IRLF LIBRARY OF THE UNIVERSITY OF CALIFORNIA. GIF ...... GL IFT OF Class 1 TO ALL TEACHERS. SCHOOL BOOKS. SMILEY'S GEOGRAPHY AND ATLAS, and SACRED AND ANCIENT GEOGRAPHY FOR SCHOOLS. The above works will be found useful and very val liable as works of refer- ence, as well as for schools. The Maps, composing the Atlases, will be found equal in execution and correctness to those on the most extensive scale. The author has received numerous recommendations, among which are the fol- lowing : Dear Sir I have looked over your " Easy Introduction to the Study of Geography^" together with your " Improved Atlas" I have no hesitation in declaring, that I consider them works of peculiar merit. They do honour to your industry, research, and talent, and I ain satisfied, will facilitate the im- provement of the student in geographical science. With sentiments of sincere consideration, I am yours truly, WM. STAUGHTON, D. D. President of Columbia College, District of Columbia. MR. THOMAS SMILEY. Philadelphia, Sept. 1, 1823. Extract from the Minutes of the Philadelphia Academy of Teachers. November 1, 1823. Resolved unanimously, That the Academy of Teachers highly approve th superior merits of Mr. Snr ley's '-''Easy Introduction to the Study of Gtogra- oAy," and the accompanying Atlas, and cordially recommend them to the pa tronage of the public. B. MAYO, President. 1. 1. HITCHCOCK, Secretary. THE NEW FEDERAL CALCULATOR, or SCHOLAR'S ASSISTANT. Containing the most concise and accurate Rules for performing the operations in common Arithmetics together with numerous Examples under each of the Rules, varied so as to make them conformable to almost every khul of business. For the Use of Schools and CounOng Houses. 11 By Thomas T. Smiley, Teacher: author of An Easy Intro- duction to the Study of Geography. Also, of Sacred Geo- graphy for the Use of Schools. Among the numerous recommendations received to the work, are the following: MR. JOHN Gaico. Phila. March 8, 1825. SIR | have examined with as much care as my time would admit, " The New Fed-eral Calculator," by Thomas T. Smiley. It appears to m* to hp. a treatise on Arithmetic of considerable merit. There are parts in Mr. Smiley's work which are very valuable ; the rules given by him in Barter, Loss and Gain, and Exchange, are a great desideratum in a new system or treatise on Arithmetic, and renders his book superior to any on the subject, now in use ; and when it is considered that the calculations in the work are made in Fede- ral Money, t!te only currency now known in the United States, and that ap- propriate questions follow the different rules, by which the learner can be ex- ercised as to his understanding of each part as he progresses ; i hesitate not to say, that, in my opinion, it is eminently calculated to promote instruction in the science on which it treats. Mr. Smiley deserves the thanks of the public and. the encouragement of teachers, for his attempt to simplify and improve the method of teaching Arithmetic. 1 am yours respectfully, VVM. P. SMITH, Preceptor of Mathematics ard Natural Philosophy^ A"o. 152, South Tenth Street. SIR I have carefully examined " The New Federal Calculator, or Scho- lar's Assistant," by Thomas T. Smiley, on which you politely requested my opinion ; and freely acknowledge that I think it better calculated for the use of the United States schools and counting-houses than any book on the sub- ject that I have seen. The author's arrangement of the four primary rules is, in my opinion, a judicious and laudable innovation, claiming the merit of im- provement; as it brings together the rules nearest related in their nature and uses. His questions upon the rules throughout, appear to me to be admirably calculated to el'cit the exertions of the learner. But above all, the preference he has gii en to the currency of his own country, in its numerous examples, has stamped a value upon this little work, which I believe has not fallen to the lot of any other book of the kind, as yet offered to the American public I am, sir, yours respectfully, JOHN MACKAY. Charleston, (S. C.) March 29, 1825. From the United States Gazette. Among the numerous publications of the present day, devoted to the im- provement of youth, -e have noticed a new edition of Siniley's Arithmetic, just published by J. Gngg. The general arrangement of this book is an improvement upon the Arith- metics in present use, being more systematic, and according to the affinities of different rules. The chief advantage of the present over the first edition, is a correction of several typographical errors, a circumstance which will render is peculiarly acceptable to teachers, Tn referring to the merits of this little worti, it is proper to Mention that a greater portiou of its pages are devoted to iii Federal calculation, than is generally allowed in primary works in this branch of study. The heavy tax of time and patience which our youth are now compelled to pay to the errors of their Ancestors, by performing the various operations of pounds, shillings, and pence, should be remitted, and we arr glad to notice that ths Federal computation is becoming the prominent practice of school arithmetic. In recommending Mr. Smiley's book to the notice of parents and teachers, we believe that we invite their attention to a work that will really prove an " assistant" to them, and a " guide" to their interesting charge. The Editors of the New York Telegraph, speaking of Smiley's Arithmetic, observe that they have within a few days attentively examined the above Arithmetic, and say, " We do not hesitate to pronounce it an improvement upon every work of the kind previously before the public; and as such, re commend its adoption in all our Schools and Academies." A KEY to the above Arithmetic, in which all the Examples ne- cessary for a Learner are wrought at large, and also Solutions given of all the various Rules. Designed principally to facili- tate the labour of Teachers, anu assisc such as have not the opportunity of a tutor's aid. By T. T. Smiley, author of the New Federal Calculator, &c. &c. TORREY'S SPELLING BOOK, or First Book for Children. I have examined Mr. Jesse Torrey's " Familiar Spelling Book." I think it a great improvement in the primitive, and not least important branches of education, and shall introduce it into the seminaries under my care, as one su perior to any which has yet appeared. IRA HILL, A.M. Boonsborough, Feb. 2, 1825. The increasing demand for this work is the best evidence of its merits. A PLEASING COMPANION FOR LITTLE GIRLS AND BOYS, blending Instruction with Amusement; bein^a Selec- tion of Interesting Stories, Dialogues, Fables, and Poetry. Designed for the use of Primary Schools and Domestic Nur- series. By Jesse Torrey, jr. To secure the perpetuation of our republican form of government to future generations, let Divines and Philosophers, Statesmen and Patriots, unite their endeavours to renovate the age, by impressing the minds of the people with the importance of educating their little boys and girls. S. AJJAJKS. Report of the Committee of the Philadelphia dcademy of Teachers : adopted JYew. 6, 1824. The Committee, to whom was referred Mr. Jesse Torrey's " Pleasing Companion for Little Girls and Boys," beg leave to report, That they have perused the " Pleasing Companion," and have much plea- *ure in pronouncing as their opinion, that it is a compilation much better cal- culated for the exercise and improvement of small children in the art of read- ing, and especially ia the more rare art of understanding what they read, than the books in general use. All which is respectfully submitted. I. IRVINE HITCHCOCK, PARDON DAVIS, CHARLES MEAD, Committee. A true copy from the minutes of the Academy. C. B. TREGO, Secretary. Nov. 22, 1824. THE MORAL INSTRUCTOR AND GUIDE TO VIRTUE, by Jesse Torrey, Jr. Among the numerous recommendations to this valuable School Book, are the following : Extract of a note from the Hon. Thomas Jefferson, late President of the United States. I thank you, sir, for the copy of your * Moral Instructor. 9 I have read the first edition with great satisfaction, and encouraged its reading in my family." Extracts of a Letter from the Hon. James Madison, late President of the United States. * Sir I have received your letter of the 15th, with a copy of the Moral Instructor. " I have looked enough into your little volume to be satisfied, that both the original and selected parts contain information and instruction which may be useful, not only to juvenile but most other readers. * With friendly respects, JAMES MADISON. DR. TORREY. From Roberts Vanx* President of the Controllers of the Public Schools in Philadelphia. * The Moral Instructor" is a valuable compilation. It appears to be 'wefl adapted for elementary schools, and it will give me pleasure to learn that th lessons which it contains are furnished for the improvement of our youth ge- nerally. Respectfully, ROBERTS VAUX. Philadelphia, 5th month, 8 1823. HISTORY OF ENGLAND, from the First Invasion bv Julius Caesar, to the Accession of George the Fourth, in eighteen hundred and twenty: comprising every Political Event worthy of remembrance; a Progressive View of Religion, Language, and Manners; of Men eminent for their Virtue or their Learn- ing; their Patriotism, Eloquence, or Philosophical Research; of the Introduction of Manufactures, and of Colonial Esta- blishments. With an interrogative Index, for the use of Schools. By William Grimshaw, author of a History of the United States, &c. HISTORY OF THE UNITED STATES, from their first settlement as Colonies, to the cession of Florida, in 1821: comprising every Important Political Event; with a Progres- sive View of the Aborigines; Population, Religion, Agricul- ture, and Commerce; of the Arts, Sciences, and Literature; occasional Biographies of the most remarkable Colonists, Writers, and Philosophers, Warriors, and Statesmen; and a Copious Alphabetical Index. By William Grimshaw, author of a History of England, &c. Also, QUESTIONS adapted to the above History, and a KEY, adapted to the Questions, for the use of Teachers. *' Untoertity of Georgia, Athens, June 4, 1825. **DEAR SIR, u With grateful pleasure, I have read the two small volumes of Mr. Grim shaw, (a History of England, and a Histoiy of the United States) which yon some time since placed in my hands. On a careful perusal of them, I feel no difficulty in giving my opinion, that they are both, as to style and sentiment, works of uncommon merit in their kind ; and admirably adapted to excite, iii youthful minds, the love of historical research. 44 With sincere wishes for the success of his literary labours, * 4 1 am very respectfully, your friend, 44 M. WADDKL, P/wufenl "E.jACKSOIT,Esa." D. JAUDON presents his respectful compliments to Mr. Grimshaw, and if much obliged by his polite attention, and the handsome compliment of his History of the United States with the Questions and Key. " Mr. J. has been in the use of this book for some time ; but anticipates ctill more pleasure to himself, and profit to his pupils, in future, from the help and facility which the questions and key will afford in tne study of these in- teresting pages. " October 10th, 1822." Golgotha, P. Edwd. Va. Sep. 26, 1820. " DEAR SIR, " MR. GRiMSHAw'g * History of the United States,' &c. was some time ago put into my hands by Mr. B - , who requested me to give you my opinion as to the merits of the work. The history of the late war is well manag- ed by your author: it has more of detail and interest than the former part; and I consider it much superior to any of the many compilations on that subject, with which the public has been favoured. It may be said of the entire per- formance, that it is decidedly the best chronological series, and the chastest historical narrative, suited to the capacity of the juvenile mind, that has yet appeared. Its arrangement is judicious; its style neat, always perspicuous, and often elegant ; arid its principles sound. " American writings on men and things connected with America, have been long needed for the young; and I am happy to find, that Mr. Grimshaw has not only undertaken to supply this want, but also to Americanise foreign his- tory for the use of our schools. In a word, sir, I am so fond of American fa- brics, and so anxious to show myself humbly instrumental in giving our youth American feeling and character whilst at school ; that I shall without hesita- tion recommend Mr. Grimshaw's works to my young pupils, as introductory to more extensive historical reading. In fine, the work is so unobjectionable, and puts so great a mass of necessary information within the reach of school- boys, at so cheap a rate, that I feel the highest pleasure in recommending it to the public, and wish you extensive sales. Yours respectfully, ** WILLIAM BRANCH, JR. ** MR. BENJAMIN WARNER, "Philadelphia." " History of the United States, from their first settlement as Colonies , to ih Peace of Ghent, Sec. By William Grimshaw, pp. 312, 12mo. w THIS is the third time, within the space of two years, that we have had occasion to review a volume from the hand of Mr. Grimshaw. He writes with great rapidity ; and improves as he advances. This is the most cor- rectly written of all his productions. We could wish that a person so well formed for close, and persevering study, as he must be, might find encourage- ment tr devote himself to the interests of literature." u Mr. G. has our thanks for the best concise and comprehensive history oi the United States which we have seen." Theological Review^ Qctobtr t 1819. vii * History of England, from the first Invasion by Julius Cowar, to the Peace of Gktnl, &c. For the use of Schools. By William Grimshaw. Philadel- phia, 1819. Benjamin Warner. 12mo. pp. 300. "Ws have copied so much of the title of this work, barely to express our derided approbation of the book, and to recommend its general introduction into schools. It is one of the best books of the kind to be 'ound, and is in- structive even to an adult reader. We should be pleased that teachers would rank it among their class-books ; for it is well calculated to give correct im pressions, to its readers, of the gradual progress of science, religion, govern- ment, and many other institutions, a knowledge of which is beneficial in the present age. Among the many striking merits of this book, are, the perspi- cuity of the narrative, and chasteness of the style. It is with no little pleasure we have learned, that the author has prepared a similar history of the United States; u work long wanted, to nil up a deplorable chasm in the education of American youth." Anahctic Magazine^ October^ 1819. " Philadelphia^ June, 1819. ki SIR I have read with pleasure and profit your History of England. I think it is written with perspicuity, chasteness, an,l impartiality. Well writ- ten history is the best political instructor, and under a government in which it is the blessing of the country that the peopJe govern, its pafes should be con- stantly in the hands of oui youth, and lie open to the humblest citizen in our wide-spread territories. Your book is eminently calculated thus to diffuse this important knowledge, and therefore entitled to extensive circulation ; which I most cordially wish. With much respect, " Your obedient servant, "LANGDON CHEVES. M WILLIAM GRIMSHAW, Esa." GRIMSHAW'S IMPROVED EDITION OF GOLDSMITH'S GREECE. Among the numerous recommendations to this valuable School Book, are the following:- Although there are many worthier s School Books, there are but few which are equally impure and inaccurate with the original editions of Goldsmith's Histories, for the use of Schools. I congratulate both teachers and pupils, upon the appearance of Mr. Grimshaw's edition of the "History of Greece," which has been so completely expurgated, and otherwise corrected, as to give it the character of a new work, admirably adapted to the purpose for which it is intended. THOS. P. JONES, Professor of Mechanics in the Franklin Institute of the State of Pennsylvania, and late Principal of the North Carolam Female Academy. Philadelphia^ Sept. 5, 1826. vm MR. JOHN GRIGO. DEAR SIR Agreeably to youi request I have examined, with attention, " Goldsmith's Greece, revised and corrected, and a vocabulary of proper names appended, with prosodial marks, to assist in their pronunciation, by William Grimshaw;" and I feel a perfect freedom to say, that the correction of numerous grammatical and other errors, by Mr. Grimshaw, together with the rejection of many obscene and indelicate passages improper for the perusal of youth, gives this edition, in my opinion, a decided preference over the edi- tions of that work heretofore in use. The Questions and Key, likewise supplied by Mr. Grimshaw to accompany this edition, afford a facility for communicating instruction, which will be duly appreciated by every judicious teacher. I am, Sir, Yours truly, THOS. T. SMILEY. Philadelphia, Sept. 8, 1826. Tha Editor of the United States Gazette, in speaking of this work, says M Goldsmith's Greece, without a revision, is not calculated for schools ; it abounds in errors, in indelicate description, improper phrases, and is, indeed, a proof how very badly a good author can write, if indeed there is not much room to doubt Goldsmith ever composed the histories to which his name is attached. Mr. Grimshaw has adopted the easy descriptive style of that writer, retained iiis facts, connected his dates, and entirely and handsomely adapted his work to the school desk. The book of questions and the accom- panying key, are valuable additions to the work, and will be found most ser- viceable to teacher and pupil. " From a knowledge of the book, and some acquaintance with the wants oi those for whom it was especially prepared, we unhesitatingly recommend Grimshaw's Greece as one cf the best (in our opinion, the very best of) works of the kind that has been offered to the public." THE UNITED STATES SPEAKER, compiled by T. T. Smiley preferred generally to the Columbian Orator and Scott's Lessons, and works of that kind, by teachers who have examined it. GOLDSMITH'S HISTORY OF GREECE, improved by Grimshaw, with a Vocabulary of the Proper Names con- tained in the work, and the Prosodial Accents, in conformity with the Pronunciation of Lempriere with Questions and a Key, as above. GRIMSHAW'S ETYMOLOGICAL DICTIONARY AND EXPOSITOR OF THE ENGLISH LANGUAGE. CONVERSATIONS ON NATURAL PHILOSOPHY, IN WHICH THE ELEMENTS OF THAT SCIENCE ARE FAMILIARLY EXPLAINED. toitj BY THE AUTHOR OF CONVERSATIONS ON CHEMISTRY, &C. UNlvtRSIT WITH CORRECTIONS, IMPRWSMfi^TTSf'AND CONSIDERABLE ADDITION& IN THE BODY OF THE WORK ; ionis, anTr a BY DR. THOMAS P. JONES, PROFESSOR OF MECHANICS, IN THE FRANKLIN INSTITUTE. OF THE STATE OF PENNSYLVANIA. PHILADELPHIA *. PUBLISHED AND SOLD BY GRIGG AND ELLIOT, NO. 9 NORTH FOURTH STREET. Stereotyped by L. Johnson. 1839- Eastern District of Pennsylvania^ to wit: BE IT REMEMBERED, that, on the twenty-fourth day of April, in the Fiftieth year of the Independence of the United States of America, A. D. 1826, John Grigg, of the said District, hath deposited in this office the title of a book, the right whereof he claims as proprietor, in the words fol- lowing, to wit : " Conversations on Natural Philosophy, in which the Elements of that Sci ence are familiarly explained. Illustrated with Plates. By the Author of Conversations on Chemistry, &c. With Corrections, Improvements, and considerable Additions, in the Body of the. Work; appropriate Questions, and a Glossary: By Dr. Thomas P. Jones, Professor of Mechanics, in the Franklin Institute, of the State of Pennsylvania." In conformity to the Act of the Congress of the United States, entitled "An Act for the Encouragement of Learning, by securing the Copies of Maps, Charts, and Books, to the Authors and Proprietors of such Copies, duri'.g the times therein mentioned ;" And also to the Act, entitled, " An Act supplementary to an Act, entitled, * An Act for the Encouragement of Learning, by securing the Copies of Maps, Charts, and Books, to the Au- thors and Proprietors of such Copies during the times therein mentioned,' and extending the benefits thereof to the arts of designing, engraving, and etching, historical and other prints." D. CALDWELL, Clerk of the Eastern District of Pennsylvania. PRINTED BY T. K. AND p. G. COLLINS PHILADELPHIA. ( \ A ^9 PREFACE. NOTWITHSTANDING the great number of books which are written, expressly for the use of schools, and which embrace every subject on which in- struction is given, it is a lamentable fact, that the catalogue of those w r hich are well adapted to the intended purpose, is a very short one. Al- most all of them have been written, either by those who are without experience as teachers, or by teachers, deficient in a competent, knowledge of the subjects, on w r hich they treat. Every intelli- gent person, who has devoted himself to the in- struction of youth, must have felt and deplored, the truth of these observations. In most instances, the improvement of a work already in use, will be more acceptable, than one of equal merit w T ould be, which is entirely new ; the introduction of a book into schools, being al- ways attended with some difficulty. The " Conversations on Chemistry," written by Mrs. Marcet, had obtained a well-merited celebrity, and \vas very extensively adopted as a school-book, before the publication of her u Con- versations on Natural Philosophy." This, also, has been much used for the same purpose; but, the observation has been very general, among intel- ligent teachers, that, in its execution, it is very in- ferior to the former work. The editor of the edition now presented to the public, had undertaken to add to the \vork, ques- tions, for the examination of learners ; and notes, where he deemed them necessary. He soon found; however, that the latter undertaking w r ould 202368 IV PREFACE, be a very unpleasant one, as he must have pointed out at the bottom of many of the pages, the de- fects and mistakes in the text ; whilst numerous modes of illustration, or forms of expression, which his experience as a teacher, had con- vinced him would not be clear to the learner, must, of necessity, have remained unaltered. He therefore determined to revise the whole work, and with the most perfect freedom, to make such al- terations in the body of it, as should, in his opi- nion, best adapt it to the purpose for which it was designed. Were the book, as it now stands, care- fully compared with the original, it would be found, that, in conformity with this determina- tion, scarcely a page of the latter, remains un- changed. Verbal alterations have been made, er- rors, in points of fact, have been corrected ; and new modes of illustration have been introduced, whenever it was thought that those already em- ployed, could be improved ; or when it was known, that, from local causes, they are not fami- liar, in this country. The editor feels assured, that, in performing this task, he has rendered the book more valuable to the teacher, and more useful to the pupil; and he doubts not that the intelligent author of it, would prefer the mode which has been adopted, to that which was at first proposed. The judicious teacher will, of course, vary the questions according to circumstances; and those who may not employ them at all, as questions, will still find them useful, in directing the pupil to the most important points, in every page. The Glossary has been confined to such terms of science as occur in the work ; and is believed to include all those, of which a clear definition can not be found in our common dictionaries. CONTENTS. CONVERSATION I. Page OW GENERAL PROPERTIES OF BODIES. 9 INTRODUCTION. General Properties of Bodies. Impenetrability. Exten- sion. Figure. Divisibility. Inertia. Attraction. Attraction rxf Cohe- sion. Density. Rarity, Heat. Attraction of Gravitation. CONVERSATION II. ON THE ATTRACTION OF GRAVITY 22 Attraction of Gravitation, continued. Of Weight. Of the Fall of Bodies. Of the Resistance of the Air. Of the Ascent of Light Bodies. CONVERSATION III. ON THE LAWS OF MOTION. 32 Of Motion. Of the Inertia of Bodies. Of Force to produce Motion. Di- rection of Motion. Velocity, absolute and relative. Uniform Motion. Retarded Motion. Accelerated Motion. Velocity of Falling Bodies. Momentum. Action and Reaction equal. Elasticity of Bodies. Porosity of Bodies. Reflected Motion. Angles of Incidence and Reflection. CONVERSATION IV. ON COMPOUND MOTION. 46 Compound Motion, the result of two opposite forces. Of Curvilinear Motion, the result of two forces. Centre of Motion, the point at rest, while the other parts of the body move round it. Centre of Magnitude, the middle of a body. Centripetal Force, that which impels a body towards a fixed central point. Centrifugal Force, that which impels a body to fly from the centre. Fall of Bodies in a Parabola. Centre of Gravity, the point about which, the parts balance each other. A2 VI CONTENTS. Page CONVERSATION V. ON THE MECHANICAL POWERS. 54 Of the Power of Machines. Of the Lever in general. Of the Lever of iht first kind, having the Fulcrum between the power and the weight. Of the Lever of the second kind, having the Weight between the power and the fulcrum. Of the Lever of the third kind, having the Power between the fulcrum and the weight. Of the Pulley. Of the Wheel and Axle. Of the Inclined Plane. Of the Wedge. Of the Screw. CONVERSATION VI. ASTRONOMY. CAUSES OF THE MOTION OF THE HEAVENLY BODIES. 70 Of the Earth's annual motion. Of the Planets, and their motion. Of the Diurnal motion of the Earth and Planets. CONVERSATION VII. ON THE PLANETS. 80 Of the Satellites and Moons. Gravity diminishes as the Square of the Dis- tance. Of the Solar System. Of Comets. Constellations, signs of the Zodiac. Of Copernicus, Newton, &c. CONVERSATION VIII. ON THE EARTH. 91 Of the Terrestrial Globe. Of the Figure of the Earth. Of the Pendulum. Of the Variation of the Seasons, and of the Length of Days and Nights. Of the Causes of the Heat of Summer. Of Solar, Sideral, and Equal or Mean Time. CONVERSATION IX. ON THE MOON. 108 Of the Moon's Motion. Phases of the Moon. Eclipses of the Moon. Eclipses of Jupiter's Moon?. Of Latitude and Longitude. Of the Transits of the inferior Planets. Of the Tides. CONTENTS. Vll Past CONVERSATION X. * HYDROSTATICS. > ON THE MECHANICAL PROPERTIES OF FLUIDS. 118 Definition of a Fluid. Distinction between Fluids and Liquids. Of Non- Elastic Fluids, scarcely susceptible of Compression. Of the Cohesion of Fluids. Of their Gravitation. Of their Equilibrium. Of their Pressure. Of Specific Gravity. Of the Specific Gravity of Bodies heavier than Water. Of those of the same weight as Water. Of those lighter than Water. Of the Specific Gravity of Fluids. CONVERSATION XI. OF SPRINGS, FOUNTAINS, &C. 128 Of the Ascent of Vapour and the Formation of Clouds. Of the Formation and Fall of Rain, &c. Of the Formation of Springs. Of Rivers and Lakes. Of Fountains. CONVERSATION XII. PNEUMATICS. OJT THE MECHANICAL PROPERTIES OF AIR, 136 Of the Spring or Elasticity of the Air. Of the Weight of the Air. Experi- ments with the Air Pump. Of the Barometer. Mode of Weighing Air. Specific Gravity of Air.' Of Pumps. Description of the Sucking Pump Description of the Forcing Pump. CONVERSATION XIII. ON WIND AND gOUNtf. 146 Of Wind in General. Of the Trade Wind. Of the Periodical Trad Winds. Of the Aerial Tides. Of Sound in General. Of Sonorous Bo- dies. Of Musical Sounds. Of Concord or Harmony, and Melody. CONVERSATION XIV. ON OPTICS. 157 Of Luminous, Transparent, -and Opaque Bodies. Of the Radiation of Light. Of Shadows. Of the Reflection of Light. Opaque Bodies seen only by Reflected Light. Vision Explained. Camera Obscura. Image of Objects on the Retina. V1U CONTENTS. +4 CONVERSATION XV. OPTICS continued. OE THE ANGLE OF VISION, AND REFLECTION OF MIRRORS. 168 Angle of Vision. Reflection of Plain Mirrors. Reflection of Convex Mir- , rors. Reflection of Concave Mirrors. CONVERSATION XVI. ON REFRACTION AND COLOURS. 179 Transmission of Light by Transparent Bodies. Refraction. Refraction by the Atmosphere. Refraction by a Lens. Refraction by the Prism -Of Colour from the Rays of Light. Of the Colours of Bodies. CONVERSATION XVII. ON THE STRUCTURE OB THE EYE, AND OPTICAL INSTRUMENTS. 195 Description of the Eye. Of the Image on the Retina. Refraction by the Humours of the Eye. Of the use of Spectacles. Of the Single Micro- scope. Of the Double Microscope. Of the Solar Microscope. Magic Lanthorn. Refracting Telescope. Reflecting Telescope. GLOSSARY, ...... - ... 205 CONVERSATION I. ON GENERAL PROPERTIES OF BODIES. INTRODUCTION. GENERAL PROPERTIES OF BODIES. IMPENETRABILITY. EXTENSION. FIGURE. DIVISIBILITY. INERTIA. ATTRACTION. ATTRACTION OF COHESION. DENSITY. RARITY. HEAT. ATTRAC- TION OF GRAVITATION. EMILY. I MUST request your assistance, my Dear Mrs. B. in a charge which I have lately undertaken: it is that of instructing my youngest sister, a task, which I find proves more difficult than ] had at first imagined. I can teach her the common routine oi children's lessons tolerably well ; but she is such an inquisitive little creature, that she is no. satisfied without an explanation of every difficulty that occurs to her, and frequently asks me questions which I am at a loss to answer. This morning, for instance, when I had explained to her that the world was round like a ball, instead of being flat as she had supposed, and that it was surrounded by the air, she asked me what supported it. 1 told her that it required no support; she then inquired why it did not fall as every thing else did ? This I confess perplexed me ; for I had myself been satisfied with learning that the world floated in the air, without considering how unnatural it was that so heavy a body, bearing the weight of all other things, should be able to support itself. Mrs. B. I make no doubt, my dear, but that I shall be able to explain this difficulty to you ; but I believe that it would be almost impossible to render it intelligible to the comprehension cf so young a child as your sister Sophia. You, who are now in your thirteenth year, may, I think, with great propriety, learn not only the cause of this particular fact, but acquire a general knowledge of the laws by which the natural world is governed. Emily. Of all things, it is what I should most like to learn; but I was afraid it was too difficult a study even at my age. Mrs. B. Not when familiarly explained : if you have patience to attend, I will most willingly give you all the information in my power. You may perhaps find the subject rather dry at first; ' '* 10 GENERAL PROPERTIES OF BODIES. N ' but if I succeed in explaining the laws of nature, so as to make you understand them, I am sure that you will derive not only instruction, but great amusement from that study. Emily. I make no doubt of it, Mrs. B.; and pray begin by explaining why the earth requires no support; for that is the point which just now most strongly excites my curiosity. Mrs. B. My dear Emily, if I am to attempt to give you a general idea of the laws of nature, which is no less than to intro- duce you to a knowledge of the science of natural philosophy, it will be necessary for us to proceed with some degree of regu- larity. I do not wish to confine you to the systematic order of a scientific treatise, but if we were merely to examine every vague question that may chance to occur, our progress would be but very slow. Det us, therefore, begin by taking a short survey of the general properties of bodies, some of which must necessarily be explained before I can attempt to make you understand whj the earth requires no support. When I speak of bodies, I mean substances, of whatever na- ture, whether solid or fluid ; and matter is the general term used to denote the substance, whatever its nature be, of which the different bodies are composed. Thus, the wood of which this table is made, the water with which this glass is filled, and the air which we continually breathe, are each of them matter. Emily. I am very glad you have explained the meaning of the word matter, as it nas corrected an errroneous conception I had formed of it : I thought that it was applicable to solid bodies only. Mrs. B. There are certain properties which appear to be common to all bodies, and are hence called the essential or inhe- rent properties of bodies ; these are Impenetrability, Extension, Figure, Divisibility, Inertia and Attraction. These are also called the general properties of bodies, as we do not suppose any body to exist without them. By impenetrability is meant the property which bodies have of occupying a certain space, so that where one body is, another can not be, without displacing the former; for two bodies can not exist in the same place at the same time. A liquid may be more easily removed than a solid body; yet it is not the less substan- tial, since it is as impossible for a liquid and a solid to occupy the same space at the same time, as for two solid bodies to do so. For instance, if you put a spoon into a glass full of water, the water will flow over to make room for the spoon. Emily. I understand this perfectly. Liquids are in reality 1. What is intended by the term bodies ? 2. Is the term matter, restrict- ed to substances of a particular kind: 3. Name those properties of bodies, which are called inherent. 4. What is meant by impenetrability ? 5. Can a liquid be said to be impenetrable ? GENERAL PROPERTIES OF BODIES. 11 as substantial or as impenetrable as solid bodies, and they ap- pear less so, only because they are more easily displaced. Mrs. B. The air is a fluid differing in its nature from liquids, but no less impenetrable. If I endeavour to fill this phial by plunging it into this bason of water, the air, you see, rushes out of the phial in bubbles, in order to make way for the water, for the air and the water can not exist together in the same space, any more than two h?rd bodies ; and if I reverse this goblet, and plunge it perpendicularly into the water, so that the air will not be able to escape, the water will no longer be able to fill the goblet. Emily. But it rises some way into the glass. Mrs. B. Because the water compresses or squeezes the air into a smaller space in the upper part of the glass; but, as long as it remains there, no other body can occupy the same place. Emily. A difficulty has just occurred to me, with regard to the im penetrability of solid bodies ; if a nail is driven into a piece of wood, it penetrates it, and both the wood and the nail occupy the same space that the wood alone did before ? Mrs. B. The nail penetrates between the particles of the wood, by forcing them to make way for it; for you know that not a single atom of wood can remain in the space which the nail occupies ; and if the wood is not increased in size by the addition of the nail, it is because wood is a porous substance, like sponge, the particles of which may be compressed or squeez- ed closer together ; and it is thus that they make way for the nail. We may now proceed to the next general property of bodies, extension. A body which occupies a certain space must neces- sarily have extension ; that is to say, length, breadth and depth 01 thickness ; these are called the dimensions of extension : can you form an idea of any body without them ? Emily. No ; certainly I can not ; though these dimensions must, of course vary extremely in different bodies. The length, breadth and depth of a box, or of a thimble, are very different from those of a walking stick, or of a hair. But is not height also a dimension of extension? Mrs B. Height and depth are the same dimension, consider- ed in different points of view; if you measure a body, or a space, from the top to the bottom, you call it depth ; if from the bottom 6. How can you prove that air is impenetrable ? 7. If air is impenetra- ble, what causes the water to rise some way into a goblet, if I plunge it into water with its mouth downward? 8. When I drive a nuil into wood, do not both the iron and the wood occupy the same space? 9. In how many direc- tions is a body said to have extension? 10. How do we distinguish the terms height and depth? GENERAL PROPERTIES OF BODIES. upwards, you call it height; thus the depth and height of a box are, in fact, the same thing. Emily. Very true; a moment's consideration would have enabled me to discover that ; and breadth and width are also the same dimension. Mrs. B. Yes ; the limits of extension constitute figure or shape. You conceive that a body having length, breadth and depth, can not be without form, either symmetrical or irregular ? Emily. Undoubtedly ; and this property admits of almost an infinite variety. Mrs. B. Nature has assigned regular forms to many of her productions. The natural form of various mineral substances is that of crystals, of which there is a great variety. Many of them are very beautiful, and no less remarkable by their trans- parency or colour, than by the perfect regularity of their forms, as may be seen in the various museums and collections of natu- ral history. The vegetable and animal creation appears less symmetrical, but is still more diversified in figure than the mine- ral kingdom. Manufactured substances assume the various arbitrary forms which the art of man designs for them ; and an infinite number of irregular forms are produced by fractures and by the dismemberment of the parts of bodies. Emily. Such as a piece of broken china, or glass ? Mrs. B. Or the masses and fragments of stone, and other mine- ral substances, which are dug out of the earth, or found upon its surface ; many of which, although composed of minute crystals, aro in the lump of an irregular form. We may now proceed to divisibility; that is to say, a suscep tibility of being divided into an indefinite number of parts. Take any small quantity of matter, a grain of sand for instance, and cut it into two parts ; these two parts might be again divided, had we instruments sufficiently fine for the purpose ; and if by means of pounding, grinding, and other similar methods, we car- ry this division to the greatest possible extent, and reduce the body to its finest imaginable particles, yet not one of the parti- cles will be destroyed, but will each contain as many halves and quarters, as did the whole grain. The dissolving of a solid body in a liquid, affords a very striking example of the extreme divisibility of matter; when you sweeten a cup of tea, for instance, with what minuteness the sugar must be divided to be diffused throughout the whole of the liquid. 11. What constitutes the Jigure, or form of a body/ 1 12. What is said respecting the form of minerals? 13. What of the vegetable and animal creation? 14. What of artificial, and accidental forms? 15. What is meant 67 divisibility? 16. What examples can you give, to prove that the parti- teles of a body are minute in the extreme ? GENERAL PROPERTIES OF BODiES. 1 Emily. And if you pour a few drops of red wine into a glass of water, they immediately tinge the whole of the water, and must therefore be diffused throughout it. Mrs. B. Exactly so; and the perfume of this lavender water will be almost as instantaneously diffused throughout the room, if I take out the stopper. Emily. But in this case it is only the perfume of the laven- der, and not the water itself that is diffused in the room. Mrs. B. The odour or smell of a body is part of the body itself, and is produced by very minute particles or exhalations which escape from the odoriferous bodies. It would be impossi- ble that you should smell the lavender water, if particles of it did not come in actual contact with your nose. Emily. But when I smell a flower, I see no vapour rise from it; and yet I perceive the smell at a considerable distance. Mrs. B. You could, I assure you, no more smell a flower, the odoriferous particles of which did not touch your nose, than you could taste a fruit, the flavoured particles of which did not come in contact with your tongue. Emily. That is wonderful indeed ; the particles then, which exhale trom the flower and from the lavender water, are, I sup- pose, too small to be visible ? Mrs. B. Certainly: you may form some idea of their extreme minuteness, from the immense number which must have escaped in order to perfume the whole room ; and yet there is no sensible diminution of the liquid in the phial. Emily. But the quantity must really be diminished ? Mrs. B. Undoubtedly ; and were you to leave the bottle open a sufficient length of time, the whole of the water would evapo- rate and disappear. But though so minutely subdivided as to be imperceptible to any of our senses, each particle would continue to exist ; for it is not within the power of man to destroy a single particle of matter : nor is there any reason to suppose that in nature an atom is ever annihilated. Emily. Yet, when a body is burnt to ashes, part of it, at least, appears to be effectually destroyed : look how small is the resi- due of ashes in the fire place, from all the fuel which has been consumed within it. Mrs. B. That part of the fuel, which you suppose to be de- stroyed, evaporates in the form of smoke, and vapour, and air, whilst the remainder is reduced to ashes. A body, in burning, undergoes no doubt very remarkable changes; it is generally subdivided; its form and colour altered; its extension increased: but the various parts, into which it has been separated by com- 17. Waal produces the odour of bodies' 18. How do odours exemplify the minuteness of the particles of matter ? 19. Can matter be in any Way anni hilated ' : 20. What becomes of the fuel, which disappears i n our fires ? 14 GENERAL PROPERTIES OF BODIES. hustion, continue in existence, and retain all the essential pro- perties of bodies. Emily. But that part of a burnt body which evaporates in smoke has no figure ; smoke, it is true, ascends in columns into the air, but it is soon so much diffused as to lose all form ; it becomes indeed invisible. Mrs. B. Invisible, I allow; but we must not imagine that what we no longer see no longer exists. Were every parti- cle of matter that becomes invisible annihilated, the world itself would in the course of time be destroyed. The particles of smoke, when diffused in the air, continue still to be particles of matter as well as when more closely united in the form of coals: they are really as substantial in the one state as in the other, and equally so when by their extreme subdivision they become invisible. No particle of matter is ever destroyed : this'is a prin ciple you must constantly remember. Every thing in natuie decays and corrupts in the lapse of time. We die, and our bodies moulder to dust; but not a single atom of them is lost; they serve to nourish the earth, whence, while living, they drew their support. The next essential property of matter is called inertia or in- activity; this word expresses the resistance which matter makes to a change from a state of rest, to that of motion, or from a state of motion to that of rest. Bodies are equally incapable of chang- ing their actual state, whether it be of motion or of rest. You know that it requires force to put a body which is at rest in mo- tion; an exertion of strength is also requisite to stop a body which is already in motion, The resistance of the body to a change of state, in either case, arises from its inertia. .Emily. In playing at base-ball I am obliged to use all my strength to give a rapid motion to the ball; and when I have to catch it, I am sure I feel the resistance it makes to bein^ stopped. But if I did not catch it, it would soon fall to the ground and stop of itself. Mrs. B. Matter being inert it is as incapable of stopping of itself as it is of putting itself into motion : when the ball ceases to move, therefore, it must be stopped by some other cause or power; but as it is one with which you are yet unacquainted, we can not at present investigate its effects. The last property which appears to be common to ab bodies is attraction. All bodies consist of infinitely small particles of matter, each of which possesses the power of attracting or draw- ing towards it, and uniting with any other particle sufficiently 21. How can that part which evaporates, be still paid to possess a substan- tial form? 22. What do we mean by inertia? 23. Give an example to prove that force is necessary, either to give or to stop motion. 24. What ge- neral power do the particles of matter exert upon other particles ? GENERAL PROPERTIES OF BODIES. 15 aear to be within the influence of its attraction ; but in minute particles this power extends to so very small a distance around them, that its effect is not sensible, unless they are (or at least appear to be) in contact; it then makes them stick or adhere together, and is hence called the attraction of cohesion. With- out this power, solid bodies would fall in pieces, or rather crum- ble to atoms. Emily. I am so much accustomed to see bodies firm and so .id, that it never occurred to me that any power was requisite to unite the particles of which they are composed. But the attrac- tion of cohesion does not, I suppose, exist in liquids; for the particles of liquids do not remain together so as to form a body, unless confined in a vessel ? Mrs. B. I beg your pardon; it is the attraction of cohesion which holds this drop of water suspended at the end of my fin- ger, and keeps the minute watery particles of which it is com- posed united. But as this power is stronger in proportion as the particles of bodies are more closely united, the cohesive attrac- tion of solid bodies is much greater than that of fluids. The thinner and lighter a fluid is, the less is the cohesive at- traction of its particles, because they are further apart ; and in elastic fluids, such as air, there is no cohesive attraction among the particles. Emily. That is very fortunate; for it would be impossible to breathe the air in a solid mass; or even in a liquid state. But is the air a body of the same nature as other bodies ? Mrs. B. Undoubtedly, in all essential properties. Emily. Yet you say that it does not possess one of the gene- ral properties of bodies attraction. Mrs. B* The particles of air are not destitute of the power of attraction, but they are too far distant from each other to be influenced by it so as to produce cohesion : and the utmost efforts of human art have proved ineffectual in the attempt to compress them, so as to bring them within the sphere of each other's at- traction, and make them cohere. Emily. If so, how is it possible to prove that they are endow- ed with this power? Mrs. B. The air is formed of particles precisely of the same nature as those which enter into the composition of liquid and solid bodies, in each of which we have a proof of their attraction. Emily. It is then, I suppose, owing to the different degrees of cohesive attraction in different substances, that they are liard or soft, and that liquids are thick or thin. 25. What is that species of attraction called, which keeps bodies in a solid state? 26. Does the attraction of cohesion exist in liquids, and how is its ex- istence proved ? 27. If the particles of air attract each other, why do they not cohere ? 28. From what then do you infer that they possess atUuction . 29. How do you account for some bodies being hard and others soft? Ib G3NERA.L PROPERTIES OF BODIES. Mrs. B. Yes ; but you would express your meaning bettei by the term density, which denotes the degree of closeness anc compactness of the particles of a body. In philosophical Ian guage, density is said to be that property of bodies by which they contain a certain quantity of matter, under a certain bulk or magnitude. Rarity is the contrary of density; it denotes tht thinness and subtilty of bodies : thus you would say that mercu- ry or quicksilver was a very dense fluid ; ether, a very rare one. Those bodies which are the most dense, do not always cohere the most strongly; lead 's more dense than iron, yet its particles! are more easily separated. Caroline. But how are we to judge of the quantity of mattei contained in a certain bulk ? Mrs. B. By the weight : under the same bulk bodies are said to be dense in proportion as they are heavy. Emily. Then we may say that metals are dense bodies, wood comparatively a rare one, &c. But, Mrs. B., when the particles! of a body are so near as to attract each other, the effect of this power must increase as they are brought by it closer together : so that one would suppose that the body would gradually augmenli in density, till it was impossible for its particles to be more; closely united. Now, we know that this is not the case; for soflj bodies, such as cork, sponge, or butter, never become, in conse- quence of the increasing attraction of their particles, as hard as iron? Mrs. B. In such bodies as cork and sponge, the particles which come in contact are so few as to produce but a slight de- gree of cohesion : they are porous bodies, which, owing to the peculiar arrangement of their particles, abound with interstices, or pores, which separate the particles. But there is also a fluid much more subtile than air, which pervades all bodies, this is heat, Heat insinuates itself more or less between the particles of all bodies, and forces them asunder; you may therefore consider heat, and the attraction of cohesion, as constantly acting in op- position to each other. Emily. The one endeavouring to rend a body to pieces, the other to keep its parts firmly united. Mrs. B. And it is this struggle between the contending forcesi of heat and attraction, which prevents the extreme degree of j density which would result from the sole influence of the attra - tion oi cohesion. Emily. The more a body is heated then, the more its parti- cles will be separated. 30. What is meant by the term density? 31. Do the most dense bodiec always cohere the most strongly ? 32. How do we know that one body i more dense than another? 33. What is there which acts in opposition to co- hesive attraction, tending to separate the particles of bodies ? GENERAL PROPERTIES OF BODIES. 17 Mrs. B. Certainly : we find that bodies not only swell or dilate, but lose their cohesion, by heat: this effect is very sensible in butter, for instance, which expands by the application of heat, till at length the attraction of cohesion is so far diminished that the particles separate, and the butter becomes liquid. A similar effect is produced by heat on metals, and all bodies susceptible of being melted. Liquids, you know, are made to boil by the application of heat; the attraction of cohesion then yields entirely to the repulsive power ; the particles are totally separated and converted into steam or vapour. But the agency of heat is in no body more sensible than in air, which dilates and contracts by its increase or diminution in a very remarkable degree. Emily. The effects of heat appear to be one of the most in- teresting parts of natural philosophy. Mrs. B. That is true ; but heat is so intimately connected with chemistry, that you must allow me to defer the investiga- tion of its properties till you become acquainted with that science. To return to its antagonist, the attraction of cohesion ; it is this power which restores to vapour its liquid form, which unites it into drops when it falls to earth in a shower of rain, which gathers the dew into brilliant gems on the blades of grass- Emily. And I have often observed that after a shower, the water collects into large drops on the leaves of plants ; but I can not say that I perfectly understand how the attraction of cohe - sion produces this effect. Mrs. B. Rain, when it first leaves the clouds, is not in the form of drops, but in that of mist or vapour, which is composed of very small watery particles; these in their descent mutually attract each other, and those that are sufficiently near in conse- quence unite and form a drop, and thus the mist is transformed into a shower. The dew also was originally in a state of vapour, but is, by the mutual attraction of the particles, formed into small globules on the blades of grass : in a similar manner the rain upon the leaf collects into large drops, which when they become too heavy for the leaf to support, fall to the ground. Emily. All this is wonderfully curious ! I am almost bewil- dered with surprise and admiration at the number of new ideas I have already acquired. Mrs. B. Every step that you advance in the pursuit of natu- ral science, will fill your mind with admiration and gratitude towards its Divine Author. In the study of natural philosophy, 34. What would be the consequence if the repulsive power of heat were not exerted ? 35. If we continue to increase the heat, what effects will it pro- duce on bodies ? 36. What body has its dimensions most sensibly affected by change of temperature ? 37. What power restores vapours to the liquid form ? 38. What examples can you give ? 39. How are drops of rain and of dew said to be formed ? B 2 18 GENERAL PROPERTIES OF BODIES. we must consider ourselves as reading the book of nature, in which the bountiful goodness and wisdom of God are revealed to all mankind; no study can tend more to purify the heart, and raise it to a religious contemplation of the Divine" perfections. There is another curious effect of the attraction of cohesion which I must point out to you ; this is called capillary- attraction. It enables liquids to rise above their ordinary level *in capillary tubes : these are tubes, the bores of which are so extremely small that liquids ascend within them, from the cohesive attraction between the particles of the liquid and the interior surface of the tube. Do you perceive the water rising in this small glass tube, above its level in the goblet of water, into which I have put one end of it ? Emily. Oh yes ; I see it slowly creeping up the tube, but now it is stationary : will it rise no higher ? Mrs. B. No; because the cohesive attraction between the water and the internal surface of tne tube is now balanced by the weight of the water within it ; if the bore of the tube were narrower the Water would rise higher ; and if you immerse seve- ral tubes of bores of different sizes, you will see it rise to differ- ent heights in each of them. In making this experiment, you should colour the water with a little red wine, in order to ren- der the effect more obvious. AU porous substances, such as sponge, bread, linen, &c. may be considered as collections of capillary tubes: if you dip one end of a lump of sugar into water, the fluid will rise in if, and wet it considerably above the surface of the water into which you dip it Emily. In making tea I have often observed that effect, with- out being able to account for it. Mrs. B. Now that you are acquainted with the attraction of cohesion, I must endeavour to explain to you that of Grnmta- tion, which is probably a modification of the same pov/er ; the first is perceptible only in very minute particles, and at very small distances; the other acts on the largest bodies, and extends to immense distances. Emily. You astonish me : surely you do not mean to say that large bodies attract each other ? Mrs. B. Indeed I do : let us take, for example, one of the largest bodies in nature, and observe whether it does not attract other bodies. What is it that occasions the fall of this book, when I no longer support it ? 40. What is meant by a capillary tube? 41. What effect does attraction produce when these are immersed in water ? 42. What is the reason that the water rises to a certain height only ? 43. Give some familiar examples of capillary attraction. 44. In what does gravitation differ from cohesive attraction? 45. What causes bodies near the earth's surface, to have a tendency to fall towards it ? GENERAL PROPERTIES OF BODIES. 19 Entity. Can it be the attraction of the earth ? I thought that all bodies had a natural tendency to fall. Mrs. B. They have a natural tendency to fall, it is true ; but that tendency is produced entirely by the attraction of the earth: the earth being so much larger than any body on its surface, forces every body, which is not supported, to fall upon it. Emily. If the tendency which bodies have to fall results from the earth's attractive power, the earth itself can have no such tendency, since it cannot attract itself, and therefore it requires no support to prevent it from falling. Yet the idea that bodies do not fail of their own accord, but that they are drawn towards the earth by its attraction, is so new and strange to me, that I know not how to reconcile myself to it. Mrs. B. When you are accustomed to consider the fall of bodies as depending on this cause, it will appear to you as natu- ral, and surely much more satisfactory, than if the cause of their tendency to fall were totally unknown. Thus you understand that all matter is attractive, from the smallest particle to the largest mass ; and that bodies attract each other with a force pro- portional to the quantity of matter they contain. Emily. I do not perceive any difference between the attrac- tion of cohesion and that of gravitation ; is it not because every particle of matter is endowed with an attractive power, that large bodies consisting of a great number of particles, are so strongly attractive ? Mrs. B. True. There is, however, this difference between the attraction of particles and that of masses, that the former takes place only when the particles are contiguous, whilst the latter is exerted when the masses are far from each other. The attraction of particles frequently counteracts the attraction of gravitation. Of this you have an instance in the attraction of capillary tubes, in which liquids ascend by the attraction of cohe- sion, in opposition to that of gravity. It is on this account that it is necessary that the bore of the tube should be extremely small; for if the column of water within the tube is not very minute, the attraction of cohesion would not be able either to raise or support it in opposition to its gravity ; because the increase of weight, in a column of water of a given height, is much greater than the increase in the attracting surface of the tube, when its size is increased. You may observe also, that all solid bodies are enabled by the force of the cohesive attraction of their particles to resist that of gravity, which would otherwise disunite them, and bring them to 46. What remarkable difference is there between the attraction of gravita- tion, and that of cohesion? 47. In what instances does the power of cohesion counteract that of gravitation? 48. Why will water rise to a less height, if the size of the tube is increased ? 20 GENERAL PROPERTIES OF BODIES. a level with the ground, as it does in the case of a liquid, the cohesive attraction of which is not sufficient to enable it to resist the power of gravity. Emily. And some solid bodies appear to be of this nature, as sand, and powder for instance : there is no attraction of cohesion between their particles? Mrs. B. Every grain of powder, or sand, is composed of a great number of other more minute particles, firmly united by the at- traction of cohesion ; but amongst the separate grains there is no sensible attraction, because they are not in sufficientlv close con- tact. Emily. Yet tney actually touch each other ? Mrs. B. The surface ot bodies is in general so rough and uneven, that when in apparent contact, they touch each other only by a few points. Thus, when I lay this book upon the table, the binding of which appears perfectly smooth, so few of the par- ticles of its under surface come in contact with the table, that no sensible degree of cohesive attraction takes place; for you see that it does not stick or cohere to the table, and I find no diffi- culty in lifting it off. It is only when surfaces, perfectly flat and well polished, are placed in contact, that the particles approach in sufficient num- oer, and closely enough, to produce a sensible degree of cohesive attraction. Here are two plates of polished metal, I press their flat surfaces together, having previously interposed a few, drops of oil, to fill up every little porous vacancy. Now try to sepa- rate them. Emily. It requires an effort beyond my strength, though there are handles for the purpose of pulling them asunder. Is the firm adhesion of the two plates merely owing to the attrac- tion of cohesion ? Mrs. B. There is no force more powerful, since it is by this that the particles of the hardest bodies are held together. It would require a weight of several pounds to separate these plates. In the present example, however, much of the cohesive force is due to the attraction subsisting between the metal and the oil which is interposed; as without this, or some other fluid, the points of contact would still be comparatively few, although we may have employed our utmost art, in giving flat surfaces to the plates. Emily. In making a kaleidoscope, I recollect that the two plates of glass, which were to serve as mirrors, stuck so fast to- gether, that I imagined some of the gum I had been using had by chance been interposed between them ; but I am now con- 49. Why do not two bodies cohere, when laid upon each other ? 50. Can two bodies be made sufficiently flat to cohere with considerable force?. 51. What is the reason that the adhesion is greater when oil is interposed 5 GENERAL PROPERTIES OF BODIES. 1 nnced that it was their own natural cohesive attraction which produced this effect. Mrs. jB. Very probably it was so ; for plate-glass has an ex- tremely smooth, flat surface, admitting of the contact of a great number of particles, when two plates are laid upon each other. Emily. But, Mrs. B., the cohesive attraction of some sub- stances is much greater than that of others ; thus glue, gum and paste, cohere with singular tenacity. Mrs. B. Bodies which differ in their natures in other respects, differ also in their cohesive attraction ; it is probable that there are no two bodies, the particles of which attract each other with precisely the same force. There are some other modifications of attraction peculiar to certain bodies 5 namely, that of magnetism, of electricity, and of affinity, or chemical attraction ; but we shall confine our atten- tion merely to the attraction of cohesion and of gravity ; the ex- amination of the latter we shall resume at our next meeting 52. What other modifications of attraction are there, besides those of cohe ion and of gravitation? CONVERSATION II. ON THE ATTRACTION OF GRAVITY. 1TTRACTION OF GRAVITATION, CONTINUED. OP WEIGHT. OFTHEl'ALI OF BODIES. OF THE RESISTANCE OF THE AIR. OF THE ASCENT OH LIGHT BODIES. EMILY. I HAVE related to my sister Caroline all that you have taught me of natural philosophy, and she has been so much delighted by it, that she hopes you will have the goodness to admit her to your lessons. Mrs. B. Very willingly ; but I did not think you had any taste for studies of this nature, Caroline. Caroline. I confess, Mrs. B., that hitherto I had formed no very agreeable idea either of philosophy, or philosophers; but what Emily has told me has excited my curiosity so much, that I shall be highly pleased if you will allow me to become one of your pupils. Mrs. B. I fear that I shall not find you so tractable a scho- lar as Emily; I know that you are much biased in favour of your own opinions. Caroline. Then you will have the greater merit in reforming them, Mrs. 15.; and after all the wonders that Emily has related to me, I think I stand but little chance against you and your attractions. Mrs. B. You will, I doubt not, advance a number of ob- jections ; but these I shall willingly admit, as they will afford an opportunity of elucidating the subject. Emily, do you recol- lect the names of the general properties of bodies? Emily. Impenetrability, extension, figure, divisibility, inertia and attraction. Mrs. B. Very well. You must remember that these are pro- perties common to all bodies, and of which they cannot be de- prived ; all other properties of bodies are called accidental, be- cause they depend on the relation or connexion of one body to another. 