OAK ST HDSF THE UNIVERSITY OF ILLINOIS LIBRARY Prom the collection of Julius Doerner, Chicago Purchased, 1918. $84- 1835 The person charging this material is re- sponsible for its return to the library from which it was withdrawn on or before the Latest Date stamped below. Theft, mutilation, and underlining of books are reasons for disciplinary action and may result in dismissal from the University. UNIVERSITY OF ILLINOIS LIBRARY AT URBANA-CHAMPAIGN LETTERS OF EULER ON DIFFERENT SUBJECTS IN NATURAL PHILOSOPHY. ADDRESSED TO A GERMAN PRINCESS. WITH NOTES, AND A LIFE OF EULER, BY DAVID BREWSTER, LL.D. F.R.S. LOND. AND ED. CONTAINING A GLOSSARY OF SCIENTIFIC TERMS. WITH ADDITIONAL NOTES, BY JOHN GRISCOM, LL.D. IN TWO VOLUMES. VOL. II. NEW YORK : HARPER & BROTHERS, NO. 82 CLIFF-STREET. 1835. Entered, according to Act of Congress, in the year 1835, By HARPER & BROTHERS, ID the Clerk's Office of the Southern District of New-York. V , CONTENTS V? Ft THE SECOND VOLUME. v LETTER I. CONTINUATION of the Subject, and of Mis- takes in the Knowledge of Truth - - 11 II. First Class of known Truths. Conviction that Things exist externally, corresponding to the Ideas represented by the Senses. Objection of the Pyrrhonists. Reply - 14 III. Another Objection of the Pyrrhonists against the Certainty of Truths perceived by the Senses. Reply ; and Precautions for at- taining Assurance of sensible Truths - 17 IV. Of demonstrative, physical, and particularly of moral Certainty 20 V. Remarks that the Senses contribute to the Increase of Knowledge ; and Precautions for acquiring the Certainty of historical Truths 23 VI. Whether the Essence of Bodies be known by us 26 VII. The true Notion of Extension ... 30 VIII. Divisibility of Extension in infinitum - - 33 IX. Whether this Divisibility in infinitum takes place in existing Bodies - - - - 36 X. Of Monads -.;...- - - - - 39 XI. Reflections on Divisibility in infinitum, and on Monads 42 XII. Reply to the Objections of the Monadists to Divisibility in infinitum - - -46 XIII. Principle of the sufficient Reason the strongest Support of the Monadists - - - - 48 XIV. Another Argument of the Monadists derived from the Principle of the sufficient Reason. Absurdities resulting from it*" - - - 52 CONTENTS. XV. Reflections on the System of Monads - - 55 XVI. Continuation 58 XVII. Conclusion of Reflections on this System - 61 XVIII. Elucidation respecting the Nature of Colours 65 XIX. Reflections on the Analogy between Colours and Sounds 68 XX. Continuation 71 XXL How Opaque Bodies are rendered visible - 73 XXII. The Wonders of the human Voice - - 76 XXIII. A Summary of the principal Phenomena of Electricity 7ft XXIV. The true Principle of Nature on which are founded all the Phenomena of Electricity 82 XXV. Continuation. Different Nature of Bodies relatively to Electricity - - - - 85 XXVI. On the same Subject 88 XXVII. Of positive and negative Electricity. Expla- nation of the Phenomenon of Attraction - 92 XXVIII. On the same Subject 95 XXIX. On the electric Atmosphere ... 98 XXX. Communication of Electricity to a Bar of Iron, by means of a Globe of Glass - - 102 XXXI. Electrization of Men and Animals - - 106 XXXII. Distinctive Character of the two Species of Electricity 109 XXXIII. How the same Globe of Glass may furnish at once the two Species of Electricity - XXXIV. The Leyden Experiment - - - 115 XXXV. Reflections on the Cause and Nature of Elec- tricity, and on other Means proper to pro- duce it 119 XXXVI. Nature of Thunder : Explanations of the ancient Philosophers, and of DESCARTES. Resemblance of the Phenomena of Thun- der to those of Electricity - - - 122 XXXVII. Explanation of the Phenomena of Lightning and Thunder - - - - - - 126 XXXVIII. Continuation 128 XXXIX. The Possibility of preventing and of averting the Effects of Thunder - - - - 131 XL. On the celebrated Problem of the Longitude. General Description of the Earth, of its Axis, its two Poles, and the Equator - 135 XLI. Of the Magnitude of the Earth; of Meridians, and the shortest Road from Place to Place 139 XLII. Of Latitude, and its Influence on the Sea- sons and the Length of the Day - - 143 XLIII. Of Parallels, of the First Meridian, and of Longitude 140 CONTENTS. 5 X LI V. Choice of the First Meridian - - -150 XLV. Method of determining the Latitude, or the Elevation of the Pole - - - - 153 XLVI. Knowledge of the Longitude from a Calcu- lation of the Direction and of the Space passed through - - - . - - - 157 XLVII. Continuation. Defects of this Method - 161 XL VIII. Second Method of determining the Longi- tude, by Means of an exact Timepiece - 164 XLIX. Continuation, and further Elucidations - 168 L. Eclipses of the Moon a third Method of find- ing the Longitude - - ' - - 171 LI. Observation of the Eclipses of the Satellites of Jupiter, a fourth Method of finding the Longitude 175 LII. The Motion of the Moon a fifth Method - 179 LIII. Advantages of this last Method : its Degree of Precision 182 LIV. On the Mariner's Compass, and the Proper- ties of the Magnetic Needle - - -185 LV. Declination of the Compass, and Manner of observing it - - - - - -189 LVI. Difference in the Declination of the Compass at the same Place 192 LVII. Chart of Declinations ; Method of employing it for the Discovery of the Longitude - 196 LVIII. Why does the Magnetic Needle affect, in every Place of the Earth, a certain Direc- tion, differing in different Places ; and for what Reason does it change, with Time, at the same Place ? 200 LIX. Elucidations respecting the Cause and Varia- tion of the Declination of Magnetic Needles 203 LX. Inclination or Dip of Magnetic Needles - 207 LXI. True Magnetic Direction ; subtile Matter which produces the Magnetic Power - 211 LXII. Nature of the Magnetic Matter, and of its rapid Current. Magnetic Canals - 214 LXIII. Magnetic Vortex. Action of Magnets upon each other - 218 LXIV. Nature of Iron and Steel. Method of com- municating to them the Magnetic Force - 221 LXV. Action of Loadstones on Iron. Phenomena observable on placing Pieces of Iron near a Loadstone 226 LXVI. Arming of Loadstones 230 LXVII. Action and Force of armed Loadstones - 234 LXVIII. The Method of communicating to Steel A2 CONTENTS. Letter j^, the Magnetic Force, and of magnetizing Needles for the Compass. The SIMPLE TOUCH ; its Defects ; Means of remedying these 238 LXIX. On the DOUBLE TOUCH. Means of preserv-" ing the Magnetic Matter in magnetized Bars 241 LXX. The Method of Communicating to Bars of Steel a very great Magnetic Force, by Means of other Bars which have it in a very inferior Degree 246 LXXI. Construction of artificial Magnets in the Form of a Horseshoe ------ 249 LXXII. On Dioptrics. Instruments which that Sci- ence supplies : of Telescopes and Micro- scopes. Different Figures given to Glasses or Lenses 253 LXXIII. Difference of Lenses with respect to the Curve of their Surfaces. Distribution of Lenses into three Classes .... 257 LXXIV. Effect of Convex Lenses LXXV. The same Subject. Distance of the Focus of Convex Lenses - LXXVI. Distance of the Image of Objects LXXVII. Magnitude of Images - LXXVIII. Burning-glasses - 261 264 268 271 275 278 LXXIX. The Camera Obscura - ... LXXX. Reflections on the Representation in the Camera Obscura - - ... 283 LXXXI. Of the Magic Lantern, and Solar Micro- scope 286 LXXXII. Use and Effect of a simple convex Lens - 290 LXXXIII. Use and Effect of a concave Lens - - 293 LXXXIV. Of apparent Magnitude, of the Visual Angle, and of Microscopes in general - 297 LXXXV. Estimation of the Magnitude of Objects viewed through the Microscope - - 300 LXXXVI. Fundamental Proposition for the Construc- tion of simple Microscopes. Plan of some simple Microscopes ----- 304 LXXX VII. Limits and Defects of the simple Microscope 307 LXXX VIII. On Telescopes, and their Effect - - - 311 LXXXIX. Of Pocket-glasses 314 XC. On the magnifying Power of Pocket-glasses 318 XCI. Defects of Pocket-glasses. Of the apparent Field - - 322 CONTENTS. 7 Letter Page XCII. Determination of the apparent Field for Pocket-glasses ------ 326 XCIII. Astronomical Telescopes, and their magnify- ing Power 329 XCIV. Of the apparent Field, and the Place of the Eye 332 XCV. Determination of the magnifying Power ot Astronomical Telescopes, and the Con- ctruction of a Telescope which shall mag- nify Objects a given Number of Times - 336 XCVI. Degree of Clearness 339 XCVH. Aperture of Object-glasses - - - - 343 XCVIII. On Distinctness in the Expression. On the Space of Diffusion occasioned by the Aperture of Object-glasses, and considered as the first Source of Want of Distinctness in the Representation - 347 XCIX. Diminution of the Aperture of Lenses, and other Means of lessening the Space of Diffusion, till it is reduced to Nothing - 351 C. Of compound Object-glasses - - 355 CI. Formation of simple Object-glasses - - 358 CII. Second Source of Defect as to Distinct- ness of Representation by the Telescope. Different Refrangibility of Rays - - 362 Cm. Means of remedying this Defect by compound Object-glasses - - - - - - 366 CIV. Other Means more practicable ... 369 CV. Recapitulation of the Qualities of a good Telescope 373 CVI. Terrestrial Telescopes with four Lenses - 376 CVII. Arrangement of Lenses in Terrestrial Tele- scopes 379 CVIII. Precautions to be observed in the Construc- tion of Telescopes. Necessity of blacken- ing the Inside of Tubes. Diaphragms - 382 CIX. In what Manner Telescopes represent the Moon, the Planets, the Sun, and the fixed Stars. Why these last appear smaller through the Telescope than to the naked Eye. Calculation of the Distance of the fixed Stars, from a Comparison of their apparent Magnitude with that of the Sun 385 CX. Why do the Moon and the Sun appear greater at rising and setting than at a certain Ele- vation? Difficulties attending the Solu- tion of this Phenomenon .... 388 CONTENTS. Letter Page CXI. Reflections on the Question respecting the Moon's apparent Magnitude. Progress towards a Solution of the Difficulty. Ab- surd Explanation 391 CXII. An Attempt towards the true Explanation of this Phenomenon : the Moon appears more distant when in the Horizon than when at a great Elevation 395 CXIII. The Heavens appear under the Form of an Arch flattened towards the Zenith - - 398 CXIV. Reason assigned for the Faintness of the Light of Heavenly Bodies in the Horizon 401 CXV. Illusion respecting the Distance of Objects, and the Diminution of Lustre - - - 405 CXVI. On the Azure Colour of the Heavens - - 407 CXVII. What the Appearance would be were the Air perfectly transparent ----- 410 CXVIII. Refraction of Rays of Light in the Atmo- sphere, and its Effects. Of the Twilight. Of the apparent Rising and Setting of the Heavenly Bodies 414 CXIX. The Stars appear at a greater Elevation than they are. Table of Refractions - -417 LETTERS ON DIFFERENT SUBJECTS IN NATURAL PHILOSOPHY. LETTER I. Continuation of the Subject, and of Mistakes in the Knowledge of Truth. THE three classes of truths which I have now un- folded are tjje only sources of all our knowledge ; all being derived from our own experience, from reasoning, or from the report of others. It is not easy to determine which of these three sources contributes most to the increase of know- ledge. Adam and Eve must have derived theirs chiefly from the two first ; God, however, revealed many things to them, the knowledge of which is to be referred to the third source, as neither their own experience nor their powers of reasoning could have conducted them so far. Without recurring to a period so remote, we are sufficiently convinced, that if we were determined to believe nothing of what we hear from others, or read in their writings, we should be in a state of almost total ignorance. It is very far, however, from being our duty to believe every thing that is said, or that 12 MISTAKES IN THE we read. We ought constantly to employ our dis- cerning faculties, not only with respect to truths of the third class, but likewise of the two others. We are so liable to suffer ourselves to be dazzled by the senses, and to mistake in our reasonings, that the very sources laid open by the Creator for the discovery of truth very frequently plunge us into error. Notions of the third class, therefore, ought not in reason to fall under suspicion, any more than such as belong to the other two. We ought, there- fore, to be equally on our guard against deception, whatever be the class to which the notion belongs ; for we find as many instances of error in the first and second classes as in the third. The same thing holds with regard to the certainty of the particular articles of knowledge which these three sources sup- ply ; and it cannot be affirmed that the truths of any one order have a surer foundation than those of another. Each class is liable to errors, by which we may be misled ; but there are likewise precautions which, carefully observed, furnish us with nearly the same degree of conviction. I do not know whether you are more thoroughly convinced of this truth, that two triangles which have the same base and the same height are equal to one another, than of this, that the Russians have been at Berlin; though the former is founded on a chain of accurate reasoning, whereas the latter depends entirely on the veracity of your informer. Respecting the truths, therefore, of each of these classes, we must rest satisfied with such proofs as correspond to their nature ; and it would be ridicu- lous to insist upon a geometrical demonstration of the truths of experience, or of history. This is usually the fault of those who make a bad use of their penetration in intellectual truths, to require mathe- matical demonstration in proof of all the truths of religion, a great part of which belongs to the third class. KNOWLEDGE OF TRUTH. 13 There are persons determined to believe and admit nothing but what they see and touch ; whatever you would prove to them by reasoning, be it ever so solid, they are disposed to suspect, unless you place it before their eyes. Chymists, anatomists, and nat- ural philosophers, who employ themselves wholly in making experiments, are most chargeable with this fault. Every thing that the one cannot melt in his crucible, or the other dissect with his scalpel, they reject as unfounded. To no purpose would you speak to them of the qualities and nature of the soul ; they admit nothing but what strikes the senses. Thus, the particular kind of study to which every one is addicted has such a powerful influence on his manner of thinking, that the natural philosopher and chymist will have nothing but experiments, and the geometrician and logician nothing but argu- ments; which constitute, however, proofs entirely different, the one attached to the first class, the other to the second, which ought always to be care- fully distinguished, according to the nature of the objects. But can it be possible that persons should exist who, wholly absorbed in pursuits pertaining to the third class, call only for proofs derived from that source 1 I have known some of this description, who, totally devoted to the study of history and antiquity, would admit nothing as true but what you could prove by history, or the authority of some ancient author. They perfectly agree with you respecting the truth of the propositions of Euclid, but merely on the authority of that author, without paying any attention to the demonstrations by which he sup- ports them ; they even imagine that the contrary of these propositions might be true, if the ancient geome- tricians had thought proper to maintain it. This is a source of error which retards many in the pursuit of truth; but we find it rather among the learned, than among those who are beginning to VOL. II. B 14 OBJECTION OF THE PYRRHONISTS. apply themselves to the study of the sciences. We ought to have no predilection in favour of any one of the three species of proofs which each class re- quires; and provided they are sufficient in their kind, we are bound to admit them. I have seen or felt, is the proof of the first class. / can demonstrate it, is that of the second : we like- wise say, I know it is so. Finally, / receive it on the testimony of persons worthy of credit, or I believe it on solid grounds, is the proof of the third class. 4th April, 1761. LETTER II. First Class of known Truths. Conviction that Things exist externally, corresponding to the Ideas repre- sented by the Senses. Objection of the Pyrrhonists. Reply. WE include in the first class of known truths those which we acquire immediately by means of the senses. I have already remarked, that they not only supply the soul with certain representations re- lative to the changes produced in a part of the brain; but that they excite there a conviction of the real existence of things external, corresponding to the ideas which the senses present to us. The soul is frequently compared to a man shut up m a dark room, in which the images of external ob- jects are represented on the wall by means of a glass. This comparison is tolerably just, as far as it respects the man looking at the images on the wall ; for this act is sufficiently similar to that of the soul, contem- plating the impressions made in the brain ; but the comparison appears to me extremely defective, as far as it respects the conviction that the objects which occasion these images really exist. The man in the dark room will immediately sus- OBJECTION OF THE PYRRHONISTS. 15 pect the existence of these objects ; and if he has no doubt about the matter, it is because he has been out of doors, and has seen them ; besides this, knowing the nature of his glass, he is assured that nothing can be represented on the wall but the im- ages of the objects which are without the chamber before the glass. But this is not the case with the soul ; it has never quitted its place of residence to contemplate the objects themselves ; and it knows still less the construction of the sensitive organs, and the nerves which terminate in the brain. It is nevertheless much more powerfully convinced of the real existence of objects than our man in the dark room possibly can be. I am apprehensive of no objection on this subject, the thing being too clear of itself to admit any, though we do not know the true foundation of it. No one ever entertained any doubt about it, except certain visionaries who have bewildered themselves in their own reveries. Though they say that they doubt the existence of external objects, they entertain no such doubt in fact; for why would they have affirmed it, unless they had believed the existence of other men, to whom they wished to communicate their extrava- gant opinions. This conviction respecting the existence of the things whose images the senses represent, appears not only in men of every age and condition, but likewise in all animals. The dog which barks at me has no doubt of my existence, though his soul per- ceives but a slight image of my person. Hence I conclude, that this conviction is essentially con- nected with our sensations, and that the truths which the senses convey to us are as well founded as the most undoubted truths of geometry. Without this conviction no human society could subsist, for we should be continually falling into the greatest absurdities, and the grossest contradictions. Were the peasantry to dream of doubting about 16 OBJECTION OF THE PYRRHONISTS. the existence of their bailiff, or soldiers about that of their officers, into what confusion should we be plunged ! Such absurdities are entertained only by philosophers ; any other giving himself up to them would be considered as having lost his reason. Let us then acknowledge this conviction as one of the principal laws of nature, and that it is complete, though we are absolutely ignorant of its true rea- sons, and very far from being able to explain them in an intelligible manner. However important this reflection may be, it is by no means, however, exempted from difficulties ; but were they ever so great, and though it might be impossible for us to solve them, they do not in the smallest degree affect the truth which I have just es- tablished, and which we ought to consider as the most solid foundation of human knowledge. It must be allowed that our senses sometimes de- ceive us ; and hence it is that those subtile philoso- phers who value themselves on doubting of every thing deduce the consequence, that we ought never to depend on our senses. I have perhaps oftener than once met an unknown person in the street, whom I mistook for an acquaintance : as I was de- ceived in that instance, nothing prevents my being always deceived ; and I am, therefore, never assured that the person to whom I speak is in reality the one 1 imagine. Were I to go to Magdeburg, and to present my- self to your highness, I ought always to be appre- hensive of grossly mistaking : nay, perhaps I should not be at Magdeburg, for there are instances of a man's sometimes taking one city for another. It is even possible I may never have had the happiness of seeing you, but was always under the power of delusion when I thought myself to be enjoying that felicity. Such are the natural consequences resulting from the sentiments of certain philosophers ; and you OBJECTION OF THE PYRRHONISTS. 17 must be abundantly sensible that they not only lead to manifest absurdity, but have a tendency to dis- solve all the bonds of society. 7th April, 1761. LETTER III. Another Objection of the Pyrrhonists against the Cer- tainty of Truths perceived by the Senses. Reply ; and Precautions for attaining Assurance of Sensible Truths. THOUGH the objection raised against the certainty of truths perceived by the senses, of which I have been speaking, may appear sufficiently powerful, at- tempts have been made to give it additional support from the well-known maxim, that we ought never to trust him who has once deceived us. A single ex- ample, therefore, of mistake in the senses, is suf- ficient to destroy all their credit. If this objection is well founded, it must be admitted that human soci- ety is, of course, completely subverted. By way of reply, I remark, that the two other sources of knowledge are subject to difficulties of a similar nature, nay, perhaps still more formidable. How often are our reasonings erroneous ! I venture to affirm, that we are much more frequently de- ceived by these than by our senses. But does it follow that our reasonings are always fallacious, and that we can have no dependence on any truth dis- covered to us by the understanding 1 It must be a matter of doubt, then, whether two and two make four, or whether the three angles of a triangle be equal to two right angles ; it would even be ridicu- lous to pretend that this should pass for truth. Though, therefore, men may have frequently rea- soned inconclusively, it would be almost absurd to B2 18 ANOTHER OBJECTION OF infer that there are not many intellectual truths of which we have the most complete conviction. The same remark applies to the third source of human knowledge, which is unquestionably the most subject to error. How often have we been deceived by a groundless rumour, or false report, respecting certain events ! And who would be so weak as to believe all that gazetteers and historians have writ- ten ? At the same time, whoever should think of maintaining that every thing related or written by others is false would undoubtedly fall into greater absurdities than the person who believed every thing. Accordingly, notwithstanding so many groundless reports and false testimonies, we are perfectly assured of the truth of numberless facts, of which we have no evidence but testimony. There are certain characters which enable us to distinguish truth ; and each of the three sources has characters peculiar to itself. When my eyes have deceived me, in mistaking one man for another, I presently discover my error: it is evident, there- fore, that precautions may be used for the prevention of error. If there were not, it would be impossible ever to perceive that we had been deceived. Those, then, who maintain that we so often deceive our- selves are obliged to admit that it is possible for us to perceive we have been deceived, or they must ac- knowledge that they themselves are deceived when they charge us with error. It is remarkable, that truth is so well established that the most violent propensity to doubt of every thing must come to this, in spite of itself. There- fore, as logic prescribes rules for just reasoning, the observance of which will secure us from error, where intellectual truth is concerned; there are likewise certain rules, as well for the first source, that of our senses, as for the third, that of belief The rules of the first are so natural to us, that all men, the most stupid not excepted, understand and THE PYRRHONISTS. 19 practise them much better than the greatest scholars are able to describe them. Though it may be easy sometimes to confound a clown, yet when the hail destroys his crop, or the thunder breaks upon his cottage, the most ingenious philosopher will never persuade him that it was a mere illusion ; and every man of sense must admit that the country-fellow is in the right, and that he is not always the dupe of the fallaciousness of his senses. The philosopher may be able, perhaps, to perplex him to such a de- gree that he shall be unable to reply ; but he will inwardly treat all the fine reasonings which at- tempted to confound him with the utmost scorn. The argument, that the senses sometimes deceive us, will make but a very slight impression on his mind ; and when he is told, with the greatest elo- quence, that every thing the senses represent to us has no more reality than the visions of the night, it will only provoke laughter. But if the clown should pretend to play the phi- losopher in his turn, and maintain that the bailiff is a mere phantom, and that all who consider him as something real, and submit to his authority, are fools; this sublime philosophy would be in a mo- ment overturned, and the leader of the sect soon made to feel, to his cost, the force of the proofs which the bailiff could give him of the reality of his ex- istence. You must be perfectly satisfied, then, that there are certain characters which destroy every shadow of doubt respecting the reality and truth of what we know by the senses ; and these same characters are so well known, and so strongly impressed on our minds, that we are never deceived when we employ the precautions necessary to that effect. But it is extremely difficult to make an exact enumeration of these characters, and to explain their nature. We commonly say, that the sensitive organs ought to be in a good natural state ; that the air ought not to be 20 DEMONSTRATIVE, PHYSICAL, obscured by a fog ; finally, that we must employ a sufficient degree of attention, and endeavour, above all things, to examine the same object by two or more of our senses at once. But I am firmly per- suaded that every one knows, and puts in practice, rules much more solid than any which could be pre- scribed to him. llth April, 1761. LETTER IV, Of Demonstrative, Physical, and particularly of Moral Certainty. THERE are, therefore, three species of knowledge which we must consider as equally certain, provided we employ the precautions necessary to secure us against error. And hence likewise result three species of certainty. The first is called physical certainty. When I am convinced of the truth of any tiling, because 1 myself have seen it, I have a physical certainty of it ; and if I am asked the reason, I answer, that my own senses give me full assurance of it, and that I am, or have been, an eyewitness of it. It is thus I know that Austrians have been at Berlin, and that some of them committed great irregularities there. I know, in the same manner, that fire consumes all combustible substances ; for I myself have seen it, and I have a physical certainty of its truth. The certainty which we acquire by a process of reasoning is called logical or demonstrative certainty, because we are convinced of its truth by demonstra- tion. The truths of geometry mayliere be produced as examples, and it is logical certainty which gives us the assurance of them. Finally, the certainty which we have of the truth of what we know only by the report of others is AND MORAL CERTAINTY. 21 called moral certainty, because it is founded on the credibility of the persons who make the report. Thus you have only a moral certainty that the Russians have been at Berlin ; and the same thing applies to all historical facts. We know with a moral certainty that there was formerly at Rome a Julius Caesar, an Augustus, a Nero, &c., and the testimonies respecting these are so authentic, that we are as fully convinced of them as of the truths which we discover by our senses, or by a chain of fair rea- soning. We must take care, however, not to confound these three species of certainty physical, logical, and moral each of which is of a nature totally dif- ferent from the others. I propose to treat of each separately ; and shall begin with a more particular explanation of moral certainty, which is the third species. It is to be attentively remarked, that this third source divides into two branches, according as others simply relate what they themselves have seen, or made full proof of by their senses, or as they com- municate to us, together with these, their reflections and reasonings upon them. We might add still a third branch, w T hen they relate what they have heard from others. As to this third branch, it is generally allowed to be very liable to error, and that a witness is to be believed only respecting what he himself has seen or experienced. Accordingly, in courts of justice, when witnesses are examined, great care is taken to dis- tinguish, in their declarations, what they themselves have seen and experienced, from what they fre- quently add of their reflections and reasonings upon it. Stress is laid only on what they themselves have seen or experienced ; but their reflections, and the conclusions which they draw, however well founded they may otherwise be, are entirely set aside. The same maxim is observed with respect to historians ; 22 PHYSICAL AND MORAL CERTAINTY. and we wish them to relate only what they them- selves have witnessed, without pursuing the reflec- tions which they so frequently annex, though these may be a great ornament to history. Thus we have a greater dependence on the truth of what others have experienced by their own senses, than on what they have discovered by pursuing their meditations. Every one wishes to be master of his own judgment ; and unless he himself feels the foundation and the demonstration, he is not persuaded. Euclid would in vain have announced to us the most important truths of geometry ; we should never have believed him on his word, but have insisted on prosecuting the demonstration step by step our- selves. If I were to tell you that I had seen such or such a thing, supposing my report faithful, you would without hesitation give credit to it; nay, I should be very much mortified if you were to sus- pect me of falsehood. But when I inform you that in a right-angled triangle, the squares described on the two smaller sides are together equal to the square of the greater side, I do not wish to be believed on my word, though I am as much convinced of it as it is possible to be of any thing ; and though I could allege, to the same purpose, the authority of the greatest geniuses who have had the same conviction, I should rather wish you to discredit my assertion, and to withhold your assent, till you yourself com- prehended the solidity of the reasonings on which the demonstration is founded. It does not follow, however, that physical cer- tainty, or that which the senses supply, is greater than logical certainty, founded on reasoning; but whenever a truth of this species presents itself, it is proper that the mind should give close application to it, and become master of the demonstration. This is the best method of cultivating the sciences, and of carrying them to the highest degree of per- fection. INCREASE OF KNOWLEDGE. 23 The truths of the senses, and of history, greatly multiply the particulars of human knowledge ; but the faculties of the mind are put in action only by reflection or reasoning. We never stop at the simple evidence of the senses, or the facts related by others ; but always follow them up and blend them with reflections of our own : we insensibly supply what seems deficient, by the addition of causes and motives, and the de- duction of consequences. It is extremely difficult, for this reason, in courts of justice, to procure sim- ple unblended testimony, such as contains what the witnesses actually saw and felt, and no more ; for witnesses ever will be mingling their own reflections, without perceiving that they are doing so. Uth April, 1761. LETTER V. Remarks that the Senses contribute to the Increase of Knowledge; and Precautions for acquiring the Cer- tainty of Historical Truths. THE knowledge supplied by our senses is un- doubtedly the earliest which we acquire ; and upon this the soul founds the thoughts and reflections which discover to it a great variety of intellectual truths. In order the better to comprehend how the senses contribute to the advancement of knowledge, I begin with remarking, that the senses act only on individual things, which actually exist under circum- stances determined or limited on all sides. Let us suppose a man suddenly placed in the world, possessed of all his faculties, but entirely des- titute of experience ; let a stone be put in his hand, let him then open that hand, and observe that the stone falls. This is an experiment limited on all sides, which gives him no information, except that 24 THE SENSES CONTRIBUTE TO this stone, being in the left hand, for example, and dropped, falls to the ground; he is by no means absolutely certain that the same effect would ensue were he to take another stone, or the same stone, with his right hand. It is still uncertain whether this stone, under the same circumstances, would again fall, or whether it would have fallen had i been taken up an hour sooner. This experiment alone gives him no light respecting these particu- lars. The man in question takes another stone, ana observes that it falls likewise, whether dropped from the right hand or from the left : he repeats the ex- periment with a third and a fourth stone, and uni- formly observes the same effect. He hence con- cludes that stones have the property of falling when dropped, or when that which supports them is with- drawn. Here then is an article of knowledge which the man has derived from the experiments which he has made. He is very far from having made trial of every stone, or, supposing him to have done so, what certainty has he that the same thing would happen at all times T He knows nothing as to this, except what concerns the particular moments when he made the experiments ; and what assurance has he that the same effect would take place in the hands of another man? Might he not think that this quality of making stones fall was attached to his hands exclusively ^ A thousand other doubts might still be formed on the subject. I have never, for example, made trial of the stones which compose the cathedral church of Magdeburg, and yet I have not the least doubt that all of them, without exception, are heavy, and that each of them would fall as soon as detached from the building. I even imagine that experience has supplied me with this knowledge, though I have never tried any one of those stones. THE INCREASE OF KNOWLEDGE. 25 This example is sufficient to show how experi- ments made on individual objects only have led mankind to the knowledge of universal propositions; but it must be admitted that the understanding and the other faculties of the soul interfere in a manner which it would be extremely difficult clearly to un- fold ; and if we were determined to be over-scrupu- lous about every circumstance, no progress in sci- ence could be made, for we should be stopped short at every step. It must be allowed, that the vulgar discover in this respect much more good sense than those scru- pulous philosophers who are obstinately determined to doubt of every thing. It is necessary, at the same time, to be on our guard against falling into the opposite extreme, by neglecting to employ the necessary precautions. The three sources from which our knowledge is derived require all of them certain precautions, which must be carefully observed, in order to ac- quire assurance of the truth ; but it is possible, in each, to carry matters too far, and it is always proper to steer a middle course. The third source clearly proves this. It would undoubtedly be extreme folly to believe every thing that is told us ; but excessive distrust would be no less blameworthy. He who is determined to doubt of every thing will never want a pretence ; when a man says or writes that he has seen such or such an action, we may say at once that it is not true, and that the man takes amusement in relating things which may excite surprise ; and if his veracity is beyond suspicion, it might be said that he did not see clearly, that his eyes were dazzled ; and exam- ples are to be found in abundance of persons deceiv- ing themselves, falsely imagining they saw what they did not. The rules prescribed in this respect lose all their weight when you have to do with a wrangler. VOL II. C 26 WHETHER THE ESSENCE OF Usually, in order to be ascertained of the truth of a recital or history, it is required that the author should have been himself a witness of what he re- lates, and that he should have no interest in relating it differently from the truth. If afterward two or more persons relate the same thing, with the same circumstances, it is justly considered as a strong confirmation. Sometimes, however, a coincidence carried to extreme minuteness becomes suspicious. For two persons observing the same incident see it in different points of view ; and the one will always discern certain little circumstances which the other must have overlooked. A slight difference in two several accounts of the same event rather estab- lishes than invalidates the truth of it. But it is always extremely difficult to reason on the first principles of our knowledge, and to attempt an explanation of the mechanism and of the moving powers which the soul employs. It would be glo- rious to succeed in such an attempt, as it would elucidate a great variety of important points respect- ing the nature of the soul and its operations. But we seem destined rather to make use of our facul- ties, than to trace their nature through all its depths. 18th April, 1761. LETTER VI. Whether the Essence of Bodies be known by us. AFTER so many reflections on the nature and faculties of the soul, you will not perhaps be dis- pleased to return to the consideration of body, the principal properties of which I have already en- deavoured to explain. I have remarked, that the nature of body neces- sarily contains three things, extension, impenetrability, and inertia ; so that a being in which these three prop- BODIES BE KNOWN BY US. 27 erties do not meet at once cannot be admitted into the class of bodies ; and reciprocally, when they are united in any one being, no one will hesitate to ac- knowledge it for a body. In these three things, then, we are warranted to constitute the essence of body, though there are many philosophers who pretend that the essence of bodies is wholly unknown to us. This is not only the opinion of the Pyrrhonists, who doubt of every thing ; but there are other sects likewise who main- tain that the essence of all things is absolutely un- known : and, no doubt, in certain respects they have truth on their side : this is but too certain as to all the individual beings which exist. You will easily comprehend, that it would be the height of absurdity were I to pretend so much as to know the essence of the pen which I employ in writing this Letter. If I knew the essence of this pen (I speak not of pens in general, but of that one only now between my fingers, which is an individual 'being, as it is called in metaphysics, and which is distinguished from all the other pens in the world), if I knew, then,' the essence of this individual pen, I should be in a condition to distinguish it from every other, and it would be impossible to change it with- out my perceiving the change; I must know its nature thoroughly, the number and the arrangement of all the parts whereof it is composed. But how far am I from having such a knowledge ! Were I to rise but for a moment, one of my children might easily change it, leaving another in its room, with- out my perceiving the difference ; and were I even to put a mark upon it, how easily might that mark be counterfeited on another pen. And supposing this impossible for my children, it must, always be admitted as possible for God to make another pen so similar to this that I should be unable to discern any difference. It would be, however, another pen, really distinguishable from mine, and God would 28 WHETHER THE ESSENCE OF undoubtedly know the difference of them ; in other words, God perfectly knows the essence of both the one and the other of these two pens : but as to me, who discern no difference, it is certain that the essence is altogether beyond my knowledge. The same observation is applicable to all other individual things ; and it may be confidently main- tained, that God alone can know the essence or nature of each. It were impossible to fix on any one thing really existing of which we could have a knowledge so perfect as to put us beyond the reach of mistake : this is, if I may use the expression, the impress of the Creator on all created things, the nature of which will ever remain a mystery to us. It is undoubtedly certain, then, that we do not know the essence of individual things, or all the characters whereby each is distinguished from every other ; but the case is different with respect to genera and species : these are general notions which include at once an infinite number of individual things. They are not beings actually existing, but notions which we ourselves form in our minds when we arrange a great many individual things in the same class, which we denominate a species or genus, according as the number of individual things which it comprehends is greater or less. And to return to the example of the pen, as there are an infinite number of things to each of which I give the same name, though they all differ one from another, the notion of pen is a general idea, of which we ourselves are the creators, and which exists only in our own minds. This notion contains but the common characters which constitute the essence of the general notion of a pen ; and this essence must be well known to us, as we are in a condition to distinguish all the things which we call pens from those which we do not comprehend under that appellation. As soon as we remark in any thing certain char BODIES BE KNOWN BY US. 29 acters, or certain qualities, we say it is a pen ; and we are in a condition to distinguish it from all other things which are not pens, though we are very far from being able to distinguish it from other pens. The more general a notion is, the fewer it contains of the characters which constitute its essence ; and it is accordingly easier also to discover this essence. We comprehend more easily what is meant by a tree in general than by the term cherry-tree, pear- tree, or apple-tree ; that is, when we descend to the species. When I say such an object which I see in the garden is a tree, I run little risk of being mis- taken; but it is extremely possible I might be wrong if I affirmed it was a cherry-tree. It follows, then, that I know much better the essence of tree in general than of the species ; I should not so easily confound a tree with a stone as a cherry-tree with a plum-tree. Now a notion in general extends infinitely fur- ther; its essence accordingly comprehends only the characters which are common to all beings bear- ing the name of bodies. It is reduced, therefore, to a very few particulars, as we must exclude from it all the characters which distinguish one body from another. It is ridiculous, then, to pretend with certain phi- losophers that the essence of bodies in general is unknown to us. If it were so, we should never be in a condition to affirm with assurance that such a thing is a body, or it is not ; and as it is impossible we should be mistaken in this respect, it necessarily follows that we know sufficiently the nature or es- sence of body in general. Now this knowledge is reduced to three articles : extension, impenetrability, and inertia. 21st April, 1761. C2 30 TRUE NOTION OF EXTENSION. LETTER VII. The True Notion of Extension. I HAVE already demonstrated that the general notion of body necessarily comprehends these three qualities, exterasion, impenetrability, and inertia, without which no being can be ranked in the class of bodies. Even the most scrupulous must allow the necessity of these three qualities in order to constitute a body ; but the doubt with some is, Are these three characters sufficient? Perhaps, say they, there may be several other characters which are equally necessary to the essence of body. But I ask, were God to create a being divested of these other unknown characters, and that it pos- sessed only the three above mentioned, would they hesitate to give the name of body to such a being ? No, assuredly ; for if they had the least doubt on the subject, they could not say with certainty that the stones in the street are bodies, because they are not sure whether the pretended unknown characters are to be found in them or not. Some imagine that gravity is an essential property of all bodies, as all those which we know are heavy; but were God to divest them of gravity, would they therefore cease to be bodies 1 Let them consider the heavenly bodies, which do not fall downward ; as must be the case if they were heavy as the bodies which we touch, yet they give them the same name. And even on the supposition that all bodies were heavy, it would not follow that gravity is a property essential to them, for a body would still remain a body, though its gravity were to be destroyed by a miracle. But this reasoning does not apply to the three es- sential properties above mentioned. Were God to TRUE NOTION OF EXTENSION. 31 annihilate the extension of a body, it would cer- tainly be no longer a body; and a body divested of impenetrability would no longer be lody ; it would be a spectre, a phantom : the same holds as to inertia. You know that extension is the proper object of geometry, which considers bodies only in so far as they are extended, abstractedly from impenetrability and inertia ; the object of geometry, therefore, is a notion much more general than that of body, as it comprehends, not only bodies, but all things simply extended, without impenetrability, if any such there be. Hence it follows that all the properties deduced In geometry from the notion of extension must like- wise take place in bodies, inasmuch as they are ex- tended ; for whatever is applicable to a more general notion, to that of a tree, for example, must likewise be applicable to the notion of an oak, an ash, an elm, &c. ; and this principle is even the foundation of all the reasonings in virtue of which we always affirm and deny of the species, and of individuals, every thing that we affirm and deny of the genus. There are however philosophers, particularly among our contemporaries, who boldly deny that the properties applicable to extension in general, that is, according as we consider them in geometry, take place in bodies really existing. They allege that geometrical extension is an abstract being, from the properties of which it is impossible to draw any conclusion with respect to real objects ; thus, when I have demonstrated that the three angles of a tri- angle are together equal to two right anglesj this is a property belonging only to an abstract triangle, and not at all to one really existing. But these philosophers are not aware of the per- plexing consequences which naturally result from the difference which they establish between objects formed by abstraction and real objects ; and if it were not permitted to conclude frota the first to the 32 TRUE NOTION OF EXTENSION. last, no conclusion, and no reasoning whatever, could subsist, as we always conclude from general notions to particular. Now all general notions are as much abstract beings as geometrical extension; and a tree in general, or the general notion of trees, is formed only by abstraction, and no more exists out of our mind than geometrical extension does. The notion of man in general is of the same kind, and man in general nowhere exists : all men who exist are in- dividual beings, and correspond to individual notions. The general idea which comprehends all is formed only by abstraction. The fault which these philosophers are ever find- ing with geometricians, for employing themselves about abstractions merely, is therefore groundless, as all other sciences principally turn on general no- tions, which are no more real than the objects of geometry. The patient, in general, whom the phy- sician has in view, and the idea of whom contains all patients really existing, is only an abstract idea ; nay, the very merit of each science is so much the greater, as it extends to notions more general, that is to say, more abstract. I shall endeavour by next post to point out me tendency of the censures pronounced by these phi- losophers upon geometricians ; and the reasons why they are unwilling that we should ascribe to real ex- tended beings, that is, t.o existing bodies, the proper- ties applicable to extension in general, or to ab- stracted extension. They are afraid lest their meta- physical principles should suffer in the cause. 25th April, 1761. DIVISIBILITY OF EXTENSION. 33 LETTER VIII. Divisibility of Extension in infinitum. THE controversy between modern philosophers and geometricians, to which I have alluded, turns on the divisibility of body. This property is undoubt- edly founded on extension ; and it is only in so far as bodies are extended that they are divisible, and capable of being reduced to parts. You will recollect that Fig. 38. in geometry it is always A B c D E F o2 , ? m J * ame Cm T nt navi S ator remarks, that if one persok S2nThnnl^ h '" SeV T dayS ' k WOUld have re q uired that 80,000 *n, J r e Start K d at the creation of the w rld to have com- e p n " meratlon at ^ P resent time.-See Scoresby's Account of - Mt AND ON MONADS. 45 works of the Almighty, whose power knows no bounds, whether as to great objects or small. To imagine, that after having divided a body into a great number of parts, we arrive at length at par- ticles so small as to defy all further division, is there- fore the indication of a very contracted mind. But supposing it possible to descend to particles so mi- nute as to be, in their own nature, no longer divisi- ble, as in the case of the supposed monads ; before coming to this point, we shall have a particle com- posed of only two monads, and this particle will be of a certain magnitude or extension, otherwise it could not have been divisible into these two monads. Let us further suppose that this particle, as it has some extension, may be the thousandth part of an inch, or still smaller if you will for it is of no im- portance ; what I say of the thousandth part of an inch may be said with equal truth of every smaller part. This thousandth part of an inch, then, is com- posed of two monads, and consequently two monads together would be the thousandth part of an inch, and two thousand times nothing a whole inch ; the absurdity strikes at first sight. The partisans of the system of monads accordingly shrink from the force of this argument, and are re- duced to a terrible nonplus when asked how many monads are requisite to constitute an extension. Two, they apprehend, would appear insufficient, they therefore allow that more must be necessary. But if two monads cannot constitute extension, as each of the two has none, neither three, nor four, nor any number whatever will produce it ; and this Completely subverts the system of monads. QthMay, 1761. 46 REPLY TO THE OBJECTIONS OF LETTER XII. Reply to the Objections of the Monadists to Divisibility in infinitum. THE partisans of monads are far from submitting to the arguments adduced to establish the divisibility of body to infinity. Without attacking them directly, they allege that divisibility in infinitum is a chi- mera of geometricians, and that it is involved in con- tradiction. For if each body is divisible to infinity, it would contain an infinite number of parts, the smallest bodies as well as the greatest ; the number of these particles to which divisibility in infinitum would lead, that is to say, the most minute of which bodies are composed, will then be as great in the smallest body as in the largest, this number being infinite in both; and hence the partisans of monads triumph in their reasoning as invincible. For if the number of ultimate particles of which two bodies are composed is the same in both, it must follow, say they, that the bodies are perfectly equal to each other. Now this goes on the supposition that the ulti- mate particles are all perfectly equal to each other ; for if some were greater than others, it would not be surprising -that one of the two bodies should be much greater than the other. But it is absolutely neces- sary, say they, that the ultimate particles of all bodies should be equal to each other, as they no longer have any extension, and their magnitude abso- lutely vanishes, or becomes nothing. They even form a new objection, by alleging that all bodies would be composed of an infinite number of nothings, which is a still greater absurdity. I readily admit this ; but I remark, at the same time, that it ill becomes them to raise such an ob- THE MONADISTS TO DIVISIBILITY. 47 jection, seeing they maintain that all bodies are composed of a certain number of monads, though, relatively to magnitude, they are absolutely nothings: so that by their own confession several nothings are capable of producing a body. They are right in saying their monads are not nothings, but beings endowed with an excellent quality, on which the na- ture of the bodies which they compose is founded. Now, the only question here is respecting extension ; and as they are under the necessity of admitting that the monads have none, several nothings, according to them, would always be something. But I shall push this argument against the system of monads no farther ; my object being to make a direct reply to the objection founded on the ultimate particles of bodies, raised by the monadists in sup- port of their system, by which they flatter themselves in the confidence of a complete victory over the partisans of divisibility in infinitum. I should be glad to know, in the first place, what they mean by the ultimate particles of bodies. In their system, according to which every body is com- posed of a certain number of monads, I clearly com- prehend that the ultimate particles of a body are the monads themselves which constitute it ; but in the system of divisibility in infinitum, the term ultimate particle is absolutely unintelligible. They are right in saying, that these are the pai tides at which we arrive from the division of bodies, after having continued it to infinity. But this is just the same thing with saying, after having finished a division which never comes to an end. For divisi- bility in infinitum means nothing else but the pos- sibility of always carrying on the division, without ever arriving at the point where it would be neces- sary to stop. He who maintains divisibility in in- finitum boldly denies, therefore, the existence of the ultimate particles of body; and it is a manifest con- STRONGEST SUPPORT tradiction to suppose at once ultimate particles and divisibility in infinitum. I reply, then, to the partisans of the system of monads, that their objection to the divisibility of body to infinity would be a very solid one, did that system admit of ultimate particles; but being ex- pressly excluded from it, all this reasoning of course falls to the ground. It is false, therefore, that in the system of divisi- bility in infinitum bodies are composed of an infinity of particles. However closely connected these two propositions may appear to the partisans of monads, they manifestly contradict each other ; for whoever maintains that body is divisible in infinitum, or with- out end, absolutely denies the existence of ultimate particles, and consequently has no concern in the question. The term can only mean such particles as are no longer divisible an idea totally inconsistent with the system of divisibility in infinitum. This formidable attack, then, is completely repelled LETTER XIII, Principle of the Sufficient Reason, the strongest Support of the Monadists. You must be perfectly sensible that one of the two systems which have undergone such ample discus- sion is necessarily true, and the other false, seeing they are contradictory. It is admitted on both sides that bodies are divisi- ble ; the only question is, Whether this divisibility is limited ? or, Whether it may always be carried further, without the possibility of ever arriving- at indivisible particles 1 The system of monads is established in the former case, since after having divided a body into indivisi- OF THE MONADISTS. 49 ble particles, these very particles are monads, and there would be reason for saying that all bodies are composed of them, and each of a certain determinate number. Whoever denies the system of monads must likewise, then, deny that the divisibility of bodies is limited. He is under the necessity of maintaining that it is always possible to carry this divisibility further, without ever being obliged to stop ; and this is the case of divisibility in infinitum, on which system we absolutely deny the existence of ultimate particles ; consequently the difficulties resulting from their infinite number fall to the ground of themselves. In denying monads, it is impossible to talk any longer of ultimate particles, and still less of the number of 'them which enters into the com- position of each body. You must have remarked that what t have hitherto produced in support of the system of monads is des- titute of solidity. I now proceed to inform you, that its supporters rest their cause chiefly on the great principle of the sufficient reason, which they know how to employ so dexterously that by means of it they are in a condition to demonstrate whatever suits their purpose, and to demolish whatever makes against them. The great discovery made, then, is this, That nothing can be without a sufficient reason : and to modern philosophers we stand indebted for it. In order to give you an idea of this principle, you have only to consider, that in every thing presented to you, it may always be asked, Why is it such? And the answer is, what they call the sufficient rea- son, supposing it really to correspond with the ques- tion proposed. Wherever the why can take place, the possibility of a satisfactory answer is taken for granted, which shall, of course, contain the sufficient reason of the thing. This is very far, however, from being a mystery of modern discovery. Men in every age have asked why an incontestable proof of their conviction that VOL. II. E 50 STRONGEST SUPPORT every thing must have a satisfying reason of its ex- istence. This principle, that nothing is without a cause, was very well known to ancient philosophers ; but unhappily this cause is for the most part concealed from us. To little purpose do we ask why ; no one is qualified to assign the reason. It is not a matter of doubt that every thing has its cause ; but a pro- gress thus far hardly deserves the name ; and so long as it remains concealed, we have not advanced a single step in real knowledge. You may perhaps imagine that modern philoso- phers, who make such a boast of the principle of a sufficient reason, have actually discovered that of all things, and are in a condition to answer every why that can be proposed to them ; which would un- doubtedly be the very summit of human knowledge : but in this respect they are just as ignorant as their neighbours ; their whole merit amounts to no more than a pretension to have demonstrated, that wher- ever it is possible to ask the question why, there must be a satisfactory answer to it, though concealed from us. They readily admit that the ancients had a know- ledge of this principle, but a knowledge very ob- scure ; whereas they pretend to have placed it in its clearest light, and to have demonstrated the truth ot it and therefore it is that they know how to turn it most to their account, and that this principle puts them in a condition to prove that bodies are com- posed of monads. Bodies, say they, must have their sufficient reason somewhere ; but if they were divisible to infinity, such reason could not take place ; and hence they conclude, with an air altogether philosophical, that as every thing must have its sufficient reason, it ts absolutely necessary that all bodies should le composed of monads which was to be demonstrated. 