion was correct. As, however, my conclusion does not in itself involve this necessity for any extensive studies, I supposed their mean- ing to be that it would require a great deal of investigation to discover whether it clashed, and how far, with any popular modern hypothesis, or how, at least, it was to be reconciled with such ; and this, of course, I could, not deny, might be the case ; although, as far as I could judge, I was not able to see that any study whatever would be required for that purpose. Many other professional men then, and afterwards, re- ceived copies of the work, and letters respecting it, but as is so usual in the case of men occupied in business, they were unable to take notice of either. In the " Corrispondenza Scientifica " (which has been published during the last thirty years, on the Campidoglio in Rome), I wrote in 1875, at the desire of the Editor, an article on one portion of the same subject, viz., on the logical defect in the Law of the Inverse Squares ; which PREFACE. article was subsequently translated into French, and much circulated among men of science in European countries. It produced, however, no discussion that I have heard of. I afterwards, in the hope of drawing attention to the subject, offered further articles to various English Journals suggested to me by the Professors whom these Journals rely upon in such matters; but in no case were the articles published, although offered gratuitously, nor the least notice taken of the question. In 1876, I presented a "Memoire" on that subject to the French Institute, at the suggestion of an Astronomer of European fame, as well as subsequently to the Lincei in Rome, at the suggestion of another Astronomer equally distinguished; also to the Istituto Lombardo at Milan, through one of its most celebrated members ; but in all three cases without obtaining any investigation of the scientific facts I indicated. It is now by the kind advice of a foreign Physicist who deservedly takes rank among the most eminent in all that relates to Light and Optics, that I have written, with so much detail, the present pages, as, in his opinion, the most likely means of obtaining the dis- cussion I so much desire. This effort, however, to drag into view the extraordinary errors so long and so dogmatically taught under a covering of technical language, I have not entered upon until I had found it impossible to induce anyone else, Professor or not, to undertake the task of doing so, whose name alone, already in favour with the public, might have rendered it so much more easy a task for him than it is likely to prove for me. I proceed now to another department of what here requires to be explained. I have in these pages occasionally adverted in terms of discontent (or, as some will express it, of b XV111 PREFACE. reprehension and remonstrance) to the utter disregard, manifested by the advocates of this Theory, for anything like scientific certainty respecting it, and to the discourage- ment of its discussion, on the part of those who could have best promoted such discussion, as well as to this unaccount- able surreptitious recognition of a mere " opinion" as a scientific fact. But here it is my first duty to state that I have found nothing of all this in the case of unprofessional scientific men. I have found nothing whatever to complain of with regard to the attention given willingly to the subject by such men, nor to the fearless judgment which they all uniformly express respecting it; and even with regard to many Professors, especially with regard to the more refined and distinguished of these, I have nothing to utter but gratitude for such little attention as their enormous professional work allowed them to afford me. Notwithstanding this, however, or rather on account of this, the distinction between scientific men who are pro- fessional and those who are not, is, upon this question, an important one. The latter have leisure for new subjects and for subjects which are unattended with financial advantage. The former have not. Those who live by the Profession and their fame have already so many subjects, lectures, articles, books, consultations, &c., on hand, that they have no time or strength for more. They are as it were in chains ; and chained moreover to what is already before them. Besides which, there is an Orthodoxy in the profession of a Science as well as in that of a Religious form ; from the bondage of which Orthodoxy the priests of Science are no more allowed, than other priests, to con- sider themselves exempt. For this reason the free scientific PREFACE. XIX man is more open to listen to new discoveries, and to in- vestigate them, and to fling off mere Orthodoxy. Thus it is that during that quarter of a century to which I .advert as having been occupied with this subject, I have rarely found a scientific man exempt from the " business " of Science, in other words, I have rarely found an unpro- fessional scientific man, who was not disposed to examine these strangely neglected questions, which constitute, really, the whole of one of the three great departments of Physical Optics (viz., Photometry), and even, after the little attention requisite, disposed to regard my facts and reason- ings as being conclusive, i.e., as being entirely exempt from mere opinion ; whereas in that time, a long time now-a- days in scientific progress, I have found no Professor who, to say nothing of any other hindrance, had even the little leisure necessary to study these Propositions, and comparatively but few who even had patience with the unprofessional man who considered such questions his own as well as theirs. Such discontent then as, in these pages, I may be found to express, must not be misinterpreted. It is not ever against men of Science generally that it is expressed, but only against Professors ; nor against the profession gene- rally, but only (1) against some of its members whose idiosyncrasies I have had to encounter in my efforts to bring these facts in the most effective way before the public; and (2) against that lamentable incubus which weighs upon the whole Profession of Physics, to whatever source it is to be attributed, and for which its members do not seem to be responsible, but which so restricts the action of the more competent Professors that they have not the XX PREFACE. least time free from teaching, not even what would suffice to investigate the truth of what they teach. It must not therefore be supposed that I here blame professional men as a body ; I do not ; however much I could animadvert upon the conduct of individuals. The only two points which I bring, in any sense, against professional men generally are two which they will all, themselves, at once admit the truth of, even those who are the most opposed to my exertions, and which, at least on this question, they will now, I doubt not, themselves speedily rectify ; while, in contributing to this rectification as far as lies in the power of one who is not in the Profession, I cannot but consider that I am co- operating with them, certainly with the more enlightened" of them, instead of thwarting them. One of the two points to which I allude is, that they all teach the doctrines shown in these pages to be false, and which, if they could even be only suspected of being false, no Lecturer would care to teach. The second is, that they have invariably declined to examine into the truth of these doctrines, or of the facts which contradict them, whenever applied to for that pur- pose. The Profession, generally, will do me the justice to recognize that, in what I have here written, these are the only two statements I make respecting them, and that these two statements are true. However curious such circum- stances may be, and however much to be regretted, there is not much to blame individuals for in either of them ; not in the first, because we are all liable to make mistakes, especially when we indulge in traditional science, taking things on trust from our ancestors ; and not much to blame in the second of these circumstances, except only where investigation is possible yet neglected, or where it is refused "PREFACE. XXI either with childish fretfulness or under some mistaken notion of professional infallibility. One of the two statements here in question, is that all the Professors teach, for instance, the five following Principles : First, that Light spreads, thus thinning out and becoming weaker ; Secondly, that we have 900 times more Light from the Sun than Neptune has ; Thirdly, that at any distance whatever from a luminary, the Light is four times greater than at double that distance ; in other words, if we take any length in the line of dis- tance from the source, the Light at the beginning of that length is always four times greater than that at the other end of it ; and this, whether the length taken be an inch or a mile ; Fourthly, that the light of 500 candles would not require more medium to absorb it, than the light of one candle would require ; Fifthly, that no amount of Medium, however extensive or however dense, can ever wholly absorb even the light of a single candle. Here then is one of the only two points on which I can be said to remonstrate with the Profession, if indeed my words even amount to a remonstrance. Why have these doctrines, I seem to ask, been so long taught in the Royal Society and at the Royal Institution ? Ought we not to be a little ashamed of ourselves that such an extraordinary incident should have occurred among us such strange credulity have grown up in our honoured halls of science ? XX11 PREFACE. and does it not justly excite the fear that other scientific errors of equal obviousness and equal magnitude may remain behind ? But surely with regard to such Propositions as those just cited, and to this general remonstrance, if such it is, respecting them, I cannot well be found fault with until the ordinary teaching is shown to be correct, and my facts and reasonings shown to be erroneous. The other point which I bring against the Profession as a body, and which they will recognize not only as being the only other point which in these pages I do bring, but also as being something fairly and justly attributed to them, is that whenever the investigation or discussion of these five prin- ciples has been either publicly or privately proposed to them, they have not only declined it, but discouraged it. This they will all admit. It is, moreover, clearly proved by the fact that although, in one form or another, the question involving these principles has been now before them for nearly five-and-twenty years, and urgently perhaps it will be said importunately pressed upon their attention, not one of them has yet undertaken its discussion. Now, as to the truth of these two statements, call them allegations if you will, there can be no dissension between me and the Professors, the five principles in question being' universally held and taught by all of them, and all, as a body, resolutely refusing to examine them ; the more enlightened being able to combine with the strangeness of this refusal nothing but what good nature might dictate to them, and the less enlightened not, of course, even that ; the more cultivated and enlightened refusing with kindness and consideration, declaring their inability through want of leisure to study the question, or their unwillingness, through PREFACE. conviction, to encourage its discussion ; while the less cul- tivated refuse, in the usual coarse way, either by ignoring all existence of scientific knowledge outside the Profession, or by merely taking no notice whatever when addressed upon the subject, or by manifesting a curious kind of irrita- tion, almost resentment, when it is suggested, as gently as possible, that perhaps the existing opinion on this subject might be found erroneous ; acting thus, as if conscious of some intellectual incapacity to discuss such questions, or even to utter a word respecting them, and as if silence, irritation, or self-complacency were the only means whereby they could hope to conceal this incapacity from the stranger. In only two or three trifling instances did this evasion take the form of impertinence, and of that " insolent admonition" which, under similar circumstances, Dr. Young had also to complain of from the ignorant. Of the very young and inexperienced, a few seemed to think that they sufficiently " protected themselves " by recommending me to procure and study some book they had lately written, or to study the Polarization of Light, or the Conservation of Energy, &c., as all offering "views" adverse to my "views;" while others of them at once retreated, each into his own little im- promptu forest of algebraic symbols and geometrical dia- grams, out of which they did not afterwards venture to emerge. So senseless, however, and unintelligible has all this singular conduct frequently appeared, as to give an im- pression that the applicant was suspected of endeavouring to discover some professional incompetence, and of seeking to supplant the occupants in their chairs; to some alarm of which kind upon their part, I have been compelled to attri- bute not only much of the unscientific proceeding I advert XXIV PREFACE. to, but also the remarkable fact that I have generally found Astronomers to be more ready to speak, and to listen, on the neglected questions of Photometry here under con- sideration, than I have found the mere Physicist to be ; as I have also found always the unprofessional man of science more disposed to do so than the mere Professor. But while thus endeavouring to specify, with as much precision as possible, the experience, which during all these years, I have had of the professional world upon this neg- lected branch of Optics, and to explain the grounds of my dissatisfaction with a considerable number of the Professors, I have great pleasure in stating that, although I have received from none what could well be called encourage- ment, I have without exception received from all the more eminent in the professions of Physics and Astronomy that kind and often generous attention which belongs as much to the love of Science as to the courtesies of life, and which enabled these distinguished men at least to see and to say that the proposed investigation would involve more study than they had time for at their disposal ; or, as some few of them in this country preferred to express it, that, although what they taught was mere matter of opinion, what therefore they could not establish by experiment or by proof, yet they were so " completely convinced " of its truth as to regard any investigation of it but as time mis- spent and withdrawn from more profitable occupations. And among those enlightened men of whom I speak, I may be permitted to mention the world-famous names of Respighi, Schiaparelli, Tacchini, and the late Father Secchi, in Italy; Fizeau and Janssen in France ; Helmholtz and Lommel in Ger- many ; with Brewster and Herschel among ourselves ; as well PREFACE. XXV as Professor Stokes, Professor Tyndall, Mr. Proctor, and Sir William Thomson. I repeat, however, and wish it to be dis- tinctly understood that, from none of these distinguished men have I received the slightest encouragement in the task I had set myself. Nor is that all. Although none of them have pointed out a single fact or reasoning of mine which they could speak of as inaccurate, only two or three of the gentle- men I have named, and those foreigners, could recognize even the possibility of my conclusions being correct ; some of the others, however, not unnaturally perhaps, misinter- preting these conclusions, and finding fault, not with what I said, but with what they, from the cursory glance which alone they could afford, supposed that I probably intended to say. To some of the most eminent of our professional men, in consequence of their advanced age, and from unwil- lingness on that account to give them trouble, I have not applied for their co-operation in this matter, well assured however, that if I had done so, I should have received from them the same courtesy and kindness as from so many others, although probably the same discouragement as from all. . It will be seen, then, from the foregoing circumstances, why I now seek a more extended auditory, and that this is done without the slightest sense of opposition to the wishes of the great leading lecturers of the day, but rather with the purpose of co-operating with them, in my humble way, by promoting that discussion and investigation about the success of which they experience in themselves so much discouragement or which they are precluded from promoting, in consequence of the large amount of professional work which they already have on hand. In fact it is, as ' I have XXVI PREFACE. already mentioned, only after this step of a detailed exposi- tion upon my part was good-naturedly suggested to me by one of their most eminent colleagues, that I have taken it, and have thus embarked in this attempt to make intelligible to all readers the extensive principles of Physical Optics here for the first time treated of, and as I am told for the first time discovered. I have, however, taken this step not merely to arrest the attention of scientific men generally, and even of the unscientific reader, but especially in the hope of bringing all who teach in Astronomy and in Physics, both the more enlightened and the less enlightened, round at last to give a little more attention to the Theory of the Inverse Squares in their Lectures and their Articles ; and, when they see the need, to correct with all the energy necessary, the mistaken notions resulting from this theory, and now so current respecting (among other matters) this unequal illumination of the solar system by the Sun. It is also with this same object, and in the hope of enlisting the sympathy of professional men everywhere in some discus- sion of the subject, that the PRIZE OF 50 GUINEAS is here offered for disproof of the natural facts here pointed out and acknowledged by all to have been hitherto completely un- known, even unthought of, so completely unknown and unthought of that, in the eyes of professional men, these facts have now all the appearance of being impossibilities ; this disproof to have, as may be seen in the annexed Pro- spectus, exclusive reference to the judgment of those who are in the capacity of public Professors either in Astronomy, in Optics, or in general Physics ; and either in Europe or in the United States of America as well as in any of our Colonies. PREFACE. XXV11 It will not be out of place to advert here to tlie fact that the present is by no means an exceptional or isolated instance of the reluctance with which each individual Pro- fessor of Physics gives his attention to innovations or dis- coveries, when they do not proceed either from himself, which of course cannot often happen, or from some member of greater authority in the Profession than himself, (for authority with the profession of Physics has as much weight as in the Church and in the Law), or when a practical application or public excitement, called "pressure from behind," does not invest the new idea with some pecuniary interest ; a reluctance this, whether merit or defect, which is as I say, considerably increased hi its operation, when the discovery originates with some one either wholly or mainly disconnected with the Profession. It is not reluctance only that is then experienced. It is with distinct repugnance that each member of the Profession turns away from the studies of those who " work as original investi- gators," the teachers of the teacher, and who are not paid for the instruction which they furnish, who occupy them- selves with Science con amore, from love of Science only, not for gain, and who are therefore called, by the Professors, " Amateurs," a term now of ridicule if not reproach, in spite of all that, for another purpose, has been said by some Pro- fessors to encourage scientific studies outside the Profession, (i.e., studies exempt from mercenary motive) in those who have the disposition and the leisure for them ; or, as it has been expressed, " to develop and deepen sympathy between Science and the world outside of Science, deeming it good for neither world to be isolated from the other, or unsympa- thetic towards the other." PREFACE. The present is by no means a solitary case of this repug- nance. The feeling- in question would be found in such cases, on the contrary, to be the ordinary state of things. To mention but one of the many instances upon record, and to omit all disputes and discouragements of mere Professors among themselves, I may remind the reader that, in the beginning of this century, Dr. Thomas Young, the dis- tinguished physician alluded to in a former page, although his innovations were afterwards most enthusiastically adopted by all the Professors of Physics, was for twenty years unable to prevail upon Sir Humphry Davy and the other leaders of Physical Science at that time in England, to attend to the very small amount of reasoning by which he was enabled perfectly to establish his statements. They not only refused to accept his conclusions, but even to attend to his reasons for them. They all represented themselves as either "quite convinced" or "sufficiently convinced" that the ordinary "view" of matters, the ordinary " opinion," was the correct one ; and this on no other intelligible grounds than because he did not belong to the Profession, and because the subject which he urged upon them, and which they had overlooked, was one of mere reasoning instead of mere experiment. For it cannot be supposed that they were unable to understand him until later, nor can it be alleged, in palliation of such conduct, that there was, at the time, any primd facie improbability of his having fairly arrived at the conclusion which he under- took to explain. On the contrary, he was known to be eminent in his own most difficult Profession (for which per- haps he was in the habit of expressing too strong a prefer- ence to please them), and is admitted by all to have been PREFACE. XXIX endowed with the energy and the intelligence which are, when combined, so easily mistaken for that special nature of mind which we call " genius," a term now often applied to him. During all that time, then, this remarkable man was sedulously " pushed from the public mind," as it has been, well expressed, " quenched for twenty years, hidden from the appreciative intellect of his countrymen," and treated as " a dreamer," the papers he presented, from time to time, to the Royal Society, being wholly disregarded, and all by the very men- whose duty it was to have helped forward the discussion which he asked for, whether it seemed of use or not to do so, and even if his reasonings, instead of being short and simple, had been extensive and compli- cated. It has been justly said that " there is no calculating the amount of damage these twenty years of neglect may have done to Young's productiveness as an investigator ;" and again : " If you starve or otherwise kill the scientific discoverer, (in those studies whose importance you cannot understand,) nay, if you fail- to secure for him free scope and encouragement, you not only lose the motive power of intellectual progress, but infallibly sever yourselves from the springs of industrial life." The following passage also, from the same pen, has a strict application to such a case as that of Dr. Young and the Professors of Physics in his day : " Let me remind you that the work of the Lecturer is not the highest work ; that, in Science, the Lecturer is usually only the distributor of intellectual wealth amassed by better men. . . . You have scientific genius amongst you, scattered here and there. Take all unnecessary impediments out of its way. Keep your sympathetic eye XXX PREFACE. upon the originator of knowledge. Give him the freedom necessary for his researches, not demanding from him practical results, above all things, avoiding that question which ignorance so often addresses to genius, 4 What is the use of your work ? What could be the use of your dis- cussing it?' Let him make truth his sole object, however unpractical, for the time, and unprofitable the investigation may appear to you. Never mind the use of it. Give it what encouragement you can ; and if you have this con- fidence, if you give the student courage and give him sympathy, although you understand him not, if you thus, in the Eastern phrase, cast your bread upon the waters, be assured that you will find it again, though it may be after many days, in substantial and practical profit, both to your industries and to your science." [ The latter clause of this eloquent address has been here slightly paraphrased from the original, in order to prevent it from being misinterpreted as an appeal in aid of funds for the Profession, which, of course, was not intended where this passage occurs.'] A few writers of eminence, themselves Professors of Physics, seem under the strange impression that it was not the members of the Profession, but unprofessional people, nay, one unprofessional and very young man, who refused the discussion of Dr. Young's propositions, and even declined to read his papers, thus prejudicing the pro- fessional class against him, and securing his condemnation by the only tribunal before which he could have been tried ! But this is an obvious misapprehension or forgetful- ness of what occurred, a misapprehension or forgetfulness which it is extremely difficult to account for, unless we suppose it produced, to some extent, by the sense of shame PREFACE. which the odious fact in question could not fail, in these days, to excite in the mind of any of our more enlightened Professors. Unprofessional people neither prevented the professional Public from examining and discussing Dr. Young's arguments, nor would it have been possible for a whole nation of them to have done so. We all know very well, and experimentally, that no unprofessional man could prevent a proposition from being discussed or held by our leading scientific teachers if these chose to discuss it or to hold it, however preposterous such a proposition might be, nor even prevent it, if approved of and encouraged by them, from being fully recognized, or at least discussed, by the unprofessional. We know indeed that one Professor of Physics will often succeed in preventing the conclusions of another Professor from becoming popular even in the Pro- fession, or the conclusions of an unprofessional man of science from being attended to by other Professors; but how can any one suppose that the paid teachers of Physical science, at the head of their Profession in the beginning of the present century, would have been deterred from dis- cussing Dr. Young's arguments merely because some one unprofessional writer, anonymous moreover, said he thought them ridiculous, and what the Royal Society ought not to sanction. This would be giving but a poor account of the Royal Society, and a most miserable estimate of our professional community, to say nothing of the circumstance that what really occurred was entirely different, and is now well known to have been so. But, independently of our biographical records, we have abundant evidence of the apathy, if not antipathy, with which the Professors received Dr. Young's innovations, even if we go no farther than the XXX11 PREFACE. three facts admitted by all writers on this subject; viz. (1) that there is no trace of any answer, by a Professor, to the youthful satirist in the Edinburgh Review, except that written by Dr. Young himself; (2) that, of Dr. Young's answer not more than one copy was sold in England ; and (3) that there was no serious examination or discussion of his propositions by English Professors until they were already fully recognized in France as true. Surely there can be no doubt in any one's mind of the neglect and dis- couragement here in question. Dr. Young was " too strong (it has been truly said) to be tied down by professional regulations," and " he worked as an original discoverer ; " which bold proceeding the Professors of Physics only tole- rate, in their colleagues, when even in them, discouraging it strongly in Physicians and all others, notwithstanding the equivocal overtures of a contrary character, already alluded to as occasionally made to " the Public " by one or two of our leading Lecturers. For twenty years, then, he effected nothing, " overborne by the authority of his antagonists." Although " an investigator of Truth for Truth's own sake," in the truest sense of these words, seeking no pecuniary advantage from his work, he found neither " promoters nor pro- tectors " among those who, better than any one else, could have " supplied his discovery with the freedom, light, and warmth so necessary for its development ; " and we read in the sad annals of his story, that this " Amateur " of the Professors never received from any of them, even from those among them who were his personal friends, the slightest co-operation nor encouragement, until a generous foreigner, a young Engineer Officer of spirit and ability, PREFACE. XXxiil devoted to optical research, and whose first Memoire on Light had just been crowned by the French Institute, gave these personal friends and the rest to understand, even in that Memoire itself, and before the world, that there was something for scientific men to be ashamed of in their con- duct to Dr. Young ; that what this distinguished man had tried to teach them, was what everybody could easily understand, even if everybody could not have thought it out ; that he had once supposed himself the first discoverer of it, but that he now fully recognized Dr. Young's prior claim to that distinction ; and that this discovery was what thenceforward every intelligent Lecturer would have to hold and to teach. Hereupon the professional members of the Royal Society began, for the first time, to study the statement of the English Physician as printed in their " Transactions," and, " startled at last into a consciousness of their injustice to him," vied now with each other in throwing themselves, midst regrets and compliments, at the feet of him whom they had wronged. They made him their Foreign Secretary by acclamation, and were, many of them, intent upon making him their President. Thus after twenty years of this scientific exile, twenty long years passed in " the hampering toils " of this obstruc- tion and this discouragement, without being able to obtain the least attention to his discovery, " having great names arrayed against him," (that professional obstacle to pro- gress,) the obstructive "authorities" were at last, in their turn, overborne by that " pressure from without," which never fails. They could not afford to be behind the Pro- fessors of the Continent ; and the reasonableness of what Dr. Young insisted upon was fully recognized, first indeed, XXXIV PREFACE. as I have said, and as generally happens, by foreigners, but afterwards recognized, to such an extent, by English Professors themselves, that almost all of them have since rushed into the opposite extreme of the wildest admiration for everything respecting him. One great admirer evinces this enthusiasm as follows : " To give you a notion of the magnitude of this Man, let Newton stand erect in his age, and Young in his. Draw a straight line from Newton to Young, tangent to the heads of both. This line would slope downwards from Newton to Young, because Newton was certainly the taller man of the two. But the slope would not be steep, for the difference of stature was not excessive. The line would form what Engineers call a gentle gradient from Newton to Young. Place underneath this line the biggest man born in the interval between both. It may be doubted whether he would reach the line ; for if he did, he would be taller intellectually than Young, and there was probably none taller." The reader will not be surprised to hear that this was written by an eminent member of the Profession which had been so unjust to Science as well as to Dr. Young. All this discouragement, obstruction, and neglect to which I have adverted, on the part of the Koyal Society, and of the Professors to whom Dr. Young's innovation had so unnecessarily appeared unintelligible (if that is the excuse which we are to offer for their treatment of him), as well as the full appreciation of his merits, in the subsequent generation both at home and abroad, are in the following passage, concisely borne witness to by the amiable and accomplished Helmholtz : " Dr. Young's was one of the most profound minds that PREFACE. XXXV the world has ever known ; but he had the misfortune to be too much in advance of his age. He excited the wonder of his contemporaries, who, however, were unable to follow him to the heights at which his daring intellect was accus- tomed to soar. His most important ideas lay, therefore, buried and forgotten in the folios of the Royal Society, until a new generation gradually and painfully made the same discoveries, and proved the exactness of his assertions and the truth of his demonstrations." It cannot be denied that there is something no less appropriate, as instruction, than as illustration, in the cita- tion of these facts. No doubt there will be the necessary tritic to say that I am seeking to compare myself to Dr. Young ; but I am not I am comparing my case to his, not myself to him ; and the cases resemble each other in many remarkable par- ticulars, four of which I may here mention : 1. What has been, in either case, contended for, is neither an hypothesis nor a theory, as some have imagined it to be, but a natural fact which seems in neither case to have been discovered before ; in his case, the . interference of water-waves; in mine, the non-deviation of the ray of Light from its straight line, the fact that it does not spread, thus thinning out and becoming weaker, upon one size of surface more than upon another. 2. These two natural facts have been, in their respective cases, wholly discredited by all the English Professors con- nected with the subjects, who have not only refused to dis- cuss the facts, but moreover even to attend to the evidence of them, on the ground of its being " of no use to do so," as the point at issue was, in both instances, a matter of XXXVI PREFACE; mere " opinion," and one on which these Professors had " already made up their minds." 