1. What are those properties of bodies called, which are not common to alJ ? ON THE ATTRACTION OF GRAVITY. fctf Caroline. Yet surely, Mrs. B. there are other properties which are essential to bodies, besides those you have enumerated. Colour and weight, for instance, are common to all bodies, and do not arise from their connexion with each other, but exist in the bodies themselves; these, therefore, cannot be accidental qualities? Mrs. B. I beg your pardon; these properties do not exist in bodies independently of their connexion with other bodies. Caroline. What! have bodies no weight? Does not this table weigh heavier than this book ; and, if one thing weighs heavier than another, must there not be such a thing as weight? Mrs. B. No doubt : but this property does not appear to be essential to bodies; it depends upon their connexion with each other. Weight is an effect of the power of attraction, without which the table and the book would have no weight whatever. Emily. I think I understand you; it is the attraction of gra- vity which makes bodies heavy. Mrs. B. You are right. 1 told you that the attraction of gra- vity was proportioned to the quantity of matter which bodies con- tain: now the earth consisting of a much greater quantity ol matter than any body upon 'its surface, the force of its attrac- tion must necessarily be greatest, and must draw every thing so situated towards it; in consequence of which, bodies that are unsupported fall to the ground, whilst those that are supported, press upon the object which prevents their fall, with a weight equal to the force with which they gravitate towards the earth. Caroline. The same cause then which occasions the fall of bo- dies, produces their weight also. It was very dull in me not to understand this before, as it is the natural and necessary conse- quence of attraction; but the idea that bodies were not really heavy of themselves, appeared to me quite incomprehensible. But, Mrs. B. if attraction is a property essential to matter, weight must be so likewise; for how can one exist without the other ? Mrs. B. Suppose there were but one body existing in univer- sal space, what would its weight be ? Caroline. That would depend upon its size; or more accu- rately speaking, upon the quantity of matter it contained. Emily. No, no; the body would have no weight, whatever were its size ; because nothing would attract it. Am I not right, Mrs. B.? Mrs. B. You are : you must allow, therefore, that it would be possible for attraction to exist without weight ; for each of the 2. Why are they so called? 3. What is the cause of weight in bodies? 4. What is the reason that all bodies near to the surface of the earth, are tbrawn towards it? 24 ON THE ATTRACTION OF GRAVITY. particles of which the body was composed, would possess the power of attraction; but they could exert it only amongst them- selves ; the whole mass havi ng nothing to attract, or to be at- tracted by, would have no weight. Caroline. I am now well satisfied that weight is not essential to the existence of bodies; but what have you to object to co- lours, Mrs. B.; you will not, I think, deny that they really exist in the bodies themselves. Mrs. B. When we come to treat of the subject of colours, I trust that I shall be able to convince you, that colours are like- wise accidental qualities, quite distinct from the bodies to which they appear to belong. Caroline. Oh do pray explain it to us now, I am so very curi ous to know how that is possible. Mrs. B. Unless we proceed with some degree of order and method, you will in the end find yourself but little the wiser for all you learn. Let us therefore go on regularly, and make our- selves well acquainted with the general properties of bodies be- fore we proceed further. Emily. To return, then, to attraction, (which appears to me by far the most interesting of them, since it belongs equally to all kinds of matter,) it must be mutual between two bodies; and if so, when a stone falls to the earth, the earth should rise part of the way to meet the stone? Mrs. B. Certainly; but you must recollect that the force of attraction is proportioned to the quantity of matter which bodies contain, and if you consider the difference there is in that respect, between a stone and the earth, you will not be surprised that you do not perceive the earth rise to meet the stone; for though it is true that a mutual attraction takes place between the earth and the stone, that of the latter is so very small in comparison to that of the former, as to render its effect insensible. Emily. But since attraction is proportioned to the quantity of matter which bodies contain, why do not the hills attract the houses and churches towards them ? Caroline. What an idea, Emily! How can the houses and churches be moved, when they are so firmly fixed in the ground ! Mrs. B. Emily's question is not absurd, and your answer, Ca- 5. If attraction is the cause of weight, could you suppose it possible for a body to possess the former and not the latter property? 6. When a stone falls to the ground, in which of the two bodies does the power of attraction exist? 7. If the attraction be mutual, why does not the earth approach the stone, as '-.fluch as the stone approaches the earth ? 8. If attraction be in proportion to the mass, why does not a hill, draw towards itself, a house placed neat H? ON THE ATTRACTION OF GRAVITY. 25 toline, is perfectly just; but can you tell us why the houses and churches are so firmly fixed in the ground? Caroline. I am afraid I have answered right by mere chance ; for I begin to suspect that bricklayers and carpenters could give but little stability to their buildings, without the aid of at- traction. Mrs. B. It is certainly the cohesive attraction between the bricks and the mortar, which enables them to build walls, ana these are so strongly attracted by the earth, as to resist every other impulse; otherwise they would necessarily move towards the hills and the mountains; but the lesser force must yield to the greater. There are, however, some circumstances in which the attraction of a large body has sensibly counteracted that of the earth. If whilst standing on the declivity of a mountain, you hold a plumb-line in your hand, the weight will not fall perpen- dicular to the earth, but incline a little towards the mountain; and this is owing to the lateral, or sideways attraction of the mountain, interfering with the perpendicular attraction of the earth. Emily. But the size of a mountain is very trifling, compared to the whole earth. Mrs. B. Attraction, you must recollect, is in proportion to the quantity of matter, and although that of the mountain, is much less than that of the earth, it may yet be sufficient to act sensi- bly upon the plumb-line which is so near to it. Caroline. Pray Mrs. B. do the two scales of a balance hang parallel to each other? Mrs. B. You mean, I suppose, in other words to inquire whe- ther two lines which are perpendicular to the earth, are parallel to each other ? I believe I guess the reason of your question ; but I wish you would endeavour to answer it without my assist- ance. Caroline. I was thinking that such lines must both tend by gravity to the same point, the centre of the earth; now lines tending to the same point cannot be parallel, as parallel lines are always at an equal distance from each other, and would "jiever meet. Mrs. B. Very well explained ; you see now the us-e of your knowledge of parallel lines : had you been ignorant of their pro- perties, you could not have drawn such a conclusion. This may enable you to form an idea of the great advantage to be derived even from a slight knowledge of geometry, in the study of natu- ral philosophy; and if after I have made you acquainted with 9. How can the attraction of a mountain be rendered sensible? 10. Why cannot two lines which are perpendicular to tne surface of the earth be pa allcl to each other ' J . c 26 ON THE ATTRACTION OF GRAVITY. the first elements, you should be tempted to pursue the study, I would advise you to prepare yourselves by acquiring some know- ledge of geometry. This science would teach you that lines which fall perpendicular to the surface of a sphere cannot be parallel, because they would all meet, if prolonged to the centre of the sphere; while lines that fall perpendicular to a plane or flat surface, are always parallel, because if prolonged, they would never meet. Emily. And yet a pair of scales, hanging perpendicular to the earth, appear parallel ? Mrs. B. Because the sphere is so large, and the scales conse- quently converge so little, that their inclination is not percepti- ble to our senses; if we could construct a pair of scales whose beam would extend several degrees, their convergence would be very obvious; but as this cannot be accomplished, let us draw a small figure of the earth, and then we may make a pair of scales of the proportion we please, (fig. 1. pi. I.) Caroline. This figure renders it very clear: then two bodies cannot fall to the earth in parallel lines? Mrs. B. Never. Caroline. The reason that a heavy body falls quicker than a light one, is, I suppose, because the earth attracts it more strongly. Mrs. B. The earth, it is true, attracts a heavy body more than a light one; but that would not make the one fall quicker than the other. Caroline. Yet, ssince it is attraction that occasions the fall of bodies, surely the more a body is attracted, the more rapidly it will fall. Besides, experience proves it to be so. Do we not everyday see heavy bodies fall quickly, and light bodies slowly? Emily. It strikes me, as it does Caroline, that as attraction is proportioned to the quantity of matter, the earth must necessa- rily attract a body which contains a great quantity more strongly, and therefore brin; it to the ground sooner than one consisting of a smaller quantity. Mrs. B. You must consider, that if heavy bodies are attracted more strongly than light ones, they require more attraction to make them fall. Remember that bodies have no natural ten- dency to fall, any more than to rise, or to move laterally, and that they will not fall unless impelled by some force; now this force must be proportioned to the quantity of matter it has to move: a body consisting of 1000 particles ot' matter, for instance, requires ten times as much attraction to bring it to the ground in the same space of time as a body consisting of only 100 par- ticles. 11. Draw a small figure of the earth to exemplify this, as in fig. 1. plate l ON THE ATTRACTION OF GRAVITY. 27 Caroline. I do not understand that; for it seems to me, that the heavier a body is, the more easily and readily it fails. Emily. I think I now comprehend it ; let me try if I can ex- plain it to Caroline. Suppose that I draw towards me two weighty bodies, the one of lOOlbs. the other of lOOOlbs. must I not exert ten times as much strength to draw the larger one to me, in the same space of time, as is required for the smaller oner And if the earth draws a body of lOOOlbs. weight to it in the same space of time that it draws a body of lOOlbs. does it not follow that it attracts the body of lOOOlbs. weight with ten times the force that it does that of 1 OOlbs. ? Caroline. I comprehend your reasoning perfectly; but if it were so, the body of lOOOlbs. weight, and that of I OOlbs. would fall with the same rapidity; and the consequence would be, that all bodies, whether light or heavy, being at an equal distance from the ground, would fall to it in the same space of time : now it is very evident that this conclusion is absurd ; experience every instant contradicts it ; observe how much sooner this book reaches the floor than this sheet of paper, when I let them drop together. Emily. That is an objection I cannot answer. 1 must refer it to you, Mrs. B. J/rs. B. I trust that we shall not find it insurmountable. It is true that, according to the laws of attraction, all bodies at an equal distance from the earth, should fall to it in the same space of time; and this would actually take place if no obstacle inter- vened to impede their fall. But bodies fall through the air, and it is the resistance of the air which makes bodies of different density fall with different degrees of velocity. They must all force their way through the air, bat dense heavy bodies over- come this obstacle more easily than rarer or lighter ones; be- cause in. the same space they contain more gravitating parti- cles. The resistance -which the air opposes to the fall of bodies is proportioned to their surface, not to their weight; the air being inert, cannot exert a greater force to support the weight of a cannon ball, than it does to support the weight of a ball (of the same size) made of leather; but the cannon ball will overcome this resistance more easily, and fall to the ground, consequently, quicker than the leather ball. Caroline. This is very clear and solves the difficulty perfectly. The air offers the same resistance to a bit of lead and a bit of 12. If bodies were not resisted by the air, those which are light, would fall as quickly as those which are heavy, how can you account for this? 13. What then is the reason that a book, and a sheet of paper, let fall from the same heigh t, will not reach the grouixl in the same time ? 8 ON THE ATTRACTION OF GRAVITY. faather of the same size ; yet the one seems to meet with no ob- struction in its fall, whilst the other is evidently resisted and sup- ported for some time by the air. Emily. The larger the surface of a body, then, the more air it covers, and the greater is the resistance it meets with from it. Mrs. B. Certainly : observe the manner in which this sheet of paper falls; it floats awhile in the air, and then gently de- scends to the ground. I will roll the same piece of paper up into a ball : it oilers now but a small surface to the air, and encounters therefore but little resistance : see how much more rapidly it falls. The heaviest bodies may be made to float awhile in the air, by making the extent of their surface counterbalance their weight. Here is some gold, which is one of the most dense bodies we are acquainted with ; but it has been beaten into a very thin leaf, and offers so great an extent of surface in proportion to its weight, that its fall, you see, is still more retarded by the resistance of the air, than that of the sheet of paper. Caroline. That is very curious: and it is, I suppose, upon the same principle that a thin slate sinks in water more slowly than a round stone. But, Mrs. B., if the air is a real body, is it not also subjected to the laws of gravity ? Mrs. B. Undoubtedly. * Caroline. Then why does it not, like all other bodies, fall to the ground ? Mrs, B. On account of its spring or elasticity. The air is an elastic fluid ; and the peculiar property of elastic bodies is to resume, after compression, their original dimensions; and you must consider the air of which the atmosphere is composed as existing in a state of compression, for its particles being drawn towards the earth by gravity, are brought closer together than they would otherwise 'be, but the spring or elasticity of the air by which it endeavours to resist compression, gives it a con- stant tendency to expand itself, so as to resume the dimensions it would naturally have, if not under the influence of gravity. The air may therefore be said constantly to struggle with the power of gravity without being able to overcome it. Gravity thus confines the air to the regions of our globe, whilst its elasti- city prevents it from falling, like other bodies, to the ground. Emily. The air then is, I suppose, thicker, or I should rathei say more dense, near the surface of the earth, than iu the highei 14. What then will be the effect of increasing- the surface of a body? 15. What could you do to a sheet of paper, to make it fall quickly, and why? 16. Inform me how a very dense body may be made to float in the air: 7. The air is a real body, why does it not fall to the ground ? ON THE ATTRACTION OF GRAVITY. 29 regions of the atmosphere; for that part of the air which is nearer the surface of the earth must be most strongly attracted. Mrs. B. The diminution of the force of gravity, at so smal 1 a distance as that to which the atmosphere extends (compared with the size of the earth) is so inconsiderable as to be scarcely sensible ; but the pressure of the upper parts of the atmosphere on those beneath, renders the air near the surface of the ea^th much more dense than in the upper regions. The pressure of the atmosphere has been compared to that of a pile of fleeces of wool, in which the lower fleeces are pressed together by the weight of those above ; these lie light and loose, in proportion as they ap- proach the uppermost fleece, which receives no external pressure, and is confined merely by the force of its own gravity. Emily. I do not understand how it is that the air can be springy or elastic, as the particles of which it is composed must, according to the general Jaw, attract each other; yet their elas- ticity, must arise from a tendency to recede from each other, Mrs. B. Have you forgotten what I told you respecting the effects of heat, a fluid so subtile that it readily pervades all sub- stances, and even in solid bodies, counteracts the attraction of cohesion ? In air the quantity of heat interposed is so great, as to cause its particles actually to repel each other, and it is to this that we must ascribe its elasticity; this, however, does not pre- vent the earth from exerting its attraction upon the individual particles of which it consists. Caroline. It has just occurred to me that there are some bo- dies which do not gravitate towards the earth. Smoke and steam, for instance, rise instead of failing. Mrs, B. It is still gravity which produces their ascent; at least, were that power destroyed, -these bodies would not rise. Caroline. I shall be out of conceit with gravity, if it is so inconsistent in its operations. Mrs. B. There is no difficulty in reconciling this apparent inconsistency of effect. The air near the earth is heavier than smoke, steam, or other vapours ; it consequently not only sup- ports these light bodies, but forces them to rise, till they reach a part of the atmosphere, the weight of which is not greater than their own, and then they remain stationary. Look at this bason of water ; why does the piece of paper which I throw into it float on the surface ? Emily. Because, being lighter than the water, it is supported by it. 18. The air is more dense near the surface of the earth, and decreases ii density as you ascend, how is this accounted fon, and to what is it compared ? 19. What is it which causes the particles of air to recede from each other, and seems to destroy their mutual attraction ? 20. Smoke and vapour as- cend in the atmosphere, how can you reconcile this with gravitation > SO ON THE ATTRACTION OF GRAVITY. Mrs. B. And now that I pour more water into the bason, why does the paper rise ? Emily. The water being heavier than the paper, gets beneath it, and obliges it to rise. Mrs. B. In a similar manner are smoke and vapour forced upwards by the air; but these bodies do not, like the paper, ascend to the surface of the fluid, because, as we observed before, the air being less dense, and consequently lighter as it is more distant from the earth, vapours rise only till they attain a region of air of their own density. Smoke, indeed ascends but a very little way; it consists of minute particles of fuel, carried up by a current of heated air, from the fire below: heat, you recollect, expands all bodies ; it consequently rarefies air, and renders it lighter than the colder air of the atmosphere; the heated air from the fire carries up with it vapour and small particles of the com- bustible materials which are burning in the fire. When this cur- rent of hot air is cooled by mixing with the atmosphere, the minute particles of coal, or other combustible, fall ; it is this which produces the small black flakes which render the air, and every thing in contact with it, in London, so dirty. Caroline. You must, however, allow me to make one more objection to the universal gravity of bodies; which is the ascent of air balloons, the materials of which are undoubtedly heaviei than air : how, therefore, can they be supported by it ? Mrs. B. I admit that the materials of which balloons are made are heavier than the air ; but the air with which they are filled is an elastic fluid, of a different nature from atmospheric air, and considerably lighter; so that on the whole the balloon is lighter than the air which it displaces, and consequently will rise, on the same principle as smoke and vapour. Now, Emily, let me hear if you can explain how the gravity of bodies is modi- fied by the effect of the air ? Emily. The air forces bodies which are lighter than itself to ascend ; those that are of an equal weight will remain stationary in it; and those that are heavier will descend through it: but the air will have some effect on these last; for if they are not much heavier, they will with difficulty overcome the resistance they meet with in passing through it, they will be borne up by it, and their fall will be more or less retarded. Mrs. R. Very well. Observe how slowly this light feather falls to the ground, while a heavier body, like this marble, over- 21. How would you illustrate this by the floating of a piece of paper on wa- ter ? 22. Does smoke rise to a great height in the air, and if not, what prevents its so doing ? 23. What limits the height to which vapours rise ? 24. Of what does smoke consist ? 25. Air balloons are formed of heavy materials, how will you account for their rising in the air ? 26. What influence does the air exert, on bodies lesa dense than itself, on those of equal, and on those of gjeater density ? ON THE ATTRACTION OF GRAVITY. 31 comes the resistance which the air makes to its descent much more easily, and its fall is proportionally more rapid. I now throw a pebble into this tub of water; it does not reach the bot- tom near so soon as if there were no water in the tub, because it meets with resistance from the water. Suppose that we could empty the tub, not only of water, but of air also', the pebble would then fall quicker still, as it would in that case meet with no resistance at all to counteract its gravity. Thus you see that it is not the different degrees of gravity, but the resistance of the air, which prevents bodies of different weight from falling with equal velocities ; if the air did not bear up the feather, it would reach the ground as soon as the marble. Caroline. I make no doubt that it is so; and yet I do not feel quite satisfied. I wish there was any place void of air, in which the experiment could be made. Mrs. B. If that proof will satisfy your doubts, I can give it you. Here is a machine called an air pump, (fig. 2. pi. 1.) by means of which the air may be expelled from any close vessel which is placed over this opening, through which the air is pump- ed out. Glasses of various shapes, usually called receivers, are employed for this purpose. We shall now exhaust the air from this tall receiver which is placed over the opening, and we shall find that bodies within it, whatever their weight or size, will fall from the top to the bottom in the same space of time. Caroline. Oh, I shall be delighted with this experiment ; what a curious machine ! how can you put the two bodies of different weight within the glass, without admitting the air? Mrs. B. A guinea and a feather are already placed there for the purpose of the experiment: here is, you see, a contrivance to fasten mem in the upper part of the glass ; as soon as the air is pumped out, I shall turn this little screw, by which means the brass plates which support them will be removed, and the two bodies will fall. Now I believe I have pretty well exhausted the air. Caroline. Pray let me turn the screw. I declare, thev both reached the bottom at the same instant ! Did you see, Emily, the feather appeared as heavy as the guinea ? Emily. Exactly ; and fell just as quickly. How wonderful this is ! what a number of entertaining experiments might be made with this machine ! Mrs. B. No doubt there are a great many; but we shall reserve them to elucidate the subjects to which they relate : if 1 had not explained to you why the guinea and the feather fell 27. If the air could be entirely removed, what influence would this have upon the falling of heavy and light bodies ? 28, How could this be exempli fied by means of the air pump ? S2 ON 'I HE LAWS OF MOTION. with equal velocity, you would not have been so well pleased with the experiment. Emily. I should have been as much surprised, but not so much interested ; besides, experiments help to imprint on the memory the facts they are intended to illustrate ; it will be bet- ter therefore for us to restrain our curiosity, and wait for other experiments in their proper places. Caroline. Pray by what means is this receiver exhausted of its air ? Mrs. B. You must learn something of mechanics in order to understand the construction of a pump. At our next meeting, therefore, I shall endeavour to make you acquainted with the laws of motion, as an introduction to that subject. CONVERSATION HI. ON THE LAWS OF MOTION. OF MOTION. OF THK INERTIA OF BODIES. OF FORCE TO PRODUCE MO- riON. DIRECTION OF MOTION. VELOCITY, ABSOLUTE AND RELATIVE. UNIFORM MOTION. RETARDED MOTION. ACCELERATED MOTION. VELOCITY OF FALLING BODIES. MOMENTUM. ACTION AND REACTION E&UAL. ELASTICITY OF BODIES. POROSITY OF BODIES. REFLECTED MOTION. ANGLES OF INCIDENCE AND REFLECTION. MRS. B. THF, science of mechanics is founded on the laws of motion ; it will therefore be necessary to make you acquainted with these laws before we examine the mechanical powers. Tell me, Caro- line^ \\ hat. do you understand by the word motion? Caroline. I think 1 understand it perfectly, though I am at a loss to describe it. Motion is the act of moving about, of going from one place to another, it is the contrary of remaining at rest Mrs. B. Very well. Motion then consists in a change of place ; a body is in motion whenever it is changing its situation with regard to a fixed point. Now since we have observed that one of the general properties of bodies is inertia, that is, an entire passiveness, either with 1. On what is the science of mechanics foun .id* 2. In what does motion consist f ON THE LAWS OF MOTION. S3 regard to motion or rest, it follows that a body cannot move without bein put into motion; the power which puts a body into motion is calkd /arce; thus the stroke of the hammer is the force which drives the nail ; the pulling of the horse that which draws the carriage, &c. Force then is the cause which produces motion. Emily. And may we not say that gravity is the force which occasions the fall of bodies ? Mrs. B. Undoubtedly. I have given you the most familiar illustrations in order to fender the explanation clear; but since you seek for more scientific examples, you may say that cohesion is the force which binds the particles of bodies together, and heat that which drives them asunder. The motion of a body acted upon by a single force, is always in a straight line, and in the direction in which it received the impulse. Caroline. That is very natural ; for as the body is inert, and can move only because it is impelled, it will move only in the direction in which it is impelled. The degree of quickness with which it moves, must, I suppose, also depend upon the degree of force with which it is impelled. Mrs. JB. Yes ; the rate at which a body moves, or the short- ness of the time which it takes to move from one place to another, is called its velocity; and it is one of the laws of motion, that the velocity of the moving body is proportional to the force by which it is put in motion. We* must distinguish between abso- lute and relative velocity. The velocity of a body is called absolute, if we consider the motion of the body in space, without any reference to that of other bodies. When, for instance, a horse goes fifty miles in ten hours, his velocity is five miles an hour. The velocity of a body is termed relative, when compared with that of another body which is itself in motion. For instance, if one man walks at the rate of a mile an hour, and another at the rate of two miles an hour, the relative velocity of the latter is double that of the former; but the absolute velocity of the one is one mile, and that of the other two miles an hour. Emily. Let me see if I understand it The relative velocity of a body is the degree of rapidity of its motion compared with that of another body; thus if one ship sail three times as far as another ship in the same space of time, the velocity of the former is equal to three times that of the latter. 3. What is the consequence of inertia, on a body at rest ? 4. What do we call that which produces motion ? 5. Give some examples. 6. What may we say of gravity, of cohesion, and of heat, as forces? 7. How will a body move, if acted on by a single force ? 8. What is the reason of this? 9. What do we intend by the term velocity, and to what is it proportional? 10. Ve- locity is divided into absolute and relative; what is meant by absolute velo- city? ] 1. How is relative velocity distinguished? 84 ON THE LAWS OF MOTION. Mrs. J?. The general rule may be expressed thus : tne velo- city of a body is measured by the space over which it moves, divided by the time which it employs in that motion : thus if you travel one hundred miles in twenty hours, what is your velocity in each hour? Emily. I must divide the space, winch is one hundred miles, by the time, which is twenty hours, and the answer will be five miles an hour. Then. Mrs. B., may we not reverse this rule, and say that the time is equal to the space divided by the velocity; since the space, one hundred miles, divided by the velocity, five miles per hour, gives twenty hours for the time? Mrs. B. Certainly; and we may say also that the space is equal to the velocity multiplied bv the time. Can you tell me, Caroline, how many miles you will have travelled, if your velo- city is three miles an hour, and you travel six hours ? Caroline. Eighteen miles; for the product of 3 multiplied by 6, is 18. Mrs. B. I suppose that you understand what is meant by the terms uniform, accelerated and retarded motion. Emily. \ conceive uniform motion to be that of a body whose motion is regular, and at an equal rate throughout; for instance, a horse that goes an equal number of miles every hour. But the hand of a watch is a much better example, as its motion is so regular as to indicate the time. Mrs. B. You have a right idea of unifoim motion; but it would be more correctly expressed by saying, that the motion of a body is uniform when it passes over equal spaces in equal times. Uniform motion is produced by a force having acted on a body once and having ceased to act ; as, for instance, the stroke of a bat on a ball. Caroline. But the motion of a ball is not uniform; its velocity gradually diminishes till it falls to the ground. Mrs. J3. Recollect that the ball is inert, and has no more pow- er to stop, than to put itself in motion ; if it falls, therefore, it must be stopped by some force superior to that by which it was projected, and which destroys its motion. Caroline. And it is no doubt the force of gravity which coun- teracts and destroys that of projection ; but if there were no such power as gravity, would the ball never "stop ? Mrs. B. If neither gravity nor any other force, such as the resistance of the air, opposed its motion, the ball, or even a stone thrown by the hand, would proceed onwards in a right line, and with a uniform velocity for ever. 12. How do we measure the velocity of a body ? 13. The time ? 14. The space? 15. What is uniform motion? and give an example. 16. How is uniform motion produced ? 17. A ball struck by a bat gradually loses ita motion; what causes produce this effect? ON THE LAWS OF MOTION. 35 Caroline. You astonish me ! I thought that it v/as impossible to produce perpetual motion ? Mrs. B. Perpetual motion cannot be produced by art, be- cause gravity ultimately destroys all motion that human power can produce. Emily. But independently of the force of gravity, I cannot conceive that the little motion I am capable of giving to a stone would put it in motion for ever. Mrs. B. The quantity of motion you communicate to the stone would not influence its duration: if you threw it with little force it would move slowly, for its velocity you must remember, will be proportional to the force with which it is projected ; but if there is nothing to obstruct its passage, it will continue to move with the same velocity, and in the same direction as when you first projected it. Caroline. This appears to me quite incomprehensible; we do net meet with a single instance of it in nature. Mrs. B. I beg your pardon. When you come to study the motion of the celestial bodies, you will find that nature abounds with examples of perpetual motion; and that it conduces as much to the harmony of the system of the universe, as the prevalence ot it on the surface of the earth, would to the destruction of all our comforts. The wisdom of Providence has therefore or- dained insurmountable obstacles to perpetual motion here below; and though these obstacles often compel us to contend with great difficulties, yet these appear necessary to that order, regularity and repose, so essential to the preservation of all the various beings of which this world is composed. Now can you tell me what is retarded motion? Caroline. Retarded motion is that of a body which moves every moment slower and slower : thus when I am tired with walking fast, I slacken my pace; or when a stone is thrown upwards, its velocity is gradually diminished by the power of gravity. Mrs. B. Retarded motion is produced by some force acting upon the body in a direction opposite to that which first put it in motion : you who are an animated being, endowed with power and will, may slacken your pace, or stop to rest when you are tired ; but inert matter is incapable of any feeling of fatigue, can never slacken its pace, and never stop, unless retarded or arrest- ed in its course by some opposing force; and as it is the laws of inert bodies of which mechanical philosophy treats, I prefer your 18. If gravity did not draw a projected body towards the earth, and the resistance of the air were removed, what would be the consequence? 19. In this case woald not a great degree of force be required to produce a continued motion ? 20. What is retarded motion ? 21. Give some examples 36 ON THE LAWS OF MOTION. illustration of the stone retarded in its ascent. Now Emily, it is your turn; what is accelerated motion? Emily. Accelerated motion, I suppose, takes place when the velocity of a body is increased; if you had not objected to our giving such active bodies as ourselves as examples, I should say lat my motion is accelerated if I change my pace from walking to running. I cannot think of any instance of accelerated motion in inanimate bodies ; all motion of inert matter seems to be re- tarded by gravity. Mrs. JB. Not in all cases ; for the power of gravitation some- times produces accelerated motion; for instance, a stone falling from a height, moves with a regularly accelerated motion. Emily. True; because the nearer it approaches the earth, the more it is attracted by it. Mrs. B. You have mistaken the cause of its accelerated motion ; for though it is true that the force of gravity increases as a body approaches the earth, the difference is so trilling at any small distance from its surface, as not to be perceptible. Accelerated motion is produced when the force which put a body in motion^ continues to act upon it during its motion, so that its velocity is continually increased. When a stone falls from a height, the impulse which it receives from gravitation in the first instant of its fall, would be sufficient to bring it to the ground with a uniform velocity: for, as we have observed, a body having been once acted upon by a force, will continue to move with a uniform velocity; but the stone is not acted upon by gravity merely at the first instant of its fall; this power continues to im- pel it during the whole time of its descent, and it is this continu- ed impulse which accelerates its motion. Emily. I do not quite understand that. Mrs. B. Let us suppose that the instant after you have let a stone fall from a high tower, the force of gravity were annihilated ; the body would nevertheless continue to move downwards, for it would have received a first impulse from gravity; and a body once put in motion will not stop unless it meets with some ob- stacle to impede its course; in this case its velocity would be uniform, for though there would be no obstacle to obstruct its descent, there would be no force to accelerate it. Emily. That is very clear. Mrs. B. Then you have only to add the power of gravity con- stantly acting on the stone during its descent, and it will not be difficult to understand that its motion will become accelerated, since the gravity which acts on the stone at the very first instant of its descent, will continue in force every instant, till it reaches 22. What is accelerated motion? 23. Give an example. 24. Explain the mode in which gravity operates in producing this effect. ON THE LAWS OF MOTION. T the ground. Let us suppose that the impulse given by grawty to the stone during the first instant of its descent, be equal to one; the next instant we shall find that an additional impulse gives the stone an additional velocity, equal to one; so that the accumulated velocity is now equal to two; the following instant another impulse increases the velocity to three, and so on till the stone reaches the ground. Caroline. Now I understand it; the effects of preceding im- pulses continue, whilst gravity constantly adds new ones, and thus the velocity is perpetually increased. Mrs. JL Yes ; it has been ascertained, both by experiment, and calculations which it would be too difficult for us to enter into, that heavy bodies near the surface of the earth, descending from a height by the force of gravity, fall sixteen feet the first second of time, three times that distance in the next, five times in the third second, seven times in the fourth, and so on, regularly in- creasing their velocities in the proportion of the odd numbers 1, 3, 5, T, 9, &c. according to the number of seconds during which the body has been falling. Emily. If you throw a stone perpendicularly upwards, is it riot the same length of time in ascending, that it is in descending? Mrs. B. Exactly; in ascending, the velocity is diminished by the force of gravity; in descending, it is accelerated by it. Caroline. I should then imagine that ic would fall, quicker than it rose? Mrs. B. You must recollect that the force with which it is pro- jected, must be taken into the account; and that this force is overcome and destroyed by gravity, before the body begins to fall. Caroline. But the force of projection given to a stone in throw- ing it upwards, cannot always be equal to the force of gravity in bringing it down again ; for the force of gravity is always the same, whilst the degree of impulse given to the stone is optional; I may throw it up gently, or with violence. Mrs. B. If you throw it gently, it will not rise high ; perhaps only sixteen feet, in which case it will fall in one 'second of time. Now it is proved by experiment, that an impulse requisite to project a body sixteen feet upwards, will make it ascend that neight in one second ; here then the times of the ascent and de- scent are equal. But supposing it be required to throw a stone twice that height, the force must be proportionally greater. You see then, that the impulse of projection in throwing a body upwards, is always equal to the action of the force of gravity 25. What number of feet will a heavy body descend in the first second of its fall, and at what rate will its velocity increase ? 26. What is the differ- ence in the time of the ascent and descent, of a stone, or other body thrown upwards ? 27. By what reasoning is it proved that ther is no difference ? ON THE LAWS Ol MOTION. during its descent; and that whether the body rises to a greater or less distance, these two forces balance each other. I must now explain to you what is meant by the moment'tm of bodies. It is the force, or power, with which a body in mo- tion, strikes against another body. The momentum of a body is the product of its quantity of matter, multiplied by its quantity of motion; in other words, its weight multiplied by its velocity. Caroline. The quicker a body moves, the greater, no doubt, must be the force which it would strike against another body. Emily. Therefore a light body may have a greater momen- tum than a heavier one, provided its velocity be sufficiently in- creased ; for instance, the momentum of an arrow shot from a bow, must be greater than that of a stone thrown by the hand. Caroline. We know also by experience, that the heavier a body is, the greater is its force; it is not therefore difficult to understand, mat the whole power, or momentum of a body, must be composed of these two properties, its weight and its velocity: but I do not understand why they should be multiplied, the one by the other ; I should have supposed that the quantity of mat- ter, should have been added to the quantity of motion ? Mrs. B. It is found by experiment, that if the weight of a body is represented by the number 3, and its velocity also by 3, its momentum will be represented by 9, not by 6, as would be the case, were these figures added, instead of being multiplied together. Emily. I think that I now understand the reason of this ; if the quantity of matter is increased three-fokl, it must require three times the force to move it with the same velocity; and then if we wish to give it three times the velocity, it will again require three times the force to produce that effect, which is three times three, or nine; which number therefore, would represent the momentum. Caroline. I am not quite sure that I fully comprehend what is intended, when weight, and velocity, are represented by num- bers alone ; I am so used to measure space by yards and miles, and weight by pounds and ounces, that I still want to associate them together in my mind. Mrs. B. This difficulty will be of very short duration : you have only to be careful, that when you represent weights and velocities by numbers, the denominations or values of the weights and spaces, must not be changed. Thus, if we estimate the weight of one body in ounces, the weight of others with which it is com- pared, must be estimated in ounces, and not in pounds ; and in 28. What is meant by the momentum of a body ? 29. How do we ascertain the momentum ? 30. How may a light body have a greater momentum than one which is heavier ? 31. Why must we multiply the weight aod velocity tqjethar in ordf to find the momentum ? ON THE LAWS OF MOTION. 39 like manner, in comparing velocities, we must throughout, pre- serve the same standards both of space and of time; as for in- stance, the number of feet in one second, or of miles in one hour. Caroline. I now understand it perfectly, and think that I shall never forget a thing which you have rendered so clear. Mrs. B. I recommend it to you to be very careful to remem- ber the definition of the momentum of bodies, as it is one of the most important points in mechanics : you will find that it is from opposing velocity, to quantity of matter, that machines derive their powers. The reaction of bodies, is the next law of motion which I must explain to you. When a body in motion strikes against another body, it meets with resistance from it ; the resistance of the body at rest will be equal to the blow struck by the body in motion; or to express myself in philosophical language, action and reaction will be equal, and in opposite directions. Caroline. Do you mean to say, that the action of the body which strikes, is returned with equal force by the body which receives the blow ? Mrs. B. Exactly. Caroline. But if a man strike another on tli3 face with his fist, he surely does not receive as much paia by the reaction, as ne inflicts by the blow ? Mrs. B. No ; but this is simply owing to the knuckles, having much less feeling than the face. Here are two ivory balls suspended by threads, (plate 1. fig. 3.) draw one of them, A, a little on one side, now let it go ; it strikes, you see, against the other ball B, and drives it oft; to a distance equal to that through which the first ball fell ; but the motion of A is stopped; because when it struck B, it received in return a blow equal to that it gave, and its motion was conse- quently destroyed. Emily. I should have supposed, that the motion of the ball A was destroyed, because it had communicated all its motion to B. Mrs. B. It is perfectly true, that when one body strikes against another, the quantity of motion communicated to the second body, is lost by the first; but this loss proceeds from the reaction of the body which is struck. Here are six ivory balls hanging in a row, (fig. 4.) draw the first out of the perpendicular, and let it fall against the second. You see none of the balls except the last, appear to move, this flies off as far as the first ball fell; can you explain this ? 32. When we lepresent weight and velocity by numbers, what must we carefully observe ? 33. Why is it particularly important, to understand the nature of momentum ? 34. What is meant by reaction, and what is the rule respecting it? 35. How is this exemplified bv the ivory balls represented in plate 1. fig. 3? 40 ON THE LAWS OF MOTION. Caroline. I believe so. When the first ball struck the second, it received a blow in return, which destroyed its motion ; the second bail, though it did not appear to move, must have struck against the third ; the reaction of which set it at rest; the action of the third ball must have been destroyed by the reaction of the fourth, and so on till motion was communicated to the last ball, which, not being reacted upon, flies off. Mrs. B. Very well explained. Observe, that it is only when bodies are elastic, as these ivory balls are, and when their masses are equal, that the stroke returned is equal to the stroke given, and that the striking body loses all its motion. I will show you the differ- ence with these two balls of clay, (fig. 5.) which are not elastic; when you raise one of these, 1), out of the perpendicular, and let it fall against the other, E, the reaction of the latter, on account of its not being elastic, is not sufficient to destroy the motion of the former ; only part of the motion of D will be communicated to E, and the two balls will move on together to d and e, which is not so great a distance as that through which D fell. Observe how useful reaction is in nature. Birds in flying strike the air with their wings, and it is the reaction cf the air, which enables them to rise, or advance forwards; reaction being always in a contrary direction to action. Caroline. I thought that birds might be lighter than the air, when their wings were expanded, and were by that means ena- bled to fly. Mrs. j5. When their wings are spread, this does not alter their weight, but they are better supported by the air, as they cover a greater extent of surface; yet they are still much to; heavy to remain in that situation, without continually flapping their wings, as you may have noticed when birds hover over their nests: the force with which their wings .strike against the air, must equal the weight of their bodies, in order that the reaction of the air, may be able to support that weight; the bird will then remain stationary. If the stroke of the wings is greater than is required merely to support the bird, the reaction of the air will make it rise ; if it be less, it will gently descend ; and vou may have observed the lark, sometimes remaining with its wings ex- tended, but motionless; in this state it drops quietly into its nest. Caroline. This is indeed a beautiful effect of the law of reac- tion! But if flying is merely a mechanical operation, Mrs. B., 36. Explain the manner in which the six balls represented in fig. 4, illus- trate this fact. 37. What must be the nature of bodies, in which the whole motion is communicated from one to the other ? S8. What is the result if the balls are not elastic, and how is this" explained by fig. 5 ? 39. How will reaction assist us in explaining the flight of a bir.l ? 40. How must theii Wings operate in enabling them to remain stationary, to rise, and to descend? ON THK LAWS OF MOTION. 41 why should we not construct wings, adapted to the size of our bodies, fasten them to our shoulders, move them with our arms, and soar into the air ? Mrs. B. Such an experiment has been repeatedly attempted, but never with success; and it is now considered as totally im- practicable. The muscular power of birds, is incomparably greater ID. proportion to their weignt, than that of man ; were we there- fore furnished with wings sufficiently large to enable us to fly, we should not have strength to put them in motion. In swimming, a similar action is produced on the water, to that on the air, in flying; in rowing, also, you strike the water with the oars, in a direction opposite to that in which the boat is re- quired to move, and it is the reaction of the water on the oars which drives the boat along. Emily. You said, that it was in elastic bodies only, that the whole motion of one body, would be communicated to another; pray what bodies are elastic, besides the air? Mrs. B. In speaking of the air, I think we defined elasticity to be a property, by means of which bodies that are compressed, return to their former state. If I bend this cane, as soon as* I leave it at liberty, it recovers its former position; if I press my finger upon your arm, as soon as I remove it, the flesh, by virtue of its elasticity, rises and destroys the impression I made. Of all bodies, the air is the most eminent for this property, and it has thence obtained the name of an elastic fluid. Hard bodies are in the next degree elastic ; if two ivory, or hardened steel ball^ are struck together, the parts at which they touch, will be flattened; but their elasticity will make them instantaneously resume their former shape. Caroline. But when two ivory balls strike against each other, as thev constantly do on a billiard table, no mark or impression is made by the stroke. Mrs. B. 1 beg your pardon ; you cannot, it is true, perceive any mark, because their elasticity instantly destroys all trace of it. Soft bodies, which easily retain impressions, such as clay, wax, tallow, butter, &c. have very little elasticity; but of all descrip- tions of bodies, liquids are the least elastic. Emily. If sealing-wax were elastic, instead of retaining the impression of a seal, it would resume a smooth surface, as soon as the weight of the seal was removed. But pray what is it that produces the elasticity of bodies? Mrs. B. There is great diversity of opinion upon that point, 41. Why cannot a man fly by the aid of wings? 42. How does reaction operate in enabling us to swim, or to row a boat ? 43. What constitutes elas ticity ? 44. Give some examples. 45. What name is given to air, and for what reason? 46. What hard bodies are mentioned as elastic? 47 Do elastic bodies exhibit any indentation after a blow ? and why not? D 42 ON THE LAWS OF MOTION. and I cannot pretend to decide which approaches nearest to the truth. Elasticity implies susceptibility of compression, and the susceptibility of compression depends upon the porosity of bo- dies ; for were there no pores or spaces between the particles of matter of which a body is composed, it could not be com- pressed. Caroline. That is to say, that if the particles of bodies were as close together as possible, they could not be squeezed closer. Emily. Bodies then, whose particles are most distant from each other, must be most susceptible of compression, and conse- quently most elastic ; and this you say is the case with air, which is perhaps the least dense of all bodies r Mrs. B. You will not in general find this rule hold good ; for liquids have scarcely any elasticity, whilst hard bodies are emi- nent for this property, though the latter are certainly of much greater density than the former; elasticity implies, therefore, not only a susceptibility of compression, but depends upon the power possessed by the body, of resuming its former state after com- pression, in consequence of the peculiar arrangement of its par- ticles. Caroline. But surely there can be no pores in ivory and me- tals, Mrs. B.; how then can they be susceptible of compression? Mrs. B. The pores of such bodies are invisible to the naked eye, but you must not thence conclude that they have none; it is, on the contrary, well ascertained that gold, one of the most dense of all bodies, is extremely porous; and that these pores are sufficiently large to admit water when strongly compressed, to pass through them. This was shown by a celebrated experiment made many years ago at Florence. Emily. If water can pass through gold, there must certainly be pores or interstices which afford it a passage; and if gold is so porous, what must other bodies be, which are so much less dense than gold ! Mrs. B. The chief difference in this respect, is I believe, that the pores in some bodies are larger than in others ; in cork t sponge and bread, they form considerable cavities; in wood and stone, when not polished, they are generally perceptible to the naked eye; whilst in ivory, metals, and all varnished and po- lished bodies, they cannot be discerned. To give you an idea of the extreme porosity of bodies, sir Isaac Nwton conjectured that if the earth were so compressed as to be absolutely without pores, its dimensions might possibly not be more than a cubic inch. 48. What do we conclude from elasticity respecting the contact of the parti- cles of a body? 49. Are those bodies always the most elastic, which are the least dense? 50. Give examples to prove that this is -not the case. 51. All bodies are believed to be porous, what is said on this subject respecting gold? ON THE LAWS OF MOTION 43 Caroline. What an idea ! Were we not indebted to sir Isaac Newton for the theory of attraction, I sHvM be tempted to laugh at him for such a supposition. What insignificant little crea- tures we should be ! Mrs. B. If our consequence arose from the size of our bodies, we should indeed be but pigmies, but remember that the mind of Newton was not circumscribed by the dimensions of its envelope. Emily. It is, however, fortunate that heat keeps the pores of matter open and distended, and prevents the attraction of co- hesion from squeezing us into a nut-shell. Mrs. B. Let us now return to the subject of reaction, on which we have some further observations to make. It is because reaction is in its direction opposite to action, that reflected mo- tion is produced. If you throw a ball against the wall, it re- bounds; this return of the ball is owing to the reaction of the wall against which it struck, and is called reflected motion. Emily. And I now understand why balls filled with air rebound better than those stuffed with bran or wool ; air being most suscepti- ble of compression and most elastic, the reaction is more complete. Caroline. 1 have observed that when I throw a ball straight against the wall, it returns straight to my hand; but if I throw it obliquely upwards, it rebounds still higher, and I catch it when it falls. Mrs. B. You should not say straight, but perpendicularly against the wall ; for straight is a general term for lines in all directions which are neither curved nor bent, and is therefore equally applicable to oblique or perpendicular lines. Caroline. I thought that perpendicularly meant either direct- ly upwards or downwards ? Mrs. B. In those directions lines are perpendicular to the earth. A perpendicular line has always a reference to some- thing towards which it is perpendicular; that is to say, that it inclines neither to the one side or the other, but makes an equal angle on every side. Do you understand what an angle is ? Caroline. Yes, I believe so : it is the space contained between two lines meeting in a point. Mrs. B. Wefl then, let the line A B (plate 2. fig. 1.) repre- sent the floor of the room, and the line C D that in which you throw a ball against it; the line C D, you will observe, forms two angles with the line A B, and those two angles are equal. Emily. How can the angles be equal, while the lines which compose them are of unequal length ? 52. What conjecture was made by sir Isap.c Newton, respecting the porosity of bodies in general? 53. If you throw an elastic body against a wall, it will rebound; what is this occasioned by, and what is this return motion called? 54. What do we mean by a perpendicular line ? 55. What is an angle? 66. What is repiesented by fig. 1. plate 2 ? 44 ON THE LAWS OF MOTION. Mrs. B. An angle is not measured bj the length of tae lines, but by their opening, or the space between them. Emily. Yet the longer the lines are, the greater is the open- ing between them. Mrs. B. Take a pair of compasses and draw a circle over these spaces, making the angular point the centre. Emily. To what extent must I open the compasses ? Mrs. B. You may draw the circle what size you please, pro- vided that it cuts the lines of the angles we are to measure. All circles, of whatever dimensions, are supposed to be divided into 360 equal parts, called degrees ; the opening of an angle, being therefore a portion of a circle, must contain a certain number of degrees : the larger the angle the greater is the number of degrees, and two angles are said to be equal, when they contain an equal number of degrees. Emily. Now I understand it. As the dimension of an angle depends upon the number of degrees contained between its lines, it is the opening, and not the length of its lines, which deter- mines the size or the angle. Mrs. B. Very well : now that you have a clear idea of the dimensions of angles, can you tel} me how many degrees are contained in the two angles formed by one line falling perpen- dicularly on another, as in the figure I have just drawn ? Emily. You must allow me to put one foot of the compasses at the point of the angles, and draw a circle round them, and then I think I shall be able to answer \our question : the two angles are together just equal to half a circle, they contain there- fore 90 degrees each ; 90 degrees being a quarter of 360. Mrs. B. An angle of 90 degrees or one-fourth of a circle is called a right angle, and when one line is perpendicular to an- other, and distant from its ends, it forms, you see, (fig. 1.) a right angle on either side. Angles containing more than 90 degrees are called obtuse angles, (fag. 2.) and those containing less than 90 degrees are called acute angles, (fig. 3.) Caroline. The angles of this square table are right angles, but those of the octagon table are obtuse angles ; and the angles of sharp pointed instruments are acute angles. Mrs. B. Very well. To return now to your observation, that 57. Have the length of the lines which meet in a point, any thing to do with the measurement of an angle ? 58. What use can we make of com- passes in measuring an angle ? 59. Into what number of parts do we suppose a whole circle divided, and what are these parts called ? 60. When are two angles said to be equal ? 61. Upon what does the dimension of an angle de- pend ? 62. What number of degrees, and what portion of a circle is there in a right angle ? 63. How must one line be situated on another to form two right angles ? (fig. 1.) 64. Figure 2 represents an angle of more than 90 de- grees, what is that called ? 65. What are those of less than 90 degrees called as in fig. 3 ? /;;//: \ : 7 JU _ v r &~ CN THE LAWS OF MOTION. 45 if a ball is thrown obliquely against the wall, it will not rebound in the same direction ; tell me, have you ever played at billiards ? Caroline. Yes, frequently; and I have observed that when I push the ball perpendicularly against the cushion, it returns in the same direction ; but when I send it obliquely to the cushion, it rebounds obliquely, but on an opposite side ; the ball in this latter case describes an angle, the point of which is at the cushion. I have observed too, that the more obliquely the ball is struck against the cushion, the more obliquely it rebounds on the oppo- site side, so that a billiard player can calculate with great accu- racy in what direction it will return. Mrs. B. Very well. This figure (fig. 4. plate 2.) represents a billiard table; now if you draw a line A B from the point where the ball A strikes perpendicular to the cushion, you will find that it will divide the angle which the ball describes into two parts, or two angles; the one will show the obliquity of the direction of the ball in its passage towards the cushion, the other its obliquity in its passage back from the cushion. The first is called the angle of incidence, the other the angle of reflection; and these angles are always equal, if the bodies are perfectly elastic. Caroline. This then is the reason why, when I throw a ball obliquely against the wall, it rebounds in an opposite oblique direction, forming equal angles of incidence and of rejection. Mrs. B. Certainly; and you will find that the more obliquely vou throw the ball, the more obliquely it will rebound. We must now conclude ; but I shall have some further obser- vations to make upon the laws of motion, at our next meeting. 66. If you make an elastic ball strike a body at right angles, how will it re turn? 67. How if it strikes obliquely? 68. Explain by fig. 4 what is meant by the angles of incidence and of reflection. CONVERSATION IV. ON COMPOUND MOTION. COMPOUND MOTION, THE RESULT OF TWO OPPOSITE FORCES. OF CURVI- LINEAR MOTION, THE RESULT OF TWO FORCES. CENTRE OF MOTION, THE POINT AT REST WHILE THE OTHER PARTS OF THE BODY MOVE ROUND IT. CENTRE OF MAGNITUDE, THE MIDDLE OF A BODY. CEN- TRIPETAL FORCE, THAT WHICH IMPELS A BODY TOWARDS A FIXED CENTRAL POINT. CENTRIFUGAL FORCE, THAT WHICH IMPELS A BODY TO FLY FROM THE CENTRE. FALL OF BODIES IN A PARABOLA. CEN TRE OF GRAVITY, THE POINT ABOUT WHICH THE PARTS BALANCE EACH OTHER. MRS. B. I MUST now explain to you the nature of compound motion. Let us suppose a body to be struck by two equal forces in oppo- site directions, how will it move ? Emily. If the forces are equal, and their directions are in exact opposition to each other, I suppose the body would not move at all. Mrs. B. You are perfectly right; but suppose the forces instead of acting upon the body in direct opposition to each other, were to move in lines forming an angle of ninety degrees, as the lines YA, XA, (fig. 5. plate 2.) and were to strike the ball A, at the same instant; would it not move? Emily. The force X alone, would send it towards B, and the force Y towards C ; and since these forces are equal, I do not know how the body can obey one impulse rather than the other; and yet I think the ball would move, because as the two forces do not act in direct opposition, they cannot entirely destroy the effect of each other. Mrs. B. Very true; the ball therefore will not follow the di- rection of either of the forces, but will move in a line between them, and will reach D in the same space of time, that the force X would have sent it to B, and the force Y would have sent it to C. Now if you draw two lines, one from B, parallel to A C, and the other from C, parallel to A B, they will meet in D, and 1. If a body be struck by two equal forces in opposite directions, what wil) be the result? 2. What is fig. 5. plate 2. intended to represent? ON COMPOUND MOTION. 