1 his, 1 must admit, is a demonstration not to be resisted. It were greatly to be wished that a reasoning so OF THE MONADISTS. 51 slight could elucidate to us questions of this import- ance ; but I frankly confess I comprehend nothing of the matter. They talk of the sufficient reason of bodies, by which they mean to reply to a certain wherefore, which remains unexplained. But it would be proper, undoubtedly, clearly to understand and carefully to examine a question, before a reply is attempted ; in the present case, the answer is given before the question is formed. Is it asked, Why do bodies exist ? It would be ridiculous, in my opinion, to reply, Because they are composed of monads ; as if they contained the cause of that existence. Monads have not created bodies ; and when I ask, Why such a being exists T: I see no other reason that can be given but this, Because the Creator has given it existence ; and as to the man- ner in which creation is performed, philosophers, I think, would do well honestly to acknowledge their ignorance. But they maintain, that God could not have pro- duced bodies without having created monads, which were necessary to form the composition of them. This manifestly supposes that bodies are composed of monads, the point which they meant to prove by this reasoning. And you are abundantly sensible, that it is not fair reasoning to take for granted the truth of a proposition which you are bound to prove by reasoning. It is a sophism known in logic by the name of a petitio principii, or begging the quea tion. Wth May, 1761, 52 ANOTHER ARGUMENT LETTER XIV. Another Argument of the Monadists, derived from the Principle of the Sufficient Reason. Absurdities re- sulting from it. THE partisans of monads likewise derive their grand argument from the principle of the sufficient reason, by alleging that they could not even com- prehend the possibility of bodies, if they were divisi- ble to infinity, as there would be nothing in them capable of checking imagination ; they must have ultimate particles or elements, the composition of which must serve to explain the composition of bodies. But do they pretend to understand the possibility of all the things which exist ? This would savour too much of pride ; nothing is more common among philosophers than this kind of reasoning I cannot comprehend the possibility of this, unless it is such as I imagine it to be : therefore it necessarily must be such. You clearly comprehend the frivolousness of such reasoning ; and that in order to arrive at truth, re- search much more profound must be employed. Ig- norance can never become an argument to conduct us to the knowledge of truth, and the one in question is evidently founded on ignorance of the different manners which may render the thing possible. But on the supposition that nothing exists but that whose possibility they are able to comprehend, is it possible for them to explain how bodies would be composed of monads ! Monads, having no exten- sion, must be considered as points in geometry, or as we represent to ourselves spirits and souls. Now it is well known that many geometrical points, let the number be supposed ever so great, never can OF THE MONADISTS. 53 produce a line, and consequently still less a surface, or a body. If a thousand points were sufficient to constitute the thousandth part of an inch, each of these must necessarily have an extension, which taken a thousand times would become equal to the thousandth part of an inch. Finally, it is an incon- testable truth, that take any number of points you will, they can never produce extension. I speak here of points such as we conceive in geometry, without any length, breadth, or thickness, and which in that respect are absolutely nothing. Our philosophers accordingly admit that no ex- tension can be produced by geometrical points, and they solemnly protest that their monads ought not to be confounded with these points. They have no more extension than points, say they ; but they are invested with admirable qualities, such as represent- ing to them the whole universe by ideas, though ex- tremely obscure ; and these qualities render them proper to produce the phenomenon of extension, or rather that apparent extension which I formerly mentioned. The same idea, then, ought to be formed of monads as of spirits and souls, with this difference, that the faculties of monads are much more imperfect. The difficulty appears to me by this greatly in- creased ; and I flatter myself you will be of my opinion that two or more spirits cannot possibly be joined so as to form extension. Several spirits may very well form an assembly or a council, but never an extension ; abstraction made of the body of each counsellor, which contributes nothing to the delibe- ration going forward, for this is the production of spirits only ; a council is nothing else but an assem- bly of spirits or souls : but could such an assembly represent an extension] Hence it follows that monads are still less proper to produce extension than geometrical points are. The partisans of the system, accordingly, are not E2 54 ARGUMENT OF THE MONADISTS. agreed as to this point. Some allege, that monads are actual parts of bodies ; and that after having divided a body as far as possible, you then arrive at the monads which constitute it. Others absolutely deny that monads can be con- sidered as constituent parts of bodies ; according to them, they contain only the sufficient reason : while the body is in motion, the monads do not stir, but they contain the sufficient reason of motion. Finally, they cannot touch each other ; thus, when my hand touches a body, no one monad of my hand touches a monad of the body. What is it then, you will ask, that touches in this case, if it is not the monads which compose the hand and the body T The answer must be, that two no- things touch each other, or rather it must be denied that there is a real contact. It is a mere illusion, destitute of all foundation. They are under the ne- cessity of affirming the same thing of all bodies, which, according to these philosophers, are only phantoms formed by the imagination, representing to itself very confusedly the monads which contain the sufficient reason of all that we denominate body. In this philosophy every thing is spirit, phantom, and illusion ; and when we cannot comprehend these mysteries, it is our stupidity that keeps up an attach- ment to the gross notions of the vulgar. The greatest singularity in the case is, that these philosophers, with a design to investigate and explain the nature of bodies and of extension, are at last re- duced to deny their existence. This is undoubtedly the surest way to succeed in explaining the phe- nomena of nature ; you have only to deny them, and to allege in proof the principle of the sufficient rea- son. Into such extravagances will philosophers run rather than acknowledge their ignorance. 19th May, 1761.- SYSTEM OF MONADS. 55 LETTER XV. Reflections on the System of Monads. IT would be a great pity, however, that this inge- nious system of monads should crumble into ruins. It has made too much noise, it has cost its partisans too many sublime and profound speculations, to be permitted to sink into total oblivion. It will evei remain a striking monument of the extijavagance into which the spirit of philosophizing may run. It is well worth while, then, to present you with a more particular account of it. It is necessary, first of all, to banish from the mind every thing corporeal all extension, all motion, all time and spacefor all these are mere illusion. Nothing exists in the world but monads, the number of which undoubtedly is prodigious. No one monad is to be found in connexion with others ; and it is demonstrated by the principle of the sufficient rea- son that monads can in no manner whatever act upon each other. They are indeed invested with powers, but these are exerted only within themselves, without having the least influence externally. These powers, with which each monad is endowed, have a tendency only to be continually changing their own state, and consist in the representation of all other monads. My soul, for example, is a mo- nad, and contains in itself ideas of the state of all other monads. These ideas are for the most part very obscure ; but the powers of my soul are con- tinually employed in their further elucidation, and in carrying them to a higher degree of clearness. Other monads have, in this respect, a sufficient re- semblance to my soul; each is replete with a pro- digious quantity of obscure ideas of all other monads, and of their state ; and they are continually exerting REFLECTIONS ON THE themselves with more or less success in unfolding- ofcle * ' and ln carrying them to a hi her degree Such monads as have succeeded better than I have one are spirits more perfect; but the greater part 11 remain in a state of stagnation, in the greatest obscurity of their ideas ; and when they are the ob- ject of the ideas of my soul, they produce in it the illusory and chimerical idea of extension and of body. As often as my soul thinks of bodies and of ration, this proves that a great quantity of other monads are still buried in their obscurity; it is like- wise when I think of them that my soul forms within the idea of some extension, which is conse- quently nothing but mere illusion. The more monads there are plunged in the abyss of the obscurity of their ideas, the more is my soul dazzled with the idea of extension ; but when they come to clear up their obscure ideas, extension seems ;o me to dimmish, and this produces in my soul the illusory idea of motion. n,T OU u Wi11 ask ' no doubt ' how m Y soul perceives that other monads succeed in developing their obscure ideas, seeing there is no connexion between them and me The partisans of the system of monads are ready with this reply, that it takes place conform- ably to the perfect harmony which the Creator (who s himself only a monad) has established between monads, by which each perceives in itself, as in a mirror, every development produced in others, with- out any manner of connexion between them. t is to be hoped, then, that all monads may at length become so happy as to clear up their obscure ideas, and then we should lose all ideas of body and of motion ; and the illusion, arising merely from the obscurity of ideas, would entirely cease. * But there is little appearance of the arrival of this blessed state ; most monads, after having acquired the capacity of clearing up their obscure ideas, sud- SYSTEM OF MONADS. 57 denly relapse. When shut up in my chamber, I perceive myself but of small extension, because several monads have then unfolded their ideas ; but as soon as I walk abroad, and contemplate the vast ex- panse of heaven, they must all have relapsed into their state of dulness. There is no change of place or of motion; all that is illusion merely: my soul remains almost always in the same place, just as all other monads. But when it begins to unfold some ideas which before were but very obscure, it appears to me then that I am approaching the object which they repre- sent to me, or rather that which the monads of such idea excite in me ; and this is the real explanation of the phenomenon, when it appears to us that we are approaching to certain objects. It happens but too frequently that the elucida- tions we had acquired are again lost ; then it appears to us that we are removing from the same object. And here we must look for the true solution of our journeyings. My idea, for example, of the city of Magdeburg is produced by certain monads, of which at present I have but very obscure ideas ; and this is the reason why I consider myself as at a distance from Magdeburg. Last year these same ideas sud- denly became clear, and then I imagined I was travelling to Magdeburg, and that I remained there several days. This journey, however, was an illu- sion merely, for my soul never stirs from its place. It is likewise an illusion when you imagine yourself absent from Berlin, because the confused repre- sentation of certain monads excites an obscure idea of Berlin, which you have only to clear up, and that instant you are at Berlin. Nothing more is neces- sary. What we call journeys, and on. which we expend so much money, is mere illusion. Such is the real plan of the system of monads. You will ask, Is it possible there ever should have been persons of good sense who seriously maintained 58 REFLECTIONS ON THE these extravagances 1 I reply, there have been but too many, that I know several of them, that there are some at Berlin, nay, perhaps at Magdeburg. 23d May, 1761. LETTER XVI. Continuation. THE system of monads, such as I have been de- scribing it, is a necessary consequence from the principle that bodies are compounded of simple beings. The moment this principle is admitted, you are obliged to acknowledge the justness of all the other consequences, which result from it so naturally that it is impossible to reject any one, however absurd and contradictory. First, these simple beings, which must enter into the composition of bodies, being monads which have no extension, neither can their compounds, that is bodies, have any; and all these extensions become illusion and chimera, it being certain that parts des- titute of extension are incapable of producing a real extension ; it can be at most an appearance c phantom, which dazzles by a fallacious idea of exten- sion. In a word, every thing becomes illusion ; and upon this is founded the system of pre-established harmony, the difficulties of which I have already P lfis $ecessary then to take care that we be not entangled in this labyrinth of absurdities If you makel single false step over the threshold, you are involved beyond the power of escaping. Iwery thing depends on the first ideas formed of extension : and the manner in which the partisans of the system of monads endeavour to establish it is extremely -i nese pnuusupu do not like to speak of the ex- tension of bodies, because they clearly foresee that SYSTEM OF MONADS. 59 it must become fatal to them in the sequel; but instead of saying that bodies are extended, they denominate them compound beings, which no one can deny, as extension necessarily supposes divisi- bility, and consequently a combination of parts which constitute bodies. But they presently make a wrong use of this notion of a compound being. For, say they, a being can be compounded only so far as it is made up of simple beings ; and hence they conclude that every body is compounded of simple beings. As soon as you grant them this conclusion, you are caught beyond the power of retreating ; for you are under the necessity of admitting that these simple beings, not being compounded, are not extended. This captious argument is exceedingly seductive. If you permit yourself to be dazzled with it, they have gained their point. Only admit this proposi- tion, bodies are compounded of simple beings, that is, of parts which have no extension, and you are entangled. With all your might, then, resist this assertion every compound being is made up of simple beings ; and though you may not be able directly to prove the fallacy, the absurd consequences which immediately result would be sufficient to over- throw it. In effect, they admit that bodies are extended; from this point the partisans of the system of mo- nads set out to establish the proposition that they are compound beings ; and having hence deduced that bodies are compounded of simple beings, they are obliged to allow that simple beings are incapable of producing real extension, and consequently that the extension of bodies is mere illusion. Ah argument whose conclusion is a direct con- tradiction of the premises is singularly strange: this reasoning sets out with advancing that bodies are extended ; for if they were not, how could it be known that they are compound beings and then conies the conclusion that they are not so. Never QO REFLECTIONS ON THE was a fallacious argument, in my opinion, more com- pletely refuted than this has been The' question was, Why are bodies extended? And, after a little turning and winding, it is answered, Because they ao?so. Were I to be asked, Why has a triangle three sides ! and I should reply that it is a mere illu- sionwould such a reply be deemed satisfactory 5 It is therefore certain that this proposition, "Every compound being- is necessarily made up ol simple beings," leads to a false conclusion however well founded it may appear to the partisans of monads, who even pretend to rank it among tn< axioms or first principles of human knowledge The absurdity in which it immediately issues is sut- ficient to overturn it, were there no other reasc for calling it in question. But as a compound being here means the same thing as an extended being, it is just as it it were affirmed, " Every extended being is compounded of beings which are not so." And this is precisely the question. It is asked, Whether on dividing a body you arrive at length at parts unsusceptible oi any further division, for want of extension ; or, Whether you never arrive at particles such as that the divis] bility should be unbounded ' In order to determine this important question, lo the sake of argument let it be supposed that every body is compounded of parts without extension. Certain specious reasonings may easily be employed, drawn from the noted principle of the sufficient rea- son ; and it will be said that a compound being can have its sufficient reason only in the simple beings which compose it; which might be true if the com- pound being were in fact made up of simple beings, the very point in question; and whenever this com- position is denied, the sufficient reason becomes totally inapplicable. But it is dangerous to enter the lists with persons who believe in monads ; for, besides that there SYSTEM OF MONADS. 61 nothing to be gained, they loudly exclaim that you are attacking the principle of the sufficient reason, which is the basis of all certainty, even of the ex- istence of God. According to them, whoever refuses to admit monads, and rejects the magnificent fabric, in which every thing is illusion, is an infidel and an atheist. Sure I am that such a frivolous imputation will not make the slightest impression on your mind, but that you will perceive the wild extravagances into which men are driven when they embrace the system of monads a system too absurd to need a refutation in detail ; their foundation being absolutely reduced to a wretched abuse of the principle of the sufficient reason. 2Gth May, 1761. LETTER XVII. Conclusion of Reflections on this System. WE are under the necessity of acknowledging the divisibility of bodies in infinitum, or of admitting the system of monads, with all the extravagances result- ing from it ; there is no other choice an alternative which supplies the partisans of that system with another formidable argument in support of it. They pretend, that by divisibility in infinitum we are obliged to ascribe to bodies an infinite quality, whereas it is certain that God alone is infinite. The partisans of the system of monads are very dangerous persons ; they accused us of atheism, and now they charge us with polytheism, alleging that we ascribe to all bodies infinite perfections. Thus we should be much worse than pagans, who only worship certain idols, whereas we are accused of paying homage to all bodies, as so many divinities. A dreadful imputation, no doubt, were it well founded; and I should certainly prefer embracing VOL. II. F 62 REFLECTIONS ON THE the system of monads, with all the chimeras and illusions which flow from it, to a declaration in favour of divisibility in infinitum, if it involved a conclusion so impious. You will allow, that to reproach one's adversaries with atheism or idolatry is a very strange mode of arguing; but where do they find us ascribing to bodies this divine infinity'? Are they infinitely powerful, wise, good, or happy 1 ? By no means: we only affirm, that on dividing bodies, though the division be carried on ever so far, it will always be possible to continue it further, and that you never can arrive at indivisible particles. It may accord- ingly be affirmed, that the divisibility of bodies is without limits ; and it is improper to use the term infinity, which is applicable to God alone. I must remark at the same time, that the word " infinity" is not so dangerous as these philosophers insinuate. In saying, for example, infinitely wicked, nothing is more remote from the perfections of God. They admit that our souls will never have an end, and thus Acknowledge an infinity in the duration of the soul, without marking the least disrespect to the infinite perfections of God. Again, when you ask them if the extent of the universe is bounded, are they very indecisive in their answer 1 Some of them very frankly allow that the extent of the uni- verse may very probably be infinite without our being able, however far our ideas are carried, to determine its limits. Here then is one infinity more which they do not deem heretical. For a still stronger reason, divisibility in infinitum ought not to give them the least offence. To be divisible to infinity is not surely an attribute which any one could ever think of ascribing to the Supreme Being, and does not confer on bodies a degree of perfection which would not be far from that which these philosophers allow them in compounding SYSTEM OF MONADS. 63 them of monads, which on their system are being? endowed with qualities so eminent that they do not hesitate to give to God himself the denomination of monad. In truth, the idea of a division which may be con tinued without any bounds contains so little of the character of the Deity that it rather places bodies in a rank far inferior to that which spirits and our souls occupy ; for it may well be affirmed that a soul in its essence is infinitely more valuable than all the bodies in the world. But on the system of monads, every body, even the vilest, is compounded of a vast number of monads, whose nature has a great resemblance to that of our souls. Each monad represents to itself the whole world as easily as our souls ; but, say they, their ideas of it are very ob- scure, though we have already clear, and sometimes also distinct ideas of it. But what assurance have they of this difference "? Is it not to be apprehended that the monads which compose the pen wherewith I am writing may have ideas of the universe much clearer than those of my soul ? How can I be assured of the contrary 1 I ought to be ashamed to employ a pen in conveying my feeble conceptions, while the monads of which it consists possibly conceive much more sublimely ; and you might have greater reason to be satisfied, should the pen commit its own thoughts to paper in- stead of mine. In the system of monads that is not necessary ; the soul represents to itself beforehand, by its in- herent powers, all the ideas of my pen, but in a very obscure manner. What I am now taking the liberty to suggest contributes absolutely nothing to your information. The partisans of this system have de- monstrated that simple beings cannot exercise the slightest influence on each other ; and your own soul derives from itself what I have been endeavouring 64 SYSTEM OF MONADS. to convey, without my having any concern in the matter. Conversation, reading, and writing, therefore, are merely chimerical and deceptive formalities, which illusion would impose upon us as the means of ac- quiring and extending knowledge. But I have already had the honour of pointing out to you the wonderful consequences resulting from the system of the pre- established harmony ; and I am apprehensive that these reveries may have become too severe a trial of your patience, though many persons of superior illumination consider this system as the most sub- lime production of human understanding, and are incapable of mentioning it but with the most pro- found respect.* 30tk May, 1761. * It is a consolation to reflect, that philosophy has in modern times divested itself of the lumber of such idle disputations as those of which our author has in the preceding Letters of this, and in several of the former, volume given us so full an account. The disputes about pre- established harmonies, and the nature and existence of monads, and of the essences of things appear 10 have been owing to the want of a just conception of the limitation which Divine Providence has assigned to the powers and faculties of the human mind. Infinity, whether in the great or in the small, is absolutely beyond our reach. That nature car- ries the division of matter both in the organic and inorganic world (as the microscope reveals to us in the astonishing minuteness of animalculae, and as the sense of smelling determines in the diffusion of odours) to an extent beyond our comprehension as to the means employed, no one can doubt; but with respect to the question of infinite divisibility, about which so mucli has been said, although in the abstract it may seem to be established in the affirmative by geometrical reasoning, yet it is the pre- vailing opinion of the present day that there is a limitation in nature of actual divisibility. The atoms or elementary particles of the chymist appear to furnish the ultimatum of the process of nature in the divisibility of matter. That different kinds of matter are constituted of different sorts of simple or elementary atoms, having different qualities or affinities, and that these atoms possess infinite hardness, and cannot therefore be further divided, are propositions which enable us to account more satis- factorily for the chymical changes which are constantly taking place throughout the whole domain of nature, and for the stability of the laws to which those changes are subservient. We know, indeed, little or nothing of the real nature of corpuscular action, but the theory of atomic combinations in stable and definite proportions has diffused a most salu- tary light over the whole surface of chymical science. It will be a grati- fication to every Christian reader to observe the ability with which Euler combats the skeptical philosophy which resulted from the visionary theo- ries which he has so ably confuted. Am. Ed. NATURE OF COLOURS. 65 LETTER XVIII. Elucidation respecting the Nature of Colours. I AM under the necessity of acknowledging, that the ideas respecting colour which I have already taken the liberty to suggest* come far short of that degree of evidence to which I could have wished to carry them. This subject has hitherto proved a stumbling-block to philosophers, and I must not flatter myself with the belief that I am able to clear it of every difficulty. I hope, at the same time, that the elucidations which I am going to submit to your examination may go far towards removing a con- siderable part of them. The ancient philosophers ranked colours among the bodies of which we know only the names. When they were asked, for example, why such a body was red, they answered, it was in virtue of a quality which made it appear red. You must be sensible that such an answer conveys no information, and that it would have been quite as much to the purpose to confess ignorance. Descartes, who first had the courage to plunge into the mysteries of nature, ascribes colours to a certain mixture of light and shade, which last, being nothing else but a want of light, as it is always found where the light does not penetrate, must be incapable of producing the different colours we* observe. Having remarked that the sensations of the organ of sight are produced by the rays which strike that organ, it necessarily follows that those which excite in it the sensation of red must be of quite a different nature from those which produce the sensation of the other colours ; hence it is easily comprehended * See Letters XXVII., XXVIII., and XXXI., in vol. i. F3 66 ELUCIDATION RESPECTING that each colour is attached to a certain quality of the rays which strike the organ of vision. A body appears to us red when the rays which it emits are of a nature to excite in our eyes the sensation of that colour. The whole, then, results in an inquiry into the difference of the rays which variety of colours pro- duces. This difference must be great to produce so many particular sensations in our eyes. But wherein can it consist ] This is the great question, towards the solution of which our present research is directed. The first difference between rays which presents itself is that some are stronger than others. It can- not be doubted that those of the sun, or of any other body very brilliant, or very powerfully illuminated, must be much stronger than those of a body feebly illuminated, or endowed with a slender degree of light ; our eyes are assuredly struck in a very differ- ent manner by the one and by the other. Hence it might be inferred, that different colours result from the force of the rays of light ; so that the most powerful rays should produce, for example, red ; those which are less so, yellow ; and in pro- gression, green, and blue. But there is nothing more easy than to overturn this system, as we know from experience that the same body always appears to be of the same colour, be it less or more illuminated, or whether its rays be strong or feeble. A red body, for example, ap- pears equally red, exposed to the brightest lustre of the sun, and in the shade, where the rays are ex- tremely faint. We must not, then, look for the cause of the difference of colour in the different de- grees of the force of rays of light, it being possible to represent the same colour as well by very forcible as by very faint rays. The feeblest glimmering serves equally well to discover to us difference of colours, as the brightest effulgence. It is absolutely necessary, therefore, that there THE NATURE OF COLOURS. 67 should be another difference of rays discovered, which may characterize their nature relatively to the different colours. You will undoubtedly con- clude, that in order to discover this difference we must be better acquainted with the nature of lumi- nous rays ; in other words, we must know what it is that, reaching our eyes, renders bodies visible ; this definition of a ray must be the justest, as in effect it is nothing else but that which enters into the eye by the pupil, and excites the sensation in it. I have already informed you that there are only two systems or theories which pretend to explain the origin and nature of rays of light. The one is that of Newton, who considers them as emanations proceeding from the sun and other luminous bodies ; and the other that which I have endeavoured to demonstrate, and of which I have the reputation of being the author, though others have had nearly the same ideas of it. Perhaps I may have succeeded better than they in carrying it to a higher degree of evidence. It will be of importance, then, to show, tn both systems, on what principle the difference of colours may be established. In that of emanation, which supposes the rays to issue from luminous bodies, in the form of rivers, or rather of fountains, spouting out a fluid in all direc- tions, it is alleged that the particles of light differ in size or in substance, as a fountain might emit wine, oil, and other liquids ; so that the different colours are occasioned by the diversity of the subtile matter which emanates from luminous bodies. Red would be, accordingly, a subtile matter issuing from the luminous body, and so of yellow and the other colours. This explanation would exhibit clearly enough the origin of the different colours, if the sys- tem itself had a solid foundation. I shall enter into the subject more at large in my next Letter, 2d June, 176L 08 THE ANALOGY BETWEEN LETTER XIX. Reflections on the Analogy between Colours and Sounds You will be pleased to recollect the objections I offered to the system of the emanation of light.* They appear to me so powerful as completely to overturn that system. I have accordingly succeeded in my endeavours to convince certain natural phi- losophers of distinction, and they have embraced my sentiments of the subject with expressions of singu- lar satisfaction. Rays of light, then, are not an emanation from the sun and other luminous bodies, and do not con- sist of a subtile matter emitted forcibly by the sun, and transmitted to us with a rapidity which may well fill you with astonishment. If the rays employed only eight minutes in their course from the sun to us, the torrent would be terrible,! and the mass of that luminary, however vast, must speedily be ex- hausted. According to my system, the rays of the sun, of which we have a sensible perception, do not proceed immediately from that luminary; they are only par- ticles of ether floating around us, to which the sun communicates nearer and nearer a motion of vibra- tion, and consequently they do not greatly change their place in this motion. This propagation of light is performed m a manner similar to that of sound. A bell, whose sound you hear, by no means emits the particles which enter your ears. You have only to touch it when struck to be assured that all its parts are in a very sensible ! * See Letters XVT1. and XVIIf. in vol. i. t The rapidity of the progress of light, if it be objectionable on the theory of emanation, must be equally so on that of undulation ; for the velocity is a fact derived from observation, and is independent of theory, Am, Ed. COLOURS AND SOUNDS. 69 agitation. This agitation immediately communicates itself to the more remote particles of air, so that all receive from it successively a similar motion of vi- bration, which, reaching the ear, excite in it the sen- sation of sound. The strings of a musical instru- ment put the matter beyond all doubt ; you see them tremble, go and come. It is even possible to deter- termine by calculation how often in a second each string vibrates ; and this agitation, being communi- cated to the particles of air adjacent to the organ of hearing, the ear is struck by it precisely as often in a second. It is the perception of this tremulous agitation which constitutes the nature of sound. The greater the number of vibrations produced by the string in a second, the higher or sharper is the sound. Vibrations less frequent produce lower notes. We find the circumstances which accompany the sensation of hearing, in a manner perfectly analogous, in that of sight. The medium only and the rapidity of the vibra- tions differ. In sound, it is the air through which the vibrations of sonorous bodies are transmitted. But with respect to light, it is the ether, or that me- dium incomparably more subtile and more elastic than air, which is universally diffused wherever the air and grosser bodies leave interstices. As often, then, as this ether is put into a state of vibration, and is transmitted to the eye, it excites in it the sentiment of vision, which is in that case nothing but a similar tremulous motion, whereby the small nervous fibres at the bottom of the eye are agitated. You easily comprehend that the sensation must be different, according as this tremulous agitation is more or less frequent ; or according as the number of vibrations performed in a second is greater or less. Hence there must result a difference similar to that which takes place in sounds, when the vibra- 70 THE ANALOGY BETWEEN tions are more or less frequent. This difference is clearly perceptible by the ear, as the character of sounds in respect of flat and sharp depends on it. You will recollect that the note marked C in the harpsichord performs about 100 vibrations in a sec- ond, note D 112, note E 125, note F 133, note G 150, note A 166, note B 187, and 200. Thus the nature of sounds depends on the number of vibrations per- formed in a second. It cannot be doubted that the sense of seeing may be likewise differently affected, according as the number of vibrations of the nervous fibres of the bottom of the eye is greater or less. When these fibres vibrate 1000 times in a second, the sensation must be quite different from what it would be did they vibrate 1200 or 1500 times in the same space. True it is that the organ of vision is not in a con- dition to reckon numbers so great, still less than the ear is to reckon the vibrations which constitute sound ; but it is always in our power to distinguish between the greater and the less. In this difference, therefore, we must look for the cause of difference of colour ; and it is certain that each of them corresponds to a certain number of vibrations, by which the fibres of our eyes are struck in a second, though we are not as yet in a condition to determine the number corresponding to each par- ticular colour, as we can do with respect to sounds. Much research must have been employed before it was possible to ascertain the numbers correspond- ing to all the notes of the harpsichord, though there was an antecedent conviction that their difference was founded on the diversity of those numbers. Our knowledge respecting these objects is nevertheless considerably advanced, from our being assured that there prevails a harmony so delightful between the different notes of the harpsichord and the different colours ; and that the circumstances of the one serve to elucidate those of the other. This analogy ao*. COLOURS AND SOUNDS. 71 eordingly furnishes the most convincing proofs in support of my system. But I have reasons still more solid to adduce, which will secure it from every attack. bthJune, 1761, LETTER xx k Continuation. NOTHING is more adapted to the communication Of knowledge respecting the nature of vision than the analogy discoverable, almost in every particular, between it and the hearing. Colours are to the eye what sounds are to the ear. They differ from each other as flat and sharp notes differ. ]N"ow we know that flat and sharp in sounds depends on the number of vibrations whereby the organ of hearing is struck in a given time, and that the nature of each is deter- mined by a certain number, which marks the vibra- tions performed in a second. From this I conclude that each colour is likewise restricted to a number of vibrations which act on vision ; with this differ- ence, that the vibrations which produce sound reside in gross air, whereas those of light and colours are transmitted through a medium incomparably more subtile and elastic. The same thing holds as to the objects of both senses. Those of hearing are all of them bodies adapted to the transmission of sound, that is, susceptible of a motion of vibration, or of a tremulous agitation, which, communicating itself to the air, excites in the organ the sensation of a sound corresponding to the rapidity of the vibrations. Such are all musical instruments ; and to confine myself principally to the harpsichord, we ascribe to each string a certain sound which it produces when struck. Thus, one string is named C, another D, and so on. A string is named C when its structure 72 ANALOGY BETWEEN COLOURS AND SOUNDS, and tension are such that, being struck, it produces about 100 vibrations in a second ; and if it produced less or more in the same time, it would have the name of a different note, higher or lower. You will please to recollect that the sound of a string depends on three things its length, its thick- ness, and the degree of tension ; the more it is stretched the sharper its sound becomes ; and as long as it preserves the same disposition, it emits the same sound ; but that changes as soon as the other undergoes any variation. Let us apply this to bodies which are the objects of vision. The minuter particles which compose the tissue of their surface may be considered as strings distended, in as much as they are endowed with a certain degree of elasticity and bulk, so that, being struck, they acquire a motion of vibration, of which they will finish a certain number in a second; and on this number depends the colour which we ascribe to such body. It is red when the particles of its surface have such a degree of tension that, being agitated, they perform precisely so many vi- brations in a second as are necessary to excite in us the sensation of that colour. A degree of tension which would produce vibrations more or less rapid would excite that of a different colour, and then the body would be yellow, green, or blue, &c. We have not as yet acquired the ability of assign- ing to each colour the number of vibrations which constitute its essence ; we do not so much as know which are the colours that require a greater or less rapidity of vibration, or rather, it is not yet deter- mined what colours correspond with high or low notes. It is sufficient to know that each colour is attached to a certain number of vibrations, though it has not hitherto been ascertained ; and that you have only to change the tension of elasticity of the par- ticles which form the surface of a body, to make it change colour. OPAQUE BODIES RENDERED VISIBLE. 73 We see that the most beautiful colours in flowers quickly change and disappear, from a failure of the nutritive juices ; and because their particles lose their vigour or their tension. This, too, is observa- ble in every other change of colour. To place this in a clearer light, let us suppose that the sensation of red requires such a rapidity of vibra- tion, that 1000 are performed in a second ; that orange requires 1125, yellow 1250, green 1333, blue 1500, and violet 1666. Though these numbers are only supposed, this does not affect the object I have in view. What I say as to these numbers will apply in like manner to the really corresponding numbers, if ever they are discovered. A body, then, will be red when the particles of its surface, put in vibration, complete 1000 in a second ; another body will be orange when disposed so as to complete 1 125 in a second, and so on. Hence it is obvious that there must be an endless variety of in- termediate colours between the six principal which I have mentioned ; and it is likewise evident, if the particles of a body, being agitated, should perform 1400 vibrations in a second, it would be of an inter- mediate colour between green and blue ; green cor- responding to number 1333, and blue to 1500. QthJune, 1761. LETTER XXI. How Opaque Bodies are rendered visible. You will find no difficulty in the definition I have been giving of coloured bodies. The particles of their surface are always endowed with a certain degree of elasticity, which renders them suscep- tible of a motion of vibration, as a string is always susceptible of a certain sound ; and it is the number of vibrations which these particles are capable of VOL. II. G 74 OPAQUE BODIES RENDERED VISIBLE. making in a second which determines the species of colour. If the particles of the surface have not elasticity sufficient to admit of such agitation, the body must be black, this colour being nothing else but a depri- vation of light, and all bodies from which no rays are transmitted to our eyes appearing black. I now come to a very important question, re- specting which some doubts may be entertained. It may be asked, What is the cause of the motion of vibration which constitutes the colours of bodies ? Into the discovery of this, indeed, the whole is resolved ; for as soon as the particles of bodies shall be put in motion, the ether diffused through the air will immediately receive a similar agitation, which, continued to our eyes, constitutes there that which we call rays, from which vision proceeds. I remark, first, that the particles of bodies are not put in motion by an internal, but an external power, just as a string distended would remain for ever at rest, were it not put in motion by some external force. Such is the case of all bodies in the dark ; for, as we see them not, it is a certain proof that they emit no rays, and that their particles are at rest. In other words, during the night bodies are in the same state with the strings of an instrument that is not touched, and which emit no sound; whereas bodies rendered visible may be compared to strings which emit sound. And as bodies become visible as soon as they are illuminated, that is, as soon as the rays of the sun, or of some other luminous body, fall upon them, it must follow, that the same cause which illuminates them must excite their particles to generate rays, and to produce in our eyes the sensation of vision. The rays of light, then, falling upon a body, put its particles into a state of vibration. This appears at first surprising, because on ex- posing our hands to the strongest light no sensible OPAQUE BODIES RENDERED VISIBLE. 75 impression is made on them. It is to be considered, that the sense of touch is in us too gross to perceive these subtile and slight impressions ; but that the sense of sight, incomparably more delicate, is powerfully affected by them. This furnishes an in- contestable proof that the rays of light which fall upon a body possess sufficient force to act upon the minuter particles, and to communicate to them a tremulous agitation. And in this precisely consists the action necessary to explain how bodies, when illuminated, are put in a condition themselves to produce rays, by means of which they become visible to us. It is sufficient that bodies should be luminous or exposed to the light, in order to the agitation of their particles, and thereby to their producing themselves rays which render them visible to us. The perfect analogy between hearing and sight gives to this explanation the highest degree of prob- ability. Let a harpsichord be exposed to a great noise, and you will see that not only the strings in general are put into a state of vibration, but you will hear the sound of each, almost as if it were actually touched. The mechanism of this phenome- non is easily comprehended, as soon as it is known that a string agitated is capable of communicating to the air the same motion of vibration which, trans- mitted to the ear, excites in it the sensation of the sound which thai same string emits. Now, as a string produces in the air such a mo- tion, it follows that the air reciprocally acts on the string, and gives it a tremulous motion. And as a noise is capable of putting in motion the strings of a harpsichord, and of extracting sounds from them, the same thing must take place in the objects of vision. Coloured bodies are similar to the strings of a harpsichord, and the different colours to the differ- ent notes, in respect of high and low. The light 76 WONDERS OF THE HUMAN VOICE. which falls on these bodies, being analogous to the noise to which the harpsichord is exposed, acts on the particles of their surface as that noise acts on the strings of the harpsichord ; and these particles thus put in vibration will produce the rays which shall render the body visible. This elucidation seems to me sufficient to dissi- pate every doubt relating to my theory of colours. I flatter myself, at least, that I have established the true principle of all colours, as well as explained how they become visible to us only by the light whereby bodies are illuminated, unless such doubts turn upon some other point which I have not touched upon. 13^ June, 1761. LETTER XXII. The Wonders of the Human Voice. IN explaining the theory of sounds, I considered only two respects in which sounds could differ : the one regarded the force of sound, and I remarked that it is greater in proportion as the vibrations ex- cited in the air are more violent. Thus, the noise of a discharge of cannon, or the ringing of a bell, has more force than that of a string, or of the hu- man voice. The other difference of sounds is totally inde- pendent of this, and refers to flat and sharp, accord- ing to which we say some are low and others high. My remark relatively to this difference made it to depend on the number of vibrations completed in a certain given time, say a second ; so that the greater such number is, the "higher or sharper is the sound; and the smaller it is, the sound is lower or flatter. You can easily comprehend how the same note may be either strong or faint ; accordingly, we see WONDERS OF THE HUMAN VOICE. 77 that the forte and piano employed by musicians change in no respect the nature of sounds. Among the good qualities of a harpsichord, it is required that all the notes should have nearly the same de- gree of strength ; and it is always considered as a great fault when some of the strings are wound up to a greater degree of force than the rest. Now the flat and the sharp are referable only to the simple sounds, whose vibrations follow regularly, and at equal intervals ; and in music we employ only those sounds which are denominated simple. Accords are compound sounds, or the concourse of several produced at once, among the vibrations of which a certain order must predominate, which is the found- ation of harmony. But when no relation among the vibrations is perceptible, it is a confused noise, with which it is impossible to say what note of the harpsichord is in tune, such as the report of a can- non or musket. There is still another remarkable difference among the simple sounds, which seems to have escaped the attention of philosophers. Two sounds may be of equal force, and in accord with the same note of the harpsichord, and yet very different to the ear. The sound of a flute is totally different from that of the French horn, though both may be in tune with the same note of the harpsichord, and equally strong; each sound derives a certain peculiarity from the instrument which emits it, but it is impossible to describe wherein this consists ; the same string too emits different sounds, according as it is struck, touched, or pinched. You can easily distinguish the sound of the horn, the flute, and other musical in- struments. The most wonderful diversity, to say nothing of the variety of articulation in speech, is observable in the human voice, that astonishing masterpiece of the Creator. Reflect but for a moment on the dif- ferent vowels which the mouth simply pronounces G2 78 WONDERS OF THE HUMAN VOICE. or sings. When the vowel a is pronounced or sung 1 , the sound is quite different from that of e, i, o, u, or ai pronounced or sung, though on the same tone. We must not then look for the reason of this differ- ence in the rapidity or order of the vibrations ; no investigation of philosophers has hitherto unfolded this mystery. You must be perfectly sensible, that in order to utter these different vowels, a different conformation must be given to the cavity of the mouth ; and that in man the organization of this part is much better adapted to produce these effects than that of ani- mals. We find, accordingly, that certain birds which learn to imitate the human voice are never capable of distinctly pronouncing the different vowels ; the imitation is at best extremely imperfect. In many organs there is a stop which bears the name of the human voice ; it usually, however, contains only the notes which express the vocal sounds ai or ae. I have no doubt, that with some change it might be possible to produce likewise the other vocal sounds a, e, ', o, w, ou ; but even this would not be sufficient to imitate a single word of the human voice ; for how can we combine them with the consonants, which are so many modifica- tions of the vowels ? We are so conformed, that however common the practice, it is almost impos- sible to trace and explain the real mechanism. We distinctly observe three organs employed in expressing the consonants, the lips, the tongue, and the palate ; but the nose likewise essentially concurs. On stopping it, we become incapable of pronouncing the letters m and n; the sound of b and d only is then to be heard. A striking proof of the marvel- lous structure of our mouth for the pronunciation of the letters undoubtedly is, that all the skill of man has not hitherto been capable of producing a piece of mechanism that could imitate it. The song has ">een exactly imitated, but without any articulation PHENOMENA OF ELECTRICITY. 79 of sounds, and without distinction of the different vowels. The construction of a machine capable of express- ing sounds, with all the articulations, would no doubt be a very important discovery. Were it pos- sible to execute such a piece of mechanism, and bring 1 it to such perfection that it could pronounce all words, by means of certain stops, like those of an organ or harpsichord, every one would be sur- prised, and justly, to hear a machine pronounce whole discourses or sermons together, with the most graceful accompaniments. Preachers and other orators, whose voice is either too weak or disagreeable, might play their sermons or orations on such a machine, as organists do pieces of music. The thing does not seem to me impossible.* IQth June, 1761. LETTER XXIII. A Summary of the principal Phenomena of Electricity. THE subject which I am now going to recommend to your attention almost terrifies me. The variety it presents is immense, and the enumeration of facts serves rather to confound than to inform. The sub- * Pipes have actually been constructed of such forms, by Kratzen- stein and Kempelen, as to imitate very accurately the different vowel sounds produced by the human voice. From this first attempt Kempelen proceeded to analyze the mechanism of speech, and he succeeded in con- structing a speaking machine, which uttered, not only words, but entire sentences. The four letters D, G, K, T, however, baffled all his inge- nuity ; and lie was obliged to substitute for them the letter P, which was so managed as to bear a considerable resemblance to them, so much so, at least, as to deceive the auditory. See the Edinburgh, Encyclopaedia, article ACOUSTICS, vol. i. p. 126; and AUTOMATON, vol. iii. p. 153, where a full account of this machine is given. Ed. The ingenuity of the Swiss mechanicians in constructing artificial birds, dogs, and other animals which emit sounds so nearly resembling those of their prototypes as to deceive many ears, is known to those who have visited the workshops of Geneva, Locle, Chande-lbnd s and other towns. See on this subject Brewster's Natural Magic, No. L. Harper's Family Library. Am. Ed. 80 SUMMARY OF THE PRINCIPAL ject I mean is electricity, which for some time past has become an object of such importance in phy- sics that every one is supposed to be acquainted with its effects. You must undoubtedly have frequently heard it mentioned in conversation ; but I know not whether you have ever witnessed any of the experiments. Natural philosophers of modern times prosecute the study of it with ardour, and are almost every day discovering; new phenomena, the description of which would employ many hundreds of letters ; nay, perhaps I should never have done. And here it is I am embarrassed. I could not bear to think of letting you remain unacquainted with a branch of natural philosophy so essential ; but I would willingly save you the fatigue of wading through a diffuse detail of the phenomena, which after all would not furnish the necessary informa- tion. I flatter myself, however, that I nave dis- covered a road which will lead so directly to the object, that you shall attain a knowledge of it much more perfect than that of most natural philosophers, who devote night and day to the investigation of these mysteries of nature. Without stopping to explain the various appear- ances and effects of electricity, which would engage me in a long and tedious detail, without extending your knowledge of the causes which produce these effects, I shall pursue quite a different course, and begin with unfolding the true principle of nature on which all these phenomena are founded, however various they may appear, and from which they are all easily deducible. It is sufficient to remark, in general, that elec- tricity is excited by the friction of a glass tube. It thereby becomes electrical : and then it alternately attracts and repels light bodies which are applied to it ; and on the application of other bodies, sparks of fire are mutually extracted, which, increased in strength, kindle spirits of wine and other combustible PHENOMENA OF ELECTRICITY. 81 substances. On touching such a tube with the finger, you feel, besides the spark, a puncture which may in certain circumstances be rendered so acute as to produce a commotion through the whole body. Instead of a tube of glass, we likewise employ a globe of glass, which is made to turn round an axis like a turning- wheel. During this motion it is rubbed with the hand, or with a cushion applied to it ; then the globe becomes electric, and produces the same phenomena as the tube. Besides glass, resinous bodies, such as Spanish wax, and sulphur, likewise possess the property of becoming electric by friction; but certain species of bodies only have this quality, of which glass, sealing-wax, and sulphur are the principal. Other bodies undergo friction without producing any such effect ; no sign of electricity appears : but on applying them to the first, when rendered elec- tric, they immediately acquire the same property. They become electric, then, by communication, as they touch ; and frequently the approximation only of electric bodies renders them such. All bodies, therefore, are divisible into two classes ; in the one are included those that become electric by friction, in the other those which are rendered such by communication, whereas friction produces no manner of effect on them. It is very remarkable that bodies of the first class receive no electricity from communication ; when you apply to a tube or globe of glass strongly electrified, other glasses or bodies which friction renders electric, this touch communicates no electricity to them. The distinc- tion of these two classes of bodies is worthy of attention ; the one class being disposed to become electrical by friction only, and not by communica- tion the other, on the contrary, only by com- munication.