3. Dr. Young had two aims, two propositions, both controverted ; I also have two, and both controverted. He was defending an optical hypothesis, the wave-theory, denied by most people in his day, and, in support of it, defending also, at the same time, this obscure but curious natural fact, the interference of waves in water, which was not only denied, or at least neglected, by most people, but by everybody. I am pointing out that an Optical theory, asserted by all, the theory of the Inverse Squares, is utterly and manifestly false ; and, in order to make this clear, I seek to explain that Light from its nature does not and cannot deviate from the straight line as that theory supposes that it can, a natural fact this also as stoutly denied or neglected by all, as the interference of waves can well be said to have been. 4. The refusal of the learned to study the fact extended obstinately, in Dr. Young's case, over twenty years, when at length the truth of his discovery was recognized abroad; and, in the present case, already over nearly five-and-twenty years, with, as yet, but a very little glimmering of this recognition ; and that little, as usual, not in England. In two other particulars our cases differ j these points of difference, however, so neutralize each other, that the obstacles to the triumph of truth have been, in both cases, pretty much the same. The success of the first case, there- fore, seems to augur favourably for the second: (1.) Dr. Young's fact (the principle of wave-interference) was more obscure and more difficult to be explained than mine, and, perhaps, it will be admitted, less urgent when he sought to PKEFACE. XXXV 11 draw attention to it, as well as less important ; for it was chiefly of use as being supposed to favour the undulation- hypothesis, then in little repute ; all which must have con- stituted an obstacle for him, that does not exist for me, inasmuch as, in my case, it is only for the wholly unscien- tific reader, if for any one, that the natural fact can be attended with any difficulty; and only by him, if by any one, that it can be regarded as, in any sense, uninteresting and unimportant ; since upon it there depends the truth or falsehood of the Inverse Squares in Optics, and the equality or inequality of the Solar Illumination throughout the system. (2.) The second of these two points of difference is this : There were a few foreign Professors, advocating, on the same occasion, and with considerable energy, the same Irypothesis as that in support of which Dr. Young put forward the curious fact of nature to which, as well as to the hypothesis itself, all in England refused the least attention. These few foreigners had therefore some little interest in this alleged fact of nature, and in its being successfully pointed out ; whereas this advantage I have not had at all. There is no question pending in the pro- fessional world that could give the great fact of nature which I point out, any special party interest there (the interest of all being, on the contrary, "to push it aside" and upon that point to have no discussion) nothing, therefore, offering- hope of any influence except mere brute " pressure from without," " to break through the circle here drawn, for so many generations, around the operations of the human intellect." This is a considerable and rather discouraging point of difference between Dr. Young's case and mine. The dis- XXXV111 PREFACE. tinguished Physician was, it is true, engaged in defending a proposition in which no one, in England, then took any interest (viz., the wave-hypothesis for Light), and was doing this through a physical fact, denied then, or rather un- considered, by all except himself (viz., the interference or combination of waves in water); but while he was, in England, in this hopeless condition of one crying in the wilderness, there were already in other countries some influential Professors zealously engaged, they also, in search of every indication that could be discovered in favour of the same undulation-hypothesis, although en- tirely strangers to the natural fact proposed by an English Physician in support of it; persons, therefore, who were not likely to leave unturned the stone under which this Physician told them they would find all they wanted. This co-operation, such as it was, I have not had. I seek to make known, to a singularly reluctant auditory, as far as the professional world is concerned, my great fact of nature (viz., that Light does not spread from its straight line, and thus diminish in intensity, that the theory of the Inverse Squares is therefore false, and that the solar system is all equally illuminated by the Sun), and this I do with- out any such aid as Dr. Young's fact, derived from the existing pursuit of an hypothesis ; mine being, on the contrary, a fact which not only furnishes no proof of any- thing at present in demand, but which can even be, as it has been, overlooked by all, and trampled on by all, in their headlong pursuit of far less important though more curious discoveries. I cannot boast of one single teacher of Optics or of Astronomy, even slightly interested in the truth of my fact, either in England or out of it. The only Professor, PREFACE. XXXIX but he, of universal renown, who, in his conversations with me, had the courage to say, and said it frequently, " Perhaps you are right," is no longer living, and I much doubt whether he has left any record even of his imperfect appreciation. But this great man, as the word " perhaps " here implies, had not the leisure to examine the subject further, weighed down as he then was, both with years and work. I am thus at this hour, as for so many years, wholly without co-operation in these efforts to make known the obvious fact which I have explained in the present treatise ; and this utter isolation seems to counterbalance the advantage connected with the other point of difference between Dr. Young's case and mine, leaving the difficulty, as I have said, pretty equal for both of us. But this diffi- culty, History thus teaches us, is not insurmountable. The enlightened men who fill our chairs of Optics and Astronomy are not now more completely " convinced," that the Optical theory of the Inverse Squares is true, that Light can spread, and that vast portions of the solar system have billions of times as much Light as other vast portions of it, than in Dr. Young's time, they all were, that the undulation- hypothesis for Light was false, and that his " innovation," in support of it, the interference of Water-waves, was the " pitiable nonsense " it was described to be in the Edinburgh Review. Although, therefore, my controversy has been always, as it still is, single-handed against the Profession, and has thus been, naturally enough perhaps, more prolonged than Dr. Young's, it can be. hoped that it now approaches its termination, and that this irresistible " pressure from with- out," which we are taught to consider as, in such a case, xl PREFACE. the only moving power in the professional regions, is at last about to break through the circle here also drawn for so many generations around the operations of the human intellect. " No authority," it has been truly and nobly said, " however high, can long maintain itself against the voice of Nature, when she speaks through experiment as well as common sense ;" and we need not despair that this theory of the Inverse Squares and of the ray that spreads, will, sooner perhaps than some imagine, share the fate of that hypo- thesis so long opposed without success by Dr. Young, and now, for a time at least, supplanted by its rival ; especially as, in the case before us, it is not proposed to replace the theory of the Inverse Squares by any rival theory, but only by the plain and simple facts of nature which it contradicts. As the Optical theory of the Inverse Squares is not only wholly false but also very generally misunderstood, even by those who write or lecture on the subject, there have been here two sets of errors to be pointed out instead of one set of these. It has been necessary to explain fully, as is done in PART I., the law and theory themselves, and the misconceptions current respecting them, before pro- ceeding to point out, in PARTS II. and III., the utter im- possibility of the law as well as of its theory. PART IV. relates merely to the conditions under which the Solar Light is diminished throughout the system, and under which alone all Light is diminished, when diminished by its distance from the Source. PROSPECTUS OF THE CONDITIONS, under which, for the purpose of promoting discussion, a PRIZE OP FIFTY GUINEAS is offered by the author, for the disproof of those facts and reasonings whereby in this Treatise it is shown that the whole theory of the Inverse Squares is an error in Optics, and that the Solar Illumina- tion of our system is so equally distributed that we should be unable o discern any difference in this respect between the different portions of the system. 1. The Prize is to be open for one year from the date of this Prospectus. 2. It is open to ladies as well as to gentlemen ; and to the professional as well as to the unprofessional. 3. It is open to Europe and the United States of America ; also to Canada, India, and all the British Colonies. 4. Each Essay is to have in writing, and with their respective signatures, the testimony of three Professors, selected by the candidate himself, or herself, from the professions of Astronomy, Optics, or general Physics, indis- criminately, to the effect that the Essay is, in the opinion of these gentlemen, the valid disproof required, in which testi- mony the separate propositions controverted as well as the candidate's arguments adduced against each, shall be dis- tinctly stated, and each Professor's distinct affirmation of their validity appended to each of the candidate's arguments. 5. The gentlemen selected by the candidates to declare d xH PROSPECTUS OF THE CONDITIONS. the scientific accuracy of their facts and arguments must be actually in possession of professorial chairs in Universities or National Colleges ; yet if declared in writing by such Professors to be competent judges, the testimony can be accepted of gentlemen sufficiently known who have formerly filled such chairs, or who have even merely written books on Optical or Astronomical subjects. 6. Any of these gentlemen may be selected in any of the countries to which competition for this Prize is open ; and there is no objection to remuneration being given, when it is necessary to do so, for the time and trouble of writing a testimonial. 7. No two Essays may bear the signature of any of the same Professors, or of others attesting the scientific accuracy of the disproof in question. 8. All Essays duly attested, as above indicated, to be sent in to the proposer of the Prize, through the publishers of this treatise, before the end of the year during which the Prize remains open. 9. The Essays will then be immediately submitted to some one gentleman of the highest scientific position that can be prevailed upon to arbitrate, selected by a majority of the candidates, and with whom it will rest to determine not only which Essay is the best as disproof of the propositions in question, but also whether any of the Essays constitute this disproof. 10. In case there is only one Essay sent in, or no majority of the candidates attainable, then there shall be three arbitrators chosen instead of one, to decide by their majority; and the choice of these will rest with the proposer of the Prize. PROSPECTUS OP THE CONDITIONS. xliii 11. The proposer of the Prize and author of this treatise, hereby pledges himself to pay immediately the Prize of Fifty Guineas to the candidate whose disproof shall be declared the best. 12. To render the precise subject of the Prize as clear as possible, it may be useful to specify that the two main pro- positions for the disproof of which this Prize is offered, are (1) that the illumination of the Solar System by the Sun is so equal outside the atmospheres of the Planets, that no difference which exists could be discerned by the senses ; and (2) that the law of the Inverse Squares in Optics is utterly false ; without here raising any question as to this law applied to Gravitation. It is well, also, for the same reason, to specify that the subordinate propositions by which the truth of these two main ones is established, and the dis- proof of which, or their disconnection with the main ones, it is also, therefore, indispensable to make quite clear, are (1) that Light of its own nature, does not, and cannot deviate from the straight line ; (2) that it cannot therefore diffuse itself or spread without a medium ; (3) that it does not consist of spokes (of Light) with un-illuminated intervals between these spokes ; (4) that it does not, therefore, become even rela- tively less in the larger regions of space ; (5) that when Light proceeds from a central source, z.e., from such a source that each point of the surface illuminated is equally exposed to the whole source, then the whole Light of the source exists upon each point of the surface ; (6) that there is, therefore, the same degree or amount of Light upon each part of the surface and upon the whole of it, since there cannot be more than the whole Light upon the whole surface ; (7) that Light therefore is not inversely, as the areas, upon each PROSPECTUS OF THE CONDITIONS. equal portion of them, or, as it is technically called, upon each unity of surface ; i.e., Light does not decrease as the square of the distance increases ; (8) that we, therefore, have no reason for supposing any other diminution of the Solar Light outside our atmospheres, except that resulting from the Ether or medium through which the Planets move ; and (9) that even if any such other sort of diminu- tion could be shown to exist, we have none of the data or knowledge necessary for framing the law of the Inverse Squares respecting it, either in the ordinary interpretation of this law, or in any other. July 1, 1879. ON THE SOLAR ILLUMINATION OF THE SOLAR SYSTEM; OR, THE LAW AND THEORY OF THE INVERSE SQUARES. |n Jfmtr |]arts. ON THE SOLAR ILLUMINATION OF THE SOLAR SYSTEM; OR, THE LAW AND THEORY OF THE INVERSE SQUARES. In ., the distance which is greater or less according as the two pictures differ in size from one another. The principle or measure called " the square of the dis- tance " is here and everywhere only used to define or describe the comparative sizes of the objects around us, in nature (whose sizes are all classed as the sections of a pyramid), and has no reference of any kind to their distance from a source of light. The theorists, when they use this expression, merely mean that the intensity diminishes when the object is greater on which the light falls and over which it spreads. That is all that the more intelligent and en- lightened writers mean. " The square of the distance " has no reference whatever for such men, except to the greater or smaller objects around us, upon which the light is sup- posed to spread. It has nothing whatever to do with their distance from the window, lamp, sun, or other luminary, as has been absurdly supposed by so many professors apparently unacquainted with the import of the geometrical formula; the term "distance" in which formula merely affords, as I have said, a measure of the area of such objects, and is, in this law, only used as such. But I neel not dwell upon this point. The least reflection suffices to show that PART I. SECTION 4. 21 no distance from a source of light can make one area larger or smaller than another, this difference of size being that alone which, in this theory, increases or diminishes the illumination. The square of the relative distance from the apex in a pyramid defines exactly, for instance, the relative size of two pictures ; but the relative size of no two pic- tures could ever be discovered or defined by our knowing their relative distance from a lamp, a window, or the sun. The sense in which Light is supposed to " spread," in this theory, does not present so much chance of miscon- ception as the sense in which the word " distance " is employed ; yet it has its vagueness also, and on this subject no vagueness can be allowed. The spreading of Light is always understood, by these theorists, to be, as above remarked, right and left, or up and down, upon the surface illuminated ; but not from the source outwards to that surface ; for the spreading in question is not required in that direction, that being the natural path of the rays, which proceed along it, undiminished in force or number, to the confines of the system. It is thus held that Light spreads in two dimensions of space, as it were not in the third. The law we are now speaking of has no reference, we see, to a Medium, nor to the action of a Medium. This must be well borne in mind. The spreading here meant, therefore, is not that result of a medium with which we are so familiar, and which enables Light not only to extend, but even to go round a corner. The spreading of Light, in this theory, is supposed to take place independently of all medium. The theory supposes the light, from any given central source, to be the same, in amount and degree, upon surfaces of all sizes, equally exposed to it, however much they differ from one another in size, and however nearer some may be from the source than others. For instance, the light is, by this law and theory, exactly the same at one mile from a lamp as it is at three feet from it ; and the amount which falls upon an area a mile square, all equally exposed to the lamp, is the same as that which falls upon a square 22 PART I. SECTION 4. yard. The law then states that as this same amount of light is in the one case spread out over a much larger space than in the other, the light upon this larger space is thereby diluted, and rendered feebler in proportion as the one space is more extensive than the other, or, as the favourite expression runs, has a greater square of distance. Since the illumination is thus held to be inversely as the surfaces are great or small, i.e., as they have a greater or less square of distance, the law states that it is in- versely as this size or square of distance; a square of distance, however, which the reader now sees has nothing whatever to do with the distance of the object from the window or other source of light. The law as well as the theory is, that Light loses in intensity when the surface it has to cover, or be spread over, is enlarged (z'.. tional disguise and equivocation, which it was indispensable to remove ; for unless the reader fully understood the theory which gives the unexpected results now pointed out, he could not understand what it is that is controverted in the ensuing pages. There is, moreover, in all this the received Law and Theory for the diminution of Light by the mere enlarge- ment of the space illuminated, as well as in the peculiarities of the other received law for its diminution by Absorption in a Medium, something so incredibly superficial and un- scientific that I have considered it requisite to give, in an Appendix to this Treatise, a few statements of both these Laws and of the first-mentioned Theory, in the ipsissima verba of the Professors themselves. Otherwise the asser- tions involved are so extraordinary, to say nothing else of them, that the reader would hardly be able to suppose that these assertions and Laws are here correctly represented. And the two Laws, now explained, must be carefully kept quite distinct by the reader. This is a most important point to be attended to. They have nothing whatever to do with one another. The simultaneousness of their action, as held by scientific men, implies no intermixture whatever either of the action or of the effects. It will be seen, as we go on, that both laws involve complete misapprehensions respecting the facts of nature which they profess to deal with ; but of the two, by far the more important, in this case of the solar system and its solar illumination, is the Law of the Inverse Squares. It is in fact this Law upon which the whole question depends which I wish here to place before the reader, on the Illumination of the Planets ; for, as will be seen in PART IV., the medium between the Sun and the Planets has almost no effect in diminishing the light. This Law, therefore, for the diminution of Light by the enlargement of the Space, or as it is commonly termed, by " the law of the Inverse Squares," and the alleged facts of Nature upon which this law has been founded, compre- hend together almost all that it will be necessary for me to PART I. SECTION 5. 51 treat of in order to explain the great principle that all the planets of our system are equally illuminated by the sun, although revolving round him at such unequal distances. But let us first attend to the alleged facts of Nature upon which this law professes to be founded, viz., the deviation, spreading, stretching, or diffusion of Light where there is no medium supposed to be present, and the attenuation, dilution, or impoverishment which is supposed to result in Nature to this luminous essence in consequence of the capa- city for this deviation from the straight line, this stretching, spreading, or diffusion, which we thus attribute to it inde- pendently of all Medium. END OF PART I E 2 PART II. PHYSICAL IMPOSSIBILITY OF THE ALLEGED DIMINUTION OF LIGHT BY THE MERE INCREASE OF THE SPACE ILLUMINATED, OR, AS IT IS CALLED, BY THE LAW OF THE " INVERSE SQUARES." PART IT. PHYSICAL IMPOSSIBILITY OF THE ALLEGED DIMINUTION OF LIGHT BY THE MERE INCREASE OF THE SPACE ILLUMI- NATED, OR, AS IT IS CALLED, BY THE LAW OF THE " INVERSE SQUARES." FIRST SECTION. THE ALLEGED FACT. THE reader now clearly understands, from what has been said, that, in this celebrated theory of the Inverse Squares, it is the enlarged space or area alone which diminishes the Light ; Medium and its action being here entirely set aside, not however as things which do not exist, but as things of which no account is taken in this particular theory; and that the Distance of the illuminated area from the source of the Light has no effect whatever, except in those cases where this distance is required for producing this enlargement, which, as we have seen, is for the most part only in the diagrams of Geometry. This distinction is one here of the utmost importance. It is only the enlargement or diminution of the space, or sur- face to be illuminated, the greater or lesser area alone, which has to be attended to, as that which diminishes or increases the Light. The distance of any area from the source of the light has nothing whatever to do with this diminution. (See pp. 20, 23, 59, and 61.) The enlarged space 56 PART II. SECTION 1. or surface, it is true, is connected in Geometry, but only in Geometry, with distance from the source of Size, i.e., with the greater distance at which the space or surface is placed from a given angle in the diagram not at all with any distance in Art or Nature, nor with any distance from the source of Light. In Art the greater or lesser surface results from the tools or will of the workman, and in Nature from the laws of Nature. In neither of these cases does it result from the laws of Geometry, nor depend on its distance from a source of Light. It is alone then this enlargement of the space illuminated, whether it be far from the source of light or near it, and not at all its distance from this source, which, by this, the received theory, attenuates, dilutes, or diminishes the Light; just as the diminution or contraction of the space or area has, of course, by the theory, the opposite effect. As far as the geometrical ratio of areas, or angular source of magnitude is concerned, the law, it is well to remember, is that, whatever number of times one surface or area may be greater or less, in Nature, than another, their geometrical distance, i.e., that in their pyramid or dia- gram, is the square root of their difference, and their geome- trical difference is the square of their distance from the apex, be their distance or difference, in Art or Nature, what it may ; well to remember that the geometrical fact mentioned has nothing whatever to do with the areas or distances of areas, in Art or Nature, nothing whatever, for instance, to do with the discs or areas of the planets, and their dis- tances either from one another or from the sun. The geometrical ratio in question is not at all necessary, there- fore, in this theory, for the diminution or increase of Light upon any area or surface in nature. It has no more to do with the changes of Light, even in this theory, than it has with the changes of the areas or the surfaces around us. The theory only requires that one of the two areas should be greater than the other. The Light is described, in this the received theory, as PART II. SECTION 1. 57 diminishing at the same rate as the area is enlarged that is all ; as being 4 times less, upon each spot, when the area is 4 times greater 9 times less when the area is 9 times greater, and so on. This is what is meant by diminishing in inverse ratio to the square of the distance. The whole question then here is : Can this mere enlarge- ment of the space bring about this attenuation of the Light upon it ? Has it always, or ever, this effect? That is the problem to be here examined. A given amount of Light from a single source (for we all here only speak of a single, central, or unspread source a point, as it is often called,) falling equally over a given amount of space or surface, i.e., falling so that all the space is equally exposed to all the source, becomes, we are told, attenuated or diluted, diminished in strength, intensity, amount, or degree on each square inch, when the amount of the space, thus illuminated, is enlarged ; and this impoverishment of the Light takes place, we are further told, exactly in proportion to the Enlargement of the Space. If, as I have just said, that space or surface is doubled, the Light is thus reduced to one-half of its previous intensity on the square inch. If the space thus illuminated by the single source is enlarged 900-fold, then the degree of Light, available for each square inch or other portion of this space, is supposed to be reduced to -^^ of what it was, in precisely the same position, before the enlargement of the space. This is the alleged fact of nature upon which the so- called Law of the Inverse Squares professes to be founded. We 'have now to inquire : Is this really a fact of nature? Is it a thing physically possible ? All the space surrounding any point, the lamp, sun, or other luminary, becomes more and more extensive or enlarged, at every increase of distance from that point ; and this whether the point be luminous or not. This is a mani- fest fact, and undisputed. The Enlargement of this space is found to coincide, geo- 58 rurr n. SECTION 1. metrically, with the square of the distance from the centre, whether, as I have just said, this centre be luminous or otherwise. This also is undisputed. The whole space around the lamp, or other central point, becomes greater and greater in the ratio of the distance squared ; but the objects and surfaces lying in that space do not become greater from being at a greater distance ; nor does any one given portion of that space do so. The whole sphere of distance does, and even the whole hemisphere does. It is obvious, however, that an area of 20 yards square does not become enlarged by being placed further from the centre, whether lamp or Sun, and that even the smaller hemisphere could not undergo this enlargement, if we could remove it to a greater distance from the central lamp. (The words here deceive very few.) And so, of all the bodies occupying that distance from the centre. They do not become larger merely by our placing them at a greater distance from the Sun, lamp, tree, or other centre. The surfaces occupying that distance, occupying the space at that distance, bear no relation of this kind, no relation, in fact, whatever, to their distance from the lamp or Sun, or other point, which we may think of as a centre. This is a curious over- sight (but not one here of any importance), commonly made in the geometrical pretensions connected with this subject. The bodies in question have all sorts of sizes irrespective of their distances from lamps or other luminaries. The theory therefore, as it is commonly expressed, cannot even apply at all to these bodies, but only to the whole circumambient space (the sphere of space) at each distance around the luminary, or, at least, to the hemisphere, that half of -this circumambient space, presented to the disc of the lamp or of the Sun. The oversight I allude to, however, is not the disputed allegation which we are considering in the re- ceived hypothesis. This disputed allegation is to the effect that just in proportion as any one sphere, hemisphere, or other area is enlarged, the Light, which remains in amount the same as it was at first, and all of which, by this theory, PART IT. SECT I OX 1. 59 falls upon all the enlarged area, as it did upon all the smaller one, becomes thereby impoverished, weakened, diminished in amount or intensity upon each portion, and, as it were, thinned out or diluted from being thus spread out, or expanded over a larger surface than before ; and that, according to their different areas, there is this differ- ence of Light upon each point of all bodies or surfaces illuminated from the same central point, whatever be their distance from it. This is the proposition of scientific men which will be found controverted in these pages, and easily shown to be not only utterly false, but manifestly so, if the mere explicit statement of it has not already had that effect for the reader. The real question, I repeat, here at issue, is this : When the source of the Light upon two unequal areas is a unit or central point (this is an indispensable condition), and the same unit in both cases, and the whole of both surfaces equally exposed to it, is the uniform illumination of the larger surface or space, thence resulting, less strong, less intense, than that of the smaller one ? There is no dispute as to whether there is the same amount of Light upon the whole of each area. All recognize that there is. The ques- tion is only as to the light at each point, as to the sub- divisions of the area, and as to what we may call the the divisional amount of the Light. Does, cceteris paribus, the mere increase of the space diminish the amount of Light upon each spot, leaving it in all cases the same upon the whole surface ? We are here speaking, as I have so often reminded the reader, only of Light proceeding from a point, from one concentrated, unspread source. For no one denies that when we can subdivide and distribute the source of Light, we can to any extent subdivide and distribute the Light it gives. The theorists assert that, without any subdivision of the source, there is always, with an increase of equally exposed space or surface, a commensurate decrease of illumination or of light upon each part of the surface, without any decrease in the total amount of the 60 PART II. SECTION 1. Light. We now ask: Upon what grounds do they assert this I and such is the whole question to which we here require to devote our attention. What do they mean by Light thinned out and " diluted " ? What do they mean when they tell us that Light can be f reduced in quantity or intensity at each point, by being spread out over a larger surface ; just as butter becomes less, at each spot, or thinner, when spread over a larger piece of bread? How can Light be "thinned out" or '" spread out " at all ? Upon what grounds do wo suppose it either elastic or malleable, or inclined, like water, to seek its own level, or self -expanding ? Does it not go direct from the whole source in straight lints, and only so, to each point of each surface presented to the source ? What is the meaning of this transverse spreading, so much inculcated as a scientific fact ? How is it effected ? Can a ray, without a medium, be diffused and spread ? Can it thus leave the straight line to deviate into places not in its path ? or has it some expansive power ? Such are some of the questions which these theorists have to answer, and which they have nowhere answered, nor even tried to answer. The great difficulty which the reader will here experience is probably that of bringing himself to believe that the frivolous statement, now indicated, can be what they mean ; and that of not being deterred by its extreme frivolity from thinking that scientific men, men, too, placed high, many of them, in the confidence of the public, can possibly be trying behind their technicalities to teach anything so obviously incompatible with common sense and nature ; and this merely because they have once committed themselves to the blunder. They fortunately, however, recognize can- didly enough, when it is put to them, that this is what they do. Their hypothesis is simply that just stated (it cannot be stated too often) to the effect that if we have two un- equal areas, the luminous force being the same in both cases, and both areas equally exposed to the whole of it, the larger area will have, upon each portion of it, a lower PART" II. SECTION 2. 61 degree or amount of Light from this same source than the smaller area, and this merely because it is the larger (just as the same bit of butter is thinner upon the larger bit of bread, or as heat and water spread seeking their own level), and that the outer or more distant sphere of space imagined around the sun or other luminary is in this predicament of diminished light merely because it is greater than the inner one ; it being solely on account of its being greater, not at all on account of its being more distant, that it has this smaller amount of illumination, this lower degree of Light, upon each square inch of its more extensive surface; although it is quite true that it is because the concentric sphere, thus imagined, is more distant, that it is the greater. This distance, however, is not the reason why discs and the other surfaces around us differ in size. SECOND SECTION. THE FACT AS IT IS IN NATURE. WHEN this, the received theory, is once understood, the fallacy involved in it is of course instantly manifest. The only need in this respect is to comprehend exactly what the theory means a meaning which in the lecture hall has been hitherto most scrupulously concealed, or most unaccount- ably unknown. The Light in a room, with folding doors in each of its four walls, is not diminished when the folding doors are succes- sively opened into other rooms, in which other four rooms there was previously no light. There is in such a case no " diluting " whatever, no thinning out or spreading going on, with regard to the light of the first room. The large additional amount of Light which, in Nature, we here see to be the true result from the enlargement of the space, the Light of the additional rooms, is supplied from the same single source, without any of this thinning or spreading, 62 PART II. SECTION 2. without withdrawing from the centre room the smallest amount of its original illumination. We see, moreover, that in this case, the four additional compartments of space may be indefinitely subdivided, and the Light thus indefinitely increased. . Or let us present the curved page of a quarto volume to one side of a lamp, and the curved page of a duodecimo volume in the same type to the other side of the lamp, and, on account of our Medium, but solely on that account, at the same dis- tance from the lamp, (for where there is no Medium as in this theory, the distance it is admitted, produces no other effect but that of enlarging the object) ; and is it not, I ask, rank nonsense to say that the intensity, quantity, or degree of Light is greater on each square inch or on each word of the one page than on that of the other ? How can such a statement as this be in these days designated " Science " ? and what is the meaning of the fretful impa- tience so commonly manifested by the profession when the blunder is pointed out? Why all these efforts made to defeat its exposure I In an age of Science and Progress such a state of things seems to call for some explanation. We thus see then by two very simple experiments and in our most familiar experience, that the fact of Nature here is not at all as the Theory of the Inverse Squares represents it. The enlargement of the space has not in the smallest degree the effect, in Nature, of diminishing the Light. On the contrary we see from one of these experiments, that, abs- tracting altogether the action of a medium, as in this theory all writers always do, the enlargement of the space has pre- cisely the opposite effect, viz., the effect of increasing the Light indefinitely without any increase of the source and in an exact proportion to the enlargement of the space ; also without the smallest indication in the light itself either of thinning out in the first room, or of spreading, or of being diluted. And no wonder ; for this spreading of Light is a physical impossibility. Even in this theory itself it is so. The theory declares Light to consist of nothing but straight PART II. SECTION 3. 63 lines direct from the source ; each of which lines, however much it admits of being prolonged, is held to be necessarily exempt from all lateral diversion, as well as from stretching, expansion, or enlargement of any kind. But this fact of nature, the fact that Light does not spread, is abundantly shown by these theorists themselves, even in that alone which they all write or lecture respecting the umbra and penumbra of the eclipse. There could be no such thing as a shadow anywhere if each ray had this alleged property of expansion and self-equalization, which appears to be merely imputed to it in order to carry on some other theory. And the above adjunct of our illustration, the increase of Light instead of its decrease, as a result of enlarged space, is, it will be seen from the following Section, not the only consideration of the kind, nor by any means the more important, which lies within the precincts of the re- ceived, theory. THIRD SECTION. ACCORDING TO THE RECEIVED THEORY, LIGHT WOULD IN- CREASE AS THE SQUARE OF THE DISTANCE INCREASES, INSTEAD OF DIMINISHING IN THAT RATIO. I DO not seek to show nor do I hold that (through any effect of enlarged space) Light increases directly as the illuminated area does, or, to use the favourite expression, as the square of the distance does, but it is easy to show that, by the theory and the reasoning employed, it is obviously made to do so. The theorists offer us, for instance, the alternative, with regard to the larger of two surfaces illuminated by the same source, and both equally exposed to the whole of it (see Appendix, Nos. 2, 3, and 15), either that there is a less degree of Light on each square inch of it, or a greater degree of Light on the whole of it, than occurs in the case of the 64 PART II. SECTION 3. smaller surface. Now neither alternative here represents the truth. But if, contrary to what they themselves do, we accept the second, if we assert that the degree of Light upon the whole of the greater surface is greater than that upon the smaller, as much greater as the surface itself is greater than the smaller surface, what objection have they to allege against it ? Clearly none. Reasoning as they do, they can have none. They point, indeed, to their screens (see Appendix, ibid.) ; and although they do not say as much, they nevertheless leave us to understand that, according to their ideas, Light does not converge at all ; that it only diverges ; that it does not converge, as we suppose, to each point of both screens from each point of the luminous body, giving the whole Light to each point in each converging cone. They do not, I repeat, say that it does not thus converge ; but they seem to think it does not, or, at least, leave us to think it does not. They then tell us that the divergent shadow, or shadow occasioned by the divergent Light, and which represents the measure of Light that is upon the smaller screen, may be regarded as also the measure of the Light which, if unobstructed by that smaller screen, would fall upon the space now occupied by this divergent shadow ; i.e., that the larger and the smaller area has always the same amount of Light upon it. The theory of solar radiation, of which this is a part, will be fully discussed further on (in the next Section, under the Divergence Theory). It is sufficient here merely to observe, (1) that Light converges, as well as diverges, as is commonly explained even in our most elementary text-books, and which no one at all acquainted with the subject now disputes (Appendix, Nos. 1, 2, 16, and 20); (2) that it is the convergent cones only, not the divergent ones, that can be spoken of as illuminating the points of any given surface ; and (3) that the number of convergent cones which, in this case, fall upon the screen which throws the shadow, is not the number, of those which, if not obstructed by that smaller screen, PART II. SECTION 3. 