47 you will form a square; the oblique line which the body describes, is called the diagonal of the square. Caroline. That is very clear, but supposing the two forces to be unequal, that the force X, for instance, be twice as great as the force Y ? Mrs. B. Then the force X, would drive the ball twice as far as the force Y, consequently you must draw the line A B (fig. 6.) twice as long as the line A C, the body will in this case move to D ; and if you draw lines from the points B and C, exactly as directed in the last example, they will meet in D, and you will find that the ball has moved in the diagonal of a rectangle. Emuy. Allow me to put another case. Suppose the two forces are unequal, but do not act on the ball in the direction of a right angle, but in that of an acute angle, what will result ? Mrs. B. Prolong the lines in the directions of the two forces, and you will soon discover which way the ball will be impelled ; it will move from A to D, in the diagonal of a parallelogram, (fig. 7.) Forces acting in the direction of lines forming an obtuse angle, v/ill also produce motion in the diagonal of a parallelogram. For instance, if the body set out from B, instead of A, and was im- pelled by the forces X and Y, it would move in the dotted dia- gonal B C. We may now proceed to curvilinear motion: this is the result of two forces acting on a body; by one of which, it is projected forward in a right line; whilst by the other, it is drawn or impel- led towards a fixed point. For instance, when I whirl this ball, which is fastened to my hand with a string, the ball moves in a circular direction, because it is acted on by two forces; that which I give it, which represents the force of projection, and that of the string which confines it to my hand. If, during its motion you were suddenly to cut the string, the ball would fly off in a straight line ; being released from that confinement which caused it to move round a fixed point, it would be acted on bj one force only; and motion produced by one force, you know, is always in a right line. Caroline. This circular motion, is a little more difficult to comprehend than compound motion in straight lines. Mrs. B. You have seen how the water is thrown off from a grindstone, when turned rapidly round ; the particles of the stone itself have the same tendency, and would also fly off, was not their attraction of cchesion, greater than that of water. And indeed 3. How would the ball move, and how would you represent the direction of its motion ? 4. What is supposed respecting the forces represented in fig. 6 ? 5. How would the body move if so impelled ? 6. If the forces are une- qual and not at right angles, how would the body move, as illustrated by fig. 7 ? 7. How must a body be acted on, to produce motion in a curve, and what example is given ? 48 ON COMPOUND MOTION. it sometimes happens, that large grindstones fly to pieces from the rapidity of their motion. Emily. In the same way, the rim and spokes of a wheel, when in rapid motion, would be driven straight forwards in a right line, were they not confined to a fixed point, round which they are compelled to move. Mrs. B. Very well. You must now learn to distinguish be- tween what is called the centre of motion, and the axis of motion; the former being considered as a point, the latter as a line. When a body, like the ball at the end of the string, revolves in a circle, the centre of the circle is called the centre of its motion, and the body is said to revolve in a plane; because aline extended from the revolving body, to the centre of motion, would describe a plane, or flat surface. When a body revolves round itself, as a ball suspended by a string, and made to spin round, or a top spinning on the floor whilst it remains on the same spot; this revolution is round an imaginary line passing through the body, and this line is called its axis of motion. Caroline. The axle of a grindstone, is then the axis of its motion ; but is the centre of motion always in the middle of a body? Mrs. B. No, not always. The middle point of a body, is called its centre of magnitude, or position, that is, the centre of its mass or bulk. Bodies have also another centre, called the centre of gravity, which I shall explain to vou ; but at present we must confine ourselves to the axis of motion. This line you must observe remains at rest, whilst all the other parts of the body move around it; when you spin a top, the axis is stationary, whilst every other part is in motion round it. Caroline. But a top generally has a motion forwards besides its spinning motion ; and then no point within it can be at rest ? Mrs. B. What I say of the axis of motion, relates only to circular motion ; that is to say, motion round a line, and not to that which a body may have at the same time in any other di- rection. There is one circumstance to which you must carefully attend; namely, that the further any part of a body is from the axis of motion, the greater is its velocity: as you approach that line, the velocity of the parts gradually diminish till you reach the axis of motion, which is perfectly at rest. Caroline. But, if every part of the same body did not move 8. When is a body said to revolve in a plane, and what is meant by the centre of motion ? 9. What is intended by the axis of motion, and what are examples? 10. What is the middle point of a body called? 11. What is said of the axis of motion, whilst the body is revolving ? 12. When a body revolves on an axis, do all its parts move with equal velocity ? ON COMPOUND MOTION. 49 with the same velocity, that part which moved quickest, must be separated from the rest of the body, and leave it behind ? Mrs. B. You perplex yourself by confounding the idea of circular motion, with that of motion in a right line; you must think only of the motion of a body round a fixed line, and you will find, that if the parts farthest from the centre had not the greatest velocity, those parts would not be able to keep up with the rest of the body, and would be left behind. Do not the ex- tremities of the vanes of a windmill move over a much greater space, than the parts nearest the axis of motion ? (plate 3. fig. 1.) The three dotted circles represent the paths in which three differ- ent parts of the varies move, and though the circles are of differ- ent dimensions, each of them is described in the same space of time. Caroline. Certainly they are; and I now only wonder, that we neither of us ever made the observation before: and the same effect must take place in a solid body, like the top in spinning; the most bulging part of the surface must move with the greatest rapidity. Mrs. B. The force which draws a body towards a cemre, round which it moves, is called the centripetal force; and that force, which impels a body to fly from the centre, is called the centrifugal force; when a body revolves round a centre, these two forces constantly balance each other; otherwise the revolv- ing body would either approach the centre, or recede from it, according as the one or the other prevailed. Caroline. When I see any body moving in a circle, I shall remember, that it is acted on by two forces. Mrs. B. Motion, either in a circle, an ellipsis, or any other curve-line, must be the result of the action of two forces ; for you know, that the impulse of one single force, always produces motion in a right line. Emily. And if any cause should destroy the centripetal force, the centrifugal force would alone imDel the body, and it would, I suppose, fly off in a straight line from the centre to which it had been confined. Mrs. B. It would not fly off in a right line from the centre ; but in a ri^ht line in the direction in which it was moving, at the instant of its release ; if a stone, whirled round in a sling, gets loose at the point A, (plate 3. fig. 2.) it flies off in the direction A B ; this line is called a tangent, it touches the circumference 13. How is this explained by fig. 1. plate 3 ? 14. What are the two forces called which cause a body to move in a curve ; and what proportion do these two forces bear to each other when a body revolves round a centre ? 15. If the centripetal force were destroyed, he w would a body be carried by the centrifugal? E 50 ON COMPOUND MOTION. of the circle, and forms a right angle with a line drawn from that point of the circumference to the centre of the circle C. Emily. You say, that motion in a curve-line, is owing to two forces acting upon a body; but when I throw this ball in a hori- zontal direction, it describes a curve-line in falling; and yet it is only acted upon by the force of projection; there is no centripe- tal force to confine it, or produce compound motion. Mrs. B. A ball thus thrown, is acted upon by no less than three forces ; the force of projection, which you communicate to it; the resistance of the air through which it passes, which dimi- nishes its velocity, without changing its direction ; and the force of gravity, which finally brings it to the ground. The power of gravity, and the resistance of the air, being always greater than any force of projection we can give a body, the latter is gradu- ally overcome, and the body brought to the ground; but the stronger the projectile force, the longer will these powers be in subduing it, and the further the body will go before it falls. Caroline. A shot fired from a cannon, for instance, will go much further, than a stone projected by the hand. Mrs. B. Bodies thus projected, you observe, describe a curve- line in their descent; can you account for that? Caroline. No ; I do not understand why it should not fall in the diagonal of a square. Mrs. B. You must consider that the force of projection is strongest when the ball is first thrown; this force, as it proceeds, being weakened by the continued resistance of the air, the stone, therefore, begins by moving in a horizontal direction ; but as the stronger powers prevail, the direction of the ball will gradually change from a horizontal, to a perpendicular line. Projection alone, would drive the ball A, to B, (fig. 3.) gravity would bring it to C ; therefore, when acted on in different directions, by these two forces, it moves between, gradually inclining more and more to the force of gravity, in proportion as this accumulates; instead therefore of reaching the ground at D, as you suppose it would, it falls somewhere about E. Caroline. It is precisely so ; look Emily, as I throw this ball directly upwards^ how gravity and the resistance of the air con- quer projection. Now I will throw it upwards obliquely: see, the force of projection enables it, for an instant, to act in oppo- sition to that of gravity ; but it is soon brought down again. Mrs. B. The curve-line which the ball has described, is call- ed in geometry a parabola; but when the ball is thrown perpen- dicularly upwards, it will descend perpendicularly; because the 16. Explain what is meant by a tangent, as shown in fig. 2. plate 3.-- 17. What forces impede a body thrown horizontally? 18. Give the reason Why a body so projected, falls in a curve, (fig. 3. plate 3.) ,- I ON COMPOUND MOTION. 51 force of projection, and that of gravity, are in the same line of direction. We have noticed the centres of magnitude, and of motion ; but I have not yet explained to you, what is meant by the centre of gravity; it is that point in a. body, about which all the parts ex- actly balance each other; if therefore that point be supported, the body will not fall. Do you understand this? Emily. I think so; if the parts round about this point have an equal tendency to fall, they will be in equilibrium, and as long as this point is supported, the body cannot fall. Mrs. B. Caroline, what would be the effect, were the body supported in any other single point? Caroline. The surrounding parts no longer balancing each other, the body, I suppose, would fall on the side at which the parts are heaviest. Mrs. I*. Infallibly; whenever the centre of gravity is unsup- ported, the body must fall. This sometimes happens with an overloaded wagon winding up a steep hill, one side of the road being more elevated than the other; let us suppose it to slope as is described in this figure, (plate 3. fig. 4.) we will say, that the centre of gravity of tnis loaded wagon is at the point A. Now your eye will tell you, that a wagon thus situated, will overset; and the reason is, that the centre of gravity A, is not supported; for if you draw a perpendicular line from it to the ground at C, it does not fall under the wagon within the wheels, and is there fore not supported by them. Caroline. I understand that perfectly; but what is the mean- ing of the other point B ? Mrs. B. Let us, in imagination take off the upper part of the load ; the centre of gravity will then change its situation, and descend to B, as that will now be the point about which the parts of the less heavily laden wagon will balance each other. Will the wagon now be upset? Caroline. No, because a perpendicular line from that point falls within the wheels at D, and is supported by them; and when the centre of gravity is supported, the body will not fall. Emily. Yet I should not much like to pass a wagon in that situation, for, as you see, the point D is but just within the left wheel ; if the right wheel was raised, by merely passing over a stone, the point D would be thrown on the outside of the left wheel, and the wagon would upset. Caroline. A wagon, or any carriage whatever, will then be 19. The curve in which it fafts, is not a part of a true circle : what is it de- nominated ? 20. What is the centre of gravity defined to be ? 21. What re- sults from supporting, or not supporting the centre of gravity? 22. What ia intended to be explained by fig. 4. plate 3 ? 23. What would be the effect of taking off the upper portion of the load? 52 ON COMPOUND MOTION. most firmly supported, when the centre of gravity falls exactly between the wheels; and that is the case in a level road. Mrs. B. The centre of gravity of the human body, is a point somewhere in aline extending perpendicularly through the mid- dle of it, and as lon<* as we stand upright, this point is supported by the feet; if you lean on one side, you will find that you no longer stand iirm. A rone-dancer performs all his feats of agility, by dexterously Supporting his centre of gravity; whenever he finds that he is in danger of losing his balance, he shifts the hea- vy pole which he holds in his hands, in order to throw the weight towards the side that is deficient; and thus by changing the situation of the centre of gravity, he restores his equilibrium. Caroline. When a stick is poised on the tip of the finger, is it not by supporting its centre of gravity? Mrs. B. Yes; and it is because the centre of gravity is not supported, that spherical bodies roll down a slope. A sphere be- ing perfectly round, can touch the slope but by a single point, and that point cannot be perpendicularly under the centre of gravity, and therefore cannot be supported, as you will perceive by examining this figure, (fig. 5. plate 3.) Emily. So it appears : yet I have seen a cylinder of wood roll up a slope; how is that contrived? Mrs. B. It is done by plugging or loading one side of the cylinder with lead, as at fe, (fig. 5. plate 3.) the body being no longer of a uniform density, the centre of gravity is removed from the middle of the body to some point in or near the lead, as that substance is much heavier than wood ; now you may ob- serve that should this cylinder roll down the plane, as it is here situated, the centre of gravity must rise, which is impossible ; the centre of gravity must always descend in moving, and will descend by the nearest and readiest means, which will be by forcing the cylinder up the slope, until the centre of gravity is supported, and then it stops. Caroline. The centre of gravity, therefore, is not always in the middle of a body. Mrs. B. No, that point we have called the centre of magni- tude; when the body is of ar uniform density, and of a regular form, as a cube, or sphere, the centres of gravity and of magni- tude are in the same point; but when one part of the body is composed of heavier materials than another, the centre of gravity can no longer correspond with the centre of magnitude. Thus 24. When will a carriage stand most firmly ? 25. What is said of the cen- tre of gravity of the human body, and how does a rope dancer preserve his equilibrium ? 26. Why cannot a sphere remain at rest on an inclined plane? (fig. 5. plate 3.) 27. A cylinder of wood, may be made to rise to a small dii (anoe up an inclined plane. How may this be effected ? (fig. 5. plate 3.) ON COMPOUND MOTION. 53 you see the centre of gravity of this cylinder plugged with lead, cannot be in the same spot as the centre of magnitude. Emily Bodies, therefore, consisting but of one kind of sub- stance, as wood, stone, or lead, and whose densities are conse- quently uniform, must stand more firmly, and be more difficult to overset, than bodies composed of a variety of substances, of dif- ferent densities, which may throw the centre of gravity on one side. Mrs. B. That depends upon the situation of the materials; if those which are most dense, occupy the lower part, the stabili- ty will be increased, as the centre of gravity will be near the base. But there is another circumstance which more materially affects the firmness of their position, and that is their form. Bodies that have a narrow base are easily upset, for if they are a little inclined, their centre of gravity is no longer supported, as you may perceive in fig. 6. Caroline. I have often observed with what difficulty a person carries a single pail of water; it is owing, I suppose, to the cen- tre of gravity being thrown on one side; and the opposite arm is stretched out to endeavour to bring it back to its original situa- tion; but a pail hanging to each arm is carried with less difficulty, because they balance each other, and the centre of gravity re- mains supported by the feet. Mrs. B. Very well ; I have but one more remark to make on the centre of gravity, which is, that when two bodies are fastened together by an inflexible rod, thev are to be considered as form- ing but one body ; if the two bodies be of equal weight, the cen- tre of gravity will be in the middle of the line which unites them, (fig;. 7.) but if one be heavier than the other, the centre of gravity will be proportionally nearer the heavy body than the light one. (fig. 8.) If you were to carry a rod or pole with an equal weight fastened at each end of it, you would hold it in the middle of the rod, in order that the weights should balance each other ; whilst if the weights were unequal, you would hold it nearest the greater weight, to make vhem balance each other. Emily. And in both cases we should support the centre of gravity; and if one weight be very considerably larger than the other, the centre of gravity will be thrown out of the rod into the heaviest weight, (fig. 9.) Mrs. B. Undoubtedly. 28. When r*o we find the centres of gravity, and of magnitude in different points ? 29. What influence will the density of the parts of a body exert up- on its stability ? 30. What other circumstance materially affects the firmness of position? (fig. 6. plate 3.) 31. Why is it more easy to carry a weight in each hand, than in one only ? 32. What is said respecting two bodies united by an inflexible rod? 33. What is fig. 7, plate 3, intended to illustrate? What fig. 8; what fig. 9? 2 CONVERSATION V. ON THE MECHANICAL POWERS. OB THE POWER OF MACHINES. OF THE LEVER IN GENERAL. OF THB LEVER OF THE FIRST KIND, HAVING THE FULCRUM BETWEEN THB POWER AND THE WEIGHT. OF THE LEVER OF THE SECOND KIND, HAVING THE WEIGHT BETWEEN THE POWER AND THE FULCRUM. OF THE LEVER OF THE THIRD KIND, HAVING THE POWER BETWEEN THE FULCRUM AND THE WEIGHT. MRS. B. WE may now proceed to examine the mechanical poweis; they are six in number : The lever* the pulley r , the wheel and axle, the inclined plane, the wedge and the screio; one or more of which enters into the composition of every machine. A mechanical power is an instrument by which the effect of a given force is increased, whilst the force remains the same. In order to understand the power of a machine, there are four things to be considered. 1st. The power that acts: this consists in the effort of men or horses, of weights, springs, steam, &c. 2dly. The resistanca which is to be overcome by the power: this is generally a weight to be moved. The power must always be superior to the resistance, otherwise the machine could not be put in motion. Caroline. If for instance the resistance of a carriage was greater than the strength of the horsea employed to draw it, they would not be able to make it move. Mrs. B. Sdly. We are to consider the support or prop, or as it is termed in mechanics, t\\t fulcrum; this you may recollect is the point upon which the body turns when in motion; and lastly, the respective velocities of the power, and of the resist- ance. Emily. That must in general depend upon their respective distances from the fulcrum, or from the axis of motion ; as we observed in the motion of the vanes of the windmill. Mrs. B. We shall now examine the power of the lever. The 1. How many mechanical powers are there, and what are they named? 2. What is a mechanical power defined to be ? 3. What four particulars must be observed ? 4. Upon what will the velocities depend ? ON THE MECHANICAL POWERS. 55 lever is an inflexible rod or bar, moveable about a fulcrum, and having forces applied to two or more points on it. For instance, the steel rod to which these scales are suspended is a lever, and the point in which it is supported, the fulcrum, or centre of mo- tion; now, can you tell me why the two scales are in equilibrium ? Caroline. Being both empty, and of the same weight, the> balance each other. Emily. Or, more correctly speaking, because the centre of gravity common to both, is supported. Mrs. B. Very well ; and where is the centre of gravity of this pair of scales? (fig. 1. plate 4.) Emily. You have told us that when two bodies of equal weight were fastened together, the centre of gravity was in the middle of the line that connected them; the centre of gravity of the scales must therefore be supported by the fulcrum F of the lever which unites the two scales, and which is the centre of motion. Caroline. But if the scales contained different weights, the centre of gravity would no longer be in the fulcrum of the lever, but remove towards that scale which contained the heaviest weight; and since that point would no longer be supported, the heavy scale would descend, and out-weigh the other. Mrs. B. True ; but tell me, can you imagine any mode by which bodies of different weights can be made to balance each other, either in a pair of scales, or simply suspended to the ex- tremities of the lever ? for the scales are not an essential part of the machine; they have no mechanical power, and are used merely for the convenience of containing the substance to be weighed. Caroline. What ! make a light body balance a heavy one ? I cannot conceive that possible. Mrs. B. The fulcrum of this pair of scales (fig. 2.) is movea- ble, you see ; I can take it off the beam, and fasten it on again in another part; this part is now become the fulcrum, but it is no longer in the centre of the lever. Caroline. And the scales are no longer true ; for that which hangs on the longest side of the lever descends. Mrs. B. The two parts of the lever divided by the fulcrum, are called its arms; you should therefore say the longest arm, not the longest side of the lever. Your observation is true that the balance is now destroyed ; but it will answer the purpose of enabling you to comprehend the power of a lever, when the fulcrum is not in the centre. 5. What is a lever ? 6. Give a familiar example. 7. When and why do the scales balance each other, and where is their centre of gravity? (fig. 1. plate 4.) 8. Why would they not balance with unequal weights ? 9. Were the fulcrum removed from the middle of the beam what would result? 10. What do we mean by the arms of a lever ? 56 ON THE MECHANICAL POWERS. Emily. This would be an excellent contrivance for those wh " cheat in the weight of their goods ; by making the fulcrum a lit tie on one side, and placing the goods in the scale which is sus- pended to the longest arm of the lever, they would appear to weigh more than they do in reality. Mrs. B. You do not consider how easily the fraud would be detected ; for on the scales being emptied they would not hang in equilibrium. If indeed the scale on the shorter arm was made heavier, so as to balance that on the longer, they would appear to be true, whilst they were really false. Emily. True; I did not think of that circumstance. But I do not understand why the longest arm of the lever should not be in equilibrium with the other? Caroline. It is because the momentum in the longest, is greater than in the shortest arm ; the centre of gravity, therefore, is no longer supported. Mrs. B. You are right, the fulcrum is no longer in the cen- tre of gravity; but if we can contrive to make the fulcrum in its present situation become the centre of gravity, the scales will again balance each other ; for you recollect that the centre of gravity is that point about which every part of the body is in equilibrium. Emily. It has just occurred to me how this may be accom- plished; put a great weight into the scale suspended to the shortest arm of trie lever, and a smaller one into that suspended to the longest arm. Yes, I have discovered it look Mrs. B., the scale on the shortest arm will carry 3lbs., and that on the longest arm only one, to restore the balance, (fig. 3.) Mrs. B. You see, therefore, that it is not so impracticable as you imagined, to make a heavy body balance a light one; and this is in fact tin means by which you observed that an imposi- tion in the weight of goods might be effected, as a weight ot ten or twelve ounces, might thus be made to balance a pound of goods. If you measure both arms of the lever, you will find that the length of the longer arm, is three times that of the shorter; and that to produce an equilibrium, the weights must bear the same proportion to each other, and that the greater weight, must be on the sni: ter arm. Let us now take oft the scales, that we may consider the lever simply; and in this state you see that the fulcrum is no longer the centre of gravity, because it has been removed from the middle of the lever ; but it is, and must ever be, the centre of motion, as it is the only point which remains at rest, while the other parts move about it. 11. How may a pair of scales be false, and yet appea- to be true ? 12. If the fulcrum be removed from the centre of gravity, how Hay the equilibrium be restored? 13. How is this exemplified by fig. 3. pi* * 4 ? 14. What pro- portion must thfc weights bear to the lengths of the ara,* . ? ON THE MECHANICAL POWERS. 57 Caroline. The arms of the lever being different in length, it now exactly resembles the steelyards, with which articles are so frequently weighed. Mrs. B. It may in fact be considered as a pair of steelyards, by which the same power enables us to ascertain the weight of different articles, by simply increasing the distance of the power from the fulcrum ; you know that the farther a body is from the axis of motion, the greater is its velocity. Caroline,. That i remember, and understand perfectly. Mrs. B. You comprehend then, that the extremity of the lono-est arm of a lever, must move with greater velocity than that of the shortest arm, and that its momentum is greater in propor- tion. Emily. No doubt, because it is farthest from the centre of motion. And pray, Mrs. B., when my brothers plaj 7 at see-saw, is not the plank on which they ride, a kind of lever ? Mrs. B. Certainly ; the log of wood which supports it from the ground is the fulcrum, and those who ride, represent the power and the resistance at the ends of the lever. And have you not observed that when those who ride are of equal weight, the plank must be supported in the middle, to make the two arms equal ; whilst if the persons differ in weight, the plank must be drawn a little farther over the prop, to make the arms unequal, and the lightest person, who may be supposed to represent the power, must be placed at the extremity of the longest arm. Caroline. That is always the case when I ride on a plank with my youngest brother; I have observed also that the lightest person has the best ride, as he moves both further and quicker; and I now understand that it is because he is more distant from the centre of motion. Mrs. B. The greater velocity with which your little brother moves, renders his momentum equal to yours. Caroline. Yes ; I have the most weight, he the greatest velo- city; so that upon the whole our momentums are equal. But you said, Mrs. b., that the power should be greater than the re- sistance, to put the machine in motion ; how then can the plank move if tiie momentums of the persons who ride are equal ? Mrs. B. Because each person at his descent touches and pushes against the ground with his feet; the reaction of which gives him an impulse which produces the motion ; this spring is requisite to destroy the equilibrium of the power and the resist- ance, otherwise the plank would not move. Did you ever ob- serve that a lever describes the arc of a circle in its' motion? 15. On what principle do we wei^h with a pair of steelyards, and whnt will be the difference in the motion of the extremities of such a lever ? 58 ON THE MECHANICAL POWERS. Emily. No; it appears to me to rise and descend perpendi- cularly ; at least I always thought so. Mrs. B. I believe I must,, make a sketch of you and your brother riding on a plank, in order to convince you of your error, (fig. 4. plate 4.) You may now observe that a lever can move only round the fulcrum/since that is the centre of motion ; it would be impossible for you to rise perpendicularly, to the point A; or for your brother to descend in a straight line, to the point B ; you must in rising, and he in descending, describe arcs of your respective circles. This drawing shows you also how much su- perior his velocity must be to yours ; for if you could swing quite round, you would each complete your respective circles, in the same time. Caroline. My brother's circle being much the largest, he must undoubtedly move the quickest. Mrs. B. Now tell me, do you think that your brother could raise you as easily without the aid of a lever ? Caroline. Oh no, he could not lift me oft* the ground. Mrs. B. Then I think you require no further proof of the power of a lever, since you see what it enables your brother to perform. Caroline. I now understand what you meant by saying, that in mechanics, velocity is opposed to weight, for it is my brother's velocity which overcomes my weight. Mrs. B. You may easily imagine, what enormous weights may be raised by levers of this description, for the longer, wnen compared with the other, that arm is to which the power is ap- plied, the greater will be the effect produced by it; because the greater is the velocity of the power compared to that of the weight* Levers are of three kinds ; in the first the fulcrum is between the power and the weight. Caroline. This kind then comprehends the several levers you have described. Mrs. B. Yes, when in levers of the first kind, the fulcrum is equally distant from the power and the weight, as in the balance, there will be an equilibrium, when the power and the weight are equal to each other; it is not then a mechanical power, for nothing can in this case be gained by velocity ; the two arms of the lever being equal, the velocity of their extremities must be so likewise. The balance is therefore of no assistance as a me- chanical power, although it is extremely useful in estimating the respective weights of bodies. But when (hg. 5.) the fulcrum F of a lever is not equally di?- 16. How is this exemplified by fig-. 4. plate 4 ? 17. What line is descri- bed by the ends of a lever ? fig. 4. plate 4. 18. How many kinds are there; and in the first how is the fulcrum situated? 19. When may the fulcrum be lo situated that this lever is not a mechanical power, and why ? ON THE MECHANICAL POWERS. 59 tant from the power and the weight, and the power P acts at the extremity of the longest arm, it may be less than the weight W ; its deficiency being compensated by its superior velocity, as we observed in the see-saw. Emily. Then when we want to lift a great weight, we must fasten it to the shortest arm of a lever, and apply our strength to the longest arm ? Mrs. B. If the case will admit of your putting the end of the lever under the resisting body, no fastening will be required ; as you will perceive, when a nail is drawn by means of a hammer, which, though bent, is a lever of the first kind; the handle being the longest arm, the point on which it rests, the fulcrum, and the distance from that to the part which holds the nail, the short arm. But let me hear, Caroline, whether you can explain the action of this instrument, which is composed of two levers united in one c rnimon fulcrum. Caroline. A pair of scissors ! Mrs. B. You are surprised; but if you examine their con- struction, you will discover that it is the power of the lever, that assists us in cutting with scissors. Caroline. Yes ; I now perceive that the point at which the two levers are screwed together, is the fulcrum ; the power of the fingers is applied to the handles, and the article to be cut, is the resistance ; therefore, the longer the handles, and the shorter the points of the scissors, the more easily you cut with them. Emily. That I have often observed, for when I cut paste- board or any hard substance, I always make use of that part of the scissors nearest the screw or rivet, and I now understand why it increases the power of cutting; but I confess that I never should have discovered scissors to have been double levers; and pray are not snuffers levers of a similar description ? Mrs. B. Yes, and most kinds of pincers ; the great power of which consists in the great relative length of the handles. Did you ever notice the swingle-tree of a carriage to which the horses are attached when drawing ? Emily. yes; this is a lever of the first kind, but the ful- crum being in the middle, the horses should draw with equal power, whatever may be their strength. Mrs. B. That is generally the case, but it is evident tnat by making one arm longer than the other, it might be adapted to horses of unequal strength. Caroline. And of what nature are the other two kinds of le- vers? 20. What is represented by fig. 5. plate 4? 21. Give a familiar exampl* of the use of a lever of the first kind. 22. In what instruments are two such levers combined? 23. How may two horses of unequal strength, be ad van lageously coupled in a carriage ? 60 ON THE MECHANICAL POWERS. Mrs. B. In levers of the second kind, the weight, instead of being at one end, is situated between the power and the ful- crum, (fig. 6.) Caroline. The weight and the fulcrum have here changed places ; and what advantage is gained bj this kind of lever ? Mrs. B. In moving it, the velocity of the power must neces- sarily be greater than that of the weight, as it is more distant from the centre of the motion. Have you ever seen your brother move a snow-ball by means of a strong stick, when it became too heavy for him to move without assistance ? Caroline. Oh yes ; and this ^/as a lever of the second kind, (fig. 7.) the end of the stick, which he thrusts under the ball, and which rests on the ground, becomes the fulcrum ; the ball is the weight to be moved, and the power his hands, applied to the other end of the lever. In this instance there is a great differ- ence in the length of the arms of the lever ; for the weight is al- most close to the fulcrum. Mrs. B. And the advantage gained is proportional to this difference. The most common example that we have of levers of the second kind, is in the doors of our apartments. Emily. The hinges represent the fulcrum, our hands the power applied to the other end of the lever ; but where is the weight to be moved ? Mrs. B. The door is the weight, which in this example occu- pies the whole of the space between the power and the fulcrum. Nut crackers are double levers of this kind : the hinge is the ful- crum, the nut the resistance, and the hands the power. In levers of the third kind (fig. 8.) the fulcrum is again at one extremity, the weight or resistance at the other, and the power is applied between the fulcrum and the resistance. Emily. The fulcrum, the weight, or the power, then, each in its turn, occupies some part of the lever between its extremi- ties. But in this third kind of lever, the weight being farther than the power from the centre of motion, the difficulty of rais- ing it seems increased rather than diminished. Mrs. B. That is very true; a lever of this kind is therefore never used, unless absolutely necessary, as is the case in raising \a ladder in order to place it against a wall ; the man who raises it cannot place his hands on the upper part of the ladder, the power, therefore, is necessarily placed much nearer to the ful- crum than to the weight. Caroline. Yes, the hands are the power, the ground the ful- crum, and the upper part of the ladder the weight. 24. Describe a lever of the second kind. (Fig. 6. plate 4.) 25. What is represented in fig. 7. plate 4, and in what proportion does this lever gain power? 26. What is said respecting a door? 27. Describe a lever of the third kind. 28. In what instance do we use this ? ON THE MECHANICAL POWERS. 61 Mrs. B. Nature employs this kind of lever in the structure of the human frame. In lifting a weight with the hand, the lower part of the arm becomes a lever of the third kind ; the elbow is the fulcrum, the muscles of the fleshy part of the arm, the power; and as these are nearer to the elbow than to the hand, it is ne- cessary that their power should exceed the weight to be raised. Emily. Is it not surprising that nature should have furnished us with such disadvantageous levers ? Mrs. B. The disadvantage, in respect to power, is more than counterbalanced by the convenience resulting from this structure of the ann ; and it is that no doubt which is best adapted to enable it to perform its various functions. There is one rule which applies to every lever, which is tnis . In order to produce an equilibrium, the power must bear the same proportion to the weight, as the length of the shorter arm does to ttiat of the longer; as was shown by Emily with the weights of lib. and of 3/5. Fig. 3. plate 4. We have dwelt so long on the. lever, that we must reserve the examination of the other mechanical powers, to our next interview 29. What remarks are made on its employment in the limbs of animals? SO* What are the conditions of equilibrium in every lever ? CONVERSATION V. CONTINUED. ON THE MECHANICAL POWERS. 6F THE PULLET. OF THE WHEEL AND AXLE. OF THE INCLINED FLANK OF THE WEDUE. OF THE SCREW. MRS. B. THE pulley is the second mechanical power we are to exam- ine. You both, I suppose, have seen a pulley ? Caroline. Yes, frequently: it is a circular, and flat piece of wood or metal, with a string which runs in a groove round it : by- means of which, a weight may be pulled up ; thus pulleys are used for drawing up curtains. Mrs. B. Yes ; but in that instance the pulleys are fixed ; that is, they retain their places, and merely turn round on their axis ; these do not increase the power to raise the weights, as you will perceive by this figure, (plate 5. fig. 1.) Observe that the fixed pulley is on the same principle as the lever of a pair of scales, in which the fulcrum F being in the centre of gravity, the power P and the weight \V, are equally distant from it, and no advantage is gained. Emily. Certainly; if P represents the power employed to raise the weight W, the power must be greater than the weight in order to move it. But of what use then is a fixed pulley in mechanics ? Mrs. B. Although it does not increae the power, it is fre- quently useful for altering its direction. A single fixed pulley enables us to draw a curtain up, by pulling the string connected with it downwards; and we should be at a loss to accomplish this simple operation without its assistance. Caroline. There would certainly be some difficulty in ascend- ing to the head of the curtain, in order to draw it up. Indeed I now recollect having seen workmen raise weights to a considera- ble height by means of a fixed pulley, which saved them the trouble of going up themselves. 31. Describe a pulley, and its use. 32. What is meant Jay a fixed pulley and why is not power gained by its employment? (fig. 1. plate 5.) 33. Of what use is the fixed pulley? ON THE MECHANICAL POWERS. 63 Mrs. B. The next figure represents a pulley which is not fixed; (fig. 2.) and thus situated, you will perceive that It affords us mechanical assistance. A is a moveable pulley; that is, one which is attached to the weight to be raised, and which consequently moves up or down with it. There is also a fixed pulley D, which is only of use to change the direction of the power P. Now it is evident that the velocity of the power, will be double that of the weight W ; for if the rope be pulled at P, until the pulley A ascends with the weight to the fixed pulley D, then both parts of the rope, C and B, must pass over the fixed pulley, and consequently the hand at P, will nave descended through a space equal to those two pai ts; but the weight will have ascended only one half of that distance. Caroline. That I understand : if P drew the string but one inch, the weight would be raised only half an inch, because it would shorten the strings B and C half an inch each, and conse- quently the pulley with the weight attached to it, can be-raised only half an inch. Emily. But I do not yet understand the advantage of movea- ble pulleys; they seem to me to increase rather than diminish the difficulty of raising weights, since you must draw the string double the length that you raise the weight; whilst with a single pulley, or without any pulley, the weight is raised as much as the string is shortened. Mrs. B. The advantage of a moveable pulley consists in di- viding the difficulty; we must, it is true, draw twice the length of the string, but then only half the strength is required that would be necessary to raise" the weight without the assistance of a moveable pulley. Emily. So that the difficulty is overcome in the same manner as it would be, by dividing the weight into two equal parts, and raising them successively. Mrs. B. Exactly. You must observe, that with a moveable pulley the velocity of the power, is double that of the weight; since the power P (fig. 2.) moves two inches whilst the weight W moves one inch ; therefore the power need not be more than half the weight, to make their momentums equal. Caroline. Pulleys act then on the same principle as the lever; the deficiency of weight in the power, being compensated by its superior velocity, so as to make their momenturns equal. Mrs. B. You will find, that all gain of power in mechanics is founded on the same principle. Emily. But may it not be objected to pulleys, that a longer 34. How is the power gained by a moveable pulley, explained by means of fig;. 2. plate 5? 35. What proportion must the power bear to the weight in fig. 2, that their momentums may be equal ? 64 ON THE MECHANICAL POWERS. time is required to raise a weight by their aid, than without it f for what you gain in power, you lose in time. Mrs. B. That, my dear,*is the fundamental law in mecha- nics : it is the case with the lever, as well as the pulley; and you will find it to be so with all the other mechanical powers. Caroline. I do not see any ad vantage 'in the mechanical pow- ers then, if what we gain by them in one way, is lost in anothet Mrs. B. Since we are not able to increase our natural strength, is not any instrument of obvious utility, by means of which we may reduce the resistance or weight of any body, to the, level of that strength ? This the mechanical powers enable us to accom- plish. It is true, as you observe, that it requires a sacrifice of time to attain this end, but you must be sensible how very advantage- ously it is exchanged for power. If one man by his natural strength could raise one hundred pounds only, it would require five such men to raise five hundred pounds ; and if one man performs this by the help of a suitable engine, there is then no actual loss of time; as he does the work of five men, although he is five times as long in its accomplishment. You can now understand, that the greater the number of moveable pulleys connected by a string, the more easily the weight is raised; as the difficulty is divided amongst the number of strings, or rather of parts into which the string is divided, by the pulleys. Two, or more pulleys thus connected, form what is called a tackle, or system of pulleys (fig. 3.) You may have seen them suspended from cranes to raise goods into warehouses. Emily. When there are two moveable pulleys, as in the fi- gure you have shown to us, (fig. 3.) there must also be two fixed pulleys, for the purpose of changing the direction of the string, and then the weight is supported by four strings, and of course, each must bear only one fourth part of the weight. Mrs. B. You are perfectly correct, and the rule for estimat- ing the power gained by a system of pullies, is to count the number of strings by which the weight is supported ; or, which amounts to the same thing, to multiply the number of moveable pulleys by two. In shipping, the advantages of both an increase of power, and a change of direction, by means of pulleys, are of essential im- portance: for the sails are raised up the masts by the sailors on deck, from the change of direction which the pulley effects, and the labour is facilitated by the mechanical power of a combina- tion of pulleys. 36. What is a fundamental law as respects power and time ? 37. If to gain power we must lose time, what advantage do we derive from the me- chanical powers ? 38. What name is given to two or more pulleys connected by one string ? 39. How do we estimate the power gained by a system of pulleys ? OP THE f UNIVERSITY / ON THE MECHANICAL POWERS. 65 JEmily. But the pulleys on ship-board do not appear to me to be united in the manner you have shown us. Mrs. B. They are, I believe, generally connected as describ- ed in figuie 4, both for nautical, and a variety of other pur- poses; but in whatever manner pulleys are connected by a single string, the mechanical power is the same. The third mechanical power, is the wheel and axle. Let us suppose (plate 6. fig. 5) the weight W, to be a bucket of water in a well, which we raise by winding round the axle the rope, to which it is attached ; if this be done without a wheel to turn the axle, no mechanical assistance is received. The axle with- out a wheel is as impotent as a single fixed pulley, or a lever, whose fulcrum is in the centre : but add the wheel to the axle, and you will immediately find the bucket is raised with much less difficulty. The velocity of the circumference of the wheel is as much greater than that of the axle, as it is further from the centre of motion ; for the wheel describes a great circle in the same space of time that the axle describes a small one, therefore the power is increased in the same proportion as the circumfer- ence of the wheel is greater than that of the axle. If the veloci- ty of the wheel is twelve times greater than that of the axle, a power twelves times less than the weight of the bucket, would balance it; and a small increase would raise it. Emily. The axle acts the part of the shorter arm of the lever, the wheel that of the longer arm. Caroline. In raising water, there is commonly, I believe, in- stead of a wheel attached to the axle, only a crooked handle, which answers the purpose of winding the rope round the axle, and thus raising the bucket. Mrs. B. In this manner (fig. 6;) now if you observe the dot- ted circle which the handle describes in winding up the rope, you will perceive that the branch of the handle A, which is unit- ed to the axle, represents the spoke of a wheel, and answers the purpose of an entire wheel ; the other branch B affords no me- chanical aid, merely serving as a handle to turn the wheel. Wheels are a very essential part of most machines; they are employed in various ways; but, when fixed to the axle, their mechanical power is always the same: that is, as the circumfer- ence of the wheel exceeds that of the axle, so much will the energy of the power be increased. Caroline. Then the larger the wheel, in proportion to the axle, the greater must be its effect ? 40. What is represented by fig. 5. plate 6 ? 41. How does the wheel ope- rate in increasing power? 42. How is this compared with the lever? 43. How does a handle fixed to an axle, represent a wheel, fig. 6 ? 44. How cuuld we increase the power in this instrument ? F2 66 ON THE MECHANICAL POWERS. Mrs. B. Certainly. If you have ever seen any considerable mills or manufactures, you must have admired the immense wheel, the revolution of which puts the whole of the machinery into motion; and though so great an effect is produced by it, a horse or two has sufficient power to turn it ; sometimes a stream of water is used for that purpose, but of late years, a steam-en- gine has been found both the most powerful and the most conve- nient mode of turning the wheel. Caroline. Do not the vanes of a windmill represent a wheel, Mrs. B.? Mrs. B. Yes ; and in this instance we have the advantage of a gratuitous force, the wind, to turn the wheel. One of the great benefits resulting from the use of machinery is, that it gives us a sort of empire over the powers of nature, and enables us to make them perform the labour which would otherwise fall to the lot of man. When a current of wind, a stream of water, or the expansive force of steam, performs our task, we have only to superintend and regulate their operations. The fourth mechanical power is the inclined plane; this is generally nothing more than a plank placed in a sloping direc- tion, which is frequently used to facilitate the raising ot weights, to a small height, such as the rolling of hogsheads or barrels into a warehouse. .It is not difficult to understand, that a weight may much more easily be rolled up a slope than it can be raised the same height perpendicularly. But in this, as well as the other mechanical powers, the facility is purchased by a loss of time (fig. 7;) for the weight, instead of moving directly from A to C, must move from B to C, and as the length of the plane is to its height, so much is the resistance of the weight diminished. Emily. Yes; for the resistance, instead of being confined to the short line A C, is spread over the long line B C. Mrs. B. The wedge, which is the next mechanical power, is usually viewed as composed of two inclined planes (fte. 8:) you may have seen wood-cutters use it to cleave wood. The resist- .ance consists in the cohesive attraction of the wood, or any other body which the wedge is employed to separate ; the advantage gained by this power is diiferently estimated by philosophers; but one thing is certain, its power is increased, in proportion to the decrease of its thickness, compared with its length. The wedge is a very powerful instrument, but it is always driven forward by blows from a hammer, or some other body having considera- ble momentum. Emily. The wedge, then, is rather a compound than a dis- 45. What other forces besides the power of men, do we employ to move machines? 46. What will serve as an example of an inclined plane ? 47. In what proportion does it gain power? (fig. 7.) 48. To what is the wedga compared ? (fig. 8.) 49. How does its power increase ? ON THE MECHANICAL POWERS. 6l finct mechanical power, since it is not propelled by simple pressure, or weight, like the other powers. Mrs. P* It is so. All cutting instruments are constructed upon the principle of the inclined plane, or the wedge : those that have but one edge sloped, like the chisel, may be referred to the inclined plane; whilst the axe, the hatchet, and the knife, (when used to split asunder) are used as wedges. Caroline. But a knife cuts best when it is drawn across the substance it is to divide. We use it thus in cutting meat, we do not chop it to pieces. Mrs. B. The reason of this is, that the edge of a knife is really a very fine saw, and therefore acts best when used like that instrument. The screw, which is the last mechanical power, is more com- plicated than the others. You will see by this figure, (fig. 9.) that it is composed of two parts, the screw and the nut. The screw S is a cylinder, with a spiral protuberance coiled round it, called the thread ; the nut N is perforated to receive the screw, and the inside of the nut has a spiral groove, made to fit the spi- ral thread of the screw. Caroline. It is just like this little box, the lid of which screws on the box as you have described; but what is this handle L which projects from the nut ? Mrs. B. It is a lever, which is attached to the nut, without which the screw is never used as a mechanical power. The power of the screw, complicated as it appears, is referable to one of the most simple of the mechanical powers ; which of them do you think it is ? Caroline. In appearance, it most resembles the wheel and axle. Mrs. B. The lever, it is true, has the effect of a wheel, as it is the means by which you turn the nut, or sometimes the screw, round ; but the lever is not considered as composing a part of the screw, though it is true, that it is necessarily attached to it. Emily. The spiral thread of the screw resembles, I think, an inclined plane : it is a sort of slope, by means of which the nut ascends more easily than it would do if raised perpendicularly; and it serves to support it when at rest. Mrs. B. Very well: if you cut a slip of paper in the form of an inclined plane, and wind it round your pencil, which will 50. Why is it rather a compound than a simple power? 51. What com- mon instruments act upon the principle of the inclined plane, or the wedge? 52. Why does a knife cut best when drawn across ? 53. The screw has two essential parts ; what are they? 54. What other instrument is used to turn the screw? 55. How can you compare the screw with an inclined plane? ON THE MECHANICAL POWERS. represent the cylinder, you will find that it makes a spiral line, corresponding to the spiral protuberance of the screw. (Fig. 10.) Emily. Very true ; the nut then ascends an inclined plane, but ascends it in a spiral, instead of a straight line : the closer the threads of the screw, the more easy the ascent: it is like having shallow, instead of steep steps to ascend. Mrs. B. Yes ; excepting that the nut takes no steps, as it gradually winds up or down; then observe, that the closer the threads of the screw, the less is its ascent in turning round, and the greater is its power; so that we return to the old principle, what is saved in power is lost in time. Emihj. Cannot the power of the screw be increased also, by lengthening the lever attached to the nut ? Mrs. B. Certainly. The screw, with the addition of the lever, forms a very powerful machine, employed either for com- pression or to raise heavy weights. It is used by book-binders, to press the leaves of books together; it is used also in cider and wine presses, in coining, and for a variety of other purposes. Emily. Pray Mrs. B, by what rule do you estimate the power of the screw ? Mrs. B. By measuring the circumference of the circle, which the end of the lever would form in one whole revolution, and comparing this with the distance from the centre of one thread of the screw, to that of its next contiguous turn ; for whilst the lever travels that whole distance, the screw rises or falls only through the distance from one coil to another. Caroline I think that I have sometimes seen the lever attach- ed to the screw, and not to the nut, as it is represented in the figure. Mrs. B. This is frequently done, but it does not in any degree affect the power of the instrument. All machines are composed of one or more of these six me- chanical powers we have examined ; I have but cne more remark to make to you relative to them, which is, that friction in a con- siderable degree diminishes their force : allowance must there- fore always be made for it, in the construction of machinery. Caroline. By friction, do you mean one part of the machine rubbing against another part contiguous to it f Mrs. B. Yes ; friction is the resistance which bodies meet with in rubbing against each other ; there is no such thing as perfect smoothness or evenness in nature ; polished metals, though they wear that appearance more than most other bodies, are iar 56. By what two means may the power of the screw be increased ? 57. How do we estimate the power gained by the screw ? 58. Is the lever always at- tached to the nut, as in the figure ? 59. What is said respecting the composi- tion of all machines, and for what must allowance always be made in estimat wt their power? ON THE MECHANICAL POWERS. 69 from really possessing it; and their inequalities may frequently be perceived through a good magnifying glass. When, there- fore, the surfaces of the two bodies come in contact, the promi- nent parts of the one, will often fall into the hollow parts of the other, and occasion more or less resistance to motion. Caroline. But if a machine is made of polished metal, as a watch for instance, the friction must be very trifling ? Mrs. B. In proportion as the surfaces of bodies are well polished, the friction is doubtless diminished ; but it is always considerable, and it is usually computed to destroy one-third of the power of a machine. Oil or grease is used to lessen friction : it acts as a polish, by filling up the cavities of the rubbing sur- faces, and thus making them slide more easily over each other. Caroline. Is it for this reason that wheels are greased, and the locks and hinges of doors oiled ? Mrs. B. Yes ; in these instances the contact of the rubbing surfaces is so close, and they are so constantly in use, that they i equire to be frequently oiled, or a considerable degree of fric- tion is produced. There are two kinds of friction ; the first is occasioned by the j ubbing of the surfaces of bodies against each other, the second, by the rolling of a circular body; as that of a carriage wheel upon (lie ground : the friction resulting from the first is much the most considerable, for great force is required to enable the sliding body to overcome the resistance which the asperities of the sur- faces in contact oppose to its motion, and it must be either lifted over, or break through them ; whilst, in the second kind of fric- tion, the rough parts roll over each other with comparative facility; hence it is, that wheels are often used for the sole purpose of diminishing the resistance from friction. Emily. This is one of the advantages of carriage wheels, is it not? Mrs. B. Yes ; and the larger the circumference of the wheel the more readily it can overcome any considerable obstacles, such as stones, or inequalities in the road. When, in descend- ing a steep hill, we fasten one of the wheels, we decrease the velocity of the carriage, by increasing the friction. Caroline. That is to say, by converting the rolling friction into the rubbing friction. And when you had casters put to the legs of the table, in order to move it more easily, you changed the rubbing into the rolling friction. Mrs. B. There is another circumstance which we have alrea- dy noticed, as diminishing the motion of bodies, and which great- 60. What is meant by friction, and what causes it? 61. How may friction be diminished? 62. Friction is of two kinds, what are they 5 S3. For what purpose are wheels often used ? 64. When is the friction of a carriage wheel changed from the rolling to the rubbing friction ? 70 CAUSES OF THE MOTION OF THE HEAVENLY BODIES. ly affects the power of machines. This is the resistance of the medium, in which a machine is worked. All fluids, whether elastic like air, or norielastic like water and other liquids, are called mediums; and their resistance is proportioned to their density; for the more matter a body contains, the greater the resistance it will oppose to the motion of another body striking against it. Emily. It would then be much more difficult to work a ma- chine under water than in the air ? Mrs. B. Certainly, if a machine could be worked in vacuo, and without friction, it would not be impeded, but this is unat- tainable ; a considerable reduction of power must therefore be allowed for, from friction and the resistance of the medium. We shall here conclude our observations on the mechanical powers. At our next meeting I shall endeavour to give you an explanation of the motion of the heavenly bodies. CONVERSATION VI. CAUSES OF THE MOTION OF THE HEAVENLY BODIES. o THE EARTH'S ANNUAL MOTION. OF THE PLANETS AND THEIR MO- TIOJT. OF THE DIURNAL MOTION OF THE EARTH AND PLANETS. CAROLINE. I AM come to you to-day quite elated with the spirit of oppo- sition, Mrs. B.; for I have discovered such a powerful objection to your theory of attraction, that I doubt whether even your con- juror Newton, with his magic wand of gravitation, will be able to dispel it. Mrs. B. Well, my dear, pray what is this weighty objection ? Caroline. You say that the earth revolves in its orbit round the sun once in a year, and that bodies attract in proportion to 65. What is a medium, and in what proportion does it diminish motion t 66. Under what circumstam at u.ust a body be placed, in order to move with- out impediment? CAUSES OF THE MOTION OF THE HEAVENLY BODIES. Tl the quantity of matter they contain; now we all know the sun to be much larger than the earth : why, therefore, does it not draw the earth into itself; you will not, I suppose, pretend to say that we are falling towards the sun ? Emily. However plausible your objection appears, Caroline, I think you place too much reliance upon it : when any one has given such convincing proofs of sagacity and wisdom as Sir Isaac Newton, when we find that his opinions are universally received and adopted, is it to be expected that any objection we can ad- vance should overturn them ? Caroline. Yet I confess that I am not inclined to yield impli- cit faith even to opinions of the great Newton : for what pur- pose are we endowed with reason, if we are denied the privilege of making use of it, by judging for ourselves. Mrs. $. It is reason itself which teaches us, that when we, novices in science, start objections to theories established by men of knowledge and wisdom, we should be diffident rather of our own than of their opinion. I am far from wishing to lay the least restraint on your questions ; you cannot be better convinced of the truth of a system, than by finding that it resists all your attacks, but I would advise you not to advance your objections with so much confidence, in order that the discovery of their fallacy may be attended with less mortification. In answer to that you have just proposed, I can only say, that the earth really is attracted by the sun. Caroline. Take care, at least, that we are not consumed by him, Mrs. B. Mrs. B. We are in no danger ; but Newton, our magician, as you are pleased to call him, cannot extricate himself from this difficulty without the aid of some cabalistical figures, which I must draw for him. Let us suppose the earth, at its creation, to have been pro- jected forwards into universal space : we know that if no obsta- cle impeded its course it would proceed in the same direction, and with a uniform velocity for ever. In fig. 1. plate 6, A re- presents the earth, and S the sun. We shall suppose the earth to be arrived at the point in which it is represented in the figure, having a velocity which would carry it on to B in the space of one month; whilst the sun's attraction would bring it to C in the same space of time. Observe that the * forces of projection and attraction do not act in opposition p^, pendicularly, or at a right angle to each other. Can ! me now, how the earth will move ? Emily. I recollect your teaching us that a body acted upon 1. What revolution does the earth perform .in a year? 2. Had the earth received H projectile force only, at the time of iti creation, how would it hav moved. 