* * The distinction between these two classes is not so absolute as the author's remark would lead the student to infer. The classes are, with proper precaution, convertible into each other. Am. Ed. 82 TRUE PRINCIPLE OF NATURE, All metals belong to this last class, and the com- munication extends so far, that on presenting one extremity of a wire to an electric body, the other extremity becomes so likewise, be the wire ever so long ; and on applying still another wire to the far- ther extremity of the first, the electricity is conveyed through the whole extent of that second thread and thus electricity may be transmitted to the most remote distances. Water is a substance which receives electricity by communication. Large pools have been electrified to such a degree that the application of the finger has elicited sparks and excited pain. The prevailing persuasion now is, that lightning and thunder are the effect of the electricity which the clouds acquire, from whatever cause. A thunder- storm exhibits the same phenomena of electricity, on the great scale, which the experiments of natural philosophers do in miniature. 20th June, 1761. LETTER XXIV. The true Principle of Nature on which are founded all the Phenomena of Electricity. THE summary I have exhibited of the principal phenomena of electricity has no doubt excited a cu-riosity to know what occult powers of nature are capable of producing effects so surprising. The greatest part of natural philosophers acknow- ledge their ignorance in this respect. They appear to be so dazzled by the endless variety of phenomena which every day present themselves, and by the sin-r gularly marvellous circumstances which accompany these phenomena, that they are discouraged from attempting an investigation of the true cause of them. They readily admit the existence of a subtile ON WHICH ELECTRICITY IS FOUNDED. 83 matter, which is the primary agent in the production of the phenomena, and which they denominate the electric fluid; but they are so embarrassed about determining its nature and properties, that this im- portant branch of physics is rendered only more perplexed by their researches. There is no room to doubt that we must look for the source of all the phenomena of electricity only in a certain fluid and subtile matter ; but we have no need to go to the regions of imagination in quest of it. That subtile matter denominated ether, whose reality I have already endeavoured to demonstrate,* is sufficient very naturally to explain all the sur- prising effects which electricity presents. I hope I shall be able to set this in so clear a light, that you shall be able to account for every electrical phe- nomenon, however strange an appearance it may assume. The great requisite is to have a thorough know- ledge of the nature of ether. The air which we breathe rises only to a certain height above the sur- face of the earth ; the higher you ascend the more subtile it becomes, and at last it entirely ceases. We must not affirm that beyond the region of the air there is a perfect vacuum which occupies the im- mense space in which the heavenly bodies revolve. The rays of light, which are diffused in all directions from these heavenly bodies, sufficiently demonstrate that those vast spaces are filled with a subtile matter. If the rays of light are emanations forcibly pro- jected from luminous bodies, as some philosophers have maintained, it must follow that the whole space of the heavens is filled with these rays nay, that they move through it with incredible rapidity. You have only to recollect the prodigious velocity with which the rays of the sun are transmitted to us. On this hypothesis, not only would there be no * See Letter XV. vol. 1. 84 PHENOMENA OF ELECTRICITY. vacuum, but all space would be filled with a subtile matter, and that in a state of constant and most dreadful agitation. But I think I have clearly proved that rays of light are no more emanations projected from lumi- nous bodies than sound is from sonorous bodies. It is much more certain that rays of light are no- thing else but a tremulous motion or agitation of a subtile matter, just as sound consists of a similar agitation excited in the air. And as sound is pro- duced and transmitted by the air, light is produced and transmitted by that matter, incomparably more subtile, denominated ether, which consequently fills the immense space between the heavenly bodies. Ether, then, is a medium proper for the transmis- sion of rays of light : and this same quality puts us in a condition to extend our knowledge of "its nature and properties. We have only to reflect on the properties of air, which render it adapted to the re- ception and transmission of sound. The principal cause is its elasticity or spring. You know that air has a power of expanding itself in all directions, and that it does expand the instant that obstacles are removed. The air is never at rest but when its elasticity is everywhere the same ; whenever it is greater in one place than another the air imme- diately expands. We likewise discover by experi- ment that the more the air is compressed, the more its elasticity increases : hence the force of air-guns, in which the air, being very strongly compressed, is capable of discharging the ball with astonishing ve- locity. The contrary takes place when the air is rarefied : its elasticity becomes less in proportion as it is more rarefied, or diffused over a larger spac^. On the elasticity of the air, then, relative to its density, depends the velocity of sound, which makes a progress of 1 142 feet in a second. If the elasticity of the air were increased, its density remaining the same, the velocity of sound would increase ; and the DIFFERENT NATURE OF BODIES. 85 same thing would take place if the air were more rare or less dense than it is, its elasticity being the same. In general, the mere that any medium, simi- lar to air, is elastic, and at the same time less dense, the more rapidly will the agitations excited in it be transmitted. And as light is transmitted so many thousand times more rapidly than sound, it must clearly follow that the ether, that medium whose agitations constitute light, is many thousand times more elastic than air, and, at the same time, many thousand times more rare or more subtile, both of these qualities contributing to accelerate the propa- gation of light. Such are the reasons which lead us to conclude that ether is many thousand times more elastic and more subtile than air ; its nature being in other re- spects similar to that of air, in as much as it is like- wise a fluid matter, and susceptible of compression and of rarefaction. It is this quality which will conduct us to the explanation of all the phenomena of electricity. 23d June, 1761. LETTER XXV. Continuation. Different Nature of Bodies relatively to Electricity. ETHER being a subtile matter and similar to air, but many thousand times more rare and more elastic, it cannot be at rest, unless its elasticity, or the force with which it tends to expand, be the same everywhere. As soon as the ether in one place shall be more elastic than in another, which is the case when it is more compressed there, it will expand itself into the parts adjacent, compressing what it finds there till the whole is reduced to the same degree of elasticity. VOL. II. H 86 DIFFERENT NATURE OF BODIES It is then in equilibrio, the equilibrium being nothing else but the state of rest, when the powers which have a tendency to disturb it counterbalance each other. When, therefore, the ether is not in equilibrio the same thing must take place as in air, when its equi- librium is disturbed ; it must expand itself from the place where its elasticity is greater towards that where it is less ; but, considering its greater elasticity and subtilty, this motion must be much more rapid than that of air. The want of equilibrium in the air produces wind, or the motion of that fluid from one place to another. There must therefore be pro- duced a species of wind, but incomparably more subtile than that of air, when the equilibrium of the ether is disturbed, by which this last fluid will pass from places where it was more compressed and more elastic to those where it was less so. This being laid down, I with confidence affirm that all the phenomena of electricity are a natural con- sequence of want of equilibrium in the ether, so that wherever the equilibrium of the ether is disturbed the phenomena of electricity must take place ; con- sequently, electricity is nothing else but a derange- ment of the equilibrium of the ether. In order to unfold all the effects of electricity, we must attend to the manner in which ether is blended and enveloped with all the bodies which surround us. Ether, in these lower regions, is to be found only in the small interstices which the particles of the air and of other bodies leave unoccupied. Nothing can be more natural than that the ether, from its extreme subtility and elasticity, should insinuate itself into the smallest pores of bodies which are impervious to air, and even into those of the air itself. You will recollect that all bodies, however solid they may appear, are full of pores ; and many experiments in- contestably demonstrate that these interstices occupy much more space than the solid parts ; finally, the less ponderous a body is, the more it must be filled RELATIVELY TO ELECTRICITY. 87 with these pores, which contain ether only. It is clear, therefore, that though the ether he thus dif- fused through the smallest pores of bodies, it must however be found in very great abundance in the vicinity of the earth. You will easily comprehend that the difference of these pores must be very great, both as to magnitude and figure, according to the different nature of the bodies, as their diversity probably depends on the diversity of their pores. There must be, therefore, undoubtedly, pores more close, and which have less communication with others ; so that the ether which they contain is likewise more confined, and cannot disengage itself but with great difficulty, though its elasticity may be much greater than that of the ether which is lodged in the adjoining pores. There must be, on the contrary, pores abundantly open, and of easy communication with the adjacent pores ; in this case it is evident that the ether lodged in them can with less difficulty disengage itself than in the preceding ; and if it is more or less elastic in these than in the others, it will soon recover its equilibrium. In order to distinguish these two classes of pores, I shall denominate the first dose, and the others open. Most bodies must contain pores of an inter- mediate species, which it will be sufficient to dis- tinguish by the terms more or less close, and more or less open. This being laid down, I remark, first, that if all bodies had pores perfectly close, it would be impos- sible to change the elasticity of the air contained in them ; and even though the ether in some of these pores should have acquired, from whatever cause, a higher degree of elasticity than the others, it would always remain in that state, and never recover its equilibrium, from a total want of communication. In this case no change could take place in bodies ; all would remain in the same state as if the ether 88 DIFFERENT NATURE OF BODIES were in equilibrio, and no phenomenon of electricity could be produced. This would likewise be the case if the pores of all bodies were perfectly open ; for then, though the ether might be more or less elastic in some pores than in others, the equilibrium would be instantly restored, from the entire freedom of communication and that so rapidly that we should not be in a condition to remark the slightest change. For the same reason it would be impossible to disturb the equilibrium of the ether contained in such pores ; as often as the equilibrium might be disturbed, it would be as instantaneously restored, and no sign of elec- tricity would be discoverable. The pores of all bodies being neither perfectly close nor perfectly open, it will always be possible to disturb the equilibrium of the ether which they contain : and when this happens, from whatever cause, the equilibrium cannot fail to re-establish itself; but this re-establishment will require some time, and this produces certain phenomena; and you will presently see, much to your satisfaction, that they are precisely the same which electrical experiments have discovered. It will then appear that the principles on which I am going to establish the theory of electricity are extremely simple, and at the same time absolutely incontrovertible. 27th June, 1761. LETTER XXVI. On the same Subject. I HOPE I have now surmounted the most formi- dable difficulties which present themselves in the theory of electricity. You have only to preserve the idea of ether which I have been explaining ; and which is, that extremely subtile and elastic matter RELATIVELY TO ELECTRICITY. 89 diffused, not only through all the void spaces of the universe, but through the minutest pores of all bodies in which it is sometimes more and sometimes less engaged, according as they are more or less close. This consideration conducts us to two prin- cipal species of bodies, of which the one has pores more close, and the other pores more open. Should it happen, therefore, that the ether con- tained in the pores of bodies has not throughout the same degree of elasticity, and that it is more or less compressed in some than in others, it will make an effort to recover its equilibrium ; and it is precisely from this that the phenomena of electricity take their rise, which, of consequence, will be varied in proportion as the pores in which the ether is lodged are various, and grant it a communication more or less free with the others. This difference in the pores of bodies perfectly corresponds to that which the first phenomena of electricity have made us to remark in them, by which some easily become electrical by communication, or the proximity of an electrical body, whereas others scarcely undergo any change. Hence you will im- mediately infer that bodies which receive electricity so easily by communication alone are those whose pores are open ; and that the others, which are almost insensible to electricity, must have theirs close, either entirely or to a very great degree. It is, then, by the phenomena of electricity them- selves that we are enabled to conclude what are the bodies whose pores are close or open. Respect- ing which permit me to suggest the following elu- cidations. First, the air which we breathe has its pores almost entirely close ; so that the ether which it contains cannot disengage itself but with difficulty, and must find equal difficulty in attempting to pene- trate into it. Thus, though the ether diffused through the air is not in equilibrio with that which H 2 90 DIFFERENT NATURE OF BODIES is contained in other bodies where it is more or less compressed, the re-establishment of its equilibrium is not to be produced without extreme difficulty; this is to be understood of dry air, humidity being of a different nature, as I shall presently remark. Further, we must rank in this class of bodies with close pores, glass, pitch, resinous bodies, sealing-wax, sulphur, and particularly silk. These substances have their pores so very close that it is with extreme difficulty the ether can either escape from or pene- trate into them. The other class, that of bodies whose pores are open, contains, first, water and other liquors, whose nature is totally different from that of air. For this reason, when air becomes humid it totally changes its nature with respect to electricity, and the ether can enter or escape without almost any difficulty. To this class of bodies with open pores likewise must be referred those of animals, and all metals. Other bodies, such as wood, several sorts of stones and earths, occupy an intermediate state between the two principal species which I have just mentioned ; and the ether is capable of entering or escaping with more or less facility, according to the nature of each species. After these elucidations on the different nature of bodies with respect to the ether which they con- tain, you will see with much satisfaction how all the phenomena of electricity, which have been con- sidered as so many prodigies, flow very naturally from them. All depends, then, on the state of the ether dif- fused or dispersed through the pores of all bodies, in as far as it has not throughout the same degree of elasticity, or as it is more or less compressed in some than in others : for the ether not being then in equilibrio will make an effort to recover it. It will endeavour to disengage itself as far as the openness of the pores will permit from places where it is too RELATIVELY TO ELECTRICITY. 91 much compressed, to expand itself and enter into pores where there is less compression, till it is throughout reduced to the same degree of com- pression and elasticity, and is, of consequence, in equilibrio. Lei it be remarked, that when the ether passes from a body where it was too much compressed into another where it is less so, it meets with great ob- stacles in the air which separates the two bodies on account of the pores of this fluid, which are almost entirely close. It however passes through the air as a liquid and extremely subtile matter, provided its force is not inferior, or the interval between the bodies too great. Now, this passage of the ether being very much impeded, and almost entirely pre- vented by the pores of the air, the same thing will happen to it as to air forced with velocity through small apertures a hissing sound is heard which proves that this fluid is then put into an agitation which produces such a sound. It is, therefore, extremely natural that the ether, forced to penetrate through the pores of the air, should likewise receive a species of agitation. You will please to recollect, that as agitation of the air produces sound, a similar agitation of ether produces light. As often, then, as ether escapes from one body to enter into another, its passage through the air must be accompanied with light ; which appears sometimes under the form of a spark, sometimes under that of a flash of lightning, according as its quantity is more or less considerable. Here, then, is the most remarkable circumstance which accompanies most electrical phenomena, ex- plained to a demonstration, on the principles I have laid down.* I shall now enter into a more particular * To those conversant with the various phenomena of electricity, the author's theory of close and open pores, and of the different degrees of compression of his supposed ether, will be deemed to fall very far short of a demonstration. Am. Ed 92 OF POSITIVE AND detail, which will furnish me with a very agreeable subject for some following Letters. 30th June, 1761. LETTER XXVII. Of Positive and Negative Electricity. Explanation of the Phenomenon of Attraction. You will easily comprehend, from what I have above advanced, that a body must become electrical whenever the ether contained in its pores becomes more or less elastic than that which is lodged in adjacent bodies. This takes place when a greater quantity of ether is introduced into the pores of such body, or when part of the ether which it contained is forced out. In the former case, the ether becomes more compressed, and consequently more elastic ; in the other, it becomes rarer, and loses its elasticity. In both cases it is no longer in equilibrio with that which is external ; and the efforts which it makes to recover its equilibrium produce all the phenomena of electricity. You see, then, that a body may become electric in two different ways, according as the ether con- tained in its pores becomes more or less elastic than that which is external ; hence result two species of electricity : the one, by which the ether is rendered more elastic, or more compressed, is denominated increased or positive electricity ; me other, in which the ether is less elastic, or more rarefied, is denom- inated diminished or negative electricity. The phe- nomena of both are nearly the same; a slight differ- once only is observable, which I shall mention. Bodies are not naturally electrical as the elas- ticity of the ether has a tendency to maintain it in equilibrio, it must always require a violent operation to disturb this equilibrium, and to render bodies NEGATIVE ELECTRICITY. 93 electrical ; and such operations must act on bodies with close pores, that the equilibrium, once deranged, may not be instantly restored. We accordingly find that glass, amber, sealing-wax, or sulphur are the bodies employed to excite electricity. The easiest operation and for some time past, the most universally known, is to rub a stick of seal- ing-wax with a piece of woollen cloth, in order to communicate to that wax the power of attracting small slips of paper and of other light bodies. Am- ber, by means of friction, produces the same phe- nomena; and as the ancients gave to this body the name of electrum, the power excited by friction ob- tained, and preserves, the name of electricity natural philosophers of the remotest ages having remarked that this substance acquired by friction the faculty of attracting light bodies. This effect undoubtedly arises from the derange- ment of the equilibrium of the ether by means of friction. I must begin, therefore, with explaining this well-known experiment. Amber and sealing- wax have their pores abundantly close, and those of wool are abundantly open ; during the friction, the pores of both the one and the other compress them- selves, and the ether which is contained in them is reduced to a higher degree of elasticity. According as the pores of the wool are susceptible of a com- pression greater or less than those of amber or seal- ing-wax, it must happen that a portion of ether shall pass from the wool into the amber, or, reciprocally, from the amber into the wool. In the former case, the amber becomes positively electric, and in the other negatively and its pores being close, it will remain in this state for some time; whereas the wool, though it has undergone a similar change, will presently recover its natural state. From the experiments which electric sealing-wax furnishes, we conclude that its electricity is negative, and that a part of its ether has passed during the 94 OF POSITIVE AXD friction into the wool. Hence you perceive how a stick of sealing-wax is, by friction on woollen cloth, deprived of part of the ether which it contained, and must thereby become electric. Let us now see what effects must result, from this, and how far they correspond with observation and experience. Let A B, Fig. 39, be a stick of sealing-- wax, from which, by friction, part of the Fig. 39. ether contained in its pores has been c forced out ; that which remains, being \ less compressed, will therefore have less \ force to expand itself, or, in other words, will have less elasticity than that con- tained in other bodies in the circumam- bient air : but as the pores of air are still closer than those of sealing-wax, this prevents the ether contained in the air from passing into the sealing-wax, to restore the equilibrium: at least this will not take place till after a consider- able interval of time. Let a small and very light body C, whose pores are open, be now presented to the stick of sealing-wax, the ether contained in them, finding a free pass- age, because it has more force to expand itself than is opposed to it by the ether shut up in the stick at c, will suddenly escape, will force a passage for itself through the air, provided the distance is not too great, and will enter into the sealing-wax. This passage, however, will not be effected without very considerable difficulty, as the pores of the sealing-wax have only a very small aperture, and consequently it will not be accom- panied with a vehemence capable of putting the ether in a motion of agitation, to excite a sensible light. A faint glimmering only will be perceptible in the dark, if the electricity is sufficiently strong. NEGATIVE ELECTRICITY. 95 But another phenomenon will be observable which is no less surprising the small body C will spring towards the sealing-wax as if attracted by it. To explain the cause of this, you have only to consider that the small body C, in its natural state, is equally pressed on all sides by the air which surrounds it ; but as in its present state the ether makes its escape and passes through the air in the direction C c, it is evident that this last fluid will not press so violently on the small body on this side as on any other, and that the pressure communicated to it towards c will be more powerful than in any other direction, impelling it towards the sealing-wax as if attracted by it. Thus are explained, in a manner perfectly intel- ligible, the attractions observable in the phenomena of electricity. In this experiment, the electricity is too feeble to produce more surprising effects. I shall have the honour of presenting you with a more ample detail in the following Letters. Uh July, 1761. LETTER XXVIII. On the same Subject. SUCH were the faint beginnings of the electrical phenomena ; it was not till lately that they were carried much, farther. At first a tube of glass was employed, similar to that of which barometers are made, but of a larger diameter, which was rubbed with the naked hand, or with a piece of woollen cloth, and electrical phenomena more striking were observed. You will readily comprehend, that on rubbing a tube of glass, part of the ether must pass, in virtue 96 OF POSITIVE AND of the compression of the pores of the glass, and of the rubbing body, either from the hand into the glass, or from the glass into the hand, according as the pores of the one or of the other are more susceptible of compression in the friction. The ether, after this operation, easily recovers its equilibrium in the hand, because its pores are open ; but those of the glass being abundantly close, this fluid will preserve its state in it, whether the glass is surcharged or exhausted, and consequently will be electric, and will produce phenomena similar to those of sealing- wax, but undoubtedly much stronger, as its electri- city is carried to a higher degree, as well from the greater diameter of the tube as from the very nature of glass. Experiments give us reason to conclude that the tube of glass becomes, by these means, surcharged with ether, whereas sealing-wax is exhausted of it ; the phenomena however are nearly the same. It must be observed that the glass tube retains its electricity as long as it is surrounded only with air, because the pores of the glass and those of the air are too close to allow a communication sufficiently free to the ether, and to exhaust the glass of what it has more than in its natural state ; superfluity of ether always increasing elasticity. But the air must be very dry, for only when in that state are its pores sufficiently close ; when it is humid or loaded with vapours, experiments do not succeed, whatever de- gree of friction you bestow on the glass. The reason is obvious ; for water, which renders the air humid, having its pores very open, receives every instant the superfluous ether which was in the glass, and which of course remains in its natural state. Ex- periments succeed, then, in only very dry air : let us now see what phenomena a glass tube will in that case produce, after having undergone considerable friction. J3 NEGATIVE ELECTRICITY. 97 It is clear that on presenting to it a small Fig. 40. light body C. Fig. 40, with open pores, such as gold leaf, the ether in the tube, more elastic at the nearest parts, D, E, will not make ineffectual efforts to dis- charge itself and pass into the pores of the body C. It will force a path through the air, provided the distance be not too great ; and you will even see a light between the tube and the body, occa- sioned by the agitation excited in the ether, which passes with difficulty from the tube into the body. When, instead of the body C, the finger is applied to it, you feel a pricking, occasioned by the rapid entrance of the ether ; and if you expose your face to it at some dis- tance, you feel a certain agitation in the air, excited by the transition of the ether. These circumstances are likewise accompanied sometimes with a slight crackling, produced undoubtedly by the agitation of the air, which the ether traverses with such rapidity. I must entreat you to keep in mind, that an agita- tion in the air always produces a sound, and that the motion of ether produces light ; and then the explanation of these phenomena will become abun- dantly easy. Let the small light body C be replaced in the vicinity of our electric tube ; as long as the ether is escaping from the tube, to enter into the pores of the body C, the air will be in part expelled from it, and consequently will not press so strongly on the body on that side as in every other direction ; it will happen, then, as in the preceding case, that the body C will be impelled towards the tube, and being light, will come close up to it. We see, then, that this apparent attraction equally takes place, whether the ether in the tube be too much or too little elastic, VOL. II. I 98 ON THE ELECTRIC ATMOSPHERE. or whether the elasticity of the tube be positive or negative. In both cases, the passage of the ether stops the air, and by its pressure hinders it from acting. But while the small body C is approaching the tube, the passage of the ether becomes stronger, and the body C will soon be as much surcharged with ether as the tube itself. Then the action of the ether, which arises from its elasticity only, entirely ceases, and the body C will sustain on all sides an equal pressure. The attraction will cease, and the body C will remove from the tube, as nothing detains it, and its own gravity puts it in motion. Now, as soon as it removes, its pores being open, its super- fluous ether presently escapes in the air, and it returns to its natural state. The body will then act as at the beginning, and you will see it again approach the tube, so that it will appear alternately attracted and repelled by it ; and this play will go on till the tube has lost its electricity. For as, on every attraction, it discharges some portion of its super- fluous ether, besides the insensible escape of part of it in the air, the tube will soon be re-established in its natural state, and in its equilibrium ; and this so much the more speedily as the tube is small, and the body C light ; then all the phenomena of electricity will cease. 1th July, 1761. LETTER XXIX. On the Electric Atmosphere. I HAD almost forgotten to bring forward a most essential circumstance, which accompanies all elec- tric bodies, whether positively or negatively such, and which supplies some very striking elucidations for explaining the phenomena of electricity. ON THE ELECTRIC ATMOSPHERE. 99 Though it be indubitably true that the pores of air are very close, and scarcely permit any commu- nication between the ether that they contain and what is in the vicinity, it undergoes, however, some change when near to an electric body. Let us first consider an electric body negatively so, as a stick of sealing- p^ 93 wax A B, Fig. 92, ^Bgg^&jm which has been de- ^ ; %lj-J- 1%%6%% prived by friction of I part of the ether con- *||S tained in its pores, so that what it now contains has less elasticity than that of other bodies, and consequently than that of the air which surrounds the wax. It must necessarily happen, that the ether contained in the particles of the air which immediately touch the wax, as at m, having greater elasticity, should discharge itself, in however small a degree, into the pores of the wax, and will consequently lose somewhat of its elasticity. In like manner, the particles of air more remote, suppose at n, will likewise suffer a portion of their ether to escape into the nearer at m, and so on to a certain distance beyond which the air will no longer undergo any change. In this manner, the air round the stick of wax to a certain distance will be deprived of part of its ether, and become itself electric. This portion of the air, which thus partakes of the electricity of the stick of wax, is denominated the electric atmosphere ; and you will see from the proofs which I have just adduced, that every electric body must be surrounded with an atmosphere. For if the body is positively electric, so as to contain a superfluity of ether, it will be more compressed in such a body, and consequently more elastic, as is the case with a tube of glass when rubbed ; this ether, more elastic, then discharges itself, in a small degree, into the particles of air which immediately touch it, 100 ON THE ELECTRIC ATMOSPHERE. and thence into particles more remote, to a certain distance ; this will form another electric atmosphere round the tube, in which the ether will be more compressed, and consequently more elastic than elsewhere. It is evident that this atmosphere which surrounds such bodies must gradually diminish the electricity of them, as in the first case there passes almost con- tinually a small portion of ether from the surround- ing air into the electric body, and which, in the other case, issues from the electric body and passes into the air. This is likewise the reason why electric bodies at length lose their electricity ; and this so much the sooner, as the pores of the air are more open. In a humid air, whose pores are very open, all electricity is almost instantly extin- guished ; but in very dry air it continues a consid- erable time. This electric atmosphere becomes abundantly sensible on applying your face to an electrified body ; you have a feeling similar to the application of a spider's web, occasioned by the gentle transition of the ether from the face into the electric body, or reciprocally, from this last into the face, according as it is negative or positive, to use the common expression. The electric atmosphere serves likewise more clearly to explain that alternate attraction and repulsion of light bodies placed near to electric bodies which I mentioned in the preceding Letter ; in which you must have remarked, that the explana- tion of repulsion there given is incomplete ; but the electric atmosphere will supply the defect. Let A B, Pig. 93, rep- resent an electric tube 1,, ,,,,!^' of glass surcharged with ! i ii i i^o i ether, and let C be a small light body, with pores suf- ficiently open, in its nat- ural state. Let the atmo- ON THE ELECTRIC ATMOSPHERE. 101 sphere extend as far as the distance D E. Now, as the vicinity of C contains already an ether more elastic, this will discharge itself into the pores of the body C ; there will immediately issue from the tube a new ether, which will pass from D into C, and it is the atmosphere chiefly which facilitates this passage. For if the ether contained in the air had no communication with that in the tube, the corpuscle C would not feel the vicinity of the tube ; but while the ether is passing from D to C, the pressure of the air between C and D will be dimin- ished, and the corpuscle C will no longer be pressed equally in all directions; it will therefore be im- pelled towards D, as if attracted by it. Now, in proportion as it approaches, it will be likewise more and more surcharged with ether, and will become electric as the tube itself, and consequently the electricity of the tube will no longer act upon it. But. as the corpuscle, being now arrived atD, con- tains too much ether, and more than the air at E, it will have a tendency to escape, in order to make its way to E. The atmosphere in which the compres- sion of the ether continues to diminish from D to E will facilitate this passage, and the superfluous ether will in effect flow from the corpuscle towards E. By this passage, the pressure of the air on the corpuscle will be smaller on that side than everywhere else, and consequently the corpuscle will be carried towards D, as if the tube repelled it. But as soon as it arrives at E, it discharges the superfluous ether, and recovers its natural state ; it will then be again attracted towards the tube, and having reached it, will be again repelled, for the reason which I have just been explaining. It is the electric atmosphere then chiefly which produces these singular phenomena, when we see electrified bodies alternately attract and repel small light bodies, such as little slips of paper, or particles 12 102 COMMUNICATION OF ELECTRICITY of metal, with which this experiment best succeeds, as the substances have very open pores. You will see, moreover, that what I have just now said respecting positive electricity must equally take place in negative. The transition of the ether is only reversed, by which the natural pressure of the air must always be diminished. llth July, 1761. LETTER XXX. Communication of Electricity to a Bar of Iron, ly means of a Globe of Glass. AFTER the experiments made with glass tubes, we have proceeded to carry electricity to a higher de- gree of strength. Instead of a tube, a globe or round ball of glass has been employed, which is made to turn with great velocity round an axis, and on applying the hand to it, or a cushion of some matter with open pores, a friction is produced which renders the globe completely electric. Fig. 94 represents this globe, Fig. 94. which may be made to move round an axis A B, by a mechanism simi- lar to that employed by turners. C is the cushion strongly applied to the globe, on which it rubs as it turns round. The pores of the cushion being, in this friction, com- pressed more than those of the glass, the ether con- tained in it is expelled, and forced to insinuate itself into the pores of the glass, where they continue to accumulate, because the open pores of the cushion are continually supplying it with more ether, which it is extracting, at least in part, from surrounding bodies ; and thus the globe may be surcharged with ether to a much higher degree than glass tubes. TO A BAR OF IRON. 103 The effects of electricity are accordingly rendered much more considerable, but of the same nature with those which I have described, alternately at- tracting and repelling light bodies ; and the sparks which we see on touching the electric globe are much more lively. But naturalists have not rested satisfied with such experiments, but have employed the electrical globe in the discovery of phenomena much more sur- prising. Having constructed the machine for turning the globe round its axis A B, a bar of iron F G, Fig. 95, Fig. 95. is suspended above, or on one side of the globe, and towards the globe is directed a chain of iron or other metal E D, terminating at D, in metallic filaments, which touch the globe. It is sufficient that this chain be attached to the bar of iron in any manner what- ever, or but touch it. When the globe is turned round, and in turning made to rub on the cushion at 104 COMMUNICATION OF ELECTRICITY C, in order that the glass may become surcharged with ether, which will consequently be more elastic, it will easily pass from thence into the filaments D, for, being of metal, their pores are very open ; and from thence, again, it will discharge itself by the chain D E, into the bar of iron F G. Thus, by means of the globe, the ether extracted from the cushion C will successively accumulate in the bar of iron F G, which likewise, of consequence, becomes elec- tric ; and its electricity increases in proportion as you continue to turn the globe. If this bar had a further communication with other bodies whose pores too are open, it would soon dis- charge into them its superfluous ether, and thereby lose its electricity; the ether extracted from the cushion would be dispersed over all the bodies which had an intercommunication, and its greatest com- . pression would not be more perceptible. To pre- vent this, which would prove fatal to all the phe- nomena of electricity, the bar must of necessity be supported or suspended by props of a substance whose pores are very close ; such as glass, pitch, sulphur, sealing-wax, and silk. It would be proper, then, to support the bar on props of glass or pitch, or to suspend it by cords of silk. The bar is thus secured against the transmission of its accumulated ether, as it is surrounded on all sides only by bodies with close pores, which permit hardly any admission to the ether in the bar. The bar is then said to be insulated, that is, deprived of all contact which could communicate, and thereby diminish, its electricity. You must be sensible, however, that it is not possible absolutely to prevent all waste ; for this reason, the electricity of such a bar must continually diminish, if it were not kept up by the motion of the globe. In this manner electricity may be communicated to a bar of iron, which never could be done by the most violent and persevering friction, because of the openness of its pores. And, for the same reason, TO A BAR OF IRON. 105 such a bar rendered electric by communication pro- duces phenomena much more surprising 1 . On pre- senting to it a finger, or any other part of the body, you see a very brilliant spark dart from it, which, entering into the body, excites a pungent and some- times painful sensation. I recollect having once presented to it my head, covered with my peruke and hat, and the stroke penetrated it so acutely that I felt the pain next day.* These sparks, which escape from every part of the bar on presenting to it a body with open pores, set on fire at once spirit of wine, and kill small birds whose heads are exposed to them. On plunging the end of the chain D E into a basin filled with water, and supported by bodies with close pores, such as glass, pitch, silk, the whole water becomes electric ; and some authors assure us that they have seen considerable lakes electrified in this manner, so that on applying the hand you might have seen even very pungent sparks emitted from the water. But it appears to me that the globe must be turned a very long time indeed, to convey such a portion of ether into a mass of water so enormous ; it would be likewise necessary that the bed of the lake, and every thing in contact with it, should have their pores close. f The more open, then, the pores of a body are, the more disposed it is to receive a higher degree of electricity, and to produce prodigious effects. You must admit that all this is perfectly conformable to the principles which I at first established. Uth July, 1761. * In the early period of the science, the results of electric action, were so new and surprising (hat the imaginations of many persons were highly wrought upon by them. Musehenbroeck asserted, it is said, that he would not take a second shock for the kingdom of France. Am. Ed. t Such an effect as the author alludes to is not in the least degree prob- able. Am. Ed. 106 ELECTRIZATION OF * LETTER XXXI. Electrization of Men and Animals. As electricity may be communicated from glass to a bar of iron, by means of a chain which forms that communication, it may likewise be conveyed into the hunaan body; for the bodies of animals have this property in common with metals and water, that their pores are very open ; but the man who is to be the subject of the experiment must not be in contact with other bodies whose pores are likewise open. For this purpose, the man is placed on a large lump of pitch, or seated on a chair supported by glass columns, or a chair suspended by cords of silk, as all these substances have pores sufficiently close to prevent the escape of the ether with which the body of the man becomes surcharged by electricity. This precaution is absolutely necessary, for were the man placed on the ground, the pores of which are abundantly open, as soon as the ether was con- veyed into his body to a higher degree of compres- sion, it would immediately discharge itself into the earth ; and we must be in a condition to surcharge it entirely with ether before the man could become electric. Now you must be sensible that the cushion by which the globe of glass is rubbed could not pos- sibly supply such a prodigious quantity of ether, and that were you to extract it even out of the earth itself, you could gain no ground, for you would just take away as much on the one hand as you gave on the other. Having then placed the man whom you mean to electrify in the manner which I have indicated, you have only to make him touch with his hand the globe of glass while it turns, and the ether aeeumU' MEN AND ANIMALS. 107 lated in the globe will easily pass into the open pores of the hand, and diffuse itself over the whole body, from whence it cannot so easily escape, as the air and all the bodies with which he is surrounded have their pores close. Instead of touching the globe with his hand, it will be sufficient for him to touch the chain, or even the bar, which I described in the preceding Letter; but in this case, not only the man himself must be surcharged with ether, but likewise the chain with the bar of iron ; and as this requires a greater quantity of ether, it would be necessary to labour longer in turning the globe, in order to supply a sufficient quantity.* In this manner the man becomes entirely electric, or, in other words, his whole body will be sur- charged with ether ; and this fluid will consequently be found there in the highest degree of compression and electricity, and will have a violent tendency to escape. You must be abundantly sensible that a state so violent cannot be indifferent to the man. The body is in its minutest parts wholly penetrated with ether, and the smallest fibres as well as the nerves are so filled with it, that this ether, without doubt, pervades the principal springs of animal and vital motion. It is accordingly observed, that the pulse of a man electrified beats faster he is thrown into a sweat and the motion of the more subtile fluids with which the body is filled becomes more rapid. A certain change is likewise felt over the whole body, which it is impossible to describe ; and there is every reason to believe, that this state has a powerful influence on the health, though sufficient experiments have not yet been made to ascertain in what cases this influ- ence is salutary, or otherwise. It may sometimes be * This last mode, however, of performing the experiment, would be inch the better of the two. .Am. Ed. 108 ELECTRIZATION OF MEN AND ANIMALS. highly beneficial to have the blood and humours raised to a more lively circulation ; certain obstruc- tions, which threaten dangerous consequences, might thereby be prevented ; but on other occasions an agitation too violent might prove injurious to health. The subject certainly well deserves the attention of medical gentlemen. We have heard of many sur- prising cures performed by electricity, but we are not yet enabled sufficiently to. distinguish the occasions on which we may promise ourselves success. To return to our eleqtrified man ; it is very re- markable, that in the dark we see him surrounded with a light similar to that which painters throw round the heads of saints. The reason is abundantly obvious ; as there is always escaping from the body of that man some part of the ether with which he is surcharged, this fluid meets with much resistance from the close pores of the air ; it is thereby put into a certain agitation, which is the origin of light, as I have had the honour to demonstrate. Phenomena of a very surprising nature are re- marked in this state of a man electrified. On touch- ing him, you not only see very brilliant sparks issue from the part which you touch, but the man feels besides a very pungent pain. Further, if the person who touches him be in his natural state, or not electrified, both sensibly feel this pain, which might have fatal consequences, especially if he were touched in the head, or any other part of the body of acute sensibility. You will readily comprehend, then, how little indifferent it is to us, that a part of the ether contained in our body escape from it, or that new ether is introduced, especially as this is done with such amazing rapidity. Moreover, the light with which we see the man surrounded in the dark is an admirable confirmation of my remarks respecting the electric atmosphere which is diffused round all bodies ; and you will no THE TWO SPECIES OF ELECTRICITY. 109 longer find any difficulty in the greater number of electrical phenomena, however inexplicable they may at first appear. 18th July, 1761. LETTER XXXII. Distinctive Character of the two Species of Electricity. You will please to recollect, that not only glass becomes electric by friction, but that other sub- stances, such as sealing-wax and sulphur, have the same property, in as much as their pores are likewise close ; so that whether you introduce into them an extraordinary quantity of ether, or extract a part of it, they continue for some time in that state ; nor is the equilibrium so soon restored. Accordingly, instead of a globe of glass, globes of sealing-wax and sulphur are employed, which are likewise made to revolve round an axis, rubbing at the same time against a cushion, in the same manne? which I described respecting a globe of glass. Such globes are thus rendered equally electric ; and on applying to them a bar of iron, which touches them only by slender filaments or fringes of metal, inca- pable of injuring the globe, electricity is immediately communicated to that bar, from which you may afterward transmit it to other bodies at pleasure. Here, however, a very remarkable difference is observable. A globe of glass rendered electric in this manner becomes surcharged with ether ; and the bar of iron, or other bodies brought into commu- nication with it, acquire an electricity of the same nature. This electricity is denominated positive or augmented electricity. But when a globe of sealing- wax or sulphur is treated in the same manner, an electricity directly opposite is the result, which is denominated negative or diminished electricity, as VOL. II. K 110 CHARACTER OF THE TWO *t is perceived that by friction these globes are de- Drived of part of the ether contained in their pores. You will be surprised to see that the same friction is capable of producing effects altogether opposite ; but this depends on the nature of the bodies which undergo the friction, whether by communicating or receiving it, and of the rigidity of their particles which contain the pores. In order to explain the possibility of this difference, it is evident, at first sight, that when two bodies are rubbed violently against each other, the pores of the one must in most cases undergo a greater compression than those of the other, and that then the ether contained in the pores is extruded, and forced to insinuate itself into those of the bodies which are less com- pressed. It follows, then, that in this friction of glass against a cushion, the pores of the cushion undergo a greater compression than those of the glass, and consequently the ether of the cushion must pass into the glass, and produce in it a positive or increased electricity, as I have already shown. But on substituting a globe of sealing-wax or of sulphur in place of the glass, these substances being susceptible of a greater degree of compression in their pores than the sub- stance of the cushion with which the friction is per- formed, a part of the ether contained in these globes will be forced out, and constrained to pass into the cushion ; the globe of sealing-wax or sulphur will thereby be deprived of part of its ether, and of course receive a negative or diminished electricity. The electricity which a bar of iron, or of any other metal, receives from communication with a globe of sealing-wax or sulphur, is of the same nature ; as is also that which is communicated to a man placed on a lump of pitch, or suspended by cords of silk. When such a man, or any other body with open pores electrified in the same manner, is touched, nearly the same php-nomena are observable as in the SPECIES OF ELECTRICITY. Ill case of positive electricity. The touch is here like- wise accompanied with a spark, and a puncture on both sides. The reason is obvious ; for the ether which in this case escapes from bodies in their natural state, to enter into electrified bodies, being under constraint, must be under an agitation which produces light. A sensible difference is, however, to be remarked in the figure of the spark, according as the electricity is positive or negative. See that of positive electricity, Fig. 96. If the bar A B possesses positive electricity, and the finger C is presented to it, the light which issues out of the bar appears under the form of rays diverging from the bar towards the finger m n, and the luminous point is seen next the finger. But if the bar A B, Fig. 97, is negatively electric, Fig. 97. c and the ringer C is presented to it, the luminous rays m n diverge from the finger, and you see the lumi- nous point p next the bar. This is the principal character by which positive is distinguished from negative electricity. From whencesoever the ether escapes, the spark is emitted in the figure of rays diverging from that point ; but when the ether enters into a body, the spark is a luminous point towards the recipient body.* QlstJuly, 1761. Professor Hildebrand has lately found that the size and luminous- ness of the spark depend upon the nature as we'll as upon the form of the metal from which the sparks are taken. The pieces of metal which he used were of a conical form. They had all the same shape and dimeU- 112 THE TWO SPECIES OF ELECTRICITY. LETTER XXXIII. How the same Globe of Glass may furnish at once the two Species of Electricity. You will be enabled to see still more clearly the difference between positive and negative electricity, after I have explained how it is possible to produce by one and the same globe of glass both the species ; and this will serve at the same time further to elu- cidate these wonderful phenomena of nature. Let A B, Fig. 98, be the globe of glass turning Fig. 98, eions, and were fixed in the same manner, at the end of an insulated con- ductor. The sparks differed very much in extent, as shown in the follow- ing list ; those at the top of the list giving the greatest sparks, and those at the bottom the least. Regulus of Sulphuret of Steel. Antimony. Copper. Gold. Tin. Tempered Steel. Silver. Zinc. Brass. Iron. Lad. A cone with an angle of 52 gave a much more luminous spark than one with an angle of 36. The parabolic rounding of the summit, or slight inequalities of surface, were found to be particularly favourable to tUe production of a strong light. Ed. THE TWO SPECIES OF ELECTRICITY. 113 round its axis C, and rubbed against the cushion D, in an opposite direction to which the globe is touched by the metallic filaments F attached to the bar of iron F G, which is suspended by cords of silk H and I, that it may nowhere touch bodies with open pores. This being laid down, you know that by friction against the cushion D, the ether passes from the cushion into the glass, from which it becomes more compressed, and consequently more elastic : it will pass, therefore, from thence, by the metallic fila- ments F, into the bar of iron F G ; for though the pores of glass are abundantly close, as the ether in the globe is continually accumulating by the friction, it soon becomes so overcharged that it escapes by the metallic filaments, and discharges itself into the bar, by which this last becomes equally electric. Hence you perceive that all this superfluity of ether is supplied by the cushion, which would speed- ily be exhausted unless it had a free communication with the frame which supports the machine, and thereby with the whole earth, which is every instant supplying the cushion with new ether ; so that as long as the friction continues, there is a quantity sufficient further to compress that which is in the globe and in the bar. But if the whole machinery is made to rest on pillars of glass, as M and N, or if it is suspended by cords of silk, that the cushion may have no communication with bodies whose pores are open, which might supply the deficiency of ether, it would soon be exhausted, and the elec- tricity could not be conveyed into the globe and the bar beyond a certain degree, which will be scarcely perceptible unless the cushion be of a prodigious size. To supply this defect, the cushion D is put in communication with a large mass of metal E, the ether of which is sufficient to supply the globe and the bar, and to carry it to such a high degree of compression s^- * 114 THE TWO SPECIES OF ELECTRICITY. You will thus procure to the globe and to the bar a positive electricity, as has been already explained. But in proportion as they become surcharged with ether, the cushion and the metallic mass E will lose the same quantity, and thereby acquire a negative electricity : so that we have here at once the two species of electricity ; the positive in the bar, and the negative in the metallic mass. Each produces its effect conformably to its nature. On presenting a finger to the bar, a spark with divergent rays wiS issue from the bar, and the luminous point will be seen towards the finger ; but if you present the finger to the metallic mass, the spark with divergent rays will issue from the finger, and you will see the lu- minous point towards the mass. Let us suppose two men placed on lumps of pitch, to cut off all communication between them and bodies with open pores ; let the one touch the bar, and the other the metallic mass, while the machine is put in motion : it is evident that the former will become positively electric, or surcharged with ether ; whereas the other, he who touches the metallic mass, will acquire a negative electricity, and lose his ether. Here, then, are two electric men, but in a manner totally different, though rendered such by the same machine. Both will be surrounded by an elec- tric atmosphere, which in the dark will appear like the light that painters throw about the figures of saints. The reason is, that the superfluous ether of the one insensibly escapes into the circumambient air ; and that, with respect to the other, the ether contained in the air insensibly insinuates itself into his body. This transition, though insensible, will be accompanied with an agitation of ether, which produces light. It is evident that these two species of electricity are directly opposite ; but in order to have a thorough conviction of it, let these two join hands, or only THE LEYDEN EXPERIMENT. 115 touch each other, and you will see very vehement sparks issue from their bodies, and they themselves will feel very acute pain. If they were electrified in the same manner, which would be the case if both touched the bar or the metallic mass, they might safely touch each other ; no spark and no pain would ensue, because the ether contained in both would be in the same state ; whereas, in the case laid down, their state is directly opposite. . "\ 25th 'July, 1761. LETTER XXXIV. The Ley den Experiment. I NOW proceed to describe a phenomenon of elec- tricity which has made a great deal of noise, and which is known by the name of the Leyden experi- ment, because Mr. Muschenbroeck, professor at Ley- den, is the inventor of it.