65 would fall upon the space occupied by the shadow, but, with marvellous exactness, precisely one-fourth of them ; from which we see the inaccuracy of what is here " explained" to us (some say " demonstrated ") with so much naivete by the 44 experiment " of the screens and a medium. The Light therefore which belongs to the space now occupied by the shadow on the farther screen, is represented, we see, under this mode of reasoning, as being 4 times greater than the Light which falls upon the screen which throws the shadow ; in other words, Light increases in the ratio which we speak of as the square of the distance, i.e., in the ratio of the area illuminated. As the general reader ought to make himself well acquainted with this part of the subject, it may not be inappropriate that I should here give another illustration of the curious fact that, upon the theory of these writers, and from their own reasoning, it necessarily follows (contrary to their intention) that, from the same source, the greater surface has always the greater Light, and as much more Light than the other surface, as it is itself greater than that other, or (in their geometrical phraseology) as it is the square of the greater distance. Let us take three separate surfaces, each 1 foot square. These, being equal, have, by the theory, an equal degree or amount of Light on each, however near or far from the source they may be, as they belong geometrically to the same distance ; and, by the theory also, whatever we say about them has no reference to the action of a Medium. Let us then unite two of these three equally illuminated areas ; so that we now have but two surfaces or areas, one twice as large as the other. Then, as this theory which we are examining adds together the illumination of the parts to fnd the illumination of the whole surface, the larger surface, being twice the size of the other, has, by this theory, twice the Light that the other has. If now, further, to the larger one we add successively, and within the same influence of the same source, 7 more square feet of surface with the amount of illumination belonging to each, arid which is, by 66 PART II. SECTION 3. the theory, the same on each of them, as on each of the other square feet already employed, then we have two separate areas or surfaces- a square yard and a square foot of surface the square yard, by this theory and by this mode of calculating Light, having 9 times more Light than the square foot. There are here thus two unequal surfaces, with an amount of Light, upon each ninth portion of the greater surface, equal to the amount of Light upon the whole of the smaller surface ; and therefore, by this mode of calculation, with an amount or degree of Light upon the whole of the greater surface, 9 times greater than that upon the whole of the smaller : which is an amount in exact and direct proportion to the enlargement of the space or area ; i.e., to its greater size, and therefore to the square of the geometrical distance belonging to these areas. Such is their own reasoning, and such the result of it. According to their assertions (see Appendix, ibid.) the larger space or surface has always, on the whole of it, the same amount of Light as the smaller has, but less Light on each " unity of surface," as they quaintly express it, than there is upon the smaller surface. In the above example, how- ever, we see, on the contrary, that according to the reasoning employed in the theory, the two unequal surfaces have neither of these peculiarities. The larger surface, merely from being larger, has, by this theory, the greater Light upon its whole extent ; and the smaller surface has pre- cisely the same amount upon the whole of it as the larger one has on the same " unity of surface," viz., on one-ninth of it ; the natural inference from which presents these theorists with the dilemma, that either the greater surface has more Light upon it than the smaller has, in proportion to its greater area, or that it has the same degree or amount of Light upon each point of it as it has upon the whole. It is for this latter proposition that I here contend ; and it is this which certainly all would hold, except those who advocate the Inverse Squares. In considering this matter, let the reader be carefully PART IT. SECTION 3. 67 upon his guard against all language calculated to make him suppose that there is here anything to be taken account of except the comparative size of the surfaces, or, as it is called, the square of their relative distance in the diagram. The term "distance" is, as has already been explained, very deceptively employed upon this subject. It is the size only, by this theory, or, which is the same thing, distance from the source of size, and not at all, as in a medium, the distance from the source of light, that makes the Light more or less. The distance from the source of size, or geometrical propor- tion of distance in the diagram, which people here uncon- sciously speak of so much, makes no difference whatever except difference of size. This distance is only spoken of, in their theory, as what can fix a geometrical proportion be- tween the greater and the smaller surface, when there is nothing else to fix it ; and so furnishes a mathematical term, with its flattering air of certainty, for the expression of the law ; this law, however, merely being that the greater and the smaller surface have the same amount of Light on the whole of each (the space occupied by the shadow, for in- stance, on the larger screen, and the smaller screen itself which throws the shadow), but that each portion of the smaller surface has more of this Light than the same portion of the greater, according to the difference between the sizes of the two surfaces, upon the bread-and-butter principle of the theory, as already explained. This is the whole theory of the Inverse Squares. Accord- ing to it, when one surface is twice the size of another, the smaller surface has the same amount of Light upon it as one-half of the larger surface has, while it also has the same amount upon it as the whole of the larger surface has ; which shows at once that the whole Light is on the whole and on -each portion at the same time. But passing over this obvious fact, the advocates of the theory take refuge in a complication, and say that the Light on each square inch or foot is here on the greater surface \ of what it is on the smaller ; when 4 times the size, then ^ of what it P2 68 PART II. SECTION 3. is on the smaller; when the greater surface is 20 times times greater than the smaller (as Neptune's disc is than the Earth's), then each square inch or mile of the greater surface has -^ of the Light which the smaller has on the square mile or the square inch, and so on. This is the whole of the physical law here supposed to be true of Light. The mathematical addition has, any one can see, nothing whatever to do with the Light ; and is merely to the effect that, in a geometrical diagram at twice the distance from any point, the area or space enclosed be- tween lines diverging from that point becomes 4 times greater ; that, at 4 times the distance, it becomes 1 6 times greater ; at 30 times the distance, 900 times greater ; this relative area always being the square of the relative dis- tance. What has to be proved, however, by these theorists, respecting the Light, is not this law of areas, which no one disputes and which has nothing to do with the Light upon the areas ; nor yet have they to show that, cceteris paribus, the amount of Light upon the greater surface or area is precisely the same as that upon the smaller ; for this also all are agreed about. What they have to prove is that, this being the case, the whole Light falling upon a surface from a source to which each part of it is equally exposed, is divided and distributed among any number of parts into which we may choose to divide the surface, although the source is not, in any sense, divided or distributed ; that although the whole surface is equally exposed to a given Light, each part of the surface is not; that the whole degree or amount of Light upon a surface consists of the Light of the several subdivisions effected in the surface, precisely the same as if there were this division and dis- tribution of the source ; that if one area is double the size of another, and the Light upon the larger equal to that upon the smaller, the Light upon the whole of the larger is not equal to that upon half of it ; and further, what has to be made quite clear by these writers and lecturers is, that the received theory of thus distributing the Light of any sur- PART II. SECTION 4. 69 face among all the possible subdivisions of that surface does not represent Light as increasing in the ratio of the areas, in the ratio which they describe as the square of the distance, instead of as decreasing in that ratio. FOURTH SECTION. THE TWO MAIN SOURCES OF THE ERROR RESPECTING THE FACT OF NATURE IN THIS CASE; VIZ., THE MULTIPLICATION THEORY OF FORCE, AND THE DIVERGENCE THEORY. So far it has been seen not only that, in Nature, there is none of this supposed expansion, stretching, or spreading out and enfeeblement of Light from enlarged space which is mentioned by the professors, but even that the result of their reasoning is that Light increases, through this enlargement of the space, exactly in the ratio in which they think it diminishes. I again repeat for those who need it, that I am not here engaged in discussing the question as to whether Light does so increase. I only point out that it does so according to the alleged facts and logic of these theorists ; and I do so in the hope that this discovery may help them to lay aside this logic and these " facts." I have now to speak of the two erroneous notions, formerly prevalent, which be- came the principal sources of the strange Law and Theory so long talked of and believed in as that of the Inverse Squares. When an error is so great as to be considered unaccountable, it is, by most people, or at least by many, considered to be either no error or half true. Those, there- fore, who point out extraordinary blunders are generally called upon to explain the origin of these blunders, and are told that unless this is done, their disproof of them can have no thorough effect in convincing the less profound portion of those who will undertake to judge. In accordance, then, with this principle, I proceed now to point out the two main sources of the extraordinary blunder before us. For 70 PART H. SECTION 4. there are two of these sources ; one the more plausible and popular, which might even alone have suggested the theory of the Inverse Squares (but without the second could not have had much effect), and which, although itself an obvious blunder, is still as current a conviction among the learned as it ever was. It is, therefore, necessary to analyse it minutely. This we may here call the u Theory of Divisional or Multiplied Force ; " which is to the effect that the amount of any Quality existing, or Force in action, upon any given portion of matter is equal to the amount of this Quality or Force which we find in any one of such sub- divisions of this matter as we may choose to divide it into, multiplied by the number of parts into which the mass or sur- face is thus divided ; according to which the degree of light upon a picture 5 feet square, i.e., upon 25 square feet, is 25 times greater than that on one square foot of it, being thus distributed over the whole picture. The other source of the Inverse Squares is the Divergence Theory or Spoke Theory ; which teaches that two rays, diverging from a luminous point, gradually augment the space between them more and more, as they proceed farther from the luminous point ; and can, therefore, do less and less for illuminating- that increasing space and the objects that lie within it. This Divergence Theory many will think the true origin of the blunder, and in some respects it can be said to be so, because it was the first of the two asserted with much prominence; but it could not originally have effected anything, nor could now continue to have the weight it has, without the co-opera- tion of the other source. I therefore explain both these notions ; and begin with the Theory of Multiplied Force, which, as I think, prepared the way for the other ; which, moreover, is still highly popular among professional men, and is in fact all now that gives an air of plausibility to what they teach upon this subject of the Inverse Squares. This is that popular conviction upon which the obscurer and more scientific Theory was able to work, that, in short, which constituted its basis. Without this Multiplication PART II. SECTION 4. 71 Theory, speculative minds would never have been decoyed originally into the confusions of the Divergence Hypothesis. 1. The Multiplication Theory for the Forces of Nature (one main source of the Error now being exposed). The first misapprehension here found by the Theorists ready at hand to work with, in which they were, no doubt, themselves fully immersed, the error already in possession of men's minds in connection with this subject, was the belief that when we divide a surface into any number of equal parts, we thus divide also, and lower to that extent, the degree of Light, Heat, Colour, or other Quality, i.., the effect of any Force which, it is admitted, there is in action upon the whole surface taken together ; and that we must, therefore, multiply this reduced degree of Light, &c., exist- ing upon each part, by the number of these parts, in order to find again the degree of Light or other Quality upon the whole surface. It has been fully acknowledged from the first by most of these speculators, that every surface whose parts are all equally exposed to the whole Light, has the whole Light falling upon it, whether this surface be great or small; and about that there is now little or no dispute. Some indeed have written as if they imagined that a surface could be exposed in all its parts to the whole light of the solar disc without having the whole of this light falling upon it ; but this seems to be in consequence of a misap- prehension as to what is meant. Such writers seem to imagine that by the expression " the whole light of the solar disc," we mean, not the amount of it experienced any- where, or anywhere existing, but, on the contrary, an amount of it which exists nowhere in Nature, and therefore can be nowhere experienced ; the amount, namely, which would result from the application to the sun, and pretty near him, of a lens as large as, or rather larger than the solar disc itself ; by which the whole light would be taken from all the rest of nature opposite the disc, and be all' 72 PART II. SECTION 4. concentrated upon the point of a needle. In this sense, even these curious scientific speculators themselves admit that nothing whatever has the whole light of the disc falling upon it, that nothing ever is, or ever can be exposed to it. All this then is simply a misapprehension on the part of these Writers and Lecturers. Nobody means this when we speak of anything as exposed to the whole light of the disc, or the whole of this light as falling upon a surface. We only mean this whole light as it exists in Nature, as the natural philosopher experiences it ; and they them- selves mean nothing else, except for the purpose of evading facts that are adverse to their theories. They themselves admit that the whole light of the disc is upon the whole hemisphere of space, however distant, which is opposite to the disc, which also is something very different from the point of a needle ; and the light upon it something very different from this concentrated light of the disc which they call the whole of it. In no part of that hemisphere is there the supernatural degree of it above indicated, and which they always speak of, when it suits their purpose, under the same name as the natural degree of it with which we are all familiar. I have said all this that there should be no equivocation possible ; and that it should be clearly understood that the whole light of the disc, as it is in nature^ falls upon every surface which is exposed to the disc, and is by all reasonable people considered to do so ; and nowadays, as far as I know, even by all professors. But it will be seen that it is of no importance in this dis- cussion, whether we speak of the whole light of the disc (in any sense), or only of some part of it, as falling upon any given surface. The real difficulty which our theorists profess to experience and to deal with in their theory of Diminution by Enlarged Space, is quite independent of the question as to what is, in nature or out of nature, the whole light of the disc. Their difficulty is this : If, as so many justly think, the whole light of the sun or other luminary upon the whole surface, let us divide the surface into PART II. SECTION 4. 73 any number of parts, and in doing so, we also, say they, necessarily divide the light into this same number of parts, although, it is true, the source is undivided. It follows then, they further tell us, that each part of the surface has its own separate and exclusive part of the light, instead of having the whole light upon it ; that the whole degree of light consists of all its parts, just upon the same principle as the whole surface itself, along which it exists, consists of all its parts ; and that each of these portions of the light therefore must be less than the whole of it. Or even if the whole light does not fall on each surface exposed, yet since the larger and the smaller surface have each the same degree of light from the one source upon them (as all these theorists without exception allow), how can each square inch, they ask, of the one surface have the same portion of this light as each square inch of the other surface, there being more of these square inches to supply with light in the one surface than in the other ? The answer to this difficulty of these scientific men, in both these cases, is the same. This answer is that it would be physically impossible to have any division or separa- tion of the whole light without a division and separation of the source; and we have no such division or sepa- ration of the source connected with this investigation. The source of Light here in question is an indivisible, central, unextended unit or point ; such that no one part of it acts without the rest, and the whole area in ques- tion is, in every part of it, equally exposed to the whole source ; for which reason the source is called central. It is seen, from what has been now stated, that there are here three judgments under discussion respecting the com- parative illumination of different areas ; or, to say the same thing in other words, three judgments respecting the illumi- nation of two surfaces, the one of which is four times, or nine times, or sixteen times, or 900 times, or any number of times, greater than the other ; which difference of area is, in a geometrical diagram, described as being the square of 74 PART II. SECTION 4. the distance ; relations of size and distance which, as we have seen in PART I., do not exist at all among the bodies of the solar system, and but rarely anywhere in nature ; yet in this geometrical phraseology it is that these theorists prefer to describe the area they require to speak of, thus vaguely bringing in, with the term " distance," the familiar idea of what happens in a medium, and, with the expression " square of the distance," giving to the statement an air of mathematical certainty, which they, not unnaturally, like their theory to have ; for neither of which attractive inti- mations, however, is there here the slightest pretext, as has been already so fully explained, in the portion of this Treatise just alluded to. 1. One of the three judgments in question is that the same degree of Light is on the whole surface, uniformly exposed to the source, and also on each part of this surface at the same time and in the same sense, whatever the size of the surface may be. This is what we consider the con- viction of common sense, the plain fact of nature and of science, and the ordinary judgment not only of mankind in general, but also of the scientific who are unprofessional. 2. Another judgment is that the degree of Light which is on the whole of each surface is not on each part of it ; there being on a part of the surface only a part of the degree which there is upon the whole. And if we compare two unequal surfaces, one of which is four times greater than the other, then there is, on each part of the greater sur- face, only one-fourth of the degree, amount, or intensity which there is upon an equal part of the smaller surface. This is the notion taught in their books and lectures by all profes- sional men under the name of " the Inverse Squares," which means the geometrical law (of areas), inverted or reversed. 3. Another judgment is that the whole light is upon each portion of both these surfaces, but 4 times more of it upon the whole of the greater surface than upon the whole of the smaller one, on account of its being 4 times greater. This notion is clearly as contrary to common sense as that in the PART II. SECTION 4. 75 preceding judgment is, and is even disclaimed by pro- fessional men ; but, as shown above (Section 3), it follows necessarily from their own principle ; which is that the degree of light distributed over the whole surface is the sum of that upon all the parts. Now, a capital point to be attended to, in all this, is that, according to the professional doctrine as well as to that of all scientific men, the greater and the lesser surface, what- ever be the proportion which these bear to one another, have, on each of them, precisely the same amount or degree of Light. The question at issue relates only to equal parts of both surfaces, or to what are called their "unities of surface." And, from this, we may also see it to be universally recognized, although not universally expressed, that the whole of the natural light from any luminary, from the sun's disc for instance, to which any surface, great or small, is exposed, falls upon that surface ; for, otherwise, Light from one and the same source could not be equal, in this way, upon surfaces of all dimensions ; and that there is nothing incongruous, but, on the contrary, scientifically exact in this universal judgment, respecting the totality as well as the identity of the amount or degree upon the greater and the lesser area, is proved by the fact that this totality as well as identity of amount is true also and necessarily true of the greater and the lesser of the con- centric spheres already mentioned. Even if one of these spheres is a million of times greater than the other, each of them receives upon it the whole of the central light and therefore the same degree of it. This principle is also illustrated (Appendix, No. 15) by placing a taper succes- sively in the centre of two boxes of different sizes, whereby the whole interior surface of each box receives upon it the whole light of the taper, (allowance being made for the effect of medium,) however great the difference of size may be between these boxes. On this point of TOTALITY, although, in this discussion, entirely unimportant, it is useful to 76 PART II. SECTION 4. remember the fact of nature, and that, respecting it, most professional men nowadays agree with all of us. What is here important, and what all, without exception, seem now to be agreed about, is that the smaller surface and the greater, the space occupied by the shadow for instance (see Appendix, 2, 3, and 15), and the smaller space occupied by the screen which throws the shadow, receive, upon each, the same amount of Light from the same source, when equally exposed to it; and that there is the same degree or amount of the sun's light upon Neptune as there is upon Mercury. Up to this point all are agreed. It is here that the professional theory begins. The profes- sors hold that notwithstanding this equality of light upon the two most unequal areas, equally exposed, and, in fact, in consequence of it, the light becomes diluted, attenuated, enfeebled, and diminished, by the greater number of parts over which it has to be diffused and spread out in the case of the larger area. They consider that the sun's rays undergo no diminution whatever, either in force or number, to the remotest limits of the system. They consider that one of these rays passes from each point of the sun's disc to each point of space, and therefore to each point of each surface occupying space ; that there is, therefore, a cone of the whole light with its base upon the disc extending to each point of each object, however distant and however near. They consider also, and for the same reason, that the whole of the solar light falls upon every conceivable sphere of space which has the sun as its centre, however distant it may be from that centre; which concentric spheres of space, as has been explained in a former page, necessarily increase greatly in size, as their distance from the sun increases, much more rapidly than the distance itself does, and in the ratio, as we have seen, of this distance squared. There is, then, no difficulty in comprehending that, even according to the theory of the Inverse Squares, the whole undiminished light of the sun covers equally the larger and PART II. SECTION 4. 77 the lesser sphere ; the whole undiminished light of his disc therefore, the larger and the lesser hemisphere, as well as the larger and the lesser space or surface or portion of the sphere, presented to it. All this our theorists fully recog- nize. They then ask, as I have already observed: But since there is thus only the same degree or quantity of Light for the larger area as for the smaller, on which point we are all agreed, how could there possibly be the same degree or amount of it on each square foot of the larger area as there is on each square foot of the smaller ? In other words : If there is upon the smaller surface all the light which there is upon the larger surface, how is it pos- sible that the light should not be thicker and stronger and more abundant upon each square foot or square inch of the smaller surface than upon each square foot or square inch of the larger surface ? Our answer to this is (as already given) that the thing is perfectly easy and perfectly natural. Light is not measured by feet or inches but by degrees ; nor does it thicken and strengthen, when the source does not ; nor does it thin out or spread until the source does. In physical Optics, when the central, undistributed source remains the same, the effect remains the same, how great soever may be the en- largement or contraction which takes place, or can be supposed to take place, in that which, from such a source, receives the light. One portion of the whole light does not go to one spot, and another portion to another spot ; but the whole light to each spot. What seems here, to some extent, to 'be wilder these writers and lecturers is that they forget the elements of their own theory. They forget that, according to this theory, the same degree of light from the disc falls upon each space or sphere or surface exposed to it, whether that surface be near to, or far from, the sun, whether, also, it be great or small ; inasmuch as there is a ray from each luminous point of the disc to each point of space however distant, and this ray undiminished from the first to the last. Now, this being the case where, as in this 78 PART II. SECTION 4. theory, no medium is taken account of, and being admitted by all to be so in such a case, how is it physically possible for the mere size of the space, exposed in all its parts to the same source, to make the degree of light less or more upon any part of it ? If one sphere or area be 20 times greater than the other, the greater will contain 20 parts, each part equal to the whole of the smaller area. If, then, the whole light is equally upon both areas, as all agree it is, how can the twentieth part be better lighted (have more light) in the one case than in the other ? when it is by itself, than when it is combined with 19 others? If, as in the instance pre- viously given, there is precisely the same amount of illumi- nation upon an area a foot square, and upon an area a yard square (which latter is equal to 9 square feet) how can we say that the square foot of the larger area has less of the illumination, grouped, though it is, with eight other square feet of space, than when, by itself, it constitutes a separate area which is a foot square I Since the same amount of light falls upon each part of space, upon each area and each sphere, how can we arrive at such a conclusion as this ? There is no one, I think, who will not easily see the un- reasonableness as well as the groundlessness of the hypo- thesis in question. If, as already remarked, the source illuminating both areas equally, were not a unit, a physical point, a central, unspread source, the case would be different. If a group of twenty candles, for instance, instead of giving their light thus collectively, as the Sun gives his, are separated and distributed so that each candle lights a separate area or portion of the area, the degree of Light is diminished by the division and distribution of the source, the degree being necessarily much lower from each candle separately than from the group. But this effect is not caused by the greater surface with a single central source of light ; which is what we are speaking of ; and this sub- division of the source does not occur in the case of the Sim. But, beside . the unreasonableness now pointed out, thi.s PART II. SECTION 4. 79 Multiplication Theory is, as already shown (Section 3), utterly opposed to the Law of the Inverse Squares, which it is supposed to justify. Since all admit that a square foot, presented to the sun, has the same amount of illumination, whether it is alone or is combined with eight others, then it would follow necessarily, from the supposed subdivision of the light, that the yard square would have 9 times more light than the area of one square foot has ; i.e., that the light from the source would be increased ninefold in the case of the larger area, instead of being the same for the two areas ; a conclusion which, as explained above, entirely subverts the theory of these writers, and repre- sents Light as increasing instead of decreasing, exactly in proportion to the enlargement of the area, i.e., to the square of the distance ; the common, unsophisticated interpreta- tion of nature here being that, in all such cases, there is the same intensity or amount present, the same luminous force in operation, upon the whole of each surface as upon each part of each, the same degree of light upon the square mile and its square foot, when both are, in all their parts, equally presented to an unspread undistributed unit, source. This Multiplication theory for the degree of light from a single source, so evidently the Encouragement, if not the Origin of the whole error, is almost too manifestly foolish to need that I should have said much about it ; and yet it has served to mislead some of the most distinguished Physicists, not in England only, but in the other countries of the world ; which must be my excuse for what cannot but to many seem a very needless prolixity. The intensity of the report which, when a cannon is fired, extends equally to the whole of two areas of different extent (say, the fortress walls on each side of the gun), is not only precisely as great for the greater area as for the smaller ; which we all admit it is ; but also for each square yard of each area, as it is for the whole area together, which is here what our theorists deny (Appendix, No. 15). We cannot proceed to add the noise audible on one square yard of the walls to that audible on 80 PART II. SECTION 4. another square yard, and then say, after summing up some 80 such square yards, that the whole report was, at least, 80 times louder than on any one square yard of the walls. Can this be called science ? The intensity also or depth of a Colour which exists upon two areas of different extent, is not only precisely the same, as intense arid deep, for the greater area as for the smaller, but also for each square inch of each area as for the whole of each. In neither of these cases does the intensity become divided, distributed, and diminished, merely from our having recourse to sub- divisions of the areas ; and so also the illumination does not. The entire intensity or force is upon the entire area, and upon each minutest portion of it, at the same time. The same is true of Heat and of Attraction. There is here no difference except for a theorist. If the theorist chooses or" requires it, the vibrations of the Colour or of the Sound (things which admit of Long Measure) may be subdivided and distributed over each square inch of the areas over which one intensity of colour is seen, and one intensity of sound is heard ; but even if this be true of the vibrations, it is clearly not true of the Colour itself, nor of the noise itself. We cannot say, of either, that a portion of its whole amount goes to one square foot, and another portion of the whole to another square foot ; and so on ; and then that the sum of these portions is the whole depth of the Colour, and the whole loudness of the Sound. To say that the amount of the Colour or of the Sound is not the same for the whole space as for the part, is the preposterous thing here asserted of the Light ; but is what any one, however little versed in scientific matters, can easily comprehend and easily see to be, on the part of enlightened men, a mere oversight, however much the less enlightened may be convinced of it. Those not committed to some hypothesis will at once recognize that we cannot accept this Multiplication-Theory for the Forces of Nature ; that we cannot, with any truth, pretend to estimate the amount of a Force from a given centre by subdivisions of the space, every part of which is PART II. SECTION 4. 81 equally exposed to its action. We cannot divide the space, thus equally illuminated by a lamp, into fifty equal parts, and say that the whole luminous effect, or amount, or intensity of the lamp, the degree of light it gives, is fifty times greater than it is at any one of these fifty points; for it is not. Everybody knows it is not. The same degree or intensity is on the whole, and at each point of the whole, at the same time. This is really here the important point to be attended to, and all the more so, because it is one which the Writers and Lecturers en- deavour to keep out of sight. The error seems to consist, to some extent, in a confusion made between some theories and the Natural fact, by the aid of a confusion between Long Measure and Degrees ; between the Long Measure, on the one hand, so preposterously applied to a force or agency of Nature, in order to prop up an hypothesis, and Degrees, on the other hand, or things measured by Degrees, as Heat, Attraction, or any Force naturally is ; the Long Measure referring to a supposed extended Element as cause of Attraction or Light, and being therefore, like this extended Element, a mere hypothesis ; whereas the measurement by Degrees refers to the Intensity, Attraction, Heat, or Light itself, and is therefore, here as everywhere, entirely exempt from hypothesis. Be that as it may, the whole luminous Force or degree of Light so called, whatever we may think of its cause, is not more truly upon the whole surface or space in question than it is upon each square inch of it ; which obvious fact these theorists are themselves obliged to acknowledge, when they say and truly say, that, whether the surface be great or small, a square inch or a square mile, the whole degree of Light to which it is uniformly exposed, is upon the whole of each extent. We could as reasonably multiply the degree of solar heat, experienced at any given hour, by the million hours pre- viously elapsed, averaging the same degree of heat, and thus consider the solar heat during all that time as a million of times greater than what we experience at the hour G 82 PART II. SECTION 4. mentioned, as say that the Light upon a square foot is 144 times more intense, stronger, greater in amount or in degree, than that upon any square inch of the square foot. Or, if in a room 20 feet square, the thermometer marks 70 degrees on each square foot of the floor (to take no account of the body of the room), is it common sense, on our part, to say that the heat of the floor alone amounts to 400 times more than 70 degrees of Fahrenheit? Or, if there were 100 people standing in the heat of a summer sun, is there common sense in saying that the solar heat is, in this case and on that' spot, 100 times greater than any one of these people experiences it? Would not that be simple nonsense ? Yet this is, with regard to Light, what these Writers and Lecturers inculcate. Or would it be reasonable to say that because the blue of a given yard of ribbon is very deep, this colour is 100 times deeper, in 100 yards of this same ribbon, than in one yard of it ? or that, when we divide the surface of a mahogany table into 100 equal parts, the hardness of the whole surface is 100 times greater than that of any one part? or that, because a man who has once shouted as loud as he can, does this 100 times, he therefore shouts 100 times louder than he can? It may be well that all these Writers and Lecturers should reflect a little upon the utter nonsense they thus inculcate. In all these cases the error made seems to be, as already observed, a confusion between the cause and its effects ; a confusion between Light and the supposed causes of Light, between Heat and the supposed causes of Heat, between Colour and the materials or vibrations with which it is pro- duced, &c. This confusion has led these writers to suppose that, when a larger and a smaller area are lighted, heated, coloured, rendered noisy, &c., by a common or central cause, i.e. by one to which each portion of both spaces is equally exposed, there must be a greater degree of light, heat, colour, noise, &c., upon the whole area than upon a part of it. Whereas this is never the case. If there is this single or unextended cause, this central source or point, as it is often called, i.e., PART II. SECTION 4. 