72 eAUSES OF THE MOTION F THE HEAVENLY BODIES. by two forces perpendicular to each other, would move in the diagonal of a parallelogram ; if, therefore, I complete the paral- lelogram, by drawing the lines C D, B D, the earth will move in the diagonal A D. Mrs. B. A ball struck by two forces acting perpendicularly to each other, it is true, moves in the diagonal of a parallelogram ; but you must observe that the force of attraction is continually acting upon our terrestrial ball, and producing an incessant de- viation from its course in a right line, which converts it into that of a curve-line ; every point of which may be considered as con- stituting the diagonal of an infinitely small parallelogram. Let us detain the earth a moment at the point D, and consider how it will be affected by the combined action of the two forces in its new situation. It still retains its tendency to fly off in a straight line ; but a straight line would now carry it away to F, whilst the sun would attract it in the direction b S ; how then will it proceed ? Emily. It will go on in a curve-line, in a direction between that of the two forces. Mrs. B. In order to know exactly what course the earth will follow, draw another parallelogram similar to the first, in which the line D F describes the force of projection, and the line D S that of attraction ; and you will find that the earth will proceed in the curve-line D G. Caroline. You must now allow me to draw a parallelogram, Mrs. B. Let me consider in what direction will the force of projection now impel the earth. Mrs. B. First draw a line from the earth to the sun repre senting the force of attraction ; then describe the force of pro- jection at a right angle to it. Caroline. The earth will then move in the curve G I, of the parallelogram G II I K . Mrs. S. You recollect that a body acted upon by two forces, moves through a diagonal, in the same time that it would have moved through one of the sides of the parallelogram, were it acted upon by one force only. The earth has passed through the diagonals of these three parallelograms, in the space of three months, and has performed one quarter of a circle ; and on the same principle it will go on till it has completed the whole of the circle. It will then recommence a course, which it has pur- sued ever since it first issued from the hand of its Creator, and 3. What do the lines A B, and A C, represent in fig. 1. plate 6? 4. What have you been taught respecting a body acted upon by two forces at right angles wkh each other? 5. How does the force of gravity change the diagonal into a curved line ? 6. Describe the operation of the forces of projection and of gravity as illus- trated by the parallelograms in the f.gure ? 7 What is the law respecting the time required for motion in the diagonal ? CAUSES OF THE MOTION OF THE HEAVENLY BODIES. 7S which there is every reason, to suppose it will continue to follow, as long as it remains in existence. Emily. What a grand and beautiful effect resulting from so simple a cause ! Caroline. It affords an example, on a magnificent scale, of the curvilinear motion, which you taught us in mechanics. The attrac- tion of the sun is the centripetal force, which confines the earth to a centre; and the impulse of projection, the centrifugal force, which impels the earth to quit tlie sun, and fly off in a tangent. Mrs. B. Exactly so. A simple mode of illustrating the ef- fect of these combined forces on the earth, is to cut a slip of card in the form of a carpenter's square, as A, B, C ; (fig. 2. plate 6.) the point B will be a right angle, the sides of the square being perpendicular to each other; after having done this you are to de- scribe a small circle at the angular point B, representing the earth, and to fasten the extremity of one of the legs of the square to a fixed point A, which we shall consider as the sun. Thus situated, the two sides of the square will represent both the cen- trifugal and centripetal forces ; A B, representing the centripetal, and B C, the centrifugal force ; if you now draw it round the fixed point, you will see how the direction of the centrifugal force varies, constantly forming a tangent to the circle in which the earth moves, as it is constantly at a right angle with the centripetal force. Emily. The earth then, gravitates towards the sun, without the slightest danger either of approaching nearer, or receding further from it. How admirably this is contrived ! If the I wo forces which produce this curved motion, had not been so accu- rately adjusted, one, would ultimately have prevailed over the other, and we should either have approached so near the sun as to have been burnt,, or have receded so far from it as to have been frozen. Mrs. B. What will you say, my dear, when I tell you, that these two forces are not, in fact, so proportioned as to produce circular motion in the earth? We actually revolve roun 1 the sun in an eliptical or oval orbit, the sun being situated in one of the foci or centres of the oval, so that the sun is at some periods much nearer to the earth, than at others. Caroline. You must explain to us, at least, in what manner we avoid the threatened destruction. 8. What portion of a year is represented by the three diagonals in the figure ? 9. How will what you have learned respecting motion in a curve, apply to the earth's motion? 10. In what form are you directed to cut a piece of card to aid in illustrating the two forces acting upon the earth? 11. How must you apply it to this purpose? (fig. 2. plate 6.) 12. If these two forces did not exactly balance each other, what would result? 13. Does the earth revolve in a circular orbit? 14. What results from its motion in an eclipse ? 74 CAUSES OF THE MOTION OF THE HEAVENLY BODIES. Mrs. B. Let us suppose that when the earth is at A, (fig. 3.) its projectile force should not have given it a velocity sufficient to counterbalance that of gravity, so as to enable these powers conjointly to carry it round the sun in a circle; the earth, instead of describing the line A C, as in the former figure, will approach nearer the sun in the line A B. Caroline,. Under these circumstances, I see not what is to prevent our approaching nearer and nearer the sun, till we fall into it : for its attraction increases as we advance towards it, and produces an accelerated velocity in the earth, which increases the danger. Mrs. B. There is another seeming danger, of which you are not aware. Observe, that as the earth approaches the sun, the direction of its projectile force is no longer perpendicular to that of its attraction, but inclines more nearly to it. When the earth reaches that part of its orbit at B, the force of projection would carry it to D, which brings it nearer the sun instead of bearing it away from it. Emily. If, then, we are driven by one power, and drawn by the other to this centre of destruction, how is it possible for us to escape ? Mrs. B. A little patience, and you will find that we are not without resource. The earth continues approaching the sun with a uniformly increasing accelerated motion, till it reaches the point E; in what direction will the projectile force now impel it? Emily. In the direction E F. Here then the two forces act perpendicularly to each other, the lines representing them forming a right angle, and the earth is situated just as it was in the pre- ceding figure; therefore, from this point, it should revolve round the sun in a circle. Mrs. B. No, all the ciicumstances do not agree. In motion round a centre, you recollect that the centrifugal force increases with the velocity of the body, or in other words, the quicker it moves the stronger is its tendency to fly oft* in a right line. When the earth, therefore, arrives at E, its accelerated motion will have so far increased its velocity, and consequently its cen- trifugal force, that the latter will prevail over the force of attrac- tion, and force the earth away from the sun till it reaches G. Caroline. It is thus then that we escape from the dangerous vicinity of the sun ; and in proportion as we recede from it, the force of its attraction, and, consequently, the velocity of the earth's motion, are diminished. 15. What is represented by the lines A C, A B, in fig. 3. plate 6 ? 16. Were the projectile force to carry the earth from B to D, (fig. 3.) what would ro- sult? 17. When it has arrived at E, what angle will be formed by the lines representing the two forces? 18. What effect will the acceleiated motion then pruduce? CAUSES OF THE MOTION OF THE HEAVENLY BODIES. 75 Mrs. B. Yes. From G the direction of projection is towards H, that of attraction towards S, and the earth proceeds between them with a uniformly retarded motion, till it has completed its revolution. Thus you see that the earth travels round the sun, not in a circle, but an elipsis, of which the sun occupies one of the foci; and that in its course^ the earth alternately approaches and recedes from it, without any danger of being either swallow- ed up, or being entirely carried away from it. Caroline. And I observe, that what I apprehended to be a dangerous irregularity, is the means by which the most perfect order and harmony are produced. Emily. The earth travels then at a very unequal rate, its velocity being accelerated as it approaches the sun, and retarded as it recedes from it. Mrs. B. It is mathematically demonstrable, that, in moving round a point towards which it Is attracted, a body passes over equal areas, in equal times. The whole of the space contained within the earth's orbit, is in fig. 4, divided into a number of areas or surfaces ; 1, 2, 3, 4, &c. all of which are of equal dimen- sions, though of very different forms ; some of them, you see. are long and narrow, others broad and short: but they each of them contain an equal quantity of space. An imaginary line drawn from the centre of the earth to that of the sun, and keeping pace with the earth in its revolution, passes over equal areas in et t ual times; that is to say, if it is a month going from A to B, it will be a month going from B to C, and another from C to K, and so on; and the areas A B S, B C S, C E S, will be equal 10 each other, although the lines A B, B C, C E, are unequal. Caroline. What long journeys the earth has to perform in the course of a month, in one part of her orbit, and how short they are in the other part ! Mrs. B. The inequality is not so considerable as appears in this figure ; for the earth's orbit is not so eccentric a? it is there described ; and in reality, differs but little from a circle : that part of the earth's orbit nearest the s\in is called its perihelion, that part most distant from the sun, its aphelion; and the earth is above three millions of miles nearer the sun at its perihelion than at its aphelion. Emily. I think I can trace a consequence from these differ- ent situations of the earth; are not they the cause of summer and winter ? 19. What is the form of the earth's orbit, and what circumstances produce this torm? 20. What ia the consequence as regards the regularity of the earth's motion ? 21. What law governs as regards the spaces passed over, and how is this explsnned by fig. 4. plate 3 ? 22. What is meant by periliclion, and by aphelion ? 23. What is the difference of the distance of the earth from the un, in these two points? 76 CAUSES OF THE MOTION OF THE HEAVENLY BODIES. Mrs. B. On the contrary, during the height of summer, the earth is in that part of its orbit which is most distant from the sun, and it is during the severity of winter, that it approaches nearest to it. Emily. That is very extraordinary; and how then do you account for the heat being greatest, when we are most distant from the sun ? Mrs. B. The difference of the earth's distance from the sun in summer and winter, when compared with its total distanca from the sun, is but inconsiderable. The earth, it is true, is above three millions of miles nearer the sun in winter than in. summer; but that distance, however great it at first appears, sinks into insignificance in comparison with 95 millions of miles, which is our mean distance from the sun. The change of tern perature, arising from this difference, would scarcely be sensible, even were it not completely overpowered by other causes which produce the variations of the seasons ; but these I shall defer explaining, till we have made some further observations on the neavenly bodies. Caroline. And should not the sun appear smaller in summer, when it is so much further from us ? Mrs. B. It actually does, when accurately measured; but the apparent difference in size, is, I believe, not perceptible to the naked eye. Emily. Then, since the earth moves with the greatest velo- city in that part of its orbit in which it is nearest the sun, it must have completed its journey through that half of its orbit, in a shorter time than through the other ? Mrs. B. Yes, it is about seven days longer performing the summer-half of its orbit, than the winter-half; and the summers are consequently seven days longer in the northern, than they are in the southern hemisphere. The revolution of all the planets round the sun, is the result of the same causes, and is performed in the same manner, as that of the earth. Caroline. Pray what are the planets ? Mrs. B. They are those celestial bodies, which revolve like our earth, about the sun ; they are supposed to resemble the earth also in many other respects ; and we are led by analogy, to sup- pose them to be inhabited worlds. 24. At what season of the year is it nearest to, and at what furthest from the sun ? 25. What is the mean distance of the earth from the sun ? 26. Why is but little effect produced, as regards temperature, by the change of distance? 27. Has it any influence on the sun's apparent size ? 28. Are the summer and winter, half years, of the same length ; what is their difference, and what is tne cause ? 29. What are the planets ? CAUSES OF THE MOTION OF THE HEAVENLY BODIES. 77 Caroline. I have heard so. but do you not think such an opinion too great a stretch of the imagination ? Mrs. B. Some of the planets are proved to be larger than the earth ; it is only their immense distance from us, which ren- ders their apparent dimensions so small. Now, if we consider them as enormous globes, instead of small twinkling spots, we shall be led to suppose that the Almighty would riot have cre- ated them merely for the purpose of giving us a little light in the night, as it was formerly imagines ; and we should find it more consistent with our ideas of the Divine wisdom and beneficence, to suppose that these celestial bodies should be created for the habitation of beings, who are, like us, blessed by his providence. Both in a moral, as well as a physical point of view, it appears to me more rational to consider the planets as worlds revolving round the sun ; and the fixed stars as other suns, each of them attended by their respective system of planets, to which they impart their influence. We have brought our telescopes to such a degree of perfection, that from the appearances which the moon exhibits when seen through them, we have very good reason to conclude that it is a habitable globe : for though it is true that we cannot discern its towns and people, we can plainly perceive its mountains and valleys : and some astronomers have gone so far as to imagine that they discovered volcaiios. Emily. If the fixed stars are suns, with planets revolving round them, why should we not see those planets as well as their sunsT Mrs. B. In the first place, we conclude that the planets of other systems (like those of our own) are much smaller than the suns which give tiiem light; therefore at a distance so great as to make the suns appear like fixed stars, the planets would be quite invisible. Secondly, the light of the planets being only reflected light, is much more feeble than that of the fixed stars. There is exactly the same difference as between the light of the sun and that of the moon; the first being a fixed star, the second a planet. Emily. But the planets appear to us as bright as the fixed stars, and these you tell us are suns like our own; why then do we not see them by day -light, when they must be just as lumi- nous as they are in the night ? Mrs. B. Both are invisible from the same cause : their light is so faint, compared to that of the sun, that it is entirely effaced by it : the. light emitted by the fixed stars may probably be as great as that of our sun, at an equal distance; but they being so 30. What circumstances render it probable that they are habitable globes * 31. What is believed respecting the fixed stars ? 32. What discoveries have been made in the moon ? 33. What prevents our seeing the planets, if there are any, which revolve round the fixed stars ? 34. What prevents our seeing the stars and planets in the day-time? G 2 T8 CAUSES OF THE MOTION OF THE HEAVENLY BODIES. much more remote, it is diffused over a greater space, and is in consequence proportionally lessened. Caroline. True ; I can see much better by the light of a can- dle that is near me, than by that of one at a great distance But I do not understand what makes the planets shine ? Mrs. B. What is that which makes the gilt buttons on your brother's coat shine ? Caroline. The sun. But if it was the sun which made the planets shine, we should see them in the day-time, when the sun shone upon them ; or if the faintness of their light prevented our seeing tnem in the day, we should not see them at all, for the sun cannot shine upon them in the night. Mrs. B. There you are in error. But in order to explain this to you, I must first make you acquainted with the various motions of the planets. You know, that according to the laws of attraction, the planets belonging to our system all gravitate towards the sun ; and that this force, combined with that of projection, will occasion their revolution round the sun, in orbits more or less elliptical, accord- ing to the proportion which these two forces bear to each other. But the planets have also another motion : they revolve upon their axis. The axis of a planet is an imaginary line which passes through its centre, and on which it turns ; and it is this motion which produces day and night. It is day on that side of the planet which faces the sun; and on the opposite side, which remains in darkness, it is night. Our earth, which we consider as a planet, is 24 hours in performing one revolution on its axis ; in that period of time, therefore, we have a day and a night ; hence this revolution is called the earth's diurnal or daily motion; and it is this revolution of the earth from west to east which pro- duces an apparent motion of the sun, moon and stars, in a con- trary direction. 4 Let us now suppose ourselves to be beings independent of any planet, travelling in the skies, and looking upon the earth from a point as distant from it as from other planets. Caroline. It would not be flattering to us, its inhabitants, to see ij; make so insignificant an appearance. Mrs. B. To those accustomed to contemplate it in this light, it could never appear more glorious. We are taught by science to distrust appearances ; and instead of considering the fixed stars and planets as little points, we look upon them either as brilliant suns, or habitable worlds; and we consider the whole 35. What other motions have the earth and planets, besides that in their orbits?? 36. What is the imaginary line called, round which they revolve i 37. How does this occasion night and day ? 38. In what direction does the *arth turn upon its axis, and what apparent motion of the sun, moon, and stari. a thereby produced ? CAUSES OF THE MOTION OF THE HEAVENLY BODIES. 79 together as forming one vast and magnificent system, worthy of the Divine hand by which it was created. Emily. I can scarcely conceive the idea of this immensity of creation ; it seems too sublime for our imagination ; and to think that the goodness of Providence extends over millions of worlds throughout a boundless universe Ah! Mrs. B., it is we only who become trifling and insignificant beings in so magnificent a creation ! Mrs. B. This idea should teach us humility, but without producing despondency. The same Almighty hand which guides these countless worlds in their undeviating course, conducts with equal perfection, the blood as it circulates through the veins of a fly, and opens the eye of the insect to behold His wonders. Notwithstanding this immense scale of creation, therefore, we need not fear that we shall be disregarded or forgotten. But to return to our station in the skies. We were, if you recollect, viewing the earth at a great distance, in appearance a little star, one side illumined by the sun, the other in obscurity. But would you believe it, Caroline, many of the inhabitants of this little star imagine that when that part which they inhabit is turned from the sun, darkness prevails throughout the universe, merely because it is night with them; whilst, in reality, the sun never ceases to shine upon every planet. When, therefore, these little ignorant beings look around them during their night, and behold all the stars shining, they cannot imagine why the planets, which are dark bodies, should shine ; concluding, that since the sun does not illumine themselves, the whole universe must be in darkness. Caroline. I confess that I was one of these ignorant people ; but I am now very sensible of the absurdity of such an idea. To the inhabitants of the other planets, then, we must appear as a little star? Mrs. JB. Yes, to those which revolve round our sun; for since those which may belong to other systems, (and whose exist- ence is only hypothetical) are in visible" to us, it is probable that we also are invisible to them. Emily. But they may see our sun as we do theirs, in appear- ance a fixed star ? Mrs. B. No doubt; if the beings who inhabit those planets are endowed with senses similar to ours. By the same rule we must appear as a moon to the inhabitants of our moon ; but on a larger scale, as the surface of the earth is about thirteen times as large as that of the moon. 39. What must be the appearance of the earth to an inhabitant of one of the planets ? 40. What the appearance of the sun to the inhabitants of pla- nets in other systems? 40. What the appearance of the earth to an inhabit ant of the moon ? OF THE PLANETS. Emily. The moon, Mrs. B., appears to move in a different direction, and in a different manner from the stars ? Mns. B. I shall defer the explanation of the motion of the moon till our next interview, as it would prolong our present lesson too much. CONVERSATION VII. OF THE PLANETS. Of THE SATELLITES OR MOONS. GRAVITY DIMINISHES AS THE SatTARE OF THE DISTANCE. OF THE SOLAR SYSTEM. OF COMETS. CONSTEL- LATIONS, SIGNS OF THE ZODIAC. OF COPERNICUS, NEWTON, &C. MRS. B. THE planets are distinguished into primary and secondary. Those which revolve immediately about the sun are called pri- mary. Many of these are attended in their course by smaller planets, which revolve round them : these are called secondary planets, satellites, or moons. Such is our moon which accom- panies the earth, and is carried with it round the sun. Emily. How then can you reconcile the motion of the secon dary planets to the laws of gravitation ; for the sun is much larger than any of the primary planets; and is not the power of gravity proportional to the quantity of matter ? Caroline. Perhaps the sun, though much larger, may be less dense than the planets. Fire you know, is very light, and it may contain but little matter, though of great magnitude. Mrs. B. We do not know of what kind of matter the sun is made ; but we may be certain, that since it is the general centre of attraction of our system of planets, it must be the body which contains the greatest quantity of matter in that system. You must recollect, that the force of attraction is not only 1. Into what two classes are the planets divided, and how are they distin- guished ? 2. By what reasoning do you prove that the sun contains a greuUi cuantity of matter than any other body in the system ? OF THE PLANETS. 81 proportional to the quantity of matter, but to the degree of prox- imity of the attractive body: this power is weakened by being diffused, and diminishes as the distance increases. Emily. Then if a planet was to lose one-half of its quantity of matter, it would lose one half of its attractive power; and the same eft'ect would be produced by removing it to twice its former distance from the sun; that I understand. Mrs. B. Not so perfectly as you imagine. You are correct as respects the diminution in size, because the attractive force is in the same proportion as the quantity of matter; but were you to remove a planet to double its former distance, it would retain but one-fourth part of its gravitating force ; for attraction de- creases not in proportion to the simple increase of the distance, but as the squares of the distances increase. Caroline. I do not exactly comprehend what is meant by the squares, in this case, although I know very well what is in ge- neral intended by a square. Mrs. B. By the square of a number we mean the product of a number, multiplied by itself; thus two, multiplied by two, is four, which is therefore the square of two; in like manner the square of three, is nine, because three multiplied by three, gives that product. Emily. Then if one planet is three times more distant from the sun than another, it will be attracted with but one-ninth part of the force; and if at four times the distance, with but one-six- teenth, skteen being the square of four? Mrs. B. You are coi rect; the rule is, that the attractive force is in the inverse proportion of the square of the distance. And it is easily demonstrated by the mathematics, that the same is the case with every power that emanates from a centre ; as for ex- ampk, the light from the sun, or from any other luminous body, decreases in its intensity at the same rate. Caroline. Then the more distant planets, move much slower in their orbits; for their projectile force must be proportioned to that of attraction ? But I do not see how this accounts for the motion of the secondary, round the primary planets, in preference to moving round the sun ? Emily. Is it not because the vicinity of the primary planets, renders their attraction stronger than that of the sun ? 3. What two circumstances govern the force with which bodies attract each other ? 4. Were a planet removed to double its former-distance from the sun, what would be the effect upon its attractive force ? 5. Why would it be re- duced to one-fourth ? 6. What is meant by the square of a number, and what examples can you give ? 7. What then would be the effect of removing it to three, or four times its former distance ? 8. How is the rule upon this subject expressed ? 9. Does this apply to any power excepting gravitation ? 10. How is it that a secondary planet revolves round its primary, and is not drawn off by the sun ? 82 OF THE PLANETS. Mrs. B. Exactly so. But since the attraction between bo- dies is mutual, the 'primary planets are also attracted by the satellites which revolve round them. The moon attracts the earth, as well as the earth the moon ; but as the latter is the smaller body, her attraction is proportionally less; therefore, neither the earth revolves round the rnoon, nor the moon round the earth ; but they both revolve round a point, which is their common centre of gravity, and which is as much nearer to the earth than to the moon, as the gravity of the former exceeds that of the latter. Emily. Yes, I recollect your saying, that if two bodies were fastened together by a wire or bar, their common centre of gra- vity would be in the middle of the bar, provided the bodies were of equal weight ; and if they differed in weight, it would be near- er the larger body. If then, the earth and moon had no projec- tile force which prevented their mutual attraction from bringing them together, they would meet at their common centre of gra- vity, i Caroline. The earth then has a great variety of motion, it revolves round the sun, round its own axis, and round the point towards which the moon attracts it. Mrs. B. Just so; anl this is the case with every planet which is attended by satellites. The complicated effect of this variety of motions, produces certain irregularities, which, how- ever, it is not necessary to notice at present, excepting to observe that they eventually correct each other, so that no permanent derangement exists. The planets act on the sun, in the same manner as they are themselves acted on by their satellites ; for attraction, you must remember, is always mutual ; but the gravity of the planets (even when taken collectively) is so trifling compared with that of thfj sun, that were they all placed on die same side of that luminary* they would not cause him to move so much as one-half of his diameter towards them, and the common centre of gravity, would still remain within the body of the sun. The planets do not, therefore, revolve round the centre of the sun, but round a point at a small distance from its centre, about which the sun also re- volves. >VM ^J Emily. I thought the sun had no motion ? Mrs. B. You were mistaken ; for besides that round the com- mon centre of gravity, which I have just mentioned, which is indeed very inconsiderable, he revolves on his axis in about 25 11. What is said respecting the revolution of the moon, and of the earth, round a common centre of gravity? 12. By what law in mechanics is this explained? 13. What motions then has the earth, and are these remarks confined to it alone ? 14. What effect have the planets upon the sun, and what is said of the common centre of gravity of the system OF THE PLANETS. 83 days; this motion is ascertained by observing certain spots which disappear, and reappear regularly at stated times. Caroline. A planet has frequently been pointed out to me in the heavens ; but I could not perceive that its motion diftered from that of the fixed stars, which only appear to move. Mrs. B. The great distance of the planets, renders their apparent motion so slow, that the eye is not sensible of their progress in their orbits, unless we watch them for some consi- derable length of time: but if you notice the nearness of a planet to any particular fixed star, you may in a few nights perceive that it has changed its distance from it, whilst the stars them- selves always retain their relative situations. The most accu- rate idea I can ^ive you of the situation and motion of the pla- nets in their orbits, will be by the examination of this diagram, (plate 7. fig. 1.) representing the solar system, in which you will find every planet, with its orbit delineated. Emily. But the orbits here are all circular, and you said that f;hey were eliptical. The planets appear too, to be moving round the centre of the sun ; whilst you told us that they moved round a point at a little distance from thence. Mrs. B. The orbits of the planets are so nearly circular, and the common centre of gravity of the solar system, so near the centre of the sun, that these deviations are too small to be re- presented. The dimensions of the planets, in their proportion to each other, you will find delineated in fig. 2. Mercury is the planet nearest the sun ; his orbit is consequent- ly contained within ours ; his vicinity to the sun, prevents our frequently seeing him, so that very accurate observations cannot be made upon mercury. He performs his revolution round the sun in about 87 days, which is consequently the length of his year. The time of his rotation on his axis is not known ; his distance from the sun is computed to be 37 millions of miles, and his diameter 3180 miles. The heat of this planet is supposed to be so great, that water cannot exist there but in a state of vapour, and that even quicksilver would be made to boil. Caroline. Oh, what a dreadful climate! Mrs. B. Though we could not live there, it may be perfectly adapted to other beings, destined to inhabit it; or he who created it may have so modified the heat, by provisions of which we arfc ignorant, as to make it habitable even by ourselves. Venus, the next in the order of planets, is 68 millions of miles from the sun : she revolves about her axis in 23 hours and 21 15. What other motion has the sun, and how is it proved? 16. How may you observe the motion of a planet, by means of a fixed star? 17. What is represented by fig;. 1. plate 7 ? 18. Why are the orbits represented as circu- lar? 19. In what order do the planets increase in size as represeuted.fi* 2. plate 7 T 20. What are we told respecting; Mercury? 84 OF THE PLANETS. mirmtes, and goes round the sun in 244 days, 17 hours. The orbit of Venus is also within ours ; during nearly one-half of her course in it, we see her before sun-rise, and she is then called the morning star; in the other part of her orbit she rises later than the sun. Caroline. In that case we cannot see her, for she must rise in the day time ? Mrs. B. True; but when she rises later than the sun, she also sets later; so that we perceive her approaching the horizon after sun-set : she is then called Hesperus, or the evening star. Do you recollect those beautiful lines of Milton Now came still evening on, and twilight gray Had in her sober livery all things clad ; Silence accompanied ; for beast and bird, They to their grassy couch, these to their nests Were slunk, all but the wakeful nightingale; She all night long her amorous descant sung ; Silence was pleas'd ; now glowed the firmament With living sapphires. Hesperus that led The starry host, rode brightest, till the moon Rising in clouded majesty, at length Apparent queen urweil'd her peerless light, And o'er the dark her silver mantle threw. The planet next to Venus is the Earth, of which we shall soon speak at full length. At present I shall only observe that we are 95 millions of miles distant from the sun, that we perform OUT annual revolution in 365 days 5 hours and 49 minutes; and are attended in our course by a single moon. Next follows Mars. He can never come between us and the sun, like Mercury and Venus ; his motion is, however, very per- ceptible, as he may be traced to different situations in the tiea- vens; his distance from the sun is 144 millions of miles ; he turns round his axis in 24 hours and 39 minutes ; and he performs his annual revolution, in about 687 of our days: his diameter is 4120 miles. Then follow four very small planets, Juno, Ceres, Pallas and Vesta, which have been recently discovered, but whose dimensions, and distances from the sun, have not been very accurately ascertained. They are generally called asteroids. Jupiter is next in order: this is the largest of all the planets. He is about 490 millions of miles from the sun, and completes his annual period in nearly 12 of our years. He turns round his axis in about ten hours. He is above 1200 times as big as our earth; his diameter is 86,000 miles. The respective proportions 21. What respecting Venus? 22. When does Venus become a morning, and when an evening star? 23. What is said of the Earth? 24. What of Mars ? 25. What four small planets follow next ? OF THE PLANETS. 85 of the planets cannot, therefore, you see, be conveniently deli- neated m a diagram. He is attended by four moons. The next planet is Saturn, whose distance from the sun, is about 900 millions of miles; his diurnal rotation is performed in 10 hours and a quarter: his annual revolution is nearly SO of our years. His diameter is 79,000 miles. This planet is sur- rounijed by a luminous ring, the nature of which, astronomers are much at a loss to conjecture : he has seven means. Lastly, we observe the planet Herschel, discovered by Dr. Herschel, by whom it was named the Georgium Sid us, and which is attended by six moons. Caroline. How charming it must be in the distant planets, to see several moons shining at the same time ; I think I should like to be an inhabitant of Jupiter or Saturn. Mrs. B. Not long I believe. Consider what extreme cold must prevail in a planet, situated as Saturn is, at nearly ten times the distance at which we are from the sun. Then his numerous moons are far from making so splendid an appearance as ours; for they can reflect only the light which they receive from the sun ; and both light, and heat, decrease in the same ratio or proportion to the distances, as gravity. Can you tell me now how much more light we enjoy than Saturn? Caroline. The square of ten is a hundred ; therefore, Saturn has a hundred times less or to answer your question exactly, we have a hundred times more light and heat, than Saturn this certainly does not increase my wish to become one of the poor wretches who inhabit that planet. Mrs. B. May not the inhabitants of Mercury, with equal plausibility, pity us for the insupportable coldness of our situa- tion; and those of Jupiter and Saturn for our intolerable heat? The Almighty power which created these planets, and placed them in their several orbits, has no doubt peopled them with be- ings, whose bodies are adapted to the various temperatures and elements, in which they are situated. If we judge from the analogy of our own earth, or from that of the great and univer- sal beneficence of Providence, we must conclude this to be the case. Caroline. Are not comets, in some respects similar to planets ? Airs. B. Yes, they are ; for by the reappearance of some of them, at stated times, they are known to revolve round the sun; but ia orbits so extremely eccentric, that they disappear for a great number of years. If they are inhabited, it must be by a species of beings very different, not only from the inhabitants of 26. What is said of Jupiter? 27. What of Saturn? 28. What of Her- pchel ? 29. Why do we conclude that the moons of Saturn afford less light than 'r having acquired a knowledge of these lines: in plate 8. fig. . you will find them all deline- ated : and you must learn them perfectly, if you wish to make any proficiency in astronomy. Caroline. I was taught them at so early an age, that I could not understand their meaning ; and I have often heard you say, that the only use of words, was to convey ideas. Mrs. B. A knowledge of these lines, would have conveyed some idea of the manner in which they were designed to divide the globe into parts; although the use of these divisions, might at that time, have been too difficult for you to understand. Child- hood is the season, when impressions on the memory are most strongly and most easily made : it is the period at which a large stock of terms should be treasured up, the precise application of which we may learn when the understanding is more developed. It is, I think, a very mistaken notion, that children should be taught such things only, as they can perfectly understand. Had you been early made acquainted with the terms which relate to 92 ON THE EARTH. figure and motion, how much it would have facilitated jour pro- gress in natural philosophy. I have been obliged to confine myself to the most common and familiar expressions, in explain- ing the laws of nature; although I am convinced that appropriate and scientific terms, might have conveyed more precise and ac- curate ideas, had you been prepared to understand them. Emily. You may depend upon our carefully learning the names of these lines, Mrs. B.; but before we commit them to memory, will you have the goodness to explain them to us ? Mrs. B. Most willingly. This figure of a globe, or sphere, represents the earth ; the line which passes through its centre, and on which it turns, is called its axis, and the two extremities of the axis A and B, are the poles, distinguished by the names of the north and the south pole. The circle C D, which divides the globe into two equal parts between the poles, and equally distant from them, is called the equator, or equinoctial line; that part of the globe to the north of the equator, is the northern hemisphere; that part to the south of the equator, the southern hemisphere. The small circle E F, which surrounds the north pole, is called the arctic circle; that G H, which surrounds the south pole, the antarctic circle; these are also called polar circles. There are two circles, intermediate between the polar circles and the equator; that to the north I K, called the tropic of Cancer; that to the south, L M, called the tropic of Capricorn. Lastly, this circle, L K, which divides the globe into two equal parts, crossing the equator and extending northward as far as the tro- pic of Cancer, and southward as far as the tropic of Capricorn, is called the ecliptic. The delineation of the ecliptic on the ter- restrial globe is not without danger of conveying false ideas; for the ecliptic (as I have before said) is an imaginary circle in the heavens, passing through the middle of the zodiac, and situated in the plane of the earth's orbit. Caroline. I do not understand the meaning of the plane of the earth's orbit. Mrs. B. A plane, is an even fiat surface. Were you to bend a piece of wire, so as to form a hoop, you might then stretch a piece of cloth, or paper over it, like the head of a drum; this would form a flat surface, which might be called the plane of the hoop. Now the orbit of the earth, is an imaginary circle, sur- rounding the sun, and you can readily imagine a plane extend - 1. What does the line A B, (fig. 2 plate 8.) represent, and what are its ex- tremities called? 2. What is meant by the equator, and how is it situated? 3. There are two hemispheres; how are they named and distinguished? 4. What are the circles near the poles called ? 5. What do the lines I K, and L M, represent ? 6. What circle is in part represented by the line L K ? 7. Against what mistake must you guard respecting this line? 8. What in meant by a plane, and how could one be represented ? ON THE EARTH. 93 ing from one side of this circle to the other, filling up its whole area: such a plane would pass through the centre of tne sun, di- viding it into hemispheres. You may then imagine this plane extended beyond the limits of the earth's orbit, on every side, until it reached those fixed stars which form the signs of the zodiac; passing through the middle of these signs, it would give you the place of that imaginary circle in the heavens, called the ecliptic; which is the sun's apparent path. Let fig. 1. plate 9, represent such a plane, S the sun, E the earth with its orbit, and ABC D the ecliptic passing through the middle of the zodiac. Emily. If the ecliptic relates only to the heavens, why is it described upon the terrestrial globe ? Mrs. B. It is convenient for the demonstration of a variety of problems in the use of the globes; and besides, the obliquity of this circle to the equator is rendered more conspicuous by its being described on the same globe; and the obliquity of the eclip- tic shows how much the earth's axis is inclined to the plane of its orbit. But to return to fig. 2. plate 8. The spaces between the several parallel circles on the terres- trial globe are called zones: that which is comprehended between the tropics is distinguished by the name of the torrid zone; the spaces which extend from the tropics to the polar circles, the north and south temperate zones; and the spaces contained with- in the polar circles, the frigid zones. By the term zone is meant a belt, or girdle, the frigid zones, however, are not belts, but circles, extending 283 degrees from their centres, the poles. The several lines which, you observe to be drawn from one pole to the other, cutting the equator at right angles, are called meri- dians; the number of these is unlimited, as a line passing through any place, directly to the poles, is called the meridian of that place. When any one of these meridians is exactly opposite to the sun, it is mid-day, or twelve o'clock in the day, at all the places situated any where on that meridian; and, at the places situated on the opposite meridian, it is consequently midnight. Emily. To places situated equally distant from these two meridians, it must then be six o'clock. 9. Describe what is intended by the plane of the earth's orbit. 10. Ex- tending this plane to the fixed stars, what circle would it form, and among what particular stars would it be found? 11. What is fig. 1. plate 9, design- ed to represent ? 12. The ecliptic does not properly belong to the earth, for what purpose then is it described on the terrestrial globe? 13. What does the obliquity of the ecliptic to the equator serve to show? '4. Within what limits do you find the torrid zone? 15. What two zones are there between the torrid, and the two frigid zones ? 16. Where are the frigid zones situat- ed? 17. What is meant by ths term zone ; and are the frigid zones properly so called? 18. How do meridian lines extend, and what is meant by the meridian of a place? 19. What is said of the meridian to which the sun is opposite, and where is it then midnight? 94 ON THE EARTH. and that meridian will be proceeding towards the sun. Those circles which divide the globe into two equal parts, such as the equator and the ecliptic, are called greater circles; to distinguish them from those which divide it into two unequal parts, as the tropics, and polar circles, which are called lesser circles. All circles, you know, are imagined to be divided into 560 equal parts, called degrees, and degrees are again divideu into GO equal parts, called minutes. The diameter of a circle is a right line drawn across it, and passing through its centre; were you, for instance, to measure across this round table, that would give you its diameter; but were you to measure all round the edge of it, you would then obtain its circumference. Now Emily, you may tell me exactly how many degrees are contained in a meridian? Emily. A meridian, reaching from one pole to the other, is half a circle, and must therefore contain 180 degrees. Mrs. B. Very well; and what number of degrees are there from the equator to one of the poles? Caroline. The equator being equally distant from either pole, that distance must be half of a meridian, or a quarter of the cir- cumference of a circle, and contain 90 degrees. Mrs. B. Besides the usual division of circles into degrees, the ecliptic is divided into twelve equal parts, called signs, which bear the name of the constellations through which this circle passes in the heavens. The degrees measured on the meridians from the equator, either towards the north, or towards the south, are called degrees of latitude, of which there may be 90; those measured from east to west, either on the equator, or any of the lesser circles, are called degrees of longitude, of which there maybe 180; these lesser circles are also called parallels of lati- tude. Of these parallels there may be any number; a circle drawn from -east to west, at any distance from the equator, will always be parallel to it, and is therefore called a parallel of latitude. 20. What hour is it then, at places exactly half way between these meri- dians? 21. How are greater and lesser circles distinguished? 22. What part of a circle is a degree, and how are these further divided ? 23. What is the diameter, and what the circumference of a circle, and what proportion do they bear 't) each other? 24. What part of a circle is a meridian 25. How many degrees are there between the equator and the poles? 26. Into what parts, besides degrees, is the ecliptic divided ? 27. How are degrees'of latitude measured, and to what number do they extend? 28. On what circles are degrees of longitude measured, and to what number do they extend ? 29. What is a parallel of latitude? ON THE EARTH. 95 Emily. The degrees of longitude must then vary in length, according to the dimensions of the circle on which they are reck- oned; those, for instance, at the polar circles, will be considerably smaller than those at the equator? Mrs. B. Certainly; since the degrees of circles of different dimensions do not vary in number, they must necessarily vary in length. The degrees of latitude, you may observe, never vary in length; for the meridians on which they are reckoned are all of the same dimensions. Emily. And of what length is a degree of latitude? Mrs. B. Sixty geographical miles, which is equal to 69 5 English statute miles; or about one-sixth more than a common mile. Emily. The degrees of longitude at the equator, must then be of the same dimensions, with a degree of latitude. Mrs. B. They would, were the earth a perfect sphere; but it Vs not exactly such, being somewhat protuberant about the equator, and flattened towards the poles. This form proceeds from the superior action of the centrifugal power at the equator, and as this enlarges the circle, it must, in the same proportion, increase the length of the degrees of longitude measured on it. Caroline. I thought I had understood the centrifugal force perfectly, but I do not comprehend its effects in this instance. Mrs. B. You know that the revolution of the earth on its axis, must give to every particle a tendency to fly ott* from the cen- tre, that this tendency is stronger, or weaker, in proportion to the velocity with which the particle moves; now a particle situated near to one of the poles, makes one rotation in the same space of time as a particle at the equator; the latter, therefore, having a much larger circle to describe, travels proportionally faster, consequently the centrifugal force is much stronger at the equa- tor than in the polar regions: it gradually decreases as you leave the equator and approach the poles, at which points the cen- trifugal force, entirely ceases. Supposing, therefore, the earth to have been originally in a fluid sta^e, the particles in the torrid zone would recede much farther from the centre than those in the frigid zones; thus the polar regions would become flattened, and those about the equator elevated. As a large portion of the earth is covered with water, the Creator gave to it the form, denominated an oblate spheroid, otherwise the polar regions would have been without water, 30. Degrees of longitude vary in length; what is the cause of this* 31. What is the length of a degree of latitude, and why do not these vary ? 32. What causes the equator to be somewhat larger than a great circle passing through the poles, and what effect has this on degrees of longitude measured on tho equator ? 33. What is the cause of this form being given to the earth > 96 ON THE EARTH. and those about the equator, would have been buried several miles below the surface of the ocean. Caroline. I did not consider that the particles in the neigh- bourhood of the equator, move with greater velocity than those about the poles; this was the reason 1 could not understand you. Mrs-. B. You must be careful to remember, that those parts of a body which are farthest from the centre of motion, must move with the greatest velocity: the axis of the earth is the centre of its diurnal motion, arid the equatorial regions the parts most dis- tant from the axis. Caroline. My head then moves faster than my feet; and upon the summit of a mountain, we are carried round quicker than in a valley? Mrs. B. Certainly; your head is more distant from the cen- tre of motion than your feet;; the mountain-top than the valley^ and the more distant any part of a body is from the centre of mo- tion, the larger is the circle it will describe, and the greatet therefore must be its velocity. Emily. 1 have been reflecting, that if. the earth is not a per- fect circle' Mrs. B. A sphere you mean, my dear: a circle is a round line, every part of which is equally distant from the centre; a sphere or globe is a round body, the surface of which is every where equally distant from the centre. Emily. If, then, the earth is not a perfect sphere, but pro- minent at the equator, and depressed at the poles, would not a body weigh heavier at the equator than at the poles? For the earth being thicker at the equator, the attraction of gravity per- pendiculany downwards must be stronger. Mrs. B. Your reasoning has some plausibility, but I am sorry to be obliged to add, that it is quite erroneous; for the nearer any part of the surface of a body is to the centre of attrac- tion, the more strono-ly it is attracted; because it is then nearest to the whole mass of attracting matter. In regard to its effects, you might consider the whole power of gravity, as placed at the centre of attraction. Emily. But were you to penetrate deep into the earth, would gravity increase as you approached the centre? Mrs. B. Certainly not; I am referring only to any situation on the surface of the earth. Were you to penetrate into the inte- rior, the attraction of the parts above you, would counteract that of the parts beneath you, and consequently diminish the power of gravity in proportion as you approach the centre; and if you 34. What would have been a consequence of the centrifugal force, had the earth been a perfect sphere ? 35. A body situated at the poles, is at Iracted more forcibly than if placed at the equator, what is the reasou? ON THE EARTH 97 reached that point, being equally attracted by the parts all around you, the effects of gravity would cease, and you would be with- out weight. Emily. Bodies, then, should weigh less at the equator than at the poles, since they are more distant from the centre of gra- vity in the former than in the latter situation? Mrs. B. And this is really the case; but the difference of weight would be scarcely sensible, were it not augmented by ano- ther circumstance. Caroline. And what is this singular circumstance, which seems to disturb the laws of nature? Mrs. B. One that you are well acquainted with, as conduc- ing more to the preservation than the destruction of order, the centrifugal force. This we have just observed to be strongest at the equatoi ; and as it tends to drive bodies from the centre, it is necessarily opposed to, and must lessen the power of gravity, which attracts them towards the centre. We accordingly find that bodies weigh lightest at the equator, where the centrifugal force is greatest; and heaviest at the poles, where this power is least: the weight being diminished at the equator, by both the causes mentioned. Caroline. Has the experiment been made in these different situations? Mrs. B. Louis XIV. of France, sent philosophers both to the equator, and to Lapland, for this purpose: the severity of the cli- mate, and obstruction from the ice, have hitherto rendered every attempt to reach the pole abortive; but the difference of gravity at the equator, and iii Lapland is very perceptible. Caroline. Yet I do hot comprehend how the difference of weight could be ascertained, for if the body under trial decreased in weight, the weight which was opposed to it in the opposite scale mus+ have diminished in the same proportion. For in- stance, if a pound of sugar did not weigh so heavy at the equator as at the poles, the leaden pound which served to weigh it, would not be so heavy either; therefore they would still balance each other, and the different force of gravity could not be ascertained by this means. Mrs. B. Your observation is perfectly, just: the difference of gravity in bodies situated at the poles, and at the equator, r.an- not be ascertained by weighing them; a pendulum was therefore used for that purpose. 36. What effect would be produced upon the gravity of a body, were it placed beneath the surface of the earth, and what supposing it at its centre ? 37. What two circumstances combine, to lessen the weight of a body on th equator? 38. Why cojld not this be proved by weighing a body at the poles, and at the equator ? 98 ON THE EARTH. Caroline. What, the pendulum of a clock? how could that answer the purpose? Mrs. B. A pendulum consists of a line, or rod, to one end of which a weight is attached, and by the other en.d it is suspended to a fixed point, about which it is made to vibrate. When not in motion, a pendulum, obeying the general law of attraction, hangs like a plumb line, perpendicular to the surface of the earth, but if you raise the pendulum, gravity will bring it back to its perpendicular position. It will, however, not remain station- ary there, for the momentum it has acquired during its descent, will impel it onwards, and if unobstructed, it will rise on the opposite side to an equal height; from thence it is brought back by gravity, and is again forced upwards, by the impulse of its momentum. Caroline. If so, the motion of a pendulum would be perpetual, and I thought you said, that there was no perpetual motion on the earth. Mrs. B. The motion of a pendulum is opposed by the resist- ance of the air in which it vibrates, and by the friction of the part Dy which it is suspended: were it possible to remove these obsta- cles, the motion of a pendulum would be perpetual, and its vibra- tions perfectly regular; each being of equal distance, and per- formed in equal times. Emily. That is the natural result of the uniformity of the power which produces these vibrations, for the force ot gravity being always the same, the velocity of the pendulum must conse- quently be uniform. Caroline. No, Emily, you are mistaken; the force is not every where the same, and therefore the effect will not be so either. I have discovered it, Mrs. B.; since the force of gravity is less at the equator than at the poles, the vibrations of the pen- dulum will be slower at the former place than at the latter. Mrs. B. You are perfectly right, Caroline; it was by this means that the difference of gravity was discovered, and the true figure of the earth ascertained. Emily. But how do they contrive to regulate their time in the equatorial and polar regions? for, since in our part of the earth the pendulum cf a clock vibrates exactly once in a second, if it vibrates faster at the poles, and slower at the equator, the inhabitants must regulate their clocks in a manner different from us. Mrs. B. The only alteration required is to lengthen the penc 39. What is a pendulum ? 40. What causes it to vibrate ? 41. Why are not its vibrations perpetual ? 42. Two pendulums of the same length, wiL. not, in different latitudes, perform their vibrations in equal times, what is the cause of this ? 43. To what use has this property of the pendulum been ap plied ? ON THE EARTH. 99 dulum in one case, and to shorten it in the other; for the velocity of the vibrations of a pendulum depends on its length; and when it is said that a pendulum vibrates quicker at the pole than at the equator, it is supposed to be of the same length. A pendulum which vibrates seconds in this latitude is about 39-f inches long. In order to vibrate at the equator in the same space ot time, it must be somewhat shorter; and at the poles, it must be proportionally lengthened. The vibrations of a pendulum, resemble the descent of a body on an inclined plane, and are produced by the same cause; now you must recollect, that the greater the perpendicular height of such a plane, in proportion to its length, the more rapid will be the descent of the body; a short pendulum ascends to a greater height than a larger one, in vibrating a given distance, and of course its descent must be more rapid. I shall now, I think, be able to explain to you the cause of the variation of the seasons, and the difference in the length of the days and nights in those seasons; both effects resulting from the same cause. In moving round the sun, the axis of the earth is not perpen- dicular to the plane of its orbit. Supposing this round table to represent the plane of the earth's orbit, and this little globe, the earth ; through this I have passed a wire, representing its axis and poles. In moving round the table, I do not hold the wire perpendicular to it, but obliquely. Emily. Yes, I understand, the earth does riot go round the sun in an upright position, its axis is slanting or oblique; and, it of course, iorms an angle with a line drawn perpendicular to the plane of the earth's orbit. Mrs. B. All the lines, which you learnt in your last lesson, are delineated on this little globe; you must consider the ecliptic as representing the plane ot the earth's orbit; and the equator, which ciosses the ecliptic in two places, then shows the degree of obliquity of the axis of the earth; which amounts to 2S degrees, very nearly. The points in which the ecliptic intersects the equator, arc called the equinoctial points. But I believe I shall render the effects of the obliquity of the earth's axis clearer to you, by the revolution of the little globe round a candle, which shall represent the sun. (Plate IX. fig. 2.) As I now hold it, at A, you see it in the situation in which it is 44. What change must be made in pendulums situated at the equator and at the poles, to render their vibrations equal? 45. What do the vibrations of a pendulum resemble, and why will it vibrate more rapidly if shortened ? 4*>. In the revolution of the earth round the sun, what is the position of ita axis ? 47. How much is the axis of the earth inclined, and with what lin does it form this angle ? 48. What is represented by fig. 2, plate 9 ? 100 ON THE EARTH. in the midst of summer, or what is called the summer solstice, which is on the lst of June. Emily. You hold the wire awry, I suppose, in order to show that the axis of the earth is not upright? Mrs. B. Yes; in summer, the north pole is inclined towards the sun. In this season, therefore, the northern hemisphere en- joys much more of his rays than the southern. The sun, you see, now shines over the whole of the north frigid zone, and not withstanding the earth's diurnal revolution, which I imitate by twirling- the ball on the wire, it will continue to shine upon it as lon as it remains in this situation, whilst the south frigid zone is at the same time completely in darkness. Caroline. That is very strange; I never before heard that there was constant day or night in any part of the world ! How much happier the inhabitants of the north frigid zone must be than those of the southern; the first enjoy uninterrupted day, whi'e the last are involved in perpetual darkness. Mrs. B. You judge with too much precipitation; examine a little further, and you will find, that the two frigid zones share an equal fate. We shall now make the earth set off from its position in the summer solstice, and carry it round the sun; observe that the pole is always inclined in the same direction, and points to the same spot in the heavens. There is a fixed star situated near that spot, which is hence called the north polar star. Now let us stop the earth at B, and examine it in its present situation; it has gone through one quarter of its orbit, and is arrived at that point at which the ecliptic cuts, or crosses, the equator, arid which is called the autumnal equinox. Emily. The sun now shines from one pole to the other, just as it wcuki constantly do, if the axis of the earth were perpendicu lar to its orbit. Mrs. B. Because the inclination of the axis is now neither towards the sun, nor in the contrary direction; at this period of the year, the days and nights are equal in every part of the earth. But the next step she takes in her orbit, you see, involves the north pole in darkness, whilst it illumines that of the south; this change was gradually preparing as I moved the earth from sum- mer to autumn; the arctic circle, which was at first entirely illumined, began to have short nights, which increased as the earth approached the autumnal equinox; and the instant it pass- ed that point, the long night of the north pole commences, and 49. How is the north pole inclined in the middle of our summer, and what effect has this on the north frigid zone ? 50. In what direction does the north pole always point? 51. What is shown by the position of the earth at B, in the figure ? 52. How does the sun then shine at the poles, and what is the effect on the days and nights ? CF , U ON THE EARTH. 