* What is most astonish- ing in this experiment is the terrible stroke resulting from it, by which several persons at once may re- ceive a very violent shock. Let C, Fig. 99, be a globe of glass, turned round by means of the handle E, and rubbed by th cushion D D, which is pressed upon the globe by the spring O. At Q are the metallic filaments which transmit the electricity into the bar of iron F G, by the metallic chain P. < Hitherto there is nothing different from the pro- cess already described. But in order to execute the * The first person who witnessed the shock was Cuneus, a clergyman of Leyden . Holding a tumbler of water in one hand, he allowed a stream of electric fluid to pass into the waier through a wire, which hung from the prime conductor, to ascertain its effects upon the taste of the water: When he thought the water sufficiently electrified, he was about to re- move the wire with his other hand ; and, on touching it, to his great as- louishment, received the shock. Am. Ed. 116 THE LEYDEN EXPERIMENT. Fig. 99. experiment in question, to the bar is attached an- other chain of metal H, one extremity of which I is introduced into a glass bottle K K, filled with water ; the bottle too is placed in a basin L L, likewise filled with water. You plunge at pleasure into the water in the basin another chain A, one end of which drags on the floor. Having put the machine in motion for some time, that the bar may become sufficiently electric, you know that if the finger were to be presented to the extremity of the bar at a, the usual stroke of elec- tricity would be felt from the spark issuing out of it. But were the same person at the same time to put the other hand into the water in the basin at A, or were he but to touch with any part of his body the chain pUnged in that water, he would receive a stroke incomparably more violent, by which his whole frame would undergo a severe agitation. This shock may be communicated to many per- sons at once. They have only to join hands, or to touch each other, were it but by the clothes ; then the first puts his hand into the water in the basin, or THE LEYDEN EXPERIMENT. 117 touches the chain only, one end of which is plunged into it ; and as soon as the last person applies his finger to the bar 5^ou will see a spark dart from it much more vehement than usual, and the whole chain of persons feel, at the same instant, a very violent shock over their whole body. Such is the famous Leyden experiment, which is so much the more surprising, that it is difficult to see how the bottle and the water in the basin con- tribute to increase so considerably the effect of the electricity. To solve this .difficulty, permit me to make the following reflections. 1. While by the action of the machine the ether is compressed in the bar, it passes by the chain H into the water contained in the bottle I, and there meeting a body with open pores, the water in the bottle will become as much surcharged with ether as the bar itself. 2. The bottle, being glass, has its pores close, and therefore does not permit the ether compressed within it to pierce through the substance of the glass, to discharge itself into the water in the basin ; consequently, the water in the basin remains in its natural state, and will not become electric ; or even on the supposition that a little of the ether might force its way through the glass, it would presently be lost in the basin and pedestal, the pores of which are open. 3. Let us now consider the case of a man with one hand in the water in the basin, or only in con- tact with the chain A, one extremity of which is immersed in that water ; let him present the other hand to the bar at a, the result will be as the first effect, that with the spark which issues from the bar the ether will make its escape with great ve- locity, and meeting everywhere in the body of the man open pores, will without obstruction be diffused over it. 4. Hitherto we see only the usual effect of elec- 118 THE LEYDEN EXPERIMENT. tricity ; but while the ether with such rapidity flies over the body of the man, it discharges itself with equal rapidity, by the other hand, or by the chain A, into the water in the basin ; and as it enters this with such impetuosity, it will easily overcome the obstacle opposed by the glass, and penetrate into the water which the bottle contains. 5. Now the water in the bottle containing already an ether too much compressed, it will acquire from this increase new force, and will diffuse itself with impetuosity, as well through the chain I H as through the bar itself : it will of consequence make its escape thence at a with new efforts ; and as this is performed in an instant, it will enter into the finger with increased force to be diffused over the whole body of the man. 6. Passing thence anew into the water in the basin, and penetrating the bottle, it will increase still fur- ther the agitation of the ether compressed in the water of the bottle and in the bar ; and this will con- tinue till the whole is restored to equilibrium, which will quickly take place, from the great rapidity with which the ether acts. 7. The same thing will happen if you employ several persons instead of one man. And now I flatter myself, you fully comprehend whence arises the surprising increase of force in the electricity which is produced by this experiment of Mr. Mus- chenbroeck, and which exhibits effects so prodigious. 8. If any doubt could remain respecting what I have advaaced, that the ether compressed in the water of the bottle could not penetrate through the glass, and that afterward I have allowed it a passage abundantly free such doubt will vanish when it is considered, that in the first case every thing is in a state of tranquillity, and in the last the ether is in a terrible agitation, which must undoubtedly assist its progress through the closest passages. 28th July, 1761. NATURE OF ELECTRICITY. 119 LETTER XXXV. Reflections on the Cause and Nature of Electricity, and on other Means proper to produce it. AFTER these elucidations, you can be at no loss respecting the cause of the prodigious effects ob- servable in the phenomena of electricity. Most authors who have treated the subject, per- plex the experiments in such a manner that they are rendered absolutely unintelligible, especially when they attempt an explanation. They have recourse to a certain subtile matter, which they denominate the electric fluid, and to which they ascribe qualities so extravagant, that the mind rejects them with con- tempt ; and they are constrained to acknowledge, at length, that all their efforts are insufficient to furnish us with a solid knowledge of these important phe- nomena of nature. But you are enabled to conclude, from the prin- ciples which I have unfolded, that bodies evidently become electric only so far as the elasticity, or the state of the compression of the ether in the pores of bodies, is not the same as everywhere else ; in other words, when it is more or less compressed in some than in others. For in that case the prodigious elasticity with which the ether is endowed makes violent efforts to recover its equilibrium, and to re- store everywhere the same degree of elasticity, as far as the nature of the pores, which in different bodies are more or less open, will permit ; and it is the return to equilibrium which always produces the phenomena of electricity. When the ether escapes from a body where it is more compressed, to discharge itself into another where it is less so, this passage is always obstructed by the close pores of the air ; hence it is put into a 120 ON THE CAUSE AND certain agitation, or violent motion of vibration, in which, as we have seen, light consists ; and the more violent this motion is, the more brilliant the light becomes, till it is at length capable of setting bodies on fire, and of burning them. While the ether penetrates the air with so much force, the particles of air are likewise put into a mo- tion of vibration, which occasions sound ; it is ac- cordingly observed, that the phenomena of electri- city are accompanied with a cracking noise, greater or less, according to the diversity of circumstances. And as the bodies of men and animals are filled with ether in their minutest pores, and as the action of the nerves seems to depend on the ether con- tained in them, it is impossible that men and animals should be indifferent with respect to electricity : and when the ethe'r in them is put into a great agitation, the effect must be very sensible, and, according to circumstances, sometimes salutary, and sometimes hurtful. To this last class, undoubtedly, must be referred the terrible shock of the Leyden experi- ment ; and there is every reason to believe that it might be carried to a degree of force capable of kill- ing men, for by means of it many small animals, such as mice and birds, have actually been killed. Though friction usually is employed in the pro- duction of electricity, you will easily comprehend that there may be other means besides this. What- ever is capable of carrying the ether contained in the pores of a body to a greater or less degree of com- pression than ordinary, renders it electric : and if its pores are close, there the electricity will be of some duration ; whereas, in bodies whose pores are open it cannot possibly subsist, unless surrounded by air, or other bodies with close pores. Hence it has been observed, that heat frequently supplies the place of friction. When you heat or melt sealing-wax or sulphur in a spoon, you discover a very sensible electricity in these substances after NATURE OF ELECTRICITY. 121 they are cooled. The reason is no longer a mystery, as we know that heat enlarges the pores of all bodies, for they occupy a greater space when hot than when they are cold. You know that in a thermometer the mercury rises in heat and falls in cold ; because it occupies a greater space when it is hot, and fills the tube more than when it is cold. We find, for the same reason, that a bar of iron very hot is always some- what longer than when cold a property common to all bodies with which we are acquainted. When, therefore, we melt by fire a mass of seal- ing-wax or sulphur, their pores are enlarged, and probably more open ; a greater quantity of ether must of course be introduced to fill them. When, after- ward, these substances are suffered to cool, the pores contract and close, so that the ether in them is re- duced to a smaller space, and consequently carried to a higher degree of compression, which increases its elasticity : these masses will acquire, therefore, a positive electricity, and must consequently exhibit the effects of it. This property of becoming electric by heat is remarked in most precious stones. Nay, there is a stone named tourmaline, which, when rubbed or heated, acquires at once the two species of electri- city. The ether in one part of the stone is expelled to compress more that which is in the other part ; and its pores are too close to permit the re-establish- ment of the equilibrium.* 1st August, 1761. * Very important discoveries have been made since the time of Euler, respecting the production of electricity hy friction, pressure, and heat. A very brief notice of these will be interesting to the reader. Electricity by Friction. Rock crystal, and almost all the precious stones, acquire positive or vitreous electricity with whatever substances they are rubbed ; and on the other hand, resin, sulphur, bitumen, &c. acquire negative or resinous electricity when rubbed with any non-con- ducting substance. Glass, however, when polished, gives vitreous elec- tricity by friction, whereas it gives resinous electricity when it is rough. Among the metals zinc and bismuth always acquire vitreous electri- VOL. II. L 122 NATURE OF THUNDER. LETTER XXXVI. Nature of Thunder : Explanations of the Ancient Phi- losophers, and of Descartes: Resemblance of the Phenomena of Thunder to those of Electricity. I HAVE hitherto considered electricity only as an object of curiosity and speculation to naturalists ; but city when rubbed with a piece of woollen cloth, while tin and antimony always acquire resinous electricity. In many of the other metals, and in various other substances,"the results are often irregular and anoma- lous, sometimes one kind of electricity being developed, and sometimes another. The most striking example of this is in the mineral called kyanite, some crystals of which always acquire resinous electricity by friction, while other crystals always acquire vitreous electricity. In some of these crystals, indeed, vitreous electricity is obtained by rubbing one face, and resinous electricity by rubbing the other. For further informa- tion on this subject, see Haiiy's Traitfd? Mineralogie, Paris, J822, vol. i. p. 186; and the Edinburgh Encyclopaedia, Article ELECTRICITY, vol. viii. p. 430. Electricity by Pressure. The Abb Haiiy discovered the method of producing electricity by pressure. He found that if a rhomb of Iceland spar is held in one hand by two of its opposite edges, and if with two fingers of the other hand two of its opposite faces are merely touched, it gives out vitreous electricity. When pressure is applied in place of con- tact, the effect is greatly increased. Ilaiiy found the same property in topaz, euclase, arragonite, fluate of lime, carbonate of lead, and hyalin quart/, ail of which give vitreous electricity, both by friction and pressure. Sulphate of barytes and sulphate of limn give no electricity by pressure. Elastic bitumen, which is negatively electrified by friction, is also negatively electrified by pressure. Electricity by Heat. The property possessed by tourmaline of be- coming electrical by heat seems to have been known to the ancients, When tourmaline, oxide of zinc, borate of magnesia, Auvergne meso- type, Greenland mesotype, scolezite, and mesolite, are heated, one ex- tremity of the crystal developes resinous and the other vitreous elec- tricity, the intensity of electricity diminishing rapidly from the extremi- ties to the middle or neutral point of the crystal. In the boracite there are eight electrical poles, one at each solid angle of the cube. When these minerals again reach the ordinary temperature, the elec- tricity disappears ; but M. Haiiy has lately found, that it then passes by a reduction of temperature to the opposite state. With oxide of zinc and tourmaline he invariably found, that the opposite electricity could be developed by cold, so that the pole which possessed vitreous electricity when it was hot developed resinous electricity when it was cold. When the opposite electricity is beginning to show itself,, the two poles have NATURE OF THUNDER. 123 you will presently see, not without some degree of surprise, that thunder and lightning, as well as all the terrible phenomena which accompany them, derive their origin from the same principle ; and that in these nature executes on the great scale what naturalists do in miniature by their experiments. Those philosophers who thought they saw some resemblance between the phenomena of thunder and those of electricity were at first considered as vision- aries ; and it was imagined that they made use of this pretence merely as a cover to their ignorance respecting the cause of thunder : but, you will soon be convinced that every other explanation of these grand operations of nature is destitute of founda- tion. In truth, every thing advanced on the subject pre- vious to the knowledge of electricity was a mass of absurdity, and little calculated to convey instruction respecting any of the phenomena of thunder. Ancient philosophers attributed the cause of it to sometimes at once both vitreous and resinous electricity. The disap- pearance of the opposite electricity produced by cold takes place gen- erally below the freezing point SeeHauy's Traite de Mineralogie, torn, i. p. 200. In examining the electricity of the tourmaline, I have found that it may be shown in a very satisfactory manner, by means of a thin slice taken from any part of the prism, and having its surfaces perpendicular to the axis of the prism. It must then be placed upon a piece of well polished glass, and the glass heated to a considerable degree. At the proper temperature, which is about that of boiling water, the slice will adhere to the glass so firmly, that even when the glass is above the tourmaline, the latter will adhere to it for six or eight hours. By this means slices of a very considerable breadth and thickness develop as much electricity as is capable of supporting their own weight. The slice of tourmaline adheres equally to all bodies whatever. Mr. Sivright has fitted up a tourmaline so as to bring the action of its two poles very near to one another. It resembles the letter D, with an opening in its curved part. The straight part is the tourmaline, and the two curved parts are pieces of silver wire rising out of two silver caps ; one of which embraces each pole of the tourmaline. A pith ball suspended at the opening vibrates between the extremities of the wires. Sir H. Davy (Elements of Chymical Philosophy, vol. i. p. 130) states, that when the slice is of considerable size, flashes of light may be seen along its surface. See Edinburgh Philosophical Journal, vol. i. p. 205. Ed. 124 NATURE OF THUNDER. sulphureous and bituminous vapours, which, ascend- ing from the earth into the air, mixed with the clouds, where they caught fire from some unknown cause. Descartes, who quickly perceived the insufficiency of this explanation, imagined another cause in the clouds themselves, and thought that thunder might be produced by the sudden fall of more elevated clouds on others in a lower region of the air ; that the air contained in the intermediate space was com- pressed by this fall to such a degree as was capable of exciting a noise so loud, and even of producing lightning and thunder, though it was impossible for him to demonstrate the possibility of it. But without fixing your attention on false expla- nations, which lead to nothing, I hasten to inform you that it has been discovered by incontestable proofs that the phenomena of thunder are always accompanied by the most indubitable marks of elec- tricity. Let a bar of metal, say of iron, be placed on a pillar of glass, or any other substance whose pores are close, that when the bar acquires electricity it may not escape or communicate itself to the body which supports the bar ; as soon as a thunder-storm arises, and the clouds which contain the thunder come directly over the bar, you perceive in it a very strong electricity, generally far surpassing that which art produces ; if you apply the hand to it, or any other body with open pores, you see bursting from, it, not only a spark, but a very bright flash, with a noise similar to thunder ; the man who applies his hand to it receives a shock so violent that he is stunned. This surpasses curiosity ; and there is good reason why we should be on our guard and not ap- proach the bar during a storm. A professor at Petersburg, named Richmann, has furnished a melancholy example. Having perceived NATURE OF THUNDER. 125 a resemblance so striking between the phenomena of thunder and those of electricity, this unfortunate naturalist, the more clearly to ascertain it by experi- ment, raised a bar of iron on the roof of his house, cased below in a tube of glass, and supported by a mass of pitch. To the bar he attached a wire, which he conducted into his chamber, that as soon as the bar should become electric, the electricity might have a free communication with the wire, and so enable him to prove the effects in his apartment. And it may be proper to inform you, that this wire was conducted in such a manner as nowhere to be in contact but with bodies whose pores are close, such as glass, pitch, or silk, to prevent the escape of the electricity. Having made this arrangement, he expected a thunder-storm, which, unhappily for him, soon came. The thunder was heard at a distance : Mr. Richmann was all attention to his wire, to see if he could per- ceive any mark of electricity. As the storm ap- proached, he judged it prudent to employ some pre- caution, and not keep too near the wire ; but hap- pening carelessly to advance his chest a little, he received a terrible stroke, accompanied with a loud clap, which stretched him lifeless on the floor. About the same time, the late Dr. Lieberkuhn and Dr. Ludolf were preparing to make similar experi- ments in this city, and with that view had fixed bars of iron on their houses ; but being informed of the disaster which had befallen Mr. Richmann, they had the bars of iron immediately removed ; and, in my opinion, they acted wisely. From this you will readily judge, that the air or atmosphere must become very electric during a thunder-storm, or that the ether contained in it must then be carried to a very high degree of compres- sion. This ether, with which the air is surcharged, Will pass into the bar, because of its open pores ; L9 126 THE PHENOMENA OF and it will become electric, as it would have been in the common method, but in a much higher de- gree. 4th August, 1761. LETTER XXXVII. Explanation of the Phenomena of Lightning and Thunder. THE experiments now mentioned incontestably demonstrate, therefore, that stormy clouds are ex- tremely electrical, and that consequently their pores are either surcharged with ether, or exhausted, as both states are equally adapted to electricity. But I have very powerful reasons for believing that this electricity is positive, that the ether in them is com- pressed to the highest degree, and consequently so much the more elastic than elsewhere. Such storms usually succeed very sultry weather. The pores of the air, and of the vapours floating in it, are then extremely enlarged, and filled with a prodigious quantity of ether, which easily takes pos- session of all the empty spaces of other substances. But when the vapours collect in the superior re- gions of our atmosphere, to form clouds, they have to encounter excessive cold. Of this it is impossible to doubt, from the hail which is frequently formed in these regions : this is a sufficient proof of a conge- lation, as well as the snow which we find on the tops of very high mountains, such as the Cordilleras, while extreme heat prevails below. Nothing then is more certain, or better established by proof, than the excessive cold which universally prevails in the upper regions of the atmosphere, where clouds are formed. It is equally certain, that cold contracts the pores of bodies, by reducing them to a smaller size : now, as the pores of the vapours LIGHTNING AND THUNDER. 127 have been extremely enlarged by the heat, as soon as they are formed aloft into clouds, the pores con- tract, and the ether which filled them, not being able to escape, because those of the air are very close, it must needs remain there : it will be of course com- pressed to a much higher degree of density, and consequently its elasticity will be so much the greater. The real state of stormy clouds, then, is this the ether contained in their pores is much more elastic than usual, or, in other words, the clouds have a positive electricity. A s they are only an assemblage of humid vapours, their pores are very open ; but being surrounded by the air, whose pores are close, this ether could not escape but very imperceptibly. But if any person, or any body whatever with open pores, were to approach it, the same phenomena which electricity exhibits would present themselves ; a very vehement spark, or rather a real flash, would burst forth. Nay more, the body would undergo a very violent shock by the discharge, from the inl- petuosity with which the ether in the cloud would rush into its pqres. This shock might be indeed so violent as to destroy the structure ; and, finally, the terrible agitation of the ether which bursts from the cloud, being not only light, but a real fire, it might be capable of kindling and consuming combustible bodies. Here, then, you will distinguish all the circum- stances which accompany thunder; and as to the noise of thunder, the cause is very obvious, for it is impossible the ether should be in such a state of agitation without the air itself receiving from it the most violent concussions, which forcibly impel the particles, and excite a dreadful noise. Thunder, then, bursts forth as often as the force of ether contained in the clouds is capable of penetrating into a body where the ether is in its natural state, and whose pores are open : it is not even neces- 128 PHENOMENA OF sary that such body should immediately touch the cloud. What I have said respecting the atmosphere of electrified bodies principally takes place in clouds ; and frequently, during a storm, we are made sensible of this electric atmosphere by a stifling air, which is particularly oppressive to certain persons. As soon as the cloud begins to dissolve into rain, the air, becoming humid by it, is charged with an electricity, by which the commotion maybe conveyed to bodies at a very great distance. It is observed that thunder usually strikes very elevated bodies, such as the summits of church-spires, when they consist of substances with open pores, as all metals are ; and the pointed form contributes not a little to it. Thunder frequently falls likewise on water, the pores of which are very open ; but bodies with close pores, as glass, pitch, sulphur, and silk, are not greatly susceptible of the thunder-stroke, unless they are very much moistened. It has been accordingly observed, that when thunder passes through a window, it does not perforate the glass, but always the lead or other substances which unite the panes, It is almost certain, that an apartment of glass cemented by pitch, or any other substance with close pores, would be an effectual security against the ravages of thunder. 8th August, 1761. LETTER XXXVIII. Continuation. THUNDER, then, is nothing else but the effect of the electricity with which the clouds are endowed ; and as an electrified body, applied to another in its natural state, emits a spark with some noise, and discharges into it the superfluous ether with pro- LIGHTNING AND THUNDER. 129 digious impetuosity, the same thing takes place in a cloud that is electric, or surcharged with ether, but with a force incomparably greater, because of the terrible mass that is electrified, and in which, ac- cording to every appearance, the ether is reduced to a much higher degree of compression than we are capable of producing in it by our machinery. When, therefore, such a cloud approaches bodies prepared for the admission of its ether, this dis- charge must be made with incredible violence : in- stead of a simple spark, the air will be penetrated with a prodigious flash, which, exciting a commotion in the ether contained in the whole adjoining region of the atmosphere, produces a most brilliant light ; and in this lightning consists. The air is at the same time put into a very vio- lent motion of vibration, from which results the noise of thunder. This noise must, no doubt, be excited at the same instant with the lightning ; but you know that sound always requires a certain quantity of time, in order to its transmission to any distance, and that its progress is only at the rate of about eleven hundred feet in a second; whereas light travels with a velocity inconceivably greater. Hence we always hear the thunder later than we see the lightning ; and from the number of seconds intervening between the flash and the report, we are enabled to determine the distance of the place where it is generated, allowing eleven hundred feet to a second. The body itself, into which the electricity of the cloud is discharged, receives from it a most dreadful stroke ; sometimes it is shivered to pieces some- times set on fire and consumed, if combustible sometimes melted, if it be of metal ; and, in such cases, we say it is thunder-struck, the effects of which, however surprising and extraordinary they may appear, are in perfect consistency with the well- known phenomena of electricity. 130 PHENOMENA OF LIGHTNING AND THUNDER. A sword, it is known, has sometimes been by thunder melted in the scabbard, while the last sus- tained no injury : this is to be accounted for from the openness of the pores of the metal, which the ether very easily penetrates, and exercises over it all its powers ; whereas the substance of the scab- bard is more closely allied to the nature of bodies with close pores, which do not permit the ether so free a transmission. It has likewise been found, that of several persons on whom the thunder has fallen, some only have been struck by it ; and that those who were in the middle suffered no injury. The cause of this phe- nomenon likewise is manifest. In a group exposed to a thunder-storm, they are in the greatest danger who stand in the nearest vicinity to the air that is surcharged with ether ; as soon as the ether is dis- charged upon one, all the adjoining air is brought back to its natural state, and consequently those who were nearest to the unfortunate victim feel no effect; while others, at a greater distance, where the air is still sufficiently surcharged with ether, are struck with the same thunder-clap. In a word, all the strange circumstances so fre- quently related of the effects of thunder contain nothing which may not be easily reconciled with the nature of electricity. Some philosophers have maintained, that thundei does not come from the clouds, but from the earth, or from bodies. However extravagant this senti- ment may appear, it is not so absurd, as it is difficult to distinguish in the phenomena of electricity whether the spark issues from the body which is electrified, or from that which is not so, as it equally fills the space between the two bodies ; and if the electricity is negative, the ether and the spark are in reality emitted from the natural or non-electrified body. But we are sufficiently assured, that in thun- OF AVERTING THE EFFECTS OF THUNDER. 131 der the clouds have a positive electricity, and that the lightning is emitted from the clouds. You will be justifiable, however, in asking, if by every stroke of thunder some terrestrial body is affected 1 We see, in fact, that it very rarely strikes buildings, or the human body ; but we know, at the same time, that trees are frequently affected by it, and that many thunder-strokes are discharged into the earth and into the water. I believe, however, it might be maintained, that a great many do not descend so low, and that the electricity of the clouds is very frequently discharged into the air or atmo- sphere. The small opening of the pores of the air no longer opposes any obstruction to it, when vapours )r rain have rendered it sufficiently humid ; for then we know the pores are open. It may very possibly happen in this case, that the superfluous ether of the clouds should be discharged simply into the air ; and when this takes place, the strokes are neither so violent, nor accompanied with so great a noise, as when the thunder bursts on the earth, when a much greater extent of atmosphere is put in agitation. llth August, 1761. LETTER XXXIX. The Possibility of preventing, and of averting, the Effects of Thunder. IT has been asked, Whether it might not be pos- sible to prevent or to avert the fatal effects of thun- der 1 You are well aware of the importance of the question, and under what obligation 1 should lay a multitude of worthy people, were I able to indicate an infallible method of finding protection against thunder. 132 OF PREVENTING AND AVERTING The knowledge of the nature and effects of elec- tricity permits me not to doubt that the thing is possible. I corresponded some time ago with a Moravian priest, named Procopius Divisch, who as- sured me that he had averted, during a whole sum- mer, every thunder-storm which threatened his own. habitation and the neighbourhood, by means of a machine constructed on the principles of electricity. Several persons since arrived from that country have assured me that the fact is undoubted, and confirmed by irresistible proof. But there are many respectable characters who r on the supposition that the thing is practicable, would have their scruples respecting the lawfulness of employing such a preservative. The ancient pagans, no doubt, would have considered him as* impious who should have presumed to interfere with Jupiter in the direction of his thunder. Chris- tians, who are assured that thunder is the work of God, and that Divine Providence frequently employs it to punish the wickedness of men, might with equal reason allege that it were impiety to attempt to oppose the course of sovereign justice. Without involving myself in this delicate discus- sion, I remark that conflagrations, deluges, and many other general calamities are likewise the means employed by Providence to punish the sins of men ; but no one surely ever will pretend, that it is unlawful to prevent or resist the progress of a fire or an inundation. Hence I infer, that it is pei- fectly lawful to use the means of prevention against the effects of thunder, if they are attainable. The melancholy accident which befell Mr. Rick' mann at Petersburg demonstrates that the thunder- stroke which this gentleman unhappily attracted to himself, would undoubtedly Have fallen somewhere else, and that this place thereby escaped ; it can therefore no longer remain a question whether it be possible to conduct thunder to one place in prefer- THE EFFECTS OF THUNDER. 133 ence to another ; and this seems to bring us near our mark. It would no doubt be a matter of still greater im- portance to have it in our power to divest the clouds of their electric force, without being under the necessity of exposing any one place to the ravages of thunder ; we should in that case altogether pre- vent these dreadful effects, which terrify so great a part of mankind. This appears by no means impossible ; and the Moravian priest whom I mentioned above unques- tionably effected it ; for I have been assured that his machinery sensibly attracted the clouds, and con- strained them to descend quietly in a distillation, without any but a very distant thunder-clap. The experiment of a bar of iron, in a very ele- vated situation, which becomes electric on the approach of a thunder-storm, may lead us to the construction of a similar machine, as it is certain that in proportion as the bar discharges its electricity the clouds must lose precisely the same quantity ; but it must be contrived in such a manner, that the bars may immediately discharge the ether which they have attracted. It would be necessary for this purpose to procure for them a free communication with a pool, or with the bowels of the earth, which, by means of their open pores, may easily receive a much greater quantity of ether, and disperse it over the whole immense extent of the earth, so that the compres- sion of the ether may not become sensible in any particular spot. This communication is very easy, by means of chains of iron, or any other metal, which will with great rapidity carry off the ether with which the bars are surcharged. I would advise the fixing of strong bars of iron, in very elevated situations, and several of them to- gether, their higher extremity to terminate in a point, as this figure is very much adapted to the VOL. II. M 134 OF AVERTING THE EFFECTS OF THUNDER. attraction of electricity. I would afterward attach long chains of iron to these bars, which I would conduct under ground into a pool, lake, or river, there to discharge the electricity ; and I have no doubt, that after making repeated essays, the means may be certainly discovered of rendering such ma- chinery more commodious, and more certain in its effect.* It is abundantly evident, that on the approach of a thunder-storm, the ether with which the clouds are surcharged would be transmitted in great abun- dance into these bars, which would thereby become very electric, unless the chains furnished to the ether a free passage, to spend itself in the water and in the bowels of the earth. The ether of the clouds would continue, therefore, to enter quietly into the bars, and would by its agita- tion produce a light which might be visible on the pointed extremities. Such light is, accordingly, often observed during a storm on the summit of spires an infallible proof that the ether of the cloud is there quietly discharg- ing itself; and every one considers this as a very good sign of the harmless absorption of many thun- der-strokes. Lights are likewise frequently observed at sea on the tops of the masts of ships, known to sailors by the name of Castor and Pollux ;f and when such signs are visible, they consider themselves as safe from the stroke of thunder. Most philosophers have ranked these phenomena among vulgar superstitions ; but we are now fully * As buildings are often struck laterally, the main thunder-rod, espe- cially in monumental pillars and elevated buildings, should have various lateral branches diverging from it, and extending to the air through openings in the building. By this means it is secured much more effectually than when there is only one conductor, which can do no more than protect the summit of the building. Ed. f This l phenomenon is also called the Fire^of St. Elmo. A very inter- esting account of it will be found in the Edinburgh Philosophical Jour- nal, vol. ix. p. 35.-Ed. ON THE LONGITUDE. 135 assured that such sentiments are not without foun- dation; indeed, they are infinitely better founded than many of our philosophical reveries.* 15th August, 1761. LETTER XL. On the celebrated Problem of the Longitude : General Description of the Earth, of its Axis, its two Poles, and the Equator. You will by this time, no doubt, imagine that enough has been said of electricity ; and indeed I have nothing further to add on that subject ; and am, of course, not a little embarrassed about the choice of one worthy of your attention. In order to determine my choice, I think myself obliged to take into consideration those subjects which most materially interest human knowledge, and which authors of celebrity most frequently bring * A very copious account of the recent discoveries in electricity will be found in the article on that subject, in the Edinburgh Encyclopaedia, vol. viil. p. 411. Ed. [It is remarkable that neither Euler nor his Eu- ropean editor have anywhere noticed the discoveries of Dr. Franklin, admitted as they are, almost universally, to lie at the foundation of the moat intelligible principles of the science, and to have enriched it with the most useful facts. The omission is the more surprising, since the experiments of the American philosopher which demonstrated the iden- tity of lightning and the fluid of an electrical machine were made in 1752, nine years prior to the date of Euler's Letter; and that his letters res are pliant, and easily arrange themselves in conformity to the current of the magnetic matter. Iron of this description, accordingly, appears well adapted to the production of a sudden change in ARMING OF LOADSTONES. 233 the direction of the current : the magnetic matter, too, seems to affect a progress in that direction as long as possible, and does not quit it till the continu- ance of its motion through that medium is no longer practicable: it prefers making a circuit to a pre- mature departure a thing that does not take place in the loadstone itself, in which the magnetic canals are already formed, nor in steel, whose pores do not so easily yield to the efforts of a magnetic current. But when these canals are once formed in steel, they are not so easily deranged, and much longer retain their magnetic force ; whereas soft iron, whatever force it may have exerted during its junc- tion with a loadstone, loses it almost entirely on being disjoined. Experience must be consulted as to the other cir- cumstances of arming loadstones. Respecting the plates, it has been found that a thickness either too great or too small is injurious ; but for the most part, the best adapted plates are very thin, which would appear strange, did we not know that the magnetic matter is much more subtile than ether, and that consequently the thinnest plate is sufficient to re- ceive a very great quantity of it. nth November, 1761. U2 234 ACTION AND FORCE OF Pig. 124. p;- A ' B B J " \_ LETTER LXVn. Action and Force of armed Loadstones. AT the feet of its armour, then, a loadstone exerts its greatest force, because there its poles are col- lected ; and each foot is capable of supporting a weight of iron, greater or less in proportion to the excel- lence of the loadstone. Thus a loadstone A A, B B, Fig. 124, armed with plates of iron a a and b b, terminating in the feet A' and B', will support by the foot A' not only the iron ruler C D, but this last will support another of small- er size E F, this again another still smaller G H, which will in its turn support a needle I K, which, finally, will at- tract filings of iron L; be- cause the magnetic matter runs through all these pieces to enter at the pole A' ; or if it were the other pole by which the magnetic matter issues from the loadstone, it would in like manner run through the pieces CD,EF,GH, IK. Now, as often as the matter is transmitted from one piece to another, an attraction be- tween the two pieces is ob- servable ; or rather they are impelled towards each other by the surrounding ether, because the current of the magnetic matter between them diminishes the pressure of that fluid. ARMED LOADSTONES. 235 When one of the poles of the loadstone is thus loaded, its vortex undergoes a very remarkable change of direction ; for as, without this weight, the magnetic matter which issues from the pole B', di- recting around its course, would flow towards the other pole A' ; and as now the entrance into this pole is sufficiently supplied by the pieces which it supports, the matter issuing from the pole B' must take quite a different road, which will at length con- duct it to the last piece IK. A portion of it will un- doubtedly be likewise conveyed towards the last but one G H, and towards those which precede it ; as those which follow, being smaller, do not supply in sufficient abundance those which go before : but the vortex will always be extended to the last piece. By these means, if the pieces are well proportioned to each other in length and thickness, the loadstone is capable of supporting much more than if it were loaded with a single piece, in which the figure like- wise enters principally into consideration. But in order to make it sustain the greatest possible weight, we must contrive to unite the force of both poles. For this purpose, there is applied to the two poles A. and B, Fig. 127, a piece of soft iron C D, touching the base of the feet in all points, and whose figure is such, that the magnetic mat- ter which issues from B shall find it in the most commodious pas- sage to re-enter at the other extremity A. Such a piece of iron is called the supporter of the loadstone; and as the magnetic matter en- ters into it on issuing Fig. 127. ^ I t a 1 m 236 ACTION AND FORCE OF from the loadstone at B, and enters into the other pole A, on issuing from the supporter, the iron will be attracted at both poles at once, and consequently adhere to them with great force. In order to know how much power the loadstone exerts, there is affixed to the supporter, at the middle E, a weight P, which is increased till the loadstone is no longer capable of sustaining it ; and then that weight is said to coun- terbalance the magnetic power of the loadstone : this is what you are to understand when told that such a loadstone carries ten pounds weight, such another thirty, and so on. Mahomet's coffin, they pretend, is supported by the force of a loadstone a thing by no means impossible, as artificial magnets have already been constructed which carry more than 100 pounds weight. A loadstone armed with its suppprter loses nothing of the magnetic matter, which performs its complete vortex within the loadstone and the iron, so that none of it escapes into the air. Since then mag- netism exerts its power only in so far as the matter escapes from one body to enter into another, a load- stone whose vortex is shut up should nowhere exert the magnetic power ; nevertheless, when it is touched on the plate at a with the point of a needle, a very powerful attraction is perceptible, because the mag- netic matter, being obliged suddenly to change its direction, in order to enter into the canals of the loadstone, finds a more commodious passage by running through the needle, which will consequently be attracted to the plate a a. But by that very thing the vortex will be deranged inwardly ; it will not flow so copiously into the feet ; and if you were to apply several needles to the plate, or iron rulers still more powerful, the current towards the feet would be entirely diverted, and the force which attracts the supporter would altogether disappear, so that it would drop off without effort. Hence it is evident that the feet lose their magnetic power in proportion ARMED LOADSTONES. 237 as the loadstone exercises its force in other places ; and thus we are enabled to account for a variety of very surprising phenomena, which without the the- ory, would be absolutely inexplicable. This is the proper place for introducing the experi- ment which demonstrates, that after having applied its supporter to an armed loadstone, you may go on from day to day increasing the weight which it is able to sustain, till it at length shall exceed the double of what it carried at first. It is necessary to show, therefore, how the magnetic force may in time be increased in the feet of the armour. The case above described, of the derangement of the vortex, assures us, that at the moment when the supporter is applied, the current of the magnetic matter is still abundantly irregular, that a consider- able part of it is still escaping by the plate b i, and that it will require time to form magnetic canals in the iron : it is likewise probable that, when the cur- rent shall have become more free, new canals may- be formed in the loadstone itself, considering that it contains, besides these fixed canals, moveable poles, as iron does. But on violently separating the sup- porter from the loadstone, the current being dis- turbed, and these new canals in a great measure destroyed, the force is suddenly rendered as small as at the beginning ; and some time must intervene before these canals, with the vortex, can recover their preceding state. I once constructed an arti- ficial magnet, which at first could support only ten pounds weight; and after some time I was sur- prised to find that it could support more than thirty. It is remarked, chiefly in artificial magnets, that time alone strengthens them considerably ; but that this increase of force lasts only till the supporter is sepa- rated from it. 21st November, 1761. 238 METHOD OF COMMUNICATING LETTER LXVIII. The Method of communicating to Steel the Magnetic Force, and of magnetizing Needles for the Compass: the Simple Touch, its Defects ; Means of remedying these. HAVING explained the nature of magnets in general, an article as curious as interesting still remains ; namely, the manner of communicating to iron, but especially to steel, the magnetic power, and even the highest degree possible of that power. You have seen that, by placing iron in the vortex of a loadstone, it acquires a magnetic force, but which almost totally disappears as soon as it is removed out of the vortex ; and that the Cortex of the earth alone is capable, in time, of impressing a slight mag- netic power upon iron ; now, steel being harder than iron, and almost entirely insensible to this action of the magnetic vortex, more powerful operations must be employed to magnetize it ; but then it retains the magnetic force much longer. For this purpose we must have recourse to touch- ing, and even to friction. I begin, therefore, with explaining the method formerly employed for mag- netizing the needles of compasses ; the whole opera- tion consisted in rubbing them at the pole with a good loadstone, whether naked or armed. The needle a b c, Fig. 125, p^ 135 was laid on a table ; the pole nB ** B of the loadstone was drawn IJ it, from b towards a, and, c being arrived at the extremity a, the loadstone was raised aloft, and brought back through the air to b ; this operation was repeated several times together, particular care being taken that^he other pole of the loadstone should not come THE MAGNETIC FORCE. 239 near the needle, as this would have disturbed the whole process. Having several times drawn the pole B of the loadstone over the needle, from b to a, the needle had become magnetic, and the extremity b of the same name with that of the loadstone with which it had been rubbed. In order to render the extremity b the north pole, it would have been necessary to rub with the pole of this name in the loadstone, proceeding from b to a ; but in rub- bing with the south pole, the progress must be from a to b. This method of rubbing, or touching, is denomi- nated the simple touch, because the operation is per- formed by touching with one pole only; but it is extremely defective, and communicates but very little power to the needle, let the loadstone be ever so excellent ; accordingly, it does not succeed when the steel is carried to the highest degree of hardness, though this be the state best adapted to the retention of magnetism. You will yourself readily discern the defects of this method by the simple touch. Let us suppose that B is the pole of the loadstone from which the magnetic matter issues, as the effect of the two poles is so similar that it is impossible to perceive the slightest difference ; having rested the pole on the extremity b of the needle, the magnetic matter enters into it with all the rapidity with which it moves in the loadstone, incomparably greater than that of the vortex which is in the external air. But what will become of this matter in the needle ? It cannot get out at the extremity , it will therefore make an effort to force its way through the needle towards f which they make a part. Thus, when it is said that the radius of the con- vex surface A E B, Fig. 138, is three inches, the Fig. 138. meaning is, that A E B is an arch of a circle described with a radius of three inches, the other surface A B being plane. That I may convey a still clearer idea of the dif- ference of convexities, when their radii are greater or less, I shall here present you with several figures of different convexity, Fig. 139. Fig. 139. Two Inches. One Inch Half an Icch. Third of an Inch. Fifth of an Inch f ^ <^ Z Sixth of an Inch. Eighth of an Inch. DIFFERENT KINDS OF LENSES. 259 From this you see, that the smaller the radius is the greater is the curve of the surface, or the greater its difference from the plane ; on the contrary, the greater the radius is, the more the surface approaches to a plane, or the arch of the circle to a straight line. If the radius were made still greater, the curve would at length become hardly perceptible. You scarcely perceive it in the arch M N, Fig. 138, the radius of which is six inches, or half a foot ; and if the radius were still extended to ten or a hundred times the magnitude, the curve would become alto- gether imperceptible to the eye. But this is by no means the case as to dioptrics , and I shall afterward demonstrate, that though the radius were a hundred or a thousand feet, and the curve of the lens absolutely imperceptible, the effect would nevertheless be abundantly apparent. The radius must indeed be inconceivably great to pro- duce a surface perfectly plane : from which you may conclude, that a plane surface might be considered as a convex surface whose radius is infinitely great, or as a concave of a radius infinitely great. Here it is that convexity and concavity are confounded, so that the plane surface is the medium which separates convexity from concavity. But the smaller the radii are, the greater and more perceptible do the convexities and concavities become ; and hence we say, reciprocally, that a convexity or concavity is greater in proportion as its radius, which is the measure of it, is smaller. However great in other respects maybe the variety we meet with in lenses or glasses, according as their surfaces are plane, convex, or concave, and this in an infinity of different manners ; nevertheless, with respect to the effect resulting from them in dioptrics, they may be reduced to the three following classes : The first comprehends glasses which are every- where of an equal thickness ; whether their two sur- 260 DIFFERENT KINDS OF LENSES. faces be plane and parallel to each other, Fig. 140, or the one convex and the other concave, but con- Fig-. 140. centric, or described round the same centre, Fig. 141, so that the thickness shall remain everywhere the same. It is to be remarked respecting glasses Fig. 141. of this class, that they produce no change in the appearance of the objects which we view through them; the objects appear exactly the same as. if nothing interposed ; accordingly, they are of no manner of use in dioptrics. This is not because the rays which enter into these glasses undergo no re- fraction, but because the refraction at the entrance is perfectly straightened on going off, so that the rays, after having passed through the glass, resume the same direction which they had pursued before they reached it. Glasses, therefore, of the other two classes, on account of the effect which they produce, constitute the principal object of dioptrics. The second class of lenses contains those which are thicker at the middle than at the edge, Fig. 142. Fig. 142. Their effect is the same, as long as the excess of the thickness of the middle over that of the edge has the same relation to the magnitude of the lens. All lenses of this class are commonly denominated con- EFFECT OF CONVEX LENSES. 26 . vex, as convexity predominates, though otherwise one of their surfaces may be plane, and even con- cave. The third class contains all those lenses which are thicker at the edge than in the middle, Fig. 143, Fig. 143. which all produce a similar effect, depending on the excess of thickness towards the edge over that in the middle. As concavity prevails in all such lenses, they are simply denominated -concave. They must be carefully distinguished from those of the second class, which are the convex. Lenses of these two last classes are to be the sub- ject of my following Letters, in which I shall en- deavour to explain their effects in dioptrics. 12th December, 1761. LETTER LXXIV. Effect of Convex Lenses. IN order to explain the effect produced by both convex and concave lenses in the appearance of ob- jects, two cases must be distinguished ; the one when the object is very far distant from the lens, and the other when it is nearer. But before I enter on the explanation of this, I must say a few words on what is called the axis of the lens. As the two surfaces are represented by segments of a circle, you have only to draw a straight line through the centres of the two circles ; this line is named the axis of the lens. In Fig. 144, the cen- 262 EFFECT OF CONVEX LENSES. tre of the arch A E B being at C, and that of the arch A F B at D,the straight line C D is denominated the axis of the lens A B ; and it is easy to see that this axis passes through the middle of it. The same thing would apply if the surfaces of the lens were , F concave. But if one is plane, the vr axis will be perpendicular to it, pass- jf ing through the centre of the other surface. Hence it is obvious that the axis passes through the two surfaces perpendicularly, and that accord- ingly a ray of light coming in the direction of the axis will suffer no refraction, because rays passing from one medium into another are not broken or refracted, except when they do not enter in a per- pendicular direction. It may likewise be proved that all other rays pass- ing through the middle of the lens O undergo no refraction, or rather that they again become parallel to themselves. It must be considered, in order to comprehend the reason of this, that at the points E and F the two surfaces of the lens are parallel to each other, for the angle M E B which the ray M E makes with the arch of the circle E B, or its tangent at E, is per- fectly equal to the angle P F A, which this same ray produced, or F P makes with the arch of the circle A F, or its tangent at F : you recollect that two such angles are denominated alternate, and that it is demonstrated, when the alternate angles are equal, that the straight lines are parallel to each other; consequently, the two tangents at E and at F will be parallel, and it will be the same thing as if the ray M E F P passed through a lens whose two surfaces were parallel to each other. Now we have already seen that rays do not change their direction in pass- ing- through such a lens. EFFECT OF CONVEX LENSES. 263 Having made these remarks, let us now consider a convex lens A B, Fig. 145, whose axis is p- U5 the straight line O E F P ; and let us sup- * ^ pose that there is in this line, at a great distance from the lens, an object or lu- minous point O, which diffuses rays in all directions : some of these will pass through our lens A B, such as O M, E, and O N ; of which that in the middle, O E, will undergo no refraction, but will con- tinue its direction through the lens in the same produced straight line F I P. The other two rays, O M and O N, in passing through the lens towards the edge, will be refracted both at entering and depart- ing, so that they will somewhere" meet the axis, as at I, and afterward continue their progress in the direction I Q and I R. It might likewise be demonstrated that all the rays which fall between M and N will be refracted, so as to meet with the axis in the same point I. Therefore, the rays which, had no lens interposed, would have pursued their rectilineal direction M and O N, will, after the refraction, pursue other directions, as if they had taken their departure from the point I: and if there were an eye somewhere at P, it would be affected just as if the luminous point were actually at I, though there be no reality in this. You have only to suppose for a moment, that there is at I a real object, which diffusing its rays, would be equally seen by an eye placed at P, as it now sees the object at O by means of the rays refracted by the lens, because there is at 1 an image of the object 0, and the lens A B there represents the object O, or transports it nearly to I. The point is therefore no longer the object of vision, but rather its image, represented at I ; for this is now its immediate obiect. 264 DISTANCE OF THE This lens, then, produces a very considerable change : an object very remote O is suddenly trans- ported to I, from which the eye must undoubtedly receive a very different impression from what it would do if, withdrawing the lens, it were to view the object O immediately. Let O be considered as a star, the point O being supposed extremely distant, the lens will represent at I the image of that star, but an image which it is impossible to touch, and which has no reality, as nothing exists at I, unless it be that the rays proceeding from the point O are collected there by the refraction of the lens. Nei- ther is it to be imagined that the star would appear to us in the same manner as if it really existed at I. How could a body many thousands of times bigger than the earth exist at a point I? Our senses would be very differently struck by it. We must carefully remark, then, that an image only is represented at I, like that of a star represented in the bottom of the eye, or that which we see in a mirror, the effect of which has nothing to surprise us. 15th December, 1761. LETTER LXXV. The same Subject: Distance of the Focus of Convex Lenses. ' I MEAN to employ this Letter in explaining the effect produced by convex lenses, that is, such as are thicker at the middle than at the edge. The whole consists in determining the change which rays un- dergo in their progress, on passing through such a glass. In order to place this subject in its clearest light, two cases must be carefully distinguished ; the one when the object is very distant from the lens, and the other when it is at no great distance. I FOCUS OF CONVEX LENSES. 