83 one to which the whole of each area is equally exposed, then the degree or amount of effect produced has no refer- ence whatever to the amount of space over which it is pro- duced. There is precisely one and the same amount of effect produced at every point in the case of both the spaces ; and no reasonable person ever thinks of calling the amount, at each point or square inch, a separate effect, and of adding these effects all together, in order to find the real amount of noise or colour upon the whole of either space, nor of saying that the effect is greater upon one of these two spaces than upon the other. If , on the contrary, the source or cause is not common, but divided or extended, i.e., manifold, if that which pro- duces the uniform effect on one portion of the space is not that which produces it upon another portion, then the cause in action upon the larger space must be as much greater than that in action upon the smaller, as the larger space itself is greater than the smaller, and the cause in action upon each separate portion of each space must be less than that in action upon the whole of each. To produce one uniform effect upon 20 square feet of surface in such a case of divided or extended source there must be 20 times as much of this source or cause as would be necessary to produce the same effect upon one square foot ; and thence arises the confused judgment that even the effect, instead of being the same on both spaces, is 20 times greater in the one than in the other. The confusion here, however, is evident. Even then the effect here in question is not made less or greater by this less or greater amount of source or cause. Pre- cisely the same effect extends over the larger as over the smaller surface. But when there is not the excuse of a divided and uncen- tral source, for this strange interblending of disconnected ideas on the part of men accustomed to the precision of scientific research,. when there is but the one undivided and central source to be taken account of, arid this, giving pre- cisely the same effect for the small surface and for the large G 2 84 PART II. SECTION 4. one, we easily see the unreasonableness of saying that it produces a higher degree, amount, or intensity of its effect (whether this effect be noise, heat, light, or colour) for the larger surface than for the smaller, or (if possible still more preposterous) for the smaller than for the larger. It is true, for instance, that the cause of heat for the 400 square feet of surface, in the instance at p. 82, must be 400 times greater than for one square foot. Of this there is no question ; for each of these square feet cannot be equally exposed to the action of the source which warms one of them. If this were possible, then the source of heat for one would be sufficient for all. But as things are in this supposed case, although the source must be greater for 400 square feet than for one square foot, the heat itself, the degree or amount of heat, must not be greater' for the whole floor than for one square foot of it ; and so also of Light. There may be the same intensity, amount, or degree of light on a space of 20 square feet, as on a space one foot square. If these two unequal surfaces can be so placed (say, round a lamp) as to have each square foot of the larger equally exposed to the source of light as the one Bquare foot of the smaller surface, then, no more source is required for the greater than for the lesser surface in order that precisely the same degree of light should be produced. If these two unequal surfaces cannot be so placed as here described, then it is necessary to give each square foot its cwn separate source, this source therefore being, in the case of one surface, 20 times as much as in that of the other. In like manner, although the blue in a square yard of surface be exactly the same as that in 100 square yards, the same intensity, the same shade, in short, the same colour, yet the source of this colour and its depth or quantity in the one case (be this source materials or vibra- tions) must be 1 00 times more in size, more extended, than in the other case, unless we employ a central or un- extended source, i.e., one whose efficacy does not depend upon, its extent or number ; as, for instance, a central blue PART II. SECTION 4. 85 light. So also in Sound. In all these cases it is clear that the unextended or central cause can produce its effect over any extent of surface equally exposed to it, and this, with- out either the effect or the cause being- subjected to any supernatural multiplication in the process ; and that where the concentrated or unit-cause cannot do this, it is because there is none, it is because the extent of surface, not admitting of being equally exposed to the unit-action, requires a separate cause or source for each portion of it, and therefore as many times more of this cause for the larger surface as this larger surface is greater than the smaller. But even then, as I have said, the effect here in question, whether it be Noise or Colour, Heat, Attraction, or Light, does not become multiplied or augmented by this fact. It is not more intense, not greater, not stronger, for either surface than for the other, even after all these addi- tions to the cause. We see, then, here as everywhere, the importance of carefully guarding against the least con- fusion between the cause and the effect in nature, a confusion of ideas often so much required for theoretical purposes ; and it is hoped that, from what has been said, the reader will have no difficulty in clearly recognizing the two main facts connected with the confusion in the present case: (1) that we cannot divide and distribute the effect of an unextended or central Force, because we cannot divide and distribute the central Force itself ; and (2) if we destroy this centrality (or absence of Extent and Number) by sub- dividing and distributing the Force, we do not thereby augment the effect. We do quite the reverse. We do not even preserve it. We thereby reduce at all points, and to that extent, the intensity, amount, or strength of the effect produced ; which is what our opponents suppose done, even while they retain the central Force. There are few, I feel confident, even among the most prejudiced of our professors, who, however silent they may choose to be, will not be able here to recognize the equivo- cation and confusion into which they have hitherto been 86 PART II. SECTION 4. decoyed upon this subject of Cause and Effect in Nature, and the further confusion to which that leads respecting the substitution of Long Measure for Degrees, and the mere Bulk for the Action of " the vibrating mass unseen " which is supposed to be one cause of Light ; as well as the third confusion, resulting from this latter one, and which has led so many to imagine that the degree or amount of Light upon a surface is to be regarded as something made up of all the degrees or amounts of it supposed to exist separately upon all the sections into which the surface is divided or divisible. 2. The Divergence Theory (the other main source of the Error now being exposed). The second of these two theories which have chiefly con- tributed to the Misconception by which the enlargement of the space illuminated is supposed to diminish the Light falling upon it, is commonly known as the Radiation of Light, but is more properly that peculiar form of it which may be called the " Theory of Divergence " or the " Spoke Theory" (Appendix, Nos. 1 and 3), also the "Radiation of Darkness," or the u Theory of Unilluminated Cones," a theory which supposes more than one-half of all the space around the sun, however near him, to be in utter darkness, and which makes the sun invisible, as well in parts of the system near him as in parts at a distance from him. This theory, it will presently be seen, is to the effect that Light does not leave the sun in a sheet or flood, as the Force of Gravitation leaves the Earth or the Sun, nor yet in rays laterally continuous, but, on the contrary, in disconnected rays, in fine lines or threads, gradually separating more and more from one another, and thus forming a cone of Darkness, between every two lines, along their whole length, a circumstance which would have (it is rightly supposed by its authors) the effect of preventing large portions of space from ever receiving any of the sun's rays at all, however near him these portions may be, or however PART II. SECTION 4. 87 much exposed to his whole disc. It will also t> e seen that for this hypothesis there is not, in Nature nor in reason, the smallest foundation. It is merely one of those now com- monly employed as an explanation for the supposed diminu- tion of Light without the action of any Medium, but so utterly baseless in itself as to make one suspect that it has been invented expressly for that purpose, were it not known that it has been itself to some considerable extent the origin of that notion. It will be well, therefore, to look a little further into this hypothesis also ; of which, however, one sees with pleasure that some of the theorists themselves seem already beginning to be ashamed. There are two ways in which (as well under the unfor- tunate Emission-hypothesis as under the more prosperous hypothesis of Undulations) Light, when exempt from Medium, can be supposed to exist in empty space or to pats through it ; viz., either in a connected flood as gravitation, water, and air exist and pass, or in disconnected threads, infinitesimally fine lines, called rays. In the first of these two forms of propagation scientific men hold that all dimi- nution of Light, without a Medium, would be impossible. They are therefore, we find, compelled to resort to the Ray Theory to account for the reductions theoretically supposed to take place without the action of a Medium. The reader should distinctly understand this emergency. If Light existed as a sheet or flood or aeriform mass, and proceeded thus from the solar disc as the Force of Gravitation exists in space and proceeds from its centres (there being no Ray Theory for Gravitation) professional men admit that there could in such a case be no diminution of the Light indepen- dently of a Medium ; and assuredly, it is not easy to see how there could then be any, unless upon the same principle as Gravity diminishes ; viz., because a certain amount of force or action belongs to a certain distance. The solar light would in such a case, they all admit, pass on in all directions, un- diminished, to the limits of space ; although the3 T recognize, it is true, that, notwithstanding the absence of all ray 88 PART II. SECTION 4. theory, this uniformity throughout its path does not occur in the case of Gravitation nay, assert that the same law of the Inverse Squares applies to Gravitation also without any of this Radiation theory. It is not, therefore, in this continuous sheet or flood that the luminous effect is sup- posed to exist in space, apart from the Medium, proceeding in one piece, as it were, from the whole breadth of the luminous body. On the contrary, it is supposed to leave it, as I say, in lines, in fine threads of light called rays, with equally narrow spaces of darkness between them,, and to exist in this form everywhere throughout the system. It is not found that Light could in any other way be scientifically diminished. It is not, however, in every form of this ray theory that the required diminution can be obtained. There are two different ways in which the hypothesis of lines or rays of light can be supposed to exist in space. The more obvious and natural of the two (if either of them can be called either obvious or natural) is that the light dif- fused around us, and therefore all light, consists of these fine rays, innumerable luminous lines of light, iufinitesimally attenuated, which upon leaving each point of the luminous body, diverge from one another in that point at every conceiv- able angle so as to be able to reach every conceivable point of space : this Universality of the rays being the very ground and object of the alleged Divergence. According to this form of the hypothesis, one of these rays proceeds from each of these atomic points in the solar disc or other lumi- nary, to each atomic point of exposed space, and therefore to each atomic point of exposed surface, throughout the whole system if not beyond it ; more than one could have well expected as the work of one single point. In this way each minutest point of every surface presented to the sun has upon it one ray, the extreme point of a fine line of light, derived from each minutest point of the disc (how- ever great or however small the distance may be between this point of the disc and the object), and therefore has upon it (?> upon each minutest point of every surface) the TART II. SECTION 4. 89 whole degree of light that the disc can give ; for there is no reason assigned, nor assignable, why one of these exposed points of space should have rays on it, and another not ; nor why each point so exposed to the whole disc should not have its full complement of rays upon it, i.e., a ray upon it from each point of the whole disc. The result is that no point, or other " unity of surface," has either more or fewer of these single rays upon it than all the rest have, the full degree of solar illumination being thus brought to each point ; nor more when near the sun than when distant from him ; for apart from all Medium, as in this theory, each point of each surface, and each point of space, are as completely presented to each point of the whole disc when they are distant from it as when they are near it. Mere distance alone, it is clear, does nothing, in such a theory, to diminish the number of the solar rays falling upon each minutest point of space or surface that is exposed to the rays of the disc ; and nothing to dimmish the number of these minutest points which, in space or surface, are exposed to these rays ; nothing therefore to diminish the solar illumination existing at each point in the most distant parts of the solar system, or existing upon any sur- face within that system, provided that each point of each surface be completely exposed to every one of these sup- posed threads of light, i.e., to all the disc from which they proceed. It is manifest that in such a theory we have converging cones of Light as well as diverging ones. Let us attend a little to this fact. We here find, as has been just explained, cones of Light, indefinite in number, with the apex of each in some atomic point of the solar disc, and the base of each cone upon some surface, or other extent of space ; and all these so equally and compactly interlaced and intermingled with one another as not only to render all distinction amongst them the most arbitrary affair imaginable ; but to reduce to an infinitesimal extent, if not to nothing, the dark spaces between the rays. These are the diverging cones ; 90 PART II. SECTION 4. those from each point being commonly called in the old- fashioned way, and often still called, " pencils of Light," their distinguishing characteristic being that their apex is in some point of the solar disc, or other luminary, and their base in each instance upon some distant space or distant object. It is, however, at the same time manifest that, from the opposite direction, we have, although only upon the same principle of most arbitrary distinction, OTHER CONES, formed by these very same threads of light, each of which other cones has its apex in the illuminated point of space or of surface, and its base on the entire area of the solar disc ; because from each point of the latter to the illuminated point there extends one of these fine delineations of which all Light is here theoretically and somewhat fantastically supposed to consist. These are the CONVERGING CONES ; i.e., converging from all points of the disc to each separate minutest point of the Universe which is presented to it ; and both sets of cones are, we see, essential to the full import and full deve- lopment of this Radiation Theory, for the sun as well as for all other luminaries. We see that to speak only of a " Con- vergence Theory," or only of a " Divergence Theory," would be a very partial and imperfect expression of the familiar facts upon which the ideal theory of Radiation professes to be founded ; for the whole disc, it is clear, or other luminous body, radiates TO each spot of space or surface presented to it, quite as truly as it radiates AWAY FROM all such spots. Even the theory itself involves no denial of this very obvious fact. The converging cones and the diverging cones are merely different imaginary groupings of precisely the same arbitrarily imagined threads of Light, according as we choose to place our apex in the illuminating point or in the point illuminated. It is unnecessary to add that the num- ber of luminous lines terminating at each point of disc or object is thus in this theory absolutely infinite, in the sense of " innumerable " or indefinite, depending entirely upon our own choice or power of imagination, and not in the smallest PART n. SECTION 4. 91 degree upon the distance between the object and the disc , or upon the size of either. Such is the whole Theory of Solar Radiation and of all lumi- nous radiation in its natural and uncurtailed form ; but we see at once that we have here no diminution of Light what- ever, any more than if Light proceeded like gravitation in one sheet or flood. Every point at the confines of the system has here still its full cone of rays with the base resting on the whole disc. This also these theorists acknowledge. The more obstinate, therefore, are reduced to the necessity of modifying it. Now, how do they proceed? What modification will it be supposed they suggest, in order to diminish the force of the whole solar beam (the converging cone) upon each square inch at the confines of the system. For this purpose they simply begin by abolishing the converging cones altogether. They adopt what they seem disposed to call the Spoke Theory, in which the rays are, they say, as the spokes in a wheel (Appendix, Nos. 1 and 3). They suppose an arrangement of the rays (but gratuitously, nay, frivolously suppose it) according to which no point of space, far or near, is illuminated by the whole disc (z'.e., by all the rays of all the disc) even when perfectly exposed to the whole of it. No point at all of space or surface there- fore in this new theory has the cone of rays which naturally belongs to it from its complete exposure to the disc or other luminary, viz., the converging cone ; and consequently, very few points of space or surface anywhere have even a single ray, i.e., very few compared to the universality of points exposed to the disc. Let this be attentively considered. A single ray, here and there, out of the whole disc (where even so much as that is allowed) is considered a natural and ample supply for every purpose of illumination ; the result of which is that there is, as they moreover frankly tell us, in most parts of the system only one such solitary ray, where billions of billions of points have none at all ; spotting thus or dotting with spots of Light the more distant portions of space and all the objects occupying these portions. 92 PART II. SECTION 4. This form of the Radiation Theory, which is at once both unnatural and arbitrary in the extreme, is more truly as I have said a radiation of dark cones, a Divergence Theory or Spoke Theory, than simply one of Radiation, and is the one usually adopted. Its chief propositions are : that the num- ber of rays proceeding- from each point of the solar disc, or other source of Light, is supposed to be exceedingly limited, and that there are unilluminated cones of much greater dimen- sions between them ; that rays or spokes of Light, as the theorists themselves so aptly call them, do indeed proceed from each point of the disc, but diverging con- siderably from one another ; not therefore by any means proceeding to all the objects or all the points of all the objects exposed to the disc, but only to some of these, how- ever completely all these points and objects may be exposed to the disc ; and this without any reason assigned or assign- able for the unequal distribution ; that there are therefore dark spaces between the supposed diverging rays (one such space between every pair of rays), which dark spaces, gradually expanding between the rays, more and more, as the distance from the sun, or other source, increases (and this in the true ratio of the pyramid and its square of dis- tance), are supposed to receive into their darkness such objects and such portions of objects as are not in the straight path of these isolated lines or rays ; so that even very small objects at a vast distance from the sun, but lying in the path of the ray, are brilliantly illuminated, while at the very same moment, larger objects, nearer the sun, are in utter darkness, from the fact of their lying off the lines of light, and exactly in the black spaces between the paths of these rays. Such is this most imperfect and arbitrary form of the Ray hypothesis or Radiation Theory of Light now in vogue ; the only form of it which would at all, even by the aid of an equivocation, enable us to speak of a decrease of Light by distance independently of all medium and all absorption; but it does this, we see, only in the most ridiculously equivocal and inaccurate sense ; for the mere PART II. SECTION 4. 93 introduction of unilluminated spaces between the rays, which spaces are continually becoming 1 wider and wider, does not, in the smallest degree, diminish the number of the rays, nor the luminous force of each ray at any distance whatever from the sun. The whole light of the sun remains under this theory perfectly undiminished at the confines of the system. There is not here the slightest diminution of the solar light by distance on any point to which it reaches. Imperfect, however, and unnatural and arbitrary, and, let me add, unscientific in the extreme, as this restricted form of the Radiation hypothesis is, it is nevertheless this grotesque form of it which all professors and many scientific men understand by that name, and accept as the origin arid explanation of their theory for the diminution of Light by that enlargement of the space illuminated, which is vulgarly described among them as " the square of the distance." No professor of Physics disputes this theory about " spokes of Light," however much he may seek to conceal it, the theory by which all rays diverge steadily and considerably from one another, and (having from the first a dark space between them), thus constitute a Radiation of dark cones, and render every source of Light still more truly a source of Darkness. Instead of grasping the whole of the Lineal hypothesis in its full extent (which hypothesis, however, I repeat, has as little foundation in fact as a lineal hypothesis for Gravitation or for air would have), these scientific men content themselves with one-half of it, or rather with a very much smaller part than one-half of it. Of the ray theory or Radiation hypothesis for Light, which naturally consists of the two parts, the Convergence theory and the Divergence theory, they not only take away entirely the Convergence theory, leaving nothing except the Diverging cones ; but they also at the same time, and by this very hypothesis, thus added, of non-convergence and non-uni- versality, remove from these Diverging cones, by far the larger portion of the rays belonging to them, by far the larger portion of each Diverging cone. They suppose the 94 PART II. SECTION 4. number of luminous lines in each diverging cone (the " pencil of rays"), to be so much reduced as to admit of these lines having gradually widening, unilluminated spaces between every two of them. Instead of recognizing the obvious fact that each object, and each square inch of each object, is illuminated by the whole source of Light, when exposed to the whole of it, they consider that, however completely it may be exposed to the whole source, it re- ceives Light nevertheless from a very small portion of the whole. Instead of seeing that, as above remarked, the hypothesis in question, when complete, requires a thread of Light, or ray, to proceed from each point in the sun's disc to each point of every surface exposed to it, so that there should be, in the case of each object illuminated, a cone of light with its apex on each point of the object, and its base on the whole disc, which is the converging cone, as well as a corresponding cone (the ordinary "pencil"), with its apex on some point of the disc and its base upon every portion of every space or surface (which universality of the rays or lines is rendered essential by the natural facts upon which the hypothesis professes to be founded), instead of recognizing all this, these scientific writers and lecturers, many of them men of considerable shrewdness in other matters, suppose, without however assigning the slightest grounds for their opinion, that the number of rays proceed- ing from each point of the disc and constituting each so-called " pencil " or diverging cone is, in all probability, extremely limited ; that rays probably go from the sun to some parts of exposed surfaces, and to some parts of exposed space, but not to others ; that there is not, proceeding from each point of the solar disc, a separate and special ray or line of light, for each point in the object illuminated, which rays, all thus concentrated at that minute point, however dis- tant, would affect a plant or a retina as much as if it were quite near the disc, that all this universality has been a mistake ; that on the contrary, there are, comparatively speaking, very few of these lines at all that emanate from the same PART II. SECTION 4. 95 spot of disc, and accordingly a vast number of surfaces and points of surfaces, nay, by far the larger portions of our whole solar system, which receive none of them ; that the rays therefore do not leave each point of the disc at every conceivable angle, as one might suppose they would, to reach every conceivable point of exposed surface or exposed space, but only at a few, not very well defined, angles in each " pencil ;" and that these rays fall therefore more or less thickly upon some objects and rniss others altogether, just according to the size of the object and to the direction thus arbitrarily given to these rays ; small objects even when near the sun, as well as large ones at a sufficient distance from it, being thus frequently unable to receive any of these extremely divergent rays at all upon them ; while not unfrequently the larger object near the sun may be in one of the blank intervals, while the smaller object at a vast distance is strongly illuminated. And it is most im- portant here to remember that these theorists assign no natural cause or other reason of any kind for the extra- ordinary divergence and reduction they thus make and represent as so probably true, in the lines of light, proceed- ing from each point of the disc; and not only do they assign no natural cause for this divergence and reduction ; they assign no reason of any kind whatever for either. Nor do they indicate any principle that should determine to which surfaces or points of surfaces rays should proceed and to which not ; the sole requirement being that they shall not proceed to all, nor even to many, however much all may be exposed to all the points of the disc ; and they regard this hypothesis of theirs (this hypothesis of mere divergence or Partial Radiation) as what is most probably the arrangement in nature. Now, it is quite true and quite clear that in such a theory, in this arbitrary and unnatural form of a theory in itself so arbitrary and so unnatural, the mere distance alone without any medium would, in this Radiation of un- illuminated cones, determine whether a point of space or of 96 PART II. SECTION 4. some surface should or should not be illuminated, should or should not receive a line of light upon it ; but this would no longer be a diminution of light in any received sense of the expression, but merely a diminution of the space or objects that can be illuminated. There would here be no diminution of force (or degree) in any given ray of light, nor in the number of such rays. The whole solar light at any conceivable distance from the Sun, would, even accord- ing to this theory, remain undiminished in the slightest degree, and under every circumstance. All that would hereby be diminished, would be the number of points or objects exposed to the source, and from which it could be seen by an eye placed there ; obviously presenting a mere equivocation entirely unconscious, no doubt, on the part of these theorists ; also a very transparent, as well as a very useless one. For this theory really amounts to nothing more than a mere confession that certain objects, and certain points of certain objects, are arbitrarily supposed by our theorists not to be exposed to the solar disc in their theory, while they allow themselves, nevertheless, to speak and to calculate in the lecture-room as if all such points and objects were fully exposed to it. We are here, how- ever, as in all things, bound to stand by Common Sense and honest Language ; and Common Sense, as well as Science, revolts against such conduct and against such language as this. Common Sense teaches us that, if these points and objects are fully exposed to the whole disc (i.e., to each point of it) they receive upon each of them, upon each point of each, the whole light of the disc, whether they happen to be in some particular theoretical path or not ; and science stoutly confirms this teaching. If, on the other hand, we are bold enough to deny this fact respecting the Light on each object exposed to the Source, we must be bold enough and honest enough to say we do so. We see then that the Ray Hypothesis for Light gives no diminution of Light at all, nor any room for even an equivocation respecting this diminution, unless we have PART II. SECTION 4. 97 recourse to that partial and utterly unnatural form of the hypothesis, which may be called the Spoke-Theory or Dark-cone-Theory, the Theory of Divergence, and which is so generally though timidly adopted, as the correct form of this hypothesis, by those who lecture and write upon the subject ; and we see without any difficulty that what this Spoke-Theory affords is a mere equivocation; in which we say that Light is diminished by distance, when we only mean that, by this theory, there are, at a distance, fewer objects and spaces so placed that they can receive any of it. We see that the alleged fact itself of these dark intervals these dark cones between the rays, even if it were true, would give no grounds for saying that Light itself under- goes any diminution whatever throughout space, either in the number of its rays or in their intensity, either through dilution or any other enfeeblement. I have dwelt the longer upon this Radiation Theory (Radiation we thus see of Darkness as well as of Light), whereby the diminution of Light, independent of all medium and all absorption, is supposed possible, because to explain it in all its curious bearings is to show its gratuitous con- jectures, and so, in the most effectual manner, to exhibit its unscientific character and to refute it. If this Radiation of Light existed at all, it would be universal. There would be converging cones as well as diverging ones, and there would be no unilluminated spaces gradually increasing and widening between the rays ; and if so, if universal, this Ray-Theoiy would not alter, at any distance whatever from the sun, the proportion between the solar light and the space illuminated. Even if the Theory were the partial thing supposed, the Dark-cone-Theory, Spoke-Theory, or Divergence-Theory, leaving thus an enormous amount of the solar system in utter darkness, much more than one- half of it, and as much more as the expanding dark cone is wider than the unexpanding ray, this would clearly not give rise to the slightest diminution of the solar light, wherever the solar Light existed. This would involve no 98 PART II. SECTION 4. dilution, no enfeeblement. The number and intensity of the solar rays would remain entirely unaffected by this circum- stance. Even these theorists themselves acknowledge that this is so. The only effect of such a doctrine would be to make it very evident that where there was none of the Solar Light possible there could not well be any diminution of it; that most objects, spaces, points, and surfaces in Nature, even near the Sun, as well as those at a distance from him, which are supposed presented to the disc, receive no Light whatever from it, being really not presented to it at all, the disc being invisible from them, i.e., from their position in one of the dark cones, while other objects at their side, and even still more remote than they are, are brilliantly illuminated; and that all the surfaces, upon which any rays do fall, are merely dark spaces spotted with Light, with the spots at greater or lesser distances from one another according as the object is farther from or nearer to the Sun. Thus far enough has been said to show the equivocal and utterly false sense in which the Spoke-Theory can be said to diminish Light. We have now, however, to proceed another step in this very unscientific land of Theories, in order to point out the supposed connection between the celebrated " Inverse Squares" and this Theory of Diver- gence, or Unilluminated Cones, the precise theatre of con- fusion, in fact, in which the Theory of the Inverse Squares will seem to many to have wholly originated. Absurd and frivolous as must appear, to all unbiassed and enlightened minds, this Theory of unilluminated intervals between the solar rays, which intervals increase as the square of the distance does, and of dark surfaces with strong luminous spots wherever there are any surfaces anywhere lying across the paths of these isolated and diverging rays, it is nevertheless upon this preposterous hypothesis that the further Theory, whose connection with it we must next attend to, the Theory of the Inverse Areas or Inverse Squares of distance, is constructed. PART II. SECTION 4. 99 This Theory of a perfectly dark cone or pyramid of space along the whole side of every ray of Light, and thus constituting a pyramid of darkness between every two of these rays, treats only, as we have seen, of the diverging rays which form these cones. It altogether ignores the existence of the converging rays, which have been explained in a former page, as the more important element in the hypothesis of Radiation ; and ignores it obviously because it presents no dark cone whatever, no machinery therefore for this alleged diminution of Light without a Medium ; which is here looked upon as the great scientific desideratum. Our business now therefore is with these diverging rays only, and their cones of utter darkness, in order to show in what way these helped to originate the Theory of the Inverse Squares. (See Appendix, Nos. 10, 12, 13.) It is important to attend to the fact that we have here no cone or pyramid of Light whatever. The only cone we have is a cone of darkness. The assertion to the contrary is a mere misuse of language. The Cone of Darkness is, in this Spoke- Theory, bounded, it is true, by Light, but only by a single fine line of Light, not by a Cone of Light. If we had a cone of light, there could not be the decrease of Light which the theorists advocate. No ray, in their theory, has the form of a cone. The ray is held by them to be an infinitesimally fine thread, in no sense a pyramid or cone. The only cone or pyramid that we have to speak of, in this theory, is the pyramid of darkness which the theory supposes between every two rays, or the compound pyramid composed of many single ones, and placed between any two rays that we may think proper to select as the boundaries of this compound pyramid. It is the fashion, among eloquent lecturers, to speak of the " pencil of rays " as a pyramid or cone of Light. But this, except in a medium, it manifestly is not. If it consists, as they tell us, of threads separated from one another by a dark space, and diverging from one another so that this dark space increases in width as they extend, it is, in that case, distinctly a pyramid or cone of Darkness, not of H 2 100 PART II. SECTION 4, Light. Or if there be several such cones placed beside each other, they thus constitute one large cone of Darkness with threads of Light in it, and spots of Light upon the black surface at the end of it. It is still a black cone or pyramid, a combination of several fine cones of Darkness which are united into one large one, and merely separated from one another by these fine threads ; and it is only the dark unilluminated intervals (between diverging rays), whether these intervals be compound or simple, which have the form called " the pyramid " or " cone," and which can have the calculations belonging to such a form. No one pretends that a ray has the form of a cone or pyramid ; and the cone of Darkness cannot be called a cone of Light merely because it has rays of Light around it, or even some isolated threads that extend along the cone, inside it. We have seen in PART I. of this Treatise that the areas or sections of the pyramid or cone, in the diagrams of Geometry, are in the same ratio as the squares of their distance from the apex ; and it has been there explained that, and how, this is true of all areas in nature, of all the objects around us, although these are almost never actually sections of any existing pyramid. Every object has its area or size, and every two areas that differ have, in Geometry, their pyramid or cone ; and these areas or sizes differ as the square of their distance from the hypothetical or geometrical apex differs. So that, when we know the relative areas of bodies, we can tell their relative distance, and vice versa, when we know the relative distance we can tell the relative area. This is the universal law of sizes or areas. We further see that when we have a cone made by and between the divergent rays issuing from a luminous point with this luminous point therefore as the apex of the cone, we have, by this Divergence Theory (or Theory of Unil- luminated Cones, commonly called the Radiation Theory), a Radiation of Darkness as well as a Radiation of Light. "We have fine threads of Light proceeding from the lumi- PART II. SECTION 4. 