101 the south pole begins to enjoy the light of the sun. We shall now make the earth proceed in its orbit, and you may observe that as it advances, the days shorten and the nights lengthen, throughout the northern hemisphere, until it arrives at the win- ter solstice, on the 21st of December, when the north frigid zone is entirely in darkness, and the southern has uninterrupted day- light. Caroline. Then, after all, the sun which I thought so partial, confers his favours equally on all. Mrs. B. Not so either: the inhabitants of the torrid zone have much more heat than we have, as the sun's rays fall per- pendicularly twice in the course of a year, on every place within the tropics, while they shine more or less obliquely on the rest of the world, and almost horizontally at the poles; for dur- ing their long day of six months, the sun moves round their ho- rizon without either rising or setting; the only observable dif- ereuce, is that it is more elevated by a few degrees at mid-day, than at midnight. Emily. To a person placed in the temperate zone, in the situation in which we are in England, the sun will shine neither so obliquely as it dot-s on the poles, nor vertically as at the equator; but its rays will fall upon him more obliquely in au- tumn, and winter, than in summer. Caroline. And therefore, the inhabitants of the temperate zones, will not have merely one day, and one night, in the year, as happens at the poles, nor will they have equal days, and equal nights, as at the equator; but their days and nights will vary in length, at different times of the year, according as their respec- tive poles incline towards, or from the sun, and the difference will be greater in proportion to their distance from the equator. M^s. B. We shall now follow the earth through the other half of her orbit, and you will observe, that now exactly the same changes take place in the southern hemisphere, as those we have just remarked in the northern. Day commences at the south pole,, when night sets in at the north pole; and in every other part of the southern hemisphere the days are longer than the nights, while, on the contrary, our nights are longer than our days. When the earth arrives at the vernal equinox, D, where the ecliptic again cuts the equator, on the 21st of March, she is situated, with respect to the sun, exactly in the same position, as in the autumnal equinox; and the only difference 53. W'.ien the earth has passed the autumnal equinox, what changes take place at the poles, and also in the whole northern and southern hemispheres ? 54. Why is the heat greatest within the torrid zone ? 55. How does the sun appear at the poles, during the period of day there ? 56. In what will the days and nights differ in the temperate zone, from those at the poles, and ut the equator ? I 2 102 ON THE EARTH. with respect to the earth, is, that it is now autumn in the southern hemisphere, whilst it is spring with us. Caroline. Then the days and nights are again every where equal. Mrs. B. Yes, for the half of the globe which is enlightened, extends exactly from one j>ole to the other, the sun has just risen to the north pole, and is just setting to the south pole ; but in every other part of the globe, the day and night is of twelve hours length; hence the word equinox, which is derived from the Latin, meaning equal night. As our summer advances, the days lengthen in the northern hemisphere, and shorten in the southern, till the earth reaches the summer solstice, when the north frigid zone is entirely illumined, and the southern is in complete darkness; and we have now brought the earth again to the spot from whence we first accompanied her. Emily. This is indeed a most satisfactory explanation of the cause of the different lengths of our days and nights, and of the variation of the seasons; and the more I learn, the more I admire the simplicity of means by which such wonderful effects are produced. Mrs* B. I know not which is most worthy of our admiration, the causes, or the effects of the earth's revolution round the sun. The mind can find no object of contemplation more sublime, than the course of this magnificent globe, impelled by the com- bined powers of projection and attraction, to roll in one invaria- ble course, around the source of light and heat: and what can be more delightful than the beneficent effects of this vivifying power on its attendant planet. It is at once the grand princi- ple which animates and fecundates nature. JZmily. There is one circumstance in which this little ivory globe appears to me to differ from the earth; it is not quite dark on that side of it which is turned from the candle, as is the case with the earth when neither moon nor stars are visible. Mrs. B. This is owing to the light of the candle, being re- flected by the walls of the room, on every part of the globe, con- sequently that side of the globe, on which the candle does not directly shine, is not in total darkness. Now the skies have no walls to reflect the sun's light on that side of our earth which is in darkness. Caroline. I beg your pardon, Mrs. B., I think that the moon, and stars, answer the purpose of walls in reflecting the sun's light to us in the night .57. Trace the earth from the winter solstice to the vernal equinox, and in- form me what changes take place. 58. What takes place at the time of the vernal equinox, and what is meant by the term ? 59. In proceeding from the vernal equinox to the summer solstice, what changes take place ? ON THE EARTH. 103 Mrs. B. Very well, Caroline; that is to sa}, the moon and planets: for the fixed stars, you know, shine by their own light. Emily. You say, that the superior heat of the equatorial parts of the earth, arises from the rays falling perpendicularly on those regions, whilst they fall obliquely on these more north- ern regions; now I do not understand why perpendicular rays should afford more heat than oblique rays. Caroline. You need only hold your hand perpendicularly over the candle, and then hold it sideways obliquely, to be sen- sible of the difference. Emily. I do not doubt the fact, but I wish to have it explained. Mrs. B. You are quite right; if Caroline had not been satis- fied with ascertaining the fact, without understanding it, she would not have brought forward the candle as an illustration; the reason why you feel so much more heat if you hold your hand perpendicularly over the candle, than if you hold it side- ways, is because a stream of heated vapour constantly ascends from the candle^ or any other burning body, which being lighter than the air of the room, does not spread laterally but rises per- pendicularly, and this led you to suppose that the rays were hotter in the latter direction. Had you reflected, you would have discovered that rays issuing from the candle sideways, are no less pei pendicular to your hand when held opposite to them, than the rays which ascend when your hand is held over them. The reason why the sun's rays afford less heat when in an oblique direction, than when perpendicular, is because fewer of them fall upon an equal portion of the earth; this will be under- stood better by referring to plate 10. fig. 1, which represents two equal portions of the sun's rays, shining upon different parts of the earth. Here it is evident, that the same quantity of ravs fall on the space A B, as fill I on the space B C; and as A B is less than B C, the heat and light will be much stronger in the former than in the latter; A B, you see, represents the equatorial regions, where the sun shines perpendicularly; and B C, the temperate and frozen climates, where his rays fall more obliquely. Emily. This accounts not only for the greater heat of the equatorial regions, but for the greater heat of our summers, as the sun shines less obliquely in summer than in winter. Mrs. B. This you will see exemplified in figure 2, in which the earth is represented, as it is situated on the 21st of June, and England receives less oblique, and consequently a greater 60. From what cause arises the superior heat of the equatorial regions ? 61. Why should oblique rays afford less heat than those which are perpendi- cular? 62. How is this explained by fig. 1. plate 10? 63. How do you ac- count for the superior heat of summer, and how is this exemplified in tig. 2 and 3, plate 10 ? 104 ON THE EARTH. number of rays, than at any other season; and figure 3, shows the situation of England on the 21st of December, when the rays of the sun fall most obliquely upon her. But there is also another reason why oblique rays give less heat, than perpendi- cular rays; which is, that they have a greater portion of the at- mosphere to traverse; and though it is true, that the atmosphere if itself a transparent body, freely admitting the passage of the sun's rays, yet it is always loadetl more or less with dense and ' r oggy vapour, which the rays of the sun cannot easily penetrate; therefore, the greater the quantity of atmosphere the sun's rays have to pass through in their way to the earth, the less heat they will retain when they reach it. This will be better understood, by referring to fig. 4. The dotted line round the earth, de- scribes the extent of the atmosphere, and the lines which pro- ceed from the sun to the earth, the passage of two equal por- tions of the sun's rays, to the equatorial and polar regions; the latter you see, from its greater obliquity, passes through a great- er extent of atmosphere. Caroline. And this, no doubt, is the reason why the sun, in the morning and in the evening, gives so much less heat, than at mid -day. Mrs. B. The diminution of heat, morning and evening, is certainly owing to the greater obliquity of the sun's rays; and they are also affected by the other, both the cause, which I have just explained to you; the difficulty of passing through a foggy atmosphere is perhaps more particularly applicable to them, as mist arid vapours are prevalent about the time of sunrise and sunset. But the diminished obliquity of the sun's rays, is not the sole cause of the heat of summer; the length of the dajs greatly conduces to it; for the longer the sun is above the hori- zon, the more heat he will communicate to the earth. Caroline. Both the longest days, and the most perpendicular rays, are on the 21st of June; and yet the greatest heat prevails in July and August. Mrs. B. Those parts of the earth which are once heated, retain the heat for some length of time, and the additional heat they receive, occasions an elevation of temperature, although the days begin to shorten, and the sun's rays to fail more ob- liquely. For the same reason, we have generally more heat at three o'clock in the afternoon, than at twelve, when the sun is on the meridian. 64. What other cause lessens the intensity of oblique rays > 65. How is this explained by fig. 4? 66. What causes conspire to lessen the solar heat in the morning and evening ? 67. The greatest heat of summer is after the solstice, and the greatest heat of the day, after 12 o'clock, although the sun's rays are then most direct, how is this accounted for ? ON THE EARTH. 105 Emily. And pray, have the other planets the same vicissi- tudes of seasons, as the earth? Mrs. B. Some of them more, some less, according as their axes deviate more or less from the perpendicular, to the plane of their orbits. The axis of Jupiter, is nearly perpendicular to the plane of his orbit: the axes of Mars, and of Saturn, are each, in- clined at angles of about sixty degrees; whilst the axis of Venus is believed to be elevated only fifteen or twenty degrees above her orbit; the vicissitudes of her seasons must therefore be con- siderably greater than ours. For further particulars respecting the planets, I shall refer you to Bonnycastle's Introduction t( Astronomy. I have but one more observation to make to you, relative i.o the earth's motion; which is, that although we have but 365 day 1 and nights in the year, she performs 366 complete revolutions OR nor axis, during that time. Caroline. How is that possible? for every complete revolu- tion must bring the same place back to the sun. It is now just twelve o'clock, the sun is, therefore, on oui meridian; in twen- ty-four hours will it not have returned to our meridian again, and will not the earth have made a complete rotation on its axis? Mrs. B. If the earth had no progressive motion in its orbit whilst it revolves on its' axis, this would be the case; but as it advances almost a degree westward in its orbit, in the same time that it completes a revolution eastward on its axis, it must re- volve nearly one degree more in order to bring the same meri- dian back to the sun. Caroline. Oh, yes ! it will require as much more of a second revolution to bring the same meridian back to the sun, as is equal to the space the earth has advanced in her orbit; that is, nearly a degree; this difference is, however, very little. Mrs. B. These small daily portions of rotation, are each equal to the three hundred and sixty -fifth part of a circle, which at tbe end of the year amounts to one complete rotation. Emily. That is extremely curious. If the earth then, had no other than its diurnal motion, we should have 366 days in the year. Mrs. B. We should have 366 days in the same period of time that we now have 365; but if we did not revolve round the sun, we should have no natural means of computing years. You will be surprised to hear, that if time is calculated by the 68. Is there any change of seasons in the other planets? 69. What is said respecting the axes of Jupiter, of Mars, and of Saturn? 70. In 365 days, how many times does the earth revolve on its axis? 71. How is this ac- counted for ? 72. Do the fixed stars require the same time as the sun, to r* turn to the same meridian I 106 ON THE EARTH. stars instead of the sun, the irregularity which we have just no- ticed does not occur, and that one complete rotation of the earth on its axis, brings the same meridian back to any fixed star. Emily. That seems quite unaccountable; for the earth ad- vances in her orbit with regard to the fixed stars, the same as with regard to the sun. Mrs. B. True, but then the distance of the fixed stars is so immense, that our solar system is in comparison to it but a spot, and the whole extent of the earth's orbit but a point; therefore, whether the earth remain stationary, or whether it revolved in its orbit during its rotation on its axis, no sensible difference would be produced with regard to the fixed stars. One com- plete revolution brings the same meridian back to the same fixed star; hence the fixed stars appear to go round the earth in a shorter time than the sun by three minutes fifty-six seconds of time. Caroline. These three minutes fifty-six seconds is the time which the earth takes to perform the additional three hundred and sixty -fifth part of the circle, in order to bring the same me- ridian back to the sun. Mrs. B. Precisely. Hence the stars gain every day three minutes fifty-six seconds on the sun, which makes them rise tha* portion of time earlier every day. When time is calculated by the stars it is called sidereal time; when by the sun, solar, or apparent time. Caroline. Then a sidereal day is three minutes fifty-six se conds shorter, than a solar day of twenty -four hours. Mrs. B. I must also explain to you what is meant by a side real year. The common year, called the solar or tropical year, contain- ing 365 days, five hours, forty-eight minutes and fifty-two se- conds, is measured from the time the sun sets out from one of the equinoxes, or solstices, till it returns to the same again; but this year is completed, before the earth has finished one entire revolu- tion in its orbit. Emily. I thought that the earth performed one complete re- volution in its orbit, every year; what is the reason of this varia- tion? Mrs. B. It is owing to the spheroidal figure of the earth. The elevation about the equator produces much the same effect as if a similar mass of matter, collected in the form of a moon, revolved round the equator. When this moon acted on the earth, in conjunction with, or in opposition to the sun, variations 73. How is this accounted for ? 74. What is meant by the solar and the idereal day . ? 75. What is the difference in time between them ? 76. What is the length of the tropical year ? ON THE EARTH. 107 in the earfn's motion would be occasioned, and these variations produce wnat is called the precession of the equinoxes. Emily. What does that mean? I thought the equinoctial points, wG'-e fixed points in the heavens, in which the equator ruts the ecliptic. Mrs. B. These points are not quite fixed, but have an appa- rently retrogn.de motion, among the signs of the zodiac; that is to say, instead of being at every revolution in the same place, they move backwards. Thus if the vernal equinox is at A, (fig. 1. plate XL) the autumnal one, will be at B, instead of C, and the following vernal equinox, at D, instead of at A, as would be the case if the equinoxes were stationary, at opposite points of the earth's orbit.. Caroline. So that when the earth moves from one equinox to the other, though it takes half a year to perform the journey, it has not travelled through half its orbit. Mrs. B. And, consequently, when it returns again to the first equinox, it has not completed the whole of its orbit. In order to ascertain when the -earth has performed an entire revo- lution in its orbit, we must observe when the sun returns in con- junction with any fixed star; and this is called a sidereal year. Supposing a fixed star situated at E, (fig. 1. plate XI.) the sun would not appear in conjunction with it, till the earth had return- ed to A, when it would have completed its orbit. Emily. And how much longer is the sidereal, than the solar year? Mrs. B. Only twenty minutes; so that the variation of the equinoctial points is very inconsiderable. I have given them a greater extent in the figure, in order to render them sensible. In regard to time, I must further add, that the earth's diurnal motion on an inclined axis, together with its annual revolution in an elliptic orbit, occasions so much complication in its motion, as to produce many irregularities; therefore the true time can- not be measured by the apparent place of the sun. A perfectly correct clock, would in some parts of the year be before the sun, and in other parts after it. There are but four periods in which the sun and a perfect clock would agree, which is the 15th of April, the 16th of June, the 23d of August, and the 24th of De- cember. 77. The solar year is completed before the earth has made a complete revo- lution in its orbit, by what is this caused ? 78. What is this called, and what is represented respecting it by fig. 1, plate 11 ? 79. By what means can we ascertain the period of a complete revolution of the earth in its orbit, as illus- tr; ted by the fixed star E, in fig. 1 ? 80. What difference is there in the length of the solar and sidereal year? 81. Why can we not always ascertain the true time by the apparent place of the sun? 108 ON THE MOOX. Emily. And is there any considerable difference between solar time, and true time? Mrs. B. The greatest difference amounts to between fifteen and sixteen minutes. Tables of equation are constructed for the purpose of pointing out, arid correcting these differences between solar time and equal or mean time, which is the denomination given by astronomers, to true time. 82. What would be the greatest difference between solar, and true time, as indicated by a perfect clock ? CONVERSATION IX. ON THE MOON. OF THE MOON'S MOTION. PHASES OP THE MOON. ECLIPSES OF TH* MOOX. ECLIPSES OF JUPITER'S MOONS. OF LATITUDE AJVD LONGI- TUDE. OF THE TRANSITS OF THE INFERIOR PLANETS. OF THE TIDES. MRS. B. WE shall, to-day, confine our attention to the moon, which offers many interesting phenomena. The moon revolves round the earth in the space of about twenty-nine days and a half; in an orbit, the plane of which is inclined upwards of five degrees to that of the earth; she ac- companies us in our revolution round the sun. Emily. Her motion then must be of a complicated nature; for as the earth is not stationary, but advances in her orbit, whilst the moon goes round her, the moon, in passing round the sun, must proceed in a sort of scolloped circle. Mrs. B. That is true; and there are also other circumstances which interfere with the simplicity, and regularity of the moon's motion, but which are too intricate for you to understand at present. The moon always presents the same face to us, by which it is evident that she turns but once upon her axis, white she per- 1. In what time does the moon revolve round the earth ? what is the incli- nation of her orbit? and how doe? she accompany the earth? 2. As f"i moon revolves lound the earth, and also accompanies it in its annual revo- lution, in what form would you draw the moon's orbit ? ON THE MOON. 109 Forms a revolution round the earth; so that the inhabitants of the moon have but one day, and one night, in the course of a lunar month. Caroline. We afford them, however, the advantage of a magnificent moon to enlighten their long nights. Mrs. B. That advantage is put partial; for since we always see the same hemisphere of the moon, the inhabitants of that hemisphere alone, can perceive us. Caroline. One half of the moon then enjoys our light, while the other half has constantly nights of darkness. If there are any astronomers in those regions, they would doubtless be tempted to visit the other hemisphere, in order to behold so grand a luminary as we must appear to them. But, pray, do they see the earth under all the changes, which the moon exhi- bits to us? Mrs.B. Exactly so. These changes are called the phases of the moon, and require some explanation. In fig. *2, plate 11, let us say, that S represents the sun, R the earth, and A B C I) E F G H, the moon, in different parts of her orbit. When the moon is at A, her dark side being turned towards the earth, we shall not see her as at a; but her disappearance is of very short duration, and as she advances in her orbit, we perceive her un- der the form of a new moon: when she has gone through one eighth of her orbit at B, one quarter of her enlightened hemis- phere will be turned towards the earth, and she will then appear domed as at b; when she has performed one quarter of her orbit, she shows us one half of her enlightened side, as at e, and this is called her first quarter; at d she is said to be gibbous, and at e the whole of the enlightened side appears to us, and the moon is at full. As she proceeds in her orbit, she becomes again gib- bous, and her enlightened hemisphere turns gradually away from us, until she arrives at G, which is her third quarter: proceeding thence she completes her orbit and disappears, and then again resumes her form of a new moon, and passes successively, through the same changes. When the moor, is new, she is said to be in conjunction with the sun, as they are then both in the same direction from tl.? earth; at the time of full moon, she is said to be in opposition* because she and the sun, are at opposite sides of the earth; at the time of her first and third quarters, she is said to be in her quad- 3. What causes the moon always to present the same face to the earth, and what must be the length of a day and night to its inhabitants ? 4. Can the earth be seen from every part of the moon, and will it always exhibit the same appearance ? 5. What are the changes of the moon called ? 6. flow are these changes explained by fig. 2. plate 11? 7. What is msunt by her first quarter? 8. What by her being horned, and her being gibbous' 9. What by her being full? 10. What by her third quarter f K MO ON THE MOON. ratures, because she is then one-fourth of a circle, or 90, from her conjunction, or the period of new moon. Emily. Are not the eclipses of the sun produced by the moon passing between the sun and the earth? Mrs. 13. Yes; when the moon passes between the sun and the earth, she intercepts his rajs, or, in other words, casts a shadow on the earth, then the sun is eclipsed, and daylight gives place to darkness, while the moon's shadow is passing over us. When, on the contrary, the earth is between the sun and the moon, it is we who intercept the sun's rays, and cast a shadow on the moon; she is then said to be eclipsed, and disappears from our view. Emily. But as the moon goes round the earth every month, she must be, once during that time, between the earth and the sun; and the earth must likewise be once between the sun and the moon, and yet we have not a solar and a lunar eclipse every month? Mis. B. I have already informed you, that the orbits of the earfti and moon are not in the same plane, but cross or intersect each other; and the moon generally passes either above or below that of the earth, when she is in conjunction with the sun, and does not therefore intercept its rays, and produce an eclipse; for this can take place only v/hen the moon is in, or near her nodes, which is the name given to those two points in which her orbit crosses that of the earth; eclipses cannot happen at anj other time, because it is then only, that they are both in a righ\ line with the sun. Emily. And a partial eclipse of the moon takes nlace, I sup- pose, when, in passing by the earth, she is not sufficiently above or below the shadow, to escape it entirely? Mrs. B. Yes, one edge of her disk then dips into the shadow, and is eclipsed; but as the earth is larger than the moon, when eclipses happen precisely at the nodes, they are not only total, but last for upwards of three hours. A total eclipse of the sun rarely occurs, and when it happens, the total darkness is confined to one particular part of the earth, the diameter of the shadow not exceeding 180 miles; evidently showing that the moon is smaller than the sun, since she cannot 11. What is meant by her conjunction ? what by her being in opposition? -what by her quadratures? 12. By what are eclipses of the sun caused? 13. What causes eclipses of the moon? 14. What is meant by the moon's nodes? 15. Why do not eclipses happen at every new and full moon? 16. What causes partial eclipses of the moon? 17. When the moon is ex- actly in one of her nodes, what length of time will she be eclipsed ? 18. Are total eclipses of the sun frequent, and when they bappen what is their extent? ON THE MOON. Ill entirely hide it from the earth. In fig. 1, plate 12, you will find a solar eclipse described; S is the sun, M the moon, and E the earth; and the moon's shadow, you see, is not large enough to cover the earth. The lunar eclipses, on the contrary, are visible from every part of the earth, where the moon is above the horizon; and we discover, by the length of time which the moon is passing through the earth's shadow, that it would be sufficient to eclipse her totally, were she many times her actual size; it follows, therefore, that the earth is much larger than the moon. In fig. 2, S represents the sun, which pours forth rays of light in straight lines, in every direction. E is the earth, and M the moon. Now a ray of light coming from one extremity of the ftun's disk, in the direction A B. will meet another, coining from the opposite extremity, in the direction C B; the shadow of the earth cannot therefore extend beyond B; as the sun is larger than the earth, the shadow of the latter is conical, or in the figure of a sugar loaf; it gradually diminishes, and is much smallei than the earth where the moon passes through it, and yet we find the moon to be, not only totally eclipsed, but to remain for a considerable length of time in darkness, and hence we are enabled to ascertain its real dimensions. Emily. When the moon eclipses the sun to us, we must be eclipsed to the moon? Mrs. B. Certainly; for if the moon intercepts the sun's rays, and casts a shadow on us, we must necessarily disappear to the moon, but only partially, as in fig. 1. Caroline. There must be a great number of eclipses in the distant planets, which have so many moons? Mrs. B. Yes, few days pass without an eclipse taking place; for among the number of satellites, one or the other of them are continually passing either between their primary and the sun; or between the planet, and each other. Astronomers are so well acquainted with the motion of the planets, and their satellites, that they have calculated not only me eclipses of our moon, but those of Jupiter, with such perfect accuracy, that it has afforded a means of ascertaining the longitude. Caroline. But is it not very easy to find both the latitude and longitude of any place by a map or globe? Mrs. B. If you know where you are situated, there is no difficulty in ascertaining the latitude or longitude of the place, by referring to a map; but supposing that you had been a length 19. What does this prove respecting the size of the moon? 20. What is shown in fig. 1, plate 12? 21. How are lunar eclipses visible, and what is proved by their duration? 22. What is illustrated by fig. 2, plate 12? 23. What remark is made respecting those planets which have several moons ? 24. What use is made of the eclipses of the satellites of Jupiter/ ON THE MOON. of time at sea, interrupted in your course by storms, a maji would afford you very little assistance in discovering where you were. Caroline. Under such circumstances, I confess I should be equally at a loss to discover either latitude, or longitude. Mrs. B. The latitude is usually found by taking the alti- tude of the sun at mid-day; that is to say, the number of degrees that it is elevated above the horizon, for the sun appears more elevated as we approach the equator, and less as we recede from it. Caroline. But unless you can see the sun, how can you take its altitude? Mrs. B. When it is too cloudy to see the sun, the latitude i* sometimes found at night, by the polar star; the north pole of the earth, points constantly towards one particular part of the hea- vens, 1*1 which a star is situated, called the Polar star: this star is visible on clear nights, from every part of the northern hemis- phere; the altitude of ihe polar star, is therefore the same number of degrees, as that of the pole; the latitude may also be deter- mined by observations made on any of the fixed stars: the situa- tion therefore of a vessel at sea, with regard to north and south, is easily ascertained. The difficulty is, respecting east and west, that is to say, its longitude. As we have no eastern poles from which we can reckon our distance, some particular spot, or line must be fixed upon for that purpose. The English, reckon from the meridian of Greenwich, where the royal observatory is situ- ated; in French maps, you will find that the longitude is reckon- ed from the meridian of Paris. The rotation of the earth on its axis in 24 hours from west to east, occasions, you know, an apparent motion of the sun and Stars in a contrary direction, and the sun appears to go round the earth in the space of 24 hours, passing over fifteen decrees, or a twenty-fourth part of the earth's circumference every nour; therefore, when it is twelve o'clock in London, it is one o'clock in any place situated fifteen degrees to the east of London, as the sun nrist have passed the meridian of that place, an hour be- fore he reaches that of London. For the same reason it is eleven o'clock in any place situated fifteen degrees to the west of London, as the sun will not come to that meridian till an hour later. If then the captain of a vessel at sea, could know precisely what was the hour at London, he could, by looking at his watch, 25. How is the latitude of a place usually found." 26. By what other mean3 may latitude be found? 27. From wnat is longitude reckoned? 2JJ. How does the rotation of the earth upon its axis, govern the time at different places? \. ON THE MOON. 113 and comparing it with the hour at the*spot in which he was, as- certain the longitude. Emily. But if he had not altered his watch, since he sailed from London, it would indicate the hour it then was in London. Mrs. B. True; but in order to know the hour of the day ,it the sp u in which he is, the captain of a vessel regulates his watch by the sun when it reaches the meridian. Emily. Then if he had two watches, he might keep one re- gulated daily, and leave the other unaltered ; the former would indicate the hour of the place in which he was situated, and the latter the hour at London; and by comparing them together, he would be able to calculate his longitude. Mrs. B. You have discovered, Emily, a mode of finding the longitude, which I have the pleasure to tell you, is universally adopted: watches of a superior construction, called chronome- ters, or time-keepers, are used for this purpose, and are now made with such accuracy, as not to vary more than four or five seconds in a whole year; but the best watches are liable to im- perfections, and should the time-keeper go too fast or too slow, there would be no means of ascertaining the error; implicit re-> liance, cannot consequently be placed upon them. Recourse, therefore, is sometimes had to the eclipses of Jupi- ter's satellites. A table is made, of the precise time at which the several moons are eclipsed to a spectator at London; when they appear eclipsed to a spectator in any other spot, he may, by consulting the table, know what is the hour at London; for the eclipse is visible at the same moment, from whatever place on the earth it is seen. He has then only to look at his watch, which he regulates by the sun, and which therefore points out the hour of the place in which, he is, and by observing the difference of time there, and at London, he may immediately determine his longi- tude. Let us suppose, that a certain moon of Jupiter is always eclipsed at six o'clock in the evening; and that a man at sea consults his watch, and finds that it is ten o'clock at night, where he is situated, at the moment the eclipse takes place, what will be his longitude? Emily. That is four hours later than in London: four times fifteen degrees, make 60; he would, therefore, be sixty degrees east of London, for the sun must have passed his meridian oefore it reaches that of London. Mrs. B. For this reason the hour is always later than in 29. What two circumstances, if known, will enable you to find your longi- tude from a given place ? 30. By what means may a captain find the time at London, and in the place where his ship may be? 31. How may the eclipses of Jupiter's satellites be used to find the longitude? 32. Give an example. K 2 114 ON THE MOON. London, when the place is east longitude, and earlier when it is west longitude. Thus the longitude can be ascertained when ever the eclipses of Jupiter's moons are visible. Caroline. But do not the primary planets, sometimes eclipse the sun from each other, as they pass round in their orbits? Mrs. B. They must of course sometimes pass between each other and the sun, but as their shadows never reach each other, they hide so little of his light, that the term eclipse is not in this case used; this phenomenon is called a transit. The primary planets do not any of them revolve in the same plane, and the times of their revolution round the sun is considerable, it therefore but rarely happens that they are at the same time, in conjunction with the sun, and in their nodes. It is evident also, that a planet must be inferior (that is within the orbit of another) in order to its apparently passing over the disk of the sun. Mercury, and Venus, have sometimes passed in a right line between us, and the sun, but being at so great a distance from us, rheir shadows did not extend so far as the earth; no darkness was therefore produced on any part of our globe; but the planet appeared like a small black spot, passing across the sun's disk. It was by the last transit of Venus, that astronomers were ena- bled to calculate, with some degree ot accuracy, the distance of the earth from the sun, and the dimensions of the latter. Emily. I havo heard that the tides are affected by the moon, but I cannot conceive what influence it can have on them. Mrs. B. They are produced by the moon's attraction, which draws up the waters of that part of the ocean over which the moon passes, so as to cause it to stand considerably higher than the surrounding parts. Caroline. Does attraction act on water more powerfully than on land? I should have thought it would have been just the con- trarv, for land is certainly a more dense body than water? Airs. B. Tides do not arise from water being more strongly attracted than land, for this certainly is not the case; but the cohesion of fluids, being much less than that of solid bodies, they more easily yield to the power of gravity; in consequence ol which, the waters immediately below the moon, are drawn up by it, producing a full tide, or what is commonly called, high water, at the spot where it happens. So far, the theory of the tides is not difficult to understand. Caroline. On the contrary, nothing can be more simple; the waters, in order to rise up under the moon, must draw the wa 33. How will you know whether the longitude is east or west ? 34. What is mennt by the '.ransit of a planet? 35. Why can we see transits of Venut und Mercury only ? 36. By what are tides caused > 37. Why is not a siini lar effect produced on the land? ON THE MOON. 115 ters from the opposite side of the globe, and occasion ebb-tide, or low water, in those parts. Mrs. B. You draw your conclusion rather too hastily, my dear; tor according to your theory, we should have full tide only once in about twenty-four hours, that is, every time that we were below the moon, while we find that in this time we have two tides, and that it is high water with us, and with our antipodes, at the same time. Caroline. Yet it must be impossible for the moon to attract the sea in opposite parts of the globe, and in opposite directions, at the same time. Mrs. B. This opposite tide, is rather more difficult to explain, than that which is immediately beneath the moon; with a little at- tention, however, I hope I shall be able to make you understand the explanation which has been given of it, by astronomers. It must be confessed, hovever, thav the theory upon this subject, is attended with some difficulties. You recollect that the earth and the moon mutually attract each other, but do you suppose that every part of the earth is equally attracted by the moon? Emily. Certainly not; you have taught us that the force of attraction decreases, with the increase of distance, and therefore that part of the earth which is farthest from the moon, must be attracted less powerfully, than that to which she is nearest. Mrs. B. This fact will aid us in the explanation which I am about to give to you In order to render the question more simple, let us suppose the earth to be every where covered by the ocean, as represented in (tig. 3. pi. 12.) M is the moon, A B C D the earth. Now the waters on the surface of the earth, about A, being more strongly attracted than any other part, will be elevated: the at- traction of the moon at B and C being; less, and at D least of all. The high tide at A, is accounted for from the direct at- traction of the moon; to produce this the waters are drawn from B and C, where it will consequently be low water. At D, the attraction of the moon being considerably decreased, the waters are left relatively high, which height is increased, by the centri- fugal force of the earth being greater at D than at A, in conse- quence of its greater distance from the common centre of gra- vity X, between the earth and the moon. Emily. The tide A, then, is produced by the moon's attrac- tion, and the tide D, is produced by the centrifugal force, and 38. In what, two parts of the world is it high water at the same time ? 39. What circumstances respecting the decrease of attraction are taken into ac- count, in explaining the tides ? 40. How are the high tides at A and D and the low ones at B and C, in fig. 3. pi. 12, accounted for? 116 ON THE MOON. increased by the feebleness of the moon's attraction, in those parts. Caroline. And when it is high water at A and D, it is low water at B and C : now I think I comprehend the nature of the tides, though I confess it is not quite so easy as I at first thought. But, Mrs. B., why does not the sun produce tides, as well as the moon; for its attraction is greater than that of the moon? Mrs. B. It would be at an equal distance, but our vicinity to the moon, makes her influence more powerful. The sun has, however, a considerable effect on the tides, and increases or di- minishes them as it acts in conjunction with, or in opposition to the moon. Emily. I do not quite understand that. Mrs. B. The moon is a month in going round the earth; twice during that time, therefore, at full and at change, she is in the same direction as the sun; both, then act in conjunction on the earth, and produce very great tides, called spring tides, as re- presented in fig. 4, at A and B; but when the moon is at the in- termediate parts of her orbit, that is in her quadratures, the sun, instead of affording assistance, weakens her power, by acting in opposition to it; and smaller tides are produced, called neap tides, as represented at M, in fig. 5. Emily. 1 have often observed the difference of these tides, when I nave been at the sea side. But since attraction is mutual between the moon and the earth, we must produce tides in the moon; and these must be more considerable in proportion as our planet is larger. And yet tho moon does not appear of an oval form. Mrs. B. You must recollect, that in order to render the e? - planation of the tides clearer, we suppose the whole surface at the earth to be covered with the ocean; but that is not really the case, either with the earth or the moon, and the land which inter- sects the water, destroys the regularity of the effect. Thus, in flowing up rivers, in passing round points of land, and into bays and inlets, the water is obstructed, and high water must happen much later, than would otherwise be the case. Caroline. True; we may, however, be certain that whenever it is high water, the moon is immediately over our heads. Mrs. B. Not so either; for as a similar effect is produced on that part of the globe immediately beneath the moon, and on that part most distant from it, it cannot be over the heads of the in- 41. Has the sun any influence on the tides, and why is it less than that of the moon ? 42. What is meant by spring tides, and how are they produced ? 43. What by neap tides, and how are they caused? 44. What circumsUirce& affect the time of the tide in rivers, bays, &c. ? ON THE MOON. habitants of both those situations, at the same time. Besides, as the orbit of the moon is very nearly parallel to that of the earth, she is never vertical, but to the inhabitants of the torrid zone. Caroline. In the torrid zone, then, I hope you will grant that the moon is immediately over, or opposite the spots where it is high water? Mrs. B. I cannot even admit that; for the ocean naturally partaking of the earth's motion, in its rotation from west to east, the moon, in forming a tide, has to contend against the eastern motion of the waves. All matter, you know, by its inertia, makes some resistance to a change of state; the waters, there- fore, do not readily yield to the attraction of the moon, and the effect of her influence is not complete, till three hours after she has passed the meridian, where it is full tide. When a body is impelled by any force, its motion may con- tinue, after the impelling force ceases to act: this is the case with all projectiles. A stone thrown from the hand, continues its motion fora length of time, proportioned to the force given to it: there is a perfect analogy between this effect, and the con- tinued rise of the water, after the moon has passed the meridian at any particular place. Emily. Pray what is the reason that the tide is three-quar- ters of an hour later every day? Mrs. B. Because it is twenty -four hours and three-quarters before the same meridian, on our globe, returns beneath the moon. The earth revolves on its axis in about twenty-four hours; if the moon were stationarv, therefore, the same part of our globe would, everv twenty-four hours, return beneath the moon; but as during our daily revolution, the moon advances in her orbit, the earth must make more than a complete rotation, in order to bring the same meridian opposite the moon: we are three-quarters of an hour in overtaking her. The tides, therefore, are retarded, for the same reason that the moon rises later by three-quarters of an hour, every day. We have now, I think, concluded the observations I had to make to you on the subject of astronomy; at our next interview, 1 shall attempt to explain to you the elements of hydrostatics. 45. Why in the open ocean, is it'toigh water, some hours after the moon has passed the meridian? 46. Why are the tides three-quarters of an hour later every day? CONVERSATION X. ON THE MECHANICAL PROPERTIES OF FLUIDS. DEFINITION OF A FLUID. DISTINCTION BETWEEN FLUIDS AND LIttUID8- OF NON-ELASTIC FLUIBS. SCARCELY SUSCEPTIBLE OF COMPRESSION, OF THE COHESION OF FLUIDS. OF THEIR GRAVITATION. OF THEIR EaUlLIBRIUM. OF THEIR PRESSURE. OF SPECIFIC GRAVITY. OE THE SPECIFIC GRAVITY OF BODIES HEAVIER THAN WATER. OF THOSE OF THE SAME WEIGHT AS WATER. OF THOSE LIGHTER THAN WA TER. OE THE SPECIFIC GRAVITY OF FLUIDS, MRS. B. WE have hitherto confined our attention to the mechanical properties of solid bodies, which have been illustrated, and, I nope, thoroughly impressed upon your memory, by the conver- sations we have subsequently had, on astronomy. It will now be necessary for me to give you some account of the mechanical properties of fluids a science which, when applied to liquids, is divided into two parts, hydrostatics and hydraulics. Hydro- statics, treats of the weight and pressure of fluids; and hydrau- lics, of the motion of fluids, and the effects produced by this motion. A fluid is a substance which yields to the slightest pressure. If you dip your hand into a basin of water, you arc scarcely sensible of meeting with any resistance. Emuy. The attraction of cohesion is then, I suppose, less powerful in fluids, than in solids? Mrs. If. Yes; fluids, generally speaking, are bodies of less density than solids. From the slight cohesion, of the particles of fluids, and the facility with which they slide over each other, it is inferred, that they have but a slight attraction for each other, and that this attraction is equal, in every position of their particles, and therefore produces no resistance to a perfect free- dom of motion among themselves. Caroline. Pray what is the distinction between a fluid and a liquid ? Mrs. B. Liquids comprehend only one class of fluids. There 1. What are the two divisions of the science which treats of the mechanical properties of liquids ? 2. Of what do hydrostatics and hydraulics treat ? 3. What is a fluid defined to be ? 4. From what is fluidity supposed to arise ? 5. Into what two classes are fluids divided . ? MECHANICAL PROPERTIES OF FLUIDS. 119 is another class, distinguished by the name of elastic fluids, or gases, which comprehends the air of the atmosphere, ana all the various kinds of air with which you will become ac- quainted, when you study chemistry. Their mechanical pro- perties we shall examine hereafter, and confine our attention this morning, to those of liquids, or non-elastic fluids. Water, and liquids in general, are scarcely susceptible of being compressed, or squeezed into a smaller space, than that w ? .\rh they naturally occupy. Such, however, is the extreme minuteness of their particles, that by strong compression, they sometimes force their wav through the pores of the substance which confines them. This was shown by a celebrated experi- ment, made at Florence many years ago. A hollow globe of gold was filled with water, and on its being submitted to great pressure, the water was seen to exude through the pores of the sold, which it covered with a fine dew. Many philosophers, however, think that this experiment is too much relied upon, as it does not appear that it has ever been repeated; it is possible, therefore, that there may have been some source of error, which was not discovered by the experimenters. Fluids, appear to gravitate more freely, than solid bodies; for the strong cohesive attraction of the particles of the latter, in some measure coun- teracts the effect of gravity. In this table, for instance, the cohesion of the particles of wood, enables four slender legs to support a considerable weight. Were the cohesion destroyed, or, in other words, the wood converted into a fluid, no support could be afforded by the legs, for the particles no longer coher- ing together, each would press separately and independently, and would be brought to a level with the surface of the earth. Emily. This want of cohesion is then the reason why fluids can never be formed into figures, or maintained in heaps; for though it is true the wind raises water into w r aves, they are im- mediately afterwards destroyed by gravity, and water always finds its level. Mrs. B. Do you understand what is meant by the level, or equilibrium of fluids? Emily. I believe I do, though I feel rather at a loss to ex- plain it, Is not a fluid level when its surface is smooth and llat, as is the case with all fluids, when in a state of rest? Mrs. B. Smooth, if you please, but not flat; for the defini- tion of the equilibrium of a fluid is, that every part of the sur- face is equally distant from the point to which they gravitate, that is to say, from the centre of the earth; hence the surface 6. What is said of the incompressibility of liquids, and what experiment 13 related? 7. Ought this experiment to be considered as conclusive ? 8. Why do fluids appear to gravitate more freely than solids . p 120 MECHANICAL PROPERTIES OF FLUIDS. of all fluids must be spherical, not flat, since they will partake of the spherical form of the globe. This is very evident in large bodies of water, such as the ocean, but the sphericity of small bodies of water, is so trifling, that their surfaces appear flat. This level, or equilibrium of fluids, is the natural result f their particles gravitating independently of each other; for when any particle of a fluid, accidentally finds itself elevated above the rest, it is attracted down to the level of the surface of the fluid, and the readiness with which fluids yield to the slightest impression, will enable the particle bj its'weight, to penetrate the surface of the fluid, arid mix with it. Caroline. But I have seen a drop of oil, float on the surface of water, without mixing with it. Mrs. J3. They do not mix, because their particles repel each other, and the oil rises to the surface, because oil is a lighter liquid than water. If you were to pour water over it, the oil would still rise, being forced up by the superior gravity of the water. Here is an instrument called a spirit-level, (fig. 1, plate 13.) which is constructed upon the principle of the equilibrium of fluids. It consists of a short tube A B, clos?d at both ends, and containing a little water, or more commonly some spirits: it is so nearly filled, as to leave only a small bubble of air; when the tube is perfectly horizontal, this bubble will occupy the middle of it, but when not perfectly horizontal, the water runs to the lower, and the bubblo of air or spirit rises to the upper end; by this instrument, the level of any situation, to which we apply it, may be ascertained. From the strong cohesion of their particles, you may there- fore consider solid bodies as gravitating in masses, while everj particle of a fluid may be considered as separate, and gravi- tating independently of each other. Hence the resistance of a fluid, is considerably less, than that of a solid body; for the resistance of the particles, acting separately, is more easily overcome. Emily. A body of water, in falling, does certainly less injury than a solid body of the same weight. Mrs. B. The particles of fluids, acting thus independent- ly, press agamst each other in every direction, not only down- wards, but upwards, and laterally or sideways; and in conse- quence of this equality of pressure, every particle remains at rest, in the fluid. If you agitate the fluid, you disturb this 9. When is a fluid said to be in equilibrium? 10. What is there in the nature of a fluid, which causes it to seek this level ? 11. What circumstances occasion oil to float upon water? 12. What is the nature and use of the in- itrument represented in fig. 1, plate 13 ? 13. What diflereuce is there in the gravitation of solid masses, and of fluids ? MECHANICAL PROPERTIES OF FLUIDS. 121 equality of pressure, and the fluid will not rest, till its equili- Drium is restored. Caroline. The pressure downwards is very natural; it is the effect of gravity; one particle, weighing upon another, presses on it; but the pressure sideways, and particularly the pressure up- wards, I cannot understand. Mrs. B. If there were no lateral pressure, water would not run out of an opening on the side of a vessel. If you till a vessel with sand, it will not continue to run out of such an opening, be- cause there is scarcely any lateral pressure among its particles. Emily. When water runs out of the side of a vessel, is it not owing to the weight of the water, above the opening? Mrs. B. If the particles of fluids were arranged in regular columns, thus, (fig;. 2.) there would be no lateral pressure, for when one particle is perpendicularly above the other, it can only press tlowirvards; but as it must continually happen, that a par- ticle presses between two particles beneath, (fig. 3.) ihese last, must suffer a lateral pressure. Emily. The same as when a wedge is driven into a piece of wood, and separates the parts, laterally. Mrs. B. Yes. The lateral pressure proceeds, therefore, en- tirely from the pressure downwards, or the weight of the liquid above; arid consequently, the lower the orifice ; s made in the vessel, the greater will be the velocity of the water rushing out of it. Here is a vessel of water (fig. 5.), with three stop cocks at different heights; we shall open them, and you will see with what different 3egrees of velocity, the water issues from them. Do you understand this, Caroline? Caroline. Oh yes. The water from the upper spout, receiv- ing but a slight pressure, on account of its vicinity to the sur- face, flows but gently; the second cock, having a greater weight above it, the water is forced out with greater velocity, whilst the lowest cock, being near the bottom of the vessel, receives the pressure of almost the whole body of water, and rushes out with the greatest impetuosity. Mrs. B. Very well; and you must observe, that as the late- ral pressure, is entirely owing to the pressure downwards, it is not affected by the horizontal dimensions of the vessel, which contains the water, but merely by its depth; for as every particle acts independently of the rest, it is only the column of particles immediately above the orifice, that can weigh upon, and press out the water. 14. What results as regards the pressure of fluids? 15. How is thi illus - tvated by fig;. 2, 3, plate 13? 16. From what does the lateral pressure pro- ceed ? and to what is it proportioned, as exemplified in fig. 5, plate 13 ? 122 MECHANICAL PROPERTIES OF FLUIDS. Emily. The breadth and width of the vessel then, can be of no consequence in this respect. The lateral pressure on one side, in a cubical vessel, is, I suppose, not so great as the pres sure downwards upon the bottom. Mrs. B. No; in a cubical vessel, the pressure downwards will be double the lateral pressure on one side; for every particle at the bottom of the vessel is pressed upon, by a colinin of the whole depth of the fluid, whilst the lateral pressure diminishes from the bottom upwards to the surface, where the particles have no pressure. Caroline. And from whence proceeds the pressure of fluids upwards? that seems to me the most unaccountable, as it is in direct opposition to gravity. Mrs. B. And yet it is in consequence of their pressure downwards. When, for example, you pour water into a tea- pot, the water rises in the spout, to a level with the water in the pot. The particles of water at the bottom of the pot, are press- ed upon by the particles above them; to this pressure they will yield, if there is any mode of making way for the superior par- ticles, and as they cannot descend, they will change their di- rection, and rise in the spout. Suppose the tea-pot to be filled with columns of particles of water, similar to that described in fig. 4., the particle 1, at the bottom, will be pressed laterally by the particle 2, and by this pressure be forced into the spout, where, meeting with the par- ticle 3, it presses it upwards, and this pressure will be continued from 3 to 4, from 4 to 5, and so on, till the water in the spout, has risen to a level with that in the pot. Emily. If it were not for this pressure upwards, forcing the water to rise in the spout, the equilibrium of the fluid would be destroyed. Caroline. True; but then a tea-pot is wide and large, and the weight of so great a body of water as the pot will contain, may easily force up and support so small a quantity, as will fill the spout. But would the same effect be produced, if the spout and the pot, were of equal dimensions? Mrs. B. Undoubtedly it would. You may even reverse the experiment, by pouring water into the spout, and you will find that the water will rise in the pot, to a level with that in the spout; for the pressure of the small quantity of water in the spout, will force up and support, the larger quantity in the pot. 17. Has the extent of the surface of a fluid, any effect upon its pressure downwards? 18. What will be the difference between the pressure upon the bottom, and upon one side of a cubical vessel? 19. What occasions the Upward pressure, and how is it explained by fig. 4, plate 13 ? MECHANICAL PROPERTIES OF FLUIDS. 123 in the pressure upwards, as well as that laterally, you see that the force of pressure, depends entirely on the height, and is quite independent of the horizontal dimensions of the fluid, As a tea-pot is not transparent, let us try the experiment by filling this large glass goblet, by means of this narrow tube, (fig. 6.) Caroline. Look, Emily, as Mrs. B. fills it, how the water rises in the goblet, to maintain an equilibrium with that in the tube. Now, Mrs. B., will you let me fill the tube, by pouring water into the goblet ? Mrs. B. That is impossible. However, you may try the experiment, and I doubt not that you will be able to account for its failure. Caroline. It is very singular, that if so small a column of water as is contained in the tube, can force up and support the whole contents of the goblet; that the weight of all the water in the goblet, should not be able to force up the small quantity re- quired to fill the tube:- oh, I see now the reason, the water in the goblet, cannot force that in the tube above its level, and as the nd of the tube, is considerably higher than the goblet, it can never be filled by pouring water into the goblet. Mrs. B. And if you continue to pour water into the goblet when it is full, the water will run over, instead of rising above its level in the tube. I shall now explain to you the meaning of the specific gravity of bodies. Caroline. What! is there another species of gravity, with which we are not yet acquainted? Mrs. B. No: the specific gravity of a body, means simply its weight, compared with that of another body, of the same size. When we say, that substances, such as lead, and stones, are heavy, and that others, such as paper and feathers, are light, we speak comparatively; that is to sav, that the first are heavy, and the latter light, in comparison with the generality of sub- stances in nature. Would you call wood, and chalk, light or heavy bodies? Caroline. Some kinds of wood are heavy, certainly, as oak and mahogany; others are light, as cedar and poplar. Emily. I think I should call wood in general, a heavy body; for cedar and poplar, are light, only in comparison to wood of a heavier description. I am at a loss to determine whether chalk 20. How could the equilibrium of fluids be exemplified by pouring water in at the spout of a tea-pot? 21. How by the apparatus represented at fig. 6, plate 13? 22. What is meant by the specific gravity of a body? 23. What do we in common mean by calling a body heavy, or light? 124 MECHANICAL PROPERTIES OF FLUIDS. should be ranked as a heavy, or a light body; I should be inclin- ed to say the former, if it was not that it is lighter than most other minerals. I perceive that we have but vague notions of light and heavy. I wish there was some standard of compari- son, to which we could refer the weight of all other bodies. Mrs. B. The necessity of such a standard, has been so much felt, that a body has been fixed upon for this purpose. What substance do you think would be best calculated to answer this end? Caro 7 ine. It must be one generally known, and easily obtain- ed; lead or iron, for instance. Mrs. B. The metals, would not answer the purpose well, for several reasons; they are not always equally compact, and they are rarely quite pure; two pieces of iron, for instance, although of the same size, might not, from the causes mentioned, weigh exactly alike. Caroline. But, Mrs. B., if you compare the weight, of equal quantities of different bodies, they will all be alike. You know the old saving, that a pound of feathers, is as heavy as a pound of lead? " Mrs. B. When therefore we compare the weight of different kinds of bodies, it would be absurd to take quantities of equal weight^ we must take quantities of equal bulk; pints or quarts, not ounces or pounds. Caroline, Very true; I perplexed myself by thinking that quantity referred to weight, rather than to measure. It is true, it would be as absurd to compare bodies of the same size, in or- der to ascertain which was largest, as to compare bodies of the same weight, in order to discover which was heaviest. Mrs. H. In estimating the specific gravity of bodies, there- fore, we must compare equal bulks, and we shall find that their specific gravity, w'-ll be proportional to their weights. The body which lias been adopted as a standard of reference, is distilled, or rain water. Emily. I am surprised that a fluid should have been chosen for this "purpose, as it must necessarily be contained in some ves sel, and the weight of the vessel, will require to be deducted. Mrs. B. You will find that the comparison will be more easily made with a fluid, than with a solid; and water you know can be every where obtained. In order to learn the specific gra- vity of a solid body, it is not necessary to put a certain measure of it in one scale, and an equal measure of water into the other scale: but simply to weigh the body under trial, first in air, and 24 Why would not the metals answer to compare other bodies with? 25. What must be supposed equal in estimating the specific gravity of a body ? 26. What has been adopted as a standard for comparison ? MECHANICAL PROPERTIES OF FLUIDS. 15 then in water. If you weigh a piece of gold, in a glass of water, will not the gold displace just as much water, as is equal to its own bulk? Caroline. Certainly, where one body is, another cannot be at the same time; so that a sufficient quantity of water must be re- moved, in order to make way for the gold. Mrs. B. Yes, a cubic inc'A of water, to make room for a cu- bic inch of gold; remember mat the bulk, alone, is to be consider- ed; the weight, has nothing to do with the quantity of water dis- placed, for an inch of gold, does not occupy more space, and therefore will not displace more water, than an inch of ivory, or any other substance, that will sink in water. Well, you will perhaps be surprised to hear that the gold will weigh less in water, than it did out of it? Emily And for what reason? Mrs. B. On account of the upward pressure of the particles of water, which in some measure supports the gold, and by so do- ing, diminishes its weight. If the body immersed in water, was of the same weight as that fluid, it would be wholly supported by it, just as the water which it displaces, was supported, previous to its making way for the solid body. If the body is heavier than the water, it cannot be wholly supported by it; but the water will offer some resistance to its descent. Caroline. And the resistance which water offers to the de- scent of heavy bodies immersed in it, (since it proceeds from the upward pressure of the particles of the fluid,) must in all cases, I suppose, be the same? Mrs. B. Yes: the resistance of the fluid, is proportioned to the bulk, and not to the weight, of the body immersed in it; all bodies of the same size, therefore, lose the same quantity of their weight in water. Can you form any idea what this loss will be? Emily. I should think it would be equal to the \veight of the water displaced; for, since that portion of the water was sup- ported before the immersion of the solid body, an equal weight of the solid body, will be supported. Mrs. B. You are perfectly right; a body weighed in water, loses just as much of its weight, as is equal to tnat of the water it displaces; so that if yon were to put the water displaced, into the scale to which the body is suspended, it would restore the balance. You must observe, that when you weigh a body in water, in order to ascertain its specific gravity, you must not sink the dish of the balance in the water , but either suspend the body to a 27. What is the first step in ascertaining the specific gravity of a solid ? 