265 begin with considering the first case, that is, when the object is extremely remote from the lens. In Fig. 146, M N is the convex lens, ^v. 145 and the straight line O A B I S its axis, passing perpendicularly through the middle. I remark, by-the-way, that this property of the axis of every lens, that of passing perpendicularly through its middle, conveys the justest idea of it that we are capable of form- ing. Let us now conceive that on this axis there is somewhere at O an object O P, which I here represent as a straight line, whatever figure it may really have; and as every point of this object emits its rays in all direc- tions, we confine our attention to those which fall on the lens. My remarks shall be at present fur- ther limited to the rays issuing from the point O, situated in the very axis of the lens. The figure represents three of these rays, O A, O M, and O N, the first cf which, O A passing through the middle of the lens, undergoes no change of direction, but proceeds, after having passed through the lens, in the same straight line BIS, that is, in the axis of the lens ; but the other two rays, O M and N, undergo a refraction both on entering into the glass and leaving it, by which they are turned aside from their first direction, so as to meet somewhere at I with the axis, from which they will proceed in their new direction, in the straight lines M I Q and N I R ; so that afterward, when they shall meet an eye, they will produce in it the same effect as if the point existed at I, as they preserve the same direction. For this reason, the convex lens is said to transport the object O to I ; but in order to distinguish this point I from the real point O, the VOL. II. Z 266 DISTANCE OF THE former is called the image of the latter, which in it* turn is denominated the object. This point I is very remarkable, and when the ob- ject O is extremely distant, the image of it is like- wise denominated the focus of the lens, of which 1 shall explain the reason. If the sun be the object at O, the rays which fall on the lens are all collected at I ; and being endowed with the quality of heating, it is natural that the concourse of so many rays at. I should produce a degree of heat capable of setting on fire any combustible matter that may be placed there. Now, the place where so much heat is col- lected we call the focus ; the reason of this denomi- nation with respect to convex lenses is evident. Hence, too, a convex lens is denominated a burning- glass, the effects of which you are undoubtedly well acquainted with. I only remark, that this property of collecting the rays of the sun in a certain point, called their focus, is common to all convex lenses : they likewise collect the rays of the moon, of the stars, and of all very distant bodies ; though their force is too small to produce any heat, we neverthe- less employ the same term, focus : the focus of a glass, accordingly, is nothing else but the spot where the image of very distant objects is represented ; to which this condition must still be added, that the object ought to be situated in the very axis of the lens ; for if it be out of the axis, its image will like- wise be represented out of the axis. I shall have occasion to speak of this afterward. It may be proper still further to subjoin the fol- lowing remarks respecting the focus : 1. As the point 0, or the object, is infinitely dis- tant, the rays O M, O A. and O N may be considered as parallel to each other ; and, for the same reason, parallel to the axis of the lens. 2. The focus I, therefore, is the point behind the glass where the rays parallel to the axis which FOCUS OF CONVEX LENSES. 267 fell on the lens are collected by the refraction of the lens. 3. The focus of a lens, and the spot where the image of an object, infinitely distant, and situated in the axis of the lens, is represented, are the same thing. 4. The distance of the point I behind the lens, that is, the length of the line B I, is called the distance of the focus of the lens. Some authors call it the focal distance, or focal length. 5. Every convex lens has its particular distance of focus- one greater, another less which is easily ascertained by exposing the lens to the sun, and ob- serving where the rays meet. 6. Lenses formed by arches of small circles, have their focuses very near behind them; but those whose surfaces are arches of great circles have more distant focuses. 7. It is of importance to know the focal distance of every convex lens employed in dioptrics ; and it is sufficient to know the focus in order to form a judgment of all the effects to be expected from it, whether in the construction of telescopes or micro- scopes. 8. If we employ lenses equally convex on both sides, so that each surface shall correspond to the same circle, then the radius of that circle gives nearly the focal distance of that lens ; thus, to make a burning-glass which shall burn at the distance of a foot, you have only to form the two surfaces arches of a circle whose radius is one foot. 9. But when the lens is plano-convex, its focal distance is nearly equal to the diameter of the circle which corresponds to the convex surface. Acquaintance with these terms will facilitate the knowledge of what I have further to advance on this subject. 19th December, 1761. 268 DISTANCE OF THE LETTER LXXVI. Distance of the Image of Objects. HAVING remarked that an object infinitely distant is represented by a convex lens in the very focus, provided the object be in the axis of the lens, I pro- ceed to nearer objects, but always situated in the axis of the glass ; and I observe, first, that the nearer the object approaches to the lens the farther the image retires. Let us accordingly suppose that F, Fig. 147. Fig. 147, is the focus of the lens MM, so that when an object is infinitely dis- tant before the glass, or at the top of the figure, the image shall be repre- sented at F ; on bringing the pbje*ct nearer to the glass, and placing it suc- cessively at P, Q, R, the image will be represented at the points p, q, r, more * fS distant from the lens than the focus : in other words, if A P is the distance of the object, B p will be the distance of the image ; and if A Q is the dis- tance of the object, B q will be that of the image ; and the distance B r of the image will correspond to the distance A R of the object. There is a rule by which it is easy to calculate the distance of the image behind the lens for every distance of the object before it, but I will not tire you with a dry exposition of this rule ; it will be sufficient to remark, in gene- ral, that the more the distance of the object be- fore the glass is diminished, the more is the distance of the image behind it increased. I shall to this IMAGE OF OBJECTS. 269 subjoin the instance of a convex lens whose focal distance is six inches, or of a lens so formed that if the distance of the object is infinitely great, the distance of the image behind the lens shall be pre- cisely six inches ; now, on bringing the object nearer to the lens, the image will retire, according to the gradations marked in the following table : Distance of the Object. Distance of the Image. Infinity. 6 42 7 h 24 8 18 9 15 10 12 12 10 15 9 18 8 24 7 42 6 Infinity. Thus, the object being 42 inches distant from the lens, the image will fall at the distance of 7 inches, that is, one inch beyond the focus. If the object is at the distance of 24 inches, the image will be re- moved to the distance of 8 inches from the lens, that is, two inches beyond the focus ; and so of the rest. Though these numbers are applicable only to a lens whose focal distance is 6 inches, some general consequences may, however, be deduced from them. 1. If the distance of the object is infinitely great the image falls exactly in the focus. * 2. If the distance of the object is double the dis- tance of the focus, the distance of the image will likewise be double the distance of the focus ; in other words, the object and the image will be equally dis- tant from the lens. In the example above exhibited; .< 2 270 IMAGE OF OBJECTS. the distance of the object being 12 inches, that of the image is likewise 12 inches. 3. When the object is brought so near the lens that the distance is precisely equal to that of the focus, say 6 inches, as in the preceding example, then the image retires to an infinite distance behind the lens. 4. It is likewise observable in general, that the distance of the object and that of the image recip- rocally correspond ; or if you put the object in the place of the image, it will fall in the place of the object. 5. If, therefore, the lens M M, Fig. 148, collects at I the rays which issue from the point O, the same lens will likewise collect at O rays issuing from the point I. 6. It is the consequence of a great principle in dioptrics, in virtue of which it may be maintained that whatever are the refractions which rays have under- gone in passing through several refract- ing media, they may always return in the same direction. This truth is of much importance in the know- ledge of lenses : thus, when I know, for example, that a lens has represented, at the distance of 8 inches, the image of an object 24 inches distant, I may confidently infer, that if the object were 8 inches distant, the same lens would represent its image at the distance of 24 inches. It is further essential to remark, that when the distance of the object is equal to that of the focus, the image will suddenly retire to an infinite distance ; which perfectly harmonizes with the relation existing between the object and the image. You will no doubt be curious to know in what place the image will be represented when the object is brought still nearer to the lens, so that its distance MAGNITUDE OF IMAGES. 271 shall become less than that of the focus. This ques- tion is the more embarrassing, that the answer must be, the distance of the image will in this case be greater than infinity, since the nearer the object ap- proaches the lens the farther does the image retire. But the image being already infinitely distant, how is it possible that distance should be increased 1 The question might undoubtedly puzzle philosophers, but is of easy solution to the mathematician. The image will pass from an infinite distance to the other side of the lens, and consequently will be on the same side with the object. However strange this answer may appear, it is confirmed, not only by reasoning, but by experience, so that it is impossible to doubt of its solidity ; to increase beyond infinity is the same thing with passing to the other side : this is unques- tionably a real paradox. 22d December, 1761. LETTER LXXVII. Magnitude of Images. You can no longer doubt that every convex lens must represent somewhere the image of an object presented to it ; and that in every case the place of the image varies as much according to the dis- tance of the object as according to the focal distance of the lens : but a very important article remains yet to be explained I mean the magnitude of the image. When such a lens represents to us the image of the sun, of the moon, or of a star, at the distance of a foot, you are abundantly sensible that these images must be incomparably smaller than the objects them- selves. A star being much greater than the whole earth, how is it possible that an image of such mag- 272 MAGNITUDE OF IMAGES. Fig. 149. nitude should be represented to us at the distance of a foot 1 But the star appearing to us only as a point, the image represented by the lens likewise resembles a point, and consequently is infinitely smaller than the object itself. There are, then, in every representation made by lenses, two things to be considered ; the one respects the place where the image is represented, and the other the real magnitude of the image, which may be very different from that of the object. The first being sufficiently elucidated, I proceed to furnish you with a very simple rule, by which you will be enabled in every case to determine what must be the magnitude of the image represented by the lens. Let O P, Fig. 149, be any object whatever situated on the axis of the convex lens M N ; we must first look for the place of the image, which is at I, so that the point I shall be the representation of the extremity O of the object, as the rays issuing from the point O are there collected by the refraction of the lens. Let us now see in what place will be repre- sented the other extremity P of the object ; for this purpose let us con- sider the rays P M, P A, P N, which, issuing from the point P, fall on the lens. I observe that the ray P A, which passes through the middle of the lens, does not change its direc- tion, but continues its progress in the straight line A K S ; it will be there- fore somewhere in this line, at K, that the other rays P M and P N will meet : in other words, the point K will be the image of the other extremity P of the- object, the point I being that of the extremity : MAGNITUDE OF IMAGES. 273 i 50 . hence it is easy to conclude that I K will be the image of the object P represented by the lens. In order, then, to determine the magnitude of this image, having found, the place I, you have only to draw from the extremity P of the object, through A, the middle of the lens, the straight line P A K S, and to raise from I the line I K perpendicular to the axis, and this line I K will be the image in question ; it is evident from this that the image is reversed, so that if the line O R were horizontal, and the object O P a man, the image would have the head K undermost, and the feet I uppermost. On this I subjoin the following remarks : 1. The nearer the image is to the lens, the smaller it is ; and the more remote it is, the greater its mag- nitude. Thus, O P, Fig. 150, being the object placed on the axis before the lens M N, if the image fell at Q, it would be smaller than if it fell at R, S, or T. For, as the straight line P A , drawn from the summit of the object P, through the middle of the lens, always terminates the image, at whatever distance it may be, it is evident that among the lines Q y, R r, S s, T t, the first Q q is the smallest, and that the others increase in pro- portion as they remove from the lens. 2. There is one case in which the image is precisely equal to the object : it is when the distance of the image is equal to that of the object ; and this takes place, as I have already re- marked, when the distance of the object A O is double that of the focus of the lens ; the image will then- be T r, so that the distance B t is equal to A O. \ ou have only then to consider the two triangles GAP and T A <, 274 MAGNITUDE OF IMAGES. which having the opposite angles at the point A, as well as the sides A O and A T, equal each to each, as likewise the angles at O and T, which are both right angles ; these two triangles will be every way equal, and consequently the side T t, which is the image, will be equal to the side O P, which is the object. 3. If the image were twice farther from the lens than the object, it would be double the object ; and in general, as many times as the image is farther from the lens than the object, so many times will it be greater than the object. For the nearer you bring the object to the glass, the farther the image retires, and consequently the greater it be- comes. 4. The contrary takes place when the image is nearer the lens than the object ; it is then as many times smaller than the object as it is nearer the lens than the object is. If, then, the 'distance of the image were one thousand times less than that of the object, it would likewise be one thousand times smaller. 5. Let us apply this to burning-glasses, which, being exposed to the sun, represent its image in the focus, or rather represent the focus, that is, the lumi- nous and brilliant circle, which burns, and which is nothing else but the image of the sun represented by the lens. You will no longer be surprised, then, at the smallness of the image, notwithstanding the pro- digious magnitude of the sun, it being as many times smaller in the focus than the real sun, as the dis- tance of the sun from the lens is greater than that of the image. 6. Hence likewise it is evident, that the greater is the distance of the focus of a burning-glass, the more brilliant also is the circle in the focus, that is, the greater will be the image of the sun ; and the diameter of the focus is always about one hundred times smaller than the distance of the focus from the lens. BURNING-GLASSES. 275 I shall afterward explain the different uses which may be made of convex lenses ; they are all suffi- ciently curious to merit attention. 26th December, 1761. LETTER LXXVIII. Burning-glasses. THE first use of convex lenses is their employ- ment as burning-glasses, the effect of which must appear altogether astonishing, even to those who already have some acquaintance with natural philo- sophy. In fact, who could believe that the image of the sun simply should be capable of exciting such a prodigious degree of heat 1 But your surprise will cease, if you please to pay some attention to the following reflections : 1. Let M N, Fig. 151, be a burn- ing-glass, which receives on its surface the rays of the sun R, R, R, refracted in such a manner as to. present at F a small luminous cir- cle, which is the image of the sun, and so much smaller as it is nearer to the glass. 2. All the rays of the sun, which fall on the surface of the glass are collected in the small space of the focus F; their effect, accord- ingly, must in that space be as many times greater as the surface of the glass exceeds the magnitude of the focus, or of the sun's image. We say that the rays, which were dispersed over the whole surface of the glass, are concentrated in the small space F. 3. The rays of the sun having a certain degree of heat, they exert their power in a very sensible man- ner at the focus ; it is possible even to calculate how 276 BURNING-GLASSES. many times the heat at the focus must exceed the natural heat of the sun's rays : we have only to observe how many times the surface of the glass is greater than the focus. 4. If the glass were not greater than the focus, the heat would not be stronger at the focus than any- where else ; hence we must conclude, that in order to the production of a strong heat by a burning- glass, it is not sufficient that it should be convex, or that it should represent the image of the sun ; it must besides have a surface which several times exceeds the magnitude of the focus, which is smaller in proportion as it is nearer to the glass. 5. France is in possession of the most excellent burning-glass : it is three feet in diameter, and its surface is calculated to be nearly two thousand times greater than the focus, or the image of the sun which it represents.* It must produce, therefore, in the focus, a heat two thousand times greater than that which we feel from the sun. Its effects are accord- ingly prodigious : wood of every kind is in a moment set on fire; metals are melted in a few minutes; and, in general, the most ardent fire which we are capable of producing is not once to be compared with the vehement heat of this focus. 6. The heat of boiling water is calculated to be about thrice greater than what we feel from the rays of the sun in summer ; or, which amounts to the same thing, the heat of boiling water is thrice greater than the natural heat of the blood in the human body. But in order to melt lead, we must have a heat thrice greater than is requisite to make water * The lens here alluded to was, we believe, one of Tschirnhausen's, that the Duke of Orleans purchased for the \cademy of Sciences. A more powerful burning lens, however, was afterward made in England by Mr. Parker, which cost above 700Z. It had 2 feet 8 inches of clear diameter. Its thickness at the centre was 3^ inches, and its focal length 6 feet 8 inches in diameter. It was made of flint-glass. This celebrated lens is now at Pekin. See Edinburgh Encyclopaedia, article Burning Instruments, vol. v. p. 141. Ed. BURNING-GLASSES. 277 boil ; and to melt copper, a heat still thrice greater is necessary. To melt gold requires a much higher degree of heat. Heat, then, one hundred times greater than that of our blood is capable of melting gold ; how far then must a heat two thousand times greater exceed the force of our ordinary fires 1 7. But how are these prodigious effects produced by the rays of the sun collected in the focus of a burning-glass? This is a very difficult question, with respect to which philosophers are very much divided. Those who maintain that the rays are an emanation from the sun, darted with the amazing velocity which I formerly described, are not greatly embarrassed for a solution ; they have only to say that the matter of the rays, striking bodies with violence, must totally break and destroy their minute particles. But this opinion is no longer admitted in sound philosophy. 8. The other system, which makes the nature of light to consist in the agitation of the ether, appears little adapted to explain these surprising effects of burning-glasses. On carefully examining, however, all the circumstances, we shall soon be convinced of the possibility of this. The natural rays of the sun, as they fall on bodies, excite the minute particles of the surface to a concussion, or motion of vibration, which, in its turn, is capable of exciting new rays ; and by these the body in question is rendered visible. And a body is illuminated only so far as these proper particles are put into a motion of vibration so rapid as to be capable of producing new rays in the ether. 9. It is clear, then, that if the natural rays of the sun have sufficient force to agitate the minute par- ticles of bodies, those which are collected in the focus must put the particles which they meet there into an agitation so violent that their mutual adhe- sion is entirely dissolved, and the body itself com- pletely destroyed, which is the effect of fire. For if VOL. II. A a 278 THE CAMERA OBSCURA. the body is combustible, as wood, the dissolution of these minute particles, joined to the most rapid agi- tation, makes a considerable part of it to fly off into air in the form of smoke, and the grosser particles remain in the form of ashes. Fusible bodies, as metals, become liquid by the dissolution of their par- ticles, whence we may comprehend how fire acts on bodies ; it is only the adhesion of their minutest par- ticles which is attacked, and the particles themselves are thereby afterward put into the most violent agita- tion. Here, then, is a very striking effect of burn- ing-glasses, which derives its origin from the nature of convex lenses.* There are besides many wonder- ful effects to be described. 28th December, 1761. LETTER LXXIX. The Camera Obscura. WE likewise employ convex lenses in the camera obscura, and by means of them all external objects are presented in the darkened room on a white sur- face, in their natural colours, in such a manner that landscapes and public buildings, or objects in general, are represented in much greater perfection than the power of the pencil is capable of producing. Painters accordingly avail themselves of this method, in order to draw with exactness landscapes and other objects which are viewed at a distance. The camera obscura, then, which is the subject of this Letter, is represented at E F G H, Fig. 152, closely shut up * In the work already quoted, in p, 262, note, I have shown how burn- ing lenses may be constructed of any size, by building them, as it were, of separate zones, each zone consisting of different segments, which are ground and polished separately. By this means the central parts of the burning lens are much less thick than when the lens is of one piece, and the error of the spherical aberration may be in a great measure cor- rected. See the Edinburgh Philosophical Journal, vol. viii. p. 160. Ed. THE CAMERA OBSCURA. 279 Fig. 152. on all sides, except one little round aperture made in one of the window-shutters, in which is fixed a convex lens, of such a focus as to throw the image of external objects, say the tree O P, exactly on the opposite wall F G, at o p. A white and moveable table is likewise employed, which is put in the place of the images represented. The rays of light, therefore, can be admitted into the chamber only through the aperture M N, in which the lens is fixed, without which total darkness would prevail. Let us now consider the point P of any object, say the stem of our tree O P. Its rays P M, P A, P N, will fall on the lens M N, and be refracted by it, so as to meet again at the point p on the wall, or on a white table* placed there for the purpose. This point p will consequently receive no other rays but such as proceed from the point P ; and in like manner every other point of the table will receive only the rays which proceed from the corresponding point of the object ; and reciprocally, to every point * The table should be made of stucco, or plaster of Paris, ground very tmnoothly, and ought to be concave, that every part of it may be equally distant from the lens. Ed. 280 THE CAMERA OBSCURA. of the external object will correspond a point on the table, which receives those rays, and no other. If the lens were to be removed from the aperture M N, the table would be illuminated in quite a different manner; for in that case every point of the object would diffuse its rays over the whole table, so that every point of the table would be illuminated at once by all the external objects, whereas at present it is so by one only, that whose rays it receives : from this you will easily comprehend that the effect must be quite different from what it would be if the rays entered simply by the aperture M N into the chamber. Let us now examine somewhat more closely wherein this difference consists ; and let us first sup- pose that the point P of the object is green ; the point of the table p will therefore receive only those green rays of the object P, and these, reuniting on the wall or table, will make a certain 'impression, which here merits consideration. For this purpose you will please to recollect the following propo- sitions, which I had formerly the honour of explain- ing to you : 1. Colours differ from each other in the same manner as musical sounds ; each colour is produced by a determinate number of vibrations, which in a given time are excited in the ether. The green colour of our point P is accordingly appropriated to a certain number of vibrations, and would no longer be green were these vibrations more or less rapid. Though we do not know the number of vibrations which produce such or such a colour, we may how- ever be permitted to suppose here that green requires twelve thousand vibrations in a second ; and what we affirm of this number, twelve thousand, may likewise be easily understood of the jeal number, whatever it be. 2. This being laid down, the point p on the white table will be struck by a motion of vibration, of which THE CAMERA OBSCURA. 281 twelve thousand will be completed in a second. Now, I have remarked that the particles of a white surface are all of such a nature as to receive every sort of agitation, more or less rapid ; whereas those of a coloured surface are adapted to receive only that degree of rapidity which corresponds to their colour. And as our table is white, the point p in it will be excited to a motion of vibration corresponding to the colour of green ; in other words, it will be agitated twelve thousand times in a second. 3. As long as the point j, or the particle of the white surface which exists there, is agitated with a similar motion, this will be communicated to the par- ticles of the ether which surround it; and this motion, diffusing itself in all directions, will generate rays of the same nature, that is to say green; just as in music, the sound of a certain note, say C, agitates a string wound up to the same tone, and makes ifr emit a sound without being touched. 4. The point p of the white table will accordingly produce green rays, as if it were died or painted that colour ; and what I affirm of the pointy will equally take place with respect to all the points of the illu- minated table, which will produce all the rays, each of the same colour with that of the object whose image it represents. Every point of the table will therefore become visible, under a certain colour, as if it were actually painted that colour. 5. You will perceive, then, on the table, all the colours of the external objects, the rays of which will be admitted into the chamber through the lens ; each point in particular will appear of the colour of that point of the object which corresponds to it, and you will see on the table a combination of various colours, disposed in the same order as you see them in the objects themselves ; that is to say, a repre- sentation, or rather the perfect picture, of all the ob- jects on the outside of the dark chamber which are before the lens N N. Aa2 282 THE CAMERA OBSCURA. 6. All these objects will, however, appear reversed on the table, as you will conclude from what I have said in my foregoing Letters. The under part of the tree will be represented at o, and the summit P at p; for, in general, each object must be represented on the white table in the place which is the termi- nation of the straight line drawn from the object P through the middle of the lens A : that which is up- ward will consequently be represented downward, and that which is to the left will be to the right ; in a word, every thing will be reversed in the picture ; the representation will nevertheless be more exact and more perfect than the most accurate painter is capable of producing. 7. You will further remark, that this picture will be so much smaller than the objects themselves in proportion as the focus of the lens is shorter. Lenses of a short focus will accordingly give the objects in miniature; and if you would wish to have them magnified, you must employ lenses of a longer focus, or which represent the images at a greater distance. 8. In order to contemplate these representations more at ease, the rays may be intercepted by a mir- ror, from which they are reflected, so as to represent the whole picture on a horizontal table ; and this is of peculiar advantage when we wish to copy the images.* 2d January, 1762. * The lens is sometimes ground on the anterior surface of a thick piece of glass, the posterior surface of which is ground flat, and inclined 45 to the axis of the lens. The picture is therefore reflected on a horizontal table, without the use of a mirror, and the image is much more perfect) as the light is totally reflected. Ed. THE CAMERA OBSCURA. 283 LETTER LXXX. Reflections on the Representation in the Camera Olscura. THOUGH you can no longer entertain any doubt respecting the representations made in a dark cham- ber by means of a convex lens, I hope the following reflections will not appear superfluous, as they serve to place this subject in a clearer light : 1. The chamber must be completely darkened, for were the light admitted the white table would be visible, and the particles of its surface, already agi- tated, would be incapable of receiving the impression of the rays which unite to form the images of exter- nal objects. Though, however, the chamber were a little illuminated, still something of the representation* would appear on the table, but by no means so vivid as if the chamber were entirely dark. 2. We must carefully distinguish the picture repre- sented on the white table from the image which the lens in virtue of its own nature represents, as I have formerly explained. It is very true, that placing the table in the very place where the image of the ob- jects is formed by the lens, this image will be con- founded by the picture we perceive on the table; these two things are nevertheless of a nature entirely different: the image is only a spectre or shadow floating in the air, which is visible but in certain places ; whereas the representation is a real picture, which every one in the chamber may see, and to which duration alone is wanting. 3. In order the more clearly to elucidate this differ- ence, you have only to consider carefully the nature of the image 0, Fig. 153, represented by the convex lens M N, the object being at O. This image is nothing else but the place in which the rays O M, O C, N, of the object, after having passed through 284 THE CAMERA OBSCURA. Fig. 153. the lens, meet by refraction, and thence continue their direction as if they proceeded from the point o, though they really originated from O, and by no means from o. 4. Hence the image is visible only to eyes situated somewhere within the angle R o Q, as at S, where an eye will actually receive the rays which come to it from the point o. But an eye situated out of this angle, as at F or V, will see nothing at all of it, because no one of the rays collected at o is directed towards it : the image at 0, therefore, differs very essentially from a real object, and is visible only in certain places. 5. But if a white table is placed at o, and its sur- face at this point o is really excited to an agitation similar to that which takes place in the object 0, this spot o of the surface itself generates rays which render it visible everywhere. Here, then, is the difference between the image of an object and its representation made in a camera obscura : the image is visible only in certain places, namely, those through which are transmitted the rays that origin- ally proceed from the object ; whereas the picture, or representation formed on the white table, is seen by its own rays, excited by the agitation of the par- ticles of its surface, and consequently visible in every place of the camera obscura. THE CAMERA OBSCURA. 285 6. It is likewise evident that the white table must absolutely be placed exactly in the place of the image formed by the lens, in order that every point of the table may receive no other rays except such as pro- ceed from a single point of the object; for if other rays were likewise to fall upon it, they would dis- turb the effect of the former, or render the repre- sentation confused. 7. Were the lens to be entirely removed, and free admission given to the rays into the dark chamber, the white table would be illuminated by it, but no picture would be visible. The rays of the different objects would fall on every point of the table, with- out expressing any one determinate image. The picture, accordingly, which we see in a camera ob- scura, on a white surface, is the effect of the convex lens fixed in the shutter : this it is which collects anew, in a single point, all the rays that proceed from one point of the object. 3. A very singular phenomenon is here however observable, when the aperture made in the window- shutter of the dark chamber is very small ; for though no lens be applied you may nevertheless perceive, on the opposite partition, the images of external ob- jects, and even with their natural colours ; but the representation is very faint and confused, and if the aperture is enlarged, this representation entirely disappears. I shall explain this phenomenon. In Fig. 154, M N is the small aperture through which the rays of external objects are admitted into the dark chamber E F G H. The wall F G opposite to the aperture is white, the better to receive the impres- sion of rays of all sorts. Let the point O be an object, of which the rays O M, N alone, with those which fall between 286 OF THE MAGIC LANTERN, them, can enter into the chamber. These rays will be confined to the small space o o of the wall, and will illuminate it. This space o o will be so much smaller, or approach the nearer to a point, in pro- portion as the aperture M N is small : if then this aperture were very small, we should have the effect already described, according to which every point of th,e white table receives only the rays proceeding from a single point of the object: there would be produced, of consequence, a representation similar to that which is produced by the application of a convex lens to an aperture in the window-shutter. But in the present case, the aperture being of a cer- tain extent, every point O of the object will illumi- nate a certain small space o o on the wall, and agitate it by its rays. The same thing, then, nearly, would take place, as if a painter, instead of making points with a fine pencil, should with a coarsS one make spots of a certain magnitude, attending, however, to design and colouring : the representation made on the wall will have a resemblance to this sort of daubing ; but it will be clearer in proportion to the smallness of the aperture by which the rays are ad- mitted. 5th January, 1762. LETTER LXXXI. Of the Magic Lantern, and Solar Microscope. THE camera obscura has properly no effect except on very distant objects, but you will easily compre- hend that its application may be equally extended to nearer objects. For this purpose, the white table must be removed farther from the lens, conformably to this general rule, that the nearer the object is brought to the convex lens, the farther does the image, where the white table ought to be placed, retire from it ; and if the chamber is not of suffi- AND SOLAR MICROSCOPE. 287 cient depth, a different lens, of a shorter focus, must be employed. You may place, then, out of the chamber, before the aperture to which the convex lens is fitted, any object or picture whatever, and you will see a copy of it on the white table within the dark chamber, greater or smaller than the original, according as the distance of the image is greater or smaller; but it would be more commodious, undoubtedly, if the object could be exposed within the dark chamber, in order to its being moved and changed at pleasure. But here a great difficulty occurs, the object itself would in this case be darkened, and consequently rendered incapable of producing the effect we wish. The thing wanted, then, is to illuminate the object as much as possible within the dark chamber, and at the same time to exclude the light. I have found out the means of doing this. You will recollect that I constructed a machine to the effect I am mentioning, which I had the honour of presenting to you six years ago ; and now you will easily com- prehend the structure, and the principles on which it is founded. This machine consists of a box very close on all sides, nearly of a figure similar to Fig. 164. The Fig. 164. 288 OF THE MAGIC LANTERN, farther side of which E G has an opening I K, in which are to be fitted the objects, portraits or other pictures, P, which you mean to represent ; on the other side, directly opposite, is a tube M N Q R, containing a convex lens M N ; this tube is move- able, for the purpose of bringing the lens nearer to the object, or of removing it, at pleasure. Then, provided the object O P be well illuminated, the lens will throw somewhere the image of it o p, and if you there place a white tablet, you will see upon it a perfect copy of the object, so much the clearer as the object itself is more illuminated. For this purpose I have contrived in this box two side wings, for the reception of lamps with large wicks, and in each wing is placed a mirror to reflect the light of the lamps on the objects O P ; above, at E F, is a chimney, by which the smoke of the lamps passes off. Such is the construction of this ma- chine, within which the object O P may be very strongly illuminated, while 'the darkness of the chamber suffers no diminution. In order to the proper use of this machine, attention must be paid to the following remarks. 1. On sliding inward the tube M N Q R, that is, bringing the lens M N nearer to the object O P, the image o p will retire ; the white tablet must there- fore be removed backwards, to receive the image at the just distance ; the image will thereby be like- wise magnified, and you may go on to enlarge it at pleasure, by pressing the lens M N nearer and nearer to the object P. 2. On removing the lens from the object, the dis- tance of the image will be diminished : the white tablet must in this case be moved nearer to the lens, in order to have a clear and distinct representation ; but the image will be reduced. 3. It is obvious that the image will be always re- versed ; but this inconvenience is easily remedied ; you have only to reverse the object O P itself, turn- AND SOLAR MICROSCOPE. 289 ing it upside down, and the image will be repre- sented upright on the white tablet. 4. It is a further general remark, that the more, the image is magnified on the white tablet, the less uminous and distinct it will be ; but on reducing the image, it is rendered more distinct and brilliant. The reason is plain the light proceeds wholly from the illumination of the object ; the greater that the space is over which it is diffused^ the more it must be weakened, and the more contracted it is, the more brilliant. 5. Accordingly, the more you wish to magnify the representation, the more you must strengthen the illumination of the object, by increasing the light of the lamps in the wings of the machine ; but for small representations a moderate illumination is sufficient. The machine which I have been describing is called the magic lantern, to distinguish it from the common camera obscura, employed for representing distant objects ; its figure, undoubtedly, has procured it the name of lantern, especially -as it is designed to contain light ; but the epithet magic must have been an invention of its first proprietors, who wished to impress the vulgar with the idea of magic or witchcraft. The ordinary magic lanterns, however, are not constructed in this manner, and serve to represent no other objects but figures painted on glass, whereas this machine may be applied to ob- jects of all sorts. It may even be employed for representing the smallest objects, and for magnifying the representa- tion to a prodigious size, so that the smallest fly shall appear as large as an elephant ; but for this purpose the strongest light that lamps can give is ffir from being sufficient; the machine must be dis- posed in such a manner that the objects may be illu- minated by the rays of the sun, strengthened by a burning-glass ; the machine, in this case> changes VOL. IL B b 290 USE AND EFFECT OF A its name, and is called the solar microscope. I shaH have occasion to speak of it more at large in the Sequel. 8th January, 1762. LETTER LXXXII. Use and Effect of a simple Convex Lens, WE likewise employ convex lenses for imme- diately looking through ; but in order to explain their different uses, we must go into a closer investigation of their nature. Having observed the focal distance of such a glass, I have already remarked, that when the ob- ject is very remote, its image is represented in the focus itself; but on bringing the object nearer to the lens, the image retires farther and farther' from it : so that if the distance of the object be equal to that of the focus of the lens, the image is removed to an infinite distance, and consequently becomes infinitely great. The reason is, that the rays OM, OM, Fig. 155, Fig. 155. F which come from the point O, are refracted by the lens, so as to become parallel to each other, as N F, N F ; and as parallel lines are supposed to proceed forward to infinity, and as the image is always in the place where the rays, issuing from one point of the object, are collected again after the refrac- tion ; in the case when the object O A is equal to that of the focus of the lens, the place of the image SIMPLE CONVEX LENS. 291 Fig. 156. removes to an infinite distance ; and as it is indifferent whether we conceive the parallel lines N F and N F to meet at an infinite distance to the left or to the right, it may be said indifferently that the image is to the right or to the left infinitely distant, the effect being always the same. Having made this remark, you will easily judge what must be the place of the image when the ob- ject is brought still nearer to the lens. Let O P, Fig. 156, be the object, and as its distance O A from the con- vex lens is less than the distance of the focus, the rays O M, O M, which fall upon it from the point O, are too divergent to admit of the possibility of their being rendered parallel to each other by the refractive power of the lens: they will therefore be still divergent after the refraction, as marked by the lines N F, N F, though much lss so than before ; therefore, if these lines are produced backward, they will meet somewhere at 0, as you may see in the dotted lines N 0, N o. The rays N F, N F, will of con- sequence, after havingpassed through p the lens, preserve the same direction as if they had proceeded from the point 0, though they have not actually passed through that point, as it is only in the lens that they have taken this new direction. An eye which receives these refracted rays N F, N F, will be therefore af- fected as if they really came from the point 0, and will imagine that the object of its vision exists at 0. There will, however, be no image at that point, as in the preceding case. To no purpose would you put a white tablet at o ; it would present no picture there for want of rays : for this reason we say that there is an imaginary image at 0, and not a 292 USE OF A SIMPLE CONVEX LENS. real one the term imaginary being opposed to that of real. Nevertheless, an eye placed at E receives the same impression as if the object O P, from which the rays originally proceed, existed at o. It is of great im- portance, then, to know, as in the preceding cases, the place and the magnitude of this imaginary image o p. As to the place, it is sufficient to remark, that if the distance of the object A O be equal to the dis- tance of the focus of the lens, the image will be at an infinite distance from it ; and this is what the present case has in common with the preceding ; but the nearer the object is brought to the lens, or the less that the distance A O becomes than that of the focus of the lens, the nearer does the imaginary image approach to the lens ; though, at the same time, it remains always at a greater distance from the lens than the object itself. To elucidate this by an example, let us suppose that the focal distance of the lens is 6 inches ; and for the different distances of the object, the an- nexed table indicates the distance of the imaginary image op. If the distance of the Object \ A Ois The distance of the imaginary Image A o will be 6 5 4 3 2 1 Infinity 30 12 6 3 1 and a fifth. The rule for ascertaining the magnitude of this imaginary image o p is easy and general ; you have only to draw through the middle of the lens, marked C, and through the extremity of the object P, the straight line C P p ; and where it meets with the line o p drawn from o at right angles with the axis USE OF A CONCAVE LENS. 293 of the lens, you will have found the magnitude of the imaginary image o p : from which it is evident, that this image is always greater than the object O P itself, as many times as it is farther from the lens than the object O P. It is likewise evident that this image is not reversed, as in the preceding case, but upright as the object. You will easily comprehend, from what I have said, the benefit that may be derived from lenses of this sort, by persons whose sight is not adapted to the view of near objects, but who can see them to more advantage at a considerable distance. They have only to look at objects through a convex lens, in order to see them as if they were very distant. The defect of sight with respect to near objects occurs usually in aged people, who consequently make use of spectacles with convex glasses, which, exposed to the sun produce the effect of a burning- glass, and this ascertains the focal distance of every glass. Some persons have occasion for spectacles of a very near focus, others of one more distant, according to the state of their sight ; but it is suffi- cient for my present purpose to have given a gen- eral idea of the use of such spectacles. 12th January, 1762. LETTER LXXXIIL Use and Effect of a Concave Lens. You have seen how convex glasses assist the sight of old people, by representing to them objects as at a greater distance than they really are ; there are eyes, on the contrary, which, in order to distinct vision, require the objects to be represented as nearer ; and concave glasses procure them this ad- vantage ; which leads me to the explanation of the Bb2 294 USE AND EFFECT OF Fig. 157. effect of concave lenses, which is directly the con- trary of that of convex ones. When the object O P, Fig. 157, is very distant, and its rays O M, O M, fall almost parallel on the concave lens T T ; in this case, instead of becoming convergent by the refraction of the lens, they, on the contrary, become more divergent, pursuing the direction N F, N F, which, pro- duced backward, meet at the point o ; so that an eye placed, for example, at E, receives these refracted rays in the same man- ner as if they proceeded from the point 0, though they really proceed from the point O ; for this reason, I have in the figure dotted the straight lines N o. No. As the object is supposed to be infinitely distant, were the lens convex the point o would be what we call the focus ; but as, in the present case, there is no real concurrence of rays, we call this point the imaginary focus of the concave lens ; some authors likewise denominate it the point of dispersion, because the rays, refracted by the glass, appear to be dispersed from this point. Concave lenses, then, have no real focus, like the convex, but only an imaginary focus, the distance of which from the lens A o is, however, denominated the focal distance of this lens, and serves, by means of a rule similar to that which is laid down for con- vex lenses, to determine the place of the image, when the object is not infinitely distant. Now, this image is always imaginary ; whereas in the case of convex lenses, it becomes so only when the object is A CONCAVE LENS. 295 nearer than the distance of the focus. Without entering into the explanation of this rule, which respects calculation merely, it is sufficient to re-' mark : 1. When the object O P is infinitely distant, the imaginary image o p is represented at the focal dis- tance of the concave lens, and this, too, on the same side with the object. Nevertheless, though this image be imaginary, the eye placed at E is quite as much affected by it as if it were real, conformably to the explanation given on the subject of convex lenses, when the object is nearer the lens than its focal distance. 2. On bringing the object O P nearer to the lens, its image o p will likewise approach nearer, but in such a manner that the image will always be nearer to the lens than the object is ; whereas, in the case of convex lenses, the image is more distant from the lens than the object. In order to elucidate this more clearly, let us suppose the focal distance of the con- cave lens to be 6 inches. If the Distance of the Object A is The Distance of the Image o A will be Infinite. 30 12 6 3 2 6 5 4 3 2 1 and a half. 3. By the same rule you may always determine the magnitude of the imaginary image o p. You draw from the middle of the lens a straight line, to the extremity of the object P, which will pass through the extremity p of the image. For, since the line P A represents a ray coming from the extremity of the object, this same ray must, after the refraction, pass through the extremity of the image ; but as 296 USE OF A CONCAVE LENS. this ray PA passes through the middle of the lens, it undergoes no refraction ; therefore it must itself pass through the extremity of the image, at the point p. 4. This image is not reversed, but in the same position with the object ; and it may be laid down as a general rule, that whenever the image falls on the same side of the lens that the object is, it is always represented upright, whether the Ions .be convex or concave; but when represented on the other side of the lens, it is always reversed ; and this can take place only in convex lenses. 5. It is evident therefore that the images repre- sented by concave lenses are always smaller than the objects ; the reason is obvious the image is always nearer than the object; you have only lp look at the figure to be satisfied of this truth. These are the principal properties to be remarked respecting the nature of concave lenses, and the manner in which objects are represented by them. It is now easy to comprehend how concave glasses may be rendered essentially serviceable to persons whose sight is short. You are acquainted with some who can neither read nor write without bringing the paper almost close to their nose. In order, therefore, to their seeing distinctly, the object must be brought very near to the organ of vision : I think I have for- merly remarked that such persons are denominated myopes. Concave lenses, then, may be made of great use to them, for they represent the most distant ob- jects as very near ; the image not being farther from such glasses than their focal distance, which, for the most part, is only a few inches. These images, it is true, are much smaller than the objects themselves ; but this by no means prevents distinctness of vision. A small object near may appear greater than a very large body at a distance. In fact, the head of a pin appears to the eye greater OF MICROSCOPES IN GENERAL. 297 than a star in the heavens, though that star far ex- ceeds the earth in magnitude. Persons whose sight is short, or myopes, have occasion, then, for glasses which represent objects , as nearer; such are concave lenses. And those whose sight is long, or presbytes, need convex glasses, which represent to them objects at a greater distance. 16th January, 1762. LETTER LXXXIV. Of apparent Magnitude, of the Visual Angle, and of Microscopes in general. I HAVE been remarking, that myopes are obliged to make use of concave glasses to assist their vision of distant objects, and that presbytes employ convex glasses in order to a more distant vision of such as are near ; each sight has a certain extent, and each requires a glass which shall represent objects per- fectly. This distance in the myopes is very small, and in the presbytes very great ; but there are eyes so happily conformed as to see nearer and more distant objects equally well. Nevertheless, of whatever nature any person's sight may be, this distance is never very small : there is no myope capable of seeing distinctly at the dis- tance of less than an inch ; you must have observed, that when the object is brought too close to the eye, it has a very confused appearance ; this depends on the structure of the organ, which is such in the hu- man species as not to admit of their seeing objects very near. To insects, on the contrary, very distant objects are invisible, while they easily see such as are nearer. I do not believe that a fly is capable of seeing the stars, because it can see extremely well at the distance of the tenth part of an inch, a dis* 298 OF MICROSCOPES IN GENERAL. tance at which the human eye can distinguish abso- lutely nothing. This leads me to an explanation of the microscope, which represents to us the smallest object as if it were very great. In order to convey a just idea of it, I must entreat you carefully to distinguish between the apparent and the real magnitude of every object. Real mag- nitude constitutes the object of geometry, and is in- variable as long as the body remains in the same state. But apparent magnitude admits of infinite variety, though the body may remain always the same. The stars, accordingly, appear to us extremely small, though their real magnitude is prodigious, because we are at an immense distance from them. Were it possible to approach them, they would appear greater; from which you will conclude that the ap- parent magnitude depends on the angle formed in our eyes by the rays which proceed from the extremities of the object. Let P O Q, Fig. 158, be the object of vision, which, if the eye were placed at A, would appear under the angle P A Q, called the visual angle, and which indicates to us the apparent magnitude of the object ; it is evident, on inspecting the figure, that the far- ther the eye withdraws from the ob- ject, the smaller this angle becomes, and that it is possible for the greatest bodies to appear to us under a very small visual angle, provided our dis- tance from them be very great, as is the case with the stars. But when the eye approaches nearer to the object, and looks at it from B, it will appear under the visual angle P B Q, which is evidently greater than P A Q. Let the eye advance still forward to C, and the visual angle P C Q is still greater. Further, the eye being placed at D, the OF MICROSCOPES IN GENERAL. 299 visual angle will be P D Q ; and on advancing for- ward to E, the visual angle will be P E Q, always greater and greater. The nearer, therefore, the eye approaches to the object, the more the visual angle increases, and consequently likewise the apparent magnitude. However small the object may be, it is possible, therefore, to increase its apparent magnitude at pleasure ; you have only to bring it so near the eye as is necessary to form such a visual angle. A fly near enough to the eye may, of consequence, appear under an angle as great as an elephan-t at the distance of ten feet. In a comparison of this sort, we must take into the account the distance at which we suppose the elephant to be viewed ; un- less this is done, we affirm absolutely nothing ; for an elephant appears great only when we are not very far from it ; at the distance of a mile, it would be impossible, perhaps, to distingush an elephant from a pig ; and, transported to the moon, he would become absolutely invisible ; and I might affirm with truth, that a fly appeared to me greater than an elephant, if the latter was removed to a very considerable distance. Accordingly, if we would express ourselves with precision, we must not speak of the apparent magnitude of a body, without taking distance likewise into the account, as the same body may appear very great or very small ac- cording as its distance is greater or less. It is very easy, then, to see the smallest bodies under very great visual angles ; they need only to be placed very close to the eye. This expedient may be well enough adapted to a fly, but the human eye could see nothing at too small a distance, however short the sight may be ; besides, persons of the best sight would wish to see likewise the smallest objects extremely magnified. The thing required, then, is to find the means of en- abling us to vi'ew an object distinctly, notwithstand- ing its great proximity to the eye. Convex lenses 300 OBJECTS VIEWED THROUGH render us this service, by removing the image of ob- jects which are too near. Let a very small convex lens M N be employed, Fig. 159, the focal distance of which shall be half an Fig. 159. inch ; if you place before it a small object O P, at a distance somewhat less than half an inch, the lens will represent the image of it o p, as far off as could be wished. On placing the eye, then, behind the lens, the object will be seen as if it were at 0, and at a sufficient distance, as if its magnitude were o p : as the eye is supposed very near the lens, the visual angle will be p I o, that is, the same as P, t O, under which the naked eye would see the object O P in that proximity ; but the vision is become distinct by means of the lens : such is the principle on which microscopes are constructed. IQth January, 1762. LETTER LXXXV. Estimation of the Magnitude of Objects viewed through the Microscope. WHEN several persons view the same object through a microscope, the foot of a fiy, for example, they all agree that they see it greatly magnified, but their judgment respecting the real magnitude will Vary ; one will say, it appears to him as large as that of a horse ; another, as that of a goat ; a third, as that of a cat. No one then advances any thing posi- tive on the subject, unless he adds at what distance he views the feet of the horse, the goat, or the cat. THE MICROSCOPE. 