101 nary, which, in a very remarkable manner, diverge or separate from one another, as they proceed ; so that the unilluminated interval between every two of these isolated and diverging- rays becomes, by this curious theory, wider and wider, as the delineating rays extend, these intervals being dark cones or pyramids of space, with their dark sections or areas, wherever we choose to mark these off, and upon which not even one spot of Light appears ; for the spots of Light can only be upon the sections of these cones when these cones are compound. : " ; The distinction here alluded to requires attention. Tfre unilluminated cones in question are either simple or com- pound. The cone lying between any two neighbouring rays is the simple one, no two such rays are without their dark cone ; and several such cones together constitute the compound cone. We easily see that the simple (or single) cone has no rays passing along inside it at all ; no spots of Light, therefore, at the end of it, i.e., upon sur- faces at its sections. We easily see also that the compound cone has as many of these rays, running within its boun- daries, from the apex to the sections, as the number of the single cones which go to constitute it. We thus see that the compound cone has several spots of Light, thrown on surfaces at its sections, by this theory, while the uncom- pounded one has none at all. The only two further points of which it is necessary to remind the reader are : (1) that the rays, in each compound cone of darkness, thus formed by rays issuing from a point, neither increase nor decrease either in force or number through their whole course within the cone from the apex to the section, and throw therefore the same number of luminous spots upon the larger (e'.e., the remoter) areas or sections of each cone as upon its smaller sections, neither more nor less; and (2) that as in this theory there is no medium to scatter or diffuse the light of the ray, from side to side or up and down, it is only as a spot that its Light can appear upon the area or section that receives it. We see, then, how it happens that, although 102 PART II. SECTION 4. the simple cone has its sections and objects, whether large or small, near or remote, entirely unillumiiiated, the com- pound cones have their sections and objects spotted with Light, but having, between these spots, all the dark spaces of the uncompounded sections, and these spaces becoming wider as the sections become larger. We see here also (3) how it happens that mere points at vast distances from the sun are brilliantly lighted, according to this theory, from merely lying in the path of some ray, while even objects Of' some size near the sun are wholly unillumiiiated, because 'tKey lie off the path of any ray whatever, and entirely 'in' the path of a dark cone. What we have now further to attend to is that these unilluminated cones or pyramids, whether simple or com- pound, increase rapidly in size while, in the language of the theory, the rays which are connected with them, decrease as rapidly in number ; nay, that the rays decrease thus, in their way, precisely because the cones increase in theirs ; and at the same rate as the cones increase. It is indispen- sable that we should understand this part, and this language, of the Theory. These black cones (and there are here no cones except black ones) become wider as they become longer and longer; but the rays which form them, and between which they exist, also the rays which run, inside, diverg- ingly along the compound cones, do not, as they become longer, become either more powerful or more numerous. Neither do they become less so. What these rays were in the beginning of the pyramid or cone they are at the end. They remain unchanged ; the same in number and the same in force. Whether it be simple or compound, it is the dark cone or pyramid alone which changes. The rays do not. But we are told that, since these rays remained unchanged, they diminish ! and diminish, moreover, as fast as the cones themselves and their sections become enlarged! This is the language of the Theory ; and this point is what we have now distinctly to disentangle and to grasp. Let us attend closely to the alleged facts. When it is PART II. SECTION 4. 103 said that, at the same rate as the sections of the dark cone increase in size, the delineating rays, between which it exists, as also the rays within it when it is a compound one, de- crease in number, this only means that they do so, compara- tively speaking. They do not really decrease. It is merely sslf-deception when we think or say they do. They only become fewer and fewer, when compared to the larger sections on which they fall in the cone they traverse or delineate, than they are when compared to the smaller sections of it. It is only in this inaccurate and frivolous sense of things compared, that the rays are said to decrease in force and number when the distance increases although they remain as they were at first. Yet such is the technical language here adopted by the Theorists. It only means (I repeat) that, comparatively speaking, the rays, although the same in number, seem fewer and weaker when the areas illuminated are large than when these are small. Compara- tively speaking, they are fewer and weaker, but not really so, as the professors teach. When the sections of the cone increase in size (i.e., at the greater distance in the cone), the light falling on them, the number of rays falling on them, seems to decrease, but does not really decrease, for by the theory it remains the same. We thus again return to the principle illustrated at pp. 62 and 67 with the bread and butter and which we may here illustrate with bread and jam. If we give to half-a-dozen children pre- cisely the same amount of bread each, and to eacli a spoon- ful of jam to eat with his bread, by then giving one of them a second spoonful of jam, we, in this phraseology, reduce his bread to one-half of what the rest have, and must give him twice as much bread as to each of the others, in order to give him as much as each of them has ! In this way our Lecturers assure us that the larger area has a lower degree of light on every part of it than the smaller area has, even when each area has precisely the same degree of it ; and this merely because it is the larger ; that where one area is double of the other, its light is half ; where 104 PART II. SECTION 4. treble, one-third, &c. ; and this is what their theory means when it says that the light is diminished by the distance, for it is distance in the cone which gives the larger area. We see here also what a misconception it is to say that the same light which is on the greater and the smaller area becomes " diluted " on the larger one. Nothing of the kind occurs. All that their theory authorizes them to say is that this same degree of light on both areas is disproportionate upon the larger one ; and that it would be necessary to increase this light upon the larger area if we wish to make it proportionate to that upon the smaller one. But they do not use the word " proportion." They simply say that if one of two areas is only half the other, the larger area must have twice the degree of light upon it which the smaller has, in order to have the same degree of it as the smaller ! Such is the equivocation and merely relative sense hi which the " Spoke-Theory " and its professors teach that Light is diminished by the divergence of its rays. We have now to see in what ratio of the distance this relative diminution takes place (Appendix, Nos. 12 and 13); and this is easily measured for us by the dark spaces or cones between the rays. Since the ratio in which the sections of these dark cones increase is the square of their distance in the cone, it is in this ratio also that the accompanying rays, whether traversing, divergingly, the cones or delineating- them (z.e., whether inside or outside the cones), have this appearance of decreasing. These rays which thus accom- pany the dark pyramid of space that lies between them and around them become proportionably fewer, and therefore proportion ably weaker, the theorists tell us, because the sections which they have to spot with light become larger, and, moreover, at the same rate as these spotted sections become larger. The sections become really larger. The rays become only relatively fewer ; but they undergo this relative or seeming diminution at the same rate as the sec- tions or sizes of objects really enlarge. This is because the PART II. SECTION 4. 10$ sections change in size, while the rays always remain un- changed in force and number. Since these sections, therefore, really enlarge as the square of their distance in the coue becomes greater, the rays become relatively fewer and therefore relatively feebler in this same ratio ; viz., as the square of their distance in the cone becomes greater. For to diminish, in any sense of the word " diminish," as the area enlarges, is to diminish as the square of the distance in the cone increases. To recapitulate now what we have here gone over, we see that, throughout the cone of black space thus marked out by rays, the dark areas or objects presented to the apex increase directly and absolutely as the square of their dis- tance in the cone ; we see also that each spotted area, each spotted section or object, in the compound cone, however near or distant, however great or small, this area may be, has upon it, by the theory, precisely the same number of rays or spots of Light, and each spot or ray in the same intensity, force, amount, or degree of Light as when these rays first left the source ; we see, therefore, that the rays being thus, by the theory, fewer compara- tively, but only comparatively, on each greater area, and more numerous comparatively and in appearance, but com- paratively and in appearance only, on each smaller one, these rays seem to increase and decrease inversely as the areas do on which they fall; i.e., in a ratio inverse to the square of the distance. They increase and decrease thus inversely and relatively while the areas or sections them- selves of the cone increase and decrease directly and even absolutely in the same ratio. We see that, although these dark cones do, by this theory, really increase in size, between and around the rays by which they are delineated or, diverg- ingly, lengthwise traversed, yet the rays themselves do not increase in number. They remain in all respects unchanged by the distance ; and for this reason are said by the pro- fessors of Physics to decrease! nay, to decrease as fast as the dark areas, which they speckle with light, increase ! 106 PART II. SECTION 4. We may here profit by this long but indispensable digres- sion on the " Spoke-Theory " and its connection with the law of the Inverse Squares, to illustrate three points con- nected with this law and already adverted to in explaining the theory of it, yet too often lost sight of even by the theorists themselves. 1. We see that when the professors consider the light upon the smaller and larger area as always equally strong when equally exposed to the same source, but as less, on each "unity of surface," upon the larger area than it is upon the smaller, they only mean, and can only mean, that it is comparatively less; that the larger area ought naturally to have the stronger light ; and that in order to bring the two unequal areas to an equality of illumination, it would be necessary to increase the strength of the light at each point of the larger area by as much as the larger area is greater than the smaller. They forget that this could not be done without reversing the dark cones of their theory, placing the base of these cones instead of the apex on the source, and increasing the spots of light in propor- tion to the increase of the area instead of leaving them unchanged. In short, they hold that the larger regions of space should have this higher degree of illumination than the more contracted regions, merely to keep them illumi- nated upon a par with these more contracted regions, and that, as this is not the case, the light of the sun is (com- paratively) diminished through the enlargement of the regions or other areas illuminated by it. They here, in their statements, omit the word "comparatively;" the import- ance of which word, in such a case, every one can judge of. 2. Nothing can be clearer than it is made by this Spoke- Theory, commonly called the Radiation-Theory, that it is the Enlargement of the Area on which the rays form spots and which stands at the greater distance in the cone, not at all a diminution in the number and intensity of the rays which fall upon that greater expanse, that makes the PART II. SECTION 4. 107 rays which fall upon it less in the only sense in which they are less; viz., less in proportion to the increased size of the object or area which receives them in the more and more isolated manner required by the theory. 3. Another point which our analysis of the Spoke-Theory may help us to discern more distinctly is, that it is distance in a cone or pyramid, i.e., distance from an apex or angle, not, as so many professional physicists have imagined, distance from a luminary (window, sun, or lamp), that makes the illuminated objects (the areas) greater or smaller. What seems to have led to confusion on this point is, that some writers, instead of using any other delineation of a cone, have illustrated the geometrical law of areas with the cone of darkness formed by rays issuing, at an angle, from a luminous point, and thus bounding the dark cone which by the theory is formed between them. (Appendix, Nos. 12 and 13). We see clearly, however, that it is not the luminary nor the distance from it which here makes one area or section big'ger than another. What does this is the angle at the apex (whether formed by rays or not), and the increasing distance from each other, maintained through their whole course by the lines which form this angle, and which therefore at each point require a certain object, or area, to fill the space between them. It is thus that the objects or areas which subtend or are opposite to this angle are greater or smaller, according as they are farther from or nearer to it ; not at all according to their distance from some luminary. We see also that the only objects whose size is regulated by the angle in question and its sides, are the areas which subtend this angle. Other objects, lying within the cone or extending beyond its sides, would not be made greater or smaller by this angle nor by their distance from it; a fortiori then, not by their distance from a window or other luminary. Nor could this angle make such objects have any relation of size or distance to one another. The planets, for instance, are not made greater or smaller by their dis<- tance from the sun, nor the pictures on the wall by their 108 PART II. SECTION 4. distance from the window. Yet all such objects have the size belonging to a particular distance from an apex, and the distance belonging to a particular size. In a word, nothing can be clearer than it is that the " distance " men- tioned in this law arid theory of the Inverse Squares is the distance which defines the size of an object, distance from the Source of Size (pp. 23, 56) ; and nothing clearer than it is that this defining distance is not at all, as so many professional Physicists think it is, the distance from a lamp or other source of light. Enough has been now said upon this subject for our present purpose; which is merely to show how the old Theory of Divergence or Unilluminated Cones and spotted Sections (the Spoke-Theory) gave rise to the clumsy asser- tion that the spots of Light upon the dark sections of the compound cones are, although in number always the same, in the same cone, yet few or many, according to the size of the dark spaces they are upon, few when these are large, and many when these are small ; or, in other words, that the illumination of objects, areas, or regions is in a ratio inverse to the size of the objects, areas, or regions illuminated; and this, although even by this Theory of Radiation, there falls always the same amount of Light, the same number of rays and each ray in the same inten- sity, upon each object equally exposed to the same source. Enough also has been said to explain from this Theory, that when the size of an object is said to be as " the square of the distance," the term " distance " here only means, as every Geometrician knows, distance in the cone, pyramid, or other diagram, which is the only distance that makes one object greater than another, not as professional Physicists suppose, distance from a lamp, or window, or other source of Light, a sort of distance which has no BUCQ effect as this of defining the size or area of the object upon which the rays fall as luminous maculce upon a black ground. PART II. SECTION 5. 109 FIFTH SECTION. RECAPITULATION OF THE RECEIVED THEORY RESPECTING THE DIMINUTION OF LIGHT BY ENLARGEMENT OF THE SURFACE ILLUMINATED ; AND OF THE PHYSICAL IMPOSSIBILITIES CONTAINED IN IT. FROM what has been said thus far, we see that the common theory the theory of the Inverse Squares consists mainly of the following four elements, which cannot be too much kept before people's eyes, and must never be lost sight of for a moment by those who desire to understand the question : 1. The diminution of Light now under consideration is not supposed to be caused at all by the distance itself which there may be between any space or surface and the sun or other source of Light (for diminution by distance is what occurs solely in the case of a medium), but merely by any enlarged space presented transversely to the sun or other luminary ; and this enlarged space, if not otherwise defined, may be described as that which would geometrically result from its greater distance in the cone, i.e., from the greater distance existing between it and the apex in its appropriate pyramid, and would be in the ratio of that distance squared, as has been already explained in PART I. (see p. 18). It is most important to stand clear of the flagrant equivocation here employed, apparently in utter unconsciousness, by many of our theorists (Appendix, Nos. 2, 3, 5, 15, &c.) when they speak of Light and its diminution, in their Theory, as dependent upon distance from a source, for this is not really what the more enlightened of them mean ; nor as has beeii seen, would this at all suit their Theory. This diminution of Light by distance from the source is what happens only when Light passes through a medium ; and this is then a result of the medium's density as well as of its length, or the distance to which it extends. They are very far from holding that distance from the source, 110 PART II. SECTION 5. without a medium, diminishes the Light. They admit, on the contrary, that the increased length of the sun's ra}^s greatly increases the illumination of space, as far as that length alone, or mere distance from the sun, is concerned. They fully admit that it is only the enlarged transverse space, area, or surface, itself exposed to the disc, and not its dis- tance from the source, that produces the diminution which their theory treats of, the enlarged space spread out on every side around the sun, not the enlarged space lying between the sun and some point of that transverse space ; for, I repeat, they completely recognize that in that (the third) dimension of space the solar illumination is, on the contrary, enormously increased by the increase of distance, holding, as they seem to do, that a long ray gives more light than a short one. 2. These theorists further hold that all rays, whether we suppose emission-rays or wave-rays, lie in straight lines, from the sun to the remotest limits of the system, com- pletely undiminished in their whole length, i.e., losing no- thing of their force nor of their number, nor as most professors admit, of their proximity to, or rather lateral continuity with, one another throughout all that distance, having no spaces whatever between them. These writers do not here pretend that there is the least diminution of Light by distance, in their theory, but quite the reverse, in consequence of the sun's rays being all thus prolonged in unabated force to the confines of the system, increasing thus in luminous masses, rapidly throughout the whole of space. This perfect equality in the sun's light, i.e., in the force and number of the sun's rays, at every point of space, from the disc outwards, is a very important item of this theory, and fully recognized as an important one by all who hold the theory. 3. They admit moreover, at least, most of them now- adays insist strongly that from each point of the disc to each point of the most distant space, there is one of these unimpaired lines of light, infinite numbers of PART II. SECTION 5. Ill them, therefore, proceeding from one and the same point of the disc to the whole of the space confronting it, and also from the whole of the disc to every separate point of this confronting space however distant ; thus forming cones of rays without number, some converging-, some diverging ; some whose base is on the whole disc, and their apex on some point of distant space ; these are the converg- ing cones ; others whose apex is on some point of the solar disc, and their base on some extent of distant area ; these are the diverging cones ; and the Theory insists strongly that, as above stated, each of these rays, at each point of its path, at each point of each concentric sphere of space it traverses, retains precisely the same undiminished force with which it left the sun, as well as that, to each minutest point of the most distant space, a converging cone of these rays extends whose base is on the solar disc (see p. 90). 4. Then fourthly and finally, combined with the three foregoing principles respecting (1) the enlargement of the space to be lighted ; (2) the unimpaired force of the ray throughout its course ; and (3) its rectilineal progress out- wards, but unintelligibly combined with them, the Theory goes on to teach that, in all this enlarged region of transverse space, in all the space at right angles to this outward progress of the Light, in all the space or surface presented, and spread out, transversely to the lamp or to the Sun, so as to receive its rays, the light here loses its force, spreads, i.e., deviates in all directions from the straight line, and thus, it is said, becomes attenuated, en- feebled, dimmed, diluted, by its greater subdivision over this enlarged space, although, on every point of it, there falls a cone of converging rays in undiminished force, just as on every point of the contracted space which is nearer to the Sun or to the lamp. Such is the whole theory. Such all that they mean when they say that Light decreases inversely in the ratio which they self-deceivingly call the Square of the distance, 112 PART II. SECTION 5. which, however, we easily see, only means, as all the more enlightened admit, in the ratio of the more extended space illuminated. Whenever there is no increased extension ; no enlargement of the space illuminated, there is then, according to these more enlightened of the professors, no diminution of Light whatever. The question for us on this point is : How can there be any of this diminution, even where there is this enlargement of the space illuminated ? Upon the least reflection the physical impossibility of this is obvious. For how can Light deviate from its straight line, its rectilineal course, in order to spread and diffuse itself, where there is no medium ? It cannot. Or where is the redistribution of Light resulting from the enlargement, when the source is central, or one for all? There is none. This could only result from some subdivision and distribu- tion of the source. And, which is the portion of the trans- verse space exposed, upon which the whole experienced light of the disc is not to be found? Which is the point of it upon which, according to this theory, a ray from each point of the disc does not fall undimiuished, brought there in its own converging cone from the disc ? Clearly there is none. If the solar light proceeds, as they say it does, un- changed in intensity to each point of space, the remotest as well as the nearest, what is the meaning of saying that there are some points of the transverse space to which the solar light does not come directly from the disc but by spreading without a medium, points upon which the sun's light is not in this undiminished force which the theory leaches, but either not upon them at all, or considerably weakened and diluted from there being more points to be illuminated than the rays can come to in straight lines ? Are these words supposed to have any coherent meaning ? If there were some points of transverse space to which, according to the theory, the converging cones of rays could not come, or did not come, on account of some overpowering divergence, as in the Spoke-Theory of some professors PART II. SECTION O. 113 (see Appendix, Nos. 1 and 3) ; or if these converging cones lost some of their rays, or the rays some of their force, in consequence of the distance they had to travel, the thing- would be intelligible enough. But the theory denies in toto, and most justly, that any such obstacles exist to an equality of illumination ; and the theorists profess not to see, in this part of their hypothesis, its incompatibility with every known principle of nature and of common sense. It is clear then, from what has been said, that we have no less than three separate cases of flagrant physical impossibility crowded together in this one Theory. 1 . Two different degrees of Light supposed to be on the. same area from the same source. It is alleged that the same degree of light upon any area differs according as this area stands alone or forms part of another area, on the square foot, for instance, when it is alone, and on this same square foot when, in conjunction with others, it forms a square yard. (See p. 66 and p. 78.) 2. Light supposed to expand or leave its straight line, and spread if we give it room. The unexpansive nature of light, the straight line theory, renders it impossible for light outside all medium to stretch or spread out of the straight line, as air does, without the spreading of the source ; i.., to exist at any point which it cannot or does not reach directly in perfectly straight lines, from the source. (See pp. 21, 60, 62, 63.) 3. No space here existing for Light to expand in, even if its nature admitted of its doing so. Even if it were true that Light was of an expanding (or deviating) instead of an un- expanding nature, yet, as each point of all transverse space is fully and equally occupied, i.e., receives the whole Light, from the source, conveyed to it in the cone terminating at that point, there are no points, no spaces, left unillumi- nated, into which Light could by any imaginable possibility spread and expand from other points and spaces better lighted than they, and thus become diluted in consequence of this expansion. As stated, however, in the last para- i 114 PART II. SECTION 6. graph, a straight line does not expand ; so that even if there existed such points and spaces, no light could reach them. SIXTH SECTION. TWO EFFORTS MADE TO JUSTIFY THE THEORY OF THE INVERSE SQUARES ; VIZ., THE THEORY THAT, WITHOUT ANY ACTION OF A MEDIUM, THE GREATER AREA ALONE PRODUCES A DIMINUTION OF LIGHT, THAT, INDEPENDENT OF ALL ABSORPTION, THE LIGHT DIMINISHES UPON THE GREATER OBJECT OR AREA, IN PROPORTION AS IT IS GREATER ; Z.6., AS ITS SQUARE OF DISTANCE IN ITS PYRAMID INCREASES. OF the manifest incongruities with nature's laws pointed out in the foregoing section, these lecturers seek to offer no explanation. Is it that they see they can offer none? or is it that they do not see the incongruities ? Be that as it may, they never even advert to them, although they state and restate, as fact, the hypothesis involving them, in every book and every lecture, and, what must astonish us as much as anything else, are listened to. But they not only take no notice of the physical impos- sibilities so patent in what they teach ; they become immersed in all sorts of further incongruities in their efforts to justify and prop up their hypothesis. They do not attempt to answer the arguments which common sense as well as common logic brings against their notion that, independent of all medium, Light is diluted by distance from the source (which is the grossest form of this mis- conception) or even " thinned out " and rendered feebler by being spread over a larger surface, or diminished in the figurative sense of " proportionate magnitude," in the figurative sense of there being less of the force and intensity of the Light at each point of the greater area, merely because it is the greater, although there is, they admit, on the greater as well as the smaller area precisely the same PART II. SECTION 6. 115 amount of this intensity, coming direct to each point from the sun or other central source. They do not seek to ex- plain or answer any of these points. Nay, overlooking all such matters, these theorists, as may be seen in the extracts from their writings given in the Appendix, insist, with remarkable naivete, upon their incoherent statements ; and just as if no such incoherencies existed, they merely employ themselves in forming hypotheses and contriving illustra- tions whereby their theory may be made plausible and natural, they think, to " unscientific people," and even pro- bably be justified in their own eyes. I shall do no more here than mention the two more remarkable instances of this, viz., the Argument from Perspective and the Argu- ment from Experiments ; in both of which Arguments what is effected by the Medium is held to be identical with that which is effected without it ; while, in the Argument from Perspective, the confusion between Physical and Physio- logical Optics becomes perfectly astounding, the diminution of Light by Distance from the eye being, throughout, con- founded with that by Distance from the source ; and both these Distances also, still further confounded, as usual, with that which is neither ; viz., with that which is called " Dis- tance in the pyramid and cone of geometrical diagrams" a sort of distance, depending wholly on the relative Areas of any two Objects and having nothing whatever special to do either with distance from a source of Light or with distance from an Eye. In this Argument drawn from the phenomena of Perspec- tive, the Physiological fact that Light is not diminished in degree and brilliancy upon a self-luminous area by its Distance from the eye, notwithstanding our powerful medium and notwithstanding the Physiological or apparent contraction of the self-illuminated area, is brought to establish the supposed Physical diminution of Light upon an area not self-luminous, a diminution of Light supposed to result from the mere enlargement of the illuminated area, without any action either of Medium or of Perspective ; i 2 116 PART II. SECTION 6. while the second Argument, drawn from a system of Experiments with a medium, which we must here call " Professorial Photometry," inasmuch as it is not employed except by Professors, deals only with the area which is not self-luminous, the Physical diminution of Light which takes place upon this area in consequence of distance from the source, where there is a medium, being represented in this strange Photometry, as being identical, in amount and ratio with the Physical diminution which ALSO takes place upon it, in consequence of the same distance independent of all medium and all absorption. We shall speak of each Argument separately, that from Perspective and Medium jointly, and that from Medium alone. It will be seen that both Arguments, as far as they prove anything, prove the very contrary of what they are brought to prove. 1. The diminutions from Perspective and from Medium em- ployed to prove the law of the Inverse Squares ; i.e., to prove that diminution of Light which is supposed to result from nothing else but the enlargement of the space illuminated. In our dense Atmosphere, which enters into all our experience and experiments respecting Light, there is always a diminution of Light upon every area, self-luminous or riot, when at a distance either from the eye only or from the source only or when, as often happens, at a distance from both ; and this diminution, the amount of which de- pends upon the amount of medium traversed, is consequently, cceteris paribus, greater or less according to this distance of the area from the eye or from the source or from both. Of course, however, if there is no area to be taken account of but the source, there is then no distance from the source that requires to be taken account of. Such is the common fact of our experience in this matter ; and to this we must here add another also much insisted on by these writers ; viz., that the physiological or apparent illumination of the diminished area, i.e.. the illumination seen PART II. SECTION 6. 117 upon the area at a distance from the eye, is not less intense and strong 1 , although there is less of it, not less in degree although less spread out, in consequence of in- creased distance from the eye. These two facts no one disputes. They belong to daily life and daily experience ; and the latter wholly to Physiological Optics. The Medium diminishes the Light upon the distant area not only physiologically, not only for the eye, but also physically; i.e., in its illuminating, chemical, and other ph} 7 sical effects ; and the Perspective diminishes the area itself, but for the eye only ; i.e., only physiologically. For the eye therefore, or physiologically, the Light existing upon the distant area being apparently drawn more together, would, if undiminished by the medium, increase in intensity in proportion as its extent is thus apparently diminished (just as when a dozen gas-burners are grouped together instead of being dispersed over some large space, or as a lens acts); but, being, at the same time, physically diminished by the Medium, does not thus increase in intensity in pro- portion as its extent is apparently diminished. The result of common observation is that it remains much the same in intensity for the eye, whatever may be the apparent change in the area ; so that the real effect of the medium counter- balances the apparent effect of the apparent contraction in the area. The medium causes one diminution, the dimi- nution of the Light. The Perspective, or distance from the eye, causes the other diminution, that of the area over which the Light exists. So far all parties appear to be agreed. Now let us attend to the use which the Professors make of these facts, in their efforts to uphold their theory of the Inverse Areas (or " Inverse Squares," as they prefer to call it), and to the result of their reasonings. They begin by saying that, in all this, it matters not whether we understand the word " distance " to mean dis- tance from the eye, in Nature, or distance from the source of Light (window, lamp, sun, &c.), also in Nature, or 118 PART II. SECTION 6. distance in Geometrical diagrams, from the Apex of their pyramid. Distance in any case (they say) is distance, and the square of the distance, in any case, is the square of the distance, without any reference to what distance is meant. All their statements involve this error and this confusion ; which of course, except themselves, no scientific man can sanction. They then argue that it matters not, for the diminution of Light, whether a medium is or is not present. They say that, since in every case the self-luminous area is diminished to the eye (i.e., seems diminished) in inverse ratio to the square of its distance from the eye, while, except in extent, the illumination on the area remains undiminished to the eye, the illumination itself must therefore be also here diminished, under the Medium, in the same inverse ratio of the distance, in order that this identical reduction should have resulted. Light, therefore, in our medium (they argue), diminishing to the eye, in inverse ratio to the square of the distance from the eye, it therefore does so also independently of all medium, and in addition to the absorption which results from the medium, and which is always, we are told, going on in a geometrical progression. This Argument, drawn from the Perspective, applies of course as much and as clearly to the illumination upon areas which are not self-luminous as to that upon those which are ; to that upon the lunar disc, for instance, as much as to that upon the solar disc, and to that upon the whole illuminated expanse of the solar system, or (which is the same thing) to the concentric spheres of space around the central sun, with their elastic illumination (pp. 24, 33,), as much as to the elastic illumination to be seen (i.e., the apparent illumination) upon the disc of the sun itself, at different distances from it. But although the argument applies equally to both kinds of areas, to the area which reflects and to the one which is self-luminous (the only essential con- dition being that the light spoken of pass through a medium, as we always experience it), it may be well, for the sake of PART II. SECTION 6. 