28. What quantity of water will the solid displace ? 29. Why will a solid weigh less in water than in air, and to what will the loss of weight be equal? L 2 126 MECHANICAL PROPERTIES OF FLUIDS. hook at the bottom of the dish, or else take off the dish, and sus- pend to the arm of the balance a weight to counterbalance the other dish, and to thisattacli the solid to be weighed, (fig. 7.) Now suppose that a cubic inch of gold, weighed 19 ounces out of wa- ter, and lost one ounce of its weight by being weighed in water, what would be its specific gravity? Caroline. The cubic inch of water it displaced, must weigh that one ounce; and as a cubic inch of gold, weighs 19 ounces, gold is 19 times, as heavy as water. Emily. I recollect having seen a table of the comparative weights of bodies, in which gold appeared to me to be estimated at 19 thousand times, the weight of water. Mrs. B. You misunderstood the meaning of the table. In the estimation you allude to, the weight of water was reckoned at 1000. You must observe, that the weight of a substance when not compared to that of any other, is perfectly arbitrary; and when water is adopted as a standard, we may denominate its weight by any number we please; but then the weight of all bodies tried by this standard, must be signified by proportional numbers. Caroline. We may call the weight of water, for example, one, and then that of gold, would be nineteen; or if we choose to call the weight of water 1000, that of gold would be 19,000. In short, specific gravity, means how many times more a body weighs, than an equal bulk of water. Mrs. B. It is rather the weight of a body compared with a portion of water equal to it in bulk; for the specific gravity of many substances,, is less than that of water. Caroline. Then you cannot ascertain the specific gravity of such substances^, in the same manner as that of gold; for a body that is lighter than water, will float on its surface, without dis- placing any of it. Mrs. B. If a body were absolutely without weight, it is true that it would not displace a drop of water, but the bodies we are treating of, have all some weight, however small; and will, there- fore, displace some quantity. If the body be lighter than wa- ter, it vvdl not sink to a level with its surface, and therefore it will not displace so much water as is equal to its bulk; but only so much, as is equal to its weight. A ship, you must have ob- served, sinks to some depth in water, and the heavier it is laden, the deeper it sinks, as it always displaces a quantity of water, equal to its own weight. 30. What is the arrangement represented by fig. 7, plate 13? 31. What is stated of gold as an example? 32. In comparing a body with water, this is sometimes called 1000, what must be observed ? 33. What quantity of water is displaced, by a body floating upon its surface ? MECHANICAL PROPERTIES OF FLUIDS. 17 Caroline. But you said just now, that in the immersion of gold, the bulk, and not the weight of body, was to be con- sidered. Mrs. B. That is the case with all substances which are hea- vier than water 5 but since those which are lighter, do not dis- place so much as their own bulk, the quantity they displace is not a test of their specific gravity. In order to obtain the specific gravity of a body which is lighter than water, you must attach to it a heavy one, whose specific gravity is known, and immerse them together; the specific gra- vity of the lighter body, may then be easily calculated from ob- serving the loss of weight it produces, in the heavy body. Emily. But are there not some bodies which have exactly the same specific gravity as water? Mrs. B. Undoubtedly; and such bodies will remain at rest in whatever situation they are placed in water. Here is a piece of wood which I have procured, because it is of a kind which is precisely the weight of an equal bulk of water; in whatever part of this vessel of water you place it, you will find that it will remain stationary. Caroline. I shall first put it at the bottom; from thence, of course, it cannot rise, because it is not lighter than water. Now I shall place it in the middle of the vessel; it neither rises nor sinks, because it is neither lighter nor heavier than the water. Now I will lay it on the surface of the water; but there it sinks a little what is the reason of that, Mrs. B.? Mrs. B. Since it is not lighter than the water, it cannot float upon its surface ; since it is not heavier than water, it cannot sink below its surface: it will sink therefore, only till the upper surface of both bodies are on a le:*el, so that the piece of wood is just covered with water. If you poured a few drops of water into the vessel, (so gently as not to give them momentum) they would mix with the water at the surface, and not sink lower. Caroline. I now understand the reason, why, in drawing up a bucket of water out of a well, the bucket feels so much hea- vier when it rises above the surface of the water in the well; for whilst you raise it in the water, the water within the bucket be- ing of the same specific gravity as the water on the outside, will be wholly supported by me upward pressure of the water beneath the bucket, and consequently very little force will be required to raise it; but as soon as the bucket rises to the surface of the well, you immediately perceive the increase of weight. 34. How can you find the specific gravity of a solid which is lighter than water ? 35. What is observed of a body whose specific gravity is the same as that of water? 36. What is the reason that in drawing a bucket of watei from a well, its weight is not perceived until it rises above the surface? 128 OF SPRINGS, FOUNTAINS, &C. # Emily. And how do you ascertain the specific gravity of fluids? Mrs. B. By means of an hydrometer; this instrument is made of various materials, and in different forms, one of which I will show you. It consists of a thin brass ball A, (fig. 8, plate 13.) with a graduated tube B, and the specific gravity of the li- quid, is estimated by the depth to which the instrumerit'sinks in it, or by the weight required to sink it to a given depth. There is a small bucket C, suspended at the lower end, and also a little dish on the graduated tube; into either of these, small weights may be put, until the instrument sinks in the fluid, to a mark on the tube B; the amount of weight necessary for this, will enable you to discover the specific gravity of the fluid. I must now take leave of you; but there remain yet many ob servations to be made on fluids: we shall, therefore, resume this subject at our next interview. 37. Describe the instrument represented by fig. 8, plate 13, and also how, and for what it is used ? CONVERSATION XL OF SPRINGS, FOUNTAINS, &c. OP THE ASCENT OF VAPOUR AND THE FORMATION OF CLOUDS. OF THH FORMATION AND FALL OF RAIN, &C. OF THE FORMATION OF SPRINGS OF RIVERS AND LAKES. OF FOUNTAINS. CAROLINE. THERE is a question I am very desirous of asking you, respect- ing fluids, Mrs. B., which has often perplexed me. What is the reason that the great quantity of rain which falls upon the earth and sinks into it, does not, in the course of time, injure its solid- ity? The sun and the wind, I know, dry the surface, but they have no effect on the interior parts, where there must be a pro- digious accumulation of moisture. Mrs. B. Do you not know, that, in the course of time, all the water which sinks into the ground, rises out of it again? It is the OF SPRINGS, FOUNTAINS, &C. 129 same water which successively forms seas, rivers, springs, clouds, rain, and sometimes hail, snow and ice. If you will take the trouble of following it through these various changes, you will un- derstand why the earth is not yet drowned, by the quantity of water which has fallen unon it, since its creation; and you will even be convinced, that it does not contain a single drop more water now, than it did at that period. Let us consider how the clouds were originally formed. When the first rays of the sun warmed the surface of the earth, the heat, by separating the particles of water, rendered them lighter than the air. This, you know, is the case with steam or vapour. What then ensues? Caroline. When lighter than the air, it will naturally rise; and now I recollect your telling us in a preceding lesson, that the heat of the sun transformed the particles of water into va- pour; in consequence of which, it ascended into the atmosphere, where it formed clouds. Mrs. B. We have then already followed water through two of its transformations; from water it becomes vapour, and from vapour clouds. Emily. But since this watery vapour is lighter than the air, why does it not continue to rise; and why does it unite again, to form clouds? M''s. B. Because the atmosphere diminishes in density, as it is more distant from the earth. The vapour, therefore, which the sun causes to exhale, not oidy from seas, rivers, and lakes, but likewise from the moisture on the land, rises till it reaches a region of air of its own specific gravity; and there, you know, it will remain stationary. By the frequent accession of fresh vapour, it gradually accumulates, so as to form those large bo- dies of vapour, which we call clouds: and the particles, at length uniting, become too heavy for the air to support, and fall to the ground. Caroline. They do tall to the ground, certainly, when it rains; but, according to your theory, I should have imagined, that when the clouds became too heavy, for the region of air in which they were situated, to support them, they would descend? till they reached a stratum of air of their own weight, and not fall to the earth; for as clouds are formed of vapour, they can- not be so heavy as the lowest regions of the atmosphere, other- wise the vapour would not have risen. Mrs. B. If you examine the manner in which the clouds descend, it will obviate this objection. In falling, several of the 1. Why do not the frequent rains, fill the earth with water ? 2. Why will vapour rise? to what height will it ascend, and what will it form? 3. How may drops of rain be formed ? 130 OF SPRINGS, FOUNTAINS, &C. watery particles come within the sphere of each other's attrac tion, and unite in the form of a drop of water. The vapour thus transformed into a shower, is heavier than any part 01 the atmosphere, and consequently descends to the earth. Caroline. How wonderfully curious! Mrs. B. It is impossible to consider any part of nature at- 'tentively, without being struck with admiration at the wisdom it displays; and I hope you will never contemplate these wonders, without feeling your heart glow with admiration and gratitude, towards their bounteous Author. Observe, that if the waters were never drawn out of the earth, all vegetation would be de- stroyed by the excess of moisture; if, on the other hand, the plants were not nourished and refreshed by occasional showers, the drought would be equally fatal to them. If the clouds con- stantly remained in a state of Vapour, they might, as you re- marked, descend into a heavier stratum of the atmosphere, but could never fall to the ground; or were the power of attraction more than sufficient to convert the vapour into drops, it would transform the cloud into a mass of water, which, instead of nourishing, would destroy the produce of the earth. Water then ascends in the form of vapour, and descends in that of rain, snow, or hail, all of which ultimately become water. Some of this falls into the various bodies of water on the sur- face of the globe, the remainder upon the land. Of the latter, part reascends in the form of vapour, part is absorbed by the roots of vegetables, and part descends into the earth, where it forms springs. Emily. Is there then no difference between rain water, and spring water ? Mrs. B. They are originally the same; but that portion of rain water which goes to supply springs, dissolves a number of foreign particles, which it meets with in its passage through the various soils it traverses. Caroline. Yet spring water is more- pleasant to the taste, appears more transparent, and, I should have supposed, would have been more pure than rain water. Mrs. B. No; excepting distilled water, rain water is the most pure we can obtain; it is its purity which renders it insipid; whilst the various salts and different ingredients, dis- solved in spring water, give it a species of flavour, which habit renders agreeable; these salts do not, in any degree, affect its transparency; and the nitration it undergoes, through gravel and 4. What becomes of the water after it has fallen to the earth ? 5. What is the difference between rain water, and that from springs ? 6. Why is rain more pure than spring water ? 7. Why is spring water more agreeable to the palate ? OF SPRINGS, FOUNTAINS, &C. 131 sand, cleanses it from all foreign matter, which it has not the power of dissolving. Emily. How is it that the rain water does not continue to descend by its gravity, instead of collecting together, and form- ing springs? Mrs. 11. When rain falls on the surface of the earth, it continues making its way downwards through the pores and crevices in the ground. When several drops meet in their sub- terraneous passage, they unite and form a little rivulet; this, in its progress, meets with other rivulets of a similar description, and they pursue their course together within the earth, till they are stopped by some substance, such as rock, or clay, which they cannot penetrate. Caroline. But you say that there is some reason to believe that water can penetrate even the pores of gold, and it cannot meet with a substance more dense? Mrs. B. But if water penetrate the pores of gold, it is only when under a strong compressive force, as in the Florentine experiment; now in its passage towards the centre of the earth, it is acted upon by no other power than gravity, which is not sufficient to make it force its way, even through a stratum of clay. This species of earth, though not remarkably dense, be- ing of great tenacity, will not admit the particles of water to pass. When water encounters any substance of this nature, therefore, its progress is stopped, and it is diffused through the porous earth, and sometimes the pressure of the accumulating waters, forms a bed, or reservoir. This will be more clearly explained by fig. 9, plate 13, which represents a section, of the interior of a hill or mountain. A, is a body of water, such as I have described, which, when filled up as high as B, (by the con- tinual accession of water it receives from the ducts or rivulets a, a, a, a,) finds a passage out of the cavity, and, impelled by gravity, it runs on, till it makes its way out of the ground at the side of the hill, and there forms a spring, C. Caroline. Gravity impels downwards towards the centre of the earth; and the spring in this figure runs in an horizontal direction. Mrs. B. Not entirely. There is some declivity from the reservoir, to the spot where the water issues out of the ground; and gravity, you know, will bring bodies down an inclined plane, as well as in a perpendicular direction. Caroline. But though the spring may descend, on first issu- ing, it must afterwards rise to reach the surface of the earth; and that is in direct opposition to gravity. 8. What causes the water to collect and form springs ? , 9. Why cannot water penetrate through ciay .' 10. What is represented by fig. 9, plate 13 ? , 132 OF SPHINGS, FOUNTAINS, &C. Mrs. B. A spring can never rise above the level of the re servoir whence it issues; it must, therefore, find a passage to some part of the surface of the earth, that is lower, or nearer the centre, than the reservoir. It is true that, in this figure, the spring rises in its passage from B to C; but this, I think, with a Jittle reflection, you will be able to account for. Emily. Oh, yes; it is owing to the pressure of fluids up- wards; and the water rises in the duct, upon the same principle as it rises in the spout of a tea-pot; that is to say, in order to preserve an equilibrium with the water in the reservoir. Now I think I understand the nature of springs: the water will flow through a duct, whether ascending or descending, provided it never rises higher than the reservoir. Mrs. B. Water may thus be conveyed to every part of a town, and to the upper part of the houses, if it is originally brought from a height, superior to any to which it is conveyed. Have you never observed, when the pavements of the streets have been mending, the pipes which serve as ducts for the con- veyance of the water through the town? Emily. Yes, frequently; and I have remarked that when any of these pipes have been opened, the water rushes upwards from them, with great velocity; which, I suppose, proceeds from the pressure of the water in the reservoir, which forces it out. Caroline. I recollect having once seen a very curious glass, called Tantalus's cup; it consists of a goblet, containing a small fignre of a man, and whatever quantity of water you pour into the goblet, it never rises Ivgher than the breast of the figure. Do you know how that is contrived? Mrs. B. It is by means of a syphon, or bent tube, which is concealed in the body of the figure. This tube rises through one of the legs, as high as the breast, and there turning, descends through the other leg, and from thence through the foot of the goblet, where the water runs out. (fig. 1, plate 14.) When you pour water into the glass A, it must rise in the syphon B, in pro- portion as it rises in the glass; and when the glass is filled to a level with the upper part of the syphon, the water will run out through the other leg of the figure, and will continue running out, as fast as you pour it in; therefore the glass can never fill any higher. Emtt,y. I think the new well that has been made at our country-house, must be of that nature. We had a great scar- city ot water, and my father has been at considerable expense to dig a well; after penetrating to a great depth, before water could 11. How can you account for its rising upwards, os represented at C? 12. In conveying water by means of pipes, how must the reservoir be situat- ed? 13. What is the instrument called, which is represented in plate 14, fig. 1, and how does it operate , ? i OF SPRINGS, FOUNTAINS, &C. 153 be found, a spring was at length discovered, but the water rose only a few feet above the bottom of the well; and sometimes it is quite dry. Mrs. B. This has, however, no analogy to Tantalus's cup; b\X is owing to the very elevated situation of your country - hou>e. Emily. I believe I guess the reason. There cannot be a re- servoir of water near the summit of a hill; as in such a situation, there will not be a sufficient number of rivulets formed, to supply one; and without a reservoir, there can be po spring. In such situations, therefore, it is necessary to dig very deep, in order to meet wrth a spring; and when we give it vent, it can rise only as high as the reservoir from whence it flows, which will be but little, as the reservoir must be situated at some considerable depth below the summit of the hill. Caroline. Your explanation appears very clear and satisfac- tory; but I can contradict it from experience. At the very top of a hill, near our country-house, there is a large pond, and, ac- cording to your theory, it would be impossible there should be springs in such a situation to supply it with water. Then you know that 1 have crossed the Alps, and I can assure you, that there is a tine lake on the summit of Mount Cenis, the highest mountain we passed over. Mrs. B. Were there a lake on the summit cf Mount Blanc, which is the highest of the Alps, it would indeed be wonderful. But that on Mount Cenis, is not at all contradictory to our the ory of springs; for this mountain is surrounded by others, much more elevated, and the springs which feed the lake must descend from reservoirs of water, formed in those mountains. This must also be the case with the pond on the top of the hill; there is doubtless some more considerable hill in the neighbourhood, which supplies it with water. Emily. I comprehend perfectly, why the water in our well never rises high: but I do not understand why it should occa- sionally be dry. Mrs. B. Because the reservoir from which it flows, b^ing in an elevated situation, is but scantily supplied with water; after a long drought, therefore, it may be drained, and the spring dry, till the reservoir be replenished by fresh rains. It is not un- common to see springs flow with great violence in wet seasons, which at other times, are perfectly dry. Caroline. But there is a spring in our grounds, which more 14. Why are wells rarely well supplied with water, in elevated situations ? 15. When water is found in elevated situations, whence is it supplied? 16 Wells and springs, at some periods well supplied, fail at others ; how is this ao couuted for? M 134 OF SPRINGS, FOUNTAINS, &C. frequently flows in dry, than in wet weather; how is that to be accounted for? Mrs. B. The spring, probably, comes from a reservoir at a great distance, and situated very deep in the ground: it is, therefore, some length of time before the rain reaches the reser- voir; and another considerable portion must elapse, whilst the water is making its way, from the reservoir, to the surface of the earth; so that the dry weather may probably have succeeded the rains, before the spring begins to flow; and the reservoir may be. exhausted, by the time the wet weather sets in again. Caroline. I doubt not but this is the case, as the spring is in a very low situation, therefore, the reservoir may be at a great distance from it. Mrs. 13. Springs which do not constantly flow, are called intermitting, and are occasioned by the reservoir being imper- fectly supplied. Independently of the situation, this is always the case, when the duct, or ducts, which convey the water into the reservoir, are smaller than those which carry it off. Caroline. If it runs out, faster than it runs in, it v/ill of course sometimes be empty. Do not rivers also, derive their source from springs? Mrs. B. Yes, they generally take their source in mountain- ous countries, where springs are most abundant. Caroline. I understood you that springs were more rare, in elevated situations. Mrs. B. You do not consider that mountainous countries, abound equally with high, and low situations. Reservoirs of wa- ter, which are formed in the bosoms of mountains, generally find a vent, either on their declivity, or in the valley beneath; while subterraneous reservoirs, formed in a plain, can seldom find a passage to the surface of the earth, but remain concealed, unless discovered by digging a well. When a spring once issues at the surface of the earth, it continues its course externally, seeking always a lower ground, for it can no longer rise. Emily. Then what is the consequence, if the spring, or, as I should now rather call it, the rivulet, runs into a situation, which is surrounded by higher ground? Mrs. B. Its course is stopped; the water accumulates, and it forms a pool, pond, or lake, according to the dimensions of the body of water. The lake of Geneva, in all probability, owes its origin to the Rhone, which passes through it: if, when this river first entered the valley, which now forms the bed of the 17. Some springs flow abundantly in dry weather, which occasionally fail in wet weather, how may this be explained? 18. What is meant by inter- miiling springs ? 19. Whence do rivers, in general, derive their water ? ?0. Why do springs abound more in mountainous, than in level countries ? OF SPRINGS, FOUNTAINS, &C. 135 Lake, it found itself surrounded by higher grounds, its waters would there accumulate, till they rose to a level with that part of the valley, where the Rhone now continues its course beyond the Lake, and from whence it flows through valleys, occasionally forming other small lakes, till it reaches the sea. Emily. And are not fountains, of the nature of springs? Mrs. B. Exactly. A fountain is conducted perpendicularly upwards, by the spout or adjutage A, through which it flows; and it will rise nearly as high as the reservoir B, from whence it proceeds. (Plate 14. fig. 2.) Caroline. Why not quite as high? Mrs. B. Because it meets with resistance from the air, in its ascent; and its motion is impeded by friction against the spout, where it rushes out. Emily. But if the tube through which the water rises be smooth, can there be any friction? especially with a fluid, whose particles yield to the slightest impression. Mrs. &. Friction, (as we observed in a former lesson,) may be diminished by polishing, but can never be entirely destroy ed; and though fluids, are less susceptible of friction, than solid bo- dies, they are still affected by it. Another reason why a foun- tain will not rise so high as its reservoir, is, that as all the water which spouts up, has to descend again, it in doing so, presses, or strikes against the under parts, and forces them sideways, spread- ing the column into a head, and rendering it both wider, and shorter, than it otherwise would be. At our next meeting, we shall examine the mechanical pro- perties of the air, which being an elastic fluid, differs in many respects, from liquids. 21. How are lakes formed? 22. What causes water to rise in fountains, and how is this explained by figure 2, plate 14 ? 23. Why will not the foun tain rise to the height of the water in the reservoir ? CONVERSATION XII. ON THE MECHANICAL PROPERTIES OF AIR. OV THE SPRING OR ELASTICITY OF THE AIR. OF THE WEIGHT OF THH AIR. EXPERIMENTS WITH THE AIR PUMP. OF THE BAROMETER. MODE OF WEIGHING AIR. SPECIFIC GRAVITY OF AIH..- OF PUMPS. DESCRIPTION OF THE SUCKING PUMP. DESCRIPTION OF TEE FORCING PUMP. MRS. B. AT our last meeting we examined the properties of fluids in general, and more particularly, of such as are called non-elastic flu; Js, or liquids. There is another class of fluids, distinguished by the name of aeriform, or elastic fluids, the principal of which is the air we breathe, which surrounds the earth, and is called the atmo- sphere. Emily. There are then other kinds of air, besides the atmo- sphere? Mrs. B. Yes; a great variety; but they differ only in their chemical, and not in their mechanical properties; and as it is the latter we are to examine, we shall not at present inquire into their composition, Dut confine our attention to the mechanical properties of elastic fluids in general. Caroline. And from whence arises this difference, between elastic, and non -elastic fluids? Mrs. B. There is no attraction of cohesion, between the par- ticles of elastic fluid?; so that the expansive power of heat, has no adversary to contend with, but gravity; any increase of tempera- ture, therefore, expands elastic fluids considerably, arid a dimi- nution, proportionally condenses them. The most essential point, in which air, differs from other fluids, is in its spring or elasticity; that is to say, its power of increas- ing, or diminishing in bulk, accordingly as it is more, or less, com- pressed: a power of which I have informed you, liquids are al- most u holly deprived , 1. Into what two kinds are fluids divided? 2. There are different kinds of elastic fluids, in what properties are they alike, and in what do they dif- fer ? 3. In what particular do elastic, differ from non-elastic, fluids ? 4, What is meant by the elasticity of air ? MECHANICAL PROPERTIES OF AIR. 137 Emily. I think I understand the elasticity of the air very well from wljat you formerly said of it; but what perplexes me is, its having gravity; if it is heavy, and we are surrounded by it, why do we not feel its weight? Caroline. It must be impossible to be sensible of the weight of such infinitely small particles, as those of which the air is composed: particles which are too small to be seen, must be too light to be felt. Mrs. B. You are mistaken, my dear; the air is much heavier than you imagine; it is true, that the particles which compose it, are small; but then, reflect on their quantity: the atmosphere extends in height, a great number of miles from the earth, and its gravity is such, that a man of middling stature, is computed (when the air is heaviest) to sustain the weight of about 14 tons. Caroline. Is it possible! I should have thought such a weight would have crushed any one to atoms. Mrs. B. That would, indeed, be the case, if it were not for the equality of the pressure, on every part of the body; but when thus diffused, we can bear even a much greater weight, without any considerable inconvenience. In bathing we support the weight and pressure of the water, in addition to that of the atmo- sphere; but because this pressure is equally distributed over the body, we are scarcely sensible of it; whilst if your shoulders, your head, or any particular part of your frame, were loaded with the additional weight of a hundred pounds, you would soon sink under the fatigue. Besides this, our bodies contain air, the spring of which, counterbalances the weight of the external air, and ren- ders us insensible of its pressure. Caroline. But if it were possible to relieve me from the weight of the atmosphere, should I not feel more light and agile? Mrs. B. On the contrary, the air within you, meeting with no external pressure to restrain its elasticity, would distend your body, and at length bursting some of the parts which con- fined it, put a period to your existence. Caroline. This weight of the atmosphere, then, which I was so apprehensive would crush me, is, in reality, essential to my preservation. Emily. I once saw a person cupped, and was told that the swelling of the part under the cup, was produced by taking away from that part, the pressure of the atmosphere; but I could not understand how this pressure produced such an effect. Mrs. B. The air pump affords us the means of making a great variety of interesting experiments, on the weight, and pressure of 5. What is said respecting the weight of the atmosphere * 6. Why do we not feel the pressure of the air ? 7 What would be the effect of relieving us from atmospheric pressure ? M 2 138 MECHANICAL PROPERTIES OF AIR. the air: some of them you have already seen. Do you not recol lect, that in a vacuum produced within the air pump, substances of various weights, fell to the bottom in the same time; why does not this happen in the atmosphere? Caroline. I remember you told us it was owing to the resist- ance which light bodies meet with, from the air, durin- their fall. Mrs. B. Or, in other words, to the support which they re- ceived from the air, and which prolonged the time of their fall. Now, if the air were destitute of weight, how could it support other bodies, or retard their fall ? I shall now show you some other experiments, which illustrate, in a striking manner, both the weight, and elasticity of air. I shall tie a piece of bladder over this glass receiver, which, you will observe, is open at the top as well as below. Caroline. Why do you wet the bladder first? Mrs. B. It expands by wetting, and contracts in drying; it is also more soft and pliable when wet, so that 1 can mate it fit better, ai*d when dry, it will be tighter. We must hold it to the fire in order to dry it; but not too near, lest it should burst by sudden contraction. Let us now fix it on the air pump, and ex- haust the air from underneath it you will not be alarmed if you hear a noise? Emily. It was as loud as the report of a gun, and the blad der is burst! Pray explain how the air is concerned in this ex periment. Mrs. B. It is the effect of the weight of the atmosphere, on the upper surface of the bladder, when I had taken away the air from the under surface, so that there was no longer anj reaction to counterbalance the pressure of the atmosphere, on the receiver. You observed how the bladder was pressed inwards, by the weight of the external air, in proportion as 1 exhausted the receiver, and before a complete vacuum was formed, the bladder, unable to sustain the violence of the pressure, burst with the explosion you have just heard. I shall now show vou an experiment, which proves the expan sion of the air, contained within a body, when it is relieved from the pressure of the external air. You would not imagine that there was any air contained within this shrivelled apple, by its appearance; but take notice of it when placed within a receiver, from which I shall exhaust the air. Caroline. How strange! it grows quite plump, and looks like a fresh -gathered apple. Mrs. B. But as soon as I let the air again into the receiver, 8. How may the weight of the air be shown by the aid of the air pump, and a piece of bladder ? 9. How is this explained ? 10. How may its elas- ticity be exploited, by an apple, and by a bladder ? MECHANICAL PROPERTIES OF AIR. 139 the apple, you see, returns to its shrivelled state. When I took iway the pressure of the atmosphere, the air within the apple, ex- panded, arid swelled it out; but the instant the atmospherical air was restored, the expansion of the internal air, was checked and repressed, and the apple shrunk to its former dimensions. You may make a similar experiment with this little bladder, which you see is perfectly flaccid, and appears to contain no air: iu thic state I shall tie up the neck of the bladder, so that what- ever air remains within it, m?.y not escape, and then place it uri der the receiver. Now observe, as I exhaust the receiver, how the bladder distends; this proceeds from the great dilatation of the small quantity of air, which was enclosed within the bladder, when I tied it up; but as soon as I let the air into the receiver, that which the bladder contains, condenses and shrinks into its small compass, within the folds of the bladder. Emily. These experiments are extremely amusing, and they afford clear proofs, both of the weight, and elasticity of the air; but I should like to know, exactly, how much the air weighs. Mrs. B. A column of air reaching to the top of the atmo- sphere, and whose base is a square inch, weighs about loios. therefore, every square inch of our bodies, sustains a weight of 15lbs, : and if you wish to know the weight cf the whole of the atmosphere, you mrst reckon how many square inches there are on the surface of the globe, and multiply them by 15. Emily. But can we net ascertain the weight of a small quan- tity of air? Mrs. B. With perfect ease. I shall exhaust the air from this little bottle, by means of the air pump: and having emptied the bottle of air, or, in other words, produced a vacuum within it, I secure it by turning this screw adapted to its neck: we may now find the exact weight of this bottle, by putting it into one of the scales of a balance. It weighs, you see, just two ounces; but when I turn the screw, so as to admit the air into the bottle, the scale which contains it, preponderates. Caroline. No doubt the bottle filled with air, is heavier than the bottle void of air; and the additional weight required to bring the scales again to a balance, must be exactly that of the air wh ad- verse winds would meet. Mrs. B. These winds do not meet, for they each change their direction before they reach the equator. The sun, in mov- ing over the equatorial regions from east to west, rarefies the air as it passes, and causes the denser eastern air to flow west- wards, in order to restore the equilibrium, thus producing a re- gular east wind, about the equator. Caroline. The air from the west, then, constantly goes to meet the sun, and repair the disturbance which his beams have produced in the equilibrium of the atmosphere. But I wonder tow you will reconcile these various winds, Mrs. B.; you first led me to suppose there was a constant struggle between oppo- site winds at the equator, producing storm and tempest; but now I hear of one regular invariable wind, which must naturally be attended by calm weather. Emily. I think I comprehend it: do not these winds from the north and south, combine with the easterly wind about the equator, and form, what are called, the trade- winds? Mrs. B. Just so, my dear. The composition of the two winds, north and east, produces a constant north-east wind; and that of the two winds, south and east, produces a regular south- east wind; these winds extend to about thirty degrees on each side of the equator, the regions further distant from it, expe- riencing only their respective northerly and southerly winds. Caroline. " But, Mrs. B., if the air is constantly flowing from the poles, to the torrid zone, there must be a deficiency of air, in the polar regions? Mrs. B. The light air about the equator, which expands, and rises into the upper regions of the atmosphere, ultimately flows from thence, back to the poles, to restore the equilibrium: if it were not for this resource, the polar, atmospheric regions, would soon be exhausted by the stream of air, which, in the lower strata of the atmosphere, they are constantly sejiding to- wards the equator. Caroline. There is then a sort of circulation of air in the at- 4, In what part of the globe is the air most rarefied, and what is the con- sequence? 5. How do these winds change their direction as they approach the equator ? 6. How are the trade- winds produced, and how far do they wctend? 7. How is the equilibrium in the air restored? 148 ON WIND AND SOUND. mosphere; the air in the lower strata, flowing from the poles to wards the equator, and in the upper strata, flowing back from the equator, towards the poles. Mrs. B. Exactly 5 I can show you an example of this circu- lation, on a smaller scale. The air of this room, being more rarefied, than the external air, a wind or current of air is pour- ing in from the crevices of the windows and doors, to restore the equilibrium; but the light air, with which the room is filled, must find some vent, in order to make way for the heavy air that en- ters. If you set the door a-jar, and hold a candle near the up- per part of it, you will find that the flame will be blown out- wards, showing that there is a current of air flowing out from the upper part of the room. Now place the candle on the floor, close by the door, and you will perceive, by the inclination of the flame, that there is also a current of air, setting into the room. Caroline. It is just so; the upper current is the warm light air, which is driven out to make way for the stream of cold dense air, which enters the room lower down. Mrs. B. Besides the general, or trade-winds, there are others, which are called periodical, because they blow in con- trary directions, at particular periods. mily. I have heard, Mrs. B., that the periodical winds, called, in the torrid zone, the sea and land breezes, blow to- wards the land, in the day time, and towards the sea, at night: what is the reason of that? Mrs. B. The land reflects into the atmosphere, a much greater quantity of the sun's rays, than the water; therefore* that part of the atmosphere which is over the land, is more heated and rarefied, than that which is over the sea: this occa- sions the wind to set in upon the land, as we find that it regu- larly does on the coast 01 Guinea, and other countries in the torrid zone. There, they have only the sea breeze, but on the islands, they have, in general, both a land and sea breeze, the latter being produced in the way described; whilst at night, during the absence of the sun, the earth cools, and the air is consequently condensed, and flows from the land, towards the sea, occasioning the land breeze. Emily. I have heard much of the violent tempests, occa- sioned by the breaking up of the monsoons; are not they also regular trade-winds?' Mrs* B. They are called periodical trade-winds, as they change their course every half year. This variation is produced 8 How can contrary currents of air be shown in a room ? 9. What cause* this? 10. What is meant by a periodical wind' 11. What occasions th land and sea breezes, and where do they prevail ? ON WIND AND SOUND. 149 by the earth's annual course round the sun; the north pole being inclined towards that luminary one half of the year, the south pole, the other half. During the summer of the northern he mi sphere, the countries of Arabia, Persia, India, and China, are much heated, and reflect great quantities of the sun's rays into the atmosphere, by which it becomes extremely rarefied, and the equilibrium consequently destroyed. In order to restore it, the air from the equatorial southern regions, where it is colder, (as well as from the colder northern parts,) must necessarily have a motion towards those parts. The current of air from the equatorial regions, produces the trade-winds for the first six months, in all the seas between the heated continent of Asia, and the equator. The other six months, when it is summer in the southern hemisphere, the ocean and countries towards the southern tropic are most heated, and the air over those pares, more rarefied: then the air about the equator alters itL course, and ilows exactly in an opposite direction. Caroline. This explanation of the monsoons is very curious; but what does their breaking up mean? Mrs. B. It is the name given by sailors to the shifting of the periodical winds; they do not change their course suddenly, but by degrees, as the sun moves from one hemisphere, to the other: this change is usually attended by storms and hurricanes, very dangerous for shipping; so that those seas are seldom navi- gated at the season of the equinoxes. Emily. I think I understand the winds in the torrid zone perfectly well; but what is it that occasions the great variety of winds, which occur in the temperate zones? for, according to your theory, there should be only north and south winds, in those climates. Mrs. B. Since so large a portion of the atmosphere, as is over the torrid zone, is in continued agitation, these agitations in an elastic fluid, which yields to the slightest impression, must extend every way, to a great distance; the air, therefore, in all climates, will suffer more or less perturbation, according to the situation of the country, the position of mountains, valleys, and a variety of other causes: hence it is easy to conceive, that al- most every climate, must be liable to variable winds; this is par- ticularly the case in high latitudes, where the earth is less pow- erfully affected by the sun's rays, than near the equator. Caroline. I have observed, that the wind, whichever way it blows, almost always falls about sun-set. 12. What are monsoons ? 13. How do they change, and what is the cause ? 14. What is meant by their breaking up, and what effect is in general pro. duced? 15. Why is the wind most variable in high latitudes? N 2 150 ON WIND AND Mrs. B. Because the rarefaction of air in the particular spot which produces the wind, diminishes as the sun declines, and consequently the velocity of the wind, abates. Emily. Since the air is a gravitating fluid, is it not affected by the attraction of the moon and the sun, in the same manner as the waters? Mrs. J3. Undoubtedly; but the aerial tides are as much great- er than those of water, as the density of water exceeds that of air, which, as you may recollect, we found to be about 800 to 1. Caroline. What a prodigious protuberance that must occa- sion ! How much the weight of such a column of air, must raise the mercury in the barometer ! Emily. As this enormous tide of air is drawn up and sup- ported, as it were, by the moon, its weight and pressure, I should suppose, would be rather diminished than increased? Mrs. B. The weight of the atmosphere is neither increased nor diminished by the aerial tides. The moon's attraction aug- ments the bulk, as much a? it diminishes the weight, of the co- lumn of air; these effects, therefore, counterbalancing each other, the ferial tides do not affect the barometer. Caroline. I do not quite understand that. Mrs. B. Let us suppose that the additional bulk of air at high tide, raises the barometer one inch; and on the other hand, that the support which the moon's attraction affords the air, di- minishes its weight or pressure, so as to occasion the mercury to fall one inch; under these circumstances the mercury must remain stationary. Thus, you see, that we can never be sensi- ble of aerial tides by the barometer, on account of the equality of pressure of the atmosphere, whatever be its height. The existence of aerial tides is not, however, hypothetical; it is proved by the effect they produce on the apparent position of the heavenly bodies; but this I cannot explain to you, till you understand the properties of light. Emily. And when shall we learn them? Mrs.^B. I shall first explain to you the nature of sound, which is intimately connected with that of air; and I think at our next meeting, we may enter upon the subject of optics. We have now considered the effects produced by the wide, and extended agitation, of the air; but there is another kind of agitation, of which the air is susceptible a vibratory trembling motion, which, striking on the drum of the ear, produces scunil. Caroline. Is not sound produced by solid bodies? The voice 16. Why is the wind apt to lessen about sunset ? 17. What effect mu?t the sun and moon produce upon the atmosphere, from their attraction* 18. Why do not the aerial tides affect the barometei ? ON WIND AND SOUND. 151 of animals, the ringing of bells, the music of instruments, all proceed from solid bodies. I know of no sound but that of the wind, which is produced by the air. Mrs. B. Sound, I assure you, results from a tremulous mo- tion of the air; and the sonorous bodies you enumerate, are merely the instruments by which that peculiar species of motion, is communicated to the air. Caroline. What! when I ring this little bell, is it the air that sounds, and not the bell? Mrs. B. Both the bell, and the air, are concerned in the pro- duction of sound. But sound, strictly speaking, is a perception excited in the mind, by the motion of the air, on the nerves of the ear; the air, therefore, as well as the sonorous bodies which put iu in motion, is only the cause of sound, the immediate ef- fect is produced by the sense of hearing: for without this sense, there would be no sound. Emily. I can with difficulty conceive that. A person born deaf, it is true, has no idea of sound, because he hears none; yet that does not prevent the real existence of sound, as all those who are not deaf, can testify. Mrs. B. I do not doubt the existence of sound, to all those who possess the sense of hearing; but it exists neither in the sonorous body, nor in the air, but in the mind of the person whose ear is struck, by the vibratory motion of the air, produced by a sonorous body. * Sound, therefore, is a sensation, produced in a living body; life, is as necessary to its existence, as it is to that of feeling or seeing. To convince you that sound does not exist in sonorous bodies, but that air or some other vehicle, is necessary to its production, endeavour to ring the little bell, after I have suspended it under a receiver in the air pump, from which I shall exhaust the air.... Caroline. This is indeed very strange: though I agitate it so violently, it produces but little sound. Mrs. B. By exhausting the receiver, I have cut off the com- munication between the air and the bell; the latter, therefore, cannot impart its motion, to the air. Caroline. Are you sure that it is not the glass, which covers the bell, that prevents our hearing it? Mrs. B. That you may easily ascertain, by letting the air into the receiver, and then ringing the bell. Caroline. Very true: I can hear it now, almost as loud, as if the glass did not cover it; and I can no longer doubt but that air is necessary to the production of sound. 19. How is sound produced ? 20. Does sound exist in the sonorous body, If not, what is it? 21. By what experiment might we prove that air is thp principal vehicle of sound ? 152 ON WIND AND SOUND. Mrs. B. Not absolutely necessary, though bv far the most common vehicle of sound. Liquids, as well as air, are capable of conveying the vibratory motion of a sonorous body, to the organ of hearing; as sound can be heard under water. Solid bodies also, convey sountt/as I can soon convince you by a very simple experiment. I shall fasten this string by the middle, round the poker; now raise the poker from the ground, by the two ends of the string, and hold one to each of your ears: I shall now strike the poker, with a key, and you will find that the sound is conveyed to the ear bv means of the strings, in a much more perfect manner, than if it had no other vehicle than the air. , Caroline. That it is, certainly, for I am almost stunned by the noise. But what is a sonorous body, Mrs. B. ? for all bo- die.s are capable of producing some kind of sound, by the motion they communicate to the air. Mrs. B* Those bodies are called sonorous, which produce clear, distinct, regular, and durable sounds, such as a bell, a . drum, musical strings, wind instruments, &c. They owe this troperty to their elasticity; for an elastic body, after having been struck, not only returns to its former situation, but having acquired momentum by its velocity, like the pendulum, it springs out on the opposite side. If I draw the string A B, (fig. 6, plate 14,) which is made fast at both ends, to C, it will not only return to its original position, but proceed onwards, to D. This is its first vibration; at the end of which, it will retain sufficient velocity to bring it to E, and back again to F, which constitutes its second vibration; the third vibration, will carry it only to G and H, and so on, till the resistance of the air destroys its motion. The vibration of a sonorous body, gives a tremulous motion to the air around it, very similar to the motion communicated to smooth water, when a stone is thrown into it. This, first pro- duces a small circular wave, around the spot in which the stone falls; the wave spreads, and gradually communicates its motion to the adjacent waters, producing similar waves to a consider- able extent. The same kind of waves are produced in the air, by the motion of a sonorous body, but with this difference, that as air, is an elastic fluid, the motion does not consist of regularly extending waves, but of vibrations; and are composed of a mo- tion, forwards and backwards, similar to those of the sonorous 22. What other bodies convey sound, and how can it be shown that they do so ? 23. What is meant by a sonorous body ? 24. To what do they owe this property? 25. How is this explained by fig. 6, plate 14? 26. How is it illustrated by a stone thrown into water, and how far does this illustration apply? ON WIND AND SOUND. 153 body. They differ also, in the one taking place in a plane, the other, in all directions: the serial undulations, being spherical. Emily. But if the air moves backwards, as well as forwards how can its motion extend so as to convey sound to a distance? Mrs. B. The first sphere of undulations, which are produced immediately around the sonorous body, by pressing against the contiguous air, condenses it. The condensed air, though im- pelled forward by the pressure, reacts on the first set of undu- lations, driving them back again. The second set of undula- tions which have been put in motion, in their turn, communicate their motion, and are themselves driven back, by reaction. Thus, there is a succession of waves in the air, corresponding with the succession of waves in the water. Caroline. The vibrations of sound, must extend much further than the circular waves in water, since sound is conveyed to a great distance. Mrs. B. The air is a fluid so much less dense than water, that motion is more easily communicated to it. The report of cannon produces vibrations of the air, which extend to seve miles around. Emily. Distant sound takes some time to reach us, since it is produced at the moment the cannon is fired; and we see the light of the flash, long before we hear the report. Mrs. B. The air is immediately put in motion, by the firing of a cannon; but it requires time for the vibrations to extend to any distant spot. The velocity of sound, is computed to be at the rate of 1142 feet in a second. Caroline. With what astonishing rapidity the vibrations must be communicated! But the velocity of sound varies, I sup- pose, with that of the air which conveys it. If the wind sets towards us from the cannon, we must hear the report sooner than if it set the other way. Mrs. B. The direction of the wind makes less difference in the velocity of sound, than you would imagine. If the wind sets from us, it bears most of the aerial waves away, and renders the sound fainter; but it is not very considerably longer in reaching the ear, than if the wind blew towards us. This uniform velo- city of sound, enables us to determine the distance of the object, from which it proceeds; as that of a vessel at sea, firing a cannon, or that of a thunder cloud. If we do not hear the thunder, till naif a minute after we see the lightning, we conclude the cloud to be at the distance of six miles and a half. 27. How are the vibrations propagated? 28. How can we prove that Bound, does not travel as rapidly as light ? 29. At what rate is sound said to travel? 30. Is the velocity much influenced by the direction of the wind? 31. How will sound enabie us to judge of the distance of objects? 154 ON WIND AND SOUND. Emily. Pray, how is the sound of an echo produced? Mrs. B. When the aerial vibrations meet with an obstacle, having a hard and regular surface, such as a wall, or rock, they are reflected back to the ear, and produce the same sound a se cond time; but the sound will then appear to proceed, from the object by which it is reflected. If the vibrations fall perpen- dicularly on the obstacle, they are reflected back in the same line; if obliquely, the sound returns obliquely, in the opposite direction, the angle of reflection being equal to the angle of in- cidence. Caroline. Oh, then, Emily, I now understand why the echo of my voice behind our house is heard so much plainer by you than it is by me, when we stand at the opposite ends of the gravel walk. My voice, or rather, I should sav, the vibrations of air it occasions, fall obliquely on the wall of the house, and are reflected by it, to the opposite end of the gravel walk. Emily. Very true; and we have observed, that when we stand in the middle of the walk, opposite the house, the echo re- turns to the person who spoke. Mrs. B. Speaking-trumpets, are constructed on the principle, that sound is reflected. The voice, instead of being diffused in the open air, is confined within the trumpet; and the vibrations which would otherwise spread laterally, fall against the sides of the instrument, and are reflected from the different points of in- cidence, so as to combine with those vibrations which proceed straight forwards. The vibrations are thus forced onwards, in the direction of the trumpet, so as greatly to increase the sound, to a person situated in that direction. Figure 7, plate 14, will give you a clearer idea, of the speaking-trumpet; in this, lines are drawn to represent the manner, in which we may imagine the sound to be reflected. There is a point in front of the trum- pet, F, which is denominated its focus, because the sound is there more intense, than at any other spot. The trumpet used by deaf persons, acts on the same principle; although it does not equally increase the sound. Emily. Are the trumpets used as musical instruments, also constructed on this principle? Mrs. B. So far as their form tends to increase the sound, they are; but, as a musical instrument, the trumpet becomes it- self the sonorous body, which is made to vibrate by blowing into it, and communicates its vibrations to the air. I will attempt to give you, in a few words, some notion of the nature of musical sounds, which, a you are fond of music, must be interesting to you. 32. How are echoes produced? 33. What is the operation and effect of the speaking-trumpet (fig. *7, plate 14) ? ON WIND AND SOUND. 155 If a sonorous body be struck in such a manner, that its vibra- fions, are all performed in regular times, the vibrations of the air, will correspond with them; and striking in the same regular manner on the drum of the ear, will produce the same uniform sensation, on the auditory nerve, and excite the same uniform idea, in the mind; or, in other words, we shall hear one musical tone. But if the vibrations of the sonorous body, are irregular, there will necessarily follow a confusion of aerial vibrations; for a second vibration may commence, before the first is finished, meet it half way on its return, interrupt it in its course, and produce harsh jarring sounds, which are called discords. Emily. But each set of these irregular vibrations, if repeated alone, and at equal intervals, would, I suppose, produce a musi- cal tone? It is only their irregular interference, which occasions discord. Mrs. B. Certainly. The quicker a sonorous body vibrates, the more acute, or sharp, is the sound produced; and the slower the vibrations, the more grave will be the note. ^ Caroline. But if I strike any one note of the piano-forte', epeatedly, whether quickly or slowly, it always gives the same cone. Mrs. B. Because the vibrations of the same string, at the same degree of tension, are always of a similar duration. The quickness, or slowness of the vibrations, relate to the single tones, not to the various sounds which they may compose, by succeed- ing each other. Striking the note in quick succession, produces a more frequent repetition of the tone, but does not increase the velocity of the vibrations of the string. The duration of the vibrations of strings, or wires, depends upon their length, their thickness, or weight, and their degree ci tension: thus, you find, the low bass notes are produced by long, thick* loose strings; and the high treble notes by short, small, and tight strings. Caroline. Then, the different length, and size, of the strings of musical instruments, serve to vary the duration of the vibra- tions, and consequently, the acuteness or gravity of the notes? Mrs. B. Yes. Among the vaiiety of tones, there are some which, sounded together, please the ear, producing what we call harmony, or concord. This arises from the agreement of the vibrations of the two sonorous bodies; so that some of the vibra- tions of each, strike upon the ear at the same time. Thus, if the 34. How is a musical tone produced? 35. What occasions discords? 36. Upon what does the acuteness or gravity of a sound depend ? 37. Does the force, with which a string is struck, affect the rapidity of its vibrations ? 38, How are the strings made to produce the high and low notes? 39. What is meant by harmony, or concord, and how is it produced? 156 ON WIND AND SOUND. vibrations of two strings are performed in equal times, the same tone is produced by both, and they are said to be in unison. Emily. Now, then, I understand why, when I tune my harp, in unison with the piano-forte, I draw the strings tighter, if it is too low, or loosen them, if it is too high a pitch: it is in order to bring them to vibrate, in equal times, with the strings of the pi arto -forte. Mrs. B. But concord, you know, is not confined to unison; for two different tones, harmonize in a variety of cases. When the vibrations of one string (or other sonorous body) vibrate in double the time of another, the second vibration of the latter, will strike upon the ear, at the same instant, as the first vibration of the former; and this is the concord of an octave. If the vibrations of two strings are as two to three, the second vibration of the first, corresponds with the third vibration of the latter, producing the harmony called, a fifth. Caroline. So, then, when I strike the key-note with its fifth, I hear every second vibration of one, and every third of the other, at the same time? Mrs. B. Yes; and the key-note, struck with the fourth, is likewise a concord, because the vibrations, are as three to four. The vibrations of a major third, with the key-note, are as four to five; and those of a minor third, as five to six. There are other tones, which, though they cannot be struck together without producing discord, if struck successively, give us that succession of pleasing sounds, which is called melody. Harmony, you perceive, arises from the combined effect of two, or more concordant sounds, while melody, is the result of certain simple sounds, which succeed each other. Upon these general principles, the science of music is founded; but, I am not suffi- ciently acquainted with it, to enter into it any further. We shall now, therefore, take leave of the subject of sound; and, at our next interview, enter upon that of optics, in which we shall consider the nature of light, vision, and colours. 40. When are strings said to be in unison? 41. How are octaves pro- duced? 42. How are fifths produced? 43. How major and minor thirds f 44. What ia meant by melody, and in what particular does it differ from har naony? I'J. \"VI XV. CONVERSATION XIV. ON OPTICS. OP LUMINOUS, TRANSPARENT, AND OPAttUE BODIES. OF THE RADIATIOH OFLIPHT. OF SHADOWS. OF THE REFLECTION OF LIGHT. OPAftUB BODIES SEEN ONLY BY REFLECTED LIGHT. VISION EXPLAINED. CAMERA OBSCURA. IMAGE OF OBJECTS ON THE RETINA. CAROLINE. I LONG to begin our lesson to day, Mrs. B., for I expect that it will be very entertaining. Mrs. B. Optics is that branch of philosophy, which treats of the nature and properties of light. It is certainly one of the most interesting branches of Natural Philosophy, but not one of the easiest to understand; I must, therefore, beg that you M'ill give me your undivided attention. I shall first inquire, whether you comprehend the meaning of a luminous body, an opaque body, and a transparent body. Caroline. A luminous body is one that shines; an opaque.... Mrs. B. Do not proceed to the second, until we have agreed upon the definition of the first. All bodies that shine, are not luminous; for a luminous body is one that shines by its own light; as the sun, the fire, a candle, &c. Emily. Polished metal then, when it shines with so much brilliancy, is not a luminous body? Mrs. B. No, for it would be dark, if it did not receive light from a luminous body; it belongs, therefore, to the class of dark, as well as of opaque bodies, which comprehends all such as are neither luminous, nor will admit the light to pass through them. Emily. And transparent bodies, are those which admit the light to pass through them, such as glass and water. Mrs. B. You are right. Transparent, or pellucid bodies, are frequently called mediums, because they allow the rays of light to pass" through them; and the rays which pass through, are* said to be transmitted by them. Light, when emanated from the sun, or any other luminous 1. What is optics? 2. What is meant by a luminous body? 3. What is meant by a dark body, and what by an opaque body ? 4. What are transpa- rent bodies? 