301 They all mean, therefore, without expressing it, a certain distance, which is undoubtedly different ; con- sequently, there is no reason to be surprised at the variety of the judgments which they pronounce, as the foot of a horse viewed at a distance, may very well appear no bigger than that of a cat viewed near to the eye. Accordingly, when the question is to be decided, How much does the microscope mag- nify an object 1 we must accustom ourselves to a more accurate mode of expression, and particularly to specify the distance, in the comparison which we mean to institute. It is improper, therefore, to compare the appear- ances presented to us by the microscope with objects of another nature, which we are accustomed to view sometimes near and sometimes at a distance. The most certain method of regulating this estimation seems to be that which is actually employed by au- thors who treat of the microscope. They compare a small object viewed through the microscope with the appearance which it would present to the naked eye on being removed to a certain distance; and they have determined, that in order to contemplate such a small object to advantage by the naked eye, it ought to be placed at the distance of eight inches, which is the standard for good eyes, for a short- sighted person would bring it closer to the eye, and one far-sighted would remove it. But this difference does not affect the reasoning, provided the regulating distance be settled ; and no reason can be assigned for fixing on any other distance than that of eight inches, the distance received by all authors who have treated of the subject. Thus, when it is said* that a microscope magnifies the object a hundred times, you are to understand that, with the assist- ance of such a microscope, objects appear a hundred times greater than if you viewed them at the dis- tance of eight inches ; and thus you will form a just idea of the effect of a microscope. VOL. II. c 802 OBJECTS VIEWED THROUGH In general, a microscope magnifies as many times as an object appears larger than if it were viewed without the aid of the glass at the distance of eight inches. You will readily admit that the effect is surprising, if an object is made to appear even a hundred times greater than it would to the naked eye at the distance of eight inches : but it has been carried much farther ; and microscopes have been constructed which magnify five hundred times a thing almost incredible. In such a case it might be with truth affirmed that the leg of a fly appears greater than that of an elephant. Nay, I have full conviction that it is possible to construct micro- scopes capable of magnifying one thousand, or even two thousand times, which would undoubtedly lead to the discovery of many things hitherto unknown. But when it is affirmed that an object p 16 appears through the microscope a hundred ' times greater than when viewed at the dis- tance of eight inches, it is to be under- stood that the object is magnified as much in length as in breadth and depth, so that each of these dimensions appears a hundred times greater. You have only, then, to conceive at the distance of eight inches another object similar to the first, but whose length is a hundred times greater, as well as its breadth and depth, and such will be the image viewed through the microscope. Now, if the length, the breadth, and depth of an object be a hundred times greater f than those of another, you will easily per- 'ceive that the whole extent will be much more than a hundred times greater. In order to put this in the clearest light, let us conceive two parallelograms A B C D, and E F G H, Fig. 160, of the same breadth, but that the length of the first, A B, shall be five times greater m THE MICROSCOPE. 303 than the length of the other, E F ; it is evident that the area, or space contained in the first, is five times greater than that contained in the other, as in fact this last is contained five times in the first. To render, then, the parallelogram A D five times greater than the parallelogram E H, it is sufficient that its length A B be five times greater, the breadth being the same ; and if, besides, the breadth were likewise five times greater, it would become five times greater still, ttfat is, five times five times, or twenty-five times greater. Thus, of two surfaces, if the one be five times longer and five times broader than the other, it is in fact twenty-five times greater. If we take, further, the height or depth into the account, the increase will be still greater. Conceive two apartments, the one of which is five times longer, five times broader, and five times higher than the other ; its contents will be five times 25 times, that is, 125 times greater. When, therefore, it is said that a microscope magnifies 100 times, as this is to be understood, not only of length, but of breadth, and depth, or thickness, that is, of three dimensions, the whole extent of the object will be increased 100 times 100 times 100 times; now 100 times 100 make 10,000, which taken again 100 times make 1,000,000 ; thus, when a microscope magnifies 100 times, the whole extent of the object is repre- sented 1,000,000 times greater. We satisfy our- selves, however, with saying that the microscope magnifies 100 times ; but it is to be understood that all the three dimensions, namely, length, breadth, and depth, are represented 100 times greater. If, then, a microscope should magnify 1000 times, the whole extent of the object would become 1000 times 1000 times 1000 times greater, which makes 1,000,000,000, or a thousand millions : a most aston- ishing effect! This remark is necessary to the 304 PLAN OF SIMPLE MICROSCOPES. formation of a just idea of what is said respecting the power of microscopes.* 23d January, 1762. LETTER LXXXVI. Fundamental Propositionfor the Construction of Simple Microscopes. Plan of some Simple Microscopes. HAVING explained in what manner we are enabled to judge of the power of microscopes, it will be easy to unfold the fundamental principle for the con- struction of simple microscopes. And here it may be necessary to remark, that there are two kinds of microscopes ; some consisting of a single lens, others of two or more, named, accordingly, simple or compound microscopes, and which require par- ticular elucidations. I shall confine myself at pres- ent to the simple microscope, which consists of a single convex lens, the effect of which is determined by the following proposition : A simple microscope magnifies as many times as its focal distance is nearer than eight inches. The demonstration follows. Let M N, Fig. 161, be a con- jvg-. 161. vex lens, whose focal distance, p^ at which the object P must \ be placed nearly, in order that o | ^ the eye may see it distinctly, shall be C O ; this object will be perceived under the angle OOP. But if it be viewed at the distance of eight inches, it would appear under an angle as many times smaller as the distance of eight inches surpasses * As it is in reality only the surface of bodies that is presented to the eye, it may be questioned whether the magnifying power of a micro- scope ought to be estimated at a higher rate than that of the square : thus, if it magnify 100 times in length, the object will appear 10,000 times greater tb.au to the naked eye. Am. Ed. PLAN OF SIMPLE MICROSCOPES. 305 the distance C O: the object will appear, therefore, as many times greater than if it were viewed at the distance of eight inches. Now, in conformity to the rule already established, a microscope magnifies as many times as it presents the object greater than if we viewed it at the distance of eight inches. Consequently, a microscope magnifies as many times as its focal distance is less than eight inches. A lens, therefore, whose focal distance is an inch will magnify precisely eight times ; and a lens whose focal distance is only half an inch will magnify six- teen times. The inch is divided into twelve parts, called lines ; half an inch, accordingly, contains six lines : hence it would be easy to determine how many times every lens, whose focal distance is given in lines, must magnify ; according to the following table : Focal distance of the lens in lines. 12, 8, 6, 4, 3, 2, 1, 4 lines, magnifies 8, 12, 16, 24, 32, 48, 96, 192 times. Thus a convex lens whose focal distance is one line magnifies ninety-six times; and if the distance be half a line, the microscope will magnify one hun- dred and ninety-two, that is, near two hundred times. Were greater effect still to be desired, lenses must be constructed of a still smaller focus.* Now, it has been already remarked, that in order to con- struct a lens of any certain given focus, it is only necessary to make the radius of each face equal to that focal distance, so that the lens may become equally convex on both sides. I now proceed, then, to place before you, Fig. 162, the form of some of these lenses or microscopes : No. I. The focal distance of this lens A O is one inch, or twelve lines. This microscope, therefore, magnifies eight times. * Lenses have been ground and polished having only a focal length of one-fiftieth of an inch, consequently their magnifying power is 400 times. -Ed. Cc2 306 PLAN OF SIMPLE MICROSCOPES. No. II. The focal distance of the Fig. 162. lens M N is eight lines. This micro- p j M <*^ scope magnifies twelve times. i '. -rfl jb- No. III. The focal distance of the & ^ lens M N is six lines. This micro- r Ji y**^ scope magnifies sixteen times. o ^v^ No. IV. The focal distance of this lens is four lines ; and such a micro- 'o~l^_ scope magnifies twenty-four times. No. V. The focal distance here is three lines. This microscope magni- fies thirty-two times. H) ;fcp No. VI. The focal distance here is ^^ two lines. This microscope magni- fies forty-eight times. ^^ No. VII. The focal distance of this lens is only one line ; and such a microscope mag- nifies ninety-six times. It is possible to construct microscopes still much smaller. They are actually executed, and much more considerable effects are produced ; whence it must be carefully remarked, that the distance of the object from the glass becomes smaller and smaller, as it must be nearly equal to the focal distance of the lens. I say nearly, as every eye brings the glass closer to it somewhat more or less, according to its formation ; the short-sighted apply it closer, the far- sighted less so. You perceive, then, that the effect is greater as the microscope or lens becomes smaller, and the closer likewise the object must be applied : this is a very great inconvenience, for, on the one hand, it is troublesome to look through a glass so very small ; and, on the other, because the object must be placed so near the eye. Attempts have been made to remedy this inconvenience by a proper mounting, which may facilitate the use of it ; but the vision of the object is considerably disturbed as soon as the distance of it undergoes the slightest change : and as in the case of a very small lens the object must DEFECTS OF THE SIMPLE MICROSCOPE. 307 almost touch it, whenever the surface of the object is in the least degree unequal, it is seen but o confusedly. For, while the eminences are viewed at the just distance, the cavities, being too far removed, must be seen very confusedly. This renders it necessary to lay aside simple microscopes when we wish to magnify very considerably, and to have recourse to the compound micro- scope. 26ik January, 1762. LETTER LXXXVII. Limits and Defects of the Simple Microscope. You have now seen how simple micro- scopes may be constructed, which shall magnify as many times as may be desired ; you have only to measure off a straight line of eight inches, like that which I have marked A B,* Fig. 163, which contains precisely eight inches of the Rhenish foot, which is the standard all over Germany. This line A B must then be subdivided into as many equal parts as correspond to the number of times you wish to magnify the object proposed, and one of these parts will give the focal distance of the lens that is requisite. Thus, if you wish to magnify a hundred times, you must take the hundredth part of the line A B; consequently, you must construct a lens whose focal distance shall be precisely equal to that part A i, which will give, at the same time, the radius of the surfaces * It being impossible here to insert a straight line of eight inches, one of half that length is employed, for the purpo.se of illustration. 308 DEFECTS OF of the lens represented in No. VII. of the preceding figure. Hence it is evident, that the greater the effect we mean to produce, the smaller must be the lens, as well as the focal distance at which the object O P must be placed before the lens, while the eye is applied behind it : and if the lens were to be made twice smaller than what I have now described, in order to magnify two hundred times, it would be- come so minute as almost to require a microscope to see the lens itself; besides, it would be neces- sary to approach so close as almost to touch the lens, which, as I have already observed, would be very inconvenient. The effect of the microscope, therefore, could hardly be carried beyond two hun- dred times ; which is by no means sufficient for the investigation of many of the minuter productions of nature. The purest water contains small ani- malcules, which, though magnified two hundred times, still appear no bigger than fleas ; and a mi- croscope which should magnify 20,000 times would be necessary to magnify their appearance to the size of a rat; and we are far from reaching this degree, even with the assistance of the compound microscope.* But besides the inconveniences attending the use of simple microscopes which have been already pointed out, all those who employ them with a view to very great effect complain of another consider- able defect; it is this the more that objects are magnified, the more obscure they appear ; they seem as if viewed in a very faint light or by moonlight, so that you can hardly distinguish any thing clearly. You will not be surprised at this, when you recol- lect that the light of the full moon is more than two hundred thousand times fainter than that of the sun. It is of much importance, therefore, to explain * It is not probable that water perfectly pure contains any animal- cnlae, that is, water prepared by the slow and careful distillation of clear tresh rain-water, and preserved in close vessels. Am. Ed. THE SIMPLE MICROSCOPE. 309 whence this diminution of light proceeds. We can easily comprehend, that if the rays which proceed from a very small object must represent it to us as if it were much larger, this small quantity of light would not be sufficient. But however well founded this reasoning may appear, it wants solidity, and throws only a false light on the question. For if the lens, as it proceeded in magnifying, necessarily produced a diminution of clearness, this must like- wise be perceptible in the smallest effects, even supposing it were not to so high a degree ; but you may magnify up to fifty times, without perceiving the least apparent diminution of light, which, how- ever, ought to be fifty times fainter, if the reasons adduced were just. We must look elsewhere, then, for the cause of this phenomenon,' and even resort to the first principles of vision. I must entreat you, then, to recollect what I have already suggested respecting the use ot the pupil, or that black aperture which we see in the eye at the middle of the iris. It is through this aperture that the rays of light are admitted into the eye ; accord- ingly, the larger this aperture is, the more rays are admitted. We must here consider two cases in. which objects are very luminous and brilliant, and in which they are illuminated by only a very faint light. In the first, the pupil contracts of itself, with- out any act of the will ; and the Creator has bestowed on it this faculty in order to preserve the interior of the eye from the too dazzling effect of light, which would infallibly injure the nerves. Whenever, there- fore, we are exposed to a very powerful light, we observe that the pupil of every eye contracts, to prevent the admission of any more rays into the eye than are necessary to paint in it an image sufficiently luminous. But the contrary takes place when we are in the dark; the pupil in that case expands, to admit the light in a greater quantity. This change is easily perceptible every time we pass from a dark 310 DEFECTS OF THE SIMPLE MICROSCOPE. to a luminous situation. With respect to the subject before us, 1 confine myself to this circumstance, that the more rays of light are admitted into the eye, the more luminous will be the image transmitted to the retina ; and reciprocally, the smaller the quantity of rays which enter the eye, the fainter does the image become, and, consequently, the more obscure does it appear. It may happen, that though the pupil is abundantly expanded, a few rays only shall be ad- mitted into the eye. You have only to prick a little hole in a card with a pin, and look at an object through it ; and then, however strongly illuminated by the sun, the object will appear dark in propor- tion as? the aperture is small ; nay, it is possible to look at the sun itself, employing this precaution. The reason is obvious, a few rays only are admitted into the eye ; however expanded the pupil may be, the pin-hole in the card determines the quantity of light which enters the eye, and not the pupil, which usually performs that function. The same thing takes place in the microscopes which magnify very much ; for when the lens is ex- tremely small, a very few rays only are transmitted, asm n, Fig. 165, which being smaller than pig. 155. the aperture of the pupil, make the object appear so much more obscure ; hence it is evident that this diminution of light takes place only when the lens M N, or rather its open, part, is smaller than the pupil. If it were possible to produce a great magnifying effect, by means of a greater lens, this obscurity would not take place ; and this is the true solution of the question. In order to remedy this inconvenience in the great effects of the microscope, care is taken to illumi- nate the object as strongly as possible, to give greater force to the few rays which are conveyed into the eye. To this effect objects are illuminated by the sun itself; mirrors likev/ise are employed, which reflect on them the light of the sun. These are ON TELESCOPES. 311 nearly all the circumstances to be considered re- specting the simple microscope, and by these you will easily form a judgment of the effect of all those which you may have occasion to inspect.* 3CM January, 1762. LETTER LXXXVIII. On Telescopes, and their Effect. BEFORE I proceed to explain the construction of compound microscopes, a digression respecting the telescope may perhaps be acceptable. These two instruments have a very intimate connexion; the one greatly assists the elucidation of the other. As microscopes serve to aid us in contemplating nearer objects, by representing them under a much greater angle than when viewed at a certain distance, say eight inches ; so the telescope is employed to assist our observation of very distant objects, by repre- senting them under a greater angle than that which they present to the naked eye. Instruments of this sort are known by several names, according to their size and use ; but they must be carefully distinguished from the glasses used by aged persons to relieve the decay of sight. A telescope magnifies as many times as it repre- sents objects under an angle greater than is pre- sented to the naked eye. The moon, for example, appears to the naked eye under an angle of half a degree ; consequently, a telescope magnifies 100 times when it represents the moon under an angle of fifty degrees, which is 100 times greater than half a de- * For an account of various improvements on the single microscope, the reader is referred to the article Optics, in the Edinburgh Encyclopaedia, vol. xv. p. 631, and Ferguson's Lectures, vol. ii. p. 294. Ed. For still later improve/rents, see a paper by Dr. Roget, in Phil, Transactions, for May, 1830. Am. Ed. 312 ON TELESCOPES, gree. If it magnified 200 times, it would represent the moon under an angle of one hundred degrees ; and the moon would in that case appear to fill more than half of the visible heavens, whose whole extent is only 180 degrees.* In common language, we say that the telescope brings the object nearer to us. This is a very equi- vocal mode of expression, and admits of two different significations. The one, that on looking through a telescope, we consider the object as many times nearer as it is magnified. But I have already re- marked, that it is impossible to know the distance of objects but by actual measurement, and that such measurement can be applied only to objects not greatly remote ; when, therefore, they are so remote as is here supposed, the estimation of distance might greatly mislead us. The other signification, which conveys the idea that telescopes represent objects as great as they would appear if we approached nearer to them, is more conformable to truth. You know that the nearer we come to any object, the greater becomes the angle under which it appears; this explanation, accordingly, reverts to that with which I set out. When, however, we look at well-known objects, say men, at a great distance, and view them through a telescope under a much greater angle, we are led to imagine such men to be a great deal nearer, as in that case we would, in effect, see them under an angle so much greater. But in examining ob- jects less approachable, such as the sun and moon, no measurement of distance can take place. This case is entirely different from that which I have for- merly submitted to you, that of a concave lens, em- * The magnifying power is ascertained by measuring the aperture of the object-glass, and that of the little image of it which is formed at the end of the eye-piece ; the proportion between these will give the ratio of the magnifying power. When single lenses are used, the power of a glass is readily discovered by dividing the focal length of the object-glass bv that of the eye-glass. Am. Ed. AND THEIR EFFECT. 313 by near-sighted persons, which represents the images of objects at a very small distance. The concave lens which I use, for example, represents to me the images of all remote objects at the distance of four inches ; it is impossible for me, however, to imagine that the sun, moon, and stars are so near : accordingly, we do not conclude that objects are where their images are found represented by glasses ; we believe this as little as we do the existence of objects in our eyes, though their images are painted there. You will please to recollect, that the esti- mation of the real distance and real magnitude of ob- jects depends on particular circumstances. The principal purpose of telescopes, then, is to increase, or multiply, the angle under which objects appear to the naked eye ; and the principal division of telescopes is estimated by the effect which they pro- cure. Accordingly, we say such a telescope magni- fies five, another ten, another twenty, another thirty times, and so on. And here I remark, that pocket- glasses rarely magnify beyond ten times; but the usual telescopes employed for examining very dis- tant terrestrial objects magnify from twenty to thirty times, and their length amounts to six feet or more. A similar effect, though very considerable with regard to terrestrial objects, is a mere nothing with respect to the heavenly bodies, which require an effect inconceivably greater. We have, accordingly, astronomical telescopes which magnify from 50 to 200 times ; and it would be difficult to go further, as, according to the usual mode of constructing them, the greater the effect is the longer they become. A telescope that shall magnify 100 times must be at least 30 feet long : and one of 100 feet in length could scarcely magnify 200 times. You must be sensible, therefore, that the difficulty of pointing and managing such an unwieldy machine, must oppose insurmountable obstacles to pushing the experiment further. The famous Hevelius, the VOL. II. D d 314 OF POCKET-GLASSES. astronomer at Dantzic, employed telescopes 200 feet long ; but such instruments must undoubtedly have been very defective, as the same things are now discovered by instruments much shorter. This is a brief general description of telescopes, and of the different kinds of them, which it is of importance carefully to remark, before we enter into a detail of their construction, and of the manner in which two or more lenses are united, in order to produce all the different effects. 2d February, 1762. LETTER LXXXIX. Of Pocket-glasses. We have no certain information respecting the person to whom we are indebted for the discovery of the telescope : whether he were a Dutch artist, or an Italian of the name of Porta.* Whoever he was, it is almost one hundred and fifty years since small pocket-glasses were first constructed, composed of two lenses, of which the one was convex, and the other concave. To pure chance, perhaps, a disco- very of so much utility is to be ascribed. It was possible, without design, to place two lenses nearer to or farther from each other, till the object appeared distinctly. The convex lens PAP, Fig. 166 is directed towards Fig. 166. * If the telescope was not actually invented by Roger Bacon, or Leonard Digges, they at least constructed combinations of lenses and mirrors which produced the same effect. Ed. OF POCKET-GLASSES. 315 the object, and the eye is applied to the concave lens Q B Q ; for which reason, the lens P A P is named the object-glass, and Q B Q the eye-glass. These two lenses are disposed on the same axis A B, perpendicular to both, and passing through their centres. The focal distance of the convex lens PAP must be greater than that of the concave ; and the lenses must be disposed in such a manner, that if A F be the focal distance of the objective PAP, the focus of the eye-glass Q Q B must fall at the same point F; accordingly, the interval between the lenses A and B is the difference between the focal dis- tances of the two lenses, A F being the focal distance of the object-glass, and B F that of the eye-glass. When the lenses are arranged, a person with good eyes will clearly see distant objects, which will ap- pear as many times greater as the line A F is greater than B F. Thus, supposing the focal distance of the object-glass to be six inches, and that of the eye- glass one inch, the object will be magnified six times, or will appear under an angle six times greater than when viewed with the naked eye ; and, in this case, the interval between the lenses A, B will be five inches, which is, at the same time, the length of the instrument. There is no need to inform you that these two lenses are cased in a tube of the same length, though not thus represented in the figure. Having shown in what manner the two lenses are to be joined together, in order to produce a good instrument, two things must be explained to you : the one, How these lenses come to represent objects distinctly ; and the other, Why they appear magni- fied as many times as the line A F exceeds the line B F. W^ith respect to the first, it must be remarked, that a good eye sees objects best, when they are so distant that the rays which fall on the eye may be considered as parallel to each other. Let us consider, then, a point V, Fig. 167, in the object towards which the instrument is directed, and on the supposition of its being very distant, the rays 316 OF POCKET-GLASSES. which fall on the object-glass PQ,0 A, Pig. 167. P Q, will be almost parallel to each other; accordingly, the object-glass, Q A Q, being a convex lens, will collect them in its focus F, so that these rays, being convergent, will not suit a good eye. But the concave lens at B, hav- ing the power of rendering the rays more divergent, or of diminishing their convergency, will refract the rays Q R, Q R, so that they shall become parallel to each other ; that is, instead of meet- ing in the point F, they will assume the direction R S, R S, parallel to the axis B F. Thus a good eye, according to which the construction of these is always regulated, on receiving these parallel rays R S, B F, R S, will see the object distinctly. The rays R S, R S become exactly parallel to each other, because the concave lens has its focus, or rather its point of dispersion, at F. You have only to recollect, that when parallel rays fall on a concave lens, they become divergent by refraction, so that being produced backward, they meet in the focus. This being laid down, we have only to reverse the case, and to consider the rays S R, S R, as falling on the concave lens : in this case it is certain they would assume the directions R Q, R Q, which produced backwards would meet in the point F, which is the common focus of the convex and concave lenses. Now it is a general law, that in whatever manner rays are refracted in their passage from one place to another, they must always undergo the same refractions in returning from the last to the first. If, therefore, the refracted rays R Q, R Q correspond to the incident rays S R, S R ; then, re- ciprocally, the rays Q R, Q R, being the incident ones, the refracted rays will be R S and R S. The matter will perhaps appear in a clearer light still, when I sav that concave lenses have the power OF POCKET-GLASSES. 317 of renderingparallel those rays which, without the re- fraction, would proceed to their focus. You will please carefully to attend to the following laws of refraction, which apply to both convex and concave lenses. Fte. 168. 1. By a convex lens, Fig. 168, paral- lel rays are rendered convergent. Fig. 169. Convergent rays become still more so, Fig. 169, and divergent less divergent. 2. By a concave lens parallel rays are rendered divergent. Fig. 170. Divergent rays be- come still more diver- gent, Fig. 171, and convergent rays less convergent. All this is founded on the nature of refraction and the figure of the lenses, the discussion of which would require a very long detail ; but the two rules which 1 have now laid down contain all that is essential. It is abundantly evident, then, that when the convex and the concave lenses are so combined that they acquire a common focus at F, they will distinctly represent distant objects, because the parallelism of the rays is restored by the concave lens after the convex lens had rendered them con- Dd2 318 MAGNIFYING POWER OF vergent. In other words, the rays of very distant objects, being nearly parallel to each other, become convergent by a convex lens; and afterward, the concave lens destroys this convergency, and again renders the rays parallel to each other. Qth February, 1762. LETTER XC. On the magnifying Power of Pocket-glasses. THE principal article respecting telescopical in- struments remains still to be explained, namely, their effect in magnifying objects. I hope to place this in so clear a light as to remove every difficulty in which the subject may be involved; and for this purpose I shall comprise what I have to say in the following propositions. 1. Let E e, Fig. 172, be the object, Fig. 172. situated on the axis of the instrument, _ which passes perpendicularly through both lenses in their centres. This object E e must be considered as at an infinite dis- tance. 2. If, then, the eye, placed at A, looks at this object, it will appear under the angle E A e, called its visual angle. It will, accordingly, be necessary to prove, that on looking at the same object through the glass it will appear under a greater angle, and exactly as many times greater as the focal distance of the object-glass PAP exceeds that of the eye-glass QBQ. 3. As the effect of all lenses consists in representing the objects in another place, and with a certain magnitude, we have only to examine the images which Siiall be successively represented by the POCKET-GLASSES. 319 two lenses, the last of which is the immediate ob- ject of the sight of the person who looks through the instrument. 4. Now, the object E e being infinitely distant from the convex lens PAP, its image will be represented behind the lens at F/, so that A F shall be equal to the focal distance of the lens ; and the magnitude of this image F / is determined by the straight line f A e, drawn from the extremity of the object e, through the centre of the lens A, by which we see that this image is inverted, and as many times smaller than the object as the distance A F is smaller than the distance A E. 5. Again, this image F/ holds the place of the object relatively to the eye-glass Q B Q, as the rays which fall on this lens are precisely those which would almost form the image F/, but are intercepted in their progress by the concave lens Q B Q ; so that this image is only imaginary : the effect, how- ever, is the same as if it were real. 6. This image F /, which we are now consider- ing as an object being at the focal distance of the lens Q B Q, will be transported almost to infinity by the refraction of this lens. The preceding figure marks this new image at G g, whose distance A G must be conceived as infinite, and the rays, refracted a second time by the lens Q B Q, will pursue the same direction as if they actually proceeded from the image G g. 7. This second image G g being, then, the object of the person who looks through the instrument, its magnitude falls to be considered. To this effect, as it is produced by the first image F/ from the refraction of the lens Q B Q, following the general rule, we have only to draw through the centre of the lens B a straight line, which shall pass through the point / of the first image, and that line will mark at g the extremity of the second image. 8. Let the spectator now apply his eye to B and as the rays which it receives pursue the same 320 MAGNIFYING POWER OF direction as if they actually proceeded from the image G g, it will appear to him under the angle G B g, which is greater than the angle E A e, under which the object E e appears to the naked eye. 9. In order the better to compare these two an- gles, it is evident, first, that the angle E A e is equal to the angle FA/, being vertical angles; for the same reason, the angle G B g- is equal to the angle F B /, being vertical and opposite at the point B. It remains to be proved, therefore, that the angle F B / exceeds the angle F A / as many times as the line A F exceeds the line B /; the former of which, A F, is the focal distance of the object-glass, and the other, B F, the focal distance of the eye- glass. 10. In order to demonstrate this, we must have recourse to certain geometrical propositions respect- ing the nature of sectors. You will recollect that the sector is part of a circle contained between two radii C M and C N, Fig. 173, and Pig.' 173. an arch or portion of the circum- ference M N. In a sector, then, there are three things to be con- sidered : 1. The radius of the circle, C M or C N ; 2. The quantity of the arch M N ; 3. The angle M C N. 11. Let us now consider two sec- tors, M C N and men, whose radii C M and c m are equal to each other ; now it is demonstrated in the ele- ments of geometry, that the angles C and c have the same proportion to each other that the arches M IV and m n have : in other words, the angle C is as many times greater than the angle c, as the arch M N is greater than the arch m n ; but, instead of this awk- ward mode of expression, we say that the angles C and c are proportional to the arches M N and m n, the radii being equal POCKET-GLASSES. 321 12. Let us likewise consider two sectors, M C N and men, Fig. 174, whose p - 1?4 angles C and c are equal to each other, but the radii un- equal : and it is demonstrated in geometry, that the arch M N %L is as many times greater than \/ c the arch m n, as the radius CM 7 is greater than the radius c m ; or, in geometrical language, the arches are in proportion to the radii, the angles being equal. The reason is obvious, for every arch contains as many degrees as its angle ; and the de- grees of a great circle exceed those of a small one as many times as the greater radius exceeds the smaller. 13. Finally, let us consider likewise the case when, as in the two sectors M C N and men, Fig. 175, the arches M N and m n are Fig. 175. equal; but the radii C M and c m un- M equal. In this case, the angle C, which cor- responds to the greater radius C M, is the smaller, and the angle c, which cor- responds to the smaller radius c m, is the greater; and this in the same pro- portion as the radii. That is, the angle c is as many times greater than the angle C as the radius C M is greater than the radius cm-, or, to speak geometrically, the angles are re- ciprocally proportional to the radii, the arches being equal. 14. This last proposition carries me forward to my conclusion, after I have subjoined this remark, that when the angles are very small, as in the case of pocket-glasses, there is no sensible difference in the chords of the arches M N and m n, that is, of the straight lines M N and m n. 15. Having made this remark, we return to Fig. 172 (p. 318). The triangles F A / and F B / may be 322 DEFECTS OF POCKET-GLASSES. considered as sectors, in which the arch F/ is the same in both. Consequently, the angle F B / ex- ceeds the angle F A / as often as the distance A F exceeds the distance B F. That is, the object E e will appear through the instrument under an pngle as many times greater as the focal distance of the object-glass A F exceeds the focal distance of the eye-glass B F, which was the thing to be demon- strated. 9th February, 1762. LETTER XCI. Defects of Pocket-glasses. Of the apparent Field. You must be sensible that no great advantage is to be expected from such small instruments ; and it has already been remarked that they do not mag- nify objects above ten times. Were the effect to be carried further, not only would the length .become too great to admit of their being carried about in the pocket, but they would become subject to other and more essential defects. This has induced art- ists entirely to lay aside glasses of this sort, when superior effect is required. The principal of these defects is the smallness of the apparent field ; and this leads me to explain an important article relative to telescopes of every description. When a telescope is directed towards the heavens, or to very distant objects on the earth, the space discovered appears in the figure of a cir- cle, and we see those objects only which are included in that space; so that if you wished to examine other objects, the position of the instrument must be altered. This circular space, presented to the eye of the spectator, is denominated the apparent field, or, in one word, the field of the instrument ; and it is abundantly obvious, that it must be a great DEFECTS OF POCKET-GLASSES, 323 advantage to have a very large field, and that, on the contrary, a small field is a very great inconve- nience in instruments of this sort. Let us suppose two telescopes directed towards the moon, by the one of which we can discover only the half of that luminary, whereas by the other we see her whole body, together with the neighbouring stars ; the field of this last is therefore much greater than that of the other. That which presents the greater field relieves us, not only from the trouble of frequently changing the position, but procures another very great advantage ; that of enabling us to compare, by viewing them at the same time, several parts of the object one with another. It is therefore one of the greatest perfections of a telescope to present a very ample field ; and it is accordingly a matter of much importance to mea- sure the field of every instrument. In this view, we are regulated by the heavens, and we determine the circular space seen through a telescope, by measuring its diameter in degrees and minutes. Thus, the apparent diameter of the full moon being about half a degree, if a telescope takes in the moon only, we say that the diameter of its field is half a degree ; and if you could see at once only the half of the moon, the diameter of the field would be the quarter of a degree. The measurement of angles, then, furnishes the means of measuring the apparent field ; besides, the thing is sufficiently clear of itself. Supposing we could see through the instrument A B, Fig. 176, only the space POP, and the objects which it contains ; this space being a circle, its diameter will be the line POP, whose mid- d'.e point is in the axis of the instrument. 324 DEFECTS OF POCKET-GLASSES. Drawing, therefore, from the extremities P P the straight lines P C, P C, the angle PGP will express the diameter of the apparent field; and the half of this angle, O C P, is denominated the semi-diameter of the apparent field of such an in- strument. You will perfectly comprehend the meaning, then, when it is said that the diameter of the apparent field of such an instrument is one de- gree, that of another two degrees, and so on; as also when it is marked by minutes, as 30 minutes, which make half a degree, or 15 minutes, which make the fourth part of a degree. But in order to form a right judgment of the value of a telescope, with respect to the apparent field, we must likewise attend to the magnifying power of the instrument. It may be remarked in general, that the more a telescope magnifies, the smaller, of necessity, must be the apparent field ; these are the bounds which nature herself has prescribed. Let us suppose an instrument which should magnify 100 times ; it is evident that the diameter of the field could not possibly be so much as two degrees ; for, as this space would appear 100 times greater, it would resemble a space of two hundred degrees ; greater, of consequence, than the whole visible heavens, which, from the one extremity to the other, contain only 180 degrees, and of which we can see but the half at most at once, that is, a circular space of 90 degrees in diameter. From this you see, that a telescope which magnifies 100 times could not contain a field of so much as one degree ; for this degree multiplied 100 times would give more than 90 degrees ; and that, accordingly, a telescope which magnified 100 times would be excellent, if the diame- ter of its field were somewhat less than one degree ; and the very nature of the instrument admits not of a greater effect. But another telescope which should magnify only 10 times would be extremely defective, if it di- DEFECTS OF POCKET-GLASSES. 325 covered a field of only one degree in diameter ; as this field magnified 10 times would give a space of no more than 10 degrees in the heavens, which would be a small matter, by setting too narrow bounds to our view. We should have good reason, then, to reject such an instrument altogether. Thus it would be very easy, with respect to the apparent field, to form a judgment of the excellence or de- fectiveness of instruments of this sort, when the effect is taken into consideration. For when it magnifies only 10 times, it may fairly be conjectured that it discovers a field of 9 degrees ; as 9 degrees taken 10 times give 90 degrees, a space which our sight is capable of embracing : and if the diameter of its field were only 5 degrees or less, this would be an instrument very defective indeed. Now, I shall be able to demonstrate, that if a telescope were to be constructed such as I have been de- scribing, which should magnify more than 10 times, it would be liable to this defect : the apparent field multiplied by the magnifying power would be very considerably under 90 degrees, and would not even show the half. But when a small effect is aimed at, this defect is not so sensible ; for if such an in- strument magnifies only 5 times, the diameter of its field is about 4 degrees, which magnified 5 times contains a space of 20 degrees, with which we have reason to be satisfied : but if we wished to magnify 25 times, the diameter of the field would be only half a degree, which taken 25 times would give little more than 12 degrees, which is too little. When, therefore, we would magnify very much, a different arrangement of lenses must be employed, which I shall afterward explain. 13th February, 1762. VOL. II. E e 326 DETERMINATION OF THE APPARENT LETTER XCII. Determination of the apparent Field for Pocket- Glasses. To ascertain the apparent field being of very great importance in the construction of telescopes, I proceed to the application of it to the small glasses which I have been describing. The lens PAP, Fig. 172 (p. 318), is the object-glass, Q B Q the eye-glass, and the straight line E F the axis of the instrument, in which is seen, at a very great distance, through the instrument, the object E e, under the angle E A e, which represents the semi- diameter of the apparent field, for it extends as far on the other side downwards. The point E, then, is the centre of the space seen through the instrument, the radius of which, E A, as it passes perpendicularly through both lenses, undergoes no refraction; and in order that this ray may have admission into the eye, the eye must be fixed some- where on the axis of the instrument B F, behind the eye-glass, so that the centre of the pupil shall be in the line B F ; and this is a general rule for every species of telescope. Let us now consider the visible extremity of the object e, whose rays exactly fill the whole opening of the object-glass PAP; but it will be sufficient to attend only to the ray E A, which passes through the centre of the object-glass A, as the others surround, and little more than strengthen this ray : so that if it is ad- mitted into the eye, the others, or at least a con- siderable part of them, find admission likewise ; and if this ray is not admitted into the eye, though per- haps some of the others may enter, they are too feeble to excite an impression sufficiently powerful. FIELD FOR POCKET-GLASSES. 327 Hence this may be laid down as a rule, that the ex- tremity e of the object is seen only so far as the ray e A, after having passed through the two lenses, is admitted into the eye. We must therefore carefully examine the direc- tion of this ray e A. Now, as it passes through the centre of the object-glass A, it undergoes no refrac- tion ; conformably to the rule laid down from the beginning, that rays passing through the centre of any lens whatever are not diverted from their direc- tion, that is, undergo no refraction. This ray, e A, therefore, after having passed through the object- glass, would continue in the same direction, to meet the other rays issuing from the same point e, to the point/ of the image represented by the object-glass at F/, the point / being the image of the point e of the object ; but the ray meeting at m, the concave lens, but not in its centre, will be diverted from that direction ; and instead of terminating in /, will as- sume the direction m n, more divergent from B F, it being the natural effect of concave lenses to render rays always more divergent. In order to ascertain this new direction m n, you will please to recollect that, the object-glass represents the object E e in an inverted position at F/, so that A F is equal to the focal distance of this lens, which transports the ob- ject E e to F/. Then this image F/ occupies the place of the object with respect to the eye-glass Q B Q, which, in its turn, transports that image to G g, whose distance B G must be as great as that of the object itself: and for this effect, it is neces- sary to place the eye-glass in such a manner that the interval B F shall be equal to its focal distance. As to the magnitude of these images, the first F/ is determined by the straight line e A/, drawn from e through the centre A of the first lens ; and the other G g by the straight line/B , drawn from the point / through the centre B of the second lens. 328 APPARENT FIELD FOR POCKET-GLASSES. This being laid down, the ray A m directed towards the point f is refracted, and proceeds in the direc- tion m n ; and this line m n, being produced back- wards, will pass through the point g, for m n has the same effect in the eye as if it actually proceeded from the point g. Now, as this line m n retires far- ther and farther from the axis B F, where the centre of the pupil is, it cannot enter into the eye, unless the opening of the pupil extends so far ; and if the opening of the pupil were reduced to nothing, the ray m n would be excluded from the eye, and the point e of the object could not be visible, nor even any other point of the object out of the axis A F. There would, therefore, be no apparent field, and nothing would be seen through such an instru- ment except the single point E of the object, which is in its axis. It is evident, then, that a telescope of this sort discovers no field but as far as the pupil expands ; so that in proportion as the expansion of the pupil is greater or less, so likewise the appa- rent field is great or small. In this case the point e will therefore be still visible to the eye if the small interval B m does not exceed half the diameter of the eye, that the ray m n may find admission into it ; but in this case, likewise, the eye must be brought as close as possible to the eye-glass : for as the ray m n removes from the axis F B, it would escape the pupil at a greater distance. Now it is easy to determine the apparent field which such an instrument would discover on the eye-glass : you have only to take the interval B m equal to the semi-diameter of the pupil, and to draw through that point m, and the centre of the object- glass A, the straight line m A e ; then this line will mark on the object the extremity e, which will be still visible through the instrument, and the angle E A e will give the semi-diameter of the apparent field. Hence you will easily judge, that whenever ASTRONOMICAL TELESCOPES. 329 the distance of the lenses A B exceeds some inches, the angle B A m must become extremely small, as the line or the distance B m is but about the twen- tieth part of an inch. Now if it were intended to magnify very much, the distance of the lenses must become considerable, and the consequence would be that the apparent field must become extremely small. The structure of the human eye, then, sets bounds to telescopes of this description, and obliges us to have recourse to others of a different construc- tion whenever we want to produce very considerable effects. L6th February, 1762. LETTER XCIII. Astronomical Telescopes, and their magnifying Power. I PROCEED to the second species of telescopes, called astronomical, and remark, that they consist of only two lenses, like those of the first species ; with this difference, that in the construction of astro- nomical telescopes, instead of a concave eye-glass, we employ a convex one. The object-glass PAP, Fig. 177, is, as in the other Fig. 177. species, convex, whose focus being at F, we place, on the same axis a smaller convex lens Q Q, in such a manner that its focus shall likewise fall on the same point F. Then placing the eye at 0, so that the distance B shall be nearly equal to the focal Ee 2 330 ASTRONOMICAL TELESCOPES, AND distance of the eye-glass Q Q, you will see objects distinctly, and magnified as many times as the focal distance of the object-glass A F shall exceed that of the eye-glass B F : but it is to be remarked that every object will appear in an inverted position ; so that if the instrument were to be pointed towards a house, the roof would appear undermost, and the ground-floor uppermost. As this circumstance would be awkward in viewing terrestrial objects, which we never see in an inverted situation, the use of this species of telescopes is confined to the heavenly bodies, it being a matter of indifference in what direction they appear ; it is sufficient to the astronomer to know that what he sees uppermost is really undermost, and reciprocally. Nothing, how- ever, forbids the application of such telescopes to ter- restrial objects ; the eye soon becomes accustomed to the inverted position, provided the object is seen distinctly, and very much magnified. Having given this description, three things fall to be demonstrated : first, that by this arrangement of 'the lenses objects must appear distinctly ; secondly, that they must appear magnified as many times as the focal distance of the object-glass exceeds that of the eye-glass, and in an inverted position ; and thirdly, that the eye must not be applied close to the eye-glass, as in the first species, but must be removed to nearly the focal distance of the ocular. 1. As to the first, it is demonstrated in the same manner as in the preceding case : the rays e P, e P, which are parallel before they enter into the object- glass, meet by refraction in the focus of this lens at F ; the eye-glass must, of course, restore the paral- lelism of these rays, and distinct vision requires that the rays proceeding from every point should be nearly parallel to each other when they enter the eye. Now, the eye-glass, having its focus at F, is placed in such a manner as to render the rays F M, F M, by the refraction, parallel, and consequently THEIR MAGNIFYING POWER. 331 178. the eye will receive the rays N o, N o, parallel to each other. 2. With respect to the second article, let us consider the object at E e, Fig. 178, but so that the distance E A shall be almost in- finite. The image of this object, represented by the object-glass, will therefore be F/, situated at the fo- cal distance of that lens A F, and determined by the straight line e A/, drawn through the centre of the lens. This image F/, which is in- verted, occupies the place of the object with respect to the eye-glass, and being in its focus, the second image will be again removed to an infinite distance by the refraction of this lens, and will fall, for exam- ple, at G g, the distance A G being considered as infinite, like that of A E. Now, in order to determine the magnitude of this image, you have only to draw through the centre B of the lens, and the extremity /of the first image, the straight line B/g-. Now this second image Gg being the immediate object of vision to the person who looks through the telescope, it is evident at once that this representation is inverted, and, as it is infinitely distant, will appear under an angle G B g. But the object itself E e will appear to the naked eye under the angle E A e : now you are sen- sible, without being reminded, that it is indifferent to take the points A and B, in order -to have the visual angles E A e and G B g, on account of the infinite distance of the object. You now see here, as in the preceding case, that the triangles FA/ and F B/may be considered as circular sectors, the line F/ measuring the arch of both ; and the angles them- selves being so very small, no sensible mistake can be committed in taking the chord for the arch. As, 332 OF THE APPARENT FIELD, AND then, the radii of these two sectors are the lines A E and B F, the arches being equal to each other, it follows, as was formerly demonstrated, that the angles FA/ (or, which is the same thing, E A e) and F B/(or, which is the same thing, G B g) have the same proportion to each other that the radii B F and A F have. Therefore, the angle G B g, under which the object is seen through the telescope, as many times exceeds the angle E A e, under which the object is seen by the naked eye, as the line A F exceeds the line B F ; which was the second point to be demonstrated. I am under the necessity of deferring the demonstration of my third proposition till next post. February, 1762. LETTER XCIV. Of the apparent Field, and the Place of the Eye. IN fulfilling my engagement respecting the third particular proposed, namely, to determine the place of the eye behind the telescope, I remark that this subject is most intimately connected with the appa- rent field, and that it is precisely the field which obliges us to keep the eye fixed at the proper dis- tance ; for if it were to be brought closer, or removed farther off, we should no longer discover so large a field. The extent of the field being an article of such importance, indeed so essential, in all telescopes, it must be of equal importance to determine exactly the place of the eye from which the largest field is discoverable. If the eye were to be applied close to the eye-glass, we should have nearly the same field as we have with the pocket-glass, which becomes insufferably small whenever the magnifying power is considerable. It is therefore a vast advantage to THE PLACE OF THE EYE. 333 astronomical telescopes, that by withdrawing the eye from the eye-glass the apparent field increases to a certain extent ; and it is precisely this which renders such telescopes susceptible of prodigious magnifying powers, whereas those of the first species are in this respect extremely limited. You know that with the astronomical telescope, the magnifying power has been carried beyond two hundred times, which gives them an inconceivable superiority over those of the first species, which can scarcely magnify ten times ; and the trifling inconvenience of the in- verted position is infinitely overbalanced by an ad- vantage so very great. I will endeavour to put this important article in the clearest light possible. 1. The object E e, Fig. 179, being in- finitely distant, let e be its extremity, still visible through the telescope, whose lenses are PAP and Q B Q, fitted on the common axis E A B ; it falls to be attentively considered what direc- tion will be pursued by the single ray which passes from the extremity e of the object, through the centre A of the object-glass. You will recollect that the other rays, which fall from the point e on the object-glass, only accom- pany and strengthen the ray in question e A, which is the principal with respect to vision. 2. Now this ray e A, passing through the centre of the lens P P, will undergo no refraction, but will pursue its direction in the straight line A /m, and passing through the extremity of the image F /, will fall on the eye-glass at the point m ; and here it is to be observed, that if the size of the eye-glass had not extended so far as the point m, this ray would never have reached the eye, and the point e would have been invisible. That is to say, it would 334 OF THE APPARENT FIELD, AND be necessary to take the extremity e nearer to the axis, in order that the ray A/m may meet the eye- glass. 3. Now this ray A m will be refracted by the eye- glass in a way which it is very easy to discover. We have only to consider the second image G g ; though infinitely distant, it is sufficient to know that the straight line B/ produced will pass through the extremity g of the second image G g, which is the immediate object of vision. Having remarked this, the refracted ray must assume the direction n O, and this produced passes through g. 4. As, therefore, the two lines n and B/meet at an infinite distance at g, they may be considered as parallel to each other ; and hence we acquire an easier method to determine the position of the re- fracted ray n O : you have only to draw it parallel to the line B/. 