119 precision and simplicity, to speak here only of self-luminous areas, of the illumination, for instance, which expands and contracts physiologically, i.e., to the eye, upon the solar disc, and upon other surfaces which are self-luminous; and the fact which these writers bring forward is, as we have seen, that the illumination on the area, not, of course, its illuminating power, but the Light seen on, or in con- nection with, the area, as long as the Light remains at all visible, remains the same, of the same strength and brilliancy, although the area itself decreases in size. They accordingly argue that, since the area decreases under the action of Perspective law, in the ratio called the Inverse Squares, the brightness or illumination must decrease under the action of the medium, in the same ratio precisely ; for, otherwise, according to their theory (p. 18), this illumina- tion would be increased as much as the area is decreased instead of remaining, as it does, the same. Light is there- fore physiologically diminished, with a medium, as well as physically without one, in a ratio inverse to the square of the distance. In reply, then, to this Argument from the phenomena of Perspective, it is enough to observe (without referring to its other absurdities) that, as there is alwa} 7 s a great diminution of Light going on in a dense medium like our atmosphere (which these writers themselves acknowledge and describe as proceeding in a rapid geometrical progression see p. 15, and Appendix, Nos. 1, 15, 16,20), the diminished amount of Light seen by us upon the solar disc or other luminous body being the result of a diminution in inverse ratio to the square of the distance, would, if true, prove (contrary to what is intended), that this is not the ratio of any diminution ascribed to Light independent of the medium ; inasmuch as, when we have deducted from the whole decrease the very considerable portion of it, which is due to Medium, and the existence of which these writers fully recognize^ we have a balance entirely different from that supposed to be required by the Inverse Squares ; the Argument from 120 PART II. SECTION 6. Perspective thus disproving the very ratio of diminution which it is adduced to prove, But, besides all this, there is no scientific man, un- hampered by theories, that does not instantly see the pre- posterous inconsistency of supposing that the diminution of Light by a medium can be regarded as identical with any- thing we may imagine respecting a possible diminution of Light without one. 2. The Experimental Photometry of the Professors, wherein the diminutions which happen where there is a Medium, are adduced to prove the existence of those which are supposed to happen where there is none. What the Professors of Physics seek here to establish by their Experiments (Appendix, 2, 3, 5, 15) is that Light with- out any action of a Medium, without its undergoing any absorption, becomes diminished in proportion to the in- crease of the illuminated area ; and this point they profess to render clear to any ordinary intelligence by the aid of our dense atmosphere and a few " candle-flames," with a screen or two and a rod. They proceed to place these articles in position very much as a conjurer would do, and then ask us : Do we not see ? Yes, no doubt, those who can see only what they see with their eyes, see all that the Lecturer desires, and admire his profound photometrical experiments. But how is a thoughtful man to see all this? What is the scientific man to think of such a lecture, and of such instruction ? The object of the Experiments in question is to show that, independently of all Medium and of all Absorption, Light diminishes inversely as the Square of the distance. The Professor undertakes to do this in a medium. With all the liveliness, and air degage that a Professor ought to exhibit, sometimes even with some effort at histrionic effect, he places everything, and shows us that the reduc- tions of Light which take place in a medium, are exactly in I' ART II. SECTION 6. 121 this peculiar ratio, exactly as the square of the distance in the cone or pyramid of sizes. Although by the profes- sional theories on this subject, there are two diminutions going on at once, one by the Medium and one entirely independent of all Medium, yet here under the action of the Medium, we have only one result, and this, the experi- menters admit, the result known as the diminution com- mensurate with the square of the distance ; the result or action of the Medium being, for the moment, we are taught to believe, completely paralysed by the grander action of the Inverse Squares, or Enlarged Areas; and this, even while no other action appears except that of the Medium. This, it must be admitted, is a peculiar form of experi- mental Teaching. How can we show what change is caused in Light outside a Medium by that which it under- goes within one I If the four " candle-flames," placed at a particular distance from an area, in a Medium, produce a particular amount of Light, how can we offer that as evidence that, outside all medium, they would produce the same effect or any effect, outside a medium, at all ? Where is the Logic of such an Experiment as this ? Where its Common Sense ? But it is useless to dwell on such a sub- ject. It can be hoped that a better Era of research is coming, an Era in which the unpaid man of science will not be so rigidly excluded by the paid ones, from that " fair field and no favour" which some enlightened minds have seen to be so essential to Scientific Progress. Here then also, as in the case of Perspective, the " Ex- periments " with a Medium and a screen and a few candles prove precisely the contrary of what they are brought to prove. They show, in the clearest manner, that when due allowance is made for the absorption of our dense atmo- sphere, there does not remain the amount of diminution here intended to be established, and here required in order to support the theory of the Inverse Squares. These Experimenters all tell us that there is this diminution by a Medium going on in geometrical progression at the same time 122 PART II. SECTION 6. as their supposed diminution by the square of the distance. But where or when do they take account of this double diminution thus simultaneously going on in all their " ex- periments?" When proving their Inverse Squares with their Medium and their candles, and the rest of their photo- metrical machinery, why do they never mention their curious law of geometrical progression, whereby all Light in our atmosphere is always enormously diminished, and can be almost as much so as some suppose it can by the Theory of the Inverse Squares f Why should not the diminution they find upon the screen of their Photometer be the sole result of the medium they are employing ? Or, do they know that they -are employing a medium ? How is it possible not to be astonished that such Experiments should be called " Science," and be taught unchallenged at the Royal Institution and at the Royal Society I END OF PART II. PART III. THE LOGICAL IMPOSSIBILITY OF THE LAW IN OPTICS CALLED THE LAW OF "THE INVERSE SQUARES." PART III. THE LOGICAL IMPOSSIBILITY OF THE LAW IN OPTICS CALLED THE LAW OF " THE INVERSE SQUARES." FIRST SECTION. DIFFERENCE BETWEEN THE THEORY AND THE LAW. TWO INTERPRETATIONS OF THE LAW VERBALLY POSSIBLE. THE ORDINARY ONE. USE OF THE TERM " INVERSE." Difference between the Theory and the Law. We have so far examined the THEORY of the Inverse Squares ; and we have seen that, according to this Theory, it is the larger object, the object with the larger area, which makes the Light less than the Light on the smaller object, while we know from other considerations, that it is distance from the apex which makes one object's area larger than another's, not distance from the window or any other source of Light. We now come to speak of the LAW which is generally supposed to express this Theory, and is therefore called, also, the Law of " the Inverse Squares." It will be seen, however, that the Law, in the only meaning ever given to it, treats of quite a different subject, and is no expression whatever of the Theory so called. The Theory applies to the illumination of all areas irrespective of their distance from the source ; whereas in the Law this distance from the source is everything. The Theory is to the effect that, 126 PART III. SECTION 1. when each point of each surface is equally exposed to the source, objects of different areas are illuminated inversely as the areas, i.e., less when these are larger, and more when these are smaller ; and this without any reference what- ever to their distance from the lamp, window, sun, or other source of Light ; while, as I say, in the Law, the distance from the source is everything. This law is that, if the distance which the Light traverses is divided into any number of equal parts, the Light, remaining after the first division of the distance, is always four times greater than that remain- ing after the second division, and always nine times greater than the Light left after the third, however short these distances may be, and although they are supposed to be entirely free from Medium. The difference then between the Theory and the Law is simply enormous, as the attentive reader will have no difficulty in discerning. Our sole business, however, now is with the Law, the cele- brated Law of the Inverse Squares ; to point out how it is interpreted, and how utterly it is without any data or any Logic ; also how, in various experiments, its absurdity admits of being easily shown. I am aware that to many of those who read these pages, and hear this Law perhaps for the first time distinctly stated, it will seem quite superfluous, especially after the explanations in PART II., that I should enter further upon the discussion of a principle so obviously false and frivolous ; but it must be remembered that every one is not so quick- sighted, and that there are many to whom everything self- evident is not self-evident; whom also nevertheless it is desirable to assist in any efforts they may be willing to make in order to understand this subject ; and with this purpose I proceed to a close analysis of the LAW in question. I have already drawn attention to the obvious facts of Nature here hitherto either controverted or neglected (1) that every point of two different areas, equally exposed to the same source, has the same amount of Light upon it ; PART III. SECTION 1. 127 (2) that what is true respecting the spreading and thinning out of Heat or Air is not true of Light ; (3) that Light, from its nature, cannot spread at all ; and (4), that even if its nature admitted of its spreading in this way, and devi- ating from the straight line between the source and object, there would be, in the present case, no vacant space for it to spread in, no space unprovided with its full complement of Light for any more of this same Light, from this same source, to deviate into or to spread into, and so, to become diluted; also (5), I have shown that the Theory of the Inverse Squares, instead of being, as is pretended, the Law of Areas in Geometry applied to Optics, is precisely the con- trary of this Geometrical Law. I have now further to point out, what, as I say, many will not require to read at all, and most others will discern at a glance, that this Law of the Inverse Squares, a proposition utterly different from the Theory of the same name, but equally devoid of all geo- metrical principle, is something entirely without founda- tion of any kind, as entirely so as the Theory itself, and, like it, completely destitute of Data, Logic, and Common Sense ; this, also, so obviously so, that it is inexplicable how it came to pass that so fanciful a " Law of Nature " could ever, among an enlightened people, have been received as this has been. Two Interpretations possible. The soi-disant "Law of Nature " however, here in question, " the Law of the Inverse Squares " as it is confusedly called, is to the effect that irrespective of all Medium, the degree, intensity, or quantity of Light, as well as that also, it would seem, of gravitation, diminishes as the square of the distance from the source increases; not, however, on account of this distance from the source, but on account of the greater space and surface supposed to be presented to the source at this greater distance from it. Now, the original expression of the Law here given, viz., " that Light diminishes as the square of the distance from the source increases," can mean either of two very different 128 PART III. SECTION 1. things. It can mean either that the Light itself becomes less, or that the Diminution becomes greater in this ratio of the distance from the source (an effect, we are told, of the larger area which, at the greater distance, is supposed to present itself to the source) ; and so little attention has hitherto been given to this subject that I have found scientific men of European celebrity imagine, on the subject being first proposed to them, that the two principles now stated (the Diminution of Light, and the increase of Diminution) mean the same thing, and that when the Diminution is four times greater, the Light is four times less. It is easy, however, to see that this confusion, as well as, no doubt, the Law itself, must have been, in the case of such men, a mere momentary oversight. Let it therefore be distinctly understood that it is only in the first of the two senses above indicated, of the trans- mitted, not of the untransmitted Light, that the Law is ever interpreted by scientific men. In the first only of these two senses therefore is it necessary to point out this utter absence of all Logic and of all data. It will be found, however, that by keeping at the same time the import of the second interpretation steadily before the mind, and com- paring the two as we proceed, we shall be greatly assisted in understanding the import of the first. To continue, then : The common interpretation of the Law among the Professors of Physics and Astronomy is riot by any means, as it might so easily be supposed to be, 'that Neptune's orbit, being 30 times farther from the sun than ours, the whole diminution (or loss) which takes place, in the solar light, between the sun and Neptune, is (30 x 30) 900 times greater than that which takes place between the sun and the atmosphere of the Earth. As far as the mere words are concerned in which the Law is usually expressed, the Law might bear that interpretation ; but this is not the one ever given to it ; nor even the subject here understood by professional men, as intended to be treated of under thr name of their Law " for the diminution of Light by distance.' PART rrr. SECTION 1. 129 The received Theory upon this point, and the received inter- pretation of the Law as " the Law of the Inverse Squares," is that the solar light which falls upon each square foot of Neptune's atmosphere is 900 times less, less strong, less intense, less in quantity, efficacy, and degree, than that which falls upon each square foot of the Earth's atmosphere ; is, in short, as I have said, only one 900th part of it ; and this, it seems, although Neptune is not 900 times a greater area than we are (as the geometry of the cone would require him to be), but because he is 30 times farther from the Source. This interpretation of the Law, as a Law of the Light trans- mitted, is the one which is always given to it by those scientific men who write or have written on the subject. It supposes the luminous force of the sun, which we have in action upon each point at the Earth's orbit, to be divided into 900 equal parts or degrees, and maintains that one of these parts or degrees, one of these riine-hundredths, is the strangely limited amount of this solar force which reaches each point at the orbit of Neptune. These writers think that this is the original import intended and the true application of that Law according to which Light is said to diminish in the same ratio as that in which the squares of the distance from its source increase. (See Appendix, Nos. 2, 3, and 12.) They think that after the first distance there is thus 4 times more light than after the second distance, 9 times more than after the third, 16 times more than after the fourth, 900 times more than after the thirtieth distance; and that, when we come to greater multiples of the distance, the light after the first distance is a million times greater than that after the thousandth distance, and a billion times greater than that after the millionth distance, however short this first of the equal dis- tances may be. So that, whether the whole distance, so divided, be a mile, or a million miles, or only a single yard, and the divisions made be into miles or inches, the light at the end of the second division is thus always one quarter of that at the end of the first division, and the K 130 PART III. SECTION 1. light at the end of a yard, a millionth or even a billionth of that at the beginning ; and this interpretation of the words they have now, happily for truth, secured to their Law by the introduction of the word " inverse." These writers and lecturers think that, since Neptune is 30 times farther, not from the apex of our cone (i.e., of the cone of which Neptune's disc and ours are sections), but simply 30 times farther from the sun than we are, our discs must also accord in the geometrical proportion belonging to that difference of distance (which, however, it is known they do not; Neptune's disc is not 900 times greater than ours); and not that only, but also that, in consequence of this supposed geometrical proportion between our areas and our distances, the Light which falls upon each point of all space at Neptune's distance must consequently be 900 times less than that which there is on each point of all space at our distance ; nay, further, they think that, on that account, although the source of Light is the same for both planets, and the whole amount (in this absence of all medium) ad- mitted to be the same on both, yet the luminous energy in action upon each point of Neptune's atmosphere must, on account of his relative distance from the sun, and therefore (so they reason) on account of his relative area, or section of the cone, produce 900 time less effect, by this geome- trical Law of sections or areas, than the luminous energy in action upon each point of ours ; and accordingly, they limit the Law to this one of its two possible interpretations (to the interpretation of Light transmitted rather than of lost light), by introducing the word " inverse " or " in- versely " into their expression of it ; saying that the trans- mitted Light increases or decreases in inverse ratio to the square of the distance ; which means that the one thing spoken of is less in proportion as the other is greater, thereby precluding all possibility of the law being inter- preted of the diminution, or Light lost, this diminution being always a thing proceeding in a direct ratio, i.e., more or less as the distance is greater or smaller. PART III. SECTION 1. 131 For most people it is not improbable that the extra- ordinary differences of Illumination just alluded to, as resulting 1 everywhere throughout the system from this Law, and never hitherto taken the least account of by the Profession, will alone be sufficient to make it clear that there must be an error somewhere, either in the Law or in its interpretation. That is therefore a useful preliminary. I now propose to analyse this Law, and to show that it does not treat of and could not treat of, could not, one feels disposed to say, have ever been intended to treat of, proportions in the Light transmitted, as in the instances just mentioned, but only probably, although also most erroneously and unaccountably, of proportions in the Light lost or untransrnitted upon these occasions (i.e., of the dark cones in the Spoke-Theory, PART II., Section 4), an equivocation and absence of distinction in the terms of the Law, wholly overlooked, and never even once alluded to by any of the writers in question. This utter impossibility of the ordinary interpretation is what I propose now in this PART III. to deal with, irrespective of all other considera- tions, for it is independent of all others, and greatly assists all others. If it is once seen that the Law cannot, by any possibility of Logic, bear the interpretation always given to it by the professors of physical science, as " the Law of the Inverse Squares " any better than it could bear the other interpretation, viz., that of the Direct Squares and the untransmitted light, we may hope that, with the help of a little time, even the more dogmatical of us will have, in this circumstance, a further reason for suspecting strongly that, to use a moderate expression, this whole department of Physical Optics requires revision. I must, however, be permitted to say that this gentle judgment is far from being the full import of what has, upon this sub- ject, presented itself as the fact to thinking men. The Law involves so manifestly an a priori impossibility, there being no data whatever nor even semblance of data for its construction, that one only wonders^ as I Jjaye ,s K2 132 PART III. SECTION 1. how it ever came to be entertained an instant among the educated ; nor is it easy to look upon it otherwise than as originally the clandestine introduction, by a few theorists, of a notion which all writers now admit to be but a mere "opinion" (see Appendix, Nos. 3, 5, 7, 14, 18, 19), unfortu- nately favoured and encouraged from the first by being always expressed in the vaguest and obscurest and most deceptive language which it was possible to devise, and which, as above explained, has only been rendered definitely and distinctly false by the occasional and now more fre- quent insertion of the term " inversely." But the importance of this distinction between the Light lost and the Light transmitted, a distinction which the theorists do all they can to obliterate, must not divert the reader's attention from the other and equally important dis- tinction respecting the equivocal import here of the word " distance," which I have already so often mentioned. All who understand the doctrine of the Inverse Squares know that, as explained in PART I., it is the enlargement of the object's area which, in this doctrine, causes the diminu- tion of Light as well as the ratio of this diminution ; and all who know this know that it is not the distance from the window or other source, that makes one object or area larger than another. To conciliate, however, the strange misapprehension of BO many upon both these points of the doctrine, and to simplify for them the statements to be now made, we shall here suppose, as they do, that there is the Sun or some other source of Light at the apex of the pyramid alluded to in the Law, as determining the relative sizes of the objects illuminated, thus, for the convenience of their understand- ings, making distance from the apex identical with distance from the lamp, window, sun, or other source, just as they suppose it to mean, although as said above, we all know that the relative sizes of objects are not determined, and do not depend upon, their relative distance from the window, or their relative distance from any other source of Light. PART III. SECTION 1. 138 Use of the term " Inverse." Here then we are speaking of a luminous point, and of three or more equal distances in a straight line from that point ; and we are told that this Light diminishes as the square of this distance increases, without any reference to what it is which enables distance to have this effect. As far as the mere words of the Law, thus unaccompanied by the term " inversely," are con- cerned, they, as has just been mentioned, may here signify either of two wholly different things ; viz., they may mean EITHER that the degree of Light at the end of the first dis- tance is 4 times greater than that at the end of the second distance, however near those points of distance may be to one another ; and 9 times greater than that at the end of the third distance, also however short these equal distances may be ; OR the words of the Law may mean that the amount of diminution produced by the first distance, alone, is 4 times less than that which is produced by the two first distances together, and 9 times less than the diminution produced by the joint action of three dis- tances. If we only regard the language used, we discern at once that this language can bear either of these two interpretations, in the absence of the term " inverse ;" but that when this term is used, it is only the first of these two interpretations that is intended ; because it is only the transmitted light, not the untransmitted, that is greater when the distance is less, and less when the distance is greater. The least reflection, however, shows us that the statement given in this first of the two interpretations never could, under any combination of circumstances, be true in fact, nor is it easy to imagine that it was ever even contemplated by the original authors of the formula, how- ever ready they may possibly have been, speaking only, as they did, of what happens in a medium, to regard the Law as true in its second interpretation, when the medium is uniform; viz., in that interpretation in which it can be understood of the "direct squares" and of the untrans- mitted light, or " Diminution ;" which latter would thus be 134 PART III. SECTION 2. made to increase directly as the square of the distance itself increases; so that twice the distance would give 4 times the diminution and 30 times the distance 900 times the diminution ; a sense of the words, in the law, which we easily confound with the other sense, in which other we speak of the Light itself, not of its diminution ; and say that the Light decreases as this square of the distance increases, i.e., becomes at once reduced to , -^ 9-^, &c. of the quantity left remaining' after the first reduction, when the distance from the source is twice or 4 times, or 30 times this first amount of distance which we choose to take, and from which the first reduction results. SECOND SECTION. LOGICAL IMPOSSIBILITY HERE OF THE TERM " INVERSE ; " NO DATA FOR IT. THE special point here to be explained is that the Law, however impossible in that sense also, could only have been intended originally as a law of diminutions, not of things diminished ; and that even if the geometrical law of areas, in the contrary or inverted sense of it, were, as is alleged, true of their illumination, instead of being so clearly and experimentally false, it is impossible that the fact should ever have been known to us. We have no date nor acces- sible source of information on the subject nor the slightest grounds for supposing that the current opinion is correct ; for even its advocates admit that it is a mere opinion which is expressed in this law (Appendix, Nos. 3, 5, and 7). What we do not know upon this Subject. The quantity itself, out of which the diminutions or reductions are taken, is, to this law a quantity wholly unknown. There is none ever specified, none that can be specified. Nor have we any notion even of its proportion to the diminution which in any case it undergoes ; nor do we know what, in any case, that diminution amounts to. Here then is an amount of ignorance, on our part, that virtually terminates the whole question. PART III. SECTION 2. 135 No such law, as this pretends to be, could ever have been put forward by the first writers, nor ever, without complete inattention or the requirements of some absurd Theory, have been advocated by the more intelligent of our modern pro- fessors. No law could, at any stage of the decrease, in this case, have given even the relative measure of the quantities remaining, the sole quantities that are here in question. The Original Amount of the light, the Reduction made in it, and the Remainder are, in every instance, hopelessly hidden from us by the Medium. This is manifest in the case of the Planets and the sun. The only amount of the solar light that we know of, is that which remains, and which we experience, after the two reductions made in it, first by the medium existing between the sun and our orbit of Atmosphere, and secondly, by our Atmosphere itself. We do not know what proportion either of these reductions bears to our amount of the solar light on the Earth's surface, nor what proportion the original undiminished solar light itself bears to the amount of it we experience. The only knowledge to which any one has ever pretended respecting either of these reductions themselves, or the reduced quantities remaining after them, consists of the two following points of relative knowledge: (1) that equal lengths of Ether (the interplanetary medium) produce nearly equal amounts of reduction in the solar light; so that 30 times a greater length of this ether (i.e., distance in it) than the first length, or distance, would produce nearly 30 times a greater reduction than the first reduction alone amounts to ; and (2) that the reduction produced in the solar light by the atmosphere of one planet is, probably, nearly the same as that produced by the atmosphere of another. Beyond these two facts, such as they are (and they are very little), we know nothing respecting even these reductions. Above all, we know nothing whatever about any other supposed sources of reduction. What is our ground for supposing any other I We have none. The pro- fessors tell us, indeed, that they have " made up their minds " to consider that there is one other source. (Appendix, Nos. 3, 136 PART III. SECTION 2. 5, 7.) Why, then, do they not state their grounds for this " opinion " ? So far are we from having any grounds for supposing any other source of reduction except the medium, that we do not know whether, notwithstanding the reduc- tions now mentioned by the interplanetary medium, the vsolar light may not be regarded as increasing instead of decreasing, as the ethereal distance increases, and precisely in. consequence of that very extension of the solar rays which thence results, and which has been even thought to involve its diminution (see p. 110). The foregoing considerations respecting our ignorance of these matters may be thus stated in other words : We do not know how much of the sun's light our atmosphere absorbs ; nor do we know what amount was withdrawn by the Ether before it reached our atmosphere. We therefore do not know, even by inference, the original or undiminished amount of the sun's light. We know nothing here what- ever but the amount of this light which remains for us after these two reductions of unknown amount, viz., that by the absorption of our Atmosphere, and that by the absorption of the interplanetary medium ; the former being, we have reason to think, much the same for each of the planets, and the latter almost in proportion to the length of Ether which the light has traversed. Our question here, however, it is well to remind the general reader, does not relate at all to the solar light upon the surface of the planets themselves, but only to that amount of it which falls upon the surface of their various atmospheres, or, as it may otherwise be expressed, the solar light as it exists at the different orbits, prior to the diminution of it effected by each atmosphere ; and with regard to this amount of illumination beyond our atmosphere, we, as already observed, know nothing. Not knowing either the original amount of the sun's light, nor the reduction effected in the passage, we cannot know the amount of this remnant which reaches either our planet's orbit or the orbit of any other planet. All the reductions (i.e., quantities withdrawn or untransmitted) art* PART III. SECTION 2. 137 wholly unknown except in their relative proportion to one another ; i.e.., wholly unknown in their relative proportion either to our known amount of light on the Earth's surface, or even to the original amount of the solar light. The remnants, therefore, which reach the successive orbits are as little known as the original amount itself of the solar light. We cannot even know their relative proportion to one another. We can only judge of their relative reductions. In a word, we neither have the original quantity in question, nor the quantity withdrawn on each successive interplanetary diminution, nor the remainders. How then, I repeat, would it be possible for us to know that the light remaining after the second reduction is a quarter of that remaining- after the first reduction ? Can anything exceed that in unreason- ableness ? Or how can we know that the light remaining after this first reduction is reduced to one-nine-hundredth part of its amount, after the thirtieth reduction has taken place? Where, with our scanty knowledge, is the Logic or Common Sense in such reasoning, or in such a Law as this ? What we should require to know in order to frame this Law. What is here essential to observe is that this Law of the Inverse Squares speaks only of the Remnants of Light which survive each diminution, and only of their proportion to one another. It does not speak either of the original amount of the undiminished Light, which it does not, in any case, profess to know anything about, nor does it speak of the diminutions which take place in it. Nevertheless in order to be able to speak of the proportion the Remnants bear to one another, we should, as observed above, know, first, what proportion the original Light bears to some amount we know, and secondly what proportion each reduc- tion bears to this known amount. We should then be able to say what multiple the first Remnant is of the second or of the thirtieth ; but Hot otherwise ; and, as just explained, we have no such knowledge ; no one pretends we have. The Law acknowledges that it knows as little about the first Remnant, in the case of Lamp or Sun, as it does about 138 PART III. SECTION 2. the original amount. The media alone prevent this know- ledge even if there were nothing else to do so. Yet the Law proceeds to teach that this first Remnant is four times greater than the second. But upon what grounds does it make this assertion ? It clearly has no data for it, no data here authorizing the statement that the second Remnant is a quarter of the first. Our ignorance here is manifestly too complete to admit of such a Law as that thus sought to be promulgated. In order to know this proportion between the Remnants of a diminishing Light, we should, I repeat, require to know the exact degree which exists previously to all diminution, and in each successive instance the exact degree or amount of this lost Light itself ; neither of which conditions exists in the case of the planets ; and even in our atmosphere they rarely exist, in any case, prior to experi- ment. We can therefore rarely say, in any case, even in our atmosphere, prior to experiment or, at least, hypothesis, that the degree of Light transmitted to one point is a certain number of times greater or less than that transmitted to another. In the case of the Planets, we never can say this, either of the Light as under the action of the Ethereal medium, or of the Light as supposed independent of this action. What we do know upon this Subject. All that we here know is, as already said, strictly limited to diminutions, and to these only as results of Medium. We know of no other diminutions of Light in its passage from one point of space to another. We only know Light as it exists in a Medium, and as it exists after the action of a Medium. All assertion respecting it or its diminutions independent of a Medium is entirely gratuitous and fictitious. We have no such knowledge. All writers both ancient and modern some more some less distinctly ac- knowledge this. The first writers who spoke of the square of the distance in connection with this subject, did so only with reference to the diminution which happens in a Medium, saying that Light in its passage through the air diminishes as the square of the distance increases (Appendix, Nos. 11 and 12) ; and the moderns also always illustrate this Law PART III. SECTION 2. 139 of the Squares by what happens in a medium. (Appendix, Nos. 2 and 3). Now, what we know respecting the diminu- tion of Light in a Medium is that the same cause produces the same effect, and that in a uniform Medium, such as all these writers always mean, equal distances give equal reductions. This obvious fact of Nature, it will be seen in PART IV., as already mentioned (p. 15), the professors deny. But they admit sufficient for our purpose here. They admit that in a very rare medium, like that which there is beyond our atmosphere, equal distances produce, as a fact, very nearly equal reductions, so that we can speak of the reduc- tions resulting there from several distances, as being this number of times greater than that resulting from only one; and we know that if there are 30 such reductions, their sum is 30 times greater than the first of them, or if there are 900 of these equal reductions, their sum is then 900 times greater than any one of these equal reductions, the original amount of luminous power being at last, 30 times or 900 times more reduced than after its first reduction; not 30 times nor 900 times less, as the theorists suppose it to be. This is what we know upon this subject, and all we know. The earlier writers thought, however, either that they observed a more rapid diminution to take place in Light at the greater distance from the source than at the nearer distance from it, or that it was most probable the divergence of the rays was attended with some such effect ; and so, we find it assumed in published writings, first by Bouguer in 1729, that this diminution, the cone of Darkness, increases when the distance from the source increases, and of course in the same ratio as the sections of the cone or pyramid ; z'.e., not merely in the ratio of the distance from the source, but in the ratio of its square. (Appendix, Nos. 11, 12, and 13. See also pp. 100-102.) We likewise find that by Lambert, in 1760, it was taught with still greater clearness, as a fact connected with our atmosphere (" the passage of Light through the Air," as Lambert calls it), that the square of the distance from the Source, is the 140 PART III. SECTION 2. ratio in which this second diminution in*! every Medium goes on (for these writers frankly stated that there were two such diminutions) the diminution thus becoming greater and greater for each length of Medium, as these lengths were measured off more and more distant from the source : so that after the second equal distance, or length of medium, the diminution is (2x2) 4 times greater than after the first, and, after the thirtieth distance, 900 times greater than after the first ; a comparison this of the sup- posed successive reductions in successive lengths of medium, which, in order to make way for the " opinion " respecting the Inverse Squares (on which a few theorists had made up their minds) seems to have been inadvertently and con- fusedly transferred from the mere reductions made in a quantity, to the quantity itself in which the reductions are made, and from what happens in a medium to what is sup- posed to happen where there is none. But even if the earlier conjecture were correct, we could not deduce the second from it. Even if we could discover these 900 equal reductions in 30 equal lengths of Medium, we could not on that account say nor know we could not, merely on that account, mean to say that the light transmitted to the orbit of Neptune is diminished to one 900th part of that transmitted to ours. We could here only mean to say that the solar light at Neptune's orbit is 900 times more reduced (not 900 times less) than ours is ; that the degree of light- giving power lost between the Sun and the Atmosphere of Neptune is (30 x 30) 900 times greater than that lost, or un- transmitted, between the Sun and the Atmosphere of the Earth ; or, to vary the expression of it, that the quantity of the solar light or the degree or intensity of the solar light call this as we may which exists at Neptune's orbit is the same as that which exists, at ours, minus 900 times the unknown amount of diminution which has taken place between our Orbit and the Sun. It will be seen from the foregoing pages, that there are here two things to be most carefully distinguished, viz., the PART III. SECTION 2. 