5. What is a medium ? o 158 ON OPTICS. body, is projected forward in straight lines, in every possible direction; so that the luminous bouy, is not only the general centre, from whence all the rays proceed; but every point of it, may be considered as a centre, which radiates light in every di- rection. (Fig. I, plate 15.) Emily. But do not the rays which are projected in different directions, and cross each other, interfere, and impede each other's course? Mrs. B. Not at all. The particle? jf light, are so extreme- ly minute, that they are never known to interfere with each other. A ray of light, is a single line of light, projected from a luminous body; and a pencil of rays, is a collection of rays, pro- ceeding from any one point of a luminous body, as fig. 2. Caroline. Is light then a substance composed of particles, like other bodies? Mrs. B. That is a disputed point, upon which I cannot pre- tend to decide. In some respects, light is obedient to the laws which govern bodies; in others, it appears to be independent of them: thus, though its course is guided by the laws of motion, it does not seem to be influenced by those of gravity. It has never been discovered to have weight, though a variety of inte resting experiments have been made with a view of ascertaining that point; but we are so ignorant of the intimate nature of light, that an attempt to investigate it, would lead us into a labyrinth of perplexity, if riot of error; we shall, therefore, confine our at- tention to those properties of light, which are well ascertained. Let us return to the examination of the effects of the radia- tion of light, from a luminous body. Since the rays of light are projected in straight lines, when they meet with an opaque body through which they are unable, to pass, they are stopped short in their course; for they cannot move in a curve line round the body. Caroline. No, certainly; for it would require some other force besides that of projection, to produce motion in a curve tine. Mrs. B. The interruption of the rays of light, by the opaque body, produces, therefore, darkness on the opposite side of it: and if this darkness fall upon a wall, a sheet of paper, or any object whatever, it forms a shadow. Emily. A shadow, then, is nothing more than darkness pro duced by the intervention of an opaque body, which prevents the rays of light from reaching an object behind it. 6. Ho tf is light projected from luminous bodies, and how, from every point of such bodies, (fig;. 1, plate 15 ?) 7. Why do not the rays of light from dif- ferent points, stop each other's progress ? 8. What is a ray, and what a pen- cil of rays ? fig. 2, plate 15. 9. Do we know whether light is a substance, similar to bodies in general ? 10. When a ray of light fails upon an opaque body, what is the result f ON OPTICS. 159 Caroline. Why then are shadows of different degrees of darkness; for I should have supposed, from your definition of a shadow, that it would have been perfectly black? Mrs. B. It frequently happens that a shadow is produced by an opaque body, interrupting the course of the rays from one luminous body, while light from another, reaches the space where the shadow is formed; in which case, the shadow is proportion- ally fainter. This happens when the opaque body is lighted by two candles: if you extinguish one of them, the sha low will be both deeper, and more distinct. Caroline. But yet it will not be perfectly dark. Mrs. B. Because it is still slightly illuminated by light reflected from the walls of the room, and other surrounding objects. You must observe, also, that when a shadow is produced by the interruption of rays from a single luminous body, the dark- ness is proportioned to the intensity of the light. Emily. I should have supposed the contrary; for as the light reflected from surrounding objects on the shadow, must be in proportion to the intensity of the light, the stronger the light, the more the shadow will be illumined. Mrs. B. Your remark is perfectly just; but as we have no means of estimating the degrees of light, and of darkness, but by comparison, the strongest light will appear to produce the deep- est shadow. Hence a total eclipse of the sun, occasions a more sensible darkness than midnight, as it is immediately contrast- ed with the strong light of noonday. Caroline. The re-appearance of the sun, after an eclipse, must, by the same contrast, appear remarkably brilliant. Mrs. B Certainly. There are several things to be observed, in regard to the form, and extent, of shadows. If the luminous body A (fig. 3.) is larger than the opaque body B, the shadow will gradually diminish in size, till it terminates in a point. Caroline. This is the case with the shadows of the earth, and the moon; as the sun, which illumines them, is larger than either of those bodies. And wlvy is it not the case with the shadows of terrestrial objects? Their shadows, far from diminishing, are always larger than the object, and increase with the distance from it. Mrs. B. In estimating the effect of shadows, we must con- sider the dimensions of the luminous body; when the luminous body is less, than the opaque body, the shadow will increase 11. In what does shadow consist? 12. Why are they, in general, but partially dark? 13. Upon what does the intensity of a shadow depend? 14. How are shadows affected by the size of the luminous body, as represent- ed In plate 15, fig. 3? 15. When is the shadow larger than the intercepting; bcdy? 1GO ON OPTICS. with the distance. This will be best exemplified, by observing the shadow of an object lighted by a candle. Emily. I have often noticed, that the shadow of my figure, against the wall, grows larger, as it is more distant from me, which is owing;, no doubt, to the candle that shines on me, be- ing much smaller than myself. Mrs. B. Yes. The shadow of a figure as A, (fig. 4.) varies in size, according to the distance of the several surfaces .BCD E, on which it is described. Caroline. I have observed, that two candles, produce two shadows from the same object; whilst it would appear, from what you said, that they should rather produce only half a sha (low, that is to say, a very faint one. Mrs. B. The number of lights (in different directions) while it decreases the intensity of the shadows, increases their number, which always corresponds with that of the lights; for each light, makes the opaque body cast a different shadow, as illustrated by fig, 5. which represents a ball A, lighted by three candles, B, C, D; and you observe the light B, produces the shadow 6, the light (/, the shadow c, and the light 3), the shadow d; but nei- ther of these shadows will be very dark, because the light of one candle only, is intercepted by the ball; and the spot is still illu- minated by the other two. Emily. I think we now understand the nature of shadows very well; but pray, what becomes of the rays of light, which opaque bodies arrest in their course, and the interruption of which, is the occasion of shadows? Mrs. B. Your question leads to a very important property of light, Reflection. When rays of light encounter an opaque body, they cannot pass through it, and par^of them are absorbed by it, and part are. reflected, arid rebound; just as an elastic ball rebounds, when struck against a wall. By reflection, we mean that the light is turned back again, through the same medium which it had traversed in its tirt course. Emily. And is light, in its reflection, governed by the same laws, as solid, elastic bodies? Mrs. B. Exactly. If a ray of light fall perpendicularly on an opaque body, it is reflected back in the. same line, towards the point whence it proceeded. If it fall obliquely, it is reflect- ed obliquely, but in the opposite direction; the ray which falls upon the reflecting surface, is called the incident ray, and that which leaves it, the reflected ray; the angle of incidence, is al- 16. What i? explained by fig. 4, plate 15 ? 17. What will be the effect of several lights, as in fig. 5, plate 15 ? 18. Why will neither of these shadow* be very dark? 19. What becomes of the light which falls upon an opaque body ? 20. What is meant by reflection ? ON OPTICS. 161 ways equal to the angle of reflection. You recollect that law in mechanics? Emily. Oh yes, perfectly. Mrs. B. If you will shut the shutters, we will admit a ray of the sun's light, through 3 very small aperture, and I can show you how it is reflected. I now hold this mirror, so that the ray shall fall perpendicularly upon it. Caroline. I see the ray which falls upon the mirror, but not that which is reflected by it. Mrs. B. Because it is turned directly back again; and the ray of incidence, and that of reflection, are confounded together, both being in the same line, though in opposite directions. Emily. The ray then, which appears to us single, is really double, and is composed of the incident ray, proceeding to the tr.iiror, arid of the reflected ray, returning from the mirror. Mrs. B. Exactly so. We will now separate them, by hold- ing the mirror M, (tig. 6,) in such a manner, that the incident ray, A B, shall fdl obliquely upon it- you see the reflected ray, B C, is marching oft' in another direction. If we draw a line from the point of incidence B, perpendicularly, to the mir- ror, it will divide the angle of incidence, from the angle of re- flection, and you will see that they are equal. Emily. Exactly; and now, that you hold the mirror, so that the ray falls more obliquely upon it, it is also reflected more obliquely, preserving the equality of the angles of incidence, and of reflection. Mrs. B. It is by reflected rays only, that we see opaque ob- jects Luminous bodies, send rays of light immediately to our eyes, but the rays which they send to other bodies, are invisible to us, and are seen, only when they are reflected by those bo- dies, to our eyes. Emily. But have we not just seen the ray of light, in its pass- age from the sun to the mirror, and its reflections? yet, in nei- ther case, were those rays in a direction to enter our eyes. Mrs. B. What you saw, was the light reflected to your eyes, by small particles of dust floating in the air, and on which the ray shone, in its passage to, and from, the mirror. Caroline. Yet I see the sun, shining on that house yonder, as clearly as possible. Mrs. B. Indeed you cannot see a single ray, which passes 21. What is meant by the incident, and reflected rays? 22. What is the result, when the incident ray falls perpendicularly, and what, when it falls obliquely ? 23. What two angles are always equal in this case ? 24. To what law in mechanics, is this analogous, as represented in fig 1 . 4, plate 2 ? 25. What is represented by fig. 6, plate 15 ? 26. By what light are we ena- bled to see opaque, and by what, luminous bodies ? 27. What enables us to see a ray of light in its passage, through a darkened room ? O2 162 ON OPTICS. from the sun to the house; you see, by the aid of those rays, which enter your eyes ; therefore, it is* the rays which are re- flected by the house, to you, and not those which proceed di- i ectly from the sun, to the house, that render the building visi- ble to you. Caroline. Wky then does one side of the house appear to be in sunshine, and the other in shade? for, if I cannot see the sun shine upon it, the whcle of the house should appear in the shade. Mrs. B. That side of the house, which the sun shines upon, receives,and reflects more light, and therefore, appears more lumi nous and vivid, than the side which is in shadow; for the latter is illumined onty ; by rays reflected upon it by other objects; these rays are, therefore, twice reflected before they reach your sight; and as light is more, or less, absorbed by the bodies it strikes upon, every time a ray is reflected, its intensity is dimin- ished. Caroline. Still I cannot reconcile to myself, the idea that we do not see the sun's rays shining on objects, but only those which such objects reflect to us. Mrs. B. I do not, however, despair of convincing you of it. Look at that large sheet of water; can you tell why the sun ap- pears to shine on one part of it only? Caroline. No, indeed; for the whole of it is equally exposed to the sun. This partial brilliancy of water, has often excited my wonder; but it has struck me more particularly by moon- light I have frequently observed a vivid streak of moonshine on the sea, while the rest of the water remained in deep obscu- rity, and yet there was no apparent obstacle to prevent the moon from shining equally on every part of the water. Mrs. B. By moonlight the effect is more remarkable, on account of the deep obscurity of the other parts of the waterj while by the sun's light, the effect is too strong for the eye to be able to observe it so distinctly. Caroline. But, if the sun really shines on every part of that sheet of water, why does not every part of it, reflect rays to my eyes? " Mrs. B. The reflected rays, are not attracted out of their natural course, by your eyes. The direction of a reflected ray, you know, depends on that of the incident ray; the sun's rays, therefore, which fall with various degrees of obliquity upon the water, are reflected in directions equally various; some of these 23. By what reasoning would you prove that an object, such, for example, as a house, Is seen by reflected light ? Zd. Why may one side of siv.h object appear more bright than another side ? 30. How is the fact exemplified by the sun, or moon, shining upon water ? 31. Why is this best evinced by moon ON OPTICS. 163 meet your eves, and you will see them, but those which fall elsewhere- are invisible to you. Caroline. The streak of sunshine, then, which we now see upon the water, is composed cf those rays which by their reflec- tion, happen to fall upon my ej'es? Mrs. B. Precisely. Emily. But is that side of the house yonder, which appears to be in shadow, really illuminated by the sun, and its rays re- flected another way? Mrs. B. No; that is a different case, from the sheet of wa- ter. That side of the house, is really in shadow; it is the west side, which the sun cannot shine upon, till the afternoon. Emily. Those objects, then, which are illumined by reflected rays, and those which receive direct rays from the sun, but which do not reflect those rays towards us, appear equally in shadow? Mrs. B. Certainly; for we see them both illumined by re- flected rays. That part of the sheet of water, over which the trees cast a shadow, by what light do you see it? Emily. Since it is not by the sun's direct rays, it must be bj those reflected on it from other objects, and which it again re- flects to us. Caroline. But if we see all terrestrial objects by reflected light, (as we do the moon,) why do they appear so bright and luminous? I should have supposed that reflected rays, would have been dull and faint, like tnose of the moon. Mrs. B. The moon reflects the sun's light, with as much vividness as any terrestrial object. If you look at it on a clear night, it will appear as bright as a sheet of water, the walls of a house, or any object seen by daylight, and on which the sun shines. The rays of the moon are doubtless feeble, when com- pared with those of the sun; but that would not be a fair coir- parison, for the former are incident, the latter, reflected rays. Caroline. True; and when we see terrestrial objects by moonlight, the light has been twice reflected, and is consequent- ly, proportionally fainter. Mrs. B. In traversing the atmosphere, the rays, both of the sun, and moon, lose some of their light. For though the pure air, is a transparent medium, which transmits the rays of light freely, we have observed, that near the surface of the earth, it is loaded with vapours and exhalations, by which some portion of them are absorbed. Caroline. I have often noticed, that an object on the summit 32. By what light do we see the moon, and why is it comparatively fee- "ble J 33. What circumstance, renders objects seen by moonlight, still lesa vivid ? 164 ON OPTICS. of a hill, appears more distinct, than one at an equal distance in a valley, or a plain; which is owing, I suppose, to the air being more free from vapours in an elevated situation, arid tne reflected rays, being consequently brighter. Mrs. B. That may have some sensible effect; but, when an object on the summit of a hill, has a back ground of light sky,, the contrast with the object, makes its outline more distinct. Caroline. I now feel well satisfied, that we see opaque ob- jects, only by reflected rays; but I do not understand, how these rays, show us the objects from which they proceed. Mrs. R. I shall hereafter describe the structure of the eye, very particularly, but will now observe, that the small round spot, which is generally called the sight of the eye, is properly denominated the pupil; arid that the retina, is an expansion of the optic nerve on the back part of the ball of the eye, upon which, as upon a screen, the rays fall, which enter at the pupil. The rays of light, enter at the pupil of the eye, and proceed to the retina; and there they describe the figure, colour, and (excepting size) form a perfect representation of the object, from which they proceed. We shall again close the shutters, and admit the light, through the small hole made for that purpose,, and you wiil see a picture, on the wall, opposite the aperture, similar to that which is delineated on the retina of the eye. The picture is somewhat confused, but by using a lens, to bring the rays to a focus, it will be rendered very distinct. Caroline. Oh, how wonderful! There is an exact picture in miniature of the garden, the gardener at work, the trees blown about by the wind. The landscape, would be perfect, if it were not reversed; the ground, being above, and the sky beneath. Mrs. B. It is riot enough to admire, you must understand, this phenomenon, which is called a camera obscura, or dark . chamber; from the necessity of darkening the room, in order to exhibit it. The camera obscura, sometimes consists of a small box, properly fitted up, to represent external objects. This picture, you now see, is produced by the rays of light, reflected from the various objects in the garden, and which are admitted through the hole in the window shutter. The rays from the glittering weathercock, at the top of the alcove, A, (plate 16.) represent it in this spot, a; for the weather- cock, a few scending 34. What is meant by the pupil of the eye? 35. What by the retina? 36. How do the rays of light operate on the eye in producing vision ? 37. How may this be exemplified, in a daikened room ? 38. What is meant by a camera obscura? 39. How is it explained in plate 16 ? I ON OPTICS. 165 you know, always move m straight lines; those, therefore, which enter the room, in a descending direction, will continue their course in the same direction, and will consequently fall upon the lower part of the wall opposite the aperture, and represent the weathercock, reversed in that spot, instead of erect, in the uppermost part of the landscape. Emily. And the rajs of light, from the steps, (B) of the alcove, in entering the aperture, ascend, and will describe those steps in the highest, instead of the owest, part of the landscape. Mrs. B. Observe, too, that the rays coming from the alcove, which is to our left, describe it on the wall, to the right; while those, which are reflected by the walnut tree, C D, to our right, delineate its figure in the picture, to the left, c d. Thus the rays, coming in different directions, and proceeding always in right lines, cross each other at their entrance through the aper- ture; those which come from above, proceed below, fhose from the right, go to the left, those from the left, towards the right; thus every object is represented in the picture, as occupying a situa- tion, the very reverse of that which it does in nature. Caroline. Excepting the flower-pot, E F, which, though its position is reversed, has not changed its situation in the land- scape. Mrs, B. The flower-pot, is directly in front of the aperture; so that its rays, fall perpendicularly upon it, and consequently proceed perpendicularly to the wall, where they delineate the object, directly behind the aperture. Emily. And is it thus, that the picture of objects, is painted on the retina of the eye? Mrs. B. Precisely. The pupil of the eye, through which the rays of light enter, represents the aperture in the window- shutter; and the image, delineated on the retina, is exactly similar to the picture on the wall. Caroline. You do not mean to say, that we see only the re- presentation of the object, which is painted on the retina, and not the object itself? Mrs. B. If, by sight, you understand that sense, by which the presence of objects is perceived by the mind, through the means of the eyes, we certainly see only the image, of those ob jects, painted on the retina. Caroline. This appears to me quite incredible. Mrs. B. The nerves, are the only part of our frame, capable of sensation^ they appear, therefore, to be the instruments, which the mind employs in its perceptions; for a sensation, al- 40. Why are the objects inverted and reversed? 41. What analogy is there between the camera obscura, and the eye ? 42. Is it the object, or its picture on the retina, which presents to the mind an idea of the object seen i 166 ON OPTICS. ways convejs an idea, to the mind. Now it is known, that our nerves can be affected only by contact; and for this reason, the organs of sense, cannot act at a distance: for instance, we are capable of smelling only particles \vhich are actually in contact with the nerves of the nose. We havd already observed, that the odour of a flower consists in effluvia, composed of very mi- nute particles, which penetrate the nostrils, and strike upon the olfactory nerves, which instantly convey the idea of odour to the mind. Emily. And sound, though it is said to be heard at a dis- tance, is, in fact, heard only when the vibrations of the air, which convey it to our ears, strike upon the auditory nerve. Caroline. There is no explanation required, to prove that the senses of feeling and of tasting, are excited only by contact. Mrs. B. And I hope to convince you, that the sense of sight, is so likewise. The nerves, which constitute the sense of sight, are not different in their nature from those of the other organs.; they are merely instruments which convey ideas to the mind, and can be affected only on contact. Now, since real objects cannot be brought to touch the optic nerve, the image of them is conveyed thither by the rays of light, proceeding from real ob- jects, which actually strike upon the optic nerve, and form that image which the mind perceives. Caroline. While I listen to your reasoning, I feel convinced; but when I look upon the objects around, arid think that I do not see them, but mere'y their image painted in my eyes, my belief is again staggered. I cannot reconcile to myself, the idea, that I do not really see this book which I hold in my hand, nor the words which I read in it. Mrs. B. Did it ever occur to you as extraordinary, that you never beheld your own face? Caroline. No; because I so frequently see an exact repre- sentation of it in the looking-glass. Mrs. B, You see a far more exact representation of objects on the retina of your eye: it is a much more perfect mirror, than any made by art. Emily. But is it possible, that the extensive landscape, which I now behold from the window, should be represented on so small a space, as the retina of the eye? Mrs. B. It would be impossible for art to paint so small and distinct a miniature; but nature works with a surer hand, and a more delicate pencil. That power alone, which forms the feathers of the butterfly, and the organs oi the minutest insect, can 43. By what organs is sensation produced, and how must these organs be affected? 44. How will the idea of contact, apply to objects not touching the eye ? ON OPTICS. 167 pourtray so admirable and perfect a miniature, as that which is represented on the retina of the eye. Caroline. But, Mrs. B., if we see only the image of objects, why do we not see them reversed, as you showed us they were, m the camera obscura? Is not that a strong argument against your theory? Mrs. B. Not an unanswerable one, I hope. The image on the retina, it is true, is reversed, like that in the camera ob- scura; as the rays, from the different parts of the landscape, in- tersect each other on entering the pupil, in the same manner as they do. on entering the camera obscura. The scene, however, does not excite the idea of being inverted, because we always see an object in the direction of the rays which it sends to us. Emily. I confess I do not understand that. Mrs. B. It is, I think, a difficult point to explain clearly. A ray which comes from the upper part of an object, describes the image on the lower part of the retina; but, experience having taught us, that the direction of that ray is from above, we con- sider that part of the object it represents as uppermost. The rays proceeding from the lower part of an object, fall upon the upper part of the retina; but as we know their direction to be from below, we see that part of the object they describe as the lowest. Caroline. When I want to see an object above me, I look up; when an object below me, I look down. Does not this prove that I see the objects themselves? for if I beheld only the image, there \vould be no necessity for looking up or down, ac- cording as the object was higher or lower, than myself. Mrs. B. 1 be- your pardon. When you look up, to an ele- vated object, it is in order that the rays reflected from it, should fall upon the retina of your eyes; but the very circumstance of directing your eyes upwards, convinces you that the object is elevated, and teaches you to consider as uppermost, the image it forms on the retina, though it is, in fact, represented in the lowest part of it. When you look down upon an object, you draw your conclusion from a similar reasoning; it is thus that we see all objects in the direction of the rays which reach out eyes. But I have a further proof in favour of what I have advanced, which, I hope, will remove your remaining doubts: I shall, how- ever, defer it till our next meeting, as the lesson has been suffi- ciently long to-day. 45. Why do not objects appear reversed to the eye, as in Ihe camera ob- scura ? CONVERSATION XV. OPTICS continued ON THE ANGLE OF VISION, AND THE REFLECTION OF MIRRORS. ANGLE OP VISION. REFLECTION OF PLAIN MIRRORS. REFLECTION OH CONVEX MIRRORS. REFLECTION OF CONCAVE MIRRORS. CAROLINE. WELL, Mrs. B., I am very impatient to hear what further proofs you have to offer, in support of your theory. You must allow, that it was rather provoking to dismiss us as you did at our last meeting. Mrs. B. You press so hard upon me with your objections, that you must give me time to recruit my forces. Can you tell me, Caroline, why objects at a distance, appear smaller than they really are? Caroline. I know no other reason than their distance. Mrs. B. It is a fact, that distance causes objects to appear smaller, but to state the fact, is not to give the reason. We must refer again to the camera obscura, to account for this circum- stance; and you will find, that the different apparent dimen- sions of objects at different distances, proceed from our seeing, not the objects themselves, but merely their image on the re- tina. Fig. 1, plate 17, represents a row of trees, as viewed in the camera obscura. I have expressed the direction of the rays, from the objects to the image, by lines. Now, observe, the ray which comes from the top of the nearest tree, and that which comes from the foot of the same tree, meet at the aperture, form- ing an angle of about twenty-five degrees; the angle under which we see any object, is called, the visual angle, or, angle of vision. These rays cross each other at the aperture, forming equal angles on each side of it, and represent the tree invert* a in the camera obscura. The degrees of the image, are consider- ably smaller tl an those of the object, but the proportions are perfectly preserved. 1. What is meant by the angle of vision, or the visual angle ? /'A/A- A77A ON THE ANGLE OF VISION. 169 Now, let us notice the upper and lower ray, from the most distant tree; they form an angle of not more than twelve or fif- teen degrees, and an image of proportional dimensions. Thus, two objects of the same size, as the two trees of the avenue, form figures of different sizes in the camera obscura, according to their distance; or, in other words, according to the angle ot vision under which they are seen. Do you understand this? Caroline. Perfectly. Mrs. B. Then you have only to suppose, that the represen- tation in the camera obscura, is similar to that on the retina. Now, since objects of the same magnitudes, appear to be of different dimensions, when at different distances from us, let me ask you which it is, that you see; the real objects, which, we know> do not vary in size, or the images, which, we know, do vary, according to the angle of vision under which we see them? Caroline. I must confess, that reason is in favour of the lat- ter. But does that chair, at the further end of the room, form an image on my retina, much smaller than this which is close to me? they appear exactly of the same size. Mrs. B. Our senses are imperfect, but the experience we acquire by the sense of touch, corrects the illusions of our sight, with regard to objects within our reach. You are so perfectly convinced, of the real size of objects, which you can handle, that you do not attend to the apparent difference. Does that house appear to you much smaller, than when you are close to it? Caroline. No, because it is very near us. Mrs. B. And yet you can see the whole of it, through one of the windows of this room. The image of the house on your retina must, therefore, be smaller than that of the window through which you see it. It is your knowledge of the real mag- nitude of the house which prevents your attending to its appa- rent size. If you were accustomed to draw from nature, you would be fully aware of this difference. Emily. And pray, what is the reason that, wh-en we look up an avenue, the trees not only appear smaller as they are more distant, but seem gradually to approach each other, till they meet in a point? Mrs. B. Not only the trees, but the road which separates the two rows, forms a smaller visual angle, in proportion as it is more distant from us; therefore, the width of the road gradu- ally diminishes, as well as the size of the trees, till at length the 2. Why do objects of the same size appear smaller when distant, than when neir? 3. Why do not two objects, known to be equal in size, appear to differ, when at different distances from the eye ? 4. How is this exemplified, by a house seen through a window? P 170 ON THE ANGLE OF VISION". road apparently terminates in a point, at which the trees seem to meet. Emily. I am very glad to understand this, for I have lately begun to !*arn perspective, which appeared to me a very dry study; but now that 1 am acquainted with some of the principles on which it is founded, I shall find it much more interesting. Caroline. In drawing a view from nature, it seems that we do not copy the real objects, but the image they form on the retina of our eyes? Mrs. B. Certainly. In sculpture, we copy nature as she really exists; in painting, we represent her, as she appears to us. We must now conclude the observations that remain to be made, on the angle of vision. If the rays, proceeding from the extremities of an object, with an ordinary degree of illumination, do not enter the eye under an angle of more than two seconds, which is the 1- 1800th part of a degree, it is invisible. There are, consequently, two cases in which objects may be invisible; if they are either so small, or so distant, as to form an angle of less, than two seconds of a degree. In like manner, if the velocity of a body does not exceed degrees in an hour, its motion is imperceptible. Caroline. A very rapid motion may then be imperceptible, provided the distance of the moving body, is sufficiently great. Mrs. B. Undoubtedly; for the greater its distance, the smaller will be the angle, under which its motion will appear to the eye. It is for this reason, that the motion of the celestial bodies is invisible, although inconceivably rapid. Emily. I am surprised, that so great a velocity as 20 degrees an hour, should be invisible. Mrs. B^ The real velocity depends upon the space compre- hended in each degree, and upon the time, in which the moving body, passes over that space. But we can only know the ex- ten{ of this space, by knowing the distance of the moving; body, from its centre of motion; for supposing two men to set off at the same moment from A and B, (fig. 2.T to walk each to the end of their respective lines, C and D; if tney perform their walk in 5. Why do rows of trees, forming an avenue, appear to approach as they recede from the eye, until they eventually seem to meet? 6. In drawing a view from nature, what do we copy ? 7. What is the difference in sculpture, in this respee* ? 8. Excepting the rays from an object enter the eye, under a certain angle, they cannot be seen ; what must this angle exceed ? 9. What two circumstances may cause the angle to be so small, as not to produce vi- sion ? 10. Motion may be so slow as to become imperceptible, what is said on this point? 11. Under what circumstances may a body, moving with great rapidity, appear to be at rest? 12;- Upon what does the real velocity of a body, depend? ON THE ANGLE OF VISION. 171 the same space of time, they must have proceeded at a very dif- ferent rate; and vet to an eye situated at E, they will appear to have moved with equal velocity, because they will both have gone through an equal number of degrees, though over a very unequal length of ground. The number of degrees over which a body moves in a given time, is called its angular velocity; two bodies, you see, may have the same angular, or apparent velo- city, whilst their real velocities may differ almost infinitely. Sight is an extremely useful sense, no doubt, but it cannot al- ways be relied on, it deceives us both in regard to the size ynd the distance of objects; indeed, our senses would be very liable to lead us into error, if experience did not set us right. Emily. Between the two, I think that we contrive to acquire a tolerably accurate idea of objects. Mrs. B, At least sufficiently so, for the general purposes of life. To convince you how requisite experience is, to correct the errors of sight, I shall relate to you, the case of a young man, who was blind from his infancy, and who recovered his sight at the age of fourteen, by the operation of couching. At first, he had no idea, either of the size, or distance of objects, but imagined that every thing he saw touched his eyes; and it was not, till alter having repeatedly felt them, and walked from one object to another, that he acquired an idea of tneir respective dimensions, their relative situations, and their dis- tances. Caroline. The idea that objects touched his e} r es, is, how- ever, not so absurd, as it at first appears; for if we consider that we see only the image of objects, this image actually touches our eyes. Mrs. B. That i?, doubtless, the reason of the opinion he formed, before the sense of touch had corrected his judgment Caroline. But since an image must be formed on the retina of each of our eyes, why do we not see objects double? Mrs. B* The action of the rays, on the optic nerve of each eye. is so perfectly similar, that they produce but a single sen- sation; the mind, therefore, receives the same idea, from the retina of both eyes, and conceives the object to be single. Caroline. This is difficult to comprehend, arid I should think, can be but conjectural. Mrs. B. I can easily convince you, that you have a distinct image of an object formed on the retina of each eye. Look 13. What must be known, to enable us to ascertain the real space contain- ed in a degree? 14. What is' explained by fig 1 . 2, plate 17? 15. What is said respecting the evidence afforded by our senses, and how do we correct the errors into which they would lead us? 16. An image of a visible object is formed upon the retina of each eye, why, therefore, are not objects seen double ? 172 REFLECTION OF MIRRORS through the window, with both eyes open, at some object exactly opposite to one of the upright bars of the sash. Caroline. I now see a tree, the body of which, appears to be in a line exactly opposite to one of the bars. Mrs. B. If you now shut your right eye, and look with the left, it will appear to the left of the bar; then by closing the left eye, and looking with the other, it will appear to the right of the bar. Caroline. That is true, indeed! M~s. B. There are, evidently, two representations of the tree in different situations, which" must be owing to an image of it being formed on each eye; if the action of the rays, there- fore, on each retina, were not so perfectly similar as to produce but one sensation, v/e should see double; and we find that to be the case with some persons, who are afflicted with a disease in one eye, which prevents the rays of light from affecting it in the same manner as the other. Emily. Pray, Mrs. B., when we see the image of an object in a looking-glass, why is it not inverted, as in the camera ob- scura, and on the retina of the eye? Mrs. B. Because the rays do not enter the mirror by a small aperture, and cross each other, as they do at the orifice of a camera obscura, or the pupil of the eye. When you view yourself in a mirror, the rays from your eyes fall perpendicularly upon it, and are reflected in the same lines the image is, therefore, described behind the glass, and is situ- ated in the same manner as the object before it. Emily. Yes, I see that it is; but the looking-glass is not nearly so tall as I am, how is it, therefore, that I can see the whole of my figure in it? Mrs. B. It is not necessary that the mirror should be more than half your height, in order that you may see the whole of your person in it, (fig. 3.) The ray of light A B, from your eye, which falls perpendicularly on the mirror B D, will be reflected back, in the same line; but the ray from your feet, will fall ob- liquely on the mirror, for it must ascend in order to reach it; it will, therefore, be reflected in the line A D: and since we view objects in the direction of the reflected rays, which reach the eye, and since the image appears at the same distance, behind the mirror, that the object is before it, we must continue the line A I) to E, and the line C D to F, at the termination of which, the image will be represented. s 1 7. By what experiment can you prove that a separate image of an object is formed in each eye? 18. Under what circumstances are objects seen dou- ble? 19. Why is not the image of an object inverted in the common mirror * 20. Your whole figure may be seen in a looking-glass, which is not mor than half your height; how is this shown in fig. 3. plate 17? REFLECTION OF MIRRORS. Emily. Then I do not understand why I should not see the whole of my person in a much smaller mirror, for a ray of light from my f**f would always reach it, though more obliquely. Mrs. B. True; but the more obliquely the ray falls on tht mirror, the more obliquely it will be reflected; the ray would, therefore, be reflected above your head, aad you coultl not see it. This is shown by the dotted line (fig. 3.) Now stand a little to the right of the mirror, so that the rays of light from your figure may fall obliquely on it Emily. There is no image formed of me in the glass now. Mrs. B. I beg your pardon, there is; but you cannot see it, because the incident rays, falling obliquely on the mirror, will be reflected obliquely, in the opposite direction; the angles of incidence, and reflection, being equal. Caroline, place your- self in the direction of the reflected rays, and tell me whether you do not see Emily's image in the glass? Caroline. Let me consider. -In order to look in the direc- tion of the reflected rays, I must place myself as much to the left of the glass, as Emily stands to the right of it. Now I see her image, not straight before me, however, but before Ler; and it appears at the same distance behind the glass, that she is in front of it. Mrs. B. You must recollect, that we always see objects in the direction of the last rays, which reach our eyes. Figure 4 represents an eye, looking at the image of a vase, reflected by a mirror; it must see it in the direction of the ray A B, as that is the ray which brings the image to the eye; prolong the ray to C, and in that spot will the image appear. Caroline. I do not understand why a looking-glass reflects the rays of light; for glass is a transparent body, which should transmit them! Mrs. B. It is not the glass that reflects the rays which form the image you behold, but the silvering behind it; this silvering is a compound of mercury and tin, which forms a brilliant me- tallic coating. The glass acts chiefly as a transparent case, through which the rays find an easy passage, to, and from, the quicksilver. Caroline. Why then should not mirrors be made simply of mercury? Mrs. B. Because mercurv is a fluid. By amalgamating it with tinfoil, it becomes of tne consistence of paste, attaches itself to the glass, and forms, in fact, a metallic mirror, which 21. Why is the image invisible to the person, when not standing directly before the glass? 22. In what situation may a second person see the imivge reflected? 23. In what direction will an object always appear to the eye? 24. How is this explained by fig. 4, plate 17? 25. What is it that reflects the ra) s in a looking-gluss ? 174 REFLECTION O* 311RRORS. would be much more perfect without its glass cover, for the purest glass is never perfectly transparent; some of the rays, therefore, are lost during their passage through it. by being either absorbed, or irregularly reflected. This imperfection of glass mirrors, has introduced the use of metallic mirrors, for optical purposes. Emily. But since all opaque bodies reflect the rays of light, I do not understand why they are not all mirrors. Caroline. A curious idea indeed, sister,- it would be very gratifying to see oneself in every object at which one looked. Mrs. B. It is very true that all opaque objects reflect light; but the surface of bodies, in general, is so rough and uneven, that the reflection from them is extremely irregular, and prevents the rays from forming an image on the retina. This, you will be able to understand better, when I shall explain to you the na- ture of vision, and the structure of the eye. You may easily conceive the variety of directions in which rays would be reflected by a nutmeg-grater, on account of the inequality of its surface, and the number of holes with which it is pierced. All solid bodies more or less resemble the nutmeg- grater, in these respects; and it is only those which are suscepti- ble of receiving a polish, that can be made to reflect the rays with regularity. As hard bodies are of the closest texture, the least porous, and capable of taking the highest polish, they make the best mirrors; none, therefore, are so well calculated for this purpose, as metals. Caroline. But the property of regular reflection, is not con- fined to this class of bodies; for I have often seen myself, in a highly polished mahogany table. Mrs. B. Certainly; but as that substance is less durable, and its reflection less perfect, than that of metals, I believe it would seldom be chosen, for the purpose of a mirror. There are three kinds of mirrors used in optics; the plain, or flat, which are the common mirrors we have just mentioned; convex mirrors, and concave mirrors. The reflection of the two latter, is very different from that of the former. The plain mir- ror, we have seen, does not alter the direction of the reflected rays, and forms an image behind the glass, exactly similar to the object before it. A convex mirror has the peculiar proper- ty of making the reflected rays diverge, by which means it diminishes the image; and a concave mirror makes the rays converge, and under certain circumstances, magnifies the image. Emily. We have a convex mirror in the drawing-room, 26. All opaque bodies reflect some light, why do they not all act as mir- rors ? 27. What substances form the most perfect mirrors, and for what rea- on ? 28. What are the three kinds of mirrors usually employ ed for optib<\ purposes ? 20. How are the rays of light affected by them ? REFLECTION OF MIRRORS. 175 winch forms a beautiful miniature picture of the objects in the room; and I have often amused myself with looking at my magnified face in a concave mirror. But I hope you will ex- plain to us, why the one enlarges, while the other diminishes the objects it reflects. Mrs. B. Let us begin by examining the reflection of a con- vex mirror. This is formed of a portion of the exterior surface of a sphere. When several parallel rays fall upon it, that ray only which, if prolonged, would pass through the centre or axis of the mirror, is perpendicular to it. In order to avoid confu- sion, I have, in fig. 1, plat2 18, drawn only three parallel lines, A B, C D, E F, to represent rays falling on the convex mirror, M N; the middle ray, you will observe, is perpendicular to the mirror, the others fall on it, obliquely. Caroline. As the three rays are parallel, why are they not all perpendicular to the mirror? Mrs. B. They would be so to a flat mirror; but as this is spherical, no ray can fall perpendicularly upon it which is not directed towards the centre of the sphere. Emily. Just as a weight falls perpendicularly to the earth, when gravity attracts it towards the centre. Mrs. B. In order, therefore, that rays may fall perpendicu- larly to the .mirror at B and F, the rays must be in the direction of the dotted lines, which, you may observe, meet at the centre O of the sphere, of which fie mirror forms a portion. Now, can you tell me in What direction the three rays, A B, C D, E F, will be reflected? Emily. Yes, I think so: the middle ray, falling perpendicu- larly on the mirror, will be reflected in the same line: the two outer rays falling obliquely, will be reflected obliquelvto Gand II ; for the dotted lines you have drawn are perpcndicufars, which divide the angles of incidence and reflection, of those two rays. Mrs. B. Extremely well, Emily: and since we see objects in the direction of the reflected ray, we shall see the image L, which is the point at which the reflected rays, if continued through the mirror, would unite and form an image. This point is equally distant, from the surface and centre of the sphere, arid is called the imaginary focus of the mirror. Caroline. Pray, what is the meaning of focus? Mrs. B. A point at which converging rays, unite. And it is 30. What is the form of a convex mirror, and how do parallel rays fall upon it, as represented in fig. 1, plate 18 ? 31. What is represented by the dotted line in the same figure ? 32. Explain by the figure, how the parallel rays will be reflected. 33. At what distance behind such a mirror, would an ima-e t produced by parallel rays, be formed? 34. What is that point denomi- nated ? 176 REFLECTION OF CONVEX MIRRORS. in this case, called an imaginary focus; because the rajs do not really unite at that point, but only appear^bo do so: for the rays do not pass through the mirror, smce'they are reflected by it. Emily. I do not jet understand why an object appears smaller, when viewed in a convex mirror. Mrs, B. It is owing to the divergence of the reflected rays. You have seen that a convex mirror, by reflection, converts parallel rays into divergent rays; rays that fall upon the mirror divergent, are rendered still more so by reflection, and conver- gent rays are reflected either parallel, or less convergent. If then, an object be placed before any part of a convex mirror, as the vase A B, fig. 2, for instance, the two rays from its extremi- ties, falling convergent on the mirror, will be reflected less con- vergent, and will not come to a focus, till they arrive at C; then an eye placed in the direction of the reflected rays, will see the image formed in (or rather behind) the mirror, at a b. Caroline. But the reflected rays, do not appear to me to con- verge less than the incident rays. I should have supposed that, on the contrary, they converged more, since they meet in a point. Mrs. B. They would unite sooner than they actually do, if they were not less convergent than the incident rays: for ob serve, that if the incident rays, instead of being reflected by the mirror, continued their course in their original direction, thev would come to a focus at D, which is considerably nearer to the mirror than at C; the image, is, therefore, seen under a smaller angle than the object; and the more distant the latter is from the mirror, the smaller is the image reflected by it. You will now easily understand the nature of the reflection of concave mirrors. These are formed of a portion of the interna/ surface of a hollow sphere, and their peculiar property is to con verge the rays of light. Can you discover, Caroline, in what direction the three parallel rajs, A B, C D, E F, are reflected, which fall on the concave mirror, M N, (ftg. 3.) ? Caroline. I believe I can. The middle ray is sent back in the same line, in which it arrives, that being the direction of the axis of the mirror; and the two others will be reflected obliquely, as they fall obliquely on the mirror. I must now draw two dotted lines perpendicular to their points of incidence, which will divide their angles of incidence and reflection; and in 35. What is meant by a focus? 36. Why is the poirt behind the mirror, colled the imaginary focus ? 37. Why does an object appear to be lessened by a convex mirror, (fig. 2.) ? 38. What is a concave mirror, and what its peculiar property ? 39. How are parallel rays reflected by a toncave mirror, as explained by fig. 3, plate 18? REFLECTION OF CONCAVE MIRRORS. 177 order that those angles may be equal, the two oblique rays must be reflected to L, whejge they will unite with the middle ray. Mrs. B. Very well explained. Thus you see, that when any number of parallel rays fall on a concave mirror, they are all reflected to a fociis: for in proportion as the rays are more distant from the axis of the mirror, they fall more obliquely upon it, and are more obliquely reflected; in consequence of winch they come to a focus in the direction of the axis of the mirror, at a point equally distant from the centre, and the surface, of the sphere; and this point is not an imaginary focus, as happens with the convex mirror, but is the true focus at which the rays unite. Emily. Can a mirror form more than one focus, by reflecting rays? Mrs. B. Yes. If rays fall convergent on a concave mirror, (fig. 4,) they- are sooner brought to a focus, L,than parallel rays; their focus is, therefore, nearer to the mirror M N. Divergent rays are brought to a more distant focus than parallel rays, as in figure 5, where the focus is at L; but what is called the true focus of mirrors, either convex or concave, is that of parallel rays, and is equally distant from the centre, and the surface of the spherical mirror. I shall now show you the real reflection of rays of light, bv a metallic concave mirror. This is one made of polished tin, which I expose to the sun, and as it shines bright, we shall be able to collect the rays into a very brilliant focus. I hold a piece of paper where I imagine the focus to be situated; you may see by the vivid spot of light on the paper, how much the rays converge: but it is not yet exactly in the focus; as I ap- proach the paper to that point, observe how the brightness of the spot of light increases, while its size diminishes, Caroline. That must be occasioned by the rays approaching closer together. I think you hold the paper just in the focus now, the light is so small and dazzling Oh, Mrs. B., the paper has taken fire! Mrs. B. The rays of light cannot be concentrated, without, at the same time, accumulating a proportional quantity of heat: hence concave mirrors have obtained the name of burning mir- rors. Emily. I have often heard of the surprising effects of burn- ing mirrors, and I am quite delighted to understand their na- ture. Caroline. It cannot be the true focus of the mirror, at which 40. Where is the focus of parallel rays, in a concave mirror? 41. If rays fall on it convergent, how are they reflected ? 42. How if divergent . ? 43 How, and why, may concave, become burning mirrors ? 178 THE REFLECTION OF MIRRORS. the rays of the sun unite, for as they proceed from so large a body, they cannot fall upon the mirror parallel to each other. Mrs. B. Strictly speaking, they certainly do not. But when rays, come from such an immense distance as the sun, they may be considered as parallel: their point of union is, therefore, the true focus of the mirror, and there the image of the object is re- presented. Now that I have removed the mirror out of the influence of the sun's rays, if I place a burning taper in the focus, how will its light be reflected? (Fig. 6.) Caroline. That, I confess, I cannot say. Mrs. B. The ray which falls in the direction of the axis of the mirror, is reflected back in the same line; but let us draw two other rays from the focus, falling on the mirror at B and F; the dotted lines are perpendicular to those points, and the two rays will, therefore, be reflected to A and E. Caroline. Oh, now I understand it clearly. The rays whicn proceed from a light placed in the focus of a concave mirror fall divergent upon it, and are reflected, parallel. It is exactly the reverse of the former experiment, in which the sun's rays foil parallel on the mirror, and were reflected to a focus. Mrs. B. Yes: when the incident rays are parallel, the re fleeted rays converge to a focus; when, on the contrary, the in cident rays proceed from the focus, they are reflected parallel. This is an important law of optics, and since you are now ac- quainted with the principles on which it is founded, 1 hope that you will not forget it. Caroline. I am sure that we shall not. But, Mrs. B., you said that the image was formed in the focus of a concave mirror; yet I have frequently seen glass concave mirrors, where the ob- ject has been represented within the mirror, in the same manner as in a convex mirror. Mrs. B. That is the case only, when the object is placed between the mirror and its focus; the image then appears magni- fied behind the mirror, or, as you would say, within it. Caroline. I do not understand why the image should be larger than the object. Mrs. B. This results from the convergent property of the concave mirror. If an object, A B, (fig. 7.) be placed between the mirror and its focus, the rays from its extremities fall diver gent on the mirror, and on being reflected, become less divergent, as if they proceeded from C : to an eye placed in that situation, 44. Why may rays of light coming from the sun, be viewed as parallel to each other? 45. If a luminous body, as a burning taper, be placed in the focus of a concave mirror, how will the rays from it, be reflected ? (figf. 6.} 46 What fact is explained by fig. 7, plate 18? ON REFRACTION AND COLOURS. 179 the image will appear magnified behind the mirror at a 5, since it is seen under a larger angle than the object. You now, I hope, understand the reflection of light by opaque bodies. At our next meeting, we shall enter upon another pro- perty of light, no less interesting, and which is called refraction CONVERSATION XVI. ON REFRACTION AND COLOURS. ITOANSMISSION OF LIGHT BY TRANSPARENT BODIES. REFRACTION. RE- FRACTION BY THE ATMOSPHERE. REFRACTION BY A LENS. REFRAC- TION BY THE PRISM. OF COLOUR FROM THE RAYS OF LIGHT. OF THE COLOURS OF BODIES. MRS. B. THE refraction of light will furnish the subject of to-day's lesson Caroline. That is a property of which I have not the faintest fdea. Mrs. B. It is the effect which transparent mediums produce on light in its passage through them. Opaque bodies, you know, reflect the rays, and transparent bodies transmit theni; but it is found, that if a ray, in passing from one medium, into another of different density, fall obliquely, it is turned out of its course. The ray of light is then said to be refracted. Caroline. It must then be acted on by some new power, otherwise it would not deviate from its first direction. Mrs. B. The power which causes the deviation of the ray, appears to be the attraction of the denser medium. Let us sup- pose the two mediums to be air, and water; if a ray of light passes from air, into water, it is more strongly attracted by the latter, on account of its superior density. Emily. In what direction does the water attract tne ray ? 1. What is meant by the refraction of light? 2. What is believed to b the cause of refraction ? 180 THE REFRACTION OF LIGHT. Mrs. B. The ray is attracted perpendicularly towards the water, in the same manner in which bodies are acted upoi by gravity. If tnen a ray, A B, (fig. 1, plate 19.) fall perpendicularly on water, the attraction of the water acts in the same direction as the course of the ray: it will riot, therefore, cause a deviation, and the ray will proceed straight on, to E. But if it fall oblique- ly, as the ray C B, the water will attract it out of its course Let us suppose the ray to have approached the surface of a den- ser medium, and that it there begins to be affected by its attrac- tion; this attraction, if not counteracted by some other power, would draw it perpendicularly to the water, at B; but it is also impelled by its projectile force, which the attraction of the den- ser medium cannot overcome; the ray, therefore, acted on by both tiiese powers, moves in a direction between them, and in- stead of pursuing its original course to D, or being implicitly guided by the water to E, proceeds towards F, so that the ray appears bent or broken. Caroline. I understand that very well; and is not this the reason that oars appear bent in the water? Mrs. B. It is owing to the refraction of the rays, reflected by the oar; but this is in passing from a dense, to a rare medium, for you know that the rays, by means of which you see the oar, pass from water into air. Emily. But I do not understand why refraction takes place, when a ray passes from a dense into a rare medium; I should suppose that it would be less attracted by the latter, than by the former. Mrs. B. And it is precisely on that account that the ray is refracted. Let the upper half of fig. 2, represent glass, and the lower half water, let C B represent a ray, passing obliquely from the glass, into water: glass, being the denser medium, the ray will be more strongly attracted by that which it leaves than by that which it enters. The attraction of the glass acts in the direction A B, while the impulse of projection would carry the ray to F; it moves, therefore, between these directions towards D. Emily. So that a contrary refraction takes place, when a ray passes from a dense, into a rare medium. Mrs. B. The rule upon this subject is this; when a ray of light passes from a rare into a dense medium, it is refracted to- wards the perpendicular; when from a dense into a rare medium) it is refracted from the perpendicular. By the perpendicular is meant a line, at right angle with the refracting surface. This 3. How is a ray refracted in passing obliquely from air into water? 4. How is this refraction explained in fig. 1, plate 19? 5. What is fig. 2 in- tended to explain ? 6. What is the rule respecting refraction, by different mediums ? THE REFRACTION OF LIGHT. 181 jnay be seen in fig. 1, and fig. 2, where the lines A E, are the perpendiculars. Caroline. But does not the attraction of the denser medium affect the ray before it touches it ? Mrs. B. The distance at which the attraction of the denser medium acts upon a raj, is so small, as to be insensible; it ap- pears, therefore, to be refracted only at the point at which it passes from one medium into the other. Now that you understand the principle of refraction, I \vill show you the real refraction of a ray of light. Do you see the flower painted at the bottom of the inside of this tea-cup? (Fig. 3.J Emily. Yes. But now you have moved it just out of sight; the rim of the cup hides it. Mrs. B. Do not s^r. I will fill the cup with water, and you will see the flower again. Emily. I do, indeed! Let me try to explain this: when you drew the cup from me, so as to conceal the flower, the rays re- flected by it, no longer met my eyes, but were directed above them; but now that you have filled the cup with water, they are refracted, and bent downwards when passing out of the water, into the air, so as again to enter my eyes. Mrs. B. You have explained it perfectly: fig. 3. will help to imprint it on your memory. You must observe that when the flower becomes visible by the refraction of the ray, you do not see it in the situation which it really occupies, but the image of the flower appears higher in the cup; for as objects always ap- pear to be situated in the direction of the rays which enter the eye, the flower will be seen at B, in the direction of the refracted ray. Emily. Then, when we see the bottom of a clear stream of water, the rays which it reflects, being refracted in their pass- ae from the water into the air, will make the bottom appear higher than it really is. Mrs. B. And the water will consequently appear more shal- low. Accidents have frequently been occasioned by this cir- cumstance; and boys, who are in the habit of bathing, should be cautioned not to trust to the apparent shallowness of water, as it will always prove deeper than it appears. The refraction of light prevents our seeing the heavenly bodies in their real situation: the light they send to us being refracted in passing into the atmosphere, we see the sun and stars in the direction of ths refracted ray; as described in fig. 4, plate 19., 7. What is meant by the perpendicular? 8. How does fig. 3, plate 19 elucidate the law of refraction? 9. What will be the effect on the apparent fituation of the flower? 10. What effect has refraction upon the apparent depth of a stream of water? 182 THE REFRACTION OF LIGHT. the dotted line represents the extent of the atmosphere, above a portion of the earth, E B E : a ray of light coming from the sun S, falls obliquely on it, at A, and' is refracted to B; then, since we see the object in the direction of the refracted ray, a specta- tor at B, will see an image of the sun at C, instead of its real situation, at S. Emily. But if the sun were immediately over our heads, its rays, falling perpendicularly on the atmosphere, would not be refracted, and we should then see the real sun, in its true situation. Mrs. B. You must recollect that the sun, is vertical only to the inhabitants of the torrid zone; its rays, therefore, are al- ways refracted, in this latitude. There is also another obstacle to our seeing the heavenly bodies in their real situations: light, though it moves with extreme velocity, is about eight minutes and a quarter, in its passage from the sun to the earth; therefore, when the rays reach us, the sun must have quitted the spot he occupied on their departure; yet we see him in the direction of those ravs, and consequently in a situation which he had aban- doned eight minutes and a quarter, before. Emily. When you speak of the sun's motion, you mean, I suppose, his apparent motion, produced by the diurnal motion of the earth? Mrs. B. Certainly; the effect being the same, whether it is our earth, or the heavenly bodies, which move: it is more easy to represent things as they appear to be, than as they really are. Cawline. During the morning, then, when the sun is rising towards the meridian, we must (from the length of time the li^ht is in reaching us) see an image of the sun below that spot which it really occupies. Emily. But the refraction of the atmosphere, counteracting this effect, we may, perhaps, between the two, see the sun in its real situation. Caroline. And in the afternoon, when the sun is sinking in the west, refraction, and the length of time which the light is in reaching the earth, will conspire to render the image of the sun, higher man it really is. Mrs. B. The refraction of the sun's rays, by the atmosphere, prolongs our days, as it occasions our seeing an image of the sun, both before he rises, and after he sets; when below our horizon, he still shines upon the atmosphere, and his rays are thence refracted to the earth: so likewise we see an image of the sun, 11. How does the atmosphere refract the rays of the sun, as represented, fig. 4? 12. Why have we the rays of the sun always refracted? 13. What length of time is required for light to travel from the sun, to the eurtn* 14. What effect has this upon his apparent place ? 15. How is the length of the day affected by refraction? THE REFRACTION OF LIGHT. 