5. Hence it is clearly evident that the ray n will somewhere meet the axis of the telescope at O, and as usually, when the magnifying power is great, the point F is much nearer to the lens Q Q than to the lens P P, the distance B m will be somewhat greater than the image F/; and as the line n is parallel to/B, the line B O will be nearly equal to B F, that is, to the focal distance of the eye-glass. 6. If, then, the eye is placed at O, it will receive, not only the rays which proceed from the middle of the object E, but those likewise which proceed from the extremity e, and consequently those also which proceed from every point of the object; the eye would even receive at once the rays B and n O, even supposing the pupil infinitely contracted. In this case, therefore, the apparent field does not de- pend on the largeness of the aperture of the pupil, provided the eye be placed at ; but the moment it recedes^ from this point, it must lose considerably in the apparent field. 7. If the point m were not in the extremity of the THE PLACE OF THE EYE. 335 eye-glass, it would transmit rays still more remote from the axis, and the telescope would, of course, discover a larger field. In order, then, to determine the real apparent field which the telescope is capable of discovering, let there be drawn, from the centre A of the object-glass, to the extremity m of the eye-glass, the straight line A m, which, produced to the object, will mark at e the visible extremity ; and consequently the angle E A e, or, which is the same thing, the angle B A m, will give the semi-diameter of the apparent field, which is consequently greater in proportion as the extent of the eye-glass is greater. 8. As, then, in the first species of telescopes, the apparent field depended entirely on the aperture of the pupil, and as in this case it depends entirely on the aperture of the eye-glass, there is an essential difference between these two species of instruments, greatly in favour of the latter. The figure which I have employed in demonstrating this last article re- specting the place of the eye and the apparent field, may greatly assist us in the elucidation of the pre- ceding articles. If you will be so good as to reflect, that the object- glass transports the object E e to F/, and that the eye-glass transports it from F/ to Gg-, this image Gg, being very distant from the immediate object of vision, ought to be seen distinctly, as a good eye re- quires a great distance in order to see thus. This was the first article. As to the second, it is evident at first sight, that as instead of the real image E e, we see through the telescope the image Gg, it must be inverted. Finally, this image is seen by the eye placed at under the angle G O g, or B n, whereas the object itself E e appears to the naked eye under the angle E A e : the telescope, therefore, magnifies as many times as the angle B n is greater than the angle E A e. Now, as the line n is partllel to B/, the angle B n is 336 MAGNIFYING POWER OF equal to the angle F B / and the angle E A e is equal to its opposite and vertical angle FA/; hence the magnifying power must be estimated from the pro- portion between the angles F B/ and FA/; accord- ingly, as the angle F B/ contains the angle F A/as often as the line A F, that is, the focal distance of the object-glass, contains the line B F, that is, the focal distance of the eye-glass, the magnifying power will be therefore expressed by the proportion of these two distances. This is proof sufficient that the ele- ments of geometry may be successfully employed in researches of quite a different nature a reflection not unpleasing to the mathematician. 23d February, 1762. LETTER XCV. Determination of the magnifying Power of Astronomi- cal Telescopes, and the Construction of a Telescope which shall magnify Objects a given Number of Times. You now have it clearly ascertained, not only how many times a proposed instrument will magnify, but what is the mode of constructing a telescope which shall magnify as many times as may be wished. In the first case, you have only to measure the focal distance of both lenses, the object-glass as well as the eye-glass, in order to discover how much the one exceeds the other. This is performed by division, and the quotient indicates the magnifying power. Having, then, a telescope, the focal distance of whose object-glass is two feet, and that of the eye- glass one inch, it is only necessary to inquire how often one inch is contained in two feet. Every one knows that a foot contains twelve inches ; two feet accordingly contain twenty-four irtches, which are to be divided bv one. But whatever number we divide ASTRONOMICAL TELESCOPES. 337 by one the quotient is always equal to the dividend : if, then, it is asked, how often one inch is contained in twenty-four inches, the answer, without hesitation, is, twenty-four times; consequently, such a tele- scope magnifies twenty-four times, that is, represents distant objects in the same manner as if they were twenty-four times greater than they really are ; in other words, you would see them through such a telescope under an angle twenty-four times greater than by the naked eye. Let us suppose another astronomical telescope, the focal distance of whose object-glass is thirty-two feet, and that of the eye-glass three inches. You see at once that these two lenses must be placed at the distance of thirty-two feet and three inches from each other ; for, in all astronomical telescopes, the distance of the lenses must be equal to the sum of the two focal distances, as has been already demon- strated. To find, then, how many times a telescope of the above description magnifies, we must divide thirty- two fefcf by three inches ; and, in order to this, re- duce these thirty-two feet into inches, by multiplying them by twelve : 32 this produces 384 inches ; and these again 12 divided by three, the focal distance, in inches, 3)384 of the eye-glass, gives a quotient of 128, T^g which indicates that the proposed telescope magnifies 128 times, which must be allowed to be very considerable. Reciprocally, therefore, in order to construct a telescope which shall magnify a given number of times, say 100, we must employ two convex lenses, the focal distance of the one of which shall be 100 times greater than that of the other ; in this case the one will give the object-glass, and the other the eye- glass. These must afterward be fitted on the same axis, so that their distance shall be equal to the sum of the two focal distances ; that is, they must be fixed VOL. II. F f 838 POWER OF ASTRONOMICAL TELESCOPES. in a tube of this length, and then the eye being placed behind the eye-glass, at its focal distance, will see objects magnified 100 times. This arrangement may be varied without end, by assuming an eye-glass at pleasure, and adapting to it an object-glass whose focal distance shall be 100 times greater. Thus, taking an eye-glass of one inch focus, the object-glass must be of 100 inches focus, and the distance of the lenses 101 inches. Or, taking an eye-glass of 2 inches focus, the object- glass must have its focus at the distance of 200 inches, and the distance of the lenses will be 202 inches. If you were to take an eye-glass of 3 inches focus, the focal distance of the object-glass must be 300 inches, and the distance of the lenses from each other 303 inches. And if you were to take an eye- glass of 4 inches focus, the object-glass must have a focal distance of 400 inches, and the distance of the two lenses 404 inches, and so on, the instrument always increasing in length. If, on the contrary, you were to assume an eye-glass of only half an inch focus, the object-glass must have a focal dis- tance of 100 half-inches, that is, of 50 inches, and the distance between the lenses would only be 50 inches and a half, which is little more than four feet. And if an eye-glass of a quarter of an inch focus were to be employed, the object-glass would require a focal distance of only 100 quarters of an inch, or 25 inches, and the distance between the two lenses 25 inches and a quarter, that is little more than two feet. Here, then, are several methods of producing the same effect, that of magnifying 100 times ; and if every thing else were equal, we should not hesitate about giving the preference to the last, as being the shortest : for here the telescope, being reduced to little more than two feet, would be more manageable than one much longer. No one, then, would hesitate about preferring the DEGREE OF CLEARNESS. 339 shortest telescopes, provided all other circumstances were the same, and all the different species repre- sented objects in the same degree of perfection. But though they all possess the same magnifying power, the representation is by no means equally clear and distinct. That of two feet in length certainly mag- nifies 100 times, as well as the others ; but on look- ing through such a telescope, objects will appear not only dark, but blunt and confused, which is un- doubtedly a very great defect. The last telescope but one, whose object-glass is 50 inches focus, is less subject to these defects : but the dimness and con- fusion are still insupportable ; and these defects diminish in proportion as we employ greater object- glasses, and are reduced to almost nothing on em- ploying an object-glass of 300 inches, with an eye- glass of 3 inches focus. On increasing these mea- surements, the representation becomes still clearer and more distinct ; so that in this respect long tele- scopes are preferable to short, though otherwise less commodious. This circumstance imposes on me a new task, that of further explaining two very essen- tial articles in the theory of telescopes : the one re- spects the clearness, or degree of light in which ob- jects are seen ; and the other the distinctness and accuracy of expression with which they are repre- sented. Without these two qualities, all magnifying power, however great, procures no advantage for the contemplation of objects. 27th February, 1762. LETTER XCVI. Degree of Clearness. IN order to form a judgment of the degree of clear- ness in which objects are represented by the tele- scope, I shall recur to the same principles which I en- 340 DEGREE OF CLEARNESS. deavoured to elucidate in treating the same subject with reference to the microscope. And, first, it must be considered, that in this re- search it is not proposed to determine the degree of light resident in objects themselves, and which may be very different, not only in different bodies, as being in their nature more or less luminous, but in the same body, according as circumstances vary. The same bodies, when illuminated by the sun, have undoubtedly more light than when the sky is over- cast, and in the night their light is wholly extin- guished ; but different bodies illuminated may differ greatly in point of brightness, according as their colours are more or less lively. We are not inquir- ing, then, into that light or brightness which resides in objects themselves ; but, be it strong or faint, we say that a telescope represents the object in perfect clearness, when it is seen through the instrument as clearly as by the naked eye ; so that if the object be dim, we are not to expect that the telescope should represent it as clear. Accordingly, in respect of clearness, a telescope is perfect when it represents the object as clearly as it appears to the naked eye. This takes place, as in the microscope, when the whole opening of the pupil is filled with the rays which proceed from every point, of the object, after being transmitted through the telescope. If a telescope furnishes rays sufficient to fill the whole opening of the pupil, no greater degree of clearness need be desired ; and supposing it could supply rays in greater profusion, this would be entirely useless, as the same quantity precisely, and no more, could find admission into the eye. Here, then, attention must be paid chiefly to the aperture of the pupil, which, being variable, prevents our laying down a fixed rule, unless we regulate our- selves according to a certain given aperture, which is sufficient, when the pupil, in a state of the greatest DEGREE OF CLEARNESS. 341 contraction, is filled with rays ; and for this purpose the diameter of the pupil is usually supposed to be one line, twelve of which make an inch ; we some- times satisfy ourselves with even the half of this, allowing to the diameter of the pupil only half aline, and in some cases still less. If you will please to consider that the light of the sun exceeds that of the moon 200,000 times, though even that of the moon is hy no means inconsiderable, you will be sensible that a small diminution in point of clearness can be of no great consequence in the contemplation of objects. Having premised this, all that remains is to examine the rays which the tele- scope transmits into the eye, and to compare them with the pupil ; and it will be sufficient to consider the rays which proceed from a single point of the object, that, for example, which is in the axis of the telescope. 1. The object being infinitely distant, the rays which fall from it on the surface of the object-glass PAP, Fig. 180, are parallel to each other : all the Fig. 180. rays, then, which come from the centre of the ob- ject will be contained within the lines L P, L P, parallel to the axis E A. All these rays taken to- gether are denominated the pencil of rays which fall on the Object-glass, and the breadth of this pencil is equal to the extent or aperture of the object-glass, the diameter of which is P A P. 2. This pencil of rays is changed by the refrac- tion of the object-glass into a conical or pointed figure P F P, and having crossed at the focus F, it Ff2 342 DEGREE OF CLEARNESS. forms a new cone m F m, terminated by the eye- glass ; hence it is evident that the base of this cone mm is as many times smaller than the breadth of the pencil P P, as the distance F B is shorter than the distance A F. 3. Now these rays F m, F m, on passing through the eye-glass Q B Q, become again parallel to each other, and form the pencil of rays n o, n 0, which enter into the eye, and there depict the image of the point of the object whence they originally pro- ceeded. 4. The question, then, resolves itself into the breadth of this pencil of rays n o, n 0, which enter into the eye ; for if this breadth n n or o o is equal to or greater than the opening of the pupil, it will be filled with them, and the eye will enjoy all pos- sible clearness ; that is, the object will seem as clear as it you were to look at it with the unassisted eye. 5. But if this pencil nn, o o were of much less breadth than the diameter of the pupil, it is evident that the representation must become so much more obscure ; which would be a great defect in the tele- scope. In order to remedy it, the pencil must there- fore be at least half a line in breadth ; and it would be still better to have it a whole line in breadth, this being the usual aperture of the pupil. 6. It is evident that the breadth of this second pencil has a certain relation to that of the first, which it is very easy to determine. You have only to settle how many times the distance nn or mm is less than the distance P P, which is the aperture of the object-glass. But the distance P P is in the same proportion to the distance m m, as the distance A F to the distance B F, on which the magnifying power depends ; accordingly, the magnifying power itself discovers how many times the pencil L P, L P is broader than the pencil n o, n o, which enters into the eye. APERTURE OF OBJECT-GLASSES. 343 7. Since, then, the breadth n n or o o must be one line, at least half a line, the aperture of the object- glass P P must at least contain as many half-lines as the magnifying power indicates ; thus, when the telescope is to magnify 100 times, the aperture of its object-glass must have a diameter of 100 half-lines, or 50 lines, which make 4 inches and 2 lines. 8. You see, then, that in order to avoid obscurity, the aperture of the object-glass must be greater in proportion as the magnifying power is greater. And, consequently, if the object-glass employed is not susceptible of such an aperture, the telescope will be defective in respect of clearness of repre- sentation. Hence it is abundantly evident, that in order to magnify very greatly it is impossible to employ small object-glasses, whose focal distance is too short, as a lens formed by the arches of small circles cannot have a great aperture. 1st March, 1762. LETTER XCVII. Aperture of Object-glasses. You have now seen that the magnifying power determines the size or extent of the object-glass, in order that objects may appear with a sufficient degree of clearness. This determination respects only the size or aperture of the object-glass ; how- ever, the focal distance is affected by it likewise, for the larger the lens is the greater must be its focal distance. The reason of this is evident, as in order to form a lens whose focal distance is, for example, two inches, its two surfaces must be arches of a circle whose ra- dius is likewise about two inches. I have therefore 344 APERTURE OF OBJECT-GLASSES. represented, Fig. 181, two lenses P and Q, the arches of which are described with a Fig. 181. radius of two inches. The lens P, being the thicker, is much greater than the lens Q ; but I shall demonstrate afterward that thick lenses are subject to other incon- p[ veniences, and these so great as to oblige us to lay them altogether aside. The lens Q, then, will be found more adapted for use, being composed of smaller arches of the same circle ; and as its focal distance is two inches, its extent or aperture m n may scarcely ex- ceed one inch. Hence this may be laid down as a general rule, that the focal distance of a lens must always be twice greater than the diameter of its aperture m n ; that is, the aperture of a lens must of necessity be smaller than half the focal distance. Having remarked, then, that in order to magnify 100 times, the aperture of the object-glass must exceed 4 inches, it follows that the focal distance must exceed 8 inches ; I shall presently demonstrate that the double 'is not sufficient, and that the focal distance of this lens must be increased beyond 300 inches. The distinctness of the expression of the image requires this great increase, as shall afterward be shown : I satisfy myself with remarking, at pres- ent, that with regard to the geometrical figure of the lens, the aperture cannot be greater than half its focal distance. Here, therefore, I shall go somewhat more into the detail respecting the aperture oT the object-glass, which every magnifying power requires ; and I re- mark, first, that though a sufficient degree of clear- ness requires an aperture of four inches, when the telescope is to magnify 100 times, we satisfy our- selves, in astronomical instruments, with one of three inches, the diminution of clearness being scarcely perceptible. Hence artists have laid it down as a rule, that in order to magnify 100 times, the aperture APERTURE OF OBJECT-GLASSES. 345 ot the object-glass must be three inches ; and for other magnifying powers in that proportion. Thus, in order to magnify 50 times, it is sufficient that the aperture of the object-glass be an inch and a half ; to magnify 25 times, three-quarters of an inch suf- fice, and so of other powers. Hence we see that for small magnifying powers a very small aperture of the object-glass is sufficient, and that, consequently, a moderate focal distance may answer. But if you wished to magnify 200 times, the aperture of the object-glass must be six inches, or half a foot, which requires a very large lens, whose focal distance must exceed even 100 feet, in order to obtain a distinct and exact expression. For this reason, great magnifying powers require very long telescopes, at least according to the usual arrangement of lenses which I have explained. But for some time past artists have been successfully employing themselves in diminishing this excessive length. The aperture of the object-glass, however, must follow the rule laid down, as clearness neces- sarily depends on it. Were you desirous, therefore, of constructing a telescope which should magnify 400 times, the aper- ture of the object-glass must be twelve inches, or a foot, let the focal distance be rendered as small as you will : and if you wished to magnify 4000 times, the aperture of the object-glass must be ten feet, a very great size indeed, and too much so for any artist to execute ; and this is the principal reason why we can never hope to carry the magnifying power so far, unless some great prince would be at the expense of providing and executing lenses of such magnitude; and, after all, perhaps they would not succeed. A telescope, however, which should magnify 4000 times, would discover many wonderful things in the heavens. The moon would appear 4000 times larger than to the naked eye ; in other words, we should 346 APERTURE OF OBJECT-GLASSES. see her as if she were 4000 times nearer to us than she is. Let us inquire, then, to what a degree we might be able to distinguish the different bodies which she may contain. The distance of the moon from the earth is calculated to be 240,000 English miles, the 4000dth part of which is 60 miles : such a telescope would accordingly show us the moon as if she were only 60 miles distant ; and, consequently, we should be enabled to discover in her the same things which we distinguish in objects removed to the same distance. Now, from the top of a moun- tain we can easily discern other mountains more than 60 miles distant. There can be no doubt, then, that with such an instrument we should discover on the surface of the moon many things to fill us with surprise. But in order to determine whether the moon is inhabited by creatures similar to those of the earth, a distance of 60 miles is still too great ; we must have, in order to this effect, a telescope which should magnify ten times more, that is 40,000 times, and this would require an object-glass of 100 feet aperture, an enterprise which human art will never be able to execute. But with such an instru- ment we should see the moon as if she were no farther distant than from Berlin to Spandau, and good eyes might easily discern men at this distance, if any there were, but too indistinctly, it must be allowed, to be completely assured of the fact. As we must rest satisfied with wishing on this subject, mine should be to have at once a telescope which should magnify 100,000 times ;* the moon would then appear as if she were only half a mile distant. The aperture of the object-glass of the telescope must be 250 feet, and we should see, at least, the larger animals which may be in the moon. 6th March, 1762. * Dr. Herschel has been able to apply a magnifying power of 6500 times to the fixed stars. Ed. ON DISTINCTNESS IN THE EXPRESSION. 347 LETTER XCVIII. On Distinctness in the Expression : On the Space of Dif- fusion occasioned by the Aperture of Object-glasses, and considered as the first Source of Want of Dis- tinctness in the Representation. DISTINCTNESS of expression is a quality of so much importance in the construction of telescopes, that it seems to take precedence of all the others which I have been endeavouring to explain ; for it must be allowed that a telescope which does not represent distinctly the images of objects must be very defect- ive. I must therefore unfold the reasons of this want of distinctness, that we may apply more suc- cessfully to the means of remedying it. They appear so much the more abstruse, that the principles hitherto laid down do not discover the source : in fact, this defect is thus to be accounted for one of the principles on which I have hitherto proceeded is not strictly true, though not far from the truth. You will recollect that it has been laid down as a principle, that a convex lens collects into one point of the image all the rays which come from one point of the object. Were this strictly true, images rep- resented by lenses would be as distinctly expressed as the object itself, and we should be under no ap- prehension of defect in regard to this. Here, then, lies the defectiveness of this principle ; lenses have the property now ascribed to them only around their centre ; the rays which pass through the extremities of a lens collect in a different point from those which pass towards the centre, though all proceed from the same point of the object ; hence are produced two different images, which occasion indistinctness. 348 ON DISTINCTNESS IN In order to set this in the clearest light, let ua Fig. 182. consider the convex lens P P, Fig. 182, on the axis of which is placed the ob- ject E e, of which the point E, situated upon the axis, emits the rays E N, E M, E A, E M, E"N, to the sur- face of the lens. To the direction of these rays, as changed by refraction, we must now pay attention. 1. The ray E A, which passes through the centre A of the lens, undergoes no refraction, but proceeds for- ward in the same direction, on the straight line A B F. 2. The rays E M and E M, which are nearest to the first, undergo a small refraction, by which they will meet with the axis somewhere at F, which is the place of the image F/, as has been explained in some of my preceding Letters on this subject. 3. The rays E N and E N, which are more remote from the axis E A, and which pass towards the ex- tremities N N of the lens, undergo a refraction some- what different, which collects them, not at the point F, but at another point G, nearer the lens : and these rays represent another image G g, different from the first F/. 4. Let us now carefully attend to this particular circumstance, not hitherto remarked ; it is this, that the rays passing through the lens, towards its ex- tremities, represent another image G g, than what is represented by those passing near the centre MAM. 5. If the rays E N, E N, were to retire still farther from the centre A, and to pass through the points P P, of the lens, their point of reunion would be still THE EXPRESSION. 349 nearer to the lens, and would form a new image, nearer than even G g. 6. Hence you will easily perceive, that the first image F/, which is named the principal image, is formed only by the rays which are almost infinitely near the centre ; and that according as the rays re- tire from it, towards the extremities of the lens, a particular image is formed nearer the lens, till those passing close to the extremities form the last, G g. 7 All the rays, therefore, which pass through the lens P P represent an infinity of images disposed between F/ and G g; and at every distance from the axis the refraction of the lens produces a par- ticular image, so that the whole space between F and G is filled with a series of images. 8. This series of images is accordingly denomi- nated the diffusion of the image ; and when all these rays afterward enter into an eye, it is natural that the vision should be so much disturbed as the space F G, through which the image is diffused, is more considerable. If this space F G could be reduced to nothing, no confusion need be apprehended. 9. The greater portions of their respective circles that the arches PAP and P B P are, the greater likewise is F G the space of diffusion. You see a good reason, then, for rejecting all lenses of too great thickness, or in which the arches which form the surfaces of the lens are considerable segments of their circles, as in Fig. 183, of which the arches PAP and P B P are the fourth Fig. 183. part of the whole circumference, so that each contains 90 ; this would, conse- quently produce an insufferable confusion. 10. The arches, then, which form the surfaces of a lens, must contain much less than 90 degrees : if they contained so much as 60, the diffusion of the image would be even then insupportable. Au- thors who have treated the subject admit VOL. II. G g 350 ON DISTINCTNESS IN THE EXPRESSION. of 30 degrees at most : and some fix the . lft , boundary at 20 degrees. A lens of this last #* description is represented by Fig-. 184, in which the arches PAP and P B P contain only 20 degrees, each being but the eigh- teenth part of the whole circumference of its respective circle. 11. But if this lens were to supply the place of the object-glass in a telescope, the arches PAP and P B P must contain still many degrees less. For though the diffusion of the image be perceptible of itself, the magnifying power mul- tiplies it as many times as it does the object. There- fore, the greater the magnifying power proposed, the fewer must be the number of degrees which the surfaces of the lens contain. 12. When the telescope is intended to magnify 100 times, you will recollect that the aperture of the object-glass must be 3 inches, and its focal dis- tance 360 inches, which is equal to the radii witft which the two arches PAP and P B P are described ; hence it follows that each of these two arches con- tains but half a degree ; and it is distinctness of ex- pression which requires an arch so small. If it were intended to magnify 200 times, half a degree would be still too much, and the measure of the arch, in that case, ought not to exceed the third part of a degree. This arch, however, must receive an extent of 6 inches ; the radius of the circle must therefore be so much greater, and consequently also the focal distance. This is the true reason why great magni- fying powers require telescopes of such considerable length. Qth March, 1762 APERTURE OF LENSES. 351 LETTER XCIX. Diminution of the Aperture of Lenses, and other means of lessening the Space of Diffusion till it is reduced to nothing. WHEN the space of an object-glass is too great to admit of distinctness of expression, it may be very easily remedied : you have only to cover the lens with a circle of pasteboard, leaving an opening in the centre, so that the lens may transmit no other rays but those which fall upon it through the opening, and that those which before passed through the ex- tremities of the lens may be excluded ; for as no rays are transmitted but through the middle of the lens, the smaller the opening is the smaller likewise will be the space of diffusion. Accordingly, by a gradual diminution of the opening, the space of diffusion may be reduced at pleasure. Here the case is the same as if the lens were no larger than the opening in the pasteboard, thus the covered part becomes useless, and the opening de- termines the size of the lens ; this then is the remedy employed to give object-glasses any given extent. P P is the object-glass, Fig. 185, before which is placed the pasteboard N N, having the opening M M, which is now the extent of the lens. This opening M M is here nearly the half of what it would be were the pasteboard removed ; the space of dif- fusion is therefore much smaller. It is remarked, that the space of diffusion in this case is only the fourth part of what it was before. An opening M M, reduced to a third of P P, would render the space of diffusion nine times less. Thus the effect of this remedy is very considerable ; and on covering the extremities of 352 DIMINUTION OF THE the lens ever so little, the effect of it becomes per- ceptible. If, therefore, a telescope labours under this defect, that it does not represent objects sufficiently distinct, as a series of images blended tog-ether must of ne- cessity produce confusion, you have only to con- tract the aperture of the object-glass by a covering of pasteboard such as I have described, and this confusion will infallibly disappear. But a defect equally embarrassing is the consequence ; the de- gree of brightness is diminished. You will recollect that every degree of the magnifying power requires a certain aperture of the object-glass, that as many rays may be transmitted as are necessary to procure a sufficient illumination. It is vexatious, therefore, in curing one defect, to fall into another; and in order to the construction of a very good telescope, it is absolutely necessary that there should be suffi- cient brightness of illumination, without injuring distinctness in the representation. But can there be no method of diminishing, nay, of totally reducing the space of diffusion of object- glasses without diminishing the aperture 1 This is the great inquiry which has for some time past en- gaged the attention of the ingenious, and the solution of which promises such a field of discovery in the science of dioptrics. I shall have the honour, at least, of laying before you the means which scientific men have suggested for this purpose. As the focus of the rays which pass through the middle of a convex lens is more distant from the lens than the focus of the rays which pass through the extremities, it has been remarked that concave lenses produce a contrary effect. This has sug- gested the inquiry, whether it might not be possible to combine a convex with a concave lens, in such a manner that the space of diffusion should be entirely annihilated ; while, in other respects, this compound lens should produce the same effect as an ordinary APERTURE OF LENSES. 353 simple object-glass 1 You know that concave lenses are measured by their focal distance as well as those which are convex; with this difference, that the focus of the concave is only imaginary, and falls be- fore the lens, whereas the focus of convex lenses is real, and falls behind them. Having made this re- mark, we reason as follows : 1. If we place, Fig. 186, behind a con- vex lens P A P, a concave one Q B Q of the same focal distance, the rays which the convex lens would collect in its focus will be refracted by the concave, so that they will again become parallel to each other, as they were before passing through the convex lens. 2. In this case, therefore, the concave lens destroys the effect of the convex, and it is the same thing as if the rays had proceeded in their natural direction, without undergoing any re- fraction. For the concave lens, having its focus at the same point F (see Fig. 178, p. 331), restores the parallelism of the rays, which would otherwise have met at the point F. 3. If the focal distance of the concave lens were smaller than that of the convex, it would produce a greater effect, and would ren- Fig. 187. der the rays divergent, as in Fig. 187 : the incident parallel rays L M, E A, L M, pass- ing through the two lenses, would assume the directions NO, B F, N 0, which are divergent from each other. These two lenses together produce, therefore, the same effect as a simple concave lens, which would impress on the incident par- allel rays the same divergence. Two such lenses joined together, of which the concave has a smaller focal distance than the convex, are therefore equivalent to a simple concave lens. Gg2 354 APERTURE OF LENSES. Fig, 188 4. But if the concave lens Q Q, Fig. 188, has a greater focal distance than the convex lens P P, it is not even suf- ficient to render parallel to each other the rays which the convex lens by it- self would collect in its focus F : these rays, therefore, continue convergent, but their convergence will be dimin- ished by the concave lens, so that the . rays, instead of meeting in the point F, will meet in the more distant point O. 5. These two lenses joined together will produce, then, the same effect as a simple convex lens which should have its focus at 0, as it would collect the parallel rays L M, E A, L M, equally in the same point. It is therefore evi- dent that two lenses may be combined an infinite variety of ways, the one being convex and the other concave, so that their combination shall be equivalent to a given convex lens. 6. Such a double object-glass may therefore be employed in the construction of telescopes, instead of the simple one, to which it is equivalent ; and the effect as to the magnifying power will be just the same. But the space of diffusion will be quite dif- ferent, and it may happen to be greater or less than that of a simple object-glass ; and in this last case the double object-glass will be greatly preferable to the simple one. 7. But, further, it has been found possible to ar- range two such lenses so that the space of diffusion is reduced absolutely to nothing, which is undoubt- edly the greatest advantage possible in the construc- tion of telescopes. Calculation enables us to deter- mine this arrangement, but no artist has hitherto been found capable of reducing it to practice. I3lh March, 1762. OF COMPOUND OBJECT-GLASSES. 355 LETTER C. Of Compound Object-glasses. THE combination of two lenses, of which I have now given the idea, is denominated a compound object-glass ; the end proposed from them is, that all the rays, as well those which pass through the extremities of a lens as those which pass through the middle, should be collected in a single point, so that only one image may be formed, without diffu- sion, as in simple object-glasses. Could artists succeed in effecting such a construction, very great advantages would result from it, as you shall see. It is evident, first, that the representation of ob- jects must be much more distinct, and more exactly expressed, as vision is not disturbed by the appari- tion of that series of images which occupy the space of diffusion when the object-glass is simple. Again, as this space of diffusion is the only reason which obliges us to give to simple object-glasses such an excessive focal distance, in order to render the inconvenience resulting from it imperceptible, by employing compound object-glasses we are relieved from that cumbersome expedient, and are enabled to construct telescopes incomparably shorter, yet possessing the same magnifying power. When, employing a single object-glass, you want to magnify a hundred times, the focal distance can- not be less than thirty feet, and the length of the telescope becomes still greater on account of the eye-glass, whose focal distance must be added; a small object-glass would produce, from its greater space of diffusion, an intolerable confusion. But a length of thirty feet is not only very incommodious, but artists seldom succeed in forming lenses of so great a focal distance. You will readily perceive 356 OF COMPOUND OBJECT-GLASSES. the reason of this ; for the radius of the surfaces of such a lens must likewise be thirty feet, and it is very difficult to describe exactly so great a circle, and the slightest aberration renders all the labour useless. Accidents of this sort are not to be apprehended in the construction of compound object-glasses, which may be formed of smaller circles, provided they are susceptible of the aperture which the mag- nifying power requires. Thus, in order to magnify one hundred times, we have seen that the aperture of the object-glass must be three inches ; but it would be easy to construct a compound object-glass whose focal distance should be only one hundred inches, and which could admit an aperture of more than three inches : therefore, as the focal distance of the eye-glass must be one hundred times smaller, it would be one inch ; and the interval between the lenses being the sum of their focal distances, the length of the telescope would be only one hundred and one inches, or eight feet five inches, which is far short of thirty feet. But it appears to me that a compound object-glass, whose focal distance should be fifty inches, might easily admit an aperture of three inches, and even more : taking, then, an eye-glass of half an inch focus, you will obtain the same magnifying power of one hundred times, and the length of the telescope will be reduced one-half, that is, to four feet and less than three inches. Such a telescope, then, would produce the same effect as a common one of thirty feet, which is assuredly carrying it as far as need be wished. If such a compound object-glass could be made to answer, you would only have to double all these measurements in order to have one which should admit an aperture of six inches ; and this might be employed to magnify two hundred times, making use of an eye glass of half an inch focus as the two mm- OF COMPOUND OBJECT-GLASSES. 357 dredth part of the focal distance of the object-glass, which would, in this case, be one hundred inches. Now, a common telescope which should magnify two hundred times, must exceed one hundred feet in length ; whereas this one, which is constructed with a compound object-glass, is reduced to about eight feet, and is perfectly accommodated to use, whereas a telescope of one hundred feet long would be an unwieldly and almost useless load. The subject might be carried still much further, and by again doubling the measurements, we might have a compound object-glass whose focal distance should be two hundred inches, or sixteen feet eight inches, which should admit of an aperture of twelve inches, or one foot : taking, then, an eye-glass of half an inch focus, as two hundred inches contain four hundred half-inches, we should have a telescope capable of magnifying four hundred times, and still abundantly manageable, being under seventeen feet; whereas, were we to attempt to produce the same magnifying power with a simple object-glass, the length of the telescope must exceed three hundred feet, and consequently could be of no manner of use on account of that enormous size. They have at Paris a telescope one hundred and twenty feet long, and one at London of one hundred and thirty feet ; but the dreadful trouble of mount- ing and pointing them to the object almost annihi- lates the advantages expected from them. From this you will conclude of what importance it would be to succeed in the construction of the compound lenses which I have been describing. I suggested the first idea of them several years ago, and since then artists of the greatest ability in England and France have been attempting to execute them. Repeated efforts and singular skill in the artist are undoubtedly requisite. Indeed, I have made, with the assistance of an able mechanician of our Acade- my, some not unsuccessful attempts ; but the ex- 358 FORMATION OF pense attending such an enterprise has obliged me to give it up. But the Royal Society of London last year an- nounced, that an eminent artist, of the name of Dol- lond* had fortunately succeeded ; and his telescopes are now universally admired. An able artist of Paris, named Passement, boasts of a simitar success. Both these gentlemen did me the honour, some time ago, to correspond with me on the subject ; but as the point in question was chiefly how to surmount certain great difficulties in the practical part, which I never attempted, it is but fair that I should relinquish to them the honour of the discovery. The theory alone is my province, and it has cost me much pro- found research, and many painful calculations, the very sight of which would terrify you. I shall therefore take care not to perplex you further with this abstruse inquiry. 16th March, 1762. LETTER CI Formation of Simple Object-glasses. IN order to give you some idea of the researches which led me to the construction of compound ob- ject-glasses, I must begin with the formation of the simple lens. Observe, first, that the two surfaces of a lens may be formed in an infinity of different ways, by taking circles of which the surfaces are segments, either equal or unequal to each other, the focal distance, however, remaining always the same. * The first achromatic telescope ever constructed was made by Chester More Hall, Esq., of More-hall, in Essex, in thu year 1733. no less than twei'ty-four years before the period alluded to by our author. This in- valuable instrument, is, therefore, in every view of the matter, a British invention. See the article Optics, in the Edinburgh Encyclopaedia, vol. XV. p. 479, note, for a full account of Mr- Hall's labours. Ed. SIMPLE OBJECT-GLASSES. 359 The same figure is usually given to both surfaces of a lens, or, as the surfaces of a lens are repre- sented by arches of a circle, both surfaces are formed with radii equal to each other. Facility of execu- tion has undoubtedly recommended this figure, as the same basin serves to form both surfaces, and most artists are provided with but few basins. Suppose, then, a convex lens, both whose surfaces are polished on the same basin, one of twenty-four inches radius, so that each surface shall be an arch of the circle whose radius is twenty-four inches : this lens will be convex on both sides, and will have its focal distance at twenty-four inches, according to the common calculation ; but as the focus depends on the refraction, and as the refraction is not abso- lutely the same in every species of glass, in which we find a very considerable diversity, according as the glass is more or less white and hard, this calculation of the focus is not strictly accurate ; and usually the focal distance of the lens is somewhat less than the radius of its two surfaces, sometimes the tenth part, sometimes the twelfth : accordingly, the sup- posed lens, the radius of whose surfaces is twenty- four inches, will have its focus at the distance of about twenty-two inches, if it is formed of the same species of glass of which mirrors are commonly manufactured ; though even in glass of this sort we meet with a small diversity in respect of refraction. We see afterward, that on making the two sur- faces of the lens unequal, an infinity of other lenses may be formed, which shall all have the same focal distance ; for on taking the radius of one of the surfaces less than twenty-four inches, that of the other surface must be taken greater in proportion, according to a certain rule. The radius of one of the surfaces may always be taken at pleasure ; and by means of a certain rule the radius of the other may be found, in order that the focal distance may become the same as if each surface had been formed 360 FORMATION OF on a radius of twenty-four inches. The following table exhibits several such lenses, which have all the same focal distance. Lenses. Radius of the first Surface. Radius of the Second Surface* I. 24 24 II. 21 28 III. 20 30 IV. 18 36 V. - 16 48 VI. 15 60 VII. 14 84 VIII. 13 156 IX. 12 infinity In the last form, the radius of one surface is only 12 inches, or the half of 24 inches ; but that of the other becomes infinite : or rather, this surface is an arch of a circle infinitely great ; and as such an arch differs nothing from a straight line, this may be con- sidered as a plane surface, and such a lens is plano- convex. Were we to assume the radius of a surface still smaller than 12 inches, the other surface must be made concave, and the lens will become convexo- concave; it will, in that case, bear the name of meniscus, several figures of which are represented in the following table : Meniscus. Radius of the Convex Radius of the Concave Surface. Surface. X. 11 132 XI. 10 60 XII. 9 36 XIII. 8 24 XIV. 6 12 XV. 4 6 XVI. 3 4 Here, then, is a new species of lenses, the last of SIMPLE OBJECT-GLASSES. 361 which is represented in Fig. 190, so that p- ^Q we have now sixteen different species, **-- ' which have all the same focal distance ; k* ^ and this is about 22 inches, a little more or less, according to the nature of the glass. When, therefore, the only question is, What focal distance the lens ought to have \ it is a matter of indifference according to which of these forms you go to work ; but there may be a very great differ- ence in the space of diffusion to which each species is subjected, this space becoming smaller in some than in others. When a simple object-glass is to be employed, as is usually done, it is by no means indifferent of what figure you assume it, for that which produces the smallest space of diffusion is to be preferred. Now, this excellent property does not belong to the first species, where the two sur- faces are equal; but nearly to species VII., which possesses the quality, that when you turn towards the object its more convex surface, or that whose radius is smallest, the space of diffusion is found to be about one-half less than when the lens is equally convex on both sides : this, therefore, is the most advantageous figure for simple object-glasses, and practitioners are accordingly agreed in the use of it. It is evident, then, that in order to ascertain the space of diffusion of a lens, it is not sufficient to know its focal distance ; its species likewise must be determined, that is, the radii of each surface ; and you must carefully distinguish which side is turned to the object. After this explanation, it is necessary to remark, that in order to discover the combination of two lenses which shall produce no diffusion of image, it is absolutely necessary to take into the account the figure of both surfaces of each glass, and to resolve the following problem: What must be the radii of the surfaces of two lenses, in order to reduce to nothing the space of diffusion ? The solution re- VOL. II. H h 362 DEFECT OF REPRESENTATION quires the most profound researches of the most sublime geometry; and supposing these to have been successful, the artist has, after all, many diffi- culties to surmount. The basins must have pre- cisely that curve which the calculation indicates; nor is that sufficient, for in the operation of forming the lens on the basin, the basin suffers from the friction in its turn ; hence it becomes necessary to rectify its figure from time to time, with all possible accuracy, for if all these precautions are not strictly observed, it is impossible to ensure success ; and it is no easy matter to prevent the lens from assuming a figure somewhat different from that of the basin in which it is moulded. You must be sensible, from all this, how difficult it must be to carry to perfec tion this important article in dioptrics. 2Qth March, 1762. LETTER GIL Second Source of Defect as to Distinctness of Represent- ation by the Telescope. Different Refrangibility of Rays. You have now seen in what manner it may be possible to remedy that defect in lenses which arises from the different refraction of rays, as those which pass through the extremities of a lens do not meet in the same point with those which pass through its middle, the effect of which is an infinity of images dispersed through the space of diffusion. But this is not the only defect ; there is another, of so much more importance that it seems impossible to apply a remedy, as the cause exists, not in the glass, but in the nature of the rays themselves. You will recollect that there is a great variety in rays, with respect to the different colours of which they convey the impression. I have compared this BY THE TELESCOPE. 363 diversity to that which we meet with in musical notes, having laid it down as a principle, that each colour is attached to a certain number of vibrations. But supposing that this explanation should still ap- pear doubtful, it is beyond all doubt that rays of different colours likewise undergo different refrac- tions in their passage from one transparent medium to another ; thus, red rays undergo the least refrac- tion, and violet the greatest, though the difference is almost imperceptible. Now, all the other colours, as orange, yellow, green, and blue, are contained, with respect to refraction, within these two limits. It must likewise be remarked, that white is a mix- ture of all the colours which by refraction are sepa- rated from each other. In fact, when a white ray P, Fig. 191, or a ray of the sun, falls obliquely on jVo-. 191. a piece of glass ABC D, instead of pursuing its course in the direction P Q, it not only deviates from this, but A \p B divides into a variety of rays, t\ P r, P s, P t, P v : the first |V\ of which P r, the one that _ i\\\ \ deviates least, represents c the red colour, and the last P , which deviates most, the violet colour. The dispersion r v is in- deed much smaller than it appears in the figure ; the divergence, however, always becomes more perceptible. From this different refrangibility of rays, accord- ing to their different colours, are produced the fol- lowing phenomena with respect to dioptric glasses : 1. Let P P, Fig. 192, be a convex lens, on the axis of which O R, at a very great distance A O, is the object O o, the image of which, as represented by the lens, we are to determine, 'putting aside here the first irregularity, that which respects diffusion; or, which amounts to the same thing, attending 364 DEFECT OF REPRESENTATION to those rays only which pass through Fig. 192. the centre of the lens A B, as if its ex- tremities were covered with a circle of pasteboard. 2. Let us now suppose the object O o to be red, so that all its rays shall be of the same nature; the lens will some- where represent the image of it R r equally red ; the point R is, in this case, denominated the focus of the red rays, or of those which undergo the least re- fraction. 3. But if the object o is violet, as rays of this colour undergo the greatest refraction, the image V v will be nearer the lens than R r ; this point v is called the focus of violet rays. 4. If the object were painted some other inter- mediate colour between red and violet, the image would fall between the points R and V, would be always very distinct, and terminated by the straight line o B, drawn from the extremity o of the object, through the centre of the lens, this being a general rule for all colours. 5. But if the colour of the object is not pure, as is the case in almost all bodies, or if the object is white, which is a mixture of all colours, the differ- ent species of rays will then be separated by refrac- tion, and each will represent an image apart. That which is formed of red rays will be at R r ; and that which is produced by the violet at V v ; and the whole space R V will be filled with images of the intermediate colours. 6. The lens P P, then, will represent a succession of images of the object O o, disposed through the small space R V, of which the most remote from the lens is red, and the nearest V v violet, and the intermediate images of the intermediate colours, BY THE TELESCOPE. 365 according to the order of the colours as they appear in the rainbow. 7. Each of these images will be abundantly dis- tinct in itself, and all terminated by the straight line o B v r, drawn from the extremity o of the object through the centre of the lens B ; but they could not be viewed together \vithout a very perceptible confusion. 8. Hence, then, is produced a new space of dif- fusion, as in the first irregularity ; but differing from it in this that the latter is independent on the aper- ture of the lens, and that each image is painted of a particular colour. 9. This space of diffusion R V depends on the focal distance of the lens, so as to be always about the 28th part ; when, therefore, the focal distance of the lens P P is 28 feet, the space R V becomes equal to an entire foot, that is, the distance between the red image R r and the violet V v is one foot, If the focal distance were twice as great, or 56 feet, the space R V would be two feet ; and so of other distances. 10. Hence the calculation of the focal distance of a lens becomes uncertain, as the rays of each colour have their separate focus ; when, therefore, the focus of a lens is mentioned, it is always necessary to announce the colour that we mean. But rays of an intermediate nature are commonly understood, those between red and violet, namely the green. 11. Thus, when it is said, without further ex- planation, that the focal distance of such a lens is 56 feet, we are to understand that it is the green image which falls at that distance ; the red image will fall about a foot farther off, and the violet a foot nearer. Here, then, is a new circumstance of essential importance, to which attention must be paid in the construction of dioptrical instruments. 23d March, 1762, Hh2 366 MEANS OF REMEDYING LETTER CIIL Means of remedying this Defect by Compound Object- glasses. IT is necessary carefully to distinguish this new diffusion or multiplication of the image, arising from the different refrangibility of rays, as being of differ- ent colours from the first diffusion, occasioned by the aperture of the lens, inasmuch as the rays which pass tnrough the extremities form another image than those which pass through its middle. This new defect must accordingly be remedied differently from the first. You will please to recollect that I have proposed two methods for remedying the preceding defect ; the one consisted in an increase of the focal dis- tance, in order to diminish the curve of the surfaces of the lens. This remedy introduces instruments extremely long whenever a great magnifying power is required. The other consists in a combination of two lenses, the one convex and the other con- cave, to modify the refraction, so that all the rays transmitted through these lenses may meet in the same point, and the space of diffusion be totally re- duced. But neither of these remedies affords the least as- sistance towards removing the inconvenience arising from the different refrangibility of rays. The first even increases the evil ; for the more that the focal distance is increased, the more considerable becomes the space through which the coloured images are dispersed. Neither does the combination of two or more lenses furnish any assistance ; for we are as- sured, from both theory and experience, that the images of different colours remain always separated, however great the number of lenses through which DEFECTS IN TELESCOPES. 367 the rays are transmitted, and that the more the lens magnifies, the more the difference increases. This difficulty appeared so formidable to the great Newton, that he despaired of finding a remedy for a defect which he believed absolutely inseparable from dioptrical instruments, when the vision is produced by refracted rays. For this reason he resolved to give up refraction altogether, and to employ mirrors instead of object-glasses, as reflection is always the same for rays of every nature. This idea has pro- cured for us those excellent reflecting telescopes, whose surprising effects are so justly admired, and which I shall describe after I have explained every thing relative to refractive instruments. On being convinced that it was impossible to remedy the different refrangibility of rays by a combination of several lenses, I remarked "that the reason of it was founded on the law of refraction, which is the same in every species of glasses ; and I perceived that if it were possible to employ other transparent substances, whose refraction should be considerably different from that of glass, it might be very possible to combine such substance with glass, in such a manner that all the rays should unite in the formation of a single image, without any space of diffusion. In pursuance of this idea, I found means to compose object-glasses of glass and water, wholly exempt from the effect of the different refrangibility of rays, which consequently would produce as good an effect as mirrors. I executed my idea with two menis- Fig. 193. cuses, or concavo-convex lenses, Fig. 193, the one of which is A A C C, and the other BBC C, which I joined together with the concave surfaces towards each other, filling the void between them with water, so that the rays which entered by the lens A A C C must pass through the water en- closed between the two lenses, before they went off 368 MEANS OF REMEDYING through C C B B. Each ray undergoes, then, four refractions : the first on passing from the air into the lens A A C C ; the second on passing from this lens into the water ; the third on passing thence into the other lens C C B B ; the fourth on passing from this lens into the air. As the four surfaces of these two lenses here en- ter into consideration, I found means to determine their semi-diameters, so that of whatever colour a ray of light might be, after having undergone these four refractions, it should reunite in the same point, and the different refrangibility no longer produce different images. These object-glasses, compounded of two lenses and water, were found subject at first to the former defect, namely, that of the rays which pass through the extremities forming a different focus from what is formed by those which pass through the middle ; but, after much painful research, 1 found means to proportion the radii of the four surfaces in such a manner that these comj wholb specif execute so exactly all the measurements prescribed by the calculation, that the slightest aberration must become fatal to the whole process ; I was therefore obliged to abandon the construction of these object- glasses.* Besides, this project could remedy only the incon- veniences which affect the object-glass, and the eye- glass might still labour under some defect as great, which it would be impossible to remedy in the same manner. Several eye-glasses are frequently em- ployed in the construction of telescopes, which I shall describe afterward : we should not, therefore, gain much by a too scrupulous adherence to the ob- * Object-glasses of this kind, even if executed in the most correct manner, are incapable of producing the effects which our author expected from them. Ed. DEFECTS IN TELESCOPES. 369 ject-glass only, while we overlook the other lenses, though their effect may not be greatly perceptible relatively to that of the object-glass. But whatever pains these researches may have cost me, I frankly declare that I entirely give up at present the construction of object-glasses com- pounded of glasses and water ; as well on account of the difficulty of execution, as that I have since discovered other means, not of destroying the effect of the different refrangibility of rays, but of render- ing it imperceptible. This shall be the subject of my next Letter. With March, 1762. LETTER CIV. Other Means more practicable. SINCE the reflecting telescope came into general use, refracting ones have been so run down that they are on the point of being wholly laid aside. The construction of them has accordingly for some time past been wholly suspended, under a firm persuasion that every effort to raise them to a state of per- fection would be useless, as the great Newton had demonstrated that the insurmountable difficulties arising from the different refrangibility of rays was absolutely inseparable from the construction of tele- scopes. If this sentiment be well founded, there is no telescope capable of representing objects but with a confusion insupportable in proportion to the great- ness of the magnifying power. However, though there are telescopes extremely defective in this respect, we likewise meet with some that are excel- lent, and nowise inferior to the so much boasted reflecting telescopes. This is undoubtedly a very great paradox ; for if this defect really attached to 370 MEANS OF REMEDYING the subject, we should not find a single exception. Such an exception, therefore and we have the testi- mony of experience that it exists well merits every degree of attention. We are to inquire, then, how it happens that cer- tain telescopes represent the object abundantly dis- tinct, while others are but too much subject to the defect occasioned by the different refrangibility of rays. I think I have discovered the reason, which I submit in the following 1 reflections : 1. It is indubitably certain that the object-glass represents an infinity of images of each object, which are all arranged over the same space of diffu- sion, and each of which is painted its own proper colour, as I have demonstrated in the preceding Letter. 2. Each of these images becomes an object, with respect to the eye-glass, which represents each sep- arately, in the colour proper to it ; so that the eye discovers, through the telescope, an infinity of im- ages, disposed in a certain order, according to the refraction of the lens. 3. And if, instead of one eye-glass, we were to employ several, the same thing will always take place, and instead of one image, the telescope will represent an infinity to the eye, or a series of im- ages, each of which expresses a separate object, but of a particular colour. 4. Let us now consider, Fig. 194, the last images Fig. 194. presented by the telescope to an eye placed at 0, and let R r be the red image, and V v the violet, those of the oth<>r colours being between these two, ac- DEFECTS IN TELESCOPES. 371 cording to the order of their different refrangibility. I have not in this figure introduced the lenses of the telescope, the only point at present being to show in what manner the eye sees the images. Only we must conceive the distance of the eye O from these images to be very great. 5. All these images R r and V , with the inter- mediate, are situated, then, on the axis of the tele- scope O R V, and terminated by a certain straight line, r v, denominated the terminatrix of all the images. 6. As I have represented these images in the figure, the red image R r is seen by the eye at O, under the angle R O r, which is greater than the angle V O v, under which the violet image V v is seen. The violet rays which, from the image V v, enter into the eye, are therefore blended with the red which come from the part R r of the red image Rr. 7. Consequently, the eye cannot see the violet image without a mixture of rays of other colours, but which correspond to different points of the ob- ject itself; thus the point n of the red image is confounded in the eye with the extremity v of the violet image, from which a very great confusion must arise. 8. But the ray r O not being mix'ed with the others, the extremity seen will appear red, or the image will seem bordered With red, which afterward successively blends with these other colours, so that the object will appear with a party-coloured border; a fault very common in telescopes, to which some, however, are less subject than others. 9. If the greater image R r were the violet, and V v the red, the confusion would be equally offen- sive, with this difference only, that the extremities of the object would then appear bordered with vio- let instead of red. 10. The confusion depends, then, on the position 372 OF REMEDYING DEFECTS IN TELESCOPES. of the terminating straight line r v with relation to the line V O, and the diversity which may take place in it ; the result must be, that the confusion will be sometimes greater and sometimes less. 11. Let us now consider the case in which the last images represented by the telescope are so arranged, that the straight terminating line v r, being produced, would pass precisely into the eye. The eye will then see, Fig. 195, along a single ray v r O, Fig. 195. all the extremities ; and, in general, all the points which correspond to one and the same point of the object will be conveyed to the eye by a single ray, and will there, consequently, be distinctly repre- sented. 12. Here, then, is a case in which, notwithstand- ing the diversity of images, the eye may see the object distinctly, without any confusion of the dif- ferent parts, as happened hi the preceding case. This advantage, then, will be obtained when the ter- minating line v r, being produced, passes through the place of the eye O. 13. As the arrangement of the last images R r and V v depends on the disposition of the eye-glasses, in order to rescue telescopes from the defect im- puted to them, nothing more is requisite but to arrange these lenses in such a manner that the ter- minating line of the last images v r shall pass through the eye; and telescopes thus constructed will always be excellent. 30th March, 1762. QUALITIES OF A GOOD TELESCOPE. 373 LETTER CV. Recapitulation of the Qualities of a good Telescope. ON taking a general review of the subject, you will readily admit that an excellent telescope is a most valuable commodity, but rarely to be met with, being subject to so many defects, and so many quali- ties being requisite, each of which has an essential influence on the construction of the instrument. As the number of the good qualities is considerable, in order that no one of them may escape your ob- servation, I shall again go over the ground, and make a distinct enumeration of them. 1. The first respects the magnifying power ; and the more that a telescope magnifies objects, the more perfect undoubtedly it is, provided that no other good quality is wanting. Now, the magnify- ing power is to be estimated from the number of times that the diameter of the object appears greater than to the naked eye. You will recollect that, in telescopes of two lenses, the magnifying power is so many times greater as the focal distance of the object-glass exceeds that of the eye-glass. In tele- scopes consisting of more lenses than two, the determination of the magnifying power is more in- tricate. 2. The second property of a good telescope is brightness. It is always very defective when it rep- resents the object obscurely, and as through a mist. In order to avoid this defect, the object-glass must be of such a size as is regulated by the magnifying power. Artists have determined that, in order to magnify 300 times, the aperture of the object-glass ought to be three inches diameter ; and for every other magnifying power in proportion. And when objects are not very luminous of themselves, it VOL. II. I i 374 QUALITIES OF A would be proper to employ object-glasses of a still greater diameter. 3. The third quality is distinctness or accuracy of representation. In order to produce this, the rays which pass through the extremities of the object- glass ought to meet in the same point with those which pass through the middle, or at least the aber- ration should not be perceptible. When a simple object-glass is employed, its focal distance must exceed a certain limit proportional to the magnify- ing power. Thus, if you wish to magnify 100 times, the focal distance of the object-glass must be at 'east 30 feet. It is the destination, therefore, which imposes the necessity of making telescopes so ex- cessively long, if we want to obtain a very great magnifying power. Now, in order to remedy this defect, an object-glass composed of two lenses may be employed ; and could artists succeed in the con- struction of them, we should be enabled very con- siderably to shorten telescopes, while the same magnifying 1 power remained. You will have the goodness to recollect what I have already suggested at some length on this subject. 4. The fourth quality regards likewise the dis- tinctness or purity of representation, as far as it is affected by the different refrangibility of rays t)f different colours. I have shown how that defect may be remedied ; and as it is impossible that the images formed by different rays should be collected in a single one, the point in question is to arrange the lenses in the manner I have described in the preceding Letter ; that is, the terminating line of the last images must pass through the eye. Without this, the telescope will have the defect of repre- senting objects surrounded with the colours of the rainbow ; but the defect will disappear on arranging the lenses in the method I have pointed out. But to this effect, more than two lenses must be em- ployed, in order to a proper arrangement. I have GOOD TELESCOPE. 375 hitherto spoken only of telescopes with two lenses, one of which is the object-glass, and the other the eye-glass ; and you know that their distance from each other is already determined by their focal dis- tances, so that here we are not at liberty to make any alteration. It happens, fortunately, however, that the terminating line which I have mentioned passes nearly through the place of the eye, so that the defect arising from the colours of the rainbow is almost imperceptible, provided the preceding de- fect is remedied, especially when the magnifying power is not very great. But when the power is considerable, it would be f -roper to employ two eye- glasses, in order entirely to annihilate the colours of the rainbow, as in this case the slightest defects, being equally magnified, become insupportable. 5. The fifth and last good quality of a telescope is a large apparent field, or the space which the in- strument discovers at once. You recollect that small pocket-glasses with a concave eye-glass are subject to the defect of presenting a very small field, which renders them incapable of magnifying greatly. The other species, that with a convex eye-glass, is less subject to this defect ; but as it represents the object inverted, telescopes of the first species would be preferable, did they discover a larger field, which depends on the diame'ter of the aperture of the eye-glass ; and you know we can- not increase this aperture at pleasure, because it is determined by focal distance. But by employing two or three, or even more eye-glasses, we have found means to render the apparent field greater ; and this is an additional reason for employing seve- ral lenses in order to procure a telescope in all re- spects excellent. To these good qualities another may be still added, that the representation shall not be inverted by the instrument, as by astronomical telescopes. But this defect may be easily remedied, if it be one, by the 376 TERRESTRIAL TELESCOPES addition of two more eye-glasses, as I shall show in my next Letter. 3d April, 1762. LETTER CVI. Terrestrial Telescopes with four Lenses. I HAVE treated at considerable length of telescopes composed of two convex lenses, known by the name of astronomical tubes, because they are commonly used for observing the heavenly bodies. You will readily comprehend that the use of such instruments, however excellent they may be, is limited to the heavens, because they represent ob- jects in an inverted position, which is very awkward in contemplating terrestrial bodies, as we would rather wish to view them in their natural situation; but on the discovery of this species of telescope, means were quickly found of remedying that defect, by doubling, if I may say so, the same telescope. For as two lenses invert the object, or represent the image inverted, by joining a similar telescope to the former, for viewing the same image, it is again in- verted, and this second representation will exhibit the objecc upright. Hence arose a new species of telescopes, composed of four lenses, called terres- trial telescopes, from their being designed to con- template terrestrial objects ; and the method of constructing them follows. 1. The four lenses A, B, C, D, Fig. 189, enclosed Fig. 189. WITH FOUR LENSES. 377 in the tube M M N N, represent the telescope in question ; the first of which, A, directed towards the object, is denominated the object-glass, and the other three, BCD, the eye-glass. These four lenses are all convex, and the eye must be placed at the extremity of the tube, at a certain distance from the last eye-glass D, the determination of which shall be afterward explained. 2. Let us consider the effect which each lens must produce when the object O 0, which is viewed through the telescope, is at a very great distance. The object-glass will first represent the image of this object at P p, its focal distance, the magnitude of the image being determined by the straight line drawn from the extremity o through the centre of the lens A. This line is not represented in the figure, that it may not be embarrassed with too many lines. 3. This image P p occupies the place of the ob- ject with respect to the second lens B, which is placed in such a manner that the interval B P shall be equal to its focal distance, in order that the second image may be thence transported to an infi- nite distance, as Q q, which will be inverted as the first P p, and terminated by the straight line drawn from the centre of the lens B through the ex- tremity p, 4. The interval between these two first lenses A, B is equal, therefore, to the sum of their focal distances ; and were the eye placed behind the lens B, we should have an astronomical telescope, through which the object O o would be seen at Q q, and consequently inverted, and magnified as many times as the distance A P exceeds the distance B P. But instead of the eye, we place behind the lens B, at some distance, the third lens C, with respect to which the image Q q occupies the place of the ob- ject, as in fact it receives the rays from this image Q q, which being at a very great distance, the lens I i 2 378 TERRESTRIAL TELESCOPES. C will represent the image of it, at its focal distance, in Rr. 5. The image Q q being inverted, the image R r will be upright, and terminated by the straight line drawn from the extremity q through the centre of the lens C, which will pass through the point r. Consequently the three lenses A, B, C together rep- resent the object O o at R r, and this image R r is upright. 0. Finally, we have only to place the last lens in such a manner that the interval D R shall be equal to its focal distance ; this lens D will again trans- port the image R r to an infinite distance, as S s, the extremity of which s will be determined by the straight line drawn from the centre of the lens D through the extremity r ; and the eye placed behind this lens will in fact see this image S s instead of the real object O o. 7. Hence it is easy to ascertain how many times this telescope, composed of four lenses, must mag- nify the object ; you have only to attend to the two couple of lenses, A, B and C, D, each of which separately would be an astronomical telescope. The first pair of lenses A and B magnifies as many times as the focal distance of the first lens A ex- ceeds that of the second lens B ; and so many times will the image formed by it, Q q, exceed the real object O o. 8. Further, this image Q q occupying the place of the object with respect to the other pair of lenses C and D, it will be again multiplied as many times as the focal distance of the lens C exceeds that of the lens D. These two magnifying powers added give the whole magnifying power produced by the four lenses. 9. If, then, the first pair of lenses, A and B, mag- nify ten times, and the other pair, C and D, three times, the telescope will magnify the object thrice ten, that is, thirty times ; and the aperture of the ARRANGEMENT OF LENSES. 379 object-glass A must correspond to this magnifying power, according to the rule formerly laid down. 10. Hence you see, then, that on separating from a terrestrial telescope the two last lenses C and D, there would remain an astronomical telescope, and that these two lenses C and D would likewise form sucn a telescope. A terrestrial telescope, therefore, consists of two astronomical ones ; and reciprocally, two astronomical telescopes combined form a ter- restrial one. This construction is susceptible of endless varia- tions, some preferable to others, as I shall afterward demonstrate. Qth April, 1762. LETTER CVII. Arrangement of Lenses in Terrestrial Telescopes. You have seen how, by the addition of two con- vex lenses to an astronomical telescope, a terres- trial one is produced, which represents the object upright. The four lenses of which a terrestrial tele- scope is composed are susceptible of an infinite variety of arrangement, with respect to both focus and distance. I shall explain those which are of most essential importance, and refer you to Fig. 196. Fig. 196. a, T> 1. With respect to their distances, I have already remarked that the interval between the two first lenses, A and B, is the sum of their focal distances ; and the same thing holds as to the last lenses C and 380 ARRANGEMENT OF LENSES D : for each pair may be considered as a simple telescope, composed of two convex lenses. But what must be the interval between the two middle lenses B and C 1 May it be fixed at pleasure 1 As it is certain that whether this interval be great or small, the magnifying- power, always compounded of the two which each pair would produce separafely, must continue the same. 2. On consulting experience we soon perceive that when the two middle lenses are placed very near each other, the apparent field almost entirely van- ishes ; and the same thing takes place when they are too far separated. In both cases, to whatever object the telescope is pointed, we discover only a very small part of it. 3. For this reason artists bring the last pair of lenses nearer to the first, or remove them to a greater distance, till they discover the largest field, and delay fixing the lenses till they have found this situation. Now they have observed, that in settling this most advantageous arrangement, the distance of the middle lenses, B and C, is always greater than the sum of the focal distances of these same two lenses. 4. You will readily conclude that this distance cannot depend on chance, but must be supported by a theory, and that affording a termination much more exact than what experience alone could have fur- nished. As it is the duty of a natural philosopher to investigate the causes of all the phenomena which experience discovers, I proceed to unfold the true principles which determine the most advantageous distance B C between the two middle lenses. For this purpose I refer to Fig. 197. Fig. 197. IN TERRESTRIAL TELESCOPES. 381 5. As all the rays must be conveyed to the eye r/ let us attend to the direction of that one which, pro- ceeding from the extremity O of the visible object, passes through the centre A of the object-glass ; for unless this ray is conveyed to the eye, this extremity O will not be visible. Now this ray undergoes no refraction in the object-glass, for it passes through the centre A ; it will therefore proceed in a straight line to the second lens, which it will meet in its ex- tremity b, as this is the last ray transmitted through the lenses. 6. This ray, being refracted by the second lens, will change its direction so as to meet somewhere at n the axis of the lenses ; this would have hap- pened to be the focus of this lens, had the ray A b been parallel to the axis ; but as it proceeds from the point A, its reunion with the axis at n will be more distant from the lens B than its focal distance. 7. We must now place the third lens C in such a manner that the ray, after having crossed the axis at n, may meet it exactly in its extremity c ; from which it is evident, that the greater the aperture of this lens C is, the farther it must be removed from the lens B, and the greater the interval B C becomes : but, on the other hand, care must be taken not to remove the lens C beyond that point, as in this case the ray would escape it, and be transmitted no far- ther. This circumstance, then, determines the just distance between the two middle lenses B and C, conformably to experience. 8. This lens C will produce a new refraction of the ray in question, which will convey it precisely to the extremity d of the last eye-glass D, which, being smaller than C, will render the line c d some- what convergent towards the axis, and will thus undergo, in the last lens, such a degree of refraction as will reunite it with the axis at less than its focal distance ; and there it is exactly that the eye must be placed, in order to receive all the rays trans- 382 CONSTRUCTION OF TELESCOPES. mitted through the lenses, and to discover the greatest field. 9. Thus we are enabled to procure a field whose diameter is almost twice as large as with an astro- nomical telescope of the same magnifying power. By means, then, of these telescopes with four lenses we obtain a double advantage ; the object is repre- sented upright, and a much larger field is discovered both circumstances of much importance. 10. Finally, it is possible to find such an arrange- ment of these four lenses as, without affecting either of the advantages now mentioned, shall entirely do away the defect arising from the colours of the rain- bow, and at the same time represent the object with all possible distinctness. But few artists can attain this degree of perfection. Wth April, 1762. LETTER CVIII. i of scopes. Necessity of blackening the Inside of Tubes. Diaphragms. AFTER these researches respecting the construc- tion of telescopes, I must suggest and explain certain precautions necessary to be used; which, though they relate neither to the lenses themselves nor to their arrangement, are nevertheless of such import- ance, that if they are not very carefully observed, the best instrument is rendered entirely useless. It is not sufficient that the lenses should be arranged in such a manner that all the rays which fall upon them shall be transmitted through these lenses to the eye ; care must be taken, besides, to prevent the transmission of extraneous rays through the tele- scope to disturb the representation. Let the fol- lowing precautions, then, be taken. CONSTRUCTION OF TELESCOPES. 383 1. The lenses of which a telescope is composed must be enclosed in a tube, that no other rays ex- cept those which are transmitted through the object- glass may reach the other lenses. For this effect, the tube must be so very close throughout that no chink admits the smallest portion of light. If by any accident the tube shall be perforated ever so slightly, the extraneous light admitted would confound the representation of the object. 2. It is likewise of importance to blacken through- out the inside of the telescope, of the deepest black possible, as it is well known that this colour does not reflect the rays of light, be they ever so power- ful. You must have observed, accordingly, that the tubes of telescopes are always blackened internally. A single reflection will show the necessity of it. 3. The object-glass A, Fig. 199, trans- mits, not only the rays of the object rep- Fig. 199. resented by the telescope, but those also \p which by the extremities enter all around in great abundance ; such is the ray b a, which falls on the inside upon the frame of the tube at i : if, therefore, the tube were white inwardly, or of any other colour, it would be illuminated by this ray, and of itself would generate new rays of light, which must of necessity be conveyed through the other lenses, and disturb the representation, by mingling with the proper rays of the object. 4. But if the inside of the tube be blackened deeply, no new rays will be produced, let the light be ever so strong. This blackening must be carried through the whole length of the telescope, as there is no black so deep as not to generate, when illuminated, some faint light. Supposing, then, that some extraneous rays were to make their way to the second lens B, the black of the tube, pursuing their course, would easily 384 CONSTRUCTION OF TELESCOPES. absorb them altogether. There is a brilliant black, which, for this reason, it would be very improper to employ. 5. But even this precaution is not sufficient, it is necessary likewise to furnish the inside of the tube with one or more diaphragms, perforated with a small circular aperture, the better to exclude all extraneous light ; but care must be taken that they do not ex- clude the rays of the object which the instrument is intended to represent. See Fig. 198. 6. It is necessary to observe at what Fig. 198. place in the tube the proper rays of the A object are most contracted ; this must be at the points where their images are represented, for there all the rays are collected together. Now, the object- glass A represents the image in its focus at M. You have only, then, to compute the magnitude of this image, and there to fix your diaphragm, whose aperture m n shall be equal to the magnitude of the image, or rather somewhat greater. For if the aperture were less than the image, there would be a proportional loss of the apparent field, which is always a great defect. 7. These are the observations respecting the dia- phragm which apply to astronomical telescopes composed of two convex lenses. In terrestrial tele- scopes two images are represented within the tube ; besides the first at M, represented by the object- glass in its focus, and which the second lens B trans- ports to an infinite distance, the third lens represents a second image in its focus N, which is upright, whereas the former was inverted. At N, therefore, is the proper place to fix a second diaphragm perfo- rated with an aperture n n, of the magnitude of the image there represented. 8. These diaphragms, aided by the blackness of OF TELESCOPES. 385 the inside of the tube, produce likewise an excellent effect with respect to distinctness of representation. It must be carefully observed, however, that the greater the field is which the telescope discovers, the less is to be expected from these diaphragms, as in that case the images become greater, so that the aperture of the diaphragms must be so enlarged as to render them incapable of any longer excluding the extraneous rays. So much the greater care, there- fore, must be taken thoroughly to blacken the inside of the tube, and to make it larger, which consider- ably diminishes the unpleasant effect of which I have been speaking. 13th April, 1762. LETTER CIX. In what manner Telescopes represent the Moon, the Planets, the Sun, and the Fixed Stars. Why these last appear smaller through the Telescope than to the naked Eye. Calculation of the Distance of the Fixed Stars, from a Comparison of their apparent Magni- tude with that of the Sun. I AM persuaded, that by this time you are very well pleased to be relieved at length from the dry theory of telescopes, which is rendered agreeable only by the importance of the discoveries which they have enabled us to make. What pleasing surprise is felt on seeing very dis- tant objects as distinctly as if they were one hundred times nearer to us, or more especially in cases where there is no possibility of reaching them, which holds with respect to the heavenly bodies ! And you are already disposed to admit, that with the aid of the telescope many wonderful things relating to the stars have been discovered. On viewing the moon one hundred times nearer VOL. II. K k 386 OF TELESCOPES. than she really is, many curious inequalities are dis- cernible ; such as excessive heights and profound depths, which from their regularity resemble rather works of art than natural mountains. Hence a very plausible argument is deduced to prove that the moon is inhabited by reasonable creatures. But we have proofs still more satisfactory in simply contemplating the almighty power, in union with the sovereign wisdom and goodness of the Great Creator. Thus the most important discoveries have been made respecting the planets, which, to the unassisted eye, appear only as so many luminous points ; but which, viewed through a good telescope, resemble the moon, and appear even still much greater. But you will be not a little surprised, when I assure you that with the assistance of the best tele- scope, even one which magnifies more than two hundred times, the fixed stars still appear only as points, nay, still smaller than to the naked eye. This is so much the more astonishing, that it is certain the telescope represents them such as they would appear were we two hundred times nearer. Are we not hence reduced to the necessity of concluding, that here telescopes fail to produce their effect"? But this idea presently vanishes, on considering that they discover to us millions of little stars which, without their aid, must have for ever escaped the eye. We likewise perceive the distances between the stars incomparably greater ; for two stars which to the naked eye seemed almost to touch each other, when viewed through the telescope are seen at a very considerable distance ; a sufficient proof of the effect of the telescope. What, then, is the reason that the fixed stars ap- pear to us smaller through the telescope than to the naked eye 1 In resolving this question, I remark, first, that the fixed stars appear greater to the naked eye than they ought to do, and that this arises from OF TELESCOPES. 387 a false light occasioned by their twinkling 1 . In fact, when the rays proceeding from a star come to paint their image at the bottom of the eye, on the retina, our nerves are struck by it only in one point ; but by the lustre of the light the adjacent nerves likewise undergo a concussion, and produce the same feeling which would be communicated if the image of the object painted on the retina were much greater. This happens on looking, in the night, at a very distant light. It appears much greater than when we view it at a small distance ; and this increase of magnitude is occasioned only by a false glare. Now, the more that a telescope magnifies, the more this accident must diminish ; not only because the rays are thereby rendered somewhat fainter, but because the real image at the bottom of the eye becomes greater ; so that it is no longer a single point which supports the whole impression of the rays. Accord- ingly, however small the stars may appear through a telescope, we may confidently affirm, that to the naked eye they would appear still much smaller but for this accidental false light, and that as many times as the telescope magnifies. Hence it follows, that as the fixed stars appear only like so many points, though magnified more than 200 times, their distance must be inconceivable. It will be easy for you to form a judgment how this distance may be computed. The diameter of the sun appears under an angle of 32 minutes : if, there- fore, the sun were 32 times farther off, he would appear under an angle of one minute ; and, conse- quently, still much greater than a fixed star viewed through the telescope, the diameter of which does not exceed two seconds, or the thirtieth part of a minute. The sun, therefore, must be thirty times more, that is 960 times, farther removed, before his appearance could be reduced to that of a fixed star observed with the assistance of a telescope. But the fixed star is 200 times farther off than the tele- APPARENT MAGNITUDE OF THE scope represents it ; and, consequently, the sun must be 200 times 960, that is, 192,000 times farther off than he is, before he could be reduced to the appear- ance of a fixed star. It follows, that if the fixed stars were bodies as large as the sun, their distances would be 192,000 times greater than that of the sun. Were they still greater, their distances must be still so many times greater; and supposing them even many times smaller, their distances must always be more than a thousand times greater than that of the sun. Now the distance of the sun from our globe is about 96,000,000 of English miles. It is impossible, undoubtedly, to think of this im- mense distance of the fixed stars, and of the extent of the whole- universe, without astonishment. What must be the power of that Great Being who created this vast fabric, and who is the absolute Master of it ] Let us adore Him with the most profound ven- eration. llth April, 1762. LETTER CX. Why do the Moon and the Sun appear greater at rising and setting than at a certain Elevation ? Difficulties attending the Solution of this Phenomenon, You must have frequently remarked, that the moon at rising and setting appears much larger than when she is considerably above the horizon ; and every one must give testimony to the truth of this phenom- enon. The same observation has been made with respect to the sun. This appearance has long been a stumbling-block to philosophers ; and, viewed in whatever light, difficulties almost insuperable pre- sent themselves. It would be ridiculous to conclude that the moon's body is really greater when she is in the horizon than when she has attained her greatest MOON AND THE SUN. 389 elevation. For, besides that such an idea would be absurd in itself, it must be considered, that when the moon appears to us in the horizon she appears to other inhabitants of our globe more elevated, and consequently smaller. Now, it is impossible that the same body should be at the same time greater and smaller. It would be almost equally ridiculous to attempt the solution of this strange phenomenon by sup- posing that the moon is nearer to us when she ap- pears in the horizon than when she is arrived at a great elevation, from our certain knowledge that a body appears greater in proportion as it is nearer us ; and you know that the more distant any object is, the smaller it appears. It is for this reason pre- cisely that the stars appear so extremely small, though their real magnitude be prodigious. But however plausible this idea may seem, it is totally destitute of foundation ; for it is undoubtedly certain, that the moon is at a greater distance from us at rising and setting, than when at a greater ele- vation. The demonstration follows : Fig. 200. Let the circle A B D be the earth, and the moon at L. This being laid down, an inhabitant at A will see the moon in his zenith, or the most elevated point of the heavens. But another inhabitant at D, where the line D L touches the surface of the earth, will see the moon at the same time in his horizon ; so that the moon will appear, at the same instant, to the spectator A in his zenith, and to the other spectator D in his horizon. It is evident, how- ever, that the last distance D L is greater than the first A L, and conse- quently the moon is more distant from those who see her in the horizon than from those who see her near their Fig. 200. 390 REFLECTIONS RESPECTING THE zenith. Hence it clearly follows, that the moon, when seen in the horizon, ought to appear smaller, being then in fact farther from us than when arrived at a great elevation. It is astonishing, therefore, that observation should be in direct contradiction to this, and that the moon should appear much greater when viewed near the horizon than in the summit of the heavens. The more this phenomenon is investigated, the more strange it appears, and the more worthy of at- tention : it being undoubtedly certain that the moon, when most remote, that is, in the horizon, ought to appear smaller, whereas, nevertheless, every one is decidedly of opinion that she then appears consid- erably greater. This contradiction is evident, and even seems to overturn all the principles laid down in optics, which, however, are as clearly demonstra- ble as any in geometry. I have purposely endeavoured to set this difficulty in its strongest light, in order to make you the more sensible of the importance of the true solution. Without entering into a discussion of this universal judgment, formed from appearances, respecting the prodigious magnitude of the moon in the horizon, I shall confine myself to the principal question : Is it true, in fact, that the moon, when near the horizon, actually appears greater ? You know that we are possessed of infallible means of exactly measuring the heavenly bodies, by ascertaining the number of degrees and minutes which they occupy in the heavens; or, which amounts to the same thing, by measuring, Fig. 201, the angle EOF, formed by the lines E and F 0, Fig. 201. MOON'S APPARENT MAGNITUDE. 391 drawn from the opposite points of the moon to the eye of the spectator ; and this angle E O F is what we call the apparent diameter of the moon. We have likewise instruments perfectly adapted to the purpose of exactly determining this angle. Now, when we employ such an instrument in measuring the moon's diameter, first at her rising, and after- ward, when she has gained her greatest elevation, we actually find her diameter somewhat less in the first case than in the other, as the inequality of dis- tance requires. There cannot remain the shadow of doubt as to this ; but, for that very reason, the difficulty, instead of diminishing, gathers strength ; and it will be asked with so much the more eager- ness, How comes it that the whole world agrees in imagining the moon to be greater when rising or setting, though her apparent diameter is then in reality smaller ] and, What can be the reason of this delusion, to which men are universally subject! The astronomer, who knows perfectly well that the moon's apparent diameter is then smaller, falls nev- ertheless into the same deception as the most igno- rant clown. 20th April, 1762. t LETTFR CXI. Reflections on the Question respecting the Moon's ap- parent Magnitude. Progress towards a Solution of the Difficulty. Absurd Explanations. You would scarcely have believed that the simple appearance of the moon involved so many difficul- ties ; but I hope I shall be able to clear the way towards a solution, by the following reflections : 1. It is not astonishing that our judgment respect- ing the magnitude of objects should not always be in correspondence with the visual angle under which 392 REFLECTIONS RESPECTING THE we see it : of this daily experience furnishes suffi- cient proof. A cat, for example, appears, when very near, under a greater angle than an ox at the dis- tance of 100 paces. I could never, at the same time, imagine the cat to be larger than the ox : and you will please to recollect, that our judgment respecting magnitude is always intimately connected with that of distance ; so that if we commit a mistake in the calculation of distance, our judgment respecting magnitude becomes, of necessity, erroneous. 2. In order to elucidate this more clearly, it some- times happens that a fly passing suddenly before the eye, without our thinking of it, if our sight is fixed on a distant object we imagine at first that the fly is at a great distance ; and as it appears under a very considerable angle, we take it for a moment to be a large fowl, which at the proper distance would ap- pear under the same angle. It is then incontestably certain, that our judgment respecting the magnitude of objects is not regulated by the visual angle under which they are seen, and that there is a very great difference between the apparent magnitude of objects and the calculated or computed magnitude. The first is regulated by the visual angle, and the other depends on the distance to which we suppose the object to be removed. 3. To avail myself of this remark, I further ob- serve, that we ought not to say that we see the moon greater in the horizon than at a considerable elevation. This is absolutely false, for we then see her even somewhat less. But, to speak accurately, we ought to say that we judge and compute the moon greater when she is in the horizon ; and this is literally true with the unanimous consent of all mankind. This is sufficient to reconcile the apparent contradiction formerly suggested ; for nothing pre- vents our judging or computing the moon to be greater when she rises or sets, though she is seen under a smaller visual angle. MOON'S APPARENT MAGNITUDE. 393 4. We are no longer, then, called upon to explain why we see the moon greater in the horizon, which is impossible, for in reality she then appears smaller, as may be demonstrated by measuring the visual angle. The difficulty, therefore, is reduced to this : Wherefore do we judge or compute the moon to be greater when in those situations'? or rather, we must endeavour to account for this whimsical com- putation. The thing is not surprising in itself, as we know a thousand cases in which we estimate objects to be very great, though we see them under very small angles. 5. We have only to say, then, that when the moon is rising or setting, we suppose her to be at a greater distance than when she has attained a cer- tain elevation. Whenever this computation is set- tled, whatever may be the cause of it, the conse- quence is necessary, that we must b'kewise conclude the moon to be greater in proportion. For, in every case, the more distant we estimate any object to be, the greater we presume it is, and this in the same proportion. As soon as I imagine, by whatever illusion, that a fly passing close before my eye is at the distance of 100 paces, I am obliged, almost whether I will or not, to suppose it as many times greater as 100 paces exceed the real distance of the fly from my eyes. 6. We are now, therefore, reduced to a new question : Wherefore do we presume that the moon is at a greater distance when she is seen in the horizon 1 and, Wherefore is this illusion so universal as not to admit of a single exception ! For the illu- sion of imagining that the moon is then at a much greater distance is altogether unaccountable. It is undoubtedly true that the moon is then really a little more distant, as I demonstrated in my last Letter ; but the difference is so trifling as to be impercepti- ble. Besides, the sun, though 100 times more dis- tant than the moon, does not appear so, and the eye 394 APPEARANCE OF THE MOON estimates even the fixed stars as nearly at the same distance. 7. Though, therefore, when the moon is in the horizon, she is actually a little more distant, this circumstance cannot affect the present question ; and this universal computation, which induces the whole world to imagine the moon to be then at a much greater distance than she really is, must be founded on reasons entirely different, and capable of producing universal illusion. For, as the com- putation is unquestionably erroneous, the reasons which determine us to make it must necessarily be very striking. 8. Some philosophers have attempted to explain this phenomenon by alleging that it is occasioned by the intervention of various objects between us and the moon, such as cities, villages, forests, and mountains. This, say they, is the reason that she then appears to be much farther off; whereas, when she has attained a considerable elevation, as no other body intervenes, she must appear to be nearer. But this explanation, however ingenious it may at first sight appear, is destitute of solidity. On looking at the moon in the horizon through a small aperture made in any body which shall conceal the interme- diate objects, she nevertheless still seems greater. Besides, we do not always imagine that objects between which and us many other bodies interpose are more distant. A great hall, for example, when quite empty, usually appears much larger than when filled with company, notwithstanding the numerous objects then interposed between us and the walls of the apartment. 24th April, 1762. IN THE HORIZON. 395 LETTER CXII. An Attempt towards the true Explanation of this Phe- nomenon, The Moon appears more distant when in the Horizon than when at a great Elevation. WE are still, then, very far from the true solu- tion of this universal illusion, under which all, without exception, are induced to imagine the moon to be much greater when in the horizon than when considerably elevated. I have already remarked, that this phenomenon is so much the more unac- countable, from its being demonstrable tf.iat the moon's apparent diameter is then even somewhat less : we ought not, therefore, to say, that we then see the moon greater, but that we imagine her to be so. Accordingly, I have very often observed our judg- ment of objects to differ very widely from vision itself. We do not hesitate, for example, to conclude that a horse 100 paces distant is larger than a dog one pace distant, though the apparent magnitude of the dog is unquestionably greater; or, which amounts to the same thing, though the image of the dog painted on the bottom of the eye be greater than that of the horse. Our judgment in this case is regulated by taking distance into the account ; and laying it down that the horse is much farther off than the dog, we conclude he is much larger. It is very probable, therefore, that the same cir- cumstance may take place respecting the moon's appearance, and induce us to reckon the moon greater when in the horizon than at a considerable elevation. In the case of the horse, our computa- tion of distance was founded in truth ; but here, as it is absolutely erroneous, the illusion must be sin- gularly unaccountable, but must, at the same time, 396 APPEARANCE OF THE MOON have a certain foundation, as its prevalence is uni- versal, and cannot therefore be imputed to caprice. Wherein can it consist ] This is to be the subject of our present inquiry. 1. Every one considers the azure expanse of heaven as a flattened arch, the summit of which is much nearer to us than the under part, where it meets the horizon. A person, accordingly, stand- ing- on a plane A B, Fig. 202, p^, 202. which extends as far as his sight, perceives the vault of heaven, commonly called the -A- c firmament, under the figure A E F B, in which the distances C A and C B are much gi eater than from the zenith to C. 2. This idea is likewise beyond all question a mere illusion, there being in reality no such vault surrounding and enclosing us on every side. It is a void of immense extent, as it reaches to the most distant of the fixed stars an interval that far ex- ceeds all power of imagination. I use the word void, to distinguish it from gross terrestrial bodies. For, near the earth, space is occupied by our at- mosphere ; and beyond, by that fluid, infinitely more subtile, which we call ether. 3. Though this vault, however, has no real exist- ence, it possesses an undoubted reality in our imagi- nation ; and all mankind, the philosopher as well as the clown, are subject to the same illusion. On the surface of *his arch we imagine the sun, the moon, and all the stars to be disposed like so many bril- liant studs affixed to it ; and though we have a per- fect conviction of the contrary, we cannot help giving way to the illusion. 4. This being laid down, when the moon is in the horizon, imagination attaches her to the point A or B of this supposed vault, and hence we conclude her distance to be as much greater as we consider the line C A or C B to be greater than C Z ; but when IN THE HORIZON. 397 she ascends and approaches the zenith, we imagine she comes nearer; and if she reaches the very zenith, we think she is at the least possible distance. 5. The illusion as to distance necessarily involves that which respects magnitude. As the moon at A appears much farther from C than in the zenith, we are in a manner forced to conclude that the moon is really so much greater; and that in the same proportion that the distance C A appears to exceed the distance C Z. All will not, perhaps, agree in determining this proportion ; one will say, the moon appears to him twice as great when in the horizon ; another will say three times; and the generality will declare for the medium between two and three; but every one will infallibly agree in asserting that the moon appears larger. 6. It may be necessary here to present you with the demonstration of this proposition. The com- putation of magnitude is necessarily involved in the computation of distance. When the moon is near the horizon, we see her. Fig. 203, under a certain angle, say MCA, the spec- p . Q tator being at C ; and when she is at a very great eleva- tion, let N C D be the angle under which we see her. It is evident that these two an- gles M C A and N C D are nearly equal to each other, the difference being im- perceptible. 7. But, in the first case, as we estimate the moon's distance to be much greater, or equal to the line C A, with reference to the imaginary vault above described, it follows, that we compute the moon's diameter to be equal to the line M A. But, in the other case, the distance of the moon C D appears much smaller; and consequently, as the angle N C D is equal to the angle MCA, the computed magni- VOL. IL L 1 398 APPEARANCE OF THE HEAVENS tude D N will be much smaller than the computed magnitude A M. 8. To put this beyond a doubt, you have only to cut off from the lines C M and C A the parts C d and C n, equal to the lines C D and C N ; and as in the two triangles C d n and C D N, the angles at the point C are equal, the triangles themselves are like- wise so, and consequently the line D N will be equal to the line d n ; but d n is evidently smaller than A M, and that as many times as the distance C d and C D is less than C A. This is a clear demon- stration of the reason why we estimate the moon to be greater when in the horizon than when near the zenith. 29th April, 1762. LETTER CXIII. The Heavens appear under the form of an Arch flattened towards the Zenith. You will charge me, no doubt, with pretending to explain one illusion by another equally unaccount- able. It may be said, that the imaginary vault of heaven is altogether as inconceivable as the in- creased appearance of the moon and the other hea- venly bodies when in or near the horizon. The objection is not without foundation, and therefore lays me under the necessity of attempting to explain the true reason why the heavens appear in the form of an arch flattened towards the summit. The fol- lowing reflections may, perhaps, be received as an acquittance of my engagement. 1. In order to account for this imaginary vault, it will be alleged that it proceeds from the appearance of the heavenly bodies, as seeming more remote when in the horizon than when near to or in the zenith. This is undoubtedly a formal petitio prin- TOWARDS THE ZENITH. 399 cipii, as logicians call it, or a begging of the ques- tion, which every one is entitled to reject as a ground of reasoning. In truth, having said above that the imaginary vault of heaven makes the moon in the horizon appear farther off than when near the zenith, it would be ridiculous to affirm, that the thing which leads us to imagine the existence of such a vault is that horizontal objects appear more distant than vertical. 2. It was not, however, useless to suggest the idea of this imaginary vault, though it may not carry us a great way forward; and after I shall have explained wherefore the heavenly bodies ap- pear more remote when viewed near the horizon, you will be enabled to comprehend, at the same time, the reason of that twofold universal illusion, namely, the apparently increased magnitude of the heavenly bodies when in the horizon, and the flattened arch of heaven. 3. The whole, then, reverts to this, to explain wherefore the heavenly bodies when seen in the horizon appear more remote than when at a con- siderable elevation. I now affirm, it is because these objects appear less brilliant ; and this imposes on me the double task of demonstrating why these objects display less brilliancy when in or near the horizon, and of explaining how this circumstance necessarily involves the idea of a greater distance. I flatter myself I shall be enabled to discharge both of these to your satisfaction. 4. The phenomenon itself will not be called in question. However greater the sun's lustre may be at noon, which it is then impossible to ascertain, you know that in the morning and evening, when he is rising or setting, it is possible to contemplate his body without any injury to the eye ; and the same thing takes place with respect to the moon and all the stars, whose brilliancy is greatly dimin- ished in the vicinity of the horizon. We accord- 400 APPEARANCE OF THE HEAVENS. ingly do not see the smaller stars when at a small elevation above the horizon, though they are suf- ficiently discernible at a certain height. 5. This being established beyond a possibility of doubt, the cause of this difference of illumination remains to be investigated. It is abundantly evident that we can trace it only in our atmosphere, or the body of air which encompasses our earth, in so far as it is not perfectly transparent. For if it were, so that all the rays should be transmitted through it without undergoing any diminution, there could be no room to doubt that the stars must always shine with the same lustre, in whatever region of the heavens they might be discovered. 6. But the air, a substance much less fine and subtile than ether, whose transparency is perfect, is continually loaded with heterogeneous particles, rising into it above the earth, such as vapours and exhalations, which destroy its transparency ; so that if a ray should fall in with such a particle, it would be intercepted, and almost extinguished by it. It is accordingly evident, that the more the air is loaded with such particles, which prevent the transmission of light, the more rays must be lost by the intercep- tion ; and you know that a very thick mist deprives the air of almost all its transparency, to such a de- gree that it is frequently impossible to distinguish objects at three paces' distance. 7. Let the points marked in Fig. 204 represent Fig. 204. * such particles scattered througti the air, whose number is greater or less, according as the air is more or less transparent. It is evident, that many LIGHT OF THE HEAVENLY BODIES. 401 of the rays which pervade that space must be lost, and that the loss must be greater in proportion as the space which they had to run through that air is greater. We see, then, that distant objects be- come invisible in a fog, while such as are very near the eye may be still perceptible, because the rays of the first meet in their progress a greater number of particles which obstruct their transmission. 8. We must hence conclude, that the longer the space is through which the rays of the heavenly bodies have to pass through the atmosphere in order to reach our eyes, the more considerable must be their loss or diminution. Of this you can no longer entertain any doubt. All that remains, then, is simply to demonstrate, that the rays of the stars which we see in or near our horizon have a longer space of the atmosphere to pervade than when nearer the zenith. When this is done, you will easily comprehend why the heavenly bodies appear much less brilliant when near the horizon than at the time of rising and setting. This shall be the subject of my next Letter. 1st May, 1762. LETTER CXIV. Reason assigned for the Faintness of the Light of the Heavenly Bodies in the Horizon. WHAT I have just advanced, namely, that the rays of the heavenly bodies, when in the horizon, have a larger portion of our atmosphere to pervade, may appear somewhat paradoxical, considering that the atmosphere universally extends to the same height, so that at whatever point the star may be, its rays must always penetrate through the whole of that height before it can reach our eyes. The following L19 402 LIGHT OF THE HEAVENLY BODIES 205. reflections, I flatter myself, will give you complete satisfaction on the subject. 1. It is first of all necessary to form a just idea of the atmosphere which surrounds our globe. For this purpose the interior circle A B C D, Fig. 205, shall represent the earth, and the exterior dotted circle abed shall mark the height of the atmosphere. Let it be re- marked, that universally in propor- tion as the air rises above the sur- face of the earth it becomes always more transparent and subtile, so that at last it is imperceptibly lost in the ether which fills the whole expanse of heaven. 2. The grosser air, that which is most loaded with the particles that intercept and extinguish the rays of light, is universally found in the lower regions, near the surface of the earth. It becomes, there- fore, more subtile as we ascend, and less obstructive of the light ; and at the height of 5 English miles has become so transparent as to occasion no per- ceptible obstruction whatever of the light. The distance, then, between the interior circle and the exterior, may be fixed at 5 English miles nearly, whereas the semi-diameter of the globe contains