141 light lost and the light transmitted, the Reductions and the Remainders. What it is important to attend to is that the equal distances give us the relative proportions of the one light but not those of the other, of the lost light, not of the light transmitted ; that it is therefore only to the former of these two, to the untransmitted or lost light, that, how- ever erroneously, the Law in question could ever possibly have been supposed to apply by those first writers who were attending to the subject ; and that it is merely through an error of inadvertence, or through the pre- judices of Theory, that professional men of influence have so long applied it to the second, viz., to the light trans- mitted. It is quite clear that as soon as such men can be prevailed upon to attend to the precise point here in ques- tion, they will be utterly' astonished at the huge blunder they have so long unguardedly made, and the professional ol TroAAoi will then of course follow them. To recapitulate then this analysis of the Law called the " Law of the Inverse Squares," constructed to aid the Theory which underlies it, and which has been already fully explained in PAKT II., it must be remembered that we only know the degree or quantity of the Sun's light which remains to us after the reduction effected in it by our atmosphere. We neither know the degree which reaches our orbit, nor the degree lost in the passage to our orbit from the sun, nor that lost between the sun and any other orbit ; nor do we know the degree of Light belonging to the solar action prior to all diminution. I ought perhaps here to mention that what we mean in this place when we speak of a degree of light as known, or not known, is that we know, or do not know, how many times our own light, or what fraction of our own light, the light we speak of amounts to. We know then none of the things mentioned. We only know that, the degree of light left for our use after the enormous but unknown reduction effected by our atmosphere, in addition to that unknown reduction effected (before our atmosphere is reached), by that infinite si nially 142 PART HI. SECTION 2. rarer medium, the Ether ; and we know that the orbits of the superior planets have less of the Sun's original light than that quantity, to us unknown, which our orbit has. This is all we know. How then, with this limited know- ledge, could we possibly pretend to say what proportion the unknown amount of the whole original solar light, minus the unknown portion not transmitted to the end of the first distance taken, bears to this Remnant minus some still greater but unknown portion not transmitted to another distance twice as remote or thirty times as re- mote ? How can we say anything, for instance, so definite as that one is four times greater or 900 times greater than the other ? that one is a fourth part or a 900th part of the other? How can we say what proportion the un- known quantity x- 1 bears to the unknown quantity x-2 ? and a fortiori what proportion the unknown quantity x y bears to the unknown quantity x - z ? It seems impossible that even to a person unversed in science, there can here present itself any difficulty. We know that between the sun and our orbit there is some decrease in the original amount of the solar illumination ; and it is possible to imagine, although not to understand as a fact, that the unknown amount of that decrease between the sun and our orbit might increase, for the superior planets, in that special ratio, which we call the square of the distance, so that the unknown amount of this Reduction at Neptune's orbit might be 900 times greater than the unknown amount of it at ours. I do not say it is possible to see that it so increases, nor even to comprehend how it could. I am far from saying this, although I have found some professors look upon it as a very natural blunder that any- body might make, and that I was making. I only say it is possible to see that it might be conceived to do so, that for many minds there might be a primd facie appearance of it . This ratio, this proportion of increase in the diminu- tion, or untransmitted light, is clearly what the Law was originally intended to teach, and all it was intended to PART III. SECTION 3. 143 teach, because all it pretended to have the data for teach- ing. It is quite clear that there is not the least foundation for the subsequent introduction here of the term "inverse," and the transfer of these proportions from one quantity to another, as effected by this term, from the light lost to the light transmitted, from the successive diminutions which take place between the sun and the planets to the successive amounts of light resulting from these diminu- tions; a transfer made under the strange impression that this was applying the geometrical law of areas to the dimi- nution of Light by distance (Appendix, No. 8), not the least foundation, I repeat, for saying, as so many of the most distinguished scientific men do here say, or seem to say, and have long taught or seemed to teach in their lectures and their books, that when a quantity undergoes 900 equal diminutions in succession, the whole of these diminu- tions together being then 900 times greater than the first of them, the quantity remaining after all the diminution is therefore 900 times less than the quantity remaining after the first (for in no way do they suppose these quantities known but by these reductions) ; not the least foundation for saying that, since the diminution of the solar light at Neptune's orbit is (however minute or vast this diminution may be) 900 times greater than it is at ours, it therefore follows that the solar light itself, otherwise wholly un- known in amount, which is transmitted to Neptune, the luminous force of the sun at Neptune, is the 900th part of what it is with us. THIRD SECTION. ILLUSTRATIONS OF THE ABSURDITY LATENT IN THE LAW OF THE INVERSE SQUARES. I HAVE thus far endeavoured to explain that the Law of the Inverse Squares for the diminution of Light, so blindly and generally adopted by the scientific, is the mere fiction of a 144 PART III. SECTION 3. few Theorists, without the slightest pretension to any foundation either in Physics, Geometry, or Logic ; and the truth of what I have said may also be rendered perfectly manifest to every intelligent person by any one of the four following very simple facts, among many others that could be mentioned: 1. One of these facts is the obvious one already alluded to, that if we understand the proportions spoken of in the Law to be, as the term " inverse " denotes, proportions in the light transmitted, instead of in the un transmit ted or lost light, the immediate result of the Law so inter- preted is that the light at the end of the first equal distance is always four times greater than the light at the end of the second distance, whether that second distance be an inch or a mile, or a million miles ! the degree of illumina- tion at the further end of any given distance always one quarter of that at the beginning of it ! 2, Another fact resulting from the Law of the Inverse Squares, and to which also allusion has already been made, is, that by dividing any given extent of the solar system into parts sufficiently minute, we shall be able to have the solar illumination of any parts we choose, riot only 900 times, but millions (nay, billions, trillions, nonillions) of times greater than the illumination of other parts ; for although, by a division of Neptune's distance into 30 parts, we find him, by this law, to have only 900 times less of this light than in various other parts of the system round the sun; yet, if we divide that same distance into 1,000 parts instead of 30, we shall have the light at Neptune a million of times less than it is at other points all round ; and if we divide Neptune's distance from the centre of the system into a million of equal parts, we shall have Neptune's share of the solar light a billion of times less than the solar light elsewhere, and so on ad infinitum. Nor is this all ; for although with this division of Nep- tune's distance from the centre of the system into a million of equal parts, we thus have the illumination, at a point I^ART III. SECTION 3. 145 hear the centre, a billion of times greater than at Neptune's orbit, yet if we divide this same interval (Neptune's dis- tance from the centre) into only two equal parts, instead of into a million such parts, we shall then have the light in the middle of the whole distance only four times greater than that at Neptune's orbit, a very small difference of light in proportion, for so vast a distance as 1,500 million of miles ; and so on throughout the whole system. : Nay, for those who desire it, the absurdity of this Law can be brought also into view by subdividing this last half of Neptune's whole distance from the sun (which last half derives all the light that travels through it from the amount of light at the commencement of it) into 1,000 equal parts ; when lo ! according to the Law of the Inverse Squares, we have Neptune's share a million of times less than that near the half-way point of his whole distance from the sun, instead of being a fourth of it, as was the case when the whole distance was divided into only two; parts ! 3. Another of the four facts which I here propose for the consideration of the scientific is the following: At a dis- tance from a lamp or other luminous body, take any point in which the light is found by the photometer to be diminished to one quarter of the original light. Then bisect the dis- tance extending from that point to the lamp ; and according 1 to the ordinary interpretation of the law in question, the degree of light at the end of the whole distance is a quarter of that at the half distance, or point of bisection ; but by the hypothesis (or construction) it is also a quarter of the; original light. ,;. 4. The last of the four facts to which I would here call attention as being any one of them instant and easy proof of this absurdity, is this : If we mark upon a rod, 3 feet long, 1,000 equal divisions, and place a point of electric light at one end of the rod, we have no difficulty in seeing that the illumination at the other end of the rod is not, a# the law asserts it is, a million of times less than the illumi-- L 146 PART III. SECTION 3. nation near the source, t'.c., at the extremity of the first of these minute divisions marked upon the rod. Nothing can be clearer than this is with regard to the light transmitted* No one will pretend to say that the light at one end of the rod is a million of times less than at the other. Yet it may be useful to the reader to observe that the Law, if under- stood of the reductions or relative quantities of lost or un- transmitted light, might conceivably, at least primd facie, be true ; as true with regard to these minute spaces as with regard to the vast intervals between the planets. The whole diminution in the distance of three feet must be supposed to be a thousand times greater, and might, as far as ap- pearances go, be a million times greater, than that which takes place in the first minute division of the rod. It is, I repeat, easy to see that, although the light transmitted to the end of the rod is not diminished even to one-half of that close to the source, nor perceptibly diminished at all, nevertheless the whole diminution at the end, however little it may be, is certainly 1,000 times greater than that after the first of the 1,000 distances, and might very well, as far as a primd facie judgment goes, be a million of times greater than that first diminution. Be that as it may, however, it is quite clear that the light itself is not here diminished to a millionth part of the original, which is all that this fact is cited here to prove. These four demonstrations of the absurdity into which those Lecturers and other scientific Expositors have fallen who all interpret the law as a law of the transmitted light, apply in all their details to heat and to gravitation as well as to Light, and it is unnecessary to multiply them. There is no one, it appears to me, who will not find it perfectly clear, from what has been said, that the thousand divisions of the rod are not employed in the Law to indicate pro- portions in the degrees of light transmitted to the different points of the rod, but only, however erroneously, proportions in the various amounts of reductions or lost light caused by the intervals (*'.., in the amounts of light disappearing, PART III. SECTION 3. '147 between the commencement and the end of each minute division marked upon the rod), and that it could only be through inadvertence that the principle of decrease thus originally intended in the law, was without much distinct- ness, it is true, transferred by subsequent writers from the one series of proportions to the other, having been after- wards however asserted distinctly and intentionally in the interests apparently of a new Theory, by the introduction of the expression "inversely" or "in an inverse ratio," simply to signify " in a contrary sense," or " in the opposite sense." " 900 times more reduced" never means " 900 times fess." In the same way it becomes also evident that when scientific men look upon it as so certain that the solar illumination at Neptune is 900 times " less " than ours, this, if we reflect upon it, can only mean, however utterly arid mani- festly erroneous even that statement is, that his light is 900 times MORE REDUCED than ours, that the reduction or lost light in his case is 900 times greater than in ours, that the degree of the luminous force there, is, as already stated, equal to ours minus the degree of this force lost between the sun and the orbit of that planet. But this does not mean that he has only the nine-hundredth part of our degree of the solar illumination. Far from it. The very simple and obvious fact that when we subtract even a known quantity from a quantity un- known, this gives no clue whatever to the quantity left remaining, in other words, the fact that a diminution of light 900 times greater than the first diminution is not the same thing as a remainder of light 900 times less than the first remainder, nor even suggests the means of knowing what proportion of the light remains after each diminution unless we know likewise the original amount of light, can also be demonstrated by supposing a gas-light illumination consisting of a million burners hi a large hall. If we extin- guish 900 of these burners one after another, the diminu- tion of light which has thus taken place in the hall (i.e., the L 2 148 PART III .SECTION 3. amount of light lost) is 900 times greater after the last burner has been extinguished than the diminution was which took place upon the extinction of the first. But how can we pretend to say that the light left in the hall is now 900 times less than it was before, 900 times less after the last extinction than after the first ? It is true that the original light is now 900 times more diminished, more reduced, than upon the first extinction, but not 900 times less, not a nine- hundredth part of what it was at first. There still remain 999,100 burners not extinguished. How can that be called a nine-hundredth part of the light existing in the hall after the first burner was extinguished ? Can anything be more evident than it here is that to be 900 times more reduced is not the same thing as to be 900 times less, not the same thing as to be a nine-hundredth part. Here also we see an illustration of what was observed respecting the absence of all data and foundation for the law of the Inverse Squares. We see that it would be impossible for us, at any point in the progress of the extinctions, to deduce even the relative number of unex- tinguished burners from the number of those extiuguished if we did not know, as we do in this supposed case, the precise number that were in the hall at first. In like manner we see that the relative degree or proportion of light trans- mitted to a certain distance could not be inferred from the degree of it lost or withdrawn in the transit, unless we know the original degree of it, as well as the exact degree that has been lost. In the case of the planets, however, we know neither of these things. We neither know at all, not even relatively, the original degree of the solar light before any diminution has taken place ; nor do we know, other- wise than relatively to one another only, the degrees lost between the centre and each planet. We therefore have no basis nor data for the knowledge thus pretended to. PART III. SECTION 4. 149 FOURTH SECTION. RECAPITULATON OF PARTS II. AND III. THUS far we have looked for the physical possibility of the alleged fact of Nature (PART II.) and the logical possibility of the alleged law of Nature (PART III.) ; and we have seen that neither exists. We have seen that the true meaning of the Optical Theory respecting the Inverse Squares is that Light is in- versely as the areas illuminated (less when they are large and more when they are small), although so many under- stand it to mean that Light is inversely as the Square of the distance from the Source, without any reference what- ever to the area illuminated ; and we have seen that although the surfaces or areas of objects are enlarged by their distance in the cone or pyramid, they are not enlarged by their distance from a window or other source of Light. We have seen moreover that even if distance from the window or other source could make the object or area larger (either than it previously was or than the other object is, which we compare with it), there would still be the same degree or amount of Light upon each part of it as there is upon the whole of it. Its Light would not be diminished upon each spot, merely by its enlargement. We see that there is no geometrical foundation, nor any other, for the assertion that it is ; yet its being so diminished, upon geometrical principles, by the spreading, dispersion or dilution of each ray, or by its deviation from the straight line into unilluminated parts, is what is here asserted by the theorists, contrary to our common knowledge, and to their own admissions respecting the umbra and penumbra of the eclipse as well as respecting all other shadows. We have seen how fully the more enlightened of them, never- theless, recognize the fact that, if we take no account of medium, the sun's rays pass undiminished in number and 14>0 PART III. SECTION 4. intensity to the remotest limits of the system, and the other fact that there is no point of the space confronting the disc and exposed to these rays, to which they do not all come, in the cases in which we cannot see this fact as well as in the cases in which we can. We see therefore that even upon the showing of these writers themselves, the sun's light is not diminished by distance from the source, nor the larger and the smaller space unequally illuminated ; all that these theorists here contend for being that the light which is equal on the whole of each is unequal on each equal portion of each, (" on each parity of surface,") the obvious fallacy of which conception has been fully exposed (pp. 73, 77). We have seen moreover that there is not the slightest pretext for saying that the solar light does not converge from the disc to each point of the space opposite as well as diverge from the disc to the whole of this space ; nor the slightest pretext for the Spoke-Theory, the Theory which teaches that there are unilluminated spaces between the solar rays which, becoming gradually wider, receive into their dark- ness a large amount of space in all parts of the system, but especially in the more distant portions of it ; and that, even if light, when left to itself, and when without a medium, did equalize itself as heat does, expanding on all sides until it found its level, it would here have no opportunity of doing so, not only because it is never left to itself, the Light pass- ing always directly to each point from the source (and so directly that, without a medium, no deviation from the direct path is possible) , but also (this is a very important consideration) because there are no spaces on either side of the rays, exempt from the same intensity of light, for these supposed self- bending and self-diluting rays to expand into. We have likewise seen the Logical Impossibility of the Law by which the light itself is said to become less as the squares of the relative distances from the source become greater ; so that, to go no further, the light itself, after the second distance, is thus represented as always being one* PART III. SECTION 4. 151 quarter of the light after the first distance, whether the second distance be a foot or a million miles. We have seen that with regard to the Sun and Planets we have not the slightest foundation in any knowledge that we possess, not the slightest imaginable data of any kind, for such an asser- tion, inasmuch as we neither know the original amount of light before the first reduction takes place, nor the amount of either the first or second reduction, nor the amount remain- ing after either reduction ; we cannot therefore say that the light after the first reduction is four times greater than that after the second, even if in nature it really were so. We have seen that this extraordinary misconception of our facts results from the still more extraordinary misconception and belief that we are on this occasion merely applying to Light the geometrical law of areas (Appendix, No. 8); whereas, far from doing this, we here apply to Light exactly the contrary of that law, or that law inverted ; the geometrical law being that the area increases as the square of the distance does, whereas for Light, we invert this law and say the Light decreases as the square of the distance increases, an inversion of the geometrical principle which we hardly seem conscious that we acknowledge with the term " inversely " meaning thereby, in the opposite sense of the geometrical law. There is reason to think that when the law of the Inverse Squares was applied to Light by the earlier writers, it was only thought of with reference to the Light lost, not to the light transmitted ; for in whatever way Light was here supposed to be reduced by distance, the law in question could be supposed to apply only to these reductions very erroneously, it is true, but still only to these not to the remnants of Light left after them ; to the " direct squares," as they may be called, not at all to the " inverse " ones. It was the diminution only, not the light itself which could possibly have been supposed to march, in any sense, part passu with the enlargement of the Area. We see also, however, that even this application of the law to the Light lost could only be true, if it be true, which 152 PART III. SECTION 4. has never yet been shown, that to double the cause in 'nature is ever, in any case, to quadruple the effect ; since 'in this theory the first step is that twice the distance gives -four times the diminution; apparently also, that two suns would give four times as much light as one ; and we see that even this application of the Law in question to the re- ductions would not give Neptune's illumination as one 900th part of ours, because it only represents the amount 'abstracted in the passage to his orbit as 900 times greater than that abstracted in the passage to ours ; in other words, that the solar light is 9<)0 times more reduced, not 900 times iess, in amount, force, and intensity at his orbit than it is at burs. Finally we see that none of the alleged reasons exist for supposing that there is any second diminution of light in nature as an effect of distance from the source, i.e., any other such diminution of it except that which is occasioned by its passing through a medium ; and that all writers are agreed that the diminution of light in a medium does not proceed by the law whose flagrant fallacy we have here seen, but by another and very different law, much more like the common one, and which shall now be examined in PART IV., whereby it will be seen, as this Treatise undertakes to show, that the solar light is so nearly equal outside the atmospheres of all the planets, that, if we were in a position to make the comparison, even the most power- ful photometers that we possess would not enable us to detect the difference of illumination that there exists between the different portions of the system. END OF PART III, PART IV. THE LAW OF DIMINUTION FOR LIGHT PASSING THROUGH A MEDIUM, AND THE EFFECT OF THIS LAW UPON THE ILLUMINATION OF THE PLANETS. PART IV. THE LAW OF DIMINUTION FOR LIGHT PASSING THROUGH A MEDIUM, AND THE EFFECT OF THIS LAW UPON THE ILLUMINATION OF THE PLANETS. FIRST SECTION. DIMINUTION IN A MEDIUM THE ONLY DIMINUTION OF LIGHT IN ITS PASSAGE FROM ONE POINT OF SPACE TO ANOTHER. WE have seen, in PART I. and in PART II., that there is no such Law of Nature, even logically possible, as that of the Inverse Squares, nor, in Nature, either of the two supposed grounds for it, viz., either the Deviation and Spreading of Light independently of the Medium, or the Spaces without Light between the rays into which it is supposed Light spreads ; and this disposes completely of the gratuitous hypo- thesis of these Inverse Squares, so persistently advanced by professional men for explaining the diminution of Light by distance from the Source ; as if the simple and natural fact of Absorption by the medium did not do this sufficiently, as well as altogether preclude, by the constancy of its action, the possibility of our knowing any other. We shall now give a little attention to such peculiarities in this dimi- nution of Light by distance from its Source (t.e., by length of Medium) as apply to the illumination of the solar system ; and from these it will be clearly seen that the whole system is equally illuminated. This the Professors themselves will be the first to discern, as soon as they are once able to see that 156 PART IV. SECTION 2. the Old Theory of the Inverse Squares is no longer tenable, nay, has been concealing from them one of the grandest facts of Nature. They will then see, without any further difficulty, that all those other professorial theories about " yards of Light," its " concentric spheres," its " dilution," " expansion," " ductibility," &c., fall at once to the ground, as being, like the theory of the Inverse Squares which they are intended to support, no less false than useless ; and that the solar light is manifestly not only not so unequally dis- tributed throughout tlie system as they have hitherto been led to imagine, but is not unequally distributed at all. Their knowledge of the details will make all this easy to such men as soon as they have once mastered the utter impos- sibility and utter nonsense of the alleged fact and alleged law on which they have been so long accustomed to de- pend. It is mainly for the sake of the reader less versed in these details that I add this Fourth Part to the Treatise, in order to point out what it is, outside our atmosphere, that really causes any diminution of Light that takes place there ; and what the law and conditions of this diminution are ; a discovery, it must be admitted, which comes unaccountably late, when we consider the vast amount of attention that Optical Research has recently obtained. This knowledge will help him materially to see the truth of that equal distribution of Light throughout the solar system which it is the object of the present pages to make known, and will also make clearer to him, on many points, the frivolity and absurdity of the old law and its old theories, from which it was represented as deducible that the Light on Neptune'a aurface was a 900th part of that which we have on Ours. SECOND SECTION. : ' THE PROFESSOBIAL LAW : ITS TWO OBVIOUS ERRORS. BUT, before we enter upon the facts of nature as they here present themselves before us, it is proper to point out the PART IV. SECTION 2. 157 curious bmnderings of so many professional men even here where one might have supposed it impossible to blunder. The common facts of nature in this place are, as mentioned already in PART I. that all Light passes through some medium, and that all media reduce its intensity by Absorp- tion, but more or less rapidly, i.e., at a shorter or longer distance, according to the density of the medium; the obvious law of nature for this diminution being that, in' nature, the same cause produces the same effect ; that, when the medium is uniform, twice the length of it (i.e., twice the distance in it) gives twice the reduction ; a three-' fold distance, a threefold reduction ; and so on ; that the length of medium which absorbs the light of 20 candles will absorb that amount of Light whether the source consists of 20 candles, or 500, or 5,000, or 5,000,000 candles; and that if, in any case, half the Light is absorbed in the first distance, the other half is absorbed in the second of these equal distances. These two simple and obvious natural principles are, as there mentioned, both of them denied by professional men. They say that the amount successively absorbed is greater or less, according to the amount that is left by the preceding distance, not according to the amount of Medium ; and that the absorption is never complete, never finished, however long and however thick, the Medium may be ; two very remarkable statements, it must be admitted, to originate with men whose time and thoughts are wholly given to these subjects. Their Theory is that the absorbent powers of a medium depend upon the degree, quantity, or intensity of Light that enters it ; that if this quantity be great, the amount absorbed is proportionably great, and, if this quantity be little, pro- portionably little of it, also, is that which is absorbed. Their law is that, whatever reduction is made by the first equal length of a uniform medium, less reduction is made by the second of these equal lengths ; still less, by the third ; and so on according as there is less Light from which the 158 PART IV. SECTION 2. reduction, in each case, is to be made. The question will naturally be asked : How much less ? Their answer is that this depends on the density of the Medium or on the length of it; on the amount of Light, therefore, absorbed or ab- stracted in the first distance traversed. If the medium is dense or extensive, and therefore absorbs much in the first of the equal distances, then the difference between the first reduction and the second is great ; whereas if the Medium is very rare even if extensive, or short even if dense, and therefore absorbing little in each length, then the differ- ence between the second reduction and the first may be very little, and can in fact be even found to be wholly imperceptible. This Law is thus expressed : The Medium being uniform and the distances equal, the Medium of each succeeding distance absorbs, not the same amount of the original Light as was absorbed by the preceding distance, but only the same proportion or fraction of Light as that taken from such Light as enters the Medium of each preceding dis- tance, whether this entering Light be the whole original uureflected Light, as in the case of the first distance, or only a part of it, as in the case of every subsequent distance. I have already given an illustration of this strange Law in PART I. The following is another instance : In a uniform Medium take any distance from the source of Light, and divide this distance (or length of Medium) into four, or any other number of equal parts, lengths, or dis- tances, through which the Light passes. Now, if the first distance reduce the original Light by one quarter, then each succeeding distance will absorb one quarter; not however one quarter of the original Light (as ordinary people hold), but a quarter of the fraction that enters it, and that is left, in each case, after the preceding distance. The second distance, then, will absorb a quarter of the Light left after the first distance ; the third distance will absorb a quarter of the Light that is left by the Medium of PART IV. SECTION 2. 159 the second distance; and the fourth distance will do the same for the fragment of Light that has been transmitted through the third distance ; and so on, to any number of these equal lengths or distances ; less and less Light enter- ing each succeeding length of Medium, and less and less being absorbed by each, because each length or distance absorbs the same fraction or proportion, but not the same amount of the Light which enters it. In like manner, if the first distance absorbs three quarters of the original Light, leaving only one quarter of it to enter the next distance, then this next distance will absorb three quarters of that quarter, transmitting to the third distance only a quarter of that quarter, or one-sixteenth of the original light ; out of which sixteenth part, the fourth dis- tance will also take its three quarters ; and so on, to any extent of Medium ; there being always, by the theory, some remainder; and each succeeding distance, although equal, absorbing less and less, on account of the light becom- ing less and less which enters each. So likewise if the medium is so rare, or its equal lengths, the distances, so short, that the first distance absorbs only a thousandth part of the original Light, then by this strange theory, the second distance will absorb only a thousandth part of what remains ; and the third distance will abstract but a thousandth part of what the second distance has left ; &c., &c. In this latter instance, according to our common notions and experience, at the end of a thousand equal dis- tances, the whole light would be extinct ; since with us a thousandth part is absorbed by each length of Medium ; but not so in the theory we are speaking of ; for in it, there is never even so much as a thousandth part of the original light absorbed by any one distance, except the first, although the distances are equal and the Medium uniform. In this case, therefore, at the end of a thousand distances, there would still be a large remainder ; which, although thus, according to the theory, continually decreasing, would nevertheless last through any number of equal distances 160 PART IV. SECTION 2. or any density of medium, AD INFINITUM. This must not be forgotten, AD INFINITUM. As to this latter point, which is the second principle involved in this theory, viz., the alleged impossibilityof light being wholly absorbed by the Medium through which it passes, however dense and extensive this Medium may be, this second principle naturally follows from the first; Since, at each distance, there is deducted only a portion (never the whole amount), of the light that enters that distance, there never comes, never can come, a distance, or length of Medium, which absorbs the whole light. These are the two favourite hypotheses of all profes- sional men and of many others, respecting the diminution of Light by the Medium, a diminution which obtains among them in the presence of the uninitiated, the mysterious but dignified, because mathematical, name of a u Geometrical Progression." Now, what are we to think of the statement that the amount of Light which enters a given medium, determines the absorbent power of the medium, and therefore the amount which is absorbed ? What sort of impression is such a statement, when distinctly put forward, likely to make upon people not imbued with the prejudices of the profession ? Is it likely to increase their confidence in the Priests of Science ? or, is it supposed that unprofessional people are all without Common Sense? For what does such a statement mean? If we have the light of two candles to deal with, and employ a medium which shall absorb half their light (i.e., the light of a single candle), we seem to learn pretty distinctly, from this circumstance, the simple fact of nature that the medium thus employed absorbs exactly the light of a single candle, neither more nor less. Now, instead of two candles, let us employ but one ; and according to the theory in question, the absorb - ing power of the same given length of Medium becomes reduced to such an extent that it now absorbs only half the illuminating force of one candle ; or if, on the contrary r we: PART IV. SECTION 2. 