183 previously to his rising, the rays that fall upon the atmosphere peing refracted to the earth. Caroline. Oa the other hand, we must recollect that light is eight minutes and a quarter on its journey; so that, by the time it reaches the earth, the sun may, perhaps, have risen above the horizon. Emily. Pray, do not glass windows, refract the light? Mrs. B. They do; but this refraction would not be percep- tible, were the surfaces of the glass, perfectly flat and parallel, because, in passing through a pane of glass, the rays suffer two refractions, which, being in contrary directions, produce nearly the same effect as if no refraction had taken place. Emily. I do not understand that Mrs. B. Fig. 5, plate 19, will make it clear to you: A A represents a thick pane of glass, seen edgeways. When the ray B approaches the glass, at C, it is refracted by it; and in- stead of continuing its course in the same direction, as the dot- ted line describes, it passes through the pane, to D; at that point returning into the air, it is again refracted by the glass, but in a contrary direction to the first refraction, and in consequence proceeds to E. Now you must observe that the ray B C and the ray D E being parallel, the light does net appear to have suffered any refraction: the apparent, differing so little from the true place "of any object, when seen through glass of ordinary thickness. Emily. So that the effect which takes place on the ray en- tering the glass, is undone on its quitting it. Or, to express myself more scientifically, when a ray of light passes from one medium into another, and through that into the first again, the two refractions being equal, and in opposite directions, no sensi- ble effect is produced. Caroline. I think the effect is very sensible, for, in looking through the glass of the window, I see objects very much dis- torted; articles which I know to be straight, appear bent and broken, and sometimes the parts seem to be separated to a dis- tance from each other. Mrs. B. That is because common window glass is not flat, its whole surface being uneven. Rays from any object, fallb^ upon it under different angles, are, consequently, refracted in various ways, and thus produce the distortion you have observed. Emily. Is it not in consequence of refraction, that the glasses in common spectacles, magnify objects seen through them? Mrs. B. Yes. Glasses of this description are called lenses; 16. How are rays refracted, which fall obliquely upon a flat pane of glass, (fig. 5, plate 19?) 17. What is the reason that objects are distorted, when seen through common window glass? 184 ON REFRACTION AND COLOURS. of these, there are several kinds, the names of which it will be necessary for you to learn. Every lens is formed of glass, ground so as to frrm a segment of a sphere, on one, or both sides. They are all represented at fig. 1, plate 20. The most common, is the double convex lens, D. This is thick in the middle, and thin at the edges, like common spectacles, or reading glasses, A B, is a plano-convex lens, being fiat on one side, and convex on the other. E is a double concave, being, in all respects, the reverse of D. is a plano-concave, fiat on one side, and concave on the other. F is called a meniscus, or concavo-convex, being concave on one, and convex on the other side. A line passing through the centre of a lens, is called its axis. Caroline. I should like to understand how the rays of light are refracted, by means of a lens. Mrs. B. When parallel rays (fig. 6.) fall on a double con- vex Ims, that only, which falls in the direction of the axis of the lens, is perpendicular to the surface; the other rays, falling obliquely, are refracted towards the axis, and will meet at a point beyond the lens, called its focus. Of the three rays, ABC, which fall on the lens D E, the rays A and C are refracted in their passage through it, to , and c/"and on quitting the lens, they undergo a second refraction in the same direction, which unites them with the ray B, at the focus F. Emily. And what is the distance of the focus, from the sur- face of the lens? Mrs. B. The focal distance depends both upon the form of the lens, and on the refracting power of the substance of which it is made: in a glass lens, both sides of which are equally con- vex, the focus is situated nearly at the centre of the sphere, of which the surface of the lens forms a portion; it is at the dis- tance, therefore, of the radius of the sphere. The property of those lenses which have a convex surface, is to collect the rays of light to a focus; and of those which have a concave surface, on the contrary, to disperse them. For the rays A and C, falling on the concave lens X Y, (fig. 7, plate 19.) instead of converging towards the ray B, in the axis of the lens, will each be attracted towards the thick edges of the lens, both on entering and quitting it, and will, therefore, by the first, re- fraction, be made to diverge to a, c, and by the second, to d, e. Caroline And lenses which have one side flat, and the other 18. What is meant by a lens? 19. What are the five kinds called, repre- sented at fig. 1, plate 20? 20. What is meant by the axis of a lens? 21. How are parallel rays, refracted by the double convex lens, fig. 6, plate 19? 22. What is meant by the focus of a lens? 23. What is the. focal distance of parallel rays, from a double convex lens ? 24. How are the rays refracted by a concave lens, fig. 7, plate 19? ON REFRACTION AND COLOURS. 185 ctuvex, or concave, as A and B, (fig. 1, plate 20.) are, I suppose, less powerful in their refractions? Mrs. B. Yes; the focus of the plano-convex, is at the dis- tance of the diameter of a sphere, of which the convex surface of the lens, forms a portion; as represented in figure 2, plate 0. The three parallel rajs, ABC, are brought to a tWus by the plano-convex lens, X Y,at F. Emily. You have not explained to us, Mrs. B., how the lens serves to magnify objects. Mrs. B. By turning again to fig. 6, plate 19. you will readi- ly understand this. Let A C, be an object placed before the lens, and suppose it to be seen by an eye at F; the ray from the point A, will be seen in the direction F G, that from C, in the direc- tion F H; the visual angle, therefore, will be greatly increased, and the object must appear larger, in proportion. I must now explain to you the refraction of a ray of light, by a triangular piece of glass, called a, prism. (Fig. 3.) Emily. The three sides of this glass are flat: it cannot, there- fore, bring the rays to a focus; nor do I suppose that its refrac- tion will be similar to that of a flat pane of glass, because it has not two sides parallel; T cannot, therefore, conjecture what eftect the refraction by a prism, can produce. Mrs. B. The refractions of the ray, both on entering and on quitting the prism, are in the same direction, (Fig. 3.) On en- tering the prism P, the ray A is refracted from B to C, and on quitting it from C to D. In the first instance it is refracted to- wards, and in the last, from the perpendicular; each causing it to deviate in the same way, from its original course, A B. I will show you this by experiment; but for this purpose it will be advisable to close the window-shutters, and admit, through the small aperture, a ray of light, wruch I shall refract, a by means of this prism. Caroline. Oh, what beautiful colours are represented on the opposite wall! There are all the colours of the rainbow, and with a brightness, I never saw equalled. (Fig. 4, plate 20.) Emily. I have seen an effect, in some respects similar to tnis, produced by the rays of the sun shining upon glass lustres; but how is it possible that a piece of white glass can produce such a variety of brilliant colours? Mrs. B. The colours are not formed by the prism, but ex- isted in the ray previously to its refraction. 25. What is the effect of one plane side in a lens ? 26. How is the focus of the plano-convex lens situated, fig. 2, plate 20? 27. How does a convex lens magnify objects, fig. 6, plate 19 ? 28. What is the article denominated which is represented at fig. 3, plate 20? 29. How will a ray be refracted, which enters on one si le of the prism, in the direction A B ? 30. What ex tect is produced by this refraction, as represented in fig. 4, plate 20 ? Q 2 188 ON REFRACTION AND COLOURS. Caroline. Yet, before its refraction, it appeared perfectly white. Mrs. B. The white rays of the sun, are composed of rays, which, when separated, produce all these colours, although wheu blended together, they appear colourless or white. Sir Isaac Newton, to whom we are indebted for the most im- portant discoveries respecting light and colours, was the first who divided a white ray of light, and found it to consist of an assemblage of coloured rays, which formed an image upon the wall, such as you now see exhibited, (fig. 4.) in which are dis- played the following series of colours: red, orange, yellow, green, blue, indigo, and violet. Emily. But how does a prism separate these coloured rays? Mrs. B. By refraction. It appears that the coloured rays have different degrees of refrangibility; in passing through the prism, therefore, they take different directions according to their susceptibility of refraction. The violet rays deviate most from their original course; they appear at one of the ends of the spec- trum, A B: contiguous to the violet, are the blue ravs, being those which have somewhat less refrangibility; then follow, in succession, the green, yellow, orange, and lastly, the red, which are the least refrangible of the coloured rays. Caroline. I cannot conceive how these colours, mixed to- gether, can become white? Mrs. B. That I cannot pretend to explain: but it is a fact, that the union of these colours, in the proportions in which they appear in the spectrum, produce in us the idea of whiteness. If you paint a circular piece of card, in compartments, with these seven colours, as nearly as possible in the proportion, and of the shade exhibited in the spectrum, and whirl it rapidly on a pin, it will appear white; as /he velocity of the motion, will have the effect of blending the colours, in the impression which they make upon the eye. But a more decisive proof of the composition of a white ray is afforded, by reuniting these coloured rays, and forming with them, a ray of white light. Caroline. If you can take a ray of white light to pieces, and put it together again, I shall be quite satisfied. Mrs. Jl. ThFs can be done by letting the coloured rays, which have been separated by a prism, fail upon a lens, which will converge them to a focus; and if, when thus reunited, we find that they appear white as they did before refraction, I hope you will be convinced that the white rays, are a compound 31. Of what are the rays of white light said to be composed? 32. What colours are produced? 33. By what property, in light, does refraction enable us to separate these different rays ? Off REFRACTION AND COLOURS. 137 of the several coloured rays. The prism P, you see, (fig, 5.) separates a ray of white light, into seven coloured rays, and the lens L L brings them to a focus at F, where they again appear white. Caroline. You succeed to perfection: this is indeed a most interesting and conclusive experiment. Emily. Yet, Mrs. B., 1 cannot help thinking, that there may, perhaps, be but three distinct colours in the spectrum, red,' yellow, arid blue; and that the four others may consist of two of these colours blended together; for, in painting, we find, that by mixing red and yellow, we produce orange; with different proportions of red and blue, \ve make violet or any shade of pur- ple: and yellow, and blue, form green. Now, it is very natural to suppose, that the refraction of a prism, may not be so perfect as to separate the coloured rays or light completely, and that those which are contiguous, in order of refrangibility, may en- croach on each other, and by mixing, produce the intermediate colours, orange, green, violet, and indigo. Mrs. B. Your observation is, I believe, neither quite wrong, nor quite right. Dr. Wollaston, who has performed many ex- periments on the refraction of light, in a more accurate manner than had been previously done, by receiving a very narrow line of light on a prism, found that it formed a spectrum, consisting of rays of four colours only; but they were not exactly those you have named as primitive colours, for they consisted of red, grsen blue, and violet. A very narrow line of yellow was visible, at the limit of the red and green, which Dr. Wollaston attributed to the overlapping of the edges of the red and green light. Caroline. But red and green mixed together, do not produce yellow? Mrs. B. Not in painting; but it may be so in the primitive rays of the spectrum. Dr. Wollaston observed, that, by increas- ing the breadth of the aperture, by which the line of light was admitted, the space occupied by each coloured ray in the spec- trum, was augmented, in proportion as each portion encroached on the neighbouring colour, and mixed with it; so that the in- tervention of orange and yellow, between the red and green, is owing, he supposes, to the mixture of these two colours; and the blue is blended on the one side with the green, and on the other with the violet, forming the spectrum, as it was originally observed by Sir Isaac Newton, arid which I have just shown you. The rainbow, which exhibits a series of colours, so analogous 34. What experiment may be performed with a piece of card, so as to exemplify the compound nature of light? 35. How can the same be shown by a lens, fig. 5. plate 20? 16. Is it certain that there are seven primitive colours in the spectrum ? 188 ON REFRACTION AND COLOURS. to those of the spectrum, is formed by the refraction of the sun's rays, in their passage through a shower of rain; every drop oi which acts as a prism, in separating the coloured rays ay Ihey pass through it; the combined effect of innumerable drops, pro- duces the bow; which you know can be seen, only when the/e are both rain, and sunshine. Emily. Pray, Mrs. B., cannot the sun's rays be collected to a focus by a lens, in the same manner as they are by a concave mirror? Mrs. B. The same effect in concentrating the rays, is pro- duced by the refraction with a lens, as by the reflection from a concave mirror: in the first, the rays pass through the glass and converge to a focus, behind it; in the latter, they are reflected from the mirror, and brought to a focus, before it. A lens, when used for the purpose of collecting the sun's rays, is called a burning ^lass. I have before explained to you, the manner in which a convex lens, refracts the rays, and brings them to a focus; (fia;. 6, plate 19.) as these rays contain both light and heat, the latter, as well as the former, is refracted; and intense heat, as well as light, will be found in the focal point. The sun now shines very bright; if we let the rays fall on this lens, you wili perceive the focus. Emily. Oh yes: the point of union of the rays, is very lumi- nous. I will hold a piece of paper in the focus, and see if it will take fire. The spot of light is extremely brilliant, but the paper does not burn? Mrs. B. Try a piece of brown paper; that, you see, takes fire almost immediately. Caroline. This is surprising; for the light appeared to shine more intensely, on the white, than on the brown paper. Mrs. B. The lens collects an equal number of rays to a focus, whether you hold the white or the brown paper, there; but the white paper appears more luminous in the focus, because most of the rays, instead of entering into the paper, are reflected by it; and this is the reason that the paper does not readily take fire: whilst, on the contrary, tiie brown paper, which absorbs more light and heat than it' reflects, soon becomes heated and takes fire. Caroline. This is extremely curious; but why should brown paper, absorb more rays, than white paper? Mrs. B. I am far from being able to give a satisfactory answer to that question. We can form but mere conjecture on this point; it is supposed that the tendency to absorb, or reflect 37. How is the rainbow produced, and what is necessary to its production? 38. How are the solar rays affected by a convex lens? 39. Why is such a lens, called a burning glass? 40. Why are bodies of a dark colour, mor* readily inflamed, than those which are white ? ON REFRACTION AND COLOURS. 189 rays, depends on the arrangement of the minute particles of the body, and that this diversity of arrangement renders some bodies susceptible of reflecting one coloured ray, and absorbing the others; whilst other bodies, have a tendency to reilect all the colours, and others again, to absorb them all. Emily. And how do you know which colours bodies have a tendency to reflect; or which to absorb? Mrs. B. Because a body always appears to be of the Colour which it reflects; for, as we see only by reflected rays, it can appear of the colour of those rays, only. Caroline. But we see all bodies of their own natural colour, Mrs. B.; the grass and trees, green; the sky, blue; the flowers of various hues. Mrs. B. True; but why is the grass green? -because it ab- sorbs all, except the green rays; it is, therefore, these only which the grass and trees reflect to our eyes, and this makes them appear green. The flowers, in the same manner, reflect the various colours of which they appear to us; the rose, the red rays; the violet, the blue; the jonquil, the yellow, &c. Caroline. But these are the permanent colours of the grass and flowers, whether the sun's lays shine on them or riot. Mrs. B. Whenever you see those colours, the flowers must be illumined by some light; and light, from whatever source it proceeds, is of the same nature; composed of the various coloured rays which paint the grass, the flowers, and every coloured ob- ject in nature. Caroline. But, Mrs. B., the grass is green, and the flowers are coloured, whether in the dark, or exposed to the light? Mrs. B. Why should you think so? Caroline. It cannot be otherwise. Mrs. B. A most philosophical reason indeed! But, as I never saw them in the dark, you will allow me to dissent from your opinion. Caroline. What colour do you suppose them to be, then, in the dark? Mrs. 3. None at all; or black, which is the same thing. You can never see objects, without light. White light is compounded of rays, from which all the colours in nature are produced; there, therefore, can be no colour without light; and though a substance is black, or without colour, in the dark, it may become co- loured, as soon as it becomes visible. It is visible, indeed, only by the coloured rays which it reflects; therefore, we can see it only when coloured. 41. What is believed to be the reason, why some bodies absorb more raya than others? 42. What determines the colour of any particular body ? 43. What exemplifications are given ? 44. By what reasoning is it proved, that bodies Jo not retain their colours in the dark ? 190 ON REFRACTION AND COLOURS. Caroline. All you say seems very true, and I know not what to object to it; yet it appears at the same time incredible! What, Mrs. B., are we all as black as negroes in the dark? you make me shudder at the thought. Mrs. B. Your vanity need not be alarmed at the idea, as you are certain of never being seen, in that state. Caroline. That is some consolation, undoubtedly; but what a meiancholy reflection it is, that all nature which appears so beautifully diversified with colours, is really one uniform mass of blackness! Mrs. B. Is nature less pleasing for bein^ coloured, as well as illumined, by the rays of light? and are colours less beautiful, for being accidental, rather than essential properties of bo- dies ? Providence seems to have decorated nature with the enchant- ing diversity of colours, which we so much admire, for the sole purpose of beautifying; the scene, and rendering it a source of sensible gratification : it is an ornament which embellishes nature, whenever we behold her. What reason is there to re- gret, that she does not wear it when she is invisible? Emily. I confess, Mrs. B., that I have had my doubts, as well as Caroline, though she has spared me the pains of express- ing them: but I have just thought of an experiment, which, if it succeed, will, I am sure, satisfy us both. It is certain, that we cannot see bodies in tne dark, to know whether they have then any colour. But we may place a coloured body in a ray of light which has been refracted by a prism; and if your theory is true > the body, of whatever colour it naturally is, must appear of the colour of the ray in which it is placed; for since it receives no other coloured rays, it can reflect no others. Caroline. Oh ! that is an excellent thought, Emily; will you stand the test, Mrs. B.? Mrs. B. I consent: but we must darken the room, and ad mit only the ray which is to be refracted; otherwise, the white rays will be reflected on the body under trial, from vanous parts of the room. With what do you choose to make the experi- ment? Caroline. This rose: look at it, Mrs. B., and tell me whe- ther it is possible to deprive it of its beautiful colour? Mrs. B. We shall see. 1 expose it first to the red rays, and the flower appears of a more brilliant hue; but observe the green leaves Caroline. They appear neither red nor green; but of a dingy brown with a reddish glow? 45. What proof of the truth of this theory of colours, may be afforded by *he priam ? ON REFRACTION AND COLOURS* 191 Mrs.B. They cannot appear green, because they have no green rays to relied; neither are they red, because green bodies ab- sorb most of the red rays. But though bodies, from the arrange- ment of their particles, iiave a tendency to absorb some rays, and reflect others, yet it is not natural to suppose, that bodies are so perfectly uniform in their arrangement, as to reflect only pure rays of one colour, and perfectly to absorb the others; it is found, on the contrary, that a body reflects, in great abundance, the rays which determine its colour, and the others in a greater or less degree, in proportion as they are nearer to or further from its own colour, in the order of refrangibility. The green leaves of the rose, therefore, will reflect a few of the red rays, which, blended with their natural blackness, give them that brown tinge: if they reflected none of the red rays, they would appear perfectly black. Now I shall hold the rose in the blue rays Caroline. Oh, Emily, Mrs. B. is right! IOOK at the rose: it is no longer red, but of a dingy blue colour. Emily. This is the most wonderful, of any thing we have yet learnt. But, Mrs. B.,what is the reason that the green leaves, are of a brighter blue than ti.ij rose? Mrs. B. The green leaves reflect both blue and yellow rays, which produce a green colour. They are now in a coloured ray, which they have a tendency to reflect; they, therefore, re- flect more of the blue rays than the rose, (which naturally ab- sorbs that colour,) and will, of course, appear of a blighter blue. Emily. Yet, in passing the rose through the different colours of the spectrum, the flower takes them more readily than the leaves. Mrs. B. Because the flower is of a paler hue. Bodies which reflect all the rays, are white; those which absorb them all, are black: between these extremes, bodies appear lighter or darker, in proportion to the quantity of rays they reflect or ab- sorb. This rose is of a pale red; it approaches nearer to white than to black, and therefore, reflects rays, more abundantly than it absorbs them. Emily. But if a rose has so strong a tendency to reflect rajs, I should imagine that it would be of a deep red colour. Mrs. JJ. I mean to say, that it has a general tendency to reflect rays. Pale coloured bodies, reflect all the coloured rays to a certain degree, their paleness, being an approach towards whiteness: but they reflect one colour more than the rest: 46. Why will green leaves, when exposed to the red ray, appear of a dingy brown ? 47. Codies, in general, when placed in a ray differing in colour from their own, appear of a mixed hue, what causes this? 48. Why will bodies of a pale, or light hue, moat perfectly, assume the different colours of the ectr am ? 192 ON REFRACTION AND COLOURS. this predominates over the white, and determines the colour of the body. Since, then, bodies of a pale colour, in some degree reflect all the rajs of light, in passing through the various co- lours of the spectrum, they will reflect them all, with tolerable brilliancy; but will appear most vivid, in the ray of their natural colour. The gieen leaves, on the contrary, are of a dark colour, bearing a stronger resemblance to black, than to white; they have, therefore, a greater tendency to absorb, than to reflect rays; and reflecting very few of any, but the blue, and yellow rays, they will appear dingy, in passing through the other co- lours of the spectrum. Caroline. They must, however, reflect great quantities of the green rays, to produce so deep a colour. Mrs. B. Deepness or darkness of colour, proceeds rather from a deficiency, than an abundance of reflected rays. Remem- ber, that if bodies reflected none of the rays, they would be black; and if a body reflects only a few green rays, it will ap- pear of a dark green; it is the brightness, and intensity of the colour, which show that a great quantity of rays are reflected. Emily. A white body, then, which reflects all the rays, will appear equally bright in all the colours of the spectrum. Mrs. B. Certainly. And this is easily proved by passing a sheet of white paper, through the rays of the spectrum. White, you perceive, results from a body reflecting all the rays which fall upon it; black, is produced, when they are all ab- sorbed: and colour, arises from a body possessing trie power to decompose the solar ray, by absorbing some parts, and reflect- ing others. Caroline. What is the reason that articles which are blue, often appear green, by candle-light? Mrs. B. The light of a candle, is not of so pure a white as that of the sun: it has a yellowish tinge, and when refracted by the prism, the yellow rays predominate; ami blue bodies reflect some of the yellow i ays, from their being next to the blue, in the order of refrangibility; the superabundance of yellow rays, which is supplied by the candle, gives to blue bodies, a greenish hue. Caroline. Candle-light must then give to all bodies, a vel- lowish tinge, from the excess of yellow rays; and yet it is a common remark, that people of a sallow complexion, appear fairer, or whiter, by candle-light. Mrs. B. The yellow cast of their complexion is not so strik- ing, when every suriounding object has a yellow tinge. Emily. Pray, why does the sun appear red, through a fog? 49. Upon what property in a body, does the darkless of its colour depend ? SO, Why do iome bodies appear white, others black, and others of different colours f 51. From what cause do blue articles appear green, by candle-light ON REFRACTION AND COLOURS. 193 Mrs. B. It is supposed to be owing to the rays, which are most refrangible, being also the most easily reflected: in pass- ing through an atmosphere, loaded with moisture, as in foggy weather, and also in the morning and evening, when mists pre- vail, the violet, indigo, blue, and green rays, are reflected back by the particles which load the air; whilst the yellow, orange, and red rays, being less susceptible of reflection, pass on, and reach the eye. Caroline. And, pray, why is the sky of a blue colour? Mrs. B. You should rather say, the atmosphere; for the sky is a very vague term, the meaning of which, it would be diffi- cult to define, philosophically. Caroline. But the colour of the atmosphere should be white, since all the rays traverse it, in their passage to the earth. Mrs. B. Do not forget that the direct rays of light which pass from the sun to the earth, do not meet our eyes, excepting when we are looking at that luminary, and thus intercept them; in which case, you know, that the sun appears white. The atmosphere is a transparent medium, through which the sun's rays pass freely to the earth; but the particles of which it is composed, also reflect the rays of light, and it appears that thev possess the property of reflecting the blue rays, the most copiously: the light, therefore, which is reflected back into the atmosphere, from the surface of the earth, falls upon these particles of air, and the blue rays are returned by reflection: this reflection is performed in every possible direction; so that whenever we look at the atmosphere, some of these rays fall upon our eyes; hence we see the air of a blue colour. If the atmosphere did not reflect any rays, though the objects, on the surface of the earth, would be illuminated, the sky would ap- pear perfectly black. Caroline. Oh, how melancholy would that be; and how per- nicious to the sight, to be constantly viewing bright objects against a black sky. But what is the reason that bodies often change their colour; as leaves, which wither in autumn, or a spot of ink, which produces an iron-mould on linen? Mrs. B. It arises from some chemical change, which takes place in the arrangement of the component parts; by which they lose their tendency to reflect certain colours, and acquire the power of reflecting others. A withered leaf thus no longer reflects the blue rays; it appears, therefore, yellow, or has a slight ten- dency to reflect several rays, which produce a dingy brown colour. 52. What is believed to be the cause, of the red appearance of the sun, through a fog, or misty atmosphere ? 53. From what is the blue colour of the sky, thought to arise ? 54. What would be the colour of the sky, did r.ot the atmosphere reflect light ? 55. From what cause do some bodies change their colour, as leaves formerly green, become brown, and ink, yellow? R 194 ON REFRACTION AND COLOURS. An ink spot on linen, at first absorbs all the rajs; but. from the action of soap, or of some other agent, it undergoes a chemi- cal chance, and the spot partially regains its tendency to reflect colours, but with a preference to reflect the yellow rays, and such is the colour of the iron-mould. Emily. Bodies, then, far from being of the colour which they appear to possess, are of that colour to which they have the greatest aversion, with which they will not incorporate, but re- ject, and drive from them. Mrs. B. It certainly is so; though I scarcely .dare venture to advance such an opinion, whilst Caroline is contemplating her beautiful rose. Caroline. My poor rose! you are not satisfied with depriving it of colour, but even make it have an aversion to it; ar.d I am unable to contradict you. Emily. Since dark bodies, absorb more solar rays than light ones, the former should sooner be heated if exposed to the sun? Mrs. B. And they are found, by experience, to be so. Have you never observed a black dress, to be warmer than a white one? Emily. Yes, and a white one more dazzling: the blac.k is heated by absorbing the rays, the white is dazzling, by reflecting them. Caroline. And this was the reason that the brown paper was burnt in the focus of the lens, whilst the white paper exhibited the most luminous spot, but did not take fire. Mrs. B. It was so. It is now full time to conclude our lesson. At our next meeting, 1 shall give you a description of the eye. 56. Why % a black dress, warmer in the sunshine, than a white one of the lane texture? CONVERSATION XVEL ON THE STRUCTURE OF THE EYE, AND OPTICAL INSTRUMENTS. DESCRIPTION OF THE EYE. OF THE IMAGE ON THE RETINA. REFRAC- TION BY THE HUMOURS OF THE EYE. OF THE USE OF SPECTACLES. OF THE SINGLE MICROSCOPE. OF THE DOUBLE MICROSCOPE. OF THE SOLAR MICROSCOPE. MAGIC LANTHORN. REFRACTING TELESCOPE. REFLECTING TELESCOPE. MRS. B. THE body of the eye, is of a spherical form: (fig. 1. plate 21.) it has two membranous coats, or coverings; the external one, a act, is called the sclerotica, this is commonly known under th'e name of the white of the eye; it has a projection hi that part of the eye which is exposed to view, b 6, which is called the trans- parent cornea, because, when dried, it has nearly the consistence of very fine horn, and is sufficiently transparent for the light to obtain free passage through it. The second membrane which lines the cornea, and envelops the eye, is called the choroid, c c c; this has an opening in front, just beneath the cornea, which forms the pupil, or sight of the eye, d d, through which the rays of light pass into tne eye. The pupil is sunounded by a coloured border called the iris, e e, which, by its muscular motion, always preserves the pupil of a circular form, whether it is expanded in the dark, or con- tracted by a strong light. This you will understand better by examining fig. 2. Emily. 1 did not know that the pupil was susceptible of va- rying its dimensions. Mrs. B. The construction of the eye is so admirable, that it is capable of adapting itself, more or less, to the circumstances in which it is placed. In a faint light, the pupil dilates so as to receive an additional quantity of rays, and in a strong light, it 1. What is the fonn of the body of the eye? fi<*. 1, plate 21. 2. What is its external coat called? 3. What is the transparent part of this coat denomi- nated? 4. What is the second coat named? 5. What opening is there in this* 6. What is the coloured part which surrounds the pupil? 7. The pupMs dilate and contract, what purpose does this answer? 196 OPTICS. contracts, in order to prevent the intensity of the light from in- juring the optic nerve. Observe Emily's eyes, as she sits look ing towards the windows: the pupils appear very small, and the iris, large. Now, Emily, turn from Mhe light, and cover your eyes with your hand, so as entirely to exclude it, for a few moments. Caroline. How very much the pupils of her eyes are now enlarged, and the iris diminished! This is, no doubt, the reason why the eyes suffer pain, when from darkness, they suddenly come into a strong light; for the pupil being dilated, a quantity of rays must rush in, before it has time to contract. JEmihj. And when we go from a strong light, into obscurity, we at first imagine ourselves in total darkness; for a sufficient number of rays cannot gain admittance into the contracted Supil, to enable us to distinguish objects: but in a few minutes it ilates, and we clearly perceive objects which were before in- visible. Mrs. B. It is just so. The choroid c c, is embued with a black liquor, which serves to absorb all the rays that are irregu- larly reflected, and to convert the body of the eye, into a more perfect camera obscura. When the pupil is expanded to its ut- most extent, it is capable of admitting ten times the quantity of light, that it does when most contracted. In cats, and animals whjch are said to see in the dark, the power of dilatation and con- traction of the pupil, is still greater; it is computed that the pupils of their eyes may admit one hundred times more light at one time than at another. Within these coverings of the eye-ball, are contained, three transparent substance?, called humours. The first occupies the space immediately behind the cornea, and is called the aqueous humour,//], from "its liquidity and its resemblance to wate*\ Be- yond this, is situated the crystalline humour, g g, so called from its clearness and transparency: it has the form of a lens, and refracts the rays of light in a greater degree of perfection, than any that have been constructed by art: it is attached by two muscles, m m, to each side of the choroid The back part of the eye, betv/een the crystalline humour ant\ the retina, is filled by the vitreous humour, h A, which derives its name from a resem- blance it is supposed to bear, to glass, or vitrified substances. The membranous coverings of the eye are intended chiefly for the preservation of the retina, i i, which is by far the most im- portant part of the eye, as it is that which receives the impres- 8. How could you observe the dilatation and contraction of the pupils ? 9. What purpose is the choroid said to answer ? 10. In what animals is tha change in the iris greatest? 11. What are the three humours denominated, and how are they situated? OPTICS. 157 *ion of the objects of sight, and conveys it to the mind. The retina is formed by the expansion of the optic nerve, and is of a most perfect whiteness: this nerve proceeds from the brain, en- ters the eye, at ??, on the side next the nose, and is finely spread over the interior surface of the choroid. The rays of light which enter the eye, by the pupil, are re- fracted by the several humours in their passage through them, and unite in a focus on the retina. Caroline. I do not understand the use of these refracting humours: the image of objects was represented in the camera obscura, without anv such assistance. Mrs. B. That is true; but the representation became much more strong and distinct, when we enlarged the opening of the camera obscura, and received the rays into it, through a lens. I have told you, that rays proceed from bodies in all possible directions. We must, therefore, consider every part of an ob- ject which sends rays to oui eyes, as points from which the rays diverge, as from a centre. jRmily. These divergent rays, issuing from a single point, I believe you told us, were called a pencil of rays? Mrs. B. Yes. Now, divergent rays, on entering the pupil, do not cross each other; the pupil, however, is sufficiently large to admit a small pencil of them; and these, if riot refracted to a focus, by the humours, would continue diverging after they had passed the pupil, would fall dispersed upon the retina, and thus the image of a single point, would be expanded over a large por- tion of the retina. The divergent raj's from every other point of the object, would be spread over a similar extent of space, and would interfere and be confounded with the first; so that no distinct image could be formed, and the representation on the re- tina would be confused, both in figure and colour. Fig. 3. repre- sents two pencils of rays, issuing from two points of the tree, A B, and entering the pupil C, refracted by the crystalline humour D, and forming on the retina, at ab, distinct images of the spot they proceed from. Fig. 4. differs from the preceding, merely from not being supplied with a lens; in consequence of which, the pencils of rays are not refracted to a focus, and no distinct im- age is formed on the retina. I have delineated only the rays issuing from two points of an object, and distinguished the two pencils in fig. 4. by describing one of them with dotted lines: the interference of these two pencils of rays on the retina, will enable you to form an idea of the confusion which would arise, T2. What is the part represented at i t, and of what does it consist? 13. What ar the respective uses of the humours, and of the retina ? 14 Why is it necessary the rays should be refracted? 15. How is this illustrat- ed by fig. 3 and 4, plate 2l"? R 2 198 OPTICS. from thousands and millions of points, at the same instant pour .ng their divergent rays upon the retina. Emily. True; but I do not yet well understand, how the refracting humours, remedy this imperfection. Mrs. B. The refraction of these several humours, unites the whole of a pencil of rays, proceeding from any one point of an object, to a corresponding point on the retina, and the image is thus rendered distinct and strong. If you conceive, in fig. 3., every point of the tree to send forth a pencil of rays, similar to those from A B, every part of the tree will be as accurately represented on the retina, as the points a b. Emily. How admirably, how wonderfully, is this contrived! Caroline. But since the eye absolutely requires refracting humours, in order to have a distinct representation formed on the retina, why is not the same refraction equally necessary, for the images formed in the camera obscura ? Mrs, B. It is; excepting the aperture through which we re- ceive the rays into the camera obscura, is extremely small; so that but very few of the rays diverging from a point, gain admit tance; but when we enlarged the aperture, and furnished it with a lens, you found the landscape more perfectly represented. Caroline. I remember how obscure and confused the image was. when you enlarged the opening, without putting in the lens Mrs. B. Such, or very similar, would be the representation on the retina, unassisted by the refracting humours. Vou will now be able to understand the nature of that imper- fection of sight, which arises from the eyes being too prominent. In such cases, the crystalline humour, D, /'fig. 5.) being extreme- ly convex, refracts the rays too much, and collects a pencil, proceeding from the object A B, into a focus, F, before they reach the retina. From this focus, the rays proceed, diverging, and consequently form a very confused image on the retina, a\ a b. This is the defect in short-sighted people. Emily. I understand it perfectly. But why is this defect remedied by bringing the object nearer to the eye, as we find tft be the case with short-sighted people? Mrs. B. The nearer you bring an object to your eye, the more divergent the rays fail upon the crystalline humour, and consequently they are not so soon converged to a focus: this focus, therefore, either falls upon the retina, or at least ap- proaches nearer to it, and the object is proportionably distinct, as in fig. 6. Emuy. The nearer, then, you bring an object to a lens, the further the image recedes behind it. 16. What causes a person to be short-sighte-1 ? fig. 5, plate 21. 17. Why does placing an object near the eye, enable such to see distinctly : fig. 6. OPTICS. 199 Mrs. B. Certainly. But short-sighted persons have another lesource, for objects which they can not bring near to their eyes; this is, to place a concave lens, C D, (tig. 1, plate 22.) before the eye, in order to increase the divergence of the rajs. The effect of a concave lens, is, you know, exactly the reverse of a convex one: it renders parallel rays divergent, and those which are already divergent, still more so. By the assistance of such glasses, therefore, the rays from a distant object, fall on the pupil, as divergent as those from a less distant object; and, with short-sighted people, they throw the image of a distant object, back, as far as the retina. Caroline. This is an excellent contrivance, indeed. Mrs. B. And tell me, what remedy would you devise for such persons as have a contrary defect in their sight; that is to say, who are long-sighted, in whom the crystalline humour, be- ing too iiat, does not refract the rays sufficiently, so that they reach the retina before they are converged to a point? Caroline. I suppose that a contrary remedy must be applied to this defect; that is to say, a convex lens, L M, fig. 2, to make up for the deficiency of convexity of the crystalline hu- mour, O P. For the convex lens would bring the rays nearer together, so that they would fall, either less divergent, or paral* lei, on the crystalline humour; and, by being sooner converged, to a focus? would fall on the retina. Mrs. B. Very well, Caroline. This is the reason why elderly people, the humours of whose eyes are decayed by age, are under the necessity of using convex spectacles. And when deprived of that resource, they hold the object at a distance from their eyes, as in fig 3, in order to bring the focus more forward. Caroline. I have often been surprised, when my grandfather reads without his spectacles, to see him hold the book at a con- siderable distance from his eyes. But I now understand the cause; the more distant the object is from the crystalline lens, the nearer to it, will the image be formed. Emily. I comprehend the nature of these two opposite de- fects very well; but I cannot now conceive, how any sight can be perfect: for, if the crystalline humour is of a proper degree of convexity, to bring the image of distant objects to a focus on the retina, it will not represent near objects distinctly; and if, on the contrary, it is adapted to give a 'clear image of near ob- jects, it will produce a very imperfect one, of distant objects. Mrs. B. Your observation is very good, Emily; and it is true, that every person would be subject to one of these two IB. A concave lens remedies this defect; how? fig. 1, plate 22. 19. What is the remedy, when a person is long-sighted? fig. 2. 20. Why does holding an object far from the eye, help such persons ? fig. 3. 00 OPTICS. defects, if we had it not in our power to adapt the ey r , to th\ distance of the object; it is believed that this is accomplished by our having a command over the crystalline lens, so as to pro ject it towards, or draw it back from tiVe object, as circum stances require, by means of the two miflscles, to which the crystalline humour is attached; so that the focus of the rays, constantly falls on the retina, and an image is formed equally distinct, either of distant objects, or of those which are near. Caroline. In the eyes of fishes, which are the only eyes I have ever seen separate from the head, the cornea does not pro- trude, in that part of the eye which is exposed to view. Mrs. B. The cornea of the eye of a fish is not more convex than the rest of the ball of the eye; but to supply this deficiency, their crystalline humour is spherical,, and refracts the rays so much, that it does not require the assistance of the cornea to bring them to a focus on the retina. Emily. Pray, what is the reason that we cannot see an ob- ject distinctly, if we place it very near to the eye? Mrs. B. Because the rays fall on the crystalline humour, too divergent to be refracted to a focus on the retina; the confusion, therefore, arising from viewing an object too near the eye, is similar to that which proceeds from a flattened crystalline hu mour; the rays reach the retina before they are collected to a focus, (fig. 4.) If it were not for this imperfection, we should be able to see and distinguish the parts of objects, which, from their minuteness, are now invisible to us; for, could we place them very near the eye, the image on the retina would be so much magnified, as to render them visible. Emily. And could there be no contrivance, to convey the rays of objects viewed, close to the eye, so that they should be refracted to a focus on the retina? Mrs. B. The microscope is constructed for this purpose. The single microscope (fig. 5.) consists simply of a convex lens, commonly called a magnifying glass; in the focus of which the object is placed, and through which it is viewed: by this means, you are enabled to place your eye very near to the object, for the lens A B, by diminishing the divergence of the rays, before they enter the pupil C, makes them fall parallel on the crystal- line humour D, by which they are refracted to a focus on the retina, at R R. Emily. This is a most admirable invention, and nothing can -be more simple; for the lens magnifies the object, merely by al- lowing us to bring it nearer to the eye. 21. How is the eye said to adapt itself to distant, and to near objects? 22. Why are objects rendered indistinct, when placed very near to the eye ? fijr 4, plate 22. 23. What is the single microscope, fi^ 5, and Low does it magnify objects? M..VJTK \\lll I OPTICS. 201 Mrs. B. Those lenses, therefore, which have the shortest focus will magnify the object most, because they enable us to place it nearest to the eye. Emily. But a lens, that has the shortest focus, is most bulg- ing or convex; and the protuberance of the lens will prevent the eye from approaching very near to the object. Mrs. B. This is remedied by making the lens extremely small: it may then be spherical without occupying much space, and thus unite the advantages of a short focus, and of allowing the eye to approach the object. There is a mode of magnifying objects, without the use of a lens: if you look through a hole, not larger than a small pin, you may place a minute object near to the eye, and it will be distinct, and greatly enlarged. This piece of tin has been per- forated for the purpose; place it close to your eye, and this small print before it. Caroline. Astonishing! the letters appear ten times as large as they do without it: 1 cannot conceive how this effect is pro- duced. Mrs. B. The smallness of ihe hole, prevents the entrance into the eye, of those parts of every pencil of rays which diverge much; so that, notwithstanding the nearness of the object, those rays from it, which enter the eye, are nearly parallel, and are, therefore, brought to a focus by the humours of the eye. Caroline. We have a microscope at home, which is a much more complicated instrument than that you have described. Mrs. B. It is a double microscope, (fig. 6.) in which you see, not the object A B, but a magnified image of it, a b. In this microscope, two lenses are employed; the one, L M, for the purpose of magnifying the object, is called the object-glass, the other, N O, acts on the principle of the single micrcscope, and is called the eye-glass. There is another kind of microscope, called the solar micro- scope, which is the most wonderful from its great magnifying power: in this we also view an image formed by a lens, not the object itself. As the sun shines, I can show you the effect of this microscope; but for this purpose, we must close the shutters, and iidmit only a small portion of light, through the hole in the window-shutter, which we used for the camera obscura. We shall now place the object A B, (plate 3, fig. 1.) which is a small insect, before the lens C D, and nearly at its focus: the image E F, will then be represented on the opposite wall, in the same manner, as the landscape was in the camera obscura; 24. If ow may objects be magnified without the aid of a lens ? 25. Why can an object, very near to the eye, be distinctly seen, when viewed through a small hole ? 26. Describe the double microscope, as represented in fig. 6| plate 22. 02 OPTICS. with this difference, that it will be magnified, instead of being diminished. I shall leave you to account for this, by examining the figure. Emily. I see it at once. The image E F is magnified, be- cause it is farther from the lens, than the object A Bj while the representation of the landscape was diminished, because it was nearer the lens, than the landscape was. A lens, then, an- swers the purpose equally well, either for magnifying or dimin- ishing objects? Mrs. B. Yes: if you wish to magnify the image, you place the object near the focus of the lensj if you wish to produce a diminished image, you place the object at a distance from the lens, in order mat the image may be formed in, or near the focus. Caroline. The magnifying power of this microscope is pro- digious: but the indistinctness of the image, for want of light, is a great imperfection. Would it not be clearer, if the opening in the shutter were enlarged,, so as to admit more light? Mrs. B. If the whole of the light admitted, does not fall upon the object, the effect will only be to make the room lighter, and the image consequently less distinct. Emily. But coulcl you not by means of another lens, bring a large pencil of rays to a focus on the object, and thus concen- trate upon it the whole of the light admitted ? Mrs. B. Very well. We shall enlarge the opening, find place the lens X Y (fig. 2.) in it, to converge the rays to a focus on the object A B. There is but one thing more wanting to complete the solar microscope, which I shall leave to Caroline's sagacity to discover. Caroline. Our microscope has a small mirror attached to it, upon a moveable joint, which can be so adjusted as to receive the sun's rays, and reflect them upon the object: if a similar mirror were placed to reflect light upon the lens, would it not be a means of illuminating the object more perfectly? Mrs. B. You are quite right. P Q (fig. 2.) is a small mir- ror, placed on the outside of the window-shutter, which receives the incident rays S S, and reflects them on the lens X Y. Now that we have completed the apparatus, let us examine the mites on this piece of cheese, which I place near the focus of the lens. Caroline. Oh, how much more distinct the image now is, and how wonderfully magnified! The mites on the cheese look like a drove of pigs scrambling over rocks. Emily. I never saw any thing so curious. Now, an immense 27. How does the solar microscope, (fig. 1 plate 23.) operate ? 28. Why may minute objects be greatly magnified by this instrument ? 29. In its more perfect form it has other appendages, as seen in fig. 2, what are they ? aud what their uses ? OPTICS. 03 piece of cheese has fallen: one might imagine it an earthquake: some of the poor mites must have been crushed; how fast they run they absolutely seem to gallop. But tiiis microscope can be used only for transparent objects; as the light must pass through them, to form the image on the wall? Mrs. JB. Very minute objects, such as are viewed in a mi- croscope, are generally transparent, but when opaque objects are to be exhibited, a mirror M N (fig. 3.) is used to reflect the light on the side of the object next the wall: the image is then formed by light reflected from the object, instead of being transmitted through it. Emily. Pray, is not a magic lanthorn constructed on the same principles? Mrs. JB. Yes, with this difference; the objects to be magni- fied, are painted upon pieces of glass, and the light is supplied by a lamp, instead of the sun. The microscope is an excellent invention to enable us to see and distinguish objects, which are too small to be visible to the naked eye. But there are objects, which, though not really small, appear so to us, from their distance; to these, we cannot apply the same remedy; for when a house is so far distant, as to be seen under the same angle as a mite which is close to us, the effect produced on the retina is the same : the angle it subtends is not large enough for it to form a distinct image on the retina. JEmily. Since it is impossible, i-n this case, to make tne object approach the eye, cannot we by means of a lens bring an im- age of it, nearer to us? Mrs. B. Yes; but then the object being very distant from the focus of the lens, the image would be too small to be visible to the naked eye. Emily. Then, why not look at the image through another lens, which will act as a microscope, enable us to bring the im- tge close to the eye, and thus render it visible? Mrs. B. Very well, Emily; I congratulate you on having invented a telescope. In figure 4, the lens C D, forms an image E F, of the object A B; and the lens X Y, serves the purpose of magnifying that image; and this is all that is required in a com- mon refracting telescope. Emily. But in fig. 4, the image is not inverted on the retina, as objects usually are: it should therefore appear to us invert- ed; and that is riot the case in the telescopes I have looked through. 30. What is added when opaque objects are to be viewed ? fig. 3. 31. In what does the magic lanthorn differ from the solar microscope . ? 32. What are the use and structure of the telescope, as shown in fig. 4 ? 204 OPTICS. Mrs. B. When it is necessary to represent the image erect, two other lenses are required; by which means a second image is formed, the reverse of the first, and consequently upright These additional glasses are used to view terrestrial objects; for no inconvenience arises from serng the celestial bodies in- verted. Emily. The difference between a microscope and a telescope, seems to be this: a microscope produces a magnified image, be- cause the object is nearest the lens; and a telescope produces a diminished image, because the object is furthest from the lens. Mrs. B. Your observation applies only to the lens C D, or object-glass, which serves to bring an image of the object nearer the eye; for the lens XY, or eye-glass, is, in fact, a microscope, as its purpose is to magnify the image. When a very great magnifying power is required, telescopes are constructed with concave mirrors, instead of lenses. These are called reflecting telescopes, because the image is reflected by metallic mirrors. Concave mirrors, you know, produce by reflection, an effect similar to that of convex lenses, by refraction. In reflecting telescopes, therefore, mirrors are used in order to bring the image nearer the eye; and a lens, or eye-glass, the same as in the refracting telescope, to magnify the image. The advantage of the reflecting telescope is, that mirrors whose focus is six feet, will magnify as much as lenses of a hun- dred feet: an instrument of this kind may, therefore, possess a high magnifying power, and yet be so short, as to be readily managed. Caroline. But I thought it was the eye-glass only which magnified the image; and that the other lens, served to bring a diminished image nearer to the eye. Mrs. B. The image is diminished in comparison with the object, it is true; but it is magnified, if you compare it to the di- mensions of which it would appear witnout the intervention of any optical instrument; and this magnifying power is greater in reflecting, than in refracting telescopes. We must now bring our observations to a conclusion, for I have communicated to you the whole of my very limited stock of knowledge of Natural Philosophy. If it enable you to make further progress in that science, my wishes will be satisfied; but remember, in order that the study of nature may be productive of happiness, it must lead to an entire confidence in the wisdom and goodness of its bounteous Author. 33. When terrestrial objects are to be viewed, why are two additional lenses employed? 34. What part of the telescope performs the part of a mi- croscope? 35. In what does the reflecting, differ from the refracting 1 tele- scope? 36. What advantages, do reflecting, possess over refracting tele- scopes ? GLOSSARY. ACCELERATED MOTION. Motion is said to be accelerated, when the ve- locity is continually increasing. ACCIDENTAL PROPERTIES. Those properties of bodies which are lia- ble to change, as colour, form, &c. ACUTE. See ANGLE. AIR. An elastic fluid. The atmo- sphere which surrounds the earth, is generally understood by this term, but there are many kinds of air. The term is synonymous with Gas. AIR PUMP. An instrument by which vessels may be exhausted of air. ALTITUDE. The height in degrees of the sun, or any heavenly body, above the horizon. A.YC.LE. The space contained be- tween two lines inclined to each other, and which meet in a point. Angles are measured in degrees, upon a segment of a circle described by placing one leg of a pair of com- passes on the angular point, and with the other, describing the seg- ment between the two lines. If the segment be exactly l-4th of a circle, it is called a right angle, and con- tains 90 deg. If more than I -4th of a circle, it is an obtuse angle. If less, an acute angle. See plate 2. ANGLE OF INCIDENCE, is the space contained between a ray which falls obliquely upon a body, and a line perpendicular to the surface of the body, at the point where the ray falls. ANGLE OF REFLECTION. The space contained between a reflected ray, and a line perpendicular to the re fleeting point. ANGLE OP VISION, or visual angle. The space contained between lines drawn from the extreme parts of any object, and meeting in the eye. ANTARCTIC CIRCLE. A circle ex- tendiug round the south pole, at the distance of 23 1-2 degrees from it. The same as the south frigid zone. APHELION. That part of the orbit of a planet, in which its distance from the sun is the greatest. AREA. The surface enclosed be- tween the lines which form the boundary of any figure, whether regular or irregular. ARIES. See SIGN. ASTEROIDS. The name given to th four small planets, Ceres, Juno, Pallas, and Vesta. ASTRONOMY. The science which treats of the motion and other phe- nomena of the sun, the planets, the stars, and the other heavenly bo- dies. ATMOSPHERE. The air which sur- rounds the earth, extending to an unknown height. Wind is this ait in motion. ATTRACTION. A tendency in bodies to approach each other, and to exist in contact. ATTRACTION or COHESION. That attraction which ca-ises matter to remain in masses, preventing them from falling into powder. For this attraction to exist, the particles must be contiguous. ATTRACTION OF GRAVITATION. By this attraction, masses of matter placed at a di?'ance, have a ten dency to approach each other. At- traction is mutual ueiween the sun and the planets. Axis OF THE EARTH, OR OF ANY or THE PLANETS. An imaginary line passing through their centre?, and terminating at their poles ; round this their diurnal revolutions are performed. Axis OF MOTION. The imaginary line, around which all the parts of a body revolve, when it has a spin- ning motion. Axis OB A LENS, oa MIRROR A S 206 GLOSSARY. line passing through the centre of a lens, or mirror, in a direction per- pendicular to its surface. BALLOON. Any hollow globe. The term is generally applied to those which are made to ascend in the air. BAROMETER. Commonly called a weather-glass. It has a glass tube, containing quicksilver, which by rising and falling, indicates any change in the pressure of the at- mosphere, and thus frequently warns us of changes in the wea- ther. BODY. The same as Matter. It may exist in the solid, liquid, or aeriform state ; and includes every thing with which we become ac- quainted by the aid of the senses. BURNING-GLASS, OR MIRROR. A lens., or a mirror, by which the rays of light, and heat, are brought to a focus, so as to set bodies on fire. CAMERA OBSCURA, a darkened room; or more frequently a box, admitting light by one opening, where a lens is placed; which, bringing the rays of light, from external objects, to a focus, presents a perfect picture of them, in miniature. CAPILLARY TUBES. Tubes, the bore of which is very small. Glass tubes are usually employed, to show the phenomenon of capillary attraction. Fluids in which they are immersed, rise in such tubes above the level of that in the con- taining vessel. CENTRE OF A CIRCLE. A point, equally distant from every part of its circumference. CENTRE OF GRAVITY. That point within a body, to which all its par- ticles tend, and around which they exactly balance each other. A sys- tem of bodies, as the planets, may have a common centre of gravity, around which they revolve in their orbits ; whilst each, like the earth, has its particular centre of gravity within itself. CENTRE OF MOTION. That point about whioh the parts of a revolv- ing body move, which point is, itse?f, considered as in a state of rest. CKNTRE OE MAGWITITDB The middle point of any body, feuppose a globe, one side of which is formed of lead, and the other of wood, the centres of magnitude and of gravity, would not be in the same points. CENTRAL FORCES. Those which either impel a body towards, or from, a centre of motion. CENTRIFUGAL. That which gives a tendency to fly from a centre. CENTRIPETAL. That which impels a body, towards a centre. CIRCLE. A figure, the periphery, or circumference of which, is every where equally distant, from the point, called its centre. CIRCLE, GREAT. On the globe, or earth, is one that divides it into two equal parts, or hemispheres. The equator, and meridian lines, are great circles. CIRCLE LESSER. Those which di- vide the globe into unequal parts. The tropical, arctic and antarctic circles, and all parallels of latitude, are lesser circles. CIRCUMFERENCE. The boundary line of any surface, as that which surrounds the centre of a circle ; the four sides of a square, &c. COMETS. Bodies which revolve round the sun, in very long ovals, approaching him very nearly in their perihelion*, but in their aphe^ lion, passing to a distance immea- surably great. COHESION. See ATTRACTION. COMPRESSIBLE. Capable of being forced into a smaller space. CONCAVE. Hollowed out; the inner surface of a watch-glass is concave, and may represent the form of a concave mirror, or lens. CONVEX. Projecting, or bulging out, as the exterior surface of a watch- glass, which may represent the form of a convex mirror, or lens. CONE. A body somewhat resembling a sugar-loaf; that is, having a round base , and sloping at the sides, until it terminates in a point. CONJUNCTION. When three of the heavenly bodies are in a straight or right line, if you take either of the extreme bodies, the other two are in conjunction with it; because a GLOSSARY. 207 straight line drawn from it, might pass through the centres of both, and join them together. At the time of new moon, the moon and sun are in conjunction with the earth ; and the moon and earth, are in conjunction with the sun. CONSTELLATION, OR SKN. A col- lection of stars. Astronomers have imagined pictures drawn in the hea- vens, so as to embrace a number of contiguous stars, and have named the group after the animal, or other article supposed to be drawn; an individual star is generally desig- nated by its fancied location ; as upon the ear of Leo, the Lion,