161 increase this original light twelvefold and employ a dozen candles, instead of one, then, according to this eccentric theory, the absorbing power of this same medium is also in- creased twelvefold, and it absorbs an amount of Light equal to half the light of the twelve candles ; i.e., it absorbs the light of six caudles. The same medium absorbs half the amount of any light that enters it ; can be made to absorb in short any amount of light that you require. If (for the sake of round numbers) you employ an electric light equal to the amount of tmrettected illumination repre- sented by 1,024 candles, and divide your uniform Medium into ten equal lengths or distances, then the first length of it absorbs half the whole light, and there remains only the light of 512 candles to enter the second length. In that second length" the light is further diminished, by this law, to one-half of that which enters it, viz., to the light of 256 candles. In the third of these equal lengths of the same Medium, the 256 candles are reduced to 128 ; in the fourth to 64 candles ; in the fifth to 32 candles ; in the sixth length to 16 candles ; in the seventh length to the light of 8 candles ; in the eighth length the reduction is to 4 candles ; in the ninth to the light of 2 candles ; and in the tenth length, we find that the same amount of Medium as can absorb the light of 512 candles when the light of 1,024 enters it, cannot absorb more than the light of one candle when the light of only 2 candles enters it from the preceding length. And thus, any given amount of Medium can be made to absorb any amount of Light that is desired. The usual rush will no doubt be here made at once by the superficial portion of the Profes- sion to some of the technical hiding-places in Optics, or to the fourth, perhaps fifth or even sixth, dimension of space, or to some other similar absurdity, in order to be thereby enabled to say something that shall seem to justify all this incoherence ; but the more enlightened members of the Profession will instantly acknowledge the utter un- reasonableness of such a Law. And can anything, we may 162 PART IV. SECTION 2. well ask, exceed such a Theory and such a Law in non- sense ? Is it possible to believe that in England, at the end of the nineteenth century, such " scientific" dogmas as these are taught, and listened to, and paid for I As to the second of the curious theories in Absorption, now under consideration, to the effect that no amount of curtains, or of London fog, or of atmosphere, or of water, or of any medium whatever, can wholly absorb the solar rays or any other rays, even those of a rushlight, it would be mere waste of time to point out, in " interesting experiments," the utter inaneness of such a theory. Every reader will discover this for himself; and many even of those very writers and lecturers who have so long refused to listen to us upon these points, admit of their own accord, although apparently without being aware of what they are doing, that this scientific statement of theirs is utterly false. They all teach that, at the bottom of the Ocean, there is no light whatever, none at least, except that singular invention of theirs called "invisible light;" and we, all, simple-minded people, know that the most pervious Medium, if it is extensive enough (i.e., if the distance is sufficient) can absorb any amount of light that we employ, even " the light that is invisible," as well as that, if the Medium is sufficiently thick, a length of it, infinitesiinally minute, is sufficient to do this. (Appendix, Nos. 1, 16, 20.) THIRD SECTION. THE OBVIOUS AND ORDINARY OR UNPROFESSIONAL LAW FOR THIS DIMINUTION IN A MEDIUM. Let us now contrast the ordinary law with the foregoing and then pass on to the facts of nature to which both laws are supposed to refer. In this latter department of the subject also, we shall see some remarkable instances of toleration, if not of oversight, on the part of those who write and lecture. pAirr iv. SECTION 3. 1C3 I propose here to speak only of the interplanetary Ether as medium, and of the Sun as luminary. It is unnecessary that I should detain the reader with any others. The Law of medium is the same for all media and for all sources of the unextended or central character here in question. This Law in its obvious form and as ordinarily received by un- professional people, is, as I have stated above, that, in Nature, the same cause always produces the same effect ; that the same amount of medium produces the same amount of absorp- tion ; that in a uniform medium, double the distance doubles the diminution ; that treble the distance trebles the diminu- tion, &c., and that any medium, if dense and long enough, can absorb the whole Light. There is here no longer any question as to twice the length of medium producing either more or less than twice the diminution, more, as when doubling the cause, (viz. the length) quadruples the effect, or less, as when the second equal length of medium, although equally dense, has not the same absorbent power as the first ; nor is there in this simple interpretation of Nature, any question as to Light when it traverses a Medium, travers- ing also at the same time, a space exempt from Medium, and being, in that second kind of space, always 4 times less at one end, than at the other, of any given length, whether this length be an inch or a mile. This latter principle of decrease could only have been listened to with reference to so obscure a decrease as that supposed to result from the enlargement of the space or from the enlargement of a ray, and seems never to have been distinctly asserted by anyone, with reference to the decrease resulting from a medium ; although it is sometimes very difficult for us to know whether the lecturers intend this principle to be applied to the medium or not. Nay, even in this matter of mere reductions (in the light), the professorial theory with regard to a uniform medium, does not represent the increase of reduction as more rapid than the distance. The professorial theory does not even consider this increase to proceed as rapidly as the distance (which we unprofessional people M 2 164 PART IV. SECTION 3. think it does), but frankly informs us on the contrary, as we have just seen, that, according to its principles, the reduction does not keep pace with the distance from the source ; that double the distance does not so much as double the reduc- tion ; and what is still more extraordinary, that this reduction is always becoming less and less, instead of more and more, as the distance from the source increases ! So that, when, under the supposition that the interplanetary medium is uniform, unprofessional men say that, since Neptune is 30 times farther from the centre than we are, he has therefore the solar light 30 times more diminished by this Ether of space than we have, (in other words, that the diminution of the solar light on reaching him is 30 times greater than on reaching us), professional men tell us that this is a mistake ; that the diminution in a uniform medium, becomes less and less in every succeeding distance, and that, upon this principle therefore, of a uniform Ether, the diminu- tion at Neptune, is not nearly 30 times greater than it is for us. Thus whatever diminution our common notions give us of the solar light at Neptune, as resulting from the medium it has traversed in order to reach him, these theorists assure us that this diminution is not really so great; that, as far as mere medium is concerned, Neptune's light from the sun is much more nearly equal to our own than even we suppose, that if we disallow their theory of the Inverse Squares, then the sun's light outside Neptune's atmosphere is not nearly 30 times as much diminished as it is outside ours. They will see however that without their law we also have this result ; and, that, even if we had not, yet the difference of solar illumination resulting from the medium between the two planets is so utterly imperceptible, that this advan- tage of their fantastic theory can well be dispensed with. PART IV. SECTION 4. 165 FOURTH SECTION. HIGHLY RAREFIED NATURE OF THE INTERPLANETARY MEDIUM, OR SOLAR ATMOSPHERE IN THE SPACES BETWEEN THE PLANETS. IT is now well known to scientific men, that the diminution of Light, resulting from Absorption, which takes place in any given length of the rare medium between the planets and the sun, is at least 250 millions of times less than it is in the same length of the ordinary atmosphere that absorbs Light, or that we breathe, upon the Earth ; inasmuch as that thin medium requires to be at least 250 millions of times less dense, less obstructive, or, as it is termed, less absorbent, less substantial, in order to admit of the rapid movements of the planets ; movements so rapid that, even in the upper regions of our atmosphere, they would meet with the same resistance, says Sir Isaac Newton, as if they were attempted in a universal medium of " molten gold." So fully is this fact recognized by men of science that the space between the planets has been frequently supposed by them to be a vacuum ; a notion which has no doubt con- tributed not a little to the other notion that the diminution of Light in its passage through this space must be conducted upon some principle independent of a medium. That it should be a vacuum, however, is considered by the more enlightened to be as impossible as any density that could obstruct the planets. I need scarcely say, after the ex- planations of PART II., that if Light could traverse a vacuum, and if this were what it did in its transit from the centre to the planets, there would then be no diminution of Light at all outside the atmospheres of the planets. By far, however, the more reasonable and general conclusion is that the space in question is not a vacuum, but that the medium which fills it, is of a nature infiiritesimally attenuated, partaking apparently, almost, as much of this infinitesimal nature, as 166 PART IV. SECTION 4. the vibrations productive of Sound, Light or Colour are now so generally supposed to do. " It has been computed," says one writer, " that a cubic inch of the air we breathe would be so much rarefied at the height of 500 miles that it would fill a sphere equal in diameter to the orbit of Saturn/' " The air in proceeding upwards," says another, "is rarefied in such a manner that a sphere of that air, which is nearest to the Earth, but of one inch diameter, if dilated to an equal rare- faction with that of the air at the height of ten semi-diameters of the Earth (40,000 miles) would fill up more space than is contained in the whole heavens on this side the fixed stars. And it likewise appears that the moon does not move in a perfectly free and unresisting medium ; although the air at a height equal to her distance is so many millions of millions of times thinner than at the Earth's surface, that it cannot resist her motion so as to be sensible in many ages." (See Ferguson's " Astronomy.") And no one else has written anything very different. Thus, then, as far as Medium is concerned, there is nothing, or next to nothing, to diminish the original amount or degree of the solar light in its long transit to the most distant of our planets. The difference which exists between the effect produced by a length of medium thirty times greater than another length of the same medium, although something, no doubt, very perceptible, and also very great, in our dense atmosphere, would, we can easily see, be completely inappreciable in a medium where this difference would be millions, nay, according to some writers, billions of times less, less per- ceptible, therefore, than it is in the lower strata of our atmosphere. Any little diminution in the vast amount of the whole solar light, resulting from a few cubic yards or cubic miles of our atmosphere, even if all concentrated upon its path through space to Neptune, would, I repeat, be utterly and manifestly what the human eye could not discern. PART IV. SECTION 5. 167 FIFTH SECTION. CONFUSION MADE OR TOLERATED BETWEEN THE DIMINUTION FROM ABSORPTION AND THE OTHER DIMINUTION WHICH IS SUPPOSED TO BE INDEPENDENT OF ABSORPTION. NOR is this substitution of 30 for 900, in consequence of our having merely to deal with the diminution of Light in a medium, the only point with respect to medium, which is here entitled to attention. It will be found that with few exceptions, the writers upon Light and Optics do not mention in their Treatises the diminution by Medium and Absorption, or the law supposed to apply to it, whereas they all mention the other diminution and the other law ; yet this diminution of Light by a Medium is the only one known or thought of, except by those more advanced in Physical Science. All the rest of the world think only of the action of the Medium, when they think at all of this diminution or the cause of it. Although the more enlightened of the Professors are aware of this fact, and sometimes laugh at it as a popular error, from which they are themselves exempt, they never, or very rarely, in their books or lectures, explain that the diminution they speak of is not at all the diminution by Absorption and the Medium, but simply and solely a diminution by Expansion or Dilution and by the enlargement of the space illuminated^ or, as they prefer to express it, by the principle of the In- verse Squares, while the class to be called 6t TTDAAOI of the Pro- fession seem entirely unconscious of there being any such difference to explain. But however much Professors may vary in information, they almost all write and lecture as if there were but the one kind of diminution in question, the better informed of them well knowing that, for their readers and auditors, that one is the diminution by medium only. When, accordingly, they say that Light diminishes in the rapid ratio known as " the square of the distance " they know that it is understood by all except those among 168 PART IV. SECTION 5. themselves who know better, as a result of Absorption and length of Medium (this, moreover, in our dense atmosphere), and that this medium, with the Law of the Inverse Squares applied to it, is supposed to be what makes the solar Light on Neptune's surface 900 times less than that which we have on ours. As if to confirm their readers and their auditors in this error, I do not say that this has always been the inten- tion, but as if it were, all the Professors, as has been pointed out (PART II. sec. 6), undertake to explain and to prove the alleged diminution by dilution, deviation, or expansion, under the name of the " Inverse Squares," by means of the diminution which results from a Medium (Appendix, Nos. 2, 3, and 15.) Yet how could one of these processes of diminution prove or explain anything of the other ? All thoughtful men are expecting and waiting for an answer to this question. Those are deceived who think that no one notices the absurdity here so patent. It being commonly believed that, as there is 30 times as much distance between the Sun and the surface of Neptune as between the Sun and the surface of the earth, there is therefore 30 times as much Medium ; and it being commonly taught that as Light diminishes by the square of this " distance'* or length of Medium (for the un- professional world, I repeat, are here taught no distinction), our amount of Light is 900 times greater than that of Neptune, it is now the general impression among all except those well versed in Physics, that there being 30 times more medium between Neptune's surface and the Sun than between the Sun and ours, is the reason why Neptune's light is held to be a 900th part of that which we experience here. When, however, it is once known that the only diminution connected with distance that we have to deal with, is that which results from the Medium, and when it is known that the Professors themselves admit that this diminution by Absorption is not only not more rapid than the distance (which the other diminution is supposed to be), but is uot PART IV. SECTION 6. 169 even as rapid as the distance, when it is once known that 30 times a greater amount of Medium not only does not reduce the amount of Light at Neptune to a 900th part of what it is with us, but does not even reduce it to a 30th part of ours, nay, does rot even give 900 times a greater amount of reduction in the one case than in the other ; when all this is thus at length known, those who read and those who listen will be astonished utterly at the strange blunder in which they, with their instructors, have been so long imprisoned. It may even be worth their while to ascertain whether their instructors were indeed always in prison with them, or whether their instructors were not sometimes their jailors. SIXTH SECTION. TWO OTHER ERRORS TOLERATED AND ENCOURAGED. THIS confusion or identification, however, of an amount of Light 900 times smaller, with an amount of reduction 30 times greater, and of a 30 fold reduction with a reduc- tion 900 fold, are not the only points that are here entitled to attention and comparison. There are two other remarkable errors hitherto tolerated, where not taught, upon this subject, apparently (whatever may have been the real object) for the purpose of giving plausibility to the enormous reductions involved in the theory of the Inverse Squares, two errors which require in this place to be taken full account of, especially one of them, also the two facts of Nature which they distort, and which seem hitherto to have entirely escaped the notice, even of the professional public, in this calculation. One of these facts of Nature is that, although Neptune is 30 times further than we are from the centre, the solar rays do not pass through thirty times as much medium on their way to the surface of Neptune as they traverse in their 170 PART IV. SECTION 7. passage to our eyes on the earth's surface. In the case of each planet, the solar light only passes through one atmo- sphere in addition to the amount of mere Ether traversed before it reaches that atmosphere. To traverse 30 times as much medium as it traverses in reaching us, it would require to traverse 30 atmospheres as well as thirty times as much Ether ; and this it does not do. The other of the two facts to which I now advert, as omitted in all the calculations on this subject, is that the ethereal medium through which the solar rays always pass is never uniform; that the highly attenuated medium between the planets becomes, through the attractive action of the Sun, more and more attenuated, according to the increase of its distance from the centre of the system, and that, upon the commonly received principle of science, it does so at the enormous rate involved in the square of the distance. Here, then, we see that there is not even 30 times as much of the Interplanetary Medium, nor nearly 30 times as much of it, for the solar light to traverse in its pas- sage to Neptune's orbit as in its passage to ours ; so that, although 30 times a greater diminution from so attenuated a medium would be imperceptible, here we have to deal with very much less than 30 times a greater diminution ; and this, be it well remembered, in a medium in which all diminution is 250 millions of times less perceptible than it would be in our atmosphere. SEVENTH SECTION. CONCLUSION AND RECAPITULATION OF THE PROPOSITIONS INSISTED UPON IN THE TREATISE. IN conclusion, then, we see that we have not, on each spot of the earth's surface, 900 times a stronger Light (a larger amount of Light) than there is upon each spot of Neptune's surface. We see, moreover, that even the amount of PART IV. SECTION 7. 171 diminution which takes place before reaching Neptune's surface is not 900 times greater than that which takes place before reaching ours. Nay, we see that, although Neptune is 30 times farther from the Sun than we are, this amount of diminution is not nearly 30 times greater between his orbit and the Sun than it is between the Sun and our orbit ; and that (which is the most important point in this Last Part of the Treatise) the very small difference of Diminution, ?'.., of Light lost, not of Light transmitted, here in question, is 250 millions of times less perceptible in the Interplanetary Medium than we find it to be in our dense atmosphere. We have no difficulty, therefore, in fully recognizing that this small difference (not nearly 30 fold) between the diminution which our light has under- gone and that undergone by the light of Neptune, is what would be entirely un appreciable, not only to our unaided powers of sight, but even with the aid of the most powerful apparatus or photometer not only that we possess or know of, but even that we can imagine. I conclude with the following brief Synopsis of my Pro- positions : (1.) All the planets receive the same (appreciable) degree of illumination from the Sun, notwithstanding the difference in his distance from them ; the whole of the solar system being thus equally illuminated. (2.) Light is not, in Nature, diminished by Distance in more than one way ; which is by Absorption in the Medium. (3.) In Nature, the Light falling upon a surface from a source to which every point of the surface is uniformly exposed, is neither diminished nor increased by the enlarge- ment of the surface illuminated, and thus uniformly exposed to it. (4.) Light, in Nature, neither seeks its own level, nor spreads at all. When we take no account of the Medium, it neither deviates from the straight line, nor can exist apart from its source, nor can be " diluted." (5.) When we take no account of Medium, the whole 172 PART IV. SECTION 7. expanse of the surface equally exposed to the source, t'.e., exposed to a point or central source, has the whole of the illumination upon each' spot of it, and this at all distances from the Source. (6.) Taking thus no account of Medium, the smaller sur- face, even when it is at the greater distance from the Sun or other central source, is, in every spot of it, as completely exposed to the whole luminous force of the disc, as the larger surface is, even when this larger is nearer to the Sun. (7.) The whole degree of Light being on each square inch which is exposed to it, does not make the square foot have 144 times more than the whole degree of Light to which it is exposed. " (8.) There are, in Nature, no rays which diverge from one another, with dark cones or spaces between them, widening as the distance from the source increases ; what are called " rays " being merely artificial or imaginary divisions of Light without, in nature, any real intervals whatever between them. (9.) In Nature, no Light is diminished merely by the con- traction of the central source, even when this contraction is real; clearly then not by the merely apparent contraction of it. (10.) The Sun's light which reaches us has been diminished by our atmosphere, and by the ethereal or interplanetary substance only, not by Perspective or the seemingly diminished disc. (11.) Doubling the cause does not, in nature, ever quad- ruple the effect, nor does trebling the cause, ever, in nature, render the effect ninefold. (12.) Light is only measured by degrees, never by yards, nor inches, nor cubic measure. It is only the object illuminated that can be so measured, or the area from which the Light proceeds, or the materials or vibrations employed to produce it. We have not, in nature, a block of Light, nor a yard of Light, although we have both of these in books and lectures. PART IV. SECTION 7. 173 (13.) Each square foot, or inch, or mile of the solar disc does not give out a Light of its own which reaches the confines of the system, or even the planets, and which is thus independent of the rest of the disc. (14.) The amount of luminous force in any given line of Light, or path, or direction, or ray, is not increased by the length of the path or ray ; i.e., by its distance from the source. This amount, or degree, in the absence of all medium, would be, it is admitted by all parties to this con- troversy, exactly the same in the whole path, taken together, and in each point of it. (15.) We have no grounds whatever for the sub-divisions of the Solar Light or of any other light, which are supposed to result from the sub-divisions of the surface upon which it falls, as indicated in the Theory and Law of the Inverse Squares. (See paragraph 12.) (16.) We do not know what proportion the Solar Light which we experience, bears to the solar light in its un- diminished state. We do not know whether we have half of it, or a millionth part of it, or almost the whole of it. We have neither test nor data for any such statements. (17.) We do not know what proportion of the Solar Light is absorbed before it reaches our orbit, nor what proportion of it is absorbed by our Atmosphere. We have here, also, neither test nor data. (18.) We do not know anything more of these three pro- portions with regard to any other planet than we know of them with regard to our own. (19.) We do not know, therefore, except relatively be- tween planet and planet, what proportion the Solar Light at any other planet, either inside or outside its atmosphere, bears to that which we have either inside or outside ours. (20.) We only know that the degrees of Light absorbed by equal amounts of Medium ?'.- pendix, Nos. 1 2, 13, 15, 16, 18. See Ab- sorption ; also (Theory of) Inverse Squares. Increase of diminution and decrease of Light, have not the same Law, nor the same result, p. 128. Distance from a source of Light and distance in a cone (or Distance from a source of Size) very different, pp. 18, 20, 21, 23, 56. Distance from the Window Sun or Lamp does not enlarge objects ; whereas distance in a cone does. Divergence, either partial (the Spoke Theory), without Convergence, or Universal, which implies Converg- ence ; both kinds treated of, pp. 88, 91. Division and Multiplication of the action of a Central Force, a source of the misconception involved in The Inverse Squares, p. 71. Ductility or Expansion of Light, p. 60. See Malleability, and Block. E. ELASTICITY of Light, expanding and contracting with the area? pp. 60, 119. Equality of the Light on surfaces of all sizes, when it proceeds from the same central source, p. 64. Equilibrium, or Level, of Light. No such thing in nature, p. 21. See Spreading of Light. Ether, the rarefied air or aeriform sub- stance outside the atmospheres of the Planets, and through which they move: its highly attenuated nature, p. 165. Ether, densest next the Sun, but more and more rarefied by distance from him at the same rate as Gravitation diminishes, p. 170. Ether. We do not know how much it absorbs of the solar Light between the Sun and our orbit, p. 135. Expansion of a ray, or diffusion of Light. No such thing possible with- out the action of a Medium. Light does not of itself deviate from its straight line, or dissolve and bend so as to become diffused, pp. 60, 62, 63. Divergence of Light and its stretch- ing or expansion very different things; see both. G. GRAVITATION has no theory of rays, or lines, although also figuratively said to radiate; and no theory of being inversely as the Areas acted upon, yet the Law of the Inverse Areas or Squares is applied to it. Appendix, Nos. 1, 15, 17, 20. Geometrical Law of Areas, illustrated by means of Screens and concentric spheres, pp. 24, 25. Appendix, Nos. 1,2,3,15,17. The contrary of the Optical Law of Areas, p. 24, though sometimes ignorantly spoken of as the same Law. Appendix, No. 8. Geometrical Progression. The absurdest principles can be, as here, in a geome- trical Progression. The received Law for diminution in a Medium is a form of it described, p. 15. Appendix, Nos. 4, 9, 10, 12. This received Law for diminution in a Medium is described as an opinion, Appendix, No. 12. HEAT expands, diffuses itself, spreads and seeks its own level in a Medium, which it probably could not do with- out one, said figuratively to radiate, but has no well declared theory of rays ; and is supposed to diminish as the square of the distance increases, but, like Gravitation, without any reference to areas. I. ILLUMINATION, the, here in question, the degree or amount of Light produced at given points of space by a central source or luminous point. That of the solar system exists throughout the whole system without any sen- sible difference anywhere outside the atmosphere of the Planets. Illustration. Four illustrations given of the absurdity latent in the Law of the Inverse Squares, p. 144. Illustration. The action of a Medium used in Photometers as an illustra- tion of what results when there is none, p. 120. See also Appendix, Nos. 2, 3. Illustration. Screens which illustrate well the Geometrical Law of Areas (Appendix, No. 17), used to prove that the Light diminishes as the area increases, Appendix, Nos. 1, 2, 3, 15. Newton's illustration of the Ether's rarity, p. 165. Illustration of the principle that the Law of Diminutions and the Law of things diminished are not the same, p. 147. Increase of Light directly as the square of the distance, the true result of the received Theory, p. 63. INDEX. 217 Inequality of Light throughout the system, alleged extent of it, pp. 1, 48 , Intensity, or amount of Illumination and Light, denotes degree always, never size or bulk, either of Light itself or of its cause, p. 86. *' Inverse," use of the word in the Law of the Inverse Squares, p 133. Inverse Squares, their Theory, pp. 16, 34, 55. Appendix, No. 12. Their Law, p. 16. Appendix, Nos. 1, 2, 3, 12, 15. Two interpretations of the Law ver- bally possible, only one received, p 127. The Law and Theory under- stood of different subjects, p. 125. The Law first published by Bouguer, but previously current, Appendix, No. 12. The correct sense of the theory as received, and the false one, pp. 125, 128. LAW of Geometrical Progression for Absorption, p. 14. Appendix, Nos. 4, 9, 10, 12. Its two errors, p. 157. Law of the 'Inverse Squares. See Inverse Squares. Level. Light does not seek its own level. Light or Illumination, often confounded with its Cause or Source, pp. 80, 82, 85. Also with the area illuminated, ibid. Always measured by Degrees, never by Long measure or by Solid measure, pp. 81, 86. See Yards. Ex- empt from Medium, the sun's light would go undiminished to the limits of the System. Appendix, Nos. 18, 20. M. MALLEABILITY of Light as absurd as its Ductility or Expansion, p. 60. Medium, the substance, dense or rare, through which Light passes. " Free Medium" a technical and deceptive expression for a vacuum or empty space ; i.e. no medium at all. Ab- sorption in, the only diminution of Light by Distance from the Source, pp. 135, 138, 162, 155. The received Law for this diminution, p. 15. Ap- pendix, Nos. 4, 9, 10, 12. Its two errors, ibid., and p. 157. The popular and natural Law for it, p. 14. The interplanetary Medium or the Ether, its extreme attenuation, p. 165. Movements of the Planets, their im- mense rapidity implies an immense attenuation of the Medium they tra- verse, p. 166. Multiplication and Division Theory for Light (as any Energy proceeding from a central source), an obvious error, p. 69, et geq., helped to suggest the Theory of the Inverse Squares, ibid. N. NATURE. One fact of Nature shows that, even without a Medium, there would be no spreading or reduction of Light , upon each spot of the larger area. p. 62; another such fact shows that even in a Medium, there is neither this Ex- pansion nor this dilution or im- poverishment, p. 61. O. OBJECT, section (of the cone), area, size, disc (of the planets), space, or sur- face, all here used as synonyms for the extent of matter presented to the source of Light without any reference to the portions of this matter not so presented. Opinion, supposition, or conviction is not science. All admit the Law of the Inverse Squares to ba a mere opinion respecting what has never been discovered, Appendix, Nos. 3, 5, 6, 7, 14. 18, 19. The received Law of diminution in a Medium also an opinion, Appendix, No. 12. Optics, divided into Physical and Physiological Optics. The Law and Theory of the Inverse Squares belong to the first of these. Confusion made respecting them, p. 115. Physical. Optics divided into three branches, The Passage, The Reflection, and the Refraction, of Light in its relation with material bodies. The first is commonly known as Photometry, and has been hitherto almost entirely neglected, although practically more important than the other two branches, Appendix, No. 11. P. PARTIAL Divergence (the Spoke-Theory) supposes the Radiation of Darkness from the source of Light, or jet black cones between the rays, which cones, as they extend into space, enlarge directly as the Square of the Distance, p- 99. Appendix, No. 20. Perspective belongs to Physiological Optics. Brought to prove the expan- sive and contractible nature of Light, p. 119. Photometry. See Optics. Photometers, in a Medium supposed to act as if there were no Medium, p. 120. Appendix, Nos. 1, 2, 3, 15, Planets, their discs not as the squares of their relative distances, the areas and distances from the sun not being in geometrical proportion, p. 46. Ap- plication of the Law of the Inverse Squares to them, p. 45. Their rapid movements prove the extreme teuuity of the Ether, p. 166. 218 INDEX. Q. QUESTION stated, p. 3. Its treatment here, and the reasons for it, p. 4. E. RAT, a fictitious atom of Light. Its rectilinear nature, Appendix, Nos. 2, 3, 4, &c. The physical impossibility of its spreading or expanding, pp. 60, K2, 63. The fact that it does not so spread, p. 63. The supposed diverg- ence of one ray from another, either partial, p. 91 (see Spoke-Theory), or universal, p. 88, making the whole Light of the disc to consist in a cone of rays proceeding from, the whole disc to each point of the area illumi- nated, p. 88. Appendix, No 20. Each ray supposed to be limited by a jet black space lying between every two rays. Appendix, No. 20. The sun's rays of Light, although not those of Gravitation, nor of Heat, go undi- minished in number and intensity to the remotest limits of the system? Appendix, Nos >8 and 20. Kadiation of Darkness, or dark cones, from the sun and other luminaries, pp. 97, 100. Radiation a figurative term, apparently, for the action of all Physical force, even where we sup- pose no rays, Appendix, No. 1. Relative diminution of Light does not mean diminution at all, p. 103. The Theory of the Inverse Squares only pretends to relative diminution, pp. 104, 105. But without the aid of the Spoke-Theory, there is not even that, ibid. S. SCREENS, even through a Medium, prove the geometrical Law of Areas, but cannot thus prove anything about the diminution of Light without a Medium, although so unaccountably used for that purpose by all the writers on Optics. Appendix, Nos. 1, 2, 3, 12, 15. The screens even dis- prove the Law of the Inverse Squares which they are everywhere brought to prove, p. 121. Shadows, the clearesft evidence that Light does not spread from its straight line, p. 63. Bee Umbra. See also Nature, for other evidence of this. Solar Light, what is true of it in this question is true of all Light, p. 5. Source or cause of Light, often con- founded with Light, p. 80. All here always speak of a central source, one to the whole of which each point of the areas illuminated is equally exposed. A diffused, spread, or un- central source is any source of Light of which this is not true. Source of Size, p. 108- See Apex. Spatial diminution of Light, that which results from mere Enlargement of the space illuminated, p. 42. Spheres, concentric, prove the Law of Areas, p. 24 ; but prove nothing, and do not even suggest anything, about the diminution of Light without a Medium. Speckled or spotted with Light, said of the jet black sections of Cones and Spheres upon which, in the Spoke-Theory, the divergent rays impinge, pp. 105, 108. Spoke-Theory, or Divergence-Theory, result of Partial Divergence, ex- plained, pp. 86, 91. A main cause why the Inverse-Squares-Theory was adopted, p. 98. Entirely fictitious ; no one reason ever assigned for it ; held now but by very few ; even those who explain it acknowledge its groundlessness. Appendix, Nos. 1, 3. Spotted with Light, see Speckled ; the condition of distant objects, in the Spoke-Theory. Spreading of Light, proved by two familiar experiments not to exist in Nature, pp. 61, 62. Sometimes con- founded with Divergence or the Spoke -Theory . The whole pretext for the Theory and the Law of the In- verse Squares. See all the Fourth Section of PART I. No space for Light to expand into, or spread into, except in the now exploded Theory of the Spokes; and even in that, the ray, it is admitted, cannot leave its straight line nor spread. In no sense, therefore is it physically possible for Light to spread from right to left, or up and down, except in the Spoke- Theory, and there only in an equivocal sense, pp. 60, 62, 63. Sun. If there were no Medium, the sun's disc would throw exactly the same degree or amount of Light upon every point of space, since space is all equally exposed to it ; i.e., the disc is a central source; and when, in this sense, we speak of the sun, it is the disc only that is meant, because one half of the sun is always turned away from the regions of space illuminated by the other half, and therefore needs not to be spoken of. Surface, the portion of bodies on which Light impinges when it is reflected or refracted. It is the transparent sub- stance itself, through which all Light passes, not the surface of this sub- stance, which absorbs the Light. T. THEORY of the Inverse Squares, its seven propositions, p 44, see also pp. 34 and 109. Its three Physical Im- possibilities, p. 113. The received Theory of Absorption, p. 15. Its two errors, p, 156. INDEX. 219 Traditional Optics, (see Preface), the principles which have descended to us from Bouguer. A.D. 1729, without the least investigation. Transmitted Light. The Law of the Inverse Squares applies only to it, not to the untransuiitted or lost Light, p. 131. Without a Medium all Light would be transmitted. Ap- pendix. Nos. 18, 20. U. UMBRA. The umbra and penumbra of the Eclipse prove both that Light does not spread, and that the Ether is infi nitesinially attenuated, p. 63. ' ' Unity of Surface, on a." The technical expression to say, on the same amount of space in each of two or more sur- faces ; familiarly expressed by, on